Globalfactcheck.org
The wealth of persons
Matt Berkley
Ambiguities and assumptions
in the foundations of economic theory;
and a description of fundamental principles
in aggregate welfare measurement
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|Change in per capita income |
|+ Demographic change |
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|= Average income gain |
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The Wealth of Persons
An exposition of some non-mathematical procedures in economics;
and
Suggestions for a scientific basis for estimating the standard of living
With particular reference to countries where most humans live.
Draft notes
2 May 2003
mattberkley@
+44 (0)1865 726768
33 Howard St, Oxford, England OX4 3AY
About this document
A note to the reader
This document has several introductory sections. The parts on the purpose of social science are aimed at students, junior researchers, politicians and other non-specialists. They may, however, be of interest to some officials, including those trained in social science, who are charged with presenting accurate information to the public.
This is not a document about right or wrong in a moral sense. It is about the validity and invalidity of ways of coming to conclusions, and therefore about the truthfulness and falsity of certain official statements and popular beliefs. It is also about professional standards in the social sciences; and it questions the wisdom of those senior officials in intergovernmental organisations who have told me it may be better if serious flaws in research on world poverty are not publicised. The facts I present may present the reader with moral questions of what to do. Where information assessing policies is found to be flawed, and the people charged with obtaining the facts do not have the skills or knowledge to find them, politicians have choices as to how to prioritise the various issues. There is, however, no point collecting more and more statistics if their meaning is consistently misrepresented.
Social science cannot cure all ills. Nor can any kind of science, if the meaning of that word has limitations as to what kinds of knowledge and wisdom it admits. But social science has its place in human affairs, and to the extent that it can improve the lot of living creatures, sometimes by making more efficient use of scarce resources, it is useful. Where the tools used are the wrong tools for the job, it can cause harm. Where they are the right tools, it can cause happiness. What the short-term effect will be of showing some tools to be the wrong ones, is not predictable. Untruth, like physical force, can have good or bad effects. Untruth, like physical force, is coercive. Untruth can kill. If there are people who would prefer the public not to know certain truths, they may be right in thinking that social stability is increased by this deceit. Or they may be wrong. Untruth stifles human ingenuity, especially co-operative ingenuity, since to argue on the basis of an untruth is to argue about nothing.
Untruth has been part of politics and diplomacy for as long as humans have been able to use it. Access to food, nesting materials and fuel, and the means to defeat disease, have been weapons in cold and hot wars throughout history. Restriction of access to food can be a weapon of mass destruction, just as it can among other species.
Scientific culture, and intellectual trends in general, have no easily-identifiable single causes. Here, I point out some flaws in an intellectual tradition. This leaves, not a void, but a vista of opportunity to look at a wider range of measures of human welfare.
A request
This draft is intended for comment and corrections. My policy on referring to other documents has been to attempt to do so without leaving out information or arguments which run counter to what I present. I would receive well-founded arguments against what I say here with great interest. It is an open secret among academics and senior officials that official statistics on world poverty and on the performance of rich countries’ policies in relation to poverty have large flaws. I hope that what I say here is above the level of debate which uses those statistics, and the conclusions commonly derived from them.
In one sense, I don’t like making mistakes - I try to do my thinking and research to the highest standards of thoroughness. But to find out where I am wrong is more interesting than to find out I am right. So where there are well-thought-out criticisms of my logic, my assumptions, or the studies I quote, I would be interested to hear them.
Average gains and rises in averages
If we want to know the average gain or loss to real people, we have to understand that
Average gain or loss to real people
=
(change in per capita income)
–
(impact of demographic change).
And most significantly for people whose only statistic is the change in per capita income:
If
(the impact of demographic change) is unknown,
then
(the average percentage gain or loss) is unknown.
Governments, and intergovernmental organisations, publish statistics on on how well or badly people have done financially. But these statements are in fact based not only on mathematics but also on assumptions for which the mathematical information is lacking. This document describes some of these assumptions.
Whether the assumptions are valid in particular cases is not something which economists are trained to find out. They are therefore in general (apart from a few who have thought about and investigated the issues) no more qualified than non-economists to say whether their conclusions are valid or not.
More important than the numbers are the words used to describe them. Words in economics are often used misleadingly, even to the extent of saying “people’s incomes had on average 1% income gains” when this is not what was measured and the truth of the statement is not known.
Another way of putting the basic point about assumptions is this: Economics seems, from headlines at least, to deal in hard data. Many people, including economists, politicians, journalists, scientists, philosophers and the general public, believe this. But some of its most important procedures, presented as mathematical, actually involve speculation. It is similar in this respect to some of the more speculative areas of cosmology. There is thus considerable doubt as to whether some well-publicised findings in economics, about much of the world’s population, are near to or far from the truth.
Some of the speculation has been commented on by economists. The existing amount, technical scope and public knowledge of such comment is limited. Economists make the comments in relation to particular findings by other economists - pointing out that there is a problem with another economist’s conclusion - or in relation to particular areas of study, such as the study of poverty.
My own perception is that academics generally try to reduce the amount of speculation, and so the number of baseless conclusions, whereas governments and intergovernmental organisations generally make more use of speculation, without admitting the fact. In any case, the comments are often couched in long words; are only read by a very small circle; and the implications for the fundamental theory of economic principles are not discussed. This allows governments to present selectively research which fails to adhere to rational principles of scientific investigation, and which is known by insiders to be fatally flawed. A small proportion of poor work thus dominates the public perception of the economic situation of real people in countries where most people live; and of the economic impact of rich countries’ foreign policies on the people of those countries.
This document explains in ordinary words how economists come to conclusions about changes in the wealth of persons, how the methods differ from the theory of economics, and the technical reasons why
- average income does not measure average outcome
(average income changes measure demographic change as well as income gains and losses, so people can have average income gains while there are negative changes in the statistic: average income will fall if poorer people survive longer)
- per capita statistics do not measure income standards of living
(they jumble up adults and children)
- “poverty reduction” statistics do not tell us that poverty was reduced
(the proportion of poor people can fall while the poor get poorer; and the proportion will go down if poor people live shorter lives)
- there is no evidence that overall the poor gain from economic growth
(all research on this question is based on a flawed concept of a theoretical dollar; jumbles up adults and children; uses unreliable survey data; confuses the people below the poverty line with the poorest 20%, who are in fact only some of the poor, or poor plus non-poor people, according to the country; and ignores any impacts of longevity).
It also presents alternative interpretations of some aspects of economic history.
There are methods available for economists to ensure that their conclusions about benefits to real people have scientific, and not just speculative, support. Where they do not have scientific (both mathematical and otherwise rational) support, other methods may be more reliable. My suggestion is that in relation to poor or hungry people, survival rates are the basic measure anyone would apply to their own family, and so are the appropriate measure for larger groups of people as well.
This document is intended for
- economists, economic historians and students of economics;
- demographers;
- other social scientists, who may find that the principles here apply to their own disciplines;
- international development agency staff;
- philosophers of social science;
- others interested in the validity of conclusions from economists as to individual economic gains; and
- anyone interested in knowing about what helps malnourished people.
About the author
Matt Berkley studied philosophy, Greek and Roman history and literature at Oxford University; and experimental psychology at Sussex University. He spent 16 months in Bangladesh with the aim of finding out why people were poor, working in development projects and living in an ordinary village. He has lived with poor people in the USA and worked with them in the UK. He has worked in mental health provision and research, and also in environments such as oil companies and the BBC. He has fluent but rusty French and Bengali, and has enjoyed making himself understood with combinations of sign language and Russian, Czech, Mandinka, German, Italian, and Spanish.
His favourite books include The Dragons of Eden: Speculations on the Evolution of Human Intelligence by Carl Sagan, The Leopard by Giuseppe di Lampedusa, and How Buildings Learn by Stewart Brand.
His interests include piano improvisation, long-exposure photography, wildlife recording, the physics of sound, the physics of gravity, Picasso, the history and scientific basis of plant-based medicine, Bach and a cappella music.
Contents
About this document 3
A note to the reader 3
A request 4
About the author 7
A brief summary of some points 12
Family size matters: The Chinas and the Indias 15
A confession of ignorance 17
Ten logical fallacies in economics: brief version 21
A note on what this document contains 30
Part I: The purpose, nature, and limitations of social science 36
I. 1 Purposes of this theoretical analysis 36
I. 2 How can we tell the truth using numbers about people? 38
I. 3 The point of welfare measurement is outcome measurement 41
I. 4 What does a science of economic welfare aim to find out? 42
I. 5 The concept of poverty 43
I. 6 The measurement of poverty 44
I. 7 Measurement is only useful in proportion to the lack of other information 45
Part II: Language, cogs, and logic 48
II. 1 Open the box, look at the mechanism 48
II. 2 A note for non-economists and others 52
II. 3 Notes on the bi-directional cogs 54
II. 4 The three bi-directional cogs of economic thought 56
II. 5 Some practical implications of the logical fallacies 57
Part III: Ten fallacies in more detail 62
1. The “rising out of poverty” fallacy 62
A. How does the mathematics work? 63
B. The inverted U-curve of nutrition 65
C. Emotional words can deceive social scientists 66
2. The “poverty reduction” fallacy 67
A. The fall tells us nothing about most poor people’s income 67
B. What social-scientific basis is there for saying that poverty was reduced? 68
C. Were those who crossed the line a representative sample? 68
D. UN statistics on the Millennium Development Goals 71
E. Temptation for governments to help the least-poor 72
F. Is child survival correlated with changes in the proportion of poor people? 72
G. Proportions + demography + depth of poverty = gain or loss to poor 75
H. The “narrow-evidence” fallacy in social science 76
I. Things to think about in relation to falling proportions of poor people 77
J. Semantic fallacies and the phrase “poverty reduction” 77
K. Theoretical dollars and assumptions about falls in proportions of poor people 80
3. The economic fallacy 82
A. “Economic growth” is not growth of the economy 83
B. “Economic growth” is not a measure of income gains 83
C. What is the “economic growth” statistic? 83
D. Demographic change and the “zero conjecture” 87
The demographic transition requires a higher per capita consumption level to keep the people at each age fed as much as people of that age had before. 90
In fact, common sense tells us that where a per capita household consumption level is used, as the World Bank has done, that is not fundamentally a welfare statistic at all, but an abstract statistic. It is a useful statistic about the economy, but not in itself a useful statistic about people’s welfare. Families with the lowest per capita consumption levels are not necessarily the one with the poorest members. Suppose you and your spouse have a baby. On the day se is born, born, your and your spouses’ per capita consumption goes down by 33%! But the baby doesn’t actually consume a third of the consumption of the household The World Bank system says that se does. Babies cost far less in poor countries. They don’t have expensive prams, expensive child care, expensive clothes, tinned food, toys, and so on. 90
In China, the effect of the demographic shift on statistics about the economy (per capita, jumbling up adults and children) was massive. The effect on consumption levels of real people at each age was significantly smaller. This is quite obvious from looking at the age structure diagram for China. Logically, for example, people aged 30 have always eaten enough to keep a 30-year-old alive. The present consumption levels of people aged 30 need therefore to be compared to the past consumption levels of people aged 30. Jumbling in a past high number of babies - which obviously depresses the per capita average consumption - into statistics misdescribed as relating to economic welfare gains is pure nonsense. This is nothing to do with politics of the right or left. It is simply a matter of logic and truth as to what the statistics refer to. Perhaps, though, it is appropriate to state here that I am not the person who praises changes in statistics about economies resulting from Communist policies. That praise comes from the particular studies, out of all those produced by the World Bank, which are promoted by its Media Department. I am the person who notes that such economic statistics are different in scope, nature, referents and implication from statistics about aggregate economic gains to individuals. An economic gain is obviously more if it comes with longer life for the individual. Economic gains to an individual can only rationally refer to lifetime economic gains, as a function of changes in longevity, and net of, at least, 90
1. Declared income gains and losses, 90
2. Asset gains and losses, 90
Without an estimate of, or specific reason to exclude any of these, a researcher is not being rational or scientific in using any one of them to make a statement about economic gains or losses to an individual. Still less are they being rational or scientific if prior to that kind of inference, they first confuse per capita changes in the population average with average gains in income or consumption to real people during the period. 91
A higher per capita income for children and adults jumbled up does not tell us that, for example, the average 30-year-old is better off than the average 30-year-old before. They may be worse off than those people were. What would be the definitions of the words “rises” or “gains” used by a social scientist who said that those 30-year-olds now had income rises, or gains? The social scientist does not know that the people had gains relative to what they could have expected at their age before. 91
The birth rate in China actually declined over 25% during the 1990s. The dependency ratio declined from 1.12 in 1985 to 0.56 in 1999. (Note to MB: Are poor households in cities smaller than those in rural areas? That would end up with an understatement of urban poverty. Do the old people stay in the villages and the young ones go to the cities?) 91
Here is a quotation from the UNFPA’ State of the World’s Population 2002, with a commentary added here. 91
E. The zero conjecture doesn’t explain much 94
F. Relative longevity theory 94
G. Emotional words about statistics lead to irrationality 96
H. Is the confusion fuelled by other concerns? 97
I. Is political will needed, or minimum standards in social science? 98
J. Imbalances in male-female survival rates in Asia 100
K. Male and female survival and prevalence of poverty 101
L. Differential survival between the sexes and quintile averages 102
M. There is no such person as “Mr or Ms Per Capita Income” 102
N. Economics and the measurement of outcomes 103
O. Preference theory in economics not testable by averages alone 103
P. E and A 104
Q. The economist’s guess 106
R. Can more statistics solve these logical problems? Probably not. 107
S. Seven conclusions from economists, but none has mathematical support 108
T. Nine axioms on economics and demography 110
U. Possible axioms 117
V. The economic fallacy is a general fallacy in social science 119
X. Suggested rules for the scientific study of average outcome 119
4. The “standard of living” fallacy 121
5. The “poorest fifth” fallacy (quintile fallacy) 122
A. Similar to the economic fallacy 122
B. The semantic fallacy of the poorest fifth 124
C. More on semantic fallacies and quintiles 124
D. “Purchasing power parity” theory not applicable to poorest fifths 126
E. Using PPP with poorest fifths creates more havoc with numbers 127
Therefore, even if we did know that certain policies helped the poorest 20% in different countries (because a real PPP system were devised and demographic factors taken into account) this would not tell us what helped the poor in the sense of the people who are in a significantly worse economic position than everyone else. 133
There is therefore a need for economists who wish to use poorest fifths to come to conclusions about “the poor” to explain what relevance the statistics have. F. Other assorted compound fallacies based on population averages 133
F. Other assorted compound fallacies based on population averages 134
6. The inequality fallacy (distribution fallacy) 135
A. Inequality fallacy (time version) 135
B. Inequality fallacy (geographical version) 136
7. The “economic gain” fallacy 137
A. Time version 137
B. Geography version 138
8. The “macroeconomics is utilitarian” fallacy 139
9. The “$1-a-day measures absolute poverty” fallacy 145
“The dollar-a-day measure is a measure of absolute poverty”. 145
10.The “$1-a-day target” fallacy 151
“The extremely poor are those who live on under $1 a day”. 151
11.The “falling headcount” fallacy ? 152
Part IV: Solutions for measuring the wealth of persons 154
Cohort studies, longevity studies and common sense 155
Solutions to the economic fallacy problem 157
A summary problems in the economic fallacy 157
Solutions to the poverty reduction fallacy 157
Checklist for researchers investigating economic gains 160
Logically-necessary research areas for economists prior to inferring average gains 161
Glossary of ambiguous terms 162
Does a writer mean by “the poor”: 163
The extremely poor 164
Is “poverty reduction” being used as: 164
Does a writer mean by “income” 166
Does a writer mean by “incidence” 167
Index 168
A brief summary of some points
This document is about measuring income gains and losses to people.
Many people think that economics is a subject which deals in hard facts and rigorous mathematics. But in the assessment of gains and losses to people, its conclusions often depend on a series of non-mathematical procedures. These are not well understood by non-specialists, some economists are unaware of all of them; many economists state conclusions as if they did not exist. The reason for this situation is that the procedures - inferences, which means well- or badly-informed guesses - are often assumed to be of no significance, so that economists are justified in missing out an essential step in their argument as to how much real people benefited. The inferential steps (guesses based on assumptions) have been neglected in economic theory. Economists often make statements about numbers as if one inferential step were equivalent to the next. In other words, they leap to conclusions.
In this document I attempt to describe the procedures. One reason for undertaking this is to shed light on some areas of disagreement between economists and non-economists, and between economists and other economists. Another is to identify questions which social scientists need to address; another is to clarify where there may be doubt about some conclusions reached by economists.
One neglected logical fact about economics is this:
A statistical fall in per capita income
is consistent with
per capita income gains to the people.
Outcomes for the economy - in terms of average income per person - are not necessarily in the same direction as
a) average individual economic outcomes, or even
b) the average increase or decrease in income or consumption expenditure expressed as a percentage (what an economist would call “people’s incomes rising by x%).[1]
Do statistics about the economy necessarily tell us about income trends among real people? No. Do they do so in practice, in real-life studies done by economists?
No-one knows.
It will come as a surprise to some, perhaps, that the economic growth statistic doesn’t tell us directly the percentage income gain or loss to real people. But this is just a statement of logical fact.
We might be able to come indirectly to a conclusion about what happened to real people’s incomes; this would need other information besides per capita income statistics. It is important to distinguish between a mathematical process and an inference. We could use maths, inferences or a bit of both in coming to conclusions as to average income gains or losses.
Statistics about the economy do not of themselves tell us anything - mathematically - about what happened to the income of individuals. This is because:
A statistical rise in average income for a geographical area
is mathematically a function of (determined by) both
demographic change
and
income gains and losses to real people.
Therefore,
Where the effect of demographic change on per capita income statistics is unknown,
average gains are not calculable from those statistics.
By “demographic change” I mean two sorts of changes:
1) changes in whole-country demographics - such as in how long retired people live, or in the ratio of children to adults;
and also
2) changes that apply more to poorer or richer people, such as increases in the longevity of poorer people.
In some countries, a social scientist might know, just from general knowledge, that the relevant demographic changes were minimal. So, we might think, it is reasonable for them to conclude that in those countries, real people’s average percentage income gain or loss was very close to the change in the per capita income figure.
But what about cases where the changes aren’t known to be minimal? We then need either data on demographic changes or a theory of how to deal with a lack of data.
A similar principle applies to comparisons of average income levels in different countries. The principle, which shows one sort of demographic difference, can be seen in this theoretical example.[2]
Family size matters: The Chinas and the Indias
Mr and Mrs China can afford 10 units of food a day each for themselves, and 5 units for China Junior.
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|So the Chinas’ per capita consumption level is |
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|10 Mr China |
|+ 10 Mrs China |
|+ 5 China Junior |
|25 units total consumption; |
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|divided by 3 |
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|= 8.33 (for adults and children jumbled up). |
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The Indias are better nourished
Mr and Mrs India, who are the same age as Mr and Mrs China, can afford to eat 11 units each for themselves and give 5.5 units each to their twin children, who are the same age as China Junior.
So Mr and Mrs India eat 10% more than Mr and Mrs China, and the twins each eat 10% more than China Junior.
And so other things being equal, we might say with some degree of sanity:
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|Everyone is 10% better off in the India household |
|than in the China household. |
But the statistic for per capita consumption for the Indias is lower:
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|11 Mr India |
|+ 11 Mrs India |
|+ 11 Twins |
|33 units total consumption; |
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|divided by 4 |
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|= 8.25 (for adults and children jumbled up). |
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In the India household, on average adults are 10% better off, and on average children are 10% better off.
But the average for (adults and children jumbled up) makes the Indias look 1% worse off than the Chinas.
Which would you say: that the Chinas are better off, or the Indias? How would you like a social scientist to go about answering the question of who is better off?
Many economists use the per capita figure. But this doesn’t fundamentally tell us how well off people are. Per capita income levels do not in themselves tell us the average standard of living, even in the terms the economist claims to be measuring - income, consumption or consumption expenditure. To find out the standard of living, even for any of these, we need to know about demographics.
A confession of ignorance
There are many things which I do not understand about economics and the use of statistics in social science. These things include:
a) Why the effects of demographic change are often ignored in coming to conclusions about individual income gains;
b) Why the phrase “poverty reduction” is used to describe a fall in the proportion of poor people;
c) Why firm statements are made about statistics without any estimate of the reliability of data, even though both consumption-expenditure data and nutritional data in countries where most of the world’s population live are known by those on the inside to be unreliable;
d) Why no significant attention has been paid by economists to looking at the extent to which population averages, quintile averages, and proportions of poor people may have mistakenly counted increases in longevity as “losses”;
e) Why a system of international comparison which calculates a halving of the price of goods which poor people buy as something less than a doubling of their purchasing power, is given the name “purchasing power parity” and why this system is held to give reliable conclusions about benefits to poor people in different countries.
*****
This document points out some gaps in economic theory.
Economists are currently allowed by their training and code of professional standards to state that individuals did better or worse, purely on the basis of rises or falls in population averages - even across populations where
a) there are varying or unknown trends in longevity,
and/or
b) there are varying or unknown birth rates.
Many public pronouncements from governments and inter-governmental organisations have been based on this logic.
Economists are also allowed to state in which countries poor people did better or worse, and under what conditions, purely on the basis of averages for the poorest fifth of people alive at different times.
But neither the single-case conclusion nor the multi-country conclusion follow logically from the data. Income gains and losses to individuals are not the only thing which can influence population averages and averages for poorest quintiles (fifths). Demographic changes can change the per capita or quintile per capita statistics.
These demographic changes are caused by various real-life events in people’s lives:
a) birth;
b) migration;
c) ageing;
d) death.
Ageing is included here because a change in per capita income can occur because of changes in age structure. Age structure is the composition of a population, in terms of the proportions of people at different ages. Demographers usually represent this as a block chart with babies at the bottom and old people at the top. It looks like a pyramid for some countries and a curvy column for others, sometimes with bulges at for particular age groups. The age structure in the China family above is different from that in the India family.
Changes in age structure usually occur because of falls in birth rates in previous years. They can influence per capita income (the average for all ages jumbled together) even if average income for each age stays the same.
The demographic changes affect statistics because of the mix of events occurring in different people’s lives during a period. So they include changes in inequality of life length among people with different levels of income.
Economists do not calculate the effects of these other factors, but are allowed to assume the effect is nil. In doing this, and in concluding that individuals on average had income gains or losses of a particular percentage, they are not in fact using a mathematical procedure but a guess. There is no procedure in academic economics -- or in any branch of professional economics - for deciding in which combinations of real-life circumstances and statistical procedures the guess is right, and in which circumstances it is wrong.
A very obvious example, cited as an exception by economists, is China’s one-child policy. This did not achieve its aims in a literal sense, but it is known to have greatly reduced the birth rate. If the birth rate falls in a country, then everyone’s income can go down while the per capita (adults and children) figure can go up. For this simple reason, there is a mismatch between economic theory (which has theorems about assessing gains to individuals) and economic practice (which is about calculating statistical rises and falls in a geographical area, whoever is in it at the time, and often about concluding purely on that basis that income gains to individuals were at the exact same level). But longevity is also a consideration. Other things being equal (if no-one’s income changes) if a person on below-mean income - that’s most of us, in any country - survives a crisis, the average income for the economy will be lower.
Similar problems arise for social scientists measuring any kind of average. The problems for the social scientist are, we might think, more acute when they are studying people whose average longevity is changing. In general, as people live longer, average levels of many characteristics of people in the population will rise. So will the prevalence: dementia and cancer are examples. In some areas of social science these problems have been considered; in others they have not. In the study of financial welfare (welfare economics) the problems have not been studied systematically.
In this document I explain the logical steps necessary to come to conclusions about average individual benefit from statistics on population averages, quintile averages and proportions of the population. A person who states a conclusion but who cannot give a reason for their assumptions is not a scientist, but someone whose conclusions are based on unfounded guesses. A person who treats the last logical step as meaning the same as the previous logical step might need to give a reason for doing this - otherwise their audience might ask them why they should believe what he or she says.
Some of what I say has been pointed out by others - for example it is well known to economists that the fact that the proportion of people below the poverty line goes down does not show that poor people on average had income rises. The standard argument known to economists is that income gains and losses to people still below the poverty line are not counted. (Despite knowing this, even senior economists often conclude, with no further argument, that poor people did better if the proportion goes down. Why the training of economists does not forbid such conclusions unless the necessary information is gathered, is unclear to me). The point about longevity makes the conclusion even more questionable.
The following questions still remain to be answered by social scientists studying poverty in poor countries. Similar questions can be asked of any procedures in social science using cross-sectional data where demographic changes are not known to have insignificant effects on the statistics, including studies of outcomes for malnourished people.
On the use of proportions of the population:
1. What is meant by the words “poverty reduction” when an economist uses the phrase to describe their finding that the proportion of poor people went down?
2. What precisely do the data show was reduced?
3. What does this fall in the proportion tell us mathematically or otherwise about benefits or losses to poor people? How do the data tell us this - in other words, what is the scientific (mathematical and inferential) procedure?
4. Why is the phrase used in the context of talking about whether poor people on the whole did better or not, when this is not what it shows?
On the use of population averages:
5. If poor people live longer, other things being equal per capita income will fall even if no-one’s income does. Further, where the birth rate falls, other things being equal per capita income will rise even if no-one’s income does. There is no theory or data as to whether other things are equal or not, or how big or small the effects were in different countries.
Why then do economists comparing different countries often ignore both of the above logical truths and assume that any change in per capita income is solely caused by individual income gains and losses?
Ten logical fallacies in economics: brief version
The following are fallacies if no other information is taken into account. In practice, economists may or may not make various assumptions about the necessary other information. But it is important to be clear which of their statements are about the maths, and which are about opinions based on assumptions.
| |
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|The “rising out of poverty” fallacy |
| |
| |
|This fallacy - to state that a certain number of people rose out of poverty, on the basis of a fall in the proportion|
|of poor people |
|- is to be found in statements by social scientists, governments and intergovernmental organisations. The truth is |
|that |
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|A fall in the proportion of people below the poverty line |
| |
|does not show mathematically that |
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|a certain number of people crossed the poverty line upwards, |
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|or even that any did. |
| |
Demographic factors, as well as the net number of people crossing the line, are mathematical determinants of the fall.
For instance, if people below the line live longer, other things being equal any fall in the proportion of people below the line will be slower.
Therefore, where the mathematical influence of demographic changes is unknown, the number of people crossing the line is unknown.
| |
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|The “poverty reduction” fallacy |
| |
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|A fall in the proportion of people below the poverty line |
|is often taken to mean that the poor benefited. |
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|The truth is that it does not show mathematically either |
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|a) how much consumption poverty[3] was reduced on average, [4] |
| |
|or even |
| |
|b) that it was reduced on average rather than aggravated. |
| |
If we found out somehow that the fall was 100% due to a net number of people crossing the line upwards (and 0% due to demographic factors), this would still be consistent with
i) large average gains among poor people;
and with
ii) large average losses among poor people.
| |
| |
|The economic fallacy [5] |
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|A 1% per cent difference in per capita income at the end of a period |
|is usually taken in economics to show that |
|individuals had average per capita income gains or losses of 1%. |
| |
|The truth is that this is not what it measures, and any relationship between the statistics and the conclusion is entirely |
|contingent on demography. |
| |
Demographic changes are also mathematical determinants of the mean income statistic for the later population.
For instance,
if
people on below-mean income live longer,
then other things being equal,
the mean will be lower among those alive at the end of the period.
In all countries, there are more people below the mean than above it.
Therefore, other things being equal.
most people will lower the mean by surviving a crisis.
