World welfare is rising: Estimation using nonparametric bounds on welfare measures

I take a new approach to measuring world inequality and welfare over time by constructing robust bounds for these series instead of imposing parametric assumