Regression Estimates of Per Capita GDP Based on Purchasing ...

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WORKING.PAPERS

SocioeconomiDc ata InternationaEl conomicsDepartment

The WorldBank August 1992 WPS 956

Regression Estimates of Per Capita GDP

Based on Purchasing Power Parities

Sultan Ahmad

Howthe Bankusesregressionsto fill gapsin purchasingpower paritybased on estimatesof per capitaincome.

Policy ResearchWorkingPapets disseminate the findings of work inprogress and enoourage theexchange ofideas among Bank staffand allothers interested in development issues. Thesepapers, distributedby theResearchAdvisory Staff, carry thenames of theauthors, reflect onlytheirviews, and should beused and cited accordingly.Thefindings,interpretations, and conclusions arethe auLhorsown.TTheyshould not be attributed to the World Bank, its Board of Directors, its management, or any of ita member countries.

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ScloeconomicData WPS 956

This paper - a product of the Socioeconomic Data Division, International Economics Department -is part of a larger effort in the Department to improve intemational comparability of national account aggregates and price structures. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Elfrida O'Reilly-Campbell, room S7-125, extension 33707 (August 1992, 22 pages).

The estimates of gross national product (GNP) per capita in U.S. dollars published in the World Bank Atlas are used throughout the world for comparing relative levels of income across countries. The Atlas method of calculating per capita GNP is designed to smooth the effects of fluctuations in prices and exchange rates. With this method, local currency values are converted to U.S. dollars by a form of average exchange rates.

Since exchange rates do not measure relative purchasing powers of currencies in domestic markets, the Arlas estimates can often show changes in the relative ranking of two countries from one year to the next even if there are no changes in real growth rates but if there are changes in exchange rates that are not in line with relative price changes.

Improved estimates can be obtained if purchasing power parities (PPP) rather than exchange rates are used as conversion factors. But PPP-based estimates of per capita incomeusually associated with Irving Kravis of the University of Pennsylvania and with the UN's International Comparison Program - have yet to cover all countries and all years needed in the Atlas.

Attempts have been made to fill the gaps by short-cut estimates using regression techniques or by using a reduced set of information. In an attempt to fill these gaps, the World Bank has used regression estimates of its own and published them in the World Development Indicators.

Ahmad describes how the Bank makes these e. timates.

Ile Policy ResearchWoTkingPaperSeriesdissemdnatesthefindingsof workmnderwayinthe Bank.Anobjective ofthe series is to get these fndings out quickly, even if presentationsare less than fully polished. The rindings, interpretationsa, nd c_onclusionsin these papersdo not necessarily Tepresenot fficial Bank policy.

Producedby the Policy ResearchDisseminationCenter

Regression Estimates of Per Capita GDP Based on Purchasing Power Parities

by Sultan Ahmad

Socio-Economic Data Division InternationalEconomicsDepartment

The World Banik Washington,D. C.

Tableof Contents

I. Introduction

I

II. Methods

2

111. Selectionof variables

2

Explanatory variables

4

Dependent variable

8

IV. Regressions

8

V. Results

9

Alternative regressionestimates

10

VI. Comparisonof REGwith PWT5estimates

11

VII. Conclusionsand directionsforfurther work

13

Tables

15

References

21

Regression Estimates of Per Capita GDP Based On Purchasing Power Parities'

I. Introduction

1. The estimates of gross national product (GNP) per capita in US dollars published in the World Bank Atlas are used throughoutthe worldfor comparingrelativelevelsof incomeacrosscountries. The Atlas method of calculatingper capita GNP is designedto smootheffects of fluctuationsin prices and exchange rates and consistsof convertinglocal currency values to US dollars by a form of average exchange rates2. Since exchangerates do not measure relative purchasing powers of currenzies in domestic markets, the Atlas estimatescan often show changes in the relative ranking of two countries from one year to the next even if there are no changes in real growth rates but if there are changes in exchangerates which are not in line withrelative price changes. Improvedestimatescan be obtainedif purchasing power parities (PPP3) rather than exchangerates are used as conversionfactors. However, PPP-based estimates of per capita income, usually associated with Professor Irving Kravis of the University of Pennsylvania,and UN InternationalComparisonProgram (ICP4) , are yet to cover all countriesand all years neededin the Atlas. There have been attemptsin the past to fill the gaps by shortcut estimatesusing regressiontechniquesor by usinga reducedset of information. In an attemptto fill these gaps, the World Bank has used regressionestimatesof its own and publishedthem in the World DevelopmentIndicators(WDI5). This paper describeshow these estimateswere made.

2. SectionsII and III deal with choice of methodsand explanatoryvariables. SectionIV presents selectedregressionsand sectionV analysesthe results. SectionVI comparesthe results withthose of the

1 D. C. Rao, John O'Connor, JitendraBorpujariand AdnanMazarei made helpfulcommentson the paper; Nam Phamnand Taranjit Kaur helped with the statistical work.

2 The Atlas method consistsof convertingcurrent price local currency GNP to US dollars by a three-yearaverage exchangerate. The average is computedas follows: the current year exchangerate is added to those of the previous two years after they have been extrapolatedto the current year by relativerates of inflationbetweenthe country and US, and dividedby three.

3 PPP is definedhere as the numberof units of a country's currencyrequiredto purchasethe same amountsof goods and services in the country as one dollar wouldbuy in the United States.

4 The ICP conductsbenchmarksurveys and publishesresults in phases. So far five phaseshave

been completedas follows:PhaseI for 1970(ten countries),PhaseII for 1973(sixteencountries),Phase III for 1975(thirty four countries),PhaseIV for 1980(sixty countries)and Phase V for 1985(about 62 countries). Phase VI for 1990have been compiotedfor the OECD and severalEast Europeancountries;

surveys in Africa, Asia and Latin Americaare beingplannedfor 1993.

i~~~~~~~

5 See World Development Report 1992

PennWorld Tables, version5 (PWT56), the latestsuch estimatesavailablein the publicdomain. Section VIl containsconcludingremarks and directionsfor further work.

I. Methods

3. A preferredapproachto makingquickestimatesfor countriesfor whichICP benchmarkestimates are not availableis to collectprices for a reducedsampleof carefullyselected itemsand make ICP type calculationsfor GDP and a small number of its components. Such a method, termed "the reduced informationmethod"', requires surveysand was not pursuedhere.

4. The paper followsthe conventionalmethodof makingshortcut estimateswhich uses regression techniques,and offersaplausiblerationalefor explainingdeviationsbetweenICP and exchangeratebased estimatesof GDP. This involvesdevelopingan estimatingequationlinkingICP estimatesof GDP per capita and a selectionof easilyobservableexplanatoryvariables for countriesfor which ICP estimates are availableand usingthe equationto estimateICP-typevaluesfor non-ICPcountries8. Estimatesmade for a reference year (1985)are extrapolatedto other years by real growth rates and adjusted for US inflationin order to bring them to currentdollars.

III. Selection of variables

5. In makingregressionestimatesof ICP type per capita GDP, the choiceof variableswas dictated by considerationsof analyticalrelevanceand availabilityof informationfor a large numberof countries, especiallythose reportedin WDI tables.

6. In general, per capita GDP convertedat PPP tends to be higher for a poorer country than the correspondingexchangerate convertedvalue. Two empiricalfacts standout in this regard:

(a) the divergencegrows inverselywith per capita GDP; and (b) the noise aroundthis relationshipincreasesinverselywith incomelevels.

This is confirmedby Chart 1 which shows the deviations betweenICP and exchange rate converted estimatesof per capitaGDP by plottingthe price level (ratio of PPP to exchangerate, which is the same thing as the ratio of Atlas GNP to ICP GDP9) againstAtlas GNP per capita for 1985. The data refer

6 Summersand Heston(1991)

7 Ahmad(1980, 1988)

8 See Ahmad (1980); Beckerman(1966); Beckermanand Bacon (1966); Clague (1986); Clague and Tanzi (1972); Isenman(1980); Kravis, Summersand Heston (1978); Summers and Heston (1984, 1988and 1991).etc.

9 The deviationbetweenPPP convertedand exchangerate convertedvalues has been describedin the literature in two ways: (1) the ratio of PPP to exchangerate (ER) calledprice level or (2) the ratio of ER to PPP, popularly known as exchangerate deviation index or ERDI, which is the reciprocalof price level. Note that price level can also be measuredby the ratio of exchangerate convertedGDP to

2

Price Level By Atlas GNP Per Capita

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to 76 ICP countries; for countriesnot in 1985ICP, the figures are extrapolationsof the latest year data available. If ICP and Atlas estimates of income were the same, PPP would be equal to the Atlas exchangerate, and the scatterwouldbe on the 100mark, the USvalue, on the Y-axis. The chart shows that the vertical distance of a data point from 100 tends to increase as one moves from right (high income)to left (low income)on the X-axis, and thatthe clusteris much more dispersedverticallyat the lower end of cheincomescaletharnat the higher.

7. The relationshipcan also be pictured in anotherway as in Chart 2 whichplots on a log-logscale Atlas GNPper capitaon the X axis and ICP GDPper capitaon the Y axis, both expressedas US = 100. Here the distance from the 45 degreeline is the measureof deviationbetweenthe two estimates. Chart 2 showsthatICP estimatestend to be higherthan Atlasestimates(indicatedby pointsabove the 45 degree line), that the differencebetweenthe two estimatesincreasesas one movesfrom higher to lower end of the incomescale, and thatdeviationstend to be more dispersedat the lowerend of the incomescalethan at the higher.

ExplanatoryVariables

8. The list of candidatevariables, therefore, includesAtlas estimatesof per capita GNP to place countrieson an incomescale and others thatwouldexplainthe noisearoundthe broad trend set byAtlas estimates.

9. It is observed that generally price levels are relatively lower in poorer countries, and the divergenceis more pronouncedin servicesthan in commodities. For instance, if the 1975price index (PPP/ER) for the US is assumedto be 100 for total GDP, then it was 41 for the poorest group of countriesand 108 for the richest. The price indicesfor commodities(definedhere as all final product commoditiesexcludingconstruction)andservices(definedhereas finalproductservicesandconstruction) were respectively60 and 25 for the poorestgroup and 119and 97 for the richest group'?. Thus while commodityprices in poorer countries are approximately50 percent (60/119) of those of the richer countries,servicepricesare onlyabout 25percent (25/97). In nominalterms, servicesaccountfor nearly 30 percent of GDP for low income countries compared with about 50 percent in high income countries". The effect of PPP conversionis to raise this share to levels comparableto those of richer countries. Since exchangerates are affected by relative prices of tradeables (commoditiesexcluding construction),and sincePPP measuresrelativeprices of all goodsand services, non-tradeableas well as tradeabie, any explanationof the differencebetweenPPP and exchangerate must includefactors which relate to differencesin price levels, especiallythoseof services.

10. We hypothesizethat the discrepancybetween ICP and Atlas estimates reflects persistenceof differencesin factorproductivityand wagedifferentialsamongnationsdue to constraintson international

PPP convertedGDP as follows:Price level = ((GDP/ER)/(GDP/PPP)}= PPP/ER, and its reciprocal, ERDI = {(GDP/PPP)/(GDP/ER))= ER/PPP.

' Kravis and Lipsey (1983), p.12.

World Development Report 1991, Table 3.

4

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