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The World Distribution of Income (from Log-Normal Country Distributions)Xavier Sala-i-MartinColumbia UniversityApril 20091GoalEstimate WDI consistent with the empirical growth evidence (which uses GDP per capita as the mean of each country/year distribution).Estimate Poverty Rates and Counts resulting from this distributionEstimate Income Inequality across the worlds citizensEstimate welfare across the worlds citizensAnalyze the relation between poverty and growth, poverty and inequality2

87Note: I decompose China and India into Rural and UrbanUse local surveys to get relative incomes of rural and urbanApply the ratio to PWT GDP and estimate per capita income in Rural and Urban and treat them as separate data points (as if they were different countries)Using GDP Per Capita we know

4GDP Per Capita Since 1970

5Annual Growth Rate of World Per Capita GDP

6-Non-Convergence 1970-2006

7-Divergence (191 countries)

8Histogram Income Per Capita (countries)

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13Adding Population Weights14

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Back19-Non-Convergence 1970-2006

20Population-Weighted -convergence (1970-2006)

21We can use Survey DataProblemNot available for every yearNot available for every countrySurvey means do not coincide with NA means

But NA Numbers do not show Personal Situation: Need Individual Income Distribution22Surveys not available every yearCan Interpolate Income Shares (they are slow moving animals)RegressionNear-ObservationCubic InterpolationOthers23Strategy 1: (Sala-i-Martin 2006)24

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27Missing CountriesCan approximate using neighboring countries28Strategy 2: Pinkovkiy and Sala-i-Martin (2009)29Method: Interpolate Income SharesBreak up our sample of countries into regions(World Bank region definitions).Interpolate the quintile shares for country-years with no data, according to the following scheme, and in the following order:Group I countries with several years of distribution dataWe calculate quintile shares of years with no income distribution data that are WITHIN the range of the set of years with data by cubic spline interpolation of the quintile share time series for the country. We calculate quintile shares of years with no data that are OUTSIDE this range by assuming that the share of each quintile rises each year after the data time series ends by beta/2^i, where i is the number of years after the series ends, and beta is the coefficient of the slope of the OLS regression of the data time series on a constant and on the year variable. This extrapolation adjustment ensures that 1) the trend in the evolution of each quintile share is maintained for the first few years after data ends, and 2) the shares eventually attain their all-time average values, which is the best extrapolation that we could make of them for years far outside the range of our sample.Group II countries with only one year of distribution data.We keep the single year of data, and impute the quintile shares for other years to have the same deviations from this year as does the average quintile share time series taken over all Group I countries in the given region, relative to the year for which we have data for the given country. Thus, we assume that the countrys inequality dynamics are the same as those of its region, but we use the single data point to determine the level of the countrys income distribution.Group III countries with no distribution data.We impute the average quintile share time series taken over all Group I countries in the given region.30Method 2: Step 1: Find the of the lognormal distribution using least squares for the country/years with survey data

31Step 2: Compute the resulting normal distributions for each country-year

32Step 3: Estimate implied Gini coefficients for country/years with available surveys33Step 4: Three Types of countriesCountries with multiple surveysIntrapolate ginis Estimate location parameter as a function of sigma(Gini) for intrapolated years and then estimate the mean with sigma and GDP per capitaCountries with ONE surveyWe keep the single year of data, and impute the Ginis for other years to have the same deviations from this year as does the average Gini time series taken over all Group I countries in the given region, relative to the year for which we have data for the given country (ie, we assume that the countrys inequality dynamics are the same as those of its region, but we use the single data point to determine the level of the countrys income distribution.)Countries with NO distribution dataWe impute the average Gini time series taken over all Group I countries in the given region.

34Step 5: Integrate across countries and get the WDI35Summary of Baseline AssumptionsWe use GDP data from PWT 6.2Sensitivity: WB, MadisonWe break up China and India into urban and rural components, and use POVCAL surveys for within country inequality. Sensitivity: China and India are treated as unitary countriesWe use piecewise cubic splines to interpolate between available survey data, and extrapolate by horizontal projection.Sensitivity Interpolation: 1) nearest-neighbor interpolation, 2) linear interpolation. Sensitivity Extrapolation: 1) assuming that the trends closest to the extrapolation period in the survey data continue unabated and extrapolating linearly using the slope of the Gini coefficient between the last two data points, and 2) a mixture of the two methods in which we assume the Gini coefficient to remain constant into the extrapolation period, except if the last two years before the extrapolation period both have true survey data. Lognormal distributionsSensitivity: 1) Gamma, 2) Weibull, 3) Optimal (Minimum Squares of residuals), 4) Kernels

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126Poverty Rates: $1/day

127Poverty Rates

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129Rates or Headcounts?Veil of Ignorance: Would you Prefer your children to live in country A or B?(A) 1.000.000 people and 500.000 poor (poverty rate = 50%)(B) 2.000.000 people and 666.666 poor (poverty rate =33%)If you prefer (A), try country (C)(C) 500.000 people and 499.999 poor.130Poverty Counts

131Poverty Counts

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133Regional Analysis134Poverty Rates

135Counts $1/day

136Poverty Rates $2/day

137Counts $2/day

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150Inequality151

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156MLD and Theil

157Decomposable Measures (Generalized Enthropy, GE)158

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165Welfare166Sen Index (=Income*(1-gini))

167Atkinson Welfare Indexcertainty equivalent for a person with a CRRA utility with risk aversion parameter gamma of a lottery over payoffs, in which the density is equal to the distribution of income. Hence, the Atkinson welfare index is the sure income a CRRA individual would find equivalent to the prospect of being randomly assigned to be a person within the community with the given distribution of income168

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177Sensitivity of Functional form: Poverty Rates ($1/day) with Kernel, Normal, Gamma, Adjusted Normal, Weibull distributions

178Sensitivity of Functional form: Gini with Kernel, Normal, Gamma, Weibull distributions

179Sensitivity of GDP Source: Poverty Rates ($1/day) with PWT, WB, and Maddison

180Sensitivity of Source of GDP: Gini with PWT, WB, and Maddison

181Sensitivity of Interpolation Method: Poverty Rates 1$/day with Nearest, Linear, Cubic and Baseline

182Sensitivity of Interpolation Method: Gini with Nearest, Linear, Cubic and Baseline

183MissreportingRich dont answerPoor dont have housesEliminate quintiles 1 and 3 and repeat the procedure184

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186The WB revised China and India GDP (PPP)Following the conclusion of the International Comparisons Project (ICP) in November 2007, the World Bank has changed its methodology with respect to calculating country GDPs at PPP. This change lowered Chinese and Indian GDPs by 40% and 35% respectivelySeveral criticisms have been made of this finding; It considers prices in urban China only (so prices are too high and real income too low). Chinese GDP in 1980 is implied to be $465, and by applying the old WB growth rates, it is $308 in 1970, which may be below the lower limit of survivalIn comparing the original and revised World Bank series, we see that the effect of the revision was largely to multiply each countrys GDP series by a time-invariant constant, which is the expected effect of applying the PPP adjustments derived from the ICP to all years from 1980 to 2006. We nevertheless compare the poverty and inequality estimates arising from the new WB series to our baseline estimates.

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190END191All is not money!Easterlin Paradox:1) Within a society, rich people tend to be much happier than poor people.2) But, rich societies tend not to be happier than poor societies (or not by much).3) As countries get richer, they do not get happier (after a given threshold)ImplicationsEconomic Sociologists: Relative IncomeUN: Human Development Index (as opposed to GDP)Environmental Movement: No growth

192Problem with Easterlin Paradox: Old data (1974)No poor countries in the data setGallup conducted a poll in 2006.Analyzed by Stevenson and Wolfers (2008)

193Source: Stevenson and Wolfers (2008). Economic Growth and Subjective Well-Being: Reassessing the Easterlin Paradox*

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