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The World Bank, Washington, DC., and was on secondment to the IMF’s Research Department while parts of this paper were written. This paper was prepared in the context of the pro-poor growth program sponsored by the World Bank’s Poverty Research and Economic Management (PREM) group. The author is grateful to Roberta Gatti, Francisco Ferreira, and Martin Ravallion for helpful discussions, and to Shaohua Chen for providing data.
A notable early exception is Ravallion and Chen (1997), who estimate regressions of changes in absolute poverty on changes in mean incomes using a panel of household surveys from developing countries.
See, for example, Bourguignon (1999) for a lognormal example.
For example, Lopez (2003) investigates the determinants of growth and change in the Gini coefficient, and then draws conclusions regarding the likely effects on poverty by assuming that the distribution of income is lognormal, so that there is a one-to-one mapping between the Gini coefficient and the Lorenz curve.
Differentiating under the integral sign in equation (1) requires the application of Leibnitz’s rule. Note that the term involving the derivative of the upper limit of integration is zero, since the poverty measures are zero when evaluated at the incomes of those at the poverty line. For EDEI both the upper and lower limits of integration are constant and so the derivative simply passes through the integral sign.
I am grateful to Shaohua Chen for kindly providing key data from all of the household surveys, including some that is not available on the poverty monitoring website.
When X and Y are normally distributed, this variance decomposition has a very natural interpretation. It tells us how much the conditional expectation of X increases for each unit that we observe the sum (X+Y) to be above its mean value.
At first glance this result seems inconsistent with Ravallion (1997), who documents that the sensitivity of poverty to growth varies significantly with initial inequality. However, using either sample of spells I can replicate the result that the interaction of growth with the initial Gini coefficient is significantly correlated with the change in headcount measures of poverty. Intuitively, the difference between the results here and those in Ravallion (1997) can be understood as follows: although the interaction of growth with initial inequality is significant in explaining changes in poverty, it does not add much to the explanatory power of the regression in my samples. Put differently, although there are cross-country differences in the sensitivity of poverty to growth which are significantly correlated with initial inequality, in the data these differences are dominated by the much larger cross-country differences in growth itself.
The Atkinson class of inequality measures is 1-EDEI(θ)/EDEI(1).
This is because EDEI(θ)1/θ is the sample average of incomes raised to the power θ. As the number of households becomes large, this converges to the expectation of income raised to the power θ. If incomes are lognormally distributed, we can use the moment generating function of the lognormal distribution to evaluate this expectation to obtain the result in the text.
This is of course especially problematic for the regressions below that involve a lagged dependent variable, which, together with unobserved country-specific effects, will make estimates of the coefficient on the lagged dependent variable inconsistent, and can bias the coefficients on the other variables in different directions depending on their correlation with the lagged dependent variable.
Ravallion (2001) documents the empirical importance of inequality convergence using the Gini coefficient. I have experimented with alternative initial inequality measures in the regressions involving the distributional change components of the various poverty measures, but I find that none are robustly significant.
In Table 4, there is an additional factor which likely biases standard errors upward. For countries with multiple spells of growth or distributional change, there is likely to be by construction a negative correlation between the errors of successive spells. Correcting for this will likely reduce standard errors somewhat.