Where
the mathematical influence of demographic changes on the per capita figure is unknown,
average gain or loss is unknown.
Where demographic changes are known to be small, there is less of a problem for the social scientist in inferring average gains or losses.
Where comparisons are made between countries, both demographic differences (see fallacy 5 below) and differences in rates of demographic change need to be taken into account in inferring different levels of average gain.
| |
| |
|The quintile fallacy |
| |
|Similar to the economic fallacy: both income gains and demographic changes are determinants of quintile means. |
| |
|The fact that |
|income in the poorest fifth of people in 2000 was 1% higher than income in the poorest fifth of people in 1990 |
| |
|in itself tells us nothing whatsover about gains or losses to individuals. |
| |
For instance,
If anyone in the poorest quintile lives longer,
then
other things being equal
the mean for those alive in the poorest quintile at a later date will be lower.
If the birth rate among the rich drops by less than the birth rate among the poor,
then
other things being equal
the quintile average will fall.
This does not mean that anyone earned or ate less.
| |
| |
|The “standard of living” fallacy[6] (the China fallacy) |
| |
|A 1% higher mean income in country X than in country Y |
| |
|does not show mathematically that |
| |
|individuals in X had on average 1% higher incomes for their age. |
Differences in age structure are also determinants of the per capita income figure.
For instance,
Everyone in country Y can have more income or consumption for their age than people in country X, and therefore be better fed and better off in terms of living standards,
but
the statistical average can still be higher in X because there are proportionally fewer children.
| |
| |
|The inequality fallacy (distribution fallacy) |
| |
|A higher level of income inequality in a later population |
| |
|does not show mathematically that |
| |
|income gains in percentage terms were lower for the poor than for the rich. |
For example,
If the poor live longer,
then
other things being equal (including no change in anyone’s income)
the level of inequality will be higher in the later population.
| |
| |
|The economic gains fallacy (“income gain = economic gain” fallacy) |
| |
|A 1% income gain to an individual |
| |
|does not tell us mathematically that there was |
| |
|a 1% increase in disposable income |
| |
|or |
| |
|a 1% improvement in financial welfare, |
| |
|even though the majority of economists imply that it does. |
| |
The same applies to both consumption and consumption expenditure. If you sell your farm to buy food, your economic welfare is worse even though your consumption has risen. Especially if your farm is your only income-generating asset.
If you have to pay higher prices for essential goods and services, then your financial welfare does not rise in line with any rise in income.
| |
| |
|The utilitarian fallacy (see separate paper) |
| |
|Macroeconomics does not measure “utility” in the sense that utilitarians understand that word. |
| |
|Macroeconomics is not, in the year 2002, based on the logico-mathematical structure of Benthamite (classical) |
|utilitarianism. Nor is any philosophy of welfare economics or social science based on population averages. |
| |
Utilitarianism is a moral view which aims for the greatest happiness for the greatest number, and counts a longer period being happy as better than a shorter period.
Macroeconomic policy aims for the highest mean income in a later set of people, whoever is alive in that later set of people.
Economics, insofar as it uses population averages of income, currently differs from the utilitarian model in the following ways, which combine to make its logico-mathematical structure radically different from that of utilitarianism.
i. In economics, the basic aggregate measure of success is not a total but an average.[7]
ii. In economics, the model is based not on longitudinal data (how real people do over time) but on cross-sectional data (averages for whoever is alive at any time). In other words, in economics the definition of “utility” as applied to a population refers to comparisons of two states of affairs at two separate times of two different but perhaps overlapping sets of people. Utilitarianism looks at the aggregate of consequences for one set of people - all people affected.
iii. Economics takes no account, in assessing aggregates of consequences, of the duration of benefits. It does, however, take account of how long rich and poor people live, which leads to paradoxical results when the wrong conclusion is drawn. Economics only counts consequences for those who make it to the end of a period. The death of a person on below-mean income (that’s most people, in any country) is, other things being equal, necessarily counted by the aggregation system of economics as an increase in “utility”. In utilitarianism, it is counted as a bad consequence - a loss of welfare, happiness or utility.
iv. Per capita income or consumption statistics do not fundamentally reflect the standard of living.
This is true even in terms of annual income, unless age structure is accounted for: see later sections on age structure. Some kinds of social statistics do not suffer from this type of problem, because they do not measure things that naturally vary with age. Basically, per capita income statistics jumble up adults and children.
Still less do they reflect changes in lifetime income, which would be structurally closer to a utilitarian concept. The relationship between lifetime income and some definition of welfare would still need explaining before the term “utilitarian” could be sensibly applied to economics.
Consideration (iii) above necessarily means that the fundamental theoretical requirement in economics, that a social welfare function must count all income gains as gains, and all losses as losses - which would correspond to one of the fundamental principles of utilitarianism - is not fulfilled by the logico-mathematical structure of the methods of inquiry in economics, which are based on the use of cross-sectional studies.
| |
| |
|The “dollar-a-day measure of absolute poverty” fallacy |
| |
|The theoretical dollar units used are not a measure of absolute poverty. |
The theoretical dollar units do not measure rises and falls in purchasing power of poor people. They do not measure differences between purchasing power of the poor in different countries, and so are not a measure of poverty.
The theoretical dollars are called “purchasing power parity” dollars. But the conversion rates - the “PPP dollar equivalents” for each time and place - are calculated not from prices of goods and services which the poor buy, but also from prices of goods and services the poor never buy. Any mathematical relationship there may be between the PPP conversion rate and the purchasing power of poor people for the goods they need to stay alive is unknown.
The procedure has a built-in distortion of the real purchasing power of poor people, and thus of their poverty. If you are a very poor person, the PPP equivalent of your income or consumption is not an absolute measure of your income, or of your consumption, or your consumption expenditure, or of your purchasing power.
It is partially an inverse measure of relative purchasing power, and thus of poverty. For instance:
If luxury goods become cheaper,
then
there is an illusory increase in purchasing power for poor people along with a real increase in the purchasing power of the rich. Inequality of purchasing power has in fact increased, but
this is not reflected in the mathematical results of this method.
Conversely:
If food prices fall (thus decreasing poverty)
then
there will be an illusion that the poor have benefited less than they have in reality
(in terms of consumption, and so in terms of impact on their poverty).
| |
| |
|The “people on under $1 a day” fallacy |
| |
|This is not a real dollar. |
| |
|It is a theoretical dollar unit as described above - a pretend dollar whose real value to poor people is unknown. Its |
|exchange-rate value in poor countries is a fraction of a dollar. Its real value in terms of purchasing power of poor |
|people is unknown. |
| |
|Failure to clarify the fact that the PPP unit is worth far less than a real dollar to poor people may lead the public, |
|including taxpayers in rich countries, to overestimate the real purchasing power of poor people. |
| |
A note on what this document contains
This document contains facts about social science, and also opinions about the way it is done, and the way it might be done.
I hope I have made clear which of my words are about facts, and which are about opinions. I refer on several occasions to a “scientist”, and by this I mean, partly but importantly, a person who takes the greatest care to separate facts from opinions, both in their own mind and for other people. I hope to have made a reasonable job of doing this; if I have failed in some places, this may be because the angle I am taking is different from the usual angle in social science. It may be because of other factual information I am aware of but which I have not included here for bad reasons (that I am ignorant) or good reasons (that I know the information is not relevant).
Some people take the view that the definition of a fact is a bit woolly anyway. They may also believe that social science is necessarily a product of its culture (which I would agree with) and so cannot be impartial (I think this is a profoundly uninteresting and distracting view. It can be made more less impartial, and we can think about how to do it. All any of us have are eyes, ears, brains and a few other tools; so whatever we think is subjective. So what? It still remains the case that some statements make sense, some don’t, some are supported by evidence, some aren’t. The whole point of doing any kind of science is to try and find things out, and to think more rather than less clearly.). The great mathematician Henri Poincare said that to doubt everything and to doubt nothing are equally lazy.
Facts come in two flavours:
Logical and Empirical,
which mean “true by definition” and “true by experience”.
Opinions come in many flavours: they can be based on various combinations of all of these:
- logical truths (including mathematical procedures),
- intuition,
- cultural and/or academic tradition,
- ignorance,
- insight,
- other people’s mistakes,
- other people’s false statements,
- other people’s opinions,
- generalisation from personal experience,
- the clarity or otherwise of the words used to describe facts,
- and so on.
The more I have learned about welfare economics (the science of making accurate statements about the financial progress of people) concerning countries which hold the majority of the world’s population) the less I have understood, both about why social science is carried out in the way it is, and about what is really going on in people’s lives. And the more I have concluded that opinion has been presented as fact. What I attempt here is to separate the two.
On references to other work
Some of what I write here has been said by others. What I am doing is
a) providing a synthesis of their work,
b) adding some observations of my own, and
c) clarifying the the implications.
But that is not how I have done the work. What I actually did was to go to Bangladesh to live with ordinary people to find out why they were poor, then work in various settings in the UK to find out about how society worked, and then to wonder in astonishment why certain obvious questions were being ignored by mainstream economists. The basic questions are very simple. For instance, if you don’t know about mortality rates among hungry people, how can average consumption statistics tell you that they did better or worse? The answer is that they can’t. What I am doing is to show that other’s work I mention here, and my own questions, raise fundamental theoretical and philosophical questions about the practice of social science, including economics.
There are two things I in particular recommend to social scientists. The most important is to understand as much as possible about the context of their work - about real life and about other disciplines’ angles on it. The other is to read old books. The internet makes it much easier to find out what people said in the past about a topic. It is important to realise that what appears to be a new discovery in academia is often something which was written about generations ago.
Here are two examples.
a. Eric Berne’s psychological theory of what’s inside every human’s mind (parent, adult, child) was based on that of Freud (superego, ego, id). Freud’s theory was similar to that of the character Socrates in Plato’s drama-documentary Politeia (fierce animal, human, wild thing)[8].
b. After I thought about purchasing-power parity, I came across a passage in Adam Smith’s The Wealth of Nations which I thought logically entailed my point about its unfairness to poor people. He talks about “the real recompence of labour”. In general, I prefer to read old books than new ones. They are often clearer in their language, and more rooted in real life.
The list of work on financial outcomes for the majority of the world’s population which I think makes methodological sense is much shorter than the list of other work. Here are some writers on poverty, welfare measurement and/or economics who have said things similar to what I say in this document.
(To be revised. I will rewrite this, checking that my short summaries here do justice to what these people have said).
I agree with Seebohm Rowntree[9] that the death rate is the best measure of the physical well-being of people at a particular level of deprivation.
I agree with Amartya Sen that longevity is a very useful indicator of economic success[10]. I hope to show here why Rowntree and Sen - whose points above are generally ignored by economists, governments and inter-governmental organisations - are even more right than they seem. Flaws in the methods of economists increase the relative value of longevity as a measure of economic success. Some points which other people have made about these flaws are worth mentioning here. Most of the points below are not in fact controversial, since they are merely statements of fact.
Sen has pointed out that using a fall in the proportion of people under the poverty line as an indicator of progress for poor people as a whole is not sensible. He has made the following points: Firstly, it does not tell us anything about gains or losses to people who stayed below the poverty line, so failing a sensible requirement of any measure of poverty. Secondly, it tells us nothing about a worsening of overall poverty where the poorest lose out to the less-poor of those below the line. This is a fundamental methodological problem which has been known for a generation. Nevertheless, governments, academics, charities, campaigners, intergovernmental organisations, broadcasters and journalists continue to speak of a fall in the proportion of people below the poverty line as “poverty reduction” and in the context of overall benefits to poor people. I have rephrased this issue, by stating that it is a fallacy to infer average benefits - which follows from what Sen says - and asking whether there is any other meaning to the phrase “poverty reduction” which could be credibly inferred from the fall.
Mark Weisbrot and his co-authors have pointed out that if the poorest families die in a crisis, average income will rise [11]. The logico-mathematical relationships between differential mortality and statistical averages are more complex than this.
N. Krishnaji has written about problems arising from the use of per capita income/consumption statistics in situations where family sizes differ.[12]
Ravi Kanbur has pointed out that many measures of poverty will look better if the poorest die. Angus Deaton has written of the same problem. Again, the mathematical relationships are in reality more complex.
Sanjay Reddy and Thomas Pogge [13] have pointed out that the current use of “purchasing power parity” dollar equivalent units is not a measure of purchasing power of the poor. This is true: it is a theoretical measure of what a person could buy if they bought a whole range of goods and services, from basic to luxury. Angus Deaton [14] and D.S. Prasada Rao [15] have made similar conceptual points, and the March 2002 meeting of the International Comparison Programme in charge of PPP acknowledged the flaws. Reddy and Pogge carried out a statistical analysis which has a bearing on the question of how inaccurate the PPP system may be: through comparing the purchasing power of poor people for food (which composes 70% of the expenditure of poor households) with that measured by overall national PPP (as used by the “dollar-a-day” measure), they provide evidence that the PPP system will overestimate the real purchasing power of the poor.
The implications of the conceptual flaw are profound: the fact that there is no known mathematical relationship between the purchasing power of a theoretical dollar for basic-to-luxury items and the real purchasing power of the poor makes it of unknown relevance as a measure of poverty, which is an inability to buy those items necessary for a reasonable life. This means that economists using the national PPP system cannot measure the number of poor people in the world, as Reddy and Pogge say. It also means that the theoretical dollars are not a measure of poverty levels in different countries. Relatively higher levels of consumption in theoretical dollar units cannot tell us whether people were better or worse off, except where there are massive changes. Where the changes are of only a few percentage points, this is of unknown relevance to the purchasing power of poor people, does not tell us whether poor people did better or worse in one country rather than another, and therefore conclusions of studies which claim to measure better or worse outcomes for poor people from certain policies, based on the PPP system, are invalid. Even one of the authors who devised the international tables which PPP (a system of comparing gross national income levels across countries) is based on, has said that it is not suitable for measuring poverty. The fact that someone’s consumption expenditure rose 3% as measured by PPP dollar units does not tell us whether their consumption went up or down.
Samuel Morley has pointed out that cross-sectional studies do not measure income gains (age-specific income gains) to the original people in countries where the population grows, and has shown this to be so in Brazil.[16]
John Broome has questioned whether the term “utility” should be applied to differences between average welfare in an earlier and a later population; he has argued for using lifetime gains as the measure. [17]
Derek Parfit [18] has said that the principle of increasing average welfare in a later population, as a moral principle, is absurd. I think it is consistent on its own terms, just as many moral principles are - it has social Darwinist implications, and if someone believes in this then there is not much that anyone else can present as a rational argument for not believing in it. It is a very different principle from the utilitarianism of Bentham, or the idea that it’s better if most people from now on have better lives.
There is also a wide range of work available which tackles questions which are opposite to some of the ones I look at: there is work on the economic effects of demographic change due to ageing populations; and on the effects of survival rates on the prevalence of dementia.
Orazio Attanasio and Hilary Hoynes have found that wealth accumulation among the elderly in the US is overestimated by ordinary economic measures (cross-sectional data averaged) because poorer people die first, raising the average: [19]
“Most empirical studies of asset accumulation use cross-sectional data to estimate mean or median wealth-age profiles, but the use of cross sections to estimate the age profile of assets is full of pitfalls. If, for example, wealth and mortality are related, in that poorer individuals die at a younger age, one overestimates the last part of the wealth-age profile when using cross-sectional data because means (or other measures of location) are taken over a population which becomes “richer” as it ages.”
Orazio Attanasio and Carl Emmerson have studied differences between the mortality rates of poor and rich people in the UK; [20] and there is at least one paper available pointing out that health care costs are reduced by excess death rates among obese people.
I generally omit any references to the thousands of articles, books, newspaper articles and government statements which come to conclusions without considering the issues I discuss. These are readily available from government sources, universities and intergovernmental organisations.
Part I: The purpose, nature, and limitations of social science
I. 1 Purposes of this theoretical analysis
One purpose of this document is to draw attention to some inconsistencies in economic thought and language.
A second purpose is to provide theoretical perspectives for other social sciences which use similar inferential procedures (ways of working out sensible things to say about numbers). Most of what I say here about economic statistics and descriptions of economic statistics applies to other social sciences as well.
Much of what I say is relevant - in my opinion, at least - to a rational assessment of the Millennium Development Goals as a social-scientific project.
Their purpose is not only about development of poor countries but is often stated to be to help poor people.
By “assessment” I mean assessment of the project as a whole, including
1) the collection of goals;
2) the targets;
3) the agreed indicators; and
4) the indicators which have been used in practice.
I have been able to find no systematic review of the theory underlying the choice of goals, targets or indicators. Nor have I come across any review of the existing emphasis on particular goals and indicators, which is substantially different from the original package of intentions. It may be that many researchers in development studies are unaware of these differences. Several of my own observations on these matters are contained in this document.
When a system of thought is applied to a new situation, it may come to appear inadequate for the task. One of my contentions is that the fundamental assumptions of welfare economics - both written and assumed - about the calculation of mean income gains to individuals from cross-sectional data do not apply in at least some countries in the world in the year 2002.
That contention is logically entailed by the statements of many economists themselves, whenever they speak of the effects of a) changes in birth rates on economic growth, or b) the effects of increased longevity on economic growth.
But to my knowledge no-one has systematically examined demographic change as an issue for measurement of outcomes for real people from a theoretical perspective. The discussions are about, for example,
1) smaller family size increasing per capita income
which is not directly concerned with how to measure aggregate welfare gains; or
2) whether to include China in multi-country studies on economic growth and poverty
because of China’s one-child policy. This decision may involve a theoretical element, but treats this case as an exception to the assumption that cross-sectional data can tell us directly about income gains to individuals.
From the point of view of someone who wants to know what the statistics are for financial gains to individuals, I think both these approaches are the wrong way round.
The statements from social scientists about welfare gains - for example, when they speak of “pro-poor” policies - are not about the economic statistics which they have calculated, but about gains to individuals. Per capita gains and losses in the wealth of persons cannot be calculated from rises or falls in per capita measures of the wealth of nations.
The burden of proof must be on a scientist to show how their methods work, and why they can be trusted, not on the public to prove them wrong. Otherwise, we don’t have science, but something else. So here I attempt to show:
1. How a very limited range of economists’ methods work in theory
(“work” in the sense of how the mathematics and inferential procedures operate)
2. Why there may be doubt as to whether they work in practice
(“work” in the sense of fulfilling the advertised function reliably, accurately and with a reasonable freedom from bias).
I. 2 How can we tell the truth using numbers about people?
Inferences are gambles.
A friend of mine once said that learning to deal successfully on the stock market was a process of learning to understand oneself. I think the same is true of poker players, scientists, historians and detectives. Any of these can learn facts about the world, and how the facts are generated by features of the world. But some of the most important lessons are about our own mental processes and how these are shaped by our desires for particular answers[21].
There are certain classic mistakes in gambling, both on the stock market and on the poker table. A common mistake among beginners in both is overconfidence, which makes itself appear overtly as taking too many risks. In science, social science, history and detection, there are often situations where the information is ambiguous, and good judgement depends on an understanding - as far as it is possible - of the odds of certain answers being right[22].
The good scientist, historian or detective will understand the ways that information outside themselves may be distorted, but also the ways that they themselves have been prone to gamble too much on risky data or inferences. This requires self-knowledge, and this self-knowledge can be vastly improved by periodic assessment, by some other means of checking, of how successful their methods have been in giving them accurate information about the world - in really telling them exactly what they thought they found out.
In some ways, we might be tempted to think that the gambler has obvious measures of success which the social scientist or historian doesn’t have: the gambler can count their money. But it is typical of humans not to do this kind of analysis in a systematic way: people enjoy the task, the process itself, and they enjoy developing their instinct as to what is a good bet and what isn’t. They think they have the right formula because they still have faith in it. This is fine, of course, up to a point: but only if it doesn’t go so far as to cause more harm than good.
The process of assessing periodically which gambles (inferences leading to conclusions) have been successful in social science is called meta-analysis. This consists of going back over a group of studies, checking the quality of the research, and then deciding what overall conclusion can be drawn from the good ones. There are statistical procedures for doing this. It’s done in medicine. (What would also be useful is meta-analysis for any particular speciality telling us the percentage of studies which were procedurally adequate, which would give an indication of how much to trust a study quoted at random; and meta-analysis telling us the percentage of studies which were procedurally adequate by the accepted standards but whose results were conclusively disconfirmed by the same methods later). But then we still wouldn’t know how to think about the relative merit of the studies as compared to other ways of finding out information. Any method of inquiry has its limitations. How can the methods of social science be made methodical, but at the same inclusive of other relevant information?
One thing I’m interested in - as a future activity - is the meta-analysis of approaches to doing science and social science. It’s the equivalent of sitting down and looking at the approaches which lost or won you money, and thinking out which ways were successful. It doesn’t have to be a very complex process; but if it’s about contemporary as well as old studies, it needs a particular kind of honesty from the start. If we don’t want to admit our lack of knowledge or understanding, then we probably won’t ask the right questions about how we came to conclusions, or look at how to assess the methods using reference points that go outside our speciality.
I think it would be very useful for there to be more of this kind of historical meta-analysis in science and social science. It is in part the meta-analysis of inferential procedures - of well- and badly-informed guesses. I think that it is an essential part of looking at how science has been approached and what yielded better results.
I think that it’s possible to go back far into the history of science and think about which kinds of theoretical thinking, experimentation and observation led to new and better ways of understanding the world. What kinds of thinking led to more effective ways of doing science? What other kinds of thinking led to stagnation of intellectual activity, and waste of resources because of ignorance of better methods? What kinds of investigation were validated by other methods of inquiry? Which intellectual traditions just carried on with no regard for other information, with practitioners applying their methods to more and more unsuitable cases out of habit? The point of this kind of meta-analysis is to take stock of how people deal with the problem of coming to conclusions under conditions of uncertainty.
I think that it is important for a government, which is always in the position of gambling other people’s money (because the future is always uncertain) to take stock of which advances in the history of science have come about by which methods.
The story of technological understanding is on the whole one of progress. But the story of the understanding of inferential procedures is not so clearly one of progress. As academics have become more specialised, the left hand often seems not to know what the right hand is doing.[23]
Science is the pursuit of knowledge. Knowledge is elusive, since nature - including our own perceptual, emotional and thinking apparatus - often presents apparent facts as the truth, using an elaborate system of smoke and mirrors. Nature - including our own nature - is an illusionist.
What is in this document is a description of some of the smoke and mirrors in social science. The smoke is the ambiguous or misused words. The distorting mirrors are mathematical procedures with inbuilt distorting tendencies, given the words which are used to describe them. I say that the smoke and mirrors exist; that is not to say that they have succeeded in distorting particular pictures which we would have had without them. But to identify them is the first step to finding out whether our vision is clear.
It is human nature to deceive oneself about one’s capabilities, knowledge, understanding - and infallibility. It is the nature of groups of humans to follow leaders and respected figures from the past, and often to unwittingly follow a distorted version of what a person stood for, be they Jesus, Mohammed, Buddha, Adam Smith, Socrates, Marx, Bentham, Darwin, or anyone else. I think it’s possible to stop and think about where the differences are between theory and practice.
I. 3 The point of welfare measurement is outcome measurement
There is more than one kind of Marxism.
Here is one. Someone said, “Life is hard”.
Groucho replied, “Compared to what?”
Social science, like any kind of science, is about comparison. It is not primarily concerned with measurement, but with differences between measurements - over time, over space, across groups and between groups.[24]
If we are trying to evaluate policies using numerical methods, then we are concerned with comparing numbers. The end products of social science are comparative statements. Therefore one of the first conceptual tasks - in devising appropriate theoretical foundations for our activities, and in looking at old foundations - is not to think about how to measure something, but about how we might make meaningful, accurate and useful statements about differences between numbers.
These statements will inevitably be - as are statements in social science at present - about
how the numbers change over time,
and about
different rates of change in different time periods, in different places and different groups of people.
In this document I examine the logico-mathematical basis on which such statements are made, in the social science of financial welfare as it is currently applied to the majority of the world’s population.
The stated purpose of this social science - not economics as a whole, but economics as it is used to infer individual benefits, which is sometimes but not always called welfare economics - is to find out about differences in statistical measures of individual outcomes under particular conditions. In other words, the point of the discipline is to find out how well or badly people do on the whole.
If we are trying to somehow evaluate overall effects on people’s welfare, we have to have a clear idea of
a) what the aim of having the numbers is, and
b) how we might collect them and do the sums.
I think the best way of thinking about this is to start from the beginning.
I. 4 What does a science of economic welfare aim to find out?
Any science of welfare must, surely, aim to find out how well or badly people’s lives go.
That’s how I think in relation to my own welfare, anyway. If a science is going to say what was good or bad for me, I want the measure to be how satisfactory (whatever definition is applied to satisfactoriness) my life is as a whole. I do not mean here how satisfactory my life at the moment is on the whole, but how satisfactory my life will have been, looking at the whole of my life. Predictions are of course dodgy, but if I look at other people older than me and how they have done, I can take this into account in thinking about how my future might go, and I would like the social scientist to look at this as well as how I’m doing at the moment and how I’ve done in the past.
The worst thing for most people would be to die young. They may choose to risk their life for a specific reason, but apart from that, they want to live a reasonable amount of time. I expect this applies to you as much as it applies to me, and I expect it applies to almost everyone else, rich or poor.
Poverty, many people think, has several dimensions.
There are conferences and papers about the “concept of poverty” and the “measurement of poverty”. These, to me, make the mistake of placing the central questions on the periphery.
I. 5 The concept of poverty
Firstly, the concept of poverty. If we’re trying to improve people’s lives, then the whole point of measuring poverty, however we define it, lies in its relationship to how well people’s lives go. What we are really concerned about - this is, again, the stated aim of welfare economics - is people having better lives. How would we, starting from scratch, think about designing a system for measuring goodness or badness of life?
Well, firstly, to have a good life, it is necessary to stay alive.
I suggest that any system for measuring benefits to people is incomplete without putting survival as the foremost measure of success, especially when the people in question don’t eat enough. We could expand the concept of poverty to include lots of things like political freedom; but I think it’s better for clarity of thought to keep in mind that any science concerned with measuring benefits, welfare, happiness and so on is concerned basically with people having better lives. There’s no short word for this. Perhaps the word “wellth” might be useful. But starting out with the word “poverty” and then saying “what do we want it to cover?” seems to me the wrong way round, because it already has particular meanings, especially in social science. We don’t want our statements to be ambiguous. The words “quality of life” might be OK for this purpose, but in fact they aren’t, because often people think of quality of life as something to be measured at a particular moment, and not as including the quantity of life, which varies greatly between people.
(Note to MB: Add a bit about words we might use for both purposes. Maybe just make clear that what most people mean by benefit includes a “long and happy life”. Life, liberty and the pursuit of happiness - the aims of measuring development for today’s population are the same as for the individuals in it. Society may have requirements for certain conditions to be met in addition, but these should not be confused with aggregate indicators of individual progress.).
I. 6 The measurement of poverty
Secondly, the measurement of poverty. Deciding that we’re satisfied with what we’re measuring at one time does not entail that our statements about progress are meaningful. The point of measuring welfare - and this is stated repeatedly in economic theory dealing with welfare (outcomes for people) - is not to find out about levels of welfare and deprivation, but to come to conclusions about the progress of real people.
So the discussion about poverty needs to start from not concepts of poverty or how to measure poverty but from how to measure the progress of poor people.
Death and taxes are certain, but so is the passage of time. The science of welfare - the science of well-being, the science of happiness, the science of wellth including the prospect of a reasonable length of time alive - is the science of outcomes.
The philosophy of welfare economics is the philosophy of outcomes.
The theory of social science is the theory of outcomes.
