LORENZ CURVES AND GINI COEFFICIENTS



LORENZ CURVES AND GINI COEFFICIENTS

Lorenz curve: A Lorenz curve shows the degree of inequality that exists in the distributions of two variables, and is often used to illustrate the extent that income or wealth is distributed unequally in a particular society.

Gini coefficient: A Gini coefficient is a summary numerical measure of how unequally one variable is related to another. The Gini coefficient is a number between 0 and 1.

• Perfect equality has a Gini coefficint of zero.

• Absolute inequality yields a Gini coefficient of 1.

This Lorenz curve illustrates the degree of inequality in the distributuion of income. A Gini coefficient can be calculated using areas on this Lorenz curve. The 45 degree line would reflect absolutely even distribution of income.

[diagram on page 2] The pink shaded area A between the line of perfect equality and Lorenz curve reflects inequality. The blue area underneath the Lorenz curve is B, and the Gini coefficient can now be calculated as A/(A+B). Gini coefficients are often expressed as percentages.

[pic]

Measuring Income Distribution

It is possible to measure how equally or unequally a price system rations by looking at the distribution of income. The table below shows that during 2008, 20% of households with the lowest level of income in the United States (groups of people living together, usually families, or single people if they live alone) received only 3.4% of the total income that households earned. The top fifth of Households with the highest level of income earned 50% of the total income earned. The rest of the table can be interpreted in the same way.

|Percent Distribution of Aggregate Household Income (US) in 2008, by Fifths of Households |

|Households |Percent of Income |

|Lowest Fifth |3.4 |

|(mean income= $11,656) | |

|Second Fifth |8.6 |

|(mean income=$29,517) | |

|Third Fifth |14.7 |

|(mean income=$50,132) | |

|Fourth Fifth |23.3 |

|(mean income=$79,760) | |

|Top Fifth |50.0 |

|(mean income=$171,057) | |

|Source: US Census Bureau. Current Population Survey. 1968-2009. Annual Social and Economic Supplements |

The information in the table can be made into a Lorenz curve such as that shown below. The further the Lorenz curve lies below the line of equality, the more unequal is the distribution of income.

[pic]

Gini Coefficients for the US 2001-09

|Year |Gini Coefficient Value |

|2008 |0.466 |

|2007 |0.463 |

|2006 |0.470 |

|2005 |0.469 |

|2004 |0.466 |

|2003 |0.464 |

|2002 |0.462 |

|2001 |0.466 |

|2000 |0.462 |

Statistics, damn statistics!

All economic statistics have problems, and the Lorenz curve and the numbers from which it is constructed are no exceptions. Problems come from two sources: do the numbers actually measure what they are supposed to measure, and are the numbers accurate?

Income distribution is intended to tell us about the rich and the poor, or about how much discrimination exists in a system of price rationing. In a system of price rationing, however, differences in the ability to use income wisely also determine how much discrimination there is. If those who receive the most income, for example, also tend to be the most capable at using that income, then the picture that the Lorenz curve shows will understate the actual amount of inequality.

If rationing is not done solely by price, but by other methods as well, then looking at income data may be meaningless. In the United States, most rationing is done with price, but not all. For example, the purpose of public housing and food stamps is to prevent rationing by price. Both of these items are ignored in the data in the table. Also, one should be cautious when comparing income distributions among countries because their rationing systems can be very different. For example, comparisons of income distribution between the United States and the Soviet Union were not meaningful--although economists sometimes made them--because the Soviet Union not only relied heavily on queuing, but those with special status, such as party members, had access to stores denied to the ordinary citizen.

Households differ in size and average age, but these differences are not reflected in the table above. Neither is the fact that the amount of time over which income is earned affects the shape of the Lorenz curve. Larger households tend to earn more than smaller households. People in their thirties tend to earn more than people in their twenties. Households with four or five members, with more than one person working, and whose working members are between 35 and 55 tend to earn more than other households.

In a paper published in the American Economic Review in September of 1975, Morton Paglin concluded that ignoring the influence of age on earnings overstates inequality by 50%. There is also variability from year to year in how much households earn. Some people appear poor because they had an unusually bad year, and others will seem rich because they had an unusually good year. The shorter the period over which income is measured, the more unequal the distribution appears. Thus, if income were measured over a decade, the distribution would be more equal than any of the yearly distributions.

The other source of problems is in making the initial measurements. The data shown in the table were obtained from questionnaires given a sample of 56,000 households. Not all of these households gave correct answers.

Despite the measuring problems, it is clear that a system of price rationing will distribute goods less equally than will alternative systems such as those using queuing or coupons. Many people consider this inequality a major shortcoming of a market economy, and most critics of market systems emphasize this characteristic. Defenders of market systems, on the other hand, tend to downplay rationing issues, and instead focus on the ability of a market economy to coordinate information and incentives. These are tasks that markets seem to perform very well in comparison to the ways other systems do them.

Questions

Table 3A: Selected Measures of Household Income Dispersion 1967-2008

1: Take the indicator Shares of Household Income of Quintiles. In the periods 1981-1988 (Reagan) and 2001-08 (George W. Bush) two Republican presidents were in power. The Republican Party in the US is often portrayed as the party of the rich and would hence preside over periods of greater inequality of income. Analysing the figures for these periods, could this assertion be correct? If, correct, what reasons could explain the greater inequality of income?

|Year (Reagan) |

| |

| |

| |77 |78 |79 |80 |

|20 |4.2 |4.2 |4.1 |4.2 |

|40 |10.2 |10.2 |10.2 |10.2 |

|60 |16.9 |16.8 |16.8 |16.8 |

|80 |24.7 |24.7 |24.6 |24.7 |

|100 |44 |44.1 |44.2 |44.1 |

|Year (Clinton) |

| |93 |94 |

|1989 | | |

|1990 | | |

|1991 | | |

|1992 | | |

| | | |

|2001 | | |

|2002 | | |

|2003 | | |

|2004 | | |

|2005 | | |

|2006 | | |

|2007 | | |

|2008 | | |

5: Are the figures you calculated in question 4, more or less extreme than the figures provided in the section Household Income Ratios of Selected Percentiles for 90th/10th? If they are more extreme, provide valid reasons for this occurrence.

Inequality: mother of all evils?

1: Considering section 1 Income gap league table, the author states that Britain has been governed on the premise that rising prosperity for the top earners would benefit all (trickle-down economics). What economic arguments could be put forward that supports this viewpoint?

2: Considering section 2 Economic divide; Social wounds, account for the different performance of Spain and Portugal. Does it surprise you that Portugal’s position is so extreme? What can be done to reverse this situation?

3: Considering section 3 The widening gap, the UK experienced the sharpest rise in income inequality in the developed world. What factors lead to this change?

4: Considering the four diagrams illustrating issues such as mental illness, obesity, number of prisoners per 100000 of the population and births per 1000 women aged 15-19 years, does the position of Japan prove that the more equal a population in terms of income distribution, the less social ills it will face?

5: Considering section 4 the price is paid by the middle class too, is the solution to greater income inequality more investment in merit goods such as education and health and more diligence on the part of the government to use transfer payments?

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