Medicine is the art of outcomes.
Medicine, like all arts, makes use of science.
The science of welfare as applied to people who are malnourished is the science of outcomes, primarily medical outcomes.
For one thing, if you are ill, you can’t earn so much money, or have as much strength to look after your children properly. Most people below the poverty lines in poor countries are thought by social scientists to be malnourished. For another, illness in childhood affects ability to promote one’s own and others’ welfare in adulthood - an example is that malnourishment in children produces not just overall stunting of physical growth but also brain damage. Good medical outcomes are essential for the welfare of people who don’t eat enough, just as they are for the welfare of people who eat too much. For another, if someone to you that income is good for people, then you might reply that surely it’s better to have income for 50 years rather than 10.
I. 7 Measurement is only useful in proportion to the lack of other information
There’s an even more fundamental point I want to make about measurement. Why measure something at all? My answer is this. The point of measuring some particular thing is to get information that’s more accurate, more reliable, more unbiased, or all three, than what we could get by not measuring it.
In fact, if you’re interested in coming to conclusions about how people are doing in terms of having satisfactory lives, you can get often quite a lot of information by not measuring at all. You can spend time with people, keeping your eyes and ears open and getting an overall impression. Nevertheless, statistics, interpreted carefully, can help confirm or disconfirm our impressions.
The usefulness of statistical conclusions is not in proportion to their own reliability, but in proportion to their reliability compared with other ways of finding things out.
If we have no other information, then we have to use statistics even if they’re unreliable. If we do have other good information (which is of course a matter of judgement) then the statistics need to be reliable if they are going to convince us that the other information is wrong.
Just using your own senses might make you have a narrow understanding of what’s going on. Just using statistics given you by other people might also narrow your understanding of what’s going on, if you don’t find out how they came to their conclusions. This doesn’t have to be very complex - it just means requiring the person making the person making statements about numbers to say publicly
1) exactly how they worked out the conclusion - in plain language - and
2) how far they trust each step of the process they used.
When people talk about “statistics”, often what they are referring to is not the statistics. In other words, not the numbers. Often, they are referring to the statements which are made about numbers.
The reliability of these statements depends on a whole load of things. With some kinds of statements, there are a lot of assumptions - about how reliable the basic information is, about, for example, how information on children and adults can be lumped in together and still make sense, and so on.
Where there is doubt about the reliability of these assumptions, the unreliability will not just add up, but will multiply.
For example, if four assumptions are each 80% reliable, then the overall reliability of the conclusion is 80 per cent of 80 per cent of 80 per cent of 80 per cent, which is 40.96%. That means two out of three studies using this method will give the wrong answer, and you are better off tossing a coin.
The data on income and nutrition in countries where most of the population of the world live are of unknown reliability. The reliability of international “purchasing power parity” dollars as a measure of ability to buy essential goods is unknown. The reliability of methods of assessing financial gains which treat children and adults as having the same expenditure needs is unknown. The reliability of using population averages and proportions of poor people as indicators of progress for poor people in countries where many of these people are malnourished, is unknown.
Worse, the inbuilt biases against poor people of some statistical procedures will multiplicative effect if they are used at the same time. The use of PPP dollars at the same time as statistical averages or proportions of poor people may come into this category.
There is another problem for social scientists whose conclusions are used to devise policies. If the conclusions are unreliable or fail to take into account the inbuilt biases, and then the policies are assessed by the same flawed methods, then any distorting effects on policies will not be noticed, but will be compounded over time. This is because if policies’ success is measured by the flawed methods, the policies themselves may be altered for the wrong reasons - in addition to other compounding effects, particularly those due to differential survival rates (a government saves money if malnourished people die earlier, and dead people don’t have any more children).
To know whether or not you are better off tossing a coin, you need to have trustworthy estimates of reliability for every step.
When a social scientist tells you something - in print, or through a politician, or by any other method - or if they say that they have good evidence - you could start by asking them “Compared to what?”
I. 8 Good news: plenty of information available on welfare outcomes
The good news is that there is plenty of information to use for testing what social scientists say about poor countries and about how poor people are doing. The other information - quantitative information and qualitative - is, in the absence of any other methods of verification, essential for the purposes of the quantitative social scientist in deciding how much to trust each of the steps they take in coming to their conclusions.
If a social scientist says “these are the best methods available”, that tells you nothing whatsoever about how trustworthy the methods are for the conclusion drawn from them, compared to tossing a coin, or guessing from your general knowledge. The same applies if they say “this is a widely accepted method”. The same applies to data. Social scientists are human. They are not omniscient, and they may not know what you know about the real world; not wanting to admit ignorance is a common human flaw. In science, what we don’t know is often more important than what we do know, and the scientist’s task is to tell us both. Knowledge is sometimes inversely proportional to certainty, because the person who is convinced they know the answer is more likely to miss what’s right in front of them.
The other good news is this. I thought that the problem of finding out how poor people were doing in poor countries was a problem of finding out about numbers. I was wrong. The problem is finding out what words mean. Numbers themselves each have only one meaning. Words and phrases often have many possible meanings, and can mean different things within the same research report, newspaper article, or government statement. People who know nothing about statistical methods can still ask scientists to state exactly what their words mean, and whether they mean the same as other people think they mean. Often, words tend to take on a life of their own - so that we think we know what we are talking about when in fact we don’t.
This document is largely about what I don’t know. I don’t know what people mean by poverty reduction, and I don’t know what relevance statistics about poorest fifths of people have to consumption gains for people below poverty lines - I don’t know why people use the words “the poor” to refer to both. What I do know about are some steps that social scientists take in the process of coming to conclusions, and that these steps are not usually mentioned in academic courses, government publications or the media.
So please consider what social scientists say, and consider what other people say. Listen to experts, look around, ask questions about reliability of statistics, ask questions about exactly what words mean, think, and make up your own mind.
Part II: Language, cogs, and logic
II. 1 Open the box, look at the mechanism
In order to understand statistics, we need to understand the mathematical mechanism that generates them. We can visualise this as a system of cogs - a clock, perhaps, or better yet, a “difference engine” like the first computer.
Statistics may be generated by simple mathematical functions such as addition or multiplication, or may be generated by more complex processes. But no matter how complex the maths, it is possible to work out what kinds of things influence conclusions in different directions. I am not talking here about complex societal processes with long names, whose significance or existence is debated. I am talking about the basic workings of the mechanism.
A scientist or social scientist may ask, “how does my difference engine work?” or “where do my conclusions come from?”. This can be quite a good idea from time to time, because otherwise although conclusions keep coming out, the social scientist may not have noticed that the type of data being put in are different now.
Conclusions from statistics can only be as reliable as the data that go into them. That doesn’t, however, mean that conclusions are as good as the data. To even begin thinking about that, we have to look inside the box.
The data go in one end, and a conclusion comes out the other. Some cogs may be of unusual shape, and in some places there may be rollers which taper towards one end like the continuous gear change in old DAF cars. How these rollers respond to some kinds of data may depend on how they are pushed by other data from some other angle, some other mechanism in the box. Some cogs may look a bit like parts of spiral sea shells: these will be the locations of the non-linear relationships. A little push on them may have a big effect, or a big push may have a small effect, depending on what’s going on elsewhere.
My observations in this document are largely about differential effects - the different effects that individuals may have on statistics over time.
The cogs I refer to as biased are those which can respond in either direction to individual benefits. If they move in one direction, this may tell us that people did better. If they move in the opposite direction, this may still tell us that people did better.
These cogs are part of what is in the machine for producing conclusions, but they are not part of any computer program. They are part of the logico-mathematical mechanisms in the heads of social scientists in generating statements as to what statistical trends mean.
Conclusions from unreliable data are themselves unreliable - unless the researcher can present a convincing argument as to why an aggregation of data of itself makes the statistics more reliable by sheer numbers of data points.[25] In either case, it is the role of a scientist, whether a social scientist or otherwise, to work out where possible what the probability is of their conclusions being correct. But there is an area of inquiry, or at least of inquisitive thought, which seems to me more important. If the method of calculation is faulty then we may get faulty results, and possibly results whose reliability is unknown even if the data are perfect. Or we may end up with a system which, when we analyse it, is found to have an obvious bias towards certain kinds of answers.
The logico-mathematical structure of international economics has three features which necessarily discriminate against poorer people, either to an insignificant extent or to a significant extent. The extent to which they do in practice produce worse policies for poor people is unknown.
The mathematical structure, of itself, does not have these features – statistics themselves, and correctly-functioning difference engines, cannot be anything but truthful.
It is the words people use to describe statistics - the logic part of the logico-mathematical structure - which produce the bias. The words, in these three cases, do not accurately describe the mathematical mechanism.
I am not saying, in anything I write in this document, that any statements by social scientists are incorrect. I am saying, however, that statements have been made by economists without any foundation in either theory or evidence. I am also saying that there is very little indication from the theory of social science as to how to assess the reliability of these statements. I am therefore saying that there is little reason to believe these statements.
The statements concern aggregates of individual financial benefits.
I have my personal hunches about these things, and I also present here some hypotheses which seem to me to provide more explanatory power for some statistical findings about the real world than do the unexamined assumptions of social scientists.
I say here “unexamined” rather than “apparently unexamined” because I have searched through hundreds of books and articles in ten specialist academic libraries and countless journals, and consulted many senior economists and statisticians in universities, government and inter-governmental organisations, in an effort to find people who have considered the logical relationships which I examine here in a systematic way. I have found no-one.
A good scientist trusts their intuitions, but only as intuitions, not as fact. Intuitions - within the limited scope of social science - are no more than a guide to
a) where the evidence may be,
or to
b) what kind of evidence may be needed,
or to
c) what kind of theory may be needed.
Don’t get me wrong - I love intuition as a way of doing science.
I believe in introspection as a way of doing psychology and medicine.
I believe in imagination, and speculative leaps.
I also try to distinguish between intuition, emotion and evidence. Perhaps my thinking in this document sometimes risks being too abstract - but then as I hope to show here, my thinking may be more concrete than the thinking of some others who profess to have concrete knowledge.
The relationship between scientific theory and scientific testing is a complex one. They both inform each other; there is mutual causation, and mutual causation is a recipe for chaos. I suppose my approach to this is to try to distinguish between fact and opinion. By “fact” I don’t mean facts about the world. I mean facts about the process of discovering the world. I mean facts about mathematical mechanisms, and about the precise definitions of words.
I say this later in this document, and I repeat it here:
There is no such thing as a dishonest scientist.
By the way, there’s no such thing as a dismal science either.[26] Parts of economics are scientific, and other parts are, like parts of cosmology, pure speculation. One of the things which constitutes a dismal state of a discipline is a failure to distinguish between science and speculation.
I am not saying here that only things which are observable or measurable are scientific. That is a mistake, which some of Western medicine makes, by trying to identify every effect of every molecule of a medicine. The human body is more complex than that, which is why older traditions of using nutrition as medicine (from Hippocrates to Ayurveda) can produce medicines with similar effects to single compounds, without the disruptive effects on the body of an imbalance in one compound. In the study of medicine, history, welfare economics and cosmology, sometimes the variables are too numerous for a researcher to add in, so they need to turn to theory to clarify exactly what their data are telling them, and what the data can’t tell them. Hard data processed with an assumption of unknown reliability add up to a soft conclusion.
A real scientist tells the whole truth, and nothing but the truth. A true scientist takes extreme care to find out the exact truth, and reports that. What do I mean by truth? For practical purposes (i.e. for us, who are a kind of chimpanzee, not omniscient beings) it is the best we can do, using all the methods at our disposal.
I once saw a question on an old philosophy exam paper. It said something like “is it as bad to deceive yourself as to deceive others?”. I remember observing myself not having much of a starting point for thinking about it. I suppose now I think that deceiving myself can have bad effects on other people. And I believe that it is easy for scientists to deceive themselves. I’ve done it myself: I’ve spent time looking through libraries, when I might have realised that my intuitions were right and that no-one had thought properly about what I write here. Whether I’ve thought properly or not is not for me to judge. But I will hold fairly stubbornly to what I think is a sound model for social science, which is to know the strength of an argument’s components. Without stress-testing of each component, we have no idea under what conditions the structure will collapse. The problem with mental constructions is that their collapse is invisible and inaudible. The whirring cogs make the same noise as before. The collapse is not the machine’s failure, but our own. It is not the machine which writes the words on the top of the paper saying what we think the machine has told us.
I have intuitions as to what is really the case for trends in incomes among poor people in poor countries. I cannot with any honesty state these as fact. What I can say is that the inherent logico-mathematical biases in economics against poor people have never been examined, to my knowledge, for their effects on statistical processes which have generated conclusions about the real world.
I can also state categorically that some economists and statisticians have not considered these methods of inference (ways of coming to conclusions which go beyond mathematics) for either bias or reliability. I know this because many economists and statisticians with whom I have spoken have failed to respond to basic questions about their methods of inference. The failures to respond have taken five forms:
1) non-response - ignoring the question;
2) saying “that’s a very interesting way of looking at it, I hadn’t thought of that before” and then stopping;
3) changing the subject - for instance, when I asked a question about the measurement of past changes in real people’s incomes, bringing in irrelevant questions about benefits to future generations;
4) bringing in irrelevant data, such as when I raise a question about differential survival rates between rich and poor, saying that the poor aren’t living shorter lives than before[27];
5) acknowledging the logical - and therefore mathematical - problems in their work which might be damaging the welfare of poor people but stating that it might a good idea not to publicise them.
II. 2 A note for non-economists and others
I have received incredulous responses from some people to the suggestion that economists could have ignored obvious problems in their calculations of individual financial gains.
I myself have had to adjust to a failure of the intellectual culture in which I grew up to address such problems. I think now that I underestimated the power of group psychology (herd behaviour) in the human species, and the human capacity for self-deception.
My investigations and thinking in this area were sparked in the spring of the year 2000. I read, in a newspaper whose motto is concerned with bravery in facing intellectual challenges, a report about a research finding concerning income rises among poor people in poor countries. My first reaction was to think “Fine, if that is what the research shows, I accept it”. But when I read the document on which the report was based, I was astounded. Income rises for individuals had not been measured at all. What had been measured was mean income in the poorest quintile in each country at different times. One of my first reactions was to think, “the result could occur because the mean for the poorest quintile went up more in countries where poor people died earlier”.
I had other reactions as well: I thought that the statistic for mean income in the poorest quintile would logically contribute to the overall growth rate for a country, so any assessment of the relationship between the overall growth rate and the growth rate for the poorest quintile had an element of circularity. I thought about the fact that birth rates had changed during the period, necessarily altering the later means, just because the ratio of adults to children had changed.
And I thought that the obvious scattering of points on the graph in the research paper could not show any kind of consistent relationship - let alone causative influence - between overall per capita income growth and even the percentage change in the poorest quintile an abstract segment of the economy. I also thought that the assumed gains were so ridiculously small anyway that the conclusion about benefit would be grossly misleading even if the rest of the procedure made sense.
So quite a few things puzzled me about economics. I became even more puzzled when I got what seemed to me to be evasive responses from economists to what seemed to me perfectly reasonable questions about what might cause statistics to go up or down.
I have come to believe that the mathematical side of economics and the speculative side have become very muddled. This certainly comes across in work on macroeconomics and poor countries, where statements are often made in very categorical terms, with one side contradicting the other absolutely. A bit like lawyers in a courtroom. This is the way it is, you’re wrong.
The odd thing is that this seems to happen irrespective of whether or not there is a right answer. In some cases, such as statistical procedures, there really are right answers, and in other cases there are certainly answers which are clearly wrong, like saying there’s a correlation when there isn’t. But these real facts can get lost in the melee of speculations stated as mathematical fact.
Where people keep arguing about something, it’s a reasonable bet that the real questions are somewhere else. I think this is true about the subjects of this document. I think the economists have all missed the point, or rather several points. I know that many economists have not thought about exactly what, logically, influences their most fundamental statistics. Perhaps they have been so busy speculating that they have not seen the real facts.
On the other hand, perhaps everything I say in the rest of this document will turn out to be in practice irrelevant to any real statistics. I’ll need a bit of convincing, and I’ll need a bit of convincing as to why an economist is qualified to say what’s relevant and what’s not. Because they don’t study the welfare of real people, but statistics about the economy. The needs of a government for financial information are completely different from the needs of people to know what’s going on. Trying to kill two birds with one stone isn’t always a good idea.
Here, I’m not doing economics, or development studies. I went to a seminar once, supposedly about major theoretical issues in development studies, for graduate students, and I felt like I was in a primary school class. Conventional wisdom, down the line and up the ladder to being paid for conventional wisdom. But the conventional wisdom, I know, and its logico-mathematical structure, had been constructed by politicians.
People who are not economists often understand what I say without any trouble. I met someone recently who trained in physics. When I told her I was doing some work on economics, she asked me to give an example. I said “they think that if the proportion of poor people goes down this means that the poor people got richer”. “Maybe they died” she said. She’s foreign. “Yes”, I said. “Or maybe there were more rich people” she said, presumably meaning something like that the birth rate fell by less for the rich. “Yes”, I said. “And maybe some poor people got richer and most of them got a lot poorer”.
My point to non-economists and non-development-industry people, and non-poverty-experts[28], is this: I can understand your belief, if you have it, that economists must have thought about demographic change and taken it into account for their conclusions about average benefits to real people. This belief is untrue. I have been surprised, as you may be, that this is the case. You can check if you like. If you have access to a telephone, you can call an economist and ask them. If you have access to the internet, you can search for writings on this.
If you find anything which has a bearing on the logical relationships which I describe here, please let me know, because I would like to make statements which are not based on either unreliable data or flawed methods of inference, but, as far as it is possible to determine, true.
II. 3 Notes on the bi-directional cogs
The three areas where economics as currently constructed has logical biases against poor people are interlinked. They all form part of the assessment, and so the formation, of international development policies. It is essential for the purposes of clarity for me to emphasise several things.
1. In the logico-mathematical mechanisms of social science, these features sometimes appear together in the same machine that generates conclusions. For instance, the assessment of the progress of poor people using falls in the proportion of people below the PPP dollar poverty line has more than one risk of bias. Both biases are against the poor.
2. Where policies are made on the basis of social science with inbuilt biases, small effects will be compounded if the policies are subsequently assessed using the same biased methods and then reselected or modified on the basis of apparent success as judged by a flawed indicator. This would produce a “vicious spiral” effect. I say more about compounding later, because changes in longevity have economic consequences. If a poor person survives, the state will have one more person to cope with. My comment is: That’s life, and that approach is an indispensable part of what people call civilisation.
3. Having said that, I do not know the size of any effects of the biases on real-life conclusions in social science. Later in the document at various points I give indications of the types of statistical circumstances which will be more likely, other things being equal, to produce significant biases.
4. The mathematical mechanism for each statistical procedure is different. Thus, regression analyses may produce wrong conclusions by treating effects of biases as if they were benefits or losses to poor people, even if in a simpler study the biases would not have a noticeable effect on the basic statistics. The power of computers to help us tell the truth depends on us understanding exactly what we are telling them to do, and also on us understanding exactly what our statistics mean and what they don’t mean, how reliable they are, and exactly which words communicate to both the initiated and the uninitiated (social scientists and the public) the precise truth which the computers have produced.
5. Many experts do not trust income or nutrition data for poor countries anyway. I think they are right. I think small changes in statistics derived from these data, even if they did not suffer from biases I describe here, are of negligible value.
6. There is, I believe, a very powerful argument which can be made for longevity as the prime measure of development. If income really increases the quality of life and the level of health, then we would expect longevity to be a reasonable indicator of income levels. It is certainly a useful indicator of lifetime income levels, and a person who thinks income is good for people might agree that if a person lives longer they have more income. Longevity statistics for a whole country, and child survival rate statistics, have an overall bias towards the poor - or at least towards the majority of the population, since poorer people live the shortest time. But that does not mean that they are always a reliable guide to progress among poor people, or to relative rates of progress in this between different countries. For that we need to know about longevity and child survival among the poor. A social science which treats the length of my life as irrelevant to the assessment of my welfare is not one I want used to make statements about a group I am in, or to inform policies purporting to be good for me.
II. 4 The three bi-directional cogs of economic thought
1) The use of population means to infer average benefit.
If someone on below-mean income lives longer, other things being equal, per capita income will be lower for the population alive at the end of the period.
Per capita means are often used in economics to infer the average percentage level of people’s income gains.
If someone in the poorest quintile lives longer, other things being equal the quintile average will fall. There is therefore some reason to doubt conclusions from macroeconomic studies on economic growth and changes in poorest-quintile averages in different countries which claim particular levels of financial benefit to poor people without looking at longevity.
2) The use of proportions of the population to infer benefit to individuals.
If people below the poverty line live longer, other things being equal, the proportion of people below the line will be higher in the population at the end of the period.
In economics and statistics, a rise in the proportion of people below the poverty line is often used to infer income losses to poor people, without looking at longevity.
3) The use of national, across-all-goods-and-services “purchasing-power-parity” units as measures of the purchasing power of poor people.
If the prices of basic goods change, this method will underestimate the resulting benefits or costs to poor people; and it will underestimate the effects of changing food prices on disparities in purchasing power between the rich and the poor. Where luxury goods or services fall in price, it is a fact of mathematics that with this method the poor will appear to have a higher consumption-expenditure level.
Simply because of the mathematics, any government measure to lower the prices of basic goods and services will necessarily appear to have a less beneficial effect on consumption levels of poor people than it really does. Conversely, any government measure resulting in raised costs for poor people will appear to have less of a detrimental effect on their consumption levels than it really does.[29]
The logico-mathematical processes in economics which generate conclusions as to average financial benefits to poor people, or statements inferring overall financial benefits to poor people have often depended on, often, two of the above methods at once.
Where two methods are used in combination, which both have logically necessary (but unknown in extent) biases against poor people, how far have they have produced policies which have harmed poor people?
I don’t know.
Nor, it seems, does anyone else.
I suggest that those interested in the welfare of poor people look at survival rates of malnourished people, and compare those survival rates with the results economists have given from their methods of inference.
II. 5 Some practical implications of the logical fallacies
1. Policies aiming to reduce individual poverty which judge success by
the fall in the proportion of people under national or international poverty
lines are based on fallacious reasoning.
Indicators of progress based on this fall have inherent biases against poor people surviving longer, against decreases in the economic poverty of people who do not cross the line upwards, and in the case of the international poverty line, against poor people in countries and time periods in which the price of food falls (see 3. below).
The extent of the biases in existing studies of poor countries is unknown. So is the extent of any damage done to poor people through policies based on the studies.
2. Policies aiming to increase the incomes of poor people which judge success by per capita income of the poorest fifth of people alive at a later date
are based on fallacious reasoning.
The statistics on per capita income of the poorest fifth have an inherent bias against poor people surviving longer. The extent of the bias in individual poor countries is unknown. So is the extent of any damage done to poor people through policies based on the studies.
3. Policies aiming to increase the purchasing power of poor people by increasing the “purchasing power parity” value of poor people’s consumption expenditure are based on an unfounded assumption that
“the purchasing power of the poor for the items they buy, in different countries and at different times, is accurately reflected by their theoretical purchasing power using a measure based on purchasing power for all types of - luxury to basic - goods and services”.
There is no evidence for such an assumption. Conclusions based on it as to aggregate benefits to poor people are logically biased against them. The extent of the bias in real studies and therefore on policies based on the studies is unknown.
For example,
If the price of basic food and other basic items falls by 50%,
then
a poor person who only bought these basic items will in reality double their purchasing power: they will in reality have 100% more consumption. But whether the PPP rate is changed or not, this will not show up in the figures for PPP consumption expenditure.
If the national “purchasing power parity” rate is not changed by social scientists to reflect this,
then other things being equal,
the poor person will appear to have the same purchasing power as before.
If the national rate is changed, then
the overall purchasing power of one unit (“PPP dollar”) for all goods and services in the country will rise by something much less than 100% - because basic foodstuffs are only one component of the index of prices, and the price of other goods did not fall.
And everyone’s consumption or income will be taken by the social scientist to have risen in PPP terms, but by something much less than 100%.
The person who can only buy basic foodstuffs will then appear to have increased their purchasing power by much less than they really have.
Benefits to poorer people of falling food prices, and costs to them of rising food prices, will therefore be underestimated by this method.
Further, if basic items stay at the same prices, but luxury goods and services fall in price,
the overall purchasing power of a theoretical unit is increased. In this case:
If the PPP rate is not changed,
then
poorer people will seem to have unchanged purchasing power
(which has a basis in reality)
and
richer people will seem to have unchanged purchasing power
(which does not have a basis in reality).
..............................................................................................................
If the rate is changed to reflect the new lower prices of luxury goods,
then
the PPP equivalent of everyone’s incomes will rise,
so
poorer people will appear to have increased their purchasing power when they haven’t.
What has really happened if the prices of luxury items fall is that the rich have increased their purchasing power, and so inequality of purchasing power has increased. The PPP system does not register the degree of increase of inequality. It has no mathematical basis for doing so.
As regards international comparisons of theoretical purchasing power (for all types of goods and services), the following are true if the PPP system is used:
In countries where basic food prices are much lower,
poor people appear, wrongly, to have only slightly higher purchasing power than poorer people in other countries,
whereas in fact they have much more purchasing power for those goods they consume.
They are therefore much better off in terms of consumption, not slightly better off as the national-PPP system will indicate.
In countries where luxury goods are cheaper,
poorer people will appear wrongly to have higher purchasing power than poorer people in other countries where in reality the purchasing power for poor people’s goods is the same.
I think there may be additional consequences from this which are especially relevant to studies of the effects of international trade on poor people’s incomes.
Where there are more imports, even if the prices of imported goods are not taken into account in determining the PPP conversion rates, more competition with local goods may decrease the price of local non-essential goods. Where these goods are not bought by poorer people, the price falls will register falsely as benefits to poorer people as well as to everyone else. It would thus be easy for a social scientist to claim falsely that poorer people had benefited from increased imports of non-essential items they didn’t buy.
We can also think about services for richer people which depend on technology. The fact that a phone call costs less isn’t relevant to people who can’t afford to eat properly, but services like phone calls, and any services which become cheaper through the automation available through computers, will make poor people’s purchasing power appear higher. So, again, it could be easy for a social scientist to say that in PPP terms the poor benefit from technology, when in reality this is just an artefact of the statistics.
We can also think about food subsidies, and about the price of food generally. Where food is subsidised, under the current PPP system the poor appear not to benefit as much as they really do; the rich appear to benefit more than they really do.
On the price of food: The law of supply and demand says that the price of food will rise when people need it most. This is what happens in famines: people hoard it to make money. People need food most when wages are low. In terms of how much food they can afford, when wages are low and prices are high, they are much worse off than in other times. But a study of poor individuals’ incomes[30] based on the PPP theory will necessarily underestimate how badly off they are in those times. I am here making a different point from the one above about the price of basic foodstuffs going up or down: the point is that poor people are especially vulnerable in countries and at times where the price of food is high due to lack of purchasing power of poor people. The PPP system is not designed to capture this vulnerability, either if the rate is changed or if the rate is kept pegged to previous prices. There is no theoretical or empirical reason to think that it does.
There may be some indirect statistical effect of changes in richer people’s incomes on the apparent purchasing power of the poor, because income trends among richer people will be likely to influence prices, and thus the PPP conversion rate.
I don’t know which way this is likely to go for any particular goods or services. It seems to me there are two possibilities for each type of good or service.
The law of supply and demand will dictate that if rich people’s incomes go up, so that they can afford more luxury goods, the prices of luxury goods will go up. But economies of scale might make the prices will go down. I don’t know. But I think economists may want to think about how income trends among richer people may affect prices of non-essential goods and services.
These price changes will make the purchasing power of people who can’t afford those goods, seem higher or lower. Their real purchasing power may not have changed, or may have changed in the other direction. Without some theory as to why this is not important, it is not clear why anyone should believe that rises in the theoretical, PPP equivalents of poorer people’s expenditure reflect rises rather than falls in their purchasing power relative to their purchasing power in the past.
A further problem for economists is that poor people generally pay higher prices for what they buy.[31] People with little or no savings cannot buy in bulk or buy when prices are low. This is part of what I call a “personal recession”. It is possible to use this concept to define economic poverty in a meaningful way. Lack of cash flow is one of the defining characteristics. Others include debt levels and the use of asset-stripping to increase cash flow.
Part III: Ten fallacies in more detail
1. The “rising out of poverty” fallacy
A fall in the proportion of poor people does not measure, or give a basis for calculating, how many people crossed the poverty line upwards or downwards.
“The proportion of poor people fell by 1%.
So n million people rose out of poverty”
is a non sequitur.
A statement that “the data show n million people rose above the poverty line” would be untrue.
The conclusion does not follow logically from the data. This is because there is no necessary mathematical relationship between the statistics (proportions at different times) and the conclusion. Knowing the population size at the start and end doesn’t help either.
“There are 1% fewer small fish in the pond this year” can’t tell us how many of last year’s small fish got bigger.
The number of people who rose out of poverty can’t be calculated from the statistics on proportions. It can only be calculated by adding into the mathematical framework the other necessary data on demographic changes. Otherwise, the figure for the number of people who rose out of poverty is based on pure guesswork.
If a person has no information as to the effects of demographic change on the statistics, then they have no mathematical basis for knowing whether the conclusion about people going into or out of poverty are even in the right direction. They might infer the direction, from some other information, but that’s not a mathematical process, and it would need some other rationale - in other words, some reason for other people to take their conclusion seriously.
A. How does the mathematics work?
| |
|A fall in the proportion of people below the poverty line is mathematically a function of: |
| |
|change in population size; |
| |
|2) change in number of poor people. |
| |
What are those two statistics determined by?
| |
|1) Changes in the number of people in a place - the population size - are logically, |
|since we’re studying mortal, mobile creatures, |
|determined by all of these: |
| |
|number who are born; |
|number who die; |
|number who immigrate; |
|number who emigrate. |
| |
| |
|2) What determines a change in the number of poor people? All of these: |
| |
|number who cross the line upwards; |
|number who cross the line downwards; |
|number who are born and now in poverty; |
|number who were in poverty and are now dead; |
|number who immigrated and are now in poverty; |
|number who were in poverty who have emigrated. |
| |
Therefore
| |
|Any mathematical relationship (for example a positive or negative correlation) between |
| |
|a fall in the proportion of poor people |
| |
|and |
| |
|net number of poor people who cross the poverty line upwards or downwards |
| |
|is entirely contingent on demographic change. |
| |
If
the influence of relevant demographic changes on the proportion of poor people
is zero,
then
the correlation is perfect.
If
it isn’t zero,
then
the correlation isn’t perfect.
If
we don’t know whether it’s zero or not,
then
we don’t know the net number of people who went into or out of poverty.
The following are logical truths.
| |
| |
|Other things being equal (including no change in anyone’s income): |
| |
| |
|If the poor live longer, the proportion of poor people will rise.[32] |
| |
|If the non-poor live longer, the proportion will fall. |
| |
|If the poor die earlier, the proportion will fall. |
| |
| |
There are other relevant logical truths involving birth rates among the poor and non-poor: for instance, if the poor reduce their birth rates by more than the rich, the proportion of poor will fall. That wouldn’t be the same as people increasing their incomes so that they rose out of poverty.
B. The inverted U-curve of nutrition
If you are a typical person in a rich country, and you ask a nutritionist how you can extend your lifespan, they will tell you to eat less. You are likely to live longer if you eat slightly less than you want to. People who don’t have all they want to eat won’t necessarily live less long than anyone else. But beyond a certain point the curve goes down again.
In poor countries, nutritional status is highly correlated with susceptibility to disease. Thin people die earlier, and the deaths may not be recorded as due to malnutrition, even where it is a major cause. Thin people die of diseases which normal people recover from. There is a great difference between being poor and being chronically malnourished. There is a great difference in vulnerability to early death between the people nearest to the poverty line and those at the bottom.
C. Emotional words can deceive social scientists
A sociological note on social science:
The phrase “rose out of poverty” and the phrase “we succeeded in raising n million people out of poverty” are in any case statements loaded with emotion, indicating in the first phrase heroism and in the second case mild heroism.
I would praise the efforts of any person who has tried honestly to help poor people by directly practical, theoretical or research means, and there are many people who work very hard at all of these. Nonetheless, the phrases about poverty reduction and people rising out of poverty have no place in social science in relation to falls in the proportion of people below the poverty line. All that we would know, if we did know that a certain number of people crossed the line, would be that they crossed the line. We would not know by how much they increased their incomes or their consumption expenditure, let alone their consumption or overall economic situation.
If they increased their incomes by 1%, or 10%, or 50%, would that mean that they rose out of poverty? They may well in any case be mostly people who were not malnourished to start with (see next section on the “poverty reduction” fallacy).
In truth, we don’t know how many people crossed the line, from any statistics on numbers of poor people at different times.
So perhaps the terminology is something to discuss at a later date, when we know more about what really happened to poor people’s incomes - both those who have been assumed to have crossed the line, and the great majority of other poor people.
2. The “poverty reduction” fallacy
The most fundamental mistake in poverty analysis is to say that “poverty was reduced” on the basis of a fall in the proportion of people under the poverty line.
The point of having a poverty line is to identify people to target resources. It is not an adequate substitute for targeting resources towards the most deprived. But more importantly, the number and proportion of people under the poverty line are not meaningful measures of progress.
A fall in the proportion of people below the poverty line is consistent with large mean income gains to poor people, and also with large mean losses to poor people.
The term “poverty reduction” is used in social science with several meanings.
Often, its meaning is not made clear.
This is an unscientific practice, and should be dropped.
“There was a 1% fall in the proportion of poor people
Therefore poverty was reduced”
is a non sequitur - if we mean by “reduced” that poor people had mean or median income gains.
A. The fall tells us nothing about most poor people’s income[33]
Even if we knew about demographic change, or by some other method of social science we found out the net number of people who crossed the line upwards, this would only tell us what happened to them, not the others.
Suppose a country of 100 million has 50 million below the poverty line.
If 2 million cross the line upwards,
then the proportion goes down from 50 to 48 per cent.
So that looks like progress - until we think about the other 48 million.
There’s no information suggesting that there was a mean income gain among the original 50 million, or that the typical person’s income (median income) went up.
So I couldn’t tell you if poor people on average had income gains or losses.
I wouldn’t tell poor people, or anyone else, that their poverty had been reduced or alleviated. I wouldn’t say this to funders of development projects, or taxpayers, or voters. Still less would I say that the original poor people had mean income gains, or that the present population of poor people, with unknown differences in demographic composition, will benefit from similar policies.
B. What social-scientific basis is there for saying that poverty was reduced?
Might we have a rational basis for concluding that if we knew that some people crossed the line upwards, the majority would be likely to have had income gains?
Is there any reason apart from wishful thinking for us to believe this?
Well, that depends on whether we think that the others were in similar situations in various respects: socially, medically, nutritionally, and in employment terms.
All the people below the poverty line were poor, but what else did they have in common, or not have in common? No-one seems to have thought about any of this. Let’s have a go.
C. Were those who crossed the line a representative sample?
The adequately-fed ?300 million and the underfed ?800 million
There are an estimated 1100 million people in the world who live on below the international poverty line.
These figures are considered by statisticians in government and UN organisations to be very unreliable, partly because of the lack of data. For many countries, the years where data are available are few and far between. There are gaps of up to 15 years between measurements. I have my own concerns about reliability. Firstly, illiterate people can't estimate consumption expenditure accurately. Secondly, people may not tell the truth about either consumption or income. But my main point in this section is not about the numbers. It is about the fact that the estimate for the number of people below the poverty line is larger than the estimate for the number of malnourished people. In order to provide an example, I have used figures here which are close to the official estimates.
Out of the estimated 1100 million, an estimated 800 million are underfed.
So there are an estimated 300 million people are below the poverty line but are adequately fed.
I am not sure if there is anyone who would seriously dispute the following:
Any adequately fed people who went above the line started the period in different nutritional, economic, and therefore possibly social and medical, status from the underfed 800 million.
We don’t know whether most of those who went above the line in any country were adequately fed to start with. But we might want to think about that quite hard. If we think it is likely that a disproportionate number of those who crossed the line were from the well-fed 300 million, then the number who go above the line might be a very bad guide indeed to whether the majority, the underfed people, ate more.
We don’t in fact know the number who go above the line, as I have explained, but what I’m trying to work out here is what conclusions we can draw from the fall in the proportion. And any part of the fall in the proportion which is due to the well-fed crossing the line doesn’t of itself tell us anything about the average (median or mean) consumption trends of real people who were malnourished.
Could there be some reason why such speculation about overall poverty reduction, on the basis of a fall in the proportion, would make sense?
If someone says “those who crossed the line upwards were a representative sample of the 1100 million poor people including the malnourished”, then we might want to think of some empirical reason for believing it. But there’s a logical problem in any case with this idea, because if some people were badly undernourished to start with but went across the line, then they had much more income gains than the many who didn’t. So their income gains couldn’t have been representative of the gains of the majority. If they had large gains, and people above them didn’t cross the line, then those people above them certainly had smaller, if any, gains.
Realistically, considering that the adequately-fed people were less susceptible to disease, death of productive family members, deaths of children (with consequent loss of the work that went into looking after them) and so on, it looks to me likely that what happens to people at the top end isn’t really very relevant to what happens to the bulk of the malnourished people, and that people who were adequately fed were most likely to cross the line.
This, of course, would mean that their gains would only need to be small anyway to make them cross the line. People who cross the line but were near the poverty line to start with didn’t come out of malnutrition. Whether they had income gains of just 1%, or more, is not information that the fall in the proportion can provide.
So it is very difficult to know what the fall in the proportion tells us at all about income gains to the majority of poor people. Sen’s basic point about the fall not recording income changes for people below the line is true, but I have tried to think whether in practice, if we knew that more people crossed the line upwards than downwards, this might for any sociological reason give us reasonable grounds for inferring that other people had income gains. I can’t think of a reason, and the point I make above about the adequately-fed people seems to be a consideration for not inferring that the majority benefit when some people cross the line. In addition, there is the temptation on the part of a government to help the adequately-fed poor and not the most-malnourished poor (who may well be more likely to make the proportion fall by dying rather than by overtaking the other 1100 million in income terms).
What we do know, however, is that the people who just manage to cross the line don’t have consumption levels where they could very sensibly be described as “non-poor”.
(Note to MB: This para to be revised)
..............the real dollar value of the theoretical, all-goods-and-services PPP dollar unit. The real dollar value may be in a poor country 40 cents in real terms. An income gain of 5% to a person whose income is 40 cents a day, in real terms, in a world which is often described as globalising, is two US cents. If this person’s income was really known to have increased by that much in real terms, and not as a function of changes in PPP rates, and if they crossed the poverty line, they would still be living on what I could afford in that country with 42 cents. Poor countries are cheap compared to rich countries, but they’re not that cheap.[34] If I were assessing income poverty, I would not talk of “halving income poverty” without some reference to people on 42 cents a day, and I would not speak of people rising out of poverty when that was the standard of living which they had attained. I am not sure why anyone else does.
D. UN statistics on the Millennium Development Goals
The internationally-agreed Millennium Goal concerned with “halving income poverty” has five agreed indicators of progress.
However, only two of these have been used - for example in the most recent report by the Secretary-General of the UN - even though the period is half over. It began in 1990. A useful indicator of progress in comparing levels of poverty would be the poverty gap ratio[35] - a measure of the depth of poverty.
The published UN statistics for the goal include poverty gap data for various dates in the 1990s for each country. But there is exactly one statistic for each country. So no changes in any country’s poverty gap ratio are available from these statistics. The poverty gap ratio has not been used as a global measure of progress for the goal. So we don’t know from these statistics whether the poor now have on average (mean or median) more or less income (consumption expenditure) than ten years ago.
Why the poverty gap statistics have not been published for more than one year for each country is not clear. Income data are available for more years than this.
What has been used in the Secretary-General’s report are two indicators:
1. the change in the proportion of people on under PPP $1, and
2. the change in the proportion of malnourished people.
I do not know what the statistical procedure was for combining these two indicators. Nor do I know the proposed procedure for combining the five indicators, or for combining any of the total of 48 indicators for their relevant Millennium Goals.
In theory, the official conclusions about the progress of malnourished people should have a bearing on my points above about the fall in the proportion of poor people not telling us much about the progress of the malnourished.
Since I do not know how the data on nutrition have been used to generate conclusions in the reports, I cannot comment on how much the nutritional data were taken into account.
But in any case, the usual conclusions drawn from the indicators for the proportion of malnourished people are in my opinion invalid. The fact that the proportion of hungry people went down does not tell us that they ate more on average. Among people classed as malnourished, there is a wide range of nutritional and medical status and thus of vulnerability to early death.
The nutritional statistics, like the income and consumption expenditure statistics, are known to be unreliable.
E. Temptation for governments to help the least-poor
Poor-country governments now have incentives from abroad to reduce the numbers of poor people. As a result, governments have more incentive to help the people most likely to go above the poverty line[36]: in the example above, the government might have more incentive to help the top, say, 10 million and less incentive to help the bottom 40 million, because the 40 million have a smaller chance of coming above the poverty line this year. Having an incentive is not the same as acting on it, but it is hard to deny that the incentive is there.
Government policies affect both individual economic progress and the length of people’s lives. If you don’t know what I mean, think of a country where health services for poor people have worked well, and then think of another country where they haven’t.
If a government allocates resources to the majority of poor people, rather than to the top section, they may increase poor people’s income, but not see a reduction in the proportion of people below the poverty line. They might, though, increase the proportion, or make the proportion fall more slowly, if the poor live longer. What will make the statistical proportion smaller is if the poor die at a disproportionate rate. People whose consumption expenditure is less usually don’t live so long.
F. Is child survival correlated with changes in the proportion of poor people?
If child mortality is bad and the proportion of poor people is falling fast, is it sensible to keep on reducing the proportion without thought, or better to stick to the intention of balanced progress on the Millennium Goals?
A possible (partial) statistical safeguard for the use of “proportions” statistics as measures of poverty outcomes is the child mortality statistic for the whole country. Why?
1. Child mortality is concentrated among the poor.
2. Child mortality is associated with family malnutrition and bad adult
health, and therefore with shortness of adult life.
3. So we can expect the parents of children who die to be mostly the poorest,
thinnest and most susceptible to disease.
In any population:
If child mortality is high compared to expected progress
and child mortality is concentrated among the poor
and child mortality is correlated with early death among adults
then a higher-than-expected proportion of poor adults are dying early.
and the proportion of poor people is smaller as a result.
Child mortality rates may be some indication of death rates among both poor adults and poor children. They are not anywhere near as useful as having child mortality information for the poor, or overall life length information for the poor, which is what we really want for our conclusions about progress among poor people.
What I am saying here is that if we look at countries where child survival rates have improved dramatically, we might expect those countries to have a slower fall in the proportion of poor people. This slowing down of the fall would represent a benefit to the poor, not a loss.
So a social scientist needs to ask themselves whether they want to count a fall in the proportion of poor people as a gain to the poor, and if so, why.
Similar points can be made in relation to other Millennium Goals phrased in terms of proportions of the population.
If more poor people die earlier on in the period of the project - over the next few years - then statistical progress on “proportions” goals by 2015 becomes easier for a government. That is because there are then fewer poor people for the government to work on. This is not the same as saying that the result was better for poor people. A government which keeps poor people alive may incur financial costs. That’s life.
It would be perhaps useful to know what the correlation is, across all poor countries, between
1. progress on child mortality and
2. falling proportions of poor people
during the period of the International Development Targets/Millennium Goals.
But perhaps not very useful. The income/consumption figures, and the nutrition figures, are known to be of low quality - often with many years between measurements. In any case, differences between the “PPP value” of income or expenditure in different countries have not been demonstrated to be an accurate measure of the purchasing power of the poor. It is thus highly questionable what the fall in the proportion of people living on under a PPP dollar really tells us.
A fall could have several explanations. It is unclear to me why the explanation of most development economists for a fall, under all circumstances, is that individual poor people’s incomes rose.
Child mortality statistics have numerous advantages for the assessment of progress among poor people.
G. Proportions + demography + depth of poverty [37] = gain or loss to poor
Without all three types of information above, we have no basis for statements that the poor did better on the whole, or even for saying anything about how the top group of well-fed poor fared.
Where there is income data, the same data can be used for calculating the depth of income poverty.
What information is available about death rates at any age among people below the poverty line for each country?
What other information is available from cohort studies, anthropology, medical research and so on that’s relevant to trying to see average income gains or losses? Or to benefits and costs as a whole, including in assets, public services and so on? After all, if we want to say what benefits the poor, we’ve got to make sure that it makes sense.
H. The “narrow-evidence” fallacy in social science
Scientists and social scientists in any field may be tempted to speak of “evidence” as “the statistical data available in my field”, which puts four limitations on the type of admissible conclusions -
first, limits on the form of data,
second, limits on the content,
third, limits on the methods of aggregation,
fourth, limits on the methods of inference towards conclusions.
The most sensible scientists, of course, try anyway to base conclusions on all that they know, and try to find out about other types of evidence relevant to their question, and about other ways of coming to conclusions. We might talk of a general logical fallacy which sometimes crops up in science and social science - a “narrow evidence fallacy” where a categorical statement is made on the basis of one kind of evidence, without any other kinds being considered. See the last chapter of C. Wright Mills, The Sociological Imagination, for how a social scientist can try to cure narrow-mindedness. See the writings of Richard Feynman for questions a scientist can ask themselves about what they really have found out and what they haven’t. Knowing what you don’t know is necessary in order to realise what you do know. Otherwise you just believe you know things, but haven’t defined the boundaries of your knowledge.
The first step in thinking about how to at least try to make sense of the fall in the proportion of people on below the poverty line is to think about, not the amount of a demographic change’s effect on the statistic, but the direction of its effect.
If, for example, we know that inequality of life length between poor and non-poor is getting worse in a country, then this is a possible cause of the proportion of poor people going down. If this inequality is getting less pronounced, then any effects of changes in life length on the fall are going to make the fall smaller. In this case, it is more likely that the fall in the proportion means the poor did see increased incomes. As long as we remember about the influence of birth rates, and the other demographic changes which can influence the statistic.
I. Things to think about in relation to falling proportions of poor people
The more poor people die early,
the less reliable a fall in the proportion of poor people
– however poverty is measured -
is as a measure of economic success,
even of any modest economics success for the best-fed of the poor.
The less you know about changes in life length,
the less you know about income gains or losses even to the best-fed poor people
from just looking at the fall.
The less you know about other demographic changes,
the less you know about any poor people having income gains or losses.
J. Semantic fallacies and the phrase “poverty reduction”
There are many semantic confusions in this area of study.
For example, ”poverty eradication” does not mean the same as “poverty alleviation”.
Reducing the prevalence[38] of poverty does not mean it was alleviated.
A statement that “the prevalence of poverty by the headcount (proportional) measure fell” does not mean the same as a statement that individuals’ poverty was reduced according to some aggregate measure.
Where a researcher does not specify the meaning of the words “poverty reduction” I would advise a reader not to assume that this implies benefit to the poor, even if the researcher makes this assumption. Science begins with definitions, because otherwise we don’t know what the scientist is talking about.
Numbers are useless if people use the wrong words about them
Policymakers use social scientists’ statements about numbers in making decisions.
The social scientists, not the policymakers, are the people who understand what the statements mean. The best social scientists have an understanding of the degree of support which any statements may or may not have from the numbers. This is a complex art - as it is in many sciences where there are elements of speculation or inference. Nevertheless, it is possible to analyse the scientific process by which the statements came to be made. The first step in this process is to define the terms.
The words which social scientists use to describe their findings are more important than the numbers themselves. There is no point in carrying out a complex mathematical process and then coming to a conclusion whose meaning, to social scientists, policymakers and/or the general public, is ambiguous, vague or liable to misinterpretation.
No-one may have thought to question the definitions; the vagueness of a term may be customary; the methods may be accepted by the majority of social scientists as reliable and the statements meaningful; but all of these are irrelevant to the question of what numerical basis a person has for making a particular statement.
A request to social scientists: If your words aren’t clear, please use other words.
There is no theoretical or empirical basis for using the phrase “poverty reduction” in talking about a fall in the proportion of people below the poverty line. The phrase “poverty reduction” is often used, but the meaning is never made clear. Here are some possible meanings.
If you know of a piece of writing which uses the phrase “poverty reduction”, which of these, if any, does it mean in each place where the phrase is used?
1. A writer may mean that “people below the poverty line, on average, increased their incomes”.
But this is not entailed (mathematically given) by the statistic: therefore it is an inferred conclusion. What is the basis for the inference about people increasing their incomes on average? Which average - mean or median? Does the writer mean the average considering people’s ages - in which case they are talking about poverty - or an average of adults and children jumbled up? Without additional information, there is no basis for inferring any conclusion from proportions of poor people to average gains.
2. If the writer uses the phrase to imply that “people below the poverty line, [39] overall, had some benefit”, then without a definition of this benefit the phrase is meaningless. If it is not an average gain then it is not clear what this could mean.
3. The writer may mean that “the net number of people crossing the line was upwards”.
But in order to be able to say this, we have to realise that this conclusion is not calculable from the statistics. They writer therefore needs some other reason to say it.
4. They may mean simply that the proportion of people below the line fell.
But in that case the words “poverty reduction” are misleading. The prevalence of poverty has fallen, but not necessarily its incidence (I explain elsewhere the difference between these two).
The fact that someone - a social scientist, a politician or anyone else - may want to think that a conclusion is given by social science does not make it a valid conclusion. The job of the social scientist is to be as clear in their words as they try to be accurate in their calculations.
What is the probability of any of the conclusions above being accurate, or in the right direction? The probability of both of these is in each case a function of
1) the reliability of the data,
2) the reliability of the method of calculation, and
3) the reliability of the inferences.
So a social scientist needs to specify all of these. Otherwise it isn’t science but guesswork. Failing to say what the assumptions are is about as far from science as you can get.
The phrase “poverty reduction” is misleading also for the following reason.
In summary assessments of the prevalence of poverty, government statements often refer to the proportion of people living on less than PPP $2 a day[40]. All of these people are poor, and therefore this is a sensible segment of the economy for a social scientist to look at. However, if these people are poor, then the real prevalence of poverty is not sensibly measured by looking only at those on under PPP $1. Aggravation and alleviation of income poverty of those on PPP $1 - $2 is not taken into account at all by the statistics on proportions of people under PPP $1 - except among those who cross the PPP $1 line. Further, early deaths of the people on between PPP$1 and PPP$2 - which we can safely infer are very often caused directly or indirectly by poverty, are not known.
Therefore, unless social scientists can come up with a specific meaning for the phrase “poverty reduction”, they should not use it.
A lower proportion of people below the PPP $1 poverty line in a later population
is consistent with
aggravation of individual poverty,
among
those on under PPP$1,
those on between PPP$1 and PPP$2,
or both.
To continue to use the term “poverty reduction” with that knowledge in mind would be profoundly unscientific and grossly irresponsible. It would not be telling the whole truth; and it would be to claim something that goes beyond the truth of what the social scientist knows.
K. Theoretical dollars and assumptions about falls in proportions of poor people
An even more basic fallacy becomes evident once we realise that it is theoretical (PPP) dollar values, not real consumption levels, which are used to make inferences about falls in the proportions of poor people in international studies.
Suppose the number of poor people (as measured by the PPP dollar) falls.
Does this tell us that the number of people with consumption expenditures below a certain purchasing power went down?
No.
There are two alternative explanations:
1) The PPP conversion rate changed disproportionately to the purchasing power of the poor.
2) Prices went up so the poor had to spend more, but this is recorded by the social scientist as an increase in consumption expenditure.
| |
|So a further fallacy on the proportion of people below the poverty line is: |
| |
|“The proportion of people below the PPP poverty line fell. |
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|Therefore the proportion of people below the original consumption-poverty line fell”. |
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The poverty line as a measure of consumption poverty may have moved.
A fall in the proportion of people on below the past-prices PPP equivalent dollar
is consistent with
a rise in the proportion of people unable to afford the consumption level that defined the poverty line.
This is because if the price of food goes up, and the PPP rate is the same as before, the poor may have more consumption expenditure. This isn’t a gain, it’s a loss. But would it not be recorded, under the present system, by a social scientist as a gain?
In any case, if the price of food goes up, the poor may be forced to spend more on food at the expense of medicine, education, or other items which prolong life; or to sell assets such as land. Even leaving aside these losses, I am wondering whether the currency value of consumption expenditure is an appropriate measure of welfare at all, since more expenditure does not necessarily tell us the person ate more.
My thought here is speculative and unexamined even by me as yet, but it is that even if a PPP rate were used which really reflected the purchasing power of the poor, price changes for basic foodstuffs may be wrongly interpreted by researchers as benefits or costs to the poor. I think this would happen with price changes which happened since the last time PPP rates were calculated, even if the PPP rate had been at that time fixed to the price of basic items.
3. The economic fallacy
On the wealth of persons.
“There was a 1% rise in per capita income.
Therefore people had mean income gains of 1%”
is a non sequitur.
This fallacy confuses
a higher per capita income in a later population
with
per capita income gains to individuals.
Where it is known that the per capita income statistic at the end of the period was not influenced by changes in birth rates, death rates or migration, the inference is valid. Without this information, the inference is fallacious.
The conclusion about mean income gains to real people is not calculable from the economic growth statistic: The statistics on per capita incomes at the start and end of a period tell us nothing about differences between the demographic composition of the population at the start and at the end.
The mathematical relationship between the economic growth statistic and mean income gains or losses to real people is determined by demographic change.
A. “Economic growth” is not growth of the economy
I shall probably drop this term, since it has an unwarranted emotional connotation, as does “poverty reduction”. What is usually called “economic growth” or simply “growth”, can occur even when the size of the economy shrinks - both of these happened after the plague in Europe. This may be good for a government, but not for the people.
B. “Economic growth” is not a measure of income gains
A higher per capita income at a later date not show us that the economy grew in total value of transactions; nor does it show us that individuals had personal income growth on average; nor does it show us that more people had income gains rather than losses. The term is a quaint but not necessarily apt metaphor for a change in one type of statistical average, a fiscal statistic for the economy as an abstract entity. It is immediately relevant to a government for planning purposes; but it is not a measure of welfare. It cannot of itself tell us the welfare of the population, even in the narrow terms of declared income. In other words, it is not a measure of costs and benefits to real people, even in those narrow terms. I shall try and devise an alternative term for this statistic, less liable to create confusion and which more accurately describes its nature.
C. What is the “economic growth” statistic?
The economic growth statistic for a geographical area is
(mean - one type of average - income among people alive at the end of a period)
divided by
(mean income among people alive at the start)
expressed as a percentage.
It is calculated from two pairs of statistics:
1) financial totals of relevant (and declared) transactions in the geographical area, at the start and end of a period,
and
2) population numbers in the place at the start and end.
| |
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|What the economic growth figure does not tell us on its own |
| |
| |
|A 1% higher or lower per capita income among |
|[those alive in a place at the end of a period] |
|than among |
|[those alive at the beginning of the period] |
| |
|cannot tell us, on its own, any of the following: |
| |
|how much more or less income in percentage terms the present population have on average* now for their age than the population |
|before; |
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|the average percentage rise or fall in individuals’ incomes over the period; |
| |
|or |
|the average income gain or loss to the original people and their descendants considering their age; |
| |
|or |
|the average percentage gain or loss during the period to those alive in the place at the end. |
| |
If we want to use per capita statistics at different times as a basis for statements about average gains or losses to individuals, we need to understand the mathematical relationships involved.
A change in the financial total (a rise in total gross national income in the geographical area) is mathematically determined by:
a) income gains to individuals considering their age
b) changes in age structure (the proportions of people at different ages)
c) addition of income of new arrivers (born or immigrated)
d) subtraction of income of people who left the place (died or emigrated).
A change in the population total is mathematically determined by
a) number born
b) number who die
c) number who immigrate
d) number who emigrate.
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|The following are logical truths, and therefore a structurally-necessary part of the mathematical relationship between population means and |
|mean income gains. |
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|Other things being equal (with no income gains or losses to anyone considering their age): |
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|If there are fewer births, the mean in the later population will be higher. |
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|A past baby boom will result in a higher mean in the later population when that generation reaches an age where income is traditionally high. |
| |
| |
|If anyone with income below the mean lives longer, the mean in the later population will be lower. The poorer the person (in income terms) |
|who lives longer, the more the mean for the later population goes down. |
| |
|If anyone on below-mean income dies, the mean in the later population will be higher. |
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| |
| |
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|If a person on above mean income survives, the mean in the later population will be higher. |
| |
|Since there are more people below the mean than above it in all countries (the distribution of incomes is always skewed, with a bulge towards|
|the bottom and a long tail towards the top) the following is also a logical truth: other things being equal, |
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|Most people will lower the mean by surviving and raise the mean by dying. |
| |
Let us be quite clear on differential longevity.
If per capita income is static, and the rich live longer than the poor, as in all countries, then other things being equal - as with any welfare measure - if everyone starts to live for the same amount of time, per capita income will fall even if there is no net loss of years of life to anyone. [41]
How do these logical relationships, which necessitate that the mathematical mechanism for computing average gains includes them, affect our interpretation of studies of economic welfare in the real world?
The answer, which has come as a surprise to me, is twofold.
Firstly, no-one knows how big or small the effects are except for a limited range of countries.
(Note to MB: This part needs revising. There are some estimates of the effects of demographic change on economic growth. I need to state the position of academic knowledge correctly in relation to a) direct effects, b) indirect effects and c) economic changes to other people which accompany and/or cause demographic changes. I need to add to 1) and 2) below a third point about the last of these; and to add in similar points relating to changes in age structure.)
Secondly, no-one knows whether other things are equal or not. In other words, no-one knows whether, in any country or for any study ever carried out by economists, the mathematical mechanisms entailed by these logical truths are disrupted by some real-life consequences of people being born or living a different amount of time. For instance, it may be that in poor families in a particular country, generally if a very young child dies, the parents have an extra child to compensate.
My birth had financial effects on other people’s incomes. My death will have effects as well. Calculating these would be a complex task, but perhaps there are some simple relationships we could work out which may apply in general for various countries. The factors may be very different in relation to me from the factors in relation to births of people among the unknown number - but perhaps one in seven people - in the world who do not have enough to eat.
So we do not know either of the following:
1) how big or small the direct[42] effects of changes in birth and death rates are on the per capita income statistic at the end of the period
2) how big or small the indirect[43] effects of changes in birth and death rates are on per capita income statistic at the end of the period.
The average income gain (defined as a mean income gain for the original population, or for them and their descendants, or even for survivors of the period) - and even the direction of the mean change in people’s incomes - cannot be calculated from the per capita statistics alone. It can only be calculated by having a complete mathematical mechanism, which would include the effects of demographic change.
Otherwise, the figure for mean percentage income gain is based on speculation. The assumption, in any particular study, that “mean income gains equalled the change in the population mean” is a conjecture about causation - about what caused the per capita income statistic at the end to be different from the one for the beginning (or even what caused the statistic at the end to be the same as the one at the beginning). I call this the zero conjecture.
D. Demographic change and the “zero conjecture”
This is a common conjecture[44] in economics in the year 2002, for all countries and all periods of history.
However, its validity is implicitly questioned by any writer who has said such things as “lower birth rates result in higher economic growth”. If the writer means not just that economic growth went up because low birth rates were conducive in the real world to higher wages, but that the growth rate went up partly because of the mathematical effect of the change in the ratio between earners and earners, and their statement is true, then in places where such a result has occurred, the following is necessarily true:
The value of (in the mathematical sense, which means “the number for”)
mean per cent income gains or losses to real people considering their age
is a different value from
the per cent difference between per capita income at the start of a period and per capita income at its end.
The writers who say that birth rates change the rate of economic growth have to assume that the zero conjecture isn’t valid for all circumstances. To assert otherwise would be to take two logically contradictory positions.
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|Here is a fuller statement of the zero conjecture as applied to countries where demographic changes are not known to be |
|insignificant. |
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|(There is no evidence and no theoretical support for such a conjecture). |
| |
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|“100% of the change in per capita income in the place was |
|due to income gains and losses to individuals; |
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|0% was due to migration; |
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|0% was due to changes in overall birth rates; |
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|0% was due to changes in differential birth rates across incomes[45]; |
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|0% was due to overall changes in longevity; |
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|0% was due to differential longevity changes across incomes; |
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|0% was due to changes in age structure; |
| |
|0% was due to differential changes in age structure across incomes”. |
| |
The above is an assumption which is permissible in the academic discipline of economics in the year 2002, no matter how malnourished the people being studied and no matter how variable the birth rates in a country.
Within economics, there is research about demographic change on per capita statistics, and people argue about China.
China’s one-child policy obviously changed the ratio of adults to children, and some research has confirmed the effects of this on per capita income statistics, and so there are economists who think that it should be excluded from big studies on poverty.
But there are no professional restrictions on economists using the zero conjecture in all circumstances, then claiming - without doing the mathematics - to know what happened to individuals’ incomes. Economists who have presented these conclusions as mathematical fact have had to my knowledge transgressed no professional codes of conduct. Perhaps it is time for some rules within academic economics as to what are to be presented as mathematical conclusions, and what are to be presented as speculation, based on conjectures or hypotheses.
Also within economics, people write about how much of the “East Asian economic miracle” was due to demographic change.[46] As a result, the common-sense view that the zero conjecture is nonsense in relation to the last few decades is supported by research, at least for countries undergoing the “demographic transition” - which means the transition from many children and short life to few children and long life.[47]
The demographic transition requires a higher per capita consumption level to keep the people at each age fed as much as people of that age had before.
In fact, common sense tells us that where a per capita household consumption level is used, as the World Bank has done, that is not fundamentally a welfare statistic at all, but an abstract statistic. It is a useful statistic about the economy, but not in itself a useful statistic about people’s welfare. Families with the lowest per capita consumption levels are not necessarily the one with the poorest members. Suppose you and your spouse have a baby. On the day se[48] is born, born, your and your spouses’ per capita consumption goes down by 33%! But the baby doesn’t actually consume a third of the consumption of the household The World Bank system says that se does. Babies cost far less in poor countries. They don’t have expensive prams, expensive child care, expensive clothes, tinned food, toys, and so on.
In China, the effect of the demographic shift on statistics about the economy (per capita, jumbling up adults and children) was massive. The effect on consumption levels of real people at each age was significantly smaller. This is quite obvious from looking at the age structure diagram for China. Logically, for example, people aged 30 have always eaten enough to keep a 30-year-old alive. The present consumption levels of people aged 30 need therefore to be compared to the past consumption levels of people aged 30. Jumbling in a past high number of babies - which obviously depresses the per capita average consumption - into statistics misdescribed as relating to economic welfare gains is pure nonsense.
This is nothing to do with politics of the right or left. It is simply a matter of logic and truth as to what the statistics refer to. Perhaps, though, it is appropriate to state here that I am not the person who praises changes in statistics about economies resulting from Communist policies. That praise comes from the particular studies, out of all those produced by the World Bank, which are promoted by its Media Department. I am the person who notes that such economic statistics are different in scope, nature, referents and implication from statistics about aggregate economic gains to individuals. An economic gain is obviously more if it comes with longer life for the individual.[49]
Economic gains to an individual can only rationally refer to lifetime economic gains, as a function of changes in longevity, and net of, at least,
Declared income gains and losses,
Asset gains and losses,
1. Changes in necessary expenditure,
2. Debt reduction or increase,
3. Undeclared income gains,
4. Earned benefits in kind
5. Unearned benefits in kind
Without an estimate of, or specific reason to exclude any of these, a researcher is not being rational or scientific in using any one of them to make a statement about economic gains or losses to an individual. Still less are they being rational or scientific if prior to that kind of inference, they first confuse per capita changes in the population average with average gains in income or consumption to real people during the period.
A higher per capita income for children and adults jumbled up does not tell us that, for example, the average 30-year-old is better off than the average 30-year-old before. They may be worse off than those people were. What would be the definitions of the words “rises” or “gains” used by a social scientist who said that those 30-year-olds now had income rises, or gains? The social scientist does not know that the people had gains relative to what they could have expected at their age before.
The birth rate in China actually declined over 25% during the 1990s. The dependency ratio declined from 1.12 in 1985 to 0.56 in 1999.[50]
(Note to MB: Are poor households in cities smaller than those in rural areas? That would end up with an understatement of urban poverty. Do the old people stay in the villages and the young ones go to the cities?)
Here is a quotation from the UNFPA’ State of the World’s Population 2002, with a commentary added here.
“Fertility Decline and Economic Growth
Half of the improvement in economic growth attributable to population has come from cashing in the demographic bonus, the other half from shifting economic consumption towards the poor (12). Many mechanisms contribute to this effect: for example, lower fertility increases women's participation in the labour force and helps improve family health and nutrition.”
The point about women’s participation in the labour force seems reasonable. But we have to be clear about what exactly the words “family... nutrition” mean.
The official statistics themselves are not measures of adequacy of nutrition .
They are, instead, measures of nutritional levels per capita in households, jumbling up adults and children [51].
Therefore, where birth rates are falling,
the incorrectly claimed increase in nutritional status of the people (adults-and-children jumbled up)
is more than
the real average increase relative to need.
In the baby boom, the per capita consumption was low. Of course it was - there were a lot of babies. That doesn’t tell us whether children’s and/or adults’ nutritional requirements were met. In the baby bust, per capita consumption which is adequate for the baby boomers now grown up, needs to be higher for those grownups than when they were babies. Since their generation contributes a bulge in the age structure, that bulge moves up over time and affects the level of a sane measure of poverty. The old per capita consumption level for (children and adults jumbled up) may have been appropriate for the baby boom times, but is no longer appropriate for the consumption requirements of the baby bust and the increased proportion of adults who live in them. A significant shift in the dependency ratio necessarily entails a significant shift in the per capita nutritional requirements of (adults and children jumbled up). That is why a per capita household expenditure or nutrition measure is inappropriate for poverty measurement. It has to distort the results if it is misdescribed as a poverty measure.
A baby bust means that the baby boomers grow up and so need more food. The proportion of people who need adult-sized portions increases. The old statistics for the baby boom overstated the poverty of children, because children don’t need the fixed per capita consumption level used. The new statistics understate the decrease in poverty if they are incorrectly described as referring to changes in poverty levels – which they do not measure, rather than consumption levels across adults and children in a big jumble, which they do measure.
The passage goes on:
“Smaller family sizes reduce dependency ratios within families and increase incentives to acquire income beyond the basic necessities of life.”
Long-term demographic and economic data from 45 developing countries show that high fertility increases poverty by slowing economic growth and by skewing the distribution of consumption against the poor. Reducing fertility - by reducing mortality, increasing education and improving access to services, especially reproductive health and family planning-counters both of these effects. The national effects on poverty reduction are clear from both average GDP increase and consumption figures.
The average poverty incidence in 1980 was 18.9 per cent, about one in every five people. Had all countries reduced net fertility by five births per thousand women of reproductive age during the 1980s (as many Asian countries did), poverty incidence would have been reduced by a third, to 12.6 per cent, or one in eight.
E. The zero conjecture doesn’t explain much
The “zero effect of demographic change in all circumstances” assumption, which is an unconsidered, unwritten, unexplored, and untested conjecture, can’t explain some other facts:
1) why non-economists sometimes say that poor people are faring better than economists say;
2) why changes in per capita statistics in Cuba, Sri Lanka and Kerala has historically been low relative to other countries. (In those places, efficient health services have ensured that people on below-mean income had dramatic increases in longevity). A “zero effect of differential survival” conjecture - which would have to form part of the overall “zero effect of demographic change” conjecture, cannot explain this at all.
F. Relative longevity theory
A “differential longevity” hypothesis can explain, at least partially, some statistical facts about the real world.
I call it a hypothesis, because there are reasons to think it may be true, whereas I can neither find nor think of any argument for believing the zero conjecture.
A hypothesis that
rich-poor differential survival rates have had a significant influence on per capita income in studies carried out over the last 50 years by economists
can provide a partial explanation for facts 1 and 2 above, about non-economists and about statistical rises in per capita income.
Firstly, the fact about the observations of non-economists:
If the poor live longer, then mean income figures may go down, or go up more slowly, while the observer sees that the poor do better.
Conversely, if inequality of life length widens, this inequality may be clear to the person who knows a place and knows the people. But if there are significant statistical effects of differential survival on the economist’s figures, the economist will mistakenly say the original people had income gains. With cross-sectional studies, the only scientific conclusion is about the statistics, not about the people. Opinions about what caused the statistics to rise or fall may or may not be interesting, but the true scientist tells their audience which of the things they say are facts and which are opinions.
Secondly, the fact about places with good health services for poor people:
In places where the poor have increased their life length dramatically (such as Sri Lanka, Cuba and Kerala) per capita GDP growth has been low. This can be partially explained by the hypothesis that life length has had a significant effect on the growth statistic.
The explanation is especially plausible given that
a) if the poor live longer they may cost the government money, and
b) if someone dies, they have no further children.
Anyone whose life is saved who goes on to have children will usually overlap in lifespan with their children. So another country where poor people are left to die early may end up with a disproportionate drop in the number of poor people - by which I mean that one death of a poor person means a drop of more-than-one in the number of poor people in the future.
At this point someone who is not poor may start to worry about the risk of overpopulation if malnourished people live longer[52]. If they have not already done so, I would advise them to read about the “demographic transition”: this is a term used by social scientists to describe processes that seem to occur as countries as health gets better. The known fact about the part of the transition which is relevant here is:
| |
|A rise in the child survival rate is usually followed by a fall in the birth rate. |
So it’s far from clear that a policy increasing child survival will really make the population rise greatly in the long term, compared to a policy which fails to increase child survival. A successful policy is likely - and this view is both common sense and the general view of demographers and economists - to increase the population in the short term. We would expect the per capita income statistic to be affected downwards during the period when child survival rates improve, and upwards when people start having fewer babies.[53]
G. Emotional words about statistics lead to irrationality
The confusion between “a rise in per capita income” which is in effect a rise in an abstract, ecological (geographical) statistic on the one hand , and “a per capita income gain” which is a statistic about mean income gains for real people, is so common that I will perhaps have to repeat the distinction many times before some people take it in fully. I say this not because I think anyone is slow, but because I have been somewhat slow to take this in fully myself. I have noticed that I have felt some uplifting emotion when I wrote about “per capita income rising” - even though I knew that such a statistic is consistent with mean income losses, as well as with losses to most people. My unconscious, emotional, unthinking reaction is to associate, or rather confuse, the two. I have to keep reminding myself that these are not the same thing. I think I am helped in this effort if I put things the other way round: a “fall in per capita income” is consistent with average income gains to real people.
I suppose that my emotional reaction has been partly because I grew up in a country and a time in which differences in longevity between rich and poor were narrowing, and also the birth rate was fairly constant. In those circumstances, the level of a rise in income per capita in the economy, if anything, understated the average gain to real people. So it was reasonable for me to come to believe, and feel, that a “rise in income per capita” told me that real people had mean income gains of at least the abstract figure.
While I am on the subject of ingrained reactions, I will also make a comment about changes in the mean as a measure of economic success for individuals, in the context of both large and small demographic changes.
My habitual emotional reaction to the mean going up (“per capita income rose”) is based, I think, on a deeply ingrained but mistaken belief that “rises and falls in the mean necessarily have a close connection to gains for most real people”. In other words, I have had an emotional reaction (which lasts a few seconds until I begin engaging my thinking brain) to reading about a rise in per capita income, as if I had read that the typical person had income gains. This doesn’t follow logically from a rise in income per capita, even where demographic change is minimal. What I really think of as average gains for real people - in a place where demographic change is an insignificant factor - is captured much more closely by the median, not the mean
I’m with Adam Smith on this one. He said that it shouldn’t be regarded [presumably by the better-off] as a bad thing if the greater part of the population do better.
A fall in the mean is consistent with the greater part of the population doing better, even where demographic change is minimal. The median is, even in these circumstances, a more useful measure of trends in typical incomes. And typical trends are what I want to know about, if I want to answer a general question about whether people in general gained or lost - if I want to know about people’s general welfare. If you use the mean, then increases in income for a few fabulously wealthy people can have the statistical effect of cancelling out losses for many other people. That would give a misleading idea about people’s welfare in general. I personally want to vote for policies on the basis of rationality, not emotional reactions to my old misguided notions about statistics. Whether Adam Smith would agree with this is a question whose answer I leave to the reader.
H. Is the confusion fuelled by other concerns?
I can, I suppose, understand to some extent the fears of non-poor people who think that population growth might somehow threaten peace and stability in the world. But then since several hundred million people are malnourished now, those fears perhaps have to be weighed against that fact. Personally, I do not agree at all with people who would be happy to control population by the neglect of poor people. What I am trying to do is to understand their fears, and see what truth there may be behind them. Often, I think, what lies behind them is ignorance of other cultures, subconscious xenophobia and racism, and fear of change. In any case, whatever the fears, from the point of view of social science, they are irrelevant to the task of telling the truth about statistics. This is not an academic point. For someone to know there are serious flaws in their methods but not to acknowledge them is to become a fraud. I would question whether peace is best served by telling people they have had benefits or losses when the evidence is universally acknowledged to be unreliable and the method invalid. This kind of practice inevitably leads to social science being open to abuse by politicians.
I. Is political will needed, or minimum standards in social science?
There is often talk of “political will” being needed to achieve better lives for the one in three people in the world who are far less economically fortunate than the other two.[54]
I suggest that there is an opportunity for social scientists - and others - can take to help politicians do this. It involves setting limits on what politicians can get away with. If politicians get the basics of social science right, then the work of social scientists on the more specific problems is vastly enhanced.
There is much room for improvement, which may be embarrassing for some social scientists but is good news for the people the policies are aimed at helping. There is plenty of talk among social scientists working on international economics about the interference of politicians in publishing particular faulty research results. They say that the problem is compounded by the fact that these faulty conclusions become conventional wisdom. My guess is that the politicians come to believe them themselves. In any case, many senior academics - and other writers, and social scientists in senior positions in government and intergovernmental organisations - say that important statistics are presented in a misleading way. They are right: research methods are applied to the wrong type of population, and research is used to support wrong conclusions. Where voters want to believe these things for their own reasons, politicians know they are onto a winner, in the sense that they get more votes.
I would like to explain what I mean by “right” and “wrong” in relation to statistical methods. I am not talking about adherence to accepted codes of practice, but about whether the method can be defended coherently, in all its major aspects. That involves sorting out the major ones from the minor ones, which can involve quite a lot of thought. In the case of welfare economics, some of the task is easy, because some of the work has already been done. Sen’s work on the “headcount ratio” measure of poverty is an example. Many common statements about benefits to poor people, based on a change in this statistic, are just baseless, in the same way as a statement by a physicist about what happened to inanimate objects would be baseless if the physicist left out part of the argument. Changes in the proportion don’t tell us whether the poor overall had benefits or costs. If there is a reason why we should believe that it does, that reason has to be made clear. This is a case where social scientists’ accepted good practice differs from accepted practice in the sense of what politicians accept. What effect this deviation has had on the hundreds of millions of poor people the policies are aimed at is unknown. The headcount measure is accepted within social science as bad practice. Students are taught that its defects make it inadequate as a measure of poverty. The political will to implement pro-poor policies, rather than ones which change statistics of unknown positive or negative value to the poor, will not come about while social scientists misrepresent their statistics in this way, either unknowingly or knowingly. Such matters are the province of professional bodies in two hundred countries.
It is true that many assumptions made in the use of public statistics are debatable. But that doesn’t mean that a state of anarchy in that field is necessary. If a social scientist finds out fact x, and then makes a statement that y is true, but cannot explain why they are saying y rather than p, q, or r, which are consistent with x, then they have not done their job. This is no different from in many other professions. Many professions have as a main function the role of finding things out by investigation. Examples are a detective, a historian, a judge, and researchers: a scientist, a mathematician, a statistician, a political scientist, a sociologist, a psychologist. (To some extent their skills and methods may overlap). If a judge ignores evidence, there may be a miscarriage of justice. We don’t say “oh well, it’s all a matter of opinion”. That would be to avoid the difficult task of thinking and researching, and prioritising. Otherwise there is anarchy.
Anarchy in social science - people saying what they feel like for no reason - is different from tolerance of rational questioning. I would encourage people to question the fundamental methods of any profession, because no human is infallible, and systems of training train the mind (like a vine) to go in particular directions. Other people with other perpectives can help professionals understand their task more fully. They can say “ah, but have you thought of doing it this way?” or “I have found cases where that assumption does not hold” and so on. People generally like to have what they do confirmed rather than dismissed, even where there are vast consequences at stake; so the fundamental questioning may not get a positive response until it sinks in, or until an authority figure confirms its importance; but the main point is that it’s possible to think about which are more and less important parts of the process for coming to conclusions. If you think that a particular fact is important to the process of deciding on the answer, why? If you think it doesn’t affect the process very much, why? If you don’t know, does that make your conclusion any less valid, and if so, why? If not, why?
Social science can go wrong by a gradual process for which no-one is to blame - a cultural shift which individuals feel (rightly) that they cannot control. As any science progresses, methods which gave meaningful results in one type of situation may not give meaningful results in a new situation. People assume that because the methods worked before, the methods must work now - and that is perhaps the best they can do anyway, because that is what they are trained in.
The fact that a method is invalid doesn’t mean the conclusion is false. It just means that the method has given no reason to believe the conclusion, so someone who wants to say the conclusion is true has to try something else. As in life in general, the fact that someone uses a bogus argument doesn’t mean that they are wrong about the conclusion. It just means they are mistaken to think their argument is relevant. It might indicate they haven’t got a better one. But since we’re all fallible, before dismissing their conclusion, it’s worth asking whether they have some other reason to believe it.
J. Imbalances in male-female survival rates in Asia
A second hypothesis that can provide another partial explanation
We also have to think, if we want to understand this, not only about differential mortality across family income levels, but about differential mortality between earners and non-earners.
If a significant percentage of women are missing (as in several countries in Asia: if I make a relatively uninformed guess, I would say that on average 10% of women are missing in the relevant countries)[55] and men are the ones who mostly earn money, then per capita income will, other things being equal, tend to be higher as a result. We might expect this absence to influence both per capita GDP growth and the proportion of people counted as poor.
The hypothesis that “there can be significant effects of differential mortality between the sexes on mean income in a population at the end of a period” can provide a partial explanation of the finding that economic growth in some countries in Asia has been relatively high. In addition to the fact that there may now be a smaller ratio of non-earners to earners, there is this to consider: where there is an imbalance of the sexes, we might expect fewer births.
And so, higher mean income in later populations. As I write this, I have the same reaction that I think many people have to the phrase: “a higher mean income” sounds good. That shows the intensity of the psychological effect which a confused terminology can have - or perhaps the psychological effect of a measure which is perhaps more appropriate in my society* but not so obviously appropriate in the case of populations with high and/or variable levels of mortality. We would be well advised to train ourselves not to have such intense emotional responses to statistics that we can’t think straight, which is what I think has happened to many people in the development industry. But anyway, the point is that it’s only a statistical rise, and this is not the same as people having income gains. There is just a different set of people (in the mathematical sense of “set”) alive at the end of the period.
K. Male and female survival and prevalence of poverty
Has the imbalance of the sexes been greater among people below the poverty line, during periods studied by economists?
If we do not know that to be false, then another hypothesis presents itself:
the fall in the proportion of people below the poverty line in several countries in Asia has been accelerated by the imbalance between the sexes.
This would make a conclusion based on a fall in the proportion of people below the poverty line overestimate the positive impact on individual poverty.
L. Differential survival between the sexes and quintile averages
Has the imbalance of the sexes been greater, in China, India or other Asian countries, among people in the poorest 20%? If we do not know that to be false, we can come up with another hypothesis about income gains in the poorest quintiles in China and India:
the rise in mean income for the poorest quintiles in China and India in the last few decades has been accelerated by the imbalance between the sexes, and does not provide a reliable guide to mean income gains or losses to individuals who were in those quintiles.
Unless there are some data on these questions, the social scientist is open to objections that their quintile income growth figures may be overestimating individual income gains.
M. There is no such person as “Mr or Ms Per Capita Income”[56]
A rise in per capita income is only a rise in a numerical sense. The statistic refers to a measure of a purely theoretical entity. If Robinson Crusoe kills Friday, and eats Friday’s dinner, per capita dinner consumption has doubled.
The theoretical entity of a “population” with a changing membership is not a group of people. It is an abstract concept based on two sets of people: first, the population (in the concrete sense of a real group of real people) at the start of the period, and second, the population at the end. The two sets of people usually overlap. The fact that this theoretical entity is hard to visualise gives us a good indication that it isn’t really a thing, but a construct based on two things. Who are the people in the theoretical entity whose incomes we know have risen purely on the basis of a rise in income for the theoretical entity? Mathematically speaking, no-one.
It would be foolish to ignore the effects of demographic change while claiming that, for example, on the basis of regression analysis of data on a range of countries a certain policy was found by to be beneficial to people’s incomes. The point is that any analysis of gains and losses under particular conditions (trade, inflation, economic growth etc) which takes no account of demographic change is invalid.
In countries where the poor live longer, or start living longer, those poor people will usually - one way or another - cost the state money, and if so, the growth rate could be expected to fall even more, while mean benefit, we might say, to individuals rises. The Economist newspaper has pointed out, in effect, a reverse analogy to this in relation to smokers in the UK: they die earlier, and save society [which logically means the population after they die] money because of unused pension. The difference is that the smoking article discusses whether this is good for the economy, whereas I am examining the claims as to average benefit to individuals. These are two conceptually distinct tasks.
The question which some people may want to opine on, of whether it will be good or bad to have more poor people in the population in the future is irrelevant to the social scientist’s job of correctly stating what happened to people’s incomes in the past. People who get these muddled up are, it seems to me, doing one or more of these: a) not thinking clearly about the function of a social scientist, and/or b) muddling up “normative” (ought) questions with “positive” (is) questions, and /or c) not really very keen on the fundamental principles of democratic and humane social arrangements.
N. Economics and the measurement of outcomes
Economists study the economy. They also study theoretical segments of the economy, such as quintiles. Development economists study the development of economies. They also study the development of theoretical segments of the economy, such as quintiles. Economists do not study individual income gains or losses, and they do not study average gains or losses. Their assertions as to individual economic gains are speculative, not mathematically calculable from cross-sectional data.
O. Preference theory in economics not testable by averages alone
Economic theory from Adam Smith onwards (226 years) has often assumed that people act to maximise their own financial benefit. People often question this assumption. But does average income tell us whether people have achieved their preferences? Fundamentally, no.
A starving person prefers to stay alive. But if they stay alive - or if anyone on below-mean income lives longer - other things being equal, per capita income will be higher. People’s preferences are not fundamentally captured by a system of thought which says that if mean income is higher in a later population, people’s preferences were satisfied more.
Whether averages do in practice capture the preferences for longer life is up to the social scientist to find out.
Where there is demographic change and the economist wants to say what is or will be good for people, they must make sure they have demographically matched samples. Otherwise they are not comparing like with like, and so cannot make sensible speculations about what may be good for the poor of today or the people of today.
K. Economic theories about gains: Social welfare functions
There are a range of mathematical formulae in economics which describe welfare gains to real people. These are known as social welfare functions.
Any social welfare function in economics which claims to refer to income gains for individuals, but which is defined in terms of comparison of an earlier population’s mean income and a later population’s mean income - or otherwise takes data solely from cross-sectional studies[57] - is invalid if it takes no account of demographic change.
The equation
(a 1% rise in income per capita) = (a 1% mean income gain to real people)
which underlies much of macroeconomics and econometrics, is incomplete.
P. E and A
The complete equation[58] is this:
Where
A is average (here, the mean) income gain or loss to individuals, and
E is economic growth, and
D is the influence on economic growth of demographic change:
A = E – D.
In other words,
Average gain or loss is the economic growth rate
minus the effect of demographic change.
So
E = A + D
and
| |
| |
|E = A if and only if D = 0 |
| |
|which means that |
| |
|(the growth figure) |
|is the same as |
|( the mean percentage income gain to individuals) |
|if and only if |
|[demographic change has no effect at all on the growth figure]. |
| |
And if I don’t know how the later mean was affected by demographic changes, I
don’t know what mean gains were to individuals:
| |
| |
|If (the influence of demographic change) is unknown, |
|and (the growth statistic) is known, |
| |
|then (average income gain or loss) is unknown. |
| |
Economists measure E. They do not measure A. Where they say they know about A, it is wise to ask them why they think this.
In practice, just as with the fall in the proportion of people below the poverty line, the speculation is likely to be more sensible where we know demographic changes are small than when we know they are large, or do not have enough information to even guess - except for the fact that this whole area of inquiry is a bit complicated. The effects of some types of demographic change may outweigh the effects of others. Or they may accentuate them. But the main point is that they may outweigh the total effects of real people’s gains and losses on the growth statistic.
So the problems for people who want to use population averages to make statements about average benefit are quite complex - particularly in places where people don’t have enough to eat.
That’s why they need other information to help them get estimates for the essential parts of the calculations of average gain that they have left out. For this purpose, I suggest cohort studies, and studies of life length. These types of studies really do look at what happens to individuals. So do anthropologists, so do visitors who stay in a place a long time, and so do the people themselves. In relation to studies of life length, I would suggest this: the measure of a country’s seriousness in tackling malnutrition is the degree to which it is prepared to make honest statements about death rates. This is a sad task, and not for faint-hearted primary researchers, or those who find talking to poor people difficult. But it is necessary.
I would also suggest that a poverty researcher’s seriousness of purpose in helping poor people (rather than for any other purpose such as lessening poverty as a social or economic problem for the non-poor) can be judged by their willingness to take seriously any possibility that death rates may make the figures look better.
I also suggest that organisations concerned with professional standards should ensure that social scientists are adequately trained in the logic of their own arguments; and that these organisations should devise a code of ethics for social scientists who may be tempted to make false statements for political purposes. For a government to make false statements is dishonest, but there are no ethical codes for politicians. There are, however, supposed to be professional standards for social scientists. For a person who has professional training in social science to persist in propagating baseless claims, which affect the lives of millions of people, is fraudulent. In those circumstances, it is difficult for other individual academics to point out the fraud; but to the extent that professional bodies allow it to happen, they are in part responsible for the results in the real world.
Q. The economist’s guess
The economist’s conclusions[59] are, for a country where relevant demographic changes are not known to be small, guesses. So it’s quite appropriate to use other types of qualitative (words rather than numbers) information to try for a better guess.
The economist’s assumption (which not all economists make, but is, surprisingly, allowable professionally) of zero effect of demographic change isn’t a very inspired guess in each case, because it’s the same every time. Nor it is an informed guess. There is in fact a lot of information available for any present population about various types of demographic change, and their direction and extent. “Information” here includes what you can get by going and asking people what they think is going on. Where social scientists’ findings inform policies affecting hundreds of millions of people, it might be worth a little effort to make some elementary checks to see that the conclusions were in the right direction. Otherwise, we may end up with policies which have the opposite effect to that intended. Where, of course, the aim of
R. Can more statistics solve these logical problems? Probably not.
Mathematics is not really very useful in correcting fundamental mistakes in a vastly complex area such as this.
A project named with appropriate lack of elegance,
“A mathematical model of the effects of demographic changes on
i) population means,
ii) quintiles and
iii) falls in the proportions of people below poverty lines”
would be an interesting challenge, perhaps, for some mathematicians. But, I suspect, not all.
Because I also suspect that
a) it would take a long time,
b) it would be fiendishly complex,
c) past data for poor countries is unavailable, since even many births and deaths aren’t registered, and
d) the mathematicians would have to learn or be told about a vast range of potential social processes with effects that they could only guess at.
How useful this - or any attempt to adjust estimates of mean income gains inferred from growth statistics - would be, depends on how reliable the other methods of estimating mean gains and losses are.
That’s because the reliability of any method of inquiry can only be judged in relation to the reliability of other methods. Science is essentially comparative. We think this because that is less likely.
The big maths project has severe limitations. Demographic changes are really the aggregate effects of many changes in the lives of individuals, and the individuals are all at different levels of income. Similar events in different people’s lives will affect statistics differently. And if you get the data for such a project, you’ve essentially already done cohort studies. But not on six billion people, and maybe not even on three.
In any case, if that sort of project took several years, by the end the figures would be different for many countries - partly, I expect, due to the influence of AIDS.
S. Seven conclusions from economists, but none has mathematical support
The professional training, philosophy, code of conduct - and employers - of economists currently allow them to make statements about average economic gains and losses to real people solely on the basis of averages of different sets of people alive at different times. Such statements go beyond what the mathematics of their data tell them, and are therefore a matter of opinion, not calculation.
Economists are allowed, on the basis of a 1% higher average income among people alive now in a place than among people alive before,, to make statements which are intended to mean, and/or which most people would take as meaning, any or all of these:
1. “on average, people now have 1% more income for their age than the people before”
2. “on average, people are now 1% better off financially for their age”
3. “on average, people are now 1% better off for their age”
4. “people’s incomes rose on average by 1%”.
5. “people had 1% average income gains”
6. “people had 1% average financial gains”
7. “people became on average 1% better off”.
None of these seven statements are logically equivalent to any other. They each mean something different. I explain more of the differences in sections which follow.
None of them are logically equivalent to a statement that “mean income in the present population of the place is 1% higher than in the previous population”.
And none of the seven conclusions are calculable from the growth statistic.
T. Nine axioms[60] on economics and demography
Axioms for rational thought about the contingent relationship between a population average and average gain/loss to individuals
Here, “other things being equal” includes the theoretical assumption that no-one receives any gains or suffers any losses in income - for their age. To talk of “income gain for an individual” only makes sense in terms of “income gain relative to age”.
If mean income for 30-year-olds is higher now than mean income for 30-year-olds five years ago (and the mean doesn’t go up just because of demographic change such as greater mortality among the poor, and the 30-year-olds all survived the period) then that’s a mean income gain.
But if mean income for 30-year-olds now is lower than the mean for 30-year-olds five years ago, but higher than the mean for 25-year-olds five years ago (and the part in brackets in the paragraph above about demographic change applies) then that’s a loss, even though technically we know the people’s incomes rose (if they all survived).
In practice people’s incomes do go up as they approach middle age. An economist who wants to say that “people on average became better off in income terms, in year X or country Y”, therefore needs to make clear that what they are talking about is not income rises but income gains. The evidence necessary for such an assertion will be different from the evidence necessary for an assertion simply that people on average had income rises.
A baby boom or a one-child policy might influence mean income in a place. People’s incomes can rise on average just because the ratio of people rose during the period of people at ages where incomes usually rise, and not because there were average gains to individuals.
If a researcher does regression analyses of several countries and time periods, on which they then base conclusions as to mean gains, we don’t want the conclusion to be an artefact of changes in age structure, rather than a genuine result of mean income gains.
This is so obvious and so fundamental, yet so neglected, that I have decided to make this the first axiom.
Axiom 1: The gain-for-age axiom.
| |
| |
|“An average gain in income” |
| |
|can only be meaningfully called a “gain” |
| |
|if it is relative to |
| |
|what people would otherwise have had at their age. |
| |
The word “otherwise” here refers to what the social scientist is comparing this average to - the average for a previous time, or for people in a different place.
Any difference in mean income - in a geographical area over time, or between geographical areas - which is due to a difference in age structure is not a mean gain or loss to individuals. That is because the average life course of their income is unchanged.
A 30-year-old might want to know that the mean income of 30-year-olds is higher now, but a statistic that the mean income of 30- year-olds is higher than the mean income of 20-year-olds ten years ago is of little interest. A higher mean for the geographical area is consistent with a mean loss to people at each age, if the age structure changes enough. If you think I’m being pedantic, please think about China, and whether you would include that country in inter-country regression analyses dealing with growth and poverty, or trade levels and poverty.
Axiom 2: The below-mean-income axiom.
| |
|If people below the per-capita mean live longer, |
|then |
|the mean in the later population will fall, |
| |
|other things being equal. |
Axiom 3: The most-people’s-life-length axiom.
| |
|If there are more people below the mean than above it |
|(which is true in all countries), |
|then |
|most people will lower the mean for the later population by surviving longer, |
| |
|other things being equal. |
The fewer people, proportionally, there are above the mean, the fewer people, other things being equal, will raise the level of the mean by surviving longer.
So a step for social scientists in thinking about how differences in life length may affect population averages is to ask what proportion of people had below-mean income.
This is in itself a very useful statistic which is already available to anyone who has calculated the mean. It is useful because it requires no calculation, yet gives a quick snapshot of inequality of income at a particular time (though it does not tell us, on its own, about the inequality of distribution of income over the preceding period: see the “inequality fallacy” below).
Do you know this statistic - the proportion of people on below-mean income - for your country? Do you know the statistic for any other country? I do not; I do not even know the median income for my own country.
Axiom 4: The median-income axiom.
| |
|If median income is used as the average instead of the mean, |
|then |
|the proportion of people who, |
|other things being equal, |
|lower the median in the later population by surviving longer |
|is 50%. |
So the statistical effects of changes in inequality of life length on the median will under many circumstances be different from the effects on the mean.
Could we say that in this respect the median is fairer than the mean? Well, if policies are devised in order to increase the median, and there are significant effects of differences in life length on both the mean and the median, then the median is unfair on half of the people rather than most of them.
Axiom 5: The higher-income-inequality axiom.
| |
| |
|The higher the inequality of income, |
|the greater the effect on the later mean (or median) |
|of any changes in inequality of life length. |
| |
Axiom 6: The higher-inequality-of-life-length axiom.
| |
|Vice versa. |
Axiom 7: The non-earner axiom.
| |
|If a non-earner[61]dies, |
|then |
|the mean[62] will rise, |
|other things being equal. |
Speculative note: The practical boundary for this axiom, I suspect, is around cases where disparities in income/consumption within a geographical area are not extreme. Where income disparities are higher, I suspect that the income or consumption as measured by a social scientist of a rich non-earner may be higher than the mean consumption expenditure of earners; this axiom would not always apply in such a case. Rich children eat more than some poor adults.
Axiom 8: The multiplication-of-lowest-consumption-level axiom.
| |
|Measures of inequality based on multiples |
|become less representative of inequalities in welfare [63], |
|the higher above zero is the lower practical limit on consumption expenditure. |
This is a point about scales of measurement.
You don’t usually need twice the food to get twice the benefit if you’re malnourished. There is an exception to this rule - beyond a certain point you need much more than twice your food budget to cure the malnutrition.
But if you aren’t as bad as that, then a little more at certain times will help you survive for much longer.
The practical lower limit on food consumption expenditure is not zero - at least, not for very long.
If you eat less, you live for less time. As you get hungrier, the value to you of a unit of food increases. This increasing marginal return is not captured by linear measures of consumption expenditure.
Perhaps this is not worth bothering about as a technical issue, since really what we need to know if we are trying to help malnourished people is how to keep them alive.
Without data on death rates, it’s impossible to work out how to help them, because it’s impossible to know what has helped them to stay alive in the past. In addition, death rate information is much simpler than nutritional or consumption data. The main thing about those kinds of data is that they may end up fairly meaningless when averaged. But then averages and proportions using cross-sectional data on malnourished people, as with any group of people vulnerable to early death, is meaningless anyway without death rate data.
Axiom 9: The birth-rate axiom.
| |
|A fall in the birth rate |
|will cause a statistically higher per capita income in the later population, |
|other things being equal (even if no-one has income gains). |
A further axiom, I feel, is likely to appear obvious concerning the use of median life length - but I’m not yet sure what it is. I would guess it is often, effectively, a measure of adult life length. Mean life length, however, is an extremely telling statistic and I would not recommend ignoring it, since it gives a good idea of health in various income strata if applied to them separately. This is what Rowntree did in the UK in 1901. [64]
The single most catastrophic failure of academic development theorists, in my opinion, has been to forget his principle that the best measure of the physical well-being of the people is the death rate. The right to life is the first right mentioned in the United Nations Declaration on Human Rights. It’s the first thing mentioned in “life, liberty and the pursuit of happiness” in the preamble to the US constitution. It’s the last thing in the priorities of the most influential development agencies. If you don’t find out what kills people, you will not develop effective policies to keep them alive. Therefore, the effect of your inaction may well be that many thousands of people will die.
U. Possible axioms
Notes on what seem to me empirically self-evident[65] relationships which have potential for future axioms:
1. The higher the level of malnourishment in a population, the greater the inequality of life length in the population as a whole. .
And so the greater likelihood that changes in mean income are a poor guide to mean gain or loss in income.
In practice, in real countries, the lower the quintile, the higher the inequality of life length within it. Whether changes to this higher inequality of life length are offset statistically by lower inequality of consumption expenditure (because the lower limit of consumption is not zero) is a fit subject for thought.
2. The lower a person’s consumption level, the greater the probability that they are borrowing money to pay for food, so reducing future net income and thus future survival chances.
3. The lower a person’s consumption level, the greater the probability that they are selling income-generating assets to pay for food, so reducing future income and thus future survival chances.
4. At the cut-off point chosen by the investigator where people’s consumption expenditure is measured rather than income, it seems to me likely that there will be a discontinuity in the curve showing survival against income/consumption.
There is therefore likely to be a discontinuity in the correlation between changes in per capita income/consumption and mean income gain/loss for individuals.
5. There is likely to be another such discontinuity in the curve towards the lowest end of the consumption spectrum.
6. Policies based on a conjecture that rises and falls in population means have accurately represented mean financial benefits and costs to real people in the past, and then subsequently assessed using methods derived from the same conjecture, will compound the effects of any errors, and of any bias against the poor, and therefore any negative effects on individual outcomes which result from the theory.
If policies are chosen for their tendency to make later means higher, and as a consequence these policies have small but significant effects of increasing inequality of life length, then the policies may be reselected or intensified simply because the faulty method makes the statistics look better.
This is a vicious circle.
Has it occurred in the last 50 years in any country?
No-one knows.
Will it occur in the future?
No-one knows.
Who cares?
7. Policies based on two conjectures - the one above and the one about reducing the number of poor people - will result in each conjecture compounding the errors of the other. Both conjectures are biased against the poorest, if they are biased against anyone.
8. The division of academic labour, among those who study the theory of welfare measurement, and those who come to professional conclusions about average benefit to individuals - philosophers, economists, statisticians, sociologists, medical researchers, nutritionists, anthropologists and biologists - has diminishing, and after a point negative, marginal returns.
V. The economic fallacy is a general fallacy in social science
The real problem for social scientists is how to use cross-sectional data - which means data on whoever is alive at the time - to come to conclusions about longitudinal changes for individuals - which means what happens to real people over time. An allied problem is how to use these data to make comparisons of benefits to real people in different places. The problem is more acute in economics than in some social sciences, because income and consumption naturally vary with age.
Cross-sectional data in themselves can give no indication whatsoever of average gains.
X. Suggested rules for the scientific study of average outcome
For populations where the relevant levels of demographic change
are not known to be negligible
(In note form. see also Part IV)
1. Any logico-mathematical tendency of an outcome measure to count negative returns as positive can be dealt with by either rigorous attention to its real-life implications, or by throwing out the measure.
2. Any outcome measure which counts the value of life length at zero is invalid.
3. Never use any data for which you do not have what you consider to be a well-considered estimate of reliability.
4. In places where demographic changes are known to be low in the relevant respects, use the median if you want to give a representative impression of trends for the people in the population, especially if the mean is far above the median (skewed distribution) as in the case of income.
The following are in many ways more useful indicators of individual progress than proportions or averages using cross-sectional data:
1) Research on longevity.
Studies of life length give you data that are known to be correlated with quite a lot of other things that we value, like health and wealth.
Longevity increases the value to us of whatever we have at any point in time. And as a measure of welfare, compared to measuring income, life’s marginal returns (benefits to the individual of having an extra unit of money or life) are relatively non-linear (quite useful to most people).
2) Cohort studies.
Cohort - longitudinal - studies follow the progress of real people. They’re studies of samples of the population not of everybody, but then so are cross-sectional income studies in poor countries.
3) Qualitative data - what people who know a place say is happening there.
If in doubt (which an honest scientist will be in, if given only data on earlier and later populations rather than on the progress of individuals), ask people who know the place what is going on there.
“The available evidence”, to a good scientist, is quite extensive.
4. The “standard of living” fallacy
Age matters.
“Mean income in country X is 1% higher than in country Y.
Therefore people in X have on average 1% more income
than people in Y”
is a non sequitur, if the speaker means that people
have on average 1% more income for their age.
The mathematical relationship between average income and average-for-age is determined by age structure (the proportions of people at different ages). Income has a mathematical relationship with age, in all countries. Babies always have less income (on average) than middle-aged people.
So, for example, if there are more babies or retired people in country Y, then this demographic difference is a mathematical determinant of the difference in per capita income figures.
[Note: Add a bit about weighting and families; researcher can choose weighting for children; this can influence results if per capita averages are calculated. So can adjustments for economies of scale according to family size.].
5. The “poorest fifth” fallacy (quintile fallacy)
(Note to MB: Needs revising.)
A. Similar to the economic fallacy
A quintile is a theoretical segment of the economy. At any one time it contains the poorest fifth of people in the country. Over time, it is a purely theoretical entity, since its membership changes. In an effort to make clear what I am referring to, I write here of “a later quintile” and “an earlier quintile”, which are real groups of people.
The quintile fallacy is the same as the economic fallacy, except for the fact that the mathematical determinants of changes in average income in a quintile are different - see below. Therefore, the social scientist who wants to come to a conclusion about income gains or losses to real people must consider different demographic factors.
When the quintile in question is the poorest quintile, for reasons of common sense, the fallacy is in some ways even more of a problem for the social scientist than the economic growth fallacy, for these reasons:
People who consume less do not live so long. So within the poorest quintile, there is greater inequality of life length than in the whole country.
For most countries, data on demographic change in the poorest quintile is less available than for the whole economy.
People who eat less are far more vulnerable to disease and early death than people who have enough to eat. In addition, anyone who has any experience of life in countries containing the bulk of the world’s population knows that there is in every village, and every area of a city, social structure. This is true of the most affluent area in the most affluent country, and it is true of the poorest area of the poorest country. Within the poorest 20% in a country, there are social divisions. Where there are social divisions, there are differences in survival rates, and there may be differences in birth rates and age structure.
The quintile fallacy, like the economic growth fallacy, is an unfounded inference from, for example,
(1% higher per capita income in a later quintile than an earlier quintile)
to
(a 1% mean income gain to real people in the quintile).
The mathematical determinants of per capita income changes in quintiles are different from those for average income in a whole population. This is because
a) People move between quintiles. They can leave a quintile and move into another, but this has a different statistical effect from them being born or dying, immigrating or emigrating.
b) Demographic changes in the whole population can have mathematical effects on the number of people in the quintile at the later date.
Here’s a silly example, but it shows one principle. Other things being equal, if the rich have fewer babies, and the economist counts rich babies as rich, then the whole population shrinks and so does the poorest quintile. Since the poor people don’t shrink, and nor do their incomes, the richest of the poor are now counted in the next quintile up. The mean for the poorest quintile at the end is lower. No-one’s income changed.
c) In contrast to the effects of changes in life length on the population mean (where other things being equal it is the mean which divides those who will raise the later mean by surviving longer and those who will lower it by surviving longer):
i. If anyone in the poorest quintile lives longer, other things being equal the mean for the poorest quintile will fall.
ii. If anyone in the poorest quintile dies earlier, other things being equal the mean will rise.
iii. The statistical effect of a person’s survival or death on the mean for the later poorest quintile will be greater the poorer the person is.
Any mathematical relationship between what is conventionally called income growth in the poorest quintile (a statistical rise, for the quintile as a statistical abstraction) and mean income gain for the people in the original quintile and their descendants (real people) is determined by demographic change.
So the quintile fallacy (time version) is:
“Income in the poorest fifth of people alive now is 1% higher than in
the poorest fifth of people alive before.
So on average people in the poorest fifth had 1% gains in income”
which is a non sequitur.
B. The semantic fallacy of the poorest fifth
There is a related semantic fallacy. The words
“Incomes of the poor rose 1%”
can only refer, we might sensibly think, to real people, not the abstract entity (quintile). But economists often talk about incomes of the poor rising or falling when they really have information about quintiles.
The semantic fallacy here is to confuse
“incomes of the poor rose 1%”
which is not known to an economist even if they have perfect cross-sectional data, with
“mean income was 1% higher in the later poorest quintile than in the earlier poorest quintile”.
which is known if the data are perfect.
If five people kill everyone else, and take their possessions, then in terms of assets, the poorest quintile has got much richer.
The words “assets of the poor rose 10000%” or “murder is good for the poor” might not be appropriate. However, there is in the discipline of economics in the year 2002 no theoretical basis for a practitioner to distinguish between cases where
demographic changes, including changes in differential longevity, were significant determinants of the later mean,
and those where
only income gains for individuals had a significant effect on the later mean.
C. More on semantic fallacies and quintiles
Let’s recap. It is a semantic fallacy to confuse two different senses of “the poor”, even where the speaker makes clear - as is often not done in social science in this area (see below) - that they are not talking here about people on below a “PPP” $1, but only about people in the poorest 20%. The semantic fallacy is to confuse
1) the poorest statistical quintile with its changing population, and
2) the real people in the quintile at the start and their descendants.
The first one seems, perhaps, odd as a definition, but I have to point it out because it’s what has been used by economists in the same published papers in which they subsequently write of what is good for “the poor” - which sounds like real people. Examples are not hard to find, since the fallacy has been repeated in national newspapers and even in British government publications.
Most people think, when they read about “the poor”, that the author means real people.
If anyone is more interested in what happens to the statistical quintile than to the original real people, then their conceptual task is easier, because they can talk about what is good for the statistics. And they can do this perfectly well without reading any of the words in this document. Some people talk of what is good for society, meaning society as they think it will be in the future (the interested reader can look up “average utilitarianism”, which is a term which should be dropped as soon as possible by philosophers who use it in relation to cross-sectional averages. It bears little logico-mathematical relationship to the utilitarianism of Bentham and Mill, which is about aggregates of good and bad consequences to individuals).
There isn’t an equivalent word, like society or population, for “the poorest fifth as they will be constituted in the future”, and “the poor” is obviously confusing, so luckily those people will have to talk in terms that make it clear their thinking is not concerned with the progress of real people, but is entirely abstract.
If “the poor” – the people whose progress was measured - are defined as the individuals in the poorest fifth at the start, plus their descendants,
then the statement
“Incomes of the poor rose”
does not mean the same thing as this statement:
“The mean for people in the poorest quintile at the end
was higher than
the mean for people in the poorest quintile at the start”.
The first one (“incomes of the poor rose”) refers to a set of real people.
The second one (“the quintile mean rose”) refers to two different, usually overlapping, sets of real people.
Any concept of “the quintile” as one thing over time is a purely abstract notion.
This might look a bit pedantic, but please remember that small numerical differences can add up, especially as more advanced computer analyses become possible. I am also here including in my thoughts the most extreme (but real) cases of countries. In any case, since no-one’s thought about any of this in depth, no-one knows what’s an extreme case and what isn’t.
The two statistics for
% change in the quintile mean (= income growth in the quintile)
and
mean % gain to the original people in the quintile and their descendants
will only be the same where
(the influence of demographic change on the quintile mean at the end) = 0.
For all countries, over all of the last 100 years, this is unknown. In countries where demographic trends are known - in direction if not in extent - or known to be small in extent, there is obviously less of a problem for economists. In countries and especially quintiles about which the economist knows very little in respect of demographic change, there’s obviously a big problem in saying that the statistics apply to individuals. Any conclusions about mean income gains to real people in poorest quintiles are speculative, not mathematically known. This needs to be made clear so that people reading the conclusions know the author was guessing.
D. “Purchasing power parity” theory not applicable to poorest fifths[66]
(Note to MB: This whole section needs revision. There are 2 problems I am trying to explain here. One is that PPP in general does not tell us about relative gains to poor people in different countries. The other is that the presence of non-poor people in some countries’ poorest quintiles (and the absence of some poor people from other countries’ poorest quintiles) make even a food-based PPP system inappropriate for the comparison of income gains for the poorest 20% of people.)
PPP dollar units are known to the experts in the official International Comparison Programme, which is responsible for them, to be an inappropriate measure of the purchasing power of the poor. When a social scientist says that a measure is inappropriate, they mean that it should not be used, because it is too likely to give the wrong results.
In multi-country studies investigating relationships between changes in per capita income in countries and per capita income in the poorest quintiles, this basic PPP problem makes the results hard to interpret - and in fact no-one has attempted this - even where demographic changes were known to be minimal.
But there is yet another problem: if the studies want to say what happened to the incomes of poor people in general, they suffer not only from a general problem that the proportion of poor and non-poor people in the poorest quintile varies across countries, but also from this problem: the validity of using PPP conversion rates to compare the purchasing power of people at different levels of income has never been established.
People at different levels of consumption expenditure buy different things. These different things have differing international price differentials. The very poor buy basic goods, and the non-poor buy more luxury goods. The PPP system takes a kind of average of the whole lot, which may give an illusory level of purchasing power to the poor.
The price of very basic food (and so the purchasing power of the poor) may be distorted equally in country A and country B by their respective PPP conversion rates. Let’s say that poor people in both countries really can only buy 80% of what the PPP system says they can buy, compared with poor people in other countries.
For these two countries, if that could be known, then the comparisons of living standards between poor people in A and poor people in B (if demography is not a factor) are comparable. Also comparable, from percentage increases in the PPP value of consumption expenditure, will be any consumption-expenditure increases (if demographic change is not a factor).
But there is still a problem. The bottom quintiles in different countries don’t just include all the poor and no-one else.
E. Using PPP with poorest fifths creates more havoc with numbers
Country A and country B have (as usually in real life) different proportions of malnourished people in the bottom 20%. In country A, the bottom 20% is half made up of malnourished people and half of adequately-fed people. In country B, the bottom 20% includes only half of the malnourished people in the country.
This is because country A has a prevalence rate of 10% for malnutrition, and country B has a 40% prevalence rate.
How does any national PPP system cope with this? It can’t. The problem is that even though we have found out (somehow) that prices for basic goods which poor people need are internationally comparable by the PPP system, we don’t know how to compare the purchasing power of the non-poor, and we don’t know how much more purchasing power (in currency terms) the non-poor in the bottom quintile in country A have than the poor in country A or the poor in country B. We know that percentage consumption-expenditure increasesto poor people in both A and B are comparable. But the non-poor in the bottom quintile in country A buy different things from what the poor buy. How can we possibly compare the percentage increases in consumption expenditure of those non-poor people in country A with percentage increases among the poor of country B? We are in effect trying to compare the purchasing power for different types of goods.
F. Can statistics on poorest fifths tell us about the global poor?
An example of misleading information: “poor” defined as “people in the poorest quintile”
The poorest 20% in a country at one time are, if the theory and data are correct, a group of relatively poor people. But they are not “the relatively poor” because the percentage is arbitrary. If they are, then the poorest 99%, the poorest 27% and the poorest 1% are also “the relatively poor”. The choice of 20% may or may not denote a real group of people who are relatively poor in any meaningful sense.
“We know that the poorest 20% increased their incomes. So the poor benefited” gives a misleading idea to people who don’t realise that there may be a huge difference between “the poorest 20%” in that sense and “the poor” in the sense of “the people on below PPP $1 a day”, in terms of both the economic condition and the physical and social functioning of the two groups - even where demographic change is not a factor at all.
The job of clarification is to some extent the responsibility of the journalist and the reader; but in the example in quotation marks above, the word “so” would naturally be taken by a journalist as meaning the social scientist had a valid reason for using the word “poor” in a context where other statements are about people below poverty lines. And the journalist might assume that this inference was valid because there was some theory and data behind it. In fact, there is not.
Even if we knew (which we don’t) about the mathematical relationship - the association - between economic growth and income gains to the poorest 20% in different countries, this wouldn’t mean that “the poor” defined as people below the poverty line had these gains. It wouldn’t measure changes to income poverty as an aggregate of shortfalls of individuals below the poverty line. It would just be a statistic about a jumble of different proportions in different countries of people above and below the poverty line.
What would a correlation between economic growth and income gains to the poorest fifth of people tell us about gains to those below the poverty line?
Supposing someone discovered the level of average individual income gains
to the poorest 20% in different countries. (This has not yet been done,
so we don’t know this information. We do have various information about
quintile averages, but that doesn’t tell us about gains). But supposing it were
done.
The only correlation this can possibly give is a correlation between
economic growth
on the one hand, and on the other hand:
for some countries: income gains for some people above the poverty line and some below it;
for other countries: income gains for only some of those below the line.
What information this method would give us about trends in income for those who have an income shortfall – which is why they are classified as poor - is not clear.
Why were they classified as poor? What was the point of the social scientist going to the trouble of drawing the poverty line? So that their progress could be measured, and from these measurements better policies for poor people could be devised.
But what the progress of the poorest fifths in different countries would tell us about the poor of the world is unknown.
However we choose a poverty line, the whole point of it is to define a level of functioning and welfare that is inadequate for a reasonable life.
Doing a study on the poorest 20% will give us information about
1) some people who are defined as having adequate resources to sustain a reasonable life, and
2) some people who have inadequate resources; and
3) in some countries, only a fraction of those who have inadequate resources.
The reason why I have rephrased this in terms of adequacy of resources is that I am trying to make clear that the point of having a poverty line at all is that there is a functional difference between those above the poverty line and those below it -
a difference in their ability to function in the economy. If you haven’t got enough to sustain life, you are unlikely to have savings; you are unlikely to have spare cash for medical treatment; you may be much more likely to have debts; if you are below the $1 level then unless you are in the lucky minority, you are malnourished. For these reasons, your income may not respond in the same way to things that affect the non-poor in your economy.
That’s not to say that the poverty line is something that is a perfect delineator of those kinds of factors[67], but the point having a poverty line at all is to identify people in serious trouble. The point of research on poor people is threefold:
1) to see how those people do,
2) to see how they do under various conditions,
3) to see how they do under various conditions compared to everybody else.
We wouldn’t need to do 3) at all if we knew that everyone in a country would do equally well in all conditions. But in the real world 3) is a sensible thing to find out, because common sense tells us that poor people may have a different response to those conditions because they are poor. But we don’t have any reason to think that the poorest 20% in all countries each form a homogeneous group - meaning a group with characteristics that may make them respond differently to the people just above them in the income distribution. Still less do we have any reason to think that the bottom 20% in all countries have much in common, apart from being generally poor.
I don’t really know why anyone would choose the bottom 20% in each country as meaningful groups to look at. They might, I suppose, have some sociological belief about hierarchies in human societies, to the effect that the poorest fifth were always in some special socially-excluded position. I can’t see any reason to believe this as a universal rule, but I can’t think of another reason why the poorest quintile would be chosen by an economist as a meaningful group.
Income levels of those in the poorest 20% are so different in different countries that it’s hard to see what comparisons of percentage increases for people in the bottom quintile in different countries would tell us about overall impact on raising incomes of poor people.
You see, if the thing we’re researching is
the correlation of economic growth and incomes of the poorest 20%,
and we ignore the fact that
different proportions of poor and non-poor are in the poorest 20% in different countries,
then a conclusion that poor people in general benefit from this or that is weakened by the fact that the results might just be due to an artefact of the varying proportions.
In other words, the artefact - quirk of statistics, rather than a really meaningful result - would be this: the countries with higher gains to the poorest 20% might be the ones which have, proportionally, the most poor people in other quintiles than the bottom quintile.
The results for those poor countries would be compromised by the fact that those countries were the ones where the progress of the bottom 20% was least representative of the progress of people below the poverty line. Apart, that is, from the other countries where progress is less representative: those with most non-poor people in the bottom quintile.
So, oddly, it’s those countries in the middle - with roughly 20% of people below the theoretical international poverty line - that give results that are meaningful to the progress of poor people in general.
Subgroups of poor people are of great importance to the social scientist in understanding what’s going on, and so are correlations between, for instance, worse income poverty among the poor and various things[68]……….
Would statistics about that mixed bag of people’s incomes, tell us directly about the incomes of poor people, in the sense of those below the poverty line?
No.
Does it tell us enough about poorer people that we can infer something about how people below the poverty line did?
I can’t see a reason why it should.
After all, the poor people as a whole might have had income losses. A belief that this jumble of information about non-poor, poor and extremely poor people in different countries adds up to meaningful information about what happens on the whole to those with seriously inadequate resources needs some reasoning behind it. In a country where 40% are poor by the $1 measure, we don’t want to make some of the poor eat more and some eat less, and then say that “the poor” got richer because the poorest 20% did. Again, the point of social research is to draw meaningful conclusions about groups of people who have things in common. That’s because we hypothesise that there may be some different response in those groups to things that happen, compared to people who don’t have that characteristic. Here, the research is supposed to be about the poor versus the non-poor. But in the country where 40% are poor, half of these people are being counted as non-poor. The more jumbled up the groups, the less reason we have to believe that the people have in common the thing we are looking at.
There’s another problem. If this is a comparison of income changes in different countries - with different proportions of the poor included in the bottom 20% in each country -
Does it give us information that is relevant to the Millennium Goal of halving income poverty (the proportion below PPP $1) - which most people take to be about the raising of incomes?[69]
I can’t see how. In countries with non-poor people in their bottom 20%, percentage changes among those non-poor people will affect the mean for the poorest 20% disproportionately, because they have higher consumption expenditure. In countries where only some of the poor are in the bottom 20%, those poor people are the very worst-off in nutritional terms, and so the mean for them is most likely to be inversely influenced by their longevity.
Now in social statistics, it should be clear to anyone doing social research of any kind that if you don’t choose meaningful groups, you may not get meaningful answers. Without meaningful groups, you will just end up with a bunch of people who don’t fit the criteria jumbled in with those who do. And the problem is you’ll never know the real answer to the question you were asking, which was about a definable and functionally and socially meaningful group. The poorest 20% of people in all countries are poorer than the others, but whether they are sensibly described in a global study as “the poor” is another matter.
Correlations between arbitrary groups will make differences between real-life groups[70] look smaller.
To just choose a percentage of the total population and call them “poor” will inevitably have a statistical effect: any real differences between the poor and non-poor, which should have influenced the statistics and shown us what we wanted to know, are very likely to have less impact on the result.
Therefore, even if we did know that certain policies helped the poorest 20% in different countries (because a real PPP system were devised and demographic factors taken into account) this would not tell us what helped the poor in the sense of the people who are in a significantly worse economic position than everyone else.
There is therefore a need for economists who wish to use poorest fifths to come to conclusions about “the poor” to explain what relevance the statistics have.
F. Other assorted compound fallacies based on population averages
We could give out a few more numbers and letters to more complex fallacies, like the “quintile-vs-overall-growth” fallacy, and the “2-country-corresponding-quintile-growth” fallacy.
We could also do this for compound fallacies relating to economic growth rates. I’ve left out one, which is the basic 2-country economic growth one (“economic growth was more in Amazonia than Bamazonia. Therefore people had more income gains in Amazonia, whatever the demographic changes were”).
There are in social science “ecological fallacies” - which means taking information about statistics for geographical areas and then erroneously coming to conclusions about individuals. I would call the above “economic fallacies” because they confuse a measure of statistical trends in the economy as an abstract entity with a measure of gains and losses in real people’s incomes.
6. The inequality fallacy (distribution fallacy)
Game theory models relationships between immortal gods. To apply game theory to social science dealing with mammals, even ones that talk, you have to make the logical rules the same as in real life.
A. Inequality fallacy (time version)
The word “distribution” can mean two things.
Firstly, it can mean how much is received by some people compared with others during a period.
Secondly, in statistics and economics, it can mean how much people were receiving at the end of a period according to their position on the scale of incomes, compared to people at the start of the period.
Statements about differences in static distribution between the start population and the end population are not equivalent to statements about the distribution of benefits among people during the period.
A change from
less income inequality in an earlier population
to
more income inequality in a later population
does not tell us, on its own, that the poor had lower percentage income
gains than other people.
Here again, demography influences the statistics if cross-sectional data are used. For instance, if the poor live longer, other things being equal inequality will be higher at a later date.
The principle that demographic changes are mathematical determinants of measures of change in inequality applies to Gini coefficients and other statistics which rely on snapshot measures of welfare of whoever is alive at the time (cross-sectional data).
A policy’s effects on distribution in a later population are logically distinct from its effects on the distribution of income among real people. A government could lower income inequality by stopping old-age pension, unemployment benefits, and free health care; or by genocide of a poorer racial group.
As in the case of social welfare functions concerned with simple averages, social welfare functions concerned with distributional effects are incomplete without equations dealing with demographic change.
Otherwise, someone who says, knowing nothing about the extent of demographic change in a place, what the effects were on real people’s incomes is not talking about statistics, but expressing an uninformed opinion.
Since people’s income and consumption have mathematical relationships with age, changes in birth rates and age structure across the income spectrum will affect inequality measures.
B. Inequality fallacy (geographical version)
Demographic differences determine differences in inequality between countries.
7. The “economic gain” fallacy[71]
An income gain is not necessarily equal to an economic gain, either for the duration of the period or for the subsequent period.
A. Time version
“I had a 1% income gain.
Therefore I became 1% richer”
is a non sequitur, if economic gains and losses depend on assets, debts, public services, and necessary outgoings as well as income.
For example:
1. If you sell your farm - your only income-generating asset - to pay for food, your consumption goes up but you become worse off financially.
Note: Landlessness is a real and very serious problem in agricultural countries.
2. If you start borrowing money to pay for food, the same applies.
Note: Debt is a real and very serious problem for many people. Debt increases outgoings.
3. If food prices go down more than your income, you may have more money at your disposal despite a loss of income.
4. If prices for water, health care and/or education go up, then you can end up worse off even if your income and consumption rise.
A social scientist who only looks at a person’s income or consumption and does not consider assets, debts, public services, and necessary outgoings cannot claim that a person was better off financially.
We might also speak of a related fallacy, the “consumption expenditure” fallacy.
If my consumption expenditure goes down, does this mean I consumed less?
No.
Prices might have risen. Lower expenditure is consistent with higher consumption.
B. Geography version
“People in country X are better off financially than those in country Y if they have more income”.
This is fallacious unless the social scientist can show a reason for believing that changes in assets, debts, public services and necessary outgoings were not a factor.
8. The “macroeconomics is utilitarian” fallacy
Macroeconomic policies to increase economic growth are not utilitarian (in the Benthamite/Millian sense) in their basic logico-mathematical structure.
Nor, incidentally, can a system of welfare economics which is based purely on cross-sectional data ensure it is Paretian - except in places and times where there is insignificant demographic change as described in the other fallacies.
A distinction between “utility” in philosophy and “utility” in economics [72]
There is in economics, and sometimes in moral philosophy, a confusion which is generally unacknowledged.
Economics is substantially[73] based, not on Benthamite utilitarianism, but on what has been called, misleadingly, “average utilitarianism”. There are many views which have been called “average utilitarianism”[74]; I am referring to the one which maintains that the best outcome is that which results in the highest level of average welfare in a later population [75].
The term “average utilitarianism” as applied to this view is misleading. Classical utilitarianism does not compare
states of affairs for the people who happen to be alive at particular times,
as macroeconomics does, but
aggregates of consequences for all people affected.
Utilitarianism looks at all consequences even at the level of the individual. A statement that
“decision X in 1990 caused me to be happier in 2000”
is not logically equivalent to the statement
“decision X in 1990 caused me to be happier during the period 1990-2000”.
The difference between these two statements, and the implications of this difference, become clearer once we think about more than one person.
Before going on to discuss this, I would like to comment on the phrase “state of affairs”. It could be defined as equivalent to talking about histories or prospects for individuals, but the ordinary meaning of the phrase is not equivalent to those. I think that it is clearer to stick to the word “consequences”.
On another term, the word “outcome” used in relation to consequences, or utility, is ambiguous: it can mean
a) overall consequences during a period or during a lifetime, or
b) the state of affairs at the end of a period.
In discussing “averagism” below, I mean “future averagism”, in the sense of “aiming for higher average welfare levels in a future population”. This sense might be made clearer by my using some phrase such as “leapfrog averagism” to clarify that what I am referring to is a view which leaves out some intermediate consequences in its overall assessment of goodness and badness.
Whatever words are used, they must be clear as to which of (a) or (b) above they refer to.
Here is why, in relation to the most important practical use of the philosophy of consequences in the world today.
Macroeconomics compares levels of welfare in two sets of people - not the consequences for one set
Any moral or social-scientific outlook which is concerned with the relative merits of later states of affairs among living people (for example, average welfare at a later date) involves comparing welfare at two times, using two sets of people -
a) one set of people at the beginning of a period, and
b) one set of people at the end.
This is the logico-mathematical structure used by the “averagist” and the macroeconomist. In economics, it forms the entire basis of calculation of “utility”. The fact that economists say their discipline has roots in Benthamism is irrelevant, because it isn’t true. An appropriate analogy would be that it has been grafted on.
The two sets of people may overlap or contain exactly the same members, but their memberships are irrelevant to the averagist. In other words, it makes no difference to the averagist - a “future-state-of-affairs-ist”, such as someone solely concerned with the state of the economy at a time in the future - whether the people in the two sets are
a) the same people, or
b) mostly the same people, or
c) different people entirely.
If there is more income per capita in the second set of people (the later population) then that is what is important to the person studying the economy. Economics uses cross-sectional studies: studies involving sets of people alive at particular times. Economists study the economy as a theoretical entity, not the progress of individual people or aggregates of the progress of individuals. They infer income gains from opinions about the insignificance of demographic change as mathematical determinants of averages. Whether these opinions in any particular case bear any relation to the truth is unknown. In practice, the speculation is justified in countries where the economist knows that demography was stable, and less justified where they have less knowledge, or knowledge of demographic change, or both.
Utilitarianism looks at one set of people
In contrast to that approach, utilitarianism with a direct line of descent from Bentham is a doctrine about
consequences for one set of people - the set of all people affected by the action.
“Utility” in economics distinguished from “utility” in philosophy
Writings about “utility” in economics do not usually refer to the differences between the logical structures of economics and classical utilitarianism:
1) Economics uses cross-sectional studies, as described above.
2) In contrast to Benthamite utilitarianism, economics measures the duration of a benefit differently for the majority and the richer minority.
3) Economcs uses averages rather than totals as the basic method of aggregation.
4) In economics, the result (aggregate “utility” as state of affairs in a later population) is mathematically determined by changes in demographic composition, as well as individual welfare gains. Classical utilitarianism, on the other hand, looks at everyone affected, so demographic change isn’t an issue [76].
Moral philosophers sometimes say that “average utilitarianism” gives the same results as classical utilitarianism if the population size does not change. This is a mistake. A further condition relates to who ends up in the later population.
This is partly about birth rates, but also about the ratio of well-off to badly-off people who survive the period. If the well-off survive disproportionately, the average will rise, other things being equal. If the less-well-off survive disproportionately, the average will fall, other things being equal. So an additional condition is necessary for classical utilitarianism and averagism to give the same results: the condition is that there is insignificant demographic change.[77]
How people do better and make the average fall [78]
If people on below-mean income [79] live longer, then other things being equal, per capita income will be lower in the later population. No-one’s income has fallen, but “per capita income” as a theoretical construct has fallen. In Benthamite terms, though - assuming for the moment a perfect correlation between income and happiness - there will be higher utility. The economist will say that there is lower utility, because the economist’s definition of utility is fundamentally different.
Logically, an inference that
“people’s incomes went down on average by x%”
based purely on
comparing averages for the two sets of people (earlier and later populations)
is invalid, if there is no information about demographic change.
In other words, if you know that
people later were better off on average than people before,
this doesn’t of itself tell you that
“people did well on average”.
This is a more subtle variant of the objection against averagism that if the best-off kill the others, average welfare in the population afterwards will be higher.
The flaw in economic thinking and its consequences
At present, if a government neglects the poor and extends the life length of the rich, and this makes per capita income 1% higher in the later population, economists are allowed by their training to state that “people’s annual incomes rose by 1%” - even if no-one’s annual income changed.
This is invalid, but economists are allowed by their training to make these kinds of statements for all geographical areas and all subsections of economies - even those segments of the economy containing the most malnourished people in the poorest country, and in situations where economists know least about birth rates and survival rates.
The fundamentals of welfare-economic theory about real people’s progress are based on the implausible assumption of no significant demographic change in any population which economists have studied or will study in the future.
On page 1 of Henri Theil’s Introduction to Econometrics (1957) there is an equation. What it means is that
“(a rise in per capita income)
[i.e. higher average income in a later population]
=
(the percentage income gains to individuals)”.
This equation is incomplete, as any similar equation would be about living creatures, but no economist has pointed this out. The complete equation logically has to include the mathematical effects of demographic change.
Per capita income at a later date
=
(income gains/losses)
+
(impact of demographic change).
Therefore,
Average gain/loss
=
(per capita income change)
minus
(impact of demographic change).
And
Where the impact of demographic change is unknown,
the average percentage gain or loss is unknown.
Here is the muddled state of economic thinking.
1) At present, if the poor live longer, and as a result average income is lower in the later population even though no-one’s income has fallen, the current, incomplete, form of the equation - and the theory and philosophy of economics, both of which fail to make the relevant distinction - allow an economist to say that “people’s incomes fell”.
2) Where the economist does not know whether the changes in the average were caused by demographic factors or income gains/losses, they are still allowed to make the same statement.
This logical problem is the result of a confusion between classical utilitarianism and leapfrog averagism. Utilitarianism comes to conclusions about benefits to real people, but averagism comes to conclusions about statistics. The difference between average welfare among those at the start and those at the end does not even fundamentally tell us whether those alive at a the end did better or worse, let alone how much better or worse.
9. The “$1-a-day measures absolute poverty” fallacy[80]
(Note: Will be added to).
See “Some practical implications of the logical fallacies (page 55)” and Glossary of Ambiguous Terms (page 152) for more on PPP.
“The dollar-a-day measure is a measure of absolute poverty”.
The statement above is false.
The “dollar-a-day” measure is in fact a measure of “purchasing power parity dollar equivalent units” where purchasing power parity - an adjustment intended to compensate for price differentials between countries - is not based on an absolute level of purchasing power among poor people, but on a level of purchasing power relative to the cost of goods and services in the rest of the economy.
The PPP conversion rate is a fiscal statistic. The PPP conversion rate takes into account the cost of all types of goods and services in the country, many of which poor people have cannot possibly purchase.
If the cost of cars or computers goes down in country X relative to other countries, then the PPP conversion rate will change. This is because, across the whole economy, the cost of goods and services has fallen. But this is not the same as saying that the poor could afford more food. The fact that in this case the purchasing power of, say, a rupee for all goods including cars and computers has risen is irrelevant to the purchasing power of a rupee for poor people.
There is no evidence even that PPP measures the purchasing power of most people in most countries.
Any claim that
“the PPP dollar is a measure of absolute poverty across time and across countries”
is logically contingent on a prior claim that
“variations in PPP conversion rates are due in insignificant measure to variations in prices of things the poor don’t buy”.
Such a prior claim would need an analysis of what differences these other goods made to the variations in PPP conversion rates, given the choices made by theoreticians of weightings for different goods and services.
If in any country food expenditure is a fraction of national expenditure by individuals, then logically those people who spend most of their money on food won’t have their incomes accurately calibrated by PPP measures unless the prices of other goods and services go up and down very closely in line with food prices.
In the real world, income multiples are high in poor countries. The result is that rich people do spend a significant portion of national income on non-basic items. A theoretician who wants to make PPP units into an absolute measure of poverty has to demonstrate that changes in prices of non-basic items have, in practice, insignificant statistical effects on the results of PPP calculations of incomes of poor people.
The basic logical point about PPP can be restated several ways. The PPP unit for each country at each time is mathematically linked not to what the poor can buy, but to what the poor could buy, theoretically, if their expenditure were on a range of goods and services in exact proportion to the national average. In a country where the cost of living for the non-poor goes down, therefore, the poor will according to the PPP measure appear to do better: the value of the money they have could buy a hundredth of a computer or a thousandth of a car, if they chose to buy those things instead of food. So their income in PPP “dollars - purely abstract units - would be rated by a social scientist using PPP as say, 93 cents rather than 92 cents even if every poor person’s income and consumption expenditure, and all the prices of the goods they consumed, stayed exactly the same.
We can make a similar logical point about comparing prices across countries. The fact that someone’s consumption expenditure in country X is converted as a national-purchasing-power-parity-for-all-types-of-goods-and-services $1 equivalent considering the prices of all goods and services in the USA does not tell us mathematically that their consumption expenditure on food and other essentials is the same as someone in country Y with the same consumption expenditure when converted to PPP units. Whether they are in fact the same, in terms of purchasing power for the goods and services poor people do consume, is entirely contingent on variations in prices of goods and services which poor people do not consume. If poor people’s incomes and consumption expenditures really do go up, these rises can be cancelled out under the PPP system if the prices of luxury goods go up. So the poor’s incomes can rise, even if a social scientist’s result using PPP shows a fall in PPP terms.
Therefore, the PPP measure of poverty is not an absolute measure but a relative measure - and one whose mathematics works in the opposite way to other measures of relative poverty. Let me explain why.
If prices for goods or services bought exclusively by the non-poor fall, then PPP conversion, of necessity makes it look like the poor have more money when they don’t.
So if imported luxury goods become cheaper, the theoretical “value” of the poor’s incomes rises!
The reality in this situation would be that inequality of purchasing power has got worse. This is because the non-poor can now buy more for their money and the poor can’t.
There is another logical consequence of this inverse relationship between purchasing power inequality and the PPP-rated incomes of the poor.
In the case described above, the proportion of people under the PPP, pretend dollar level will be smaller.
So to reduce the proportion of people under the theoretical dollar, a government doesn’t have to raise the incomes of poor people. It can instead take measures to reduce prices for goods the poor never use.
We have to remember here that it is not just goods, but also services which are included in the calculations for PPP rates. The cost of both of these rises if wages go up. If the poor get more wages for producing goods or providing services, and this results in higher costs of those goods or services to the non-poor, then the PPP virtual currency will be devalued (say, from PPP $3 = 1 US dollar to $2.99 = 1 US dollar). This has the effect not just of making a non-poor person on PPP $30 a day have less purchasing power (which really has happened) but also of making the poor person appear to have less purchasing power (which hasn’t happened).
Any claim that “a reduction in the proportion of people on under a PPP dollar shows that poor people’s incomes rose” invalid unless the social scientist can show the mathematical effects of irrelevant goods and services on changes in PPP conversion rates were small.
Without this missing part of the mathematics, the claim about raised incomes would not be one derived from mathematics, or even an estimate, but from a guess.
In science, mathematics without logic is an abuse of the scientific process.
Social science without rationality is not only meaningless, but also has the capacity to be used for destructive effect in the real world. That is why it is essential for anyone who wants to, for instance, raise incomes among poor people using social science to know exactly what they are talking about: what is a mathematical conclusion, what is an estimate and what is a guess. That is why an academic discipline which is unregulated has the potential to do more harm than good. By “regulation” here I mean the applying of guidelines as to what is permissible as a statement of fact about what has happened. The process of determining what is permissible, in some cases, could go on for ever because life is so complex. In other cases, the philosophy and theory behind statements are easily determinable from the mathematics and the meanings of words used to describe statistics.
To do social science in a scientific way, you need to ask three types of questions:
1. (Practice) What is the answer to the question at hand?
2. (Theory) How can I best answer this question?
3. (Philosophy) Why am I asking this question?
And you need to spend time on all of them.
Purchasing-power parity axioms
However we define “poor”, the following are logically true if a national purchasing power conversion is used to infer the purchasing power of the poor.
| |
|Axiom 1. |
| |
|Where a national PPP conversion rate is more influenced by goods and services the poor don’t buy: [81] |
| |
|Price changes for those goods and services will have more of the paradoxical effect on the apparent purchasing power of the |
|poor. |
| |
| |
|Axiom 2. |
| |
|Where PPP rates are changed by social scientists, the greater are changes in prices of goods and services the poor don’t use or |
|use less than other people: |
| |
|The more poor people’s incomes - in real purchasing power terms - will look as if they have gone up when they haven’t, and |
|the more their purchasing power will look as if it has fallen when it hasn’t. |
| |
| |
|Axiom 3. |
| |
|The larger the proportion is of the national PPP rate that is influenced by goods and services poor people do use, [82] |
| |
|The less anti-poor distortion there will be in the conversion to “PPP dollar values” of real changes in their consumption. |
| |
A basic-goods purchasing power parity measure would perhaps[83] avoid these statistical problems, and therefore the resulting errors in inferences about whether the incomes or consumption expenditures of poor people went up or down in real purchasing power terms.
However, I am not sure why this is necessary, rather than a calorific measure. If 70% of the consumption expenditure of people below poverty lines in poor countries goes on food, then all the problems of price fluctuations in agricultural nations would be avoided by using this non-monetary measure, and it would still give a very good indication of poverty.
10.The “$1-a-day target” fallacy
The official statement in the Millennium Goals that the “halving poverty” target is concerned with halving the proportion of people living on under $1 a day is factually incorrect.
The measure used is not a real dollar but a PPP dollar equivalent unit.
“The extremely poor are those who live on under $1 a day”.
This is, for an audience who does not know that it is PPP-converted units which are being referred to, a false statement. A person in a poor country on a level of income convertible to a PPP dollar unit may be on an income of the local equivalent of (at real exchange rates) 25 cents or 80 cents, depending on the country.
This is a separate confusion from that in fallacy 9. This one, like fallacy 9, is concerned with the natural meaning of words used by a social scientist when writing for a wider audience. But this fallacy is to give a misleading impression of the value in real dollar terms of poor people’s incomes. Fallacy 9 is about what the real purchasing power is for the poor of a pretend dollar.
See my “Review of the Millennium Goals” for more detail.
In poor countries the PPP dollar is worth a fraction of a real dollar in terms of what it can buy in the economy as a whole. Its value to the poor for the things which they buy is not known, but it is certainly not worth what a real dollar would be worth to poor people.
It is grossly irresponsible for social scientists, civil servants, politicians and journalists to give this euphemistic impression of the severity of poverty.
11.The “falling headcount” fallacy ?
This is the fallacy of inferring a fall in the proportion of people below the original poverty line, where poverty is measured by PPP dollars or real currency adjusted by the overall inflation rate in a country.
There is an alternative explanation for the fall in the proportion below an expenditure line. Food prices might have gone up as much as, or more than, the overall inflation rate or the PPP “dollar” inflation rate.
The meaning of a statement that “the proportion of poor people went down” depends on what we mean by “poor”. If “poor” means below the same level, in terms of purchasing power, as at the start of the period, then this is not necessarily captured by PPP values. The statement “the proportion of poor people went down” is only meaningful if it means that the proportion of people below the original consumption poverty line fell, rather than the proportion of poor people at the previous level of PPP-value consumption expenditure falling.
If my initial thoughts on this are right, then what is needed in social science is an approach to measurement specifically designed to provide meaningful statements about changes over time. If price changes can result in bogus assertions of “gains” to poor people, then the whole enterprise of using money to measure welfare across time and across countries looks even more shaky. I honestly don’t know why people - social scientists - try to iron out wrinkles in a fabric which has so many new wrinkles appearing all the time.
To take just one example:
Prices in poor countries for basic goods are seasonal.
So consumption expenditure levels for a minimum diet for survival depend on the season.
So the season when a social scientist gets the data will influence the levels of consumption expenditure seen in the data. Actually this is for two reasons: a) prices fluctuate and b) wages fluctuate.
The more I find out about these monetary measures, the more they seem to me completely meaningless unless a theoretician of social science can make a case as to why all the problems are of no consequence in practical terms.
My growing belief that this is impossible for a theoretician to do (because the methods really are severely flawed) gains plausibility from the weakness of the arguments put forward to defend them: these arguments include
“the PPP dollar a day, which is not based on the purchasing power specifically of poor people, is a popular measure, and easy to understand”; and
“these figures are the best we have, so we use them” - in the context of statistics whose reliability is scorned by statisticians in government and UN organisations, but used in studies with no estimate of the reliability of the data, but instead, categorical statements about what is assumed to have definitely happened in the real world.
Part IV: Solutions for measuring the wealth of persons
(Note to MB: This is all in note form. To be modified and vastly expanded. If I’m going to be honest about social science, I have to say why I think these methods are more reliable than other methods. There are plenty of problems with all of them.)
The problems for people using statistics about economies to infer average gains are fairly complex.
Part of the problem is that as always in statistics the accuracy of the conclusion depends both on the data and the statistical test. So in cross-country growth regressions (which sounds like a race but is not), small inaccuracies in inferring average gains in individual countries may make for conclusions in the wrong direction.
Some of the more complex aspects include the following, from Population dynamics and economic development: Age-specific population growth rates and economic growth in developing countries, 1965 to 1990 by Edward M. Crenshaw (Ohio State University), Ansari Z. Ameen (Lewin Group) and Matthew Christenson
(U.S. Bureau of the Census).
Finally, it is tempting to conclude from this analysis that the major effect of demographics on economics is a one-time byproduct of the demographic transition. Yet many nations have managed to attain positive economic growth rates while their dependency ratios grew (e.g., Kenya, Burundi, Honduras). This suggests the possibility of a demographic ratchet effect. Although .baby booms. may slow economic development, they do not always halt or reverse economic growth. Rather, population dynamics may ratchet up development levels over time, although population .booms. and .busts. may grow weaker in response to socioeconomic changes such as female labor force participation and urban living. In short, what is gained in a strong labor force cycle is not necessarily lost during the next .baby boom.. This possibility, in addition to the negative social aspects of population aging, calls for a more balanced view of how demography influences economic development.
The authors had noted:
For instance, in Benin the average growth in the child population equaled more than 4 percent per year from 1965 to 1980, while adult population growth averaged only 2.6 percent per year during the same period. On the other hand, the adult population of Costa Rica grew at an average of nearly 5 percent a year, but growth in the child population lagged far behind at 1.39 percent per year. Thus, while many national economies are staggering under the weight of high fertility, others are enjoying the heightened productivity of a rapidly growing labor force relatively unfettered by large cohorts of children.
One solution for the age structure part of the equation is just to ask people’s age when income surveys are done, and take the average of (the change in average income for all age groups).
As always, the median is appropriate for
a) measuring overall economic welfare in the population,
b) giving the people a good idea of how they are doing, and
c) assessing the success of government policies in relation to the welfare of the people.
whereas the mean is appropriate for government financial planning for the economy.
Three solutions for studying outcomes in geographical areas where demographic changes are unknown, and for comparing the standard of living between countries
Cohort studies, longevity studies and common sense
In order to make a credible claim from numerical data, minimal requirements of a scientist include the following:
1. Define the variables precisely
2. Decide on an appropriate research question
3. Think about the best method to answer this question
4. Collect reliable data
5. Estimate the reliability of data
6. Show that the sample data are representative of the whole population
7. Carry out appropriate statistical analyses for answering the question
8. Consider what the alternatives are for explaining their findings
9. Exclude competing explanations, showing why their hypothesis for the observed result is the most plausible one
How many of these are done by economists investigating financial outcomes?
Solutions to the economic fallacy problem
To examine the solutions, we need first to state the problem precisely.
A summary problems in the economic fallacy
The economic fallacy - what we could call the economic gains fallacy - is composed of several fallacies. Current methods of inferring average financial gains to populations suffer from the following problems.
At the level of data collection:
1. Failure to take asset changes into account
2. Failure to take changes in debt levels into account
3. Failure to take age structure changes into account
At the level of
Why do we think that a social scientist needs to know more than average income statistics to infer average gains?
Because there might be several alternative hypotheses to their hypothesis that all the changes in the average were caused by income gains and losses.
The alternative explanations are:
1. Birth rates changed
2. Death rates changed
3. Age structure changed
4. .......................
5. ...........
Solutions to the poverty reduction fallacy
Let’s restate all the elements of the poverty reduction fallacy.
4. Failure to take asset changes into account
5. Failure to take changes in debt levels into account
6. Failure to................
Solutions: Use the poverty gap ratio.
No reason not to calculate it if income/consumption expenditure data are available.
The good scientist, knowing how their mathematics works, and its limitations, will try and think of ways to ensure that they are not guessing too much, in order to make their conclusions more reliable. And as regards financial outcomes, there are ways of doing this: to supplement economic data with cohort studies, longevity studies and qualitative information.
Let’s think about longevity. Imagine that you are a social scientist studying mean income among poor people in 1990, and again among poor people in 2000. If the original people were malnourished, then what effects did premature deaths have on the mean for 2000? You don’t know, so you can’t say what mean income gain or loss was.
If, however, you have good evidence that
1) longevity among the poor increased steadily over the period, and that
2) the poorest of the poor are increasing their longevity by at least as much as the less-poor,
then your conclusion that “the change in mean income in the poorest quintile shows the mean financial benefit to poor individuals” has more plausibility. The good scientist knows what indicators are needed for this purpose: neither mean life expectancy in the whole country nor mean life expectancy among the poor are enough.
I say above that the conclusion has more plausibility, not that it is valid. The reason is that demographic changes due to changes in longevity are not the only relevant ones. If income is used as a measure, then we need to consider how changes in the age structure affect average income.
Cohort studies, too, can help us to find out what happens to real people on average. Cohort studies are carried out on samples of the population. But then, for the bulk of the world’s population, so are annual-income studies.
There are other things which a social scientist can do while collecting cross-sectional interview data on income, to minimise the risks of serious error in the final results of inferential procedures concerning financial outcomes.
In making these suggestions, I am not calling for great precision. I am calling for some kind of adjustment to be made for certain obvious measures of financial well-being which may vary significantly over time and across countries.
In this document I have pointed out various missing elements in the logic of economic conclusions about financial outcomes. Knowing about asset changes, changes in debt levels, public services, necessary outgoings, and subjects’ ages and survival rates are all essential for the task of ....................
First, they can record assets. Knowing something about asset changes is essential for finding out about material gains and losses. Assets – at least, some of them – are harder to hide than monetary income and some types of benefits in kind. They are also a very useful indicator of well-being of poor people. A family with five cows is generally better off than one with no animals but the same consumption level. If the interviewer is going to the house anyway, they might as well write simple stuff like this down. It would provide a preliminary idea of what had been missed out by studies purely concerned with income or consumption expenditure. It would thus provide a basis for deciding how precise or imprecise income or expenditure need to be.
Second, they can estimate the value of public services. Knowing something about these is also essential.
Third, they can ask and/or estimate people’s ages.
Fourth, they can ask about who has died recently in the family. This is similar to the procedure for finding out about child mortality rates, where mothers are asked about the children they have given birth to in the past.
Because some of the most influential macroeconomists have left out crucial parts of their logico-mathematical arguments, and because the hypotheses I have outlined above have explanatory power which the economists’ assumptions lack, it seems more likely than not that in some places – and as a result of particular policies - people are doing significantly worse than economists say, even purely in terms of income, while in other places, and as a result of other policies, they are doing significantly better.
Checklist for researchers investigating economic gains
Logically-necessary research areas for economists prior to inferring average gains
One of the tasks which face any economist using cross-sectional data to infer average gain is that of separating what I call
a) the primary effects of demography (the mathematical effects of there being, for example, proportionally more children in one country than in another) from
b) the secondary effects (economic effects).
Glossary of ambiguous terms
Some of their various meanings in economics and statistics
There is much confusion in social science as to the meanings of these terms. I would prefer not to have to subject the reader to this complex set of definitions, but I think it may help show where some confusions in economics have arisen.
In my personal experience, clarity of thought often comes about through an initial stage of confusion, in which apparently clear definitions turn out to be ambiguous or worse. I cannot repeat the following sentence often enough:
The words a scientist or social scientist uses to talk about their numbers are more important than the numbers themselves.
In the world today, data about most people’s income, consumption expenditure and nutritional status are known to be unreliable, partly due to their sparsity. In preparation for the appearance of more reliable data, I suggest that it is more important to know what we are talking about than to know what the numbers are.
Without definitions, conclusions are not definitive. Science begins with definitions, because otherwise the conclusions are vague and ambiguous. The scientific study of financial outcomes is no different in this respect from any other scientific enterprise. The following guide may provide students of economics and statistics, as well as philosophers of social science and the public, with a basis for questioning exactly which meanings are intended by social scientists. It may also help social scientists themselves to clarify exactly what they mean, so that they can make statements which are true, unambiguous and supported by quantitative processes rather than unspoken assumptions.
Here, then, are various meanings social scientists give to words when dealing with countries where most humans live.
Does a writer mean by “the poor”:
a. People living on below the theoretical purchasing power of $1.08 per day in the USA at 1993 prices?
This line is commonly, but misleadingly, referred to as the purchasing-power parity (PPP) “dollar”. This is not calculated on the basis of purchasing-power parity for the goods which the poor buy. Therefore, it does not tell us that the poor can buy the same amount of basic items as they could in the USA with the PPP dollar equivalent. Nor does it tell us that their purchasing power is equivalent to that of someone else in another country with the same nominal PPP dollar income or expenditure; nor does it provide a mathematical basis for calculating relative increases or decreases in the purchasing power of poor people over time.
In real terms, a PPP dollar unit is worth perhaps 30 to 70 cents in poor countries at current exchange rates.[84]
b. People living on below the local equivalent of the theoretical purchasing power of $2.16 a day in the USA at 1993 prices?
c. People in the poorest fifth of a country’s population at one time?
(a real group of people)
d. “the poorest fifth as a theoretical segment of the economy, whoever is in it at any time”?
For example, a social scientist might say “incomes of the poor rose 1%” when they have not found this. They might say this when all they have really found is a change in per capita income for the poorest quintile. This is a fundamental mistake of both logic and semantics. If the social scientist cannot show that demographic factors had insignificant effects on the later average, their conclusion about “the poor” - which can only refer to real people - is invalid.
See section on the quintile fallacy, page 23.
The extremely poor
See “a.” above.
Is “poverty reduction” being used as:
a. A general term for an increase in poor people’s nutritional, health, educational, and/or financial status?
(No specific meaning in social science).
b. A general term for raised incomes among poor people?
No specific meaning in social science, in respect of whether it refers to median increase, mean increase or only increases among those who are thought to have risen above the poverty line.
c. A fall in the proportion of poor people?
d. UN/OECD/World Bank/IMF Millennium Goal on “eliminating poverty and hunger”?
with targets of
i. ”halving the proportion of people living on under $1 a day[85]”
and
ii. “halving the proportion of malnourished people”.
e. UN/OECD/World Bank/IMF agreed measure of progress for this goal, using five indicators?
The agreed indicators were to include changes in the poverty gap ratio, which is a measure of the depth of poverty. Such changes have not been incorporated into in official reports on progress towards the Millennium Goals during the first half of the period from 1990 to 2002.
There is no published formula for combining these indicators. Without such a formula, it will be impossible for anyone to tell what the statistics will mean in the year 2015 even if all indicators are at some stage used (which they have not: see next definition)
Note: If in a country inequality of life length between those above and below the poverty line worsens, then other things being equal not only will the proportion of poor people go down faster, but also if the other indicators are brought in at a later date they may be wrongly interpreted as representing better progress for poor people. For example, the poverty gap ratio (depth of poverty) could be less severe, at a later date, in a country where the poor had died earlier.
f. The existing progress measure for this goal using two indicators?
i. changes in the proportion of people below the theoretical PPP “$1 a day”,
and
ii. changes in the proportion of malnourished people.
Without any indicator of changes in the severity of poverty or malnutrition.
There is no published formula for combining these two indicators to give statistics quoted in the latest report from the Secretary-General of the United Nations. The meanings of statements about poverty reduction in this report is therefore unknown to the outside world.
Does a writer mean by “income”
1. Income as reported by subject to researcher?
2. Consumption expenditure as reported by subject to researcher?
Often confused with consumption level.
3. A mixture of income data and consumption expenditure data?
4. Average income/consumption-expenditure level in a population?
It is essential for people attempting to comment on welfare levels to understand the implications of failing to understand what this meaning entails. For example, a social scientist might say something like
“income has a weak correlation with health improvements”.
But if they really mean “per capita income”, then their statement is not functionally equivalent to
“on average, there is a weak correlation between individuals’ income gains and their health improvements”.
Per capita income, as we know, is influenced by demographic factors as well as income levels. Per capita income is not a measure of welfare, but a fiscal statistic. In particular the proportion of children and the life length of poorer people are factors. (see for example the story of the Chinas and the Indias on page 15).
The social scientist’s statement above simply means that there is a weak correlation between
average income for whoever is alive at the time (which may be influenced by demographic changes, individual income changes or both)
and
some measure of health improvement they are referring to, which may be longitudinal or cross-sectional.
Whether a statement about individual gains and individual health improvements is justified in any particular situation in the real world is a separate question, whose answer the social scientist needs to find out by other methods.
Does a writer mean by “incidence”
1. Prevalence (as in “the prevalence of malnutrition”)?
2. Incidence?[86]
Index
(under construction - please note multiple entries here)
Age structure, 18, 25, 84, 87, 99, 105, 106, 116, 154
Attanasio, Orazio, 34
Average gain, 55, 98, 113
Average income gain, 86, 101
Axioms on economics and demography, 105
Broome, John, 34
Child survival, 54, 72, 90, 91
Cohort studies, 115, 151, 154
Concept of poverty, 41, 42
Deaton, Angus, 33
Demographic change, partial explanation for East Asian "economic miracle, 88
Differential longevity, 87, 89, 119
Differential mortality between the sexes, 97
Economic fallacy, 23, 24, 81, 114
Emmerson, Carl, 34
Inequality of life length, 18, 75, 89, 108, 110, 112, 113, 117, 161
Kanbur, Ravi, 33
Krishnaji, N., 33
Longevity studies, 151, 154
Marx, Groucho, 40
Measurement of poverty, 41, 43
Median, 22, 66, 67, 68, 70, 83, 92, 107, 108, 110, 111, 114, 160
Meta-analysis, 38, 39
Millennium Development Goals, 35, 70, 72, 73, 147, 160, 161
Millennium Goals, 73
Morley, Samuel, 33
Parfit, Derek, 34
Pogge, Thomas, 33, 122, 141
Poverty reduction, confusion over meaning, 17, 19, 22, 32, 46, 65, 66, 76, 77, 82, 90, 147, 162
Poverty reduction, confusion over meaning, 160
PPP, 53, 57, 58, 59, 60, 69, 70, 73, 79, 80, 119, 141, 145, 147, 148, 159, 160
Prices, 17, 26, 28, 55, 56, 57, 58, 59, 60, 69, 80, 134, 145, 148, 159, 160
Purchasing power parity not applicable to the poor, 17, 28, 33, 45, 57, 145, 148, 160, 161
Purchasing power parity\ unfair to the poor, 28, 33, 45, 57
Purchasing-power parity axioms, 145
Reddy, Sanjay, 33, 122, 141
Regression, 48, 54, 96, 98, 105, 106
Rowntree, Benjamin Seebohm, 32, 110
Semantic fallacies, 119
Sen, Amartya, 32, 71, 95
Social welfare functions, 28, 99
Standard of living, not measured by per capita income, 2, 16, 70, 151
United Nations, 51, 68, 70, 95, 111, 149, 160, 161, 162
Utilitarianism, 26, 27, 28, 34, 120, 135
Weisbrot, Mark, 32
Zero conjecture, 86, 87, 89, 102
-----------------------
[1] I think it is both interesting and useful to think through the fundamentals of these things. It’s not for nothing that the most advanced study is sometimes called “basic research”. In the present case, typing the words in (b) above makes me wonder about the difference, in a population with minimal demographic change, between the following:
i) the average gain, which is (present average income) divided by (previous average income)
and
ii) the average of everyone’s percentage gains and losses.
Let’s divide the population into low- and high-income halves. If low-income people gain 5% and high-income people lose 5%, that’s an “average loss” to the economist, who uses (i) above, and would call this situation a recession. But it is neutral according to (ii). It would not be difficult to construct an example where there is a “recession” but people’s percentage gains were on average positive. So we have a “recession fallacy” which consists of saying that people had percentage losses when in fact they didn’t.
This is of more than academic interest. In countries where most humans live, the people with least income have vastly less of it than the people with the most. So percentage increases to poor people - say, a cup of rice a day, which is quite a big change - don’t make much of an impact on the per capita figures. (They may make more impact on the PPP average for the country, because PPP appears to artificially distort poor people’s incomes upwards).
Where per capita income statistics are available from national accounts but there is no reliable information on the distribution of gains and losses among people at different income levels, the per capita figures give us no idea whether most people gained or lost, or by how much.
In case anyone thinks that growth is accompanied by income gains to poor people, I need to say here that contrary to popular belief, the idea that growth has had a general association with income gains to the poorest 20% is unsupported by any evidence. As with all multi-country studies looking at the effects of policies and/or conditions on per capita income in poorest quintiles,
a) the studies confused changes in quintile averages with percentage gains and losses to real people in the poorest quintiles: they neglected demographic factors, whose influence was necessary to calculate (the most basic two mistakes being i) to jumble up adults and children and ii) to fail to take survival rates into account when inferring average gains and losses to malnourished people in different countries);
b) they failed to give reasons for thinking that PPP dollar values represented relative purchasing power of the poor at different times and in different places (also necessary to calculate);
c) they left out many of the poorest countries.
[2] In this example I talk of consumption rather than money, because I want to talk about how well off people are. Income, or consumption expenditure, do not necessarily reflect the amount of goods or services bought with that money, and so cannot tell us directly about the standard of living. In the real world, many economists ignore this problem and assume that lower consumption expenditure necessarily means lower consumption, which doesn’t follow. Prices might have fallen. In the real country of India, a calorific standard is used to measure poverty, which, given the problems involved with changing prices, and with trying to compare the value of money internationally, seems sensible.
If we want to make the example apply to money, we can. All we have to do is to assume two things:
a) that both families’ money can buy the same amount of goods and services and
b) that there are no other factors involved in assessing their welfare
(neither of which are known in the real world to economists: see later sections).
If we apply the example using money, we still find that the Indias are 10% better off. But an economist using the standard methods economics would say, without thinking about the family sizes, that they are 1% worse off.
[3] I define consumption poverty as “shortfall in consumption compared to the poverty line” at the level of the individual. If this is aggregated (i.e. the sums are done) using an average, the mean will do to illustrate my point. Why mean shortfall is not used as the measure of severity of poverty in economics, I do not know. That would be my suggestion. (Mean shortfall) times (the number of people below the poverty line) = (level of poverty in a country). Why not? We could call this “the poverty level”. If it’s reduced, there is poverty reduction.
[4] “Average” defined here as mean individual income gains. The same point applies if it is defined as median (typical) individual income gain/loss.
[5] I might change the name of this fallacy to one of these:
a) the “economic growth fallacy” (which has the disadvantage that the term “economic growth” itself is a misnomer, because the economy can shrink while there is no recession - total of transactions down, average of transactions up); or
b) the “income gains fallacy” which is more accurate but uglier.
Since there are further fallacies involved when economists talk about financial benefits (for some unknown reason making a claim about individuals’ finances beyond the income they have measured: an income gain doesn’t in fact tell you someone had an economic gain - see fallacy 7) and about policies being good or bad for real people (for some reason going beyond finance) I shall probably reserve the words “economic fallacy” to refer to any assertion from financial data without the logically necessary evidence that there were benefits to real people of a certain mathematically describable level.
[6] As with fallacy 3, an accurate name is essential for this fallacy. I do not mean the name I have given it above to convey that I think someone’s income - or any purely financial measure - can possibly show their standard of living. I might call this the “higher incomes in country X” fallacy. Or the “ better off in China” fallacy (see the story of the Chinas and the Indias on page 15).
[7] A notable exception is approach of the recent report of the WHO Commission on Macroeconomics and Health’, which spoke of the economic gains from better survival rates, expressed as increases in total income in a country, not average income. I question its assumption that the economic gains are sensibly calculated on the basis of each extra survivor having the mean per capita income for their country, but it’s a start. I did write to a prominent member of this commission calling for attention to the question of whether survival rates had a paradoxical influence on development statistics, but received no reply.
[8] The word Politeia is traditionally, but erroneously, translated as “The Republic”. Its scope is in fact wider - it can mean “The Form of Government”, or “The State”, or “Citizenship”. Because of this wide scope, it could be translated into English using more than one concept: “Citizen and State”, perhaps, or using a word appropriate to Plato’s context such as my favourite, “Civilisation”.
[9] Poverty research pioneer in the UK 100 years ago.
[10] For reasons of optimism, I have inverted the logic of his paper Mortality as an indicator of economic success and failure (1998).
[11] Growth May Be Good for the Poor But are IMF and World Bank Policies Good for Growth?
A Closer Look at the World Bank's Most Recent Defense of Its Policies; Mark Weisbrot, Dean Baker, Robert Naiman, and Gila Neta. Draft released August 7, 2000.
[12] “Krishnaji, N. 1984. Family size, levels of living and differential mortality in rural India: some paradoxes, Economic and Political Weekly, 9, 6.
[13] How not to count the poor (2002). Available at , with subsequent additional papers.
[14] Counting the world’s poor: problems and possible solutions, Research Program in Development Studies, Princeton University, revised version, December 2000. He also makes the following comment:
“Because poverty counts come from the survey data, while growth measures come from the national accounts, and because they are evidently measuring different things, there is no consistent empirical basis for conclusions about the extent to which growth reduces poverty. That economic growth, as measured, has at best a weak relationship with poverty, as measured, means little more than would a finding that growth in China had failed to reduce poverty in India”.
[15] Construction of Purchasing Power Parities (PPPs) for the Study of Global and Regional Poverty: Report on A Pilot Project for the Statistics Division of the ESCAP. Revised version of the Report prepared for discussion at the Expert Group Meeting on the International Comparison Program at the Economic and Social Commission for the Asia and Pacific (ESCAP) during 27 Feb-1 March, 2002.
[16] See also (long words but worth it) Estimating Income Mobility in Colombia Using Maximum Entropy Econometrics, Samuel Morley, Sherman Robinson and Rebecca Harris; Trade and Macroeconomics Division, International Food Policy Research Institute, 2033 K Street, N.W. Washington, D.C. 20006 U.S.A. May 1998:
“While the statistical details of the income distribution are by now quite well documented and studied, less attention has been paid to the interpretation of the observations. Interpreting changes in the distribution in terms of welfare is inherently difficult in an economy where both population and income are changing over time. Morley (1981) showed the significant effect of population growth on measures of poverty and income of those at the bottom of the distribution. With income growth,
one can have substantial reduction in the extent of poverty, and presumably improvements in welfare, even if the distribution becomes substantially less equal. And, even if both aggregate income and the population are constant over time, the fact that age-earnings profiles rise and then fall (indicating “circular mobility”) will yield more equally distributed lifetime incomes of individuals, even though the distribution at any point in time is highly unequal.”
[17] John Broome is a moral philosopher. I will check to see if this is quotable in public - it may come from an unpublished manuscript.
[18] Philosopher. In Peter Singer (ed.), Applied Ethics, 1986.
[19] Differential Mortality and Wealth Accumulation, Orazio Attanasio, Institute for Research on Poverty Discussion Paper no. 1079-96, January 1996.
[20] Differential Mortality in the UK , Institute of Fiscal Studies, 2000.
[21] I originally wrote “for certain answers”. The word “certain” would have been ambiguous, but in fact either sense of the word would have been appropriate - either “particular” or “definitive”. Where people want definitive answers, there is a temptation to avoid uncertainty. But refusing to avoid uncertainty is a big part of the joy of thinking about science, poker, history or detection.
[22] Inferences from statistics using samples of populations are universally acknowledged to be gambles in one sense:
The words “statistical significance” refer to the statistical likelihood, based on how widely varying the numbers are in the sample, and how big the sample is, that an observed trend is due purely to random variation - in other words, due just to who happened to be in the sample.
This phrase has nothing to do with whether the results are significant in a more general sense - meaning whether they are of significance for any action in the real world. Nor does it have anything to do with the size of the effect observed. It refers purely to the probability that, if
1) all assumptions are valid,
2) all the data are reliable
3) all the statistical tests were both appropriately chosen and correctly applied, and
4) the words in the conclusion correctly describe the results,
the answer wasn’t generated by the random factor of who happened to be in the sample.
If you see a statement about statistical significance such as “p < 0.05”, what this means is that there is a 1 in 20 chance, from looking at how up-and-down the numbers were among different people in the sample, that the results were due to sampling error. If the numbers were all over the place, then it’s more likely that some statistical result was due just to wild variations. For example, if the scores in a test were not all over the place, but people who were more ill had worse scores, then it’s more likely that there really is a connection between (illness) and (bad score on the test). So if we see p ................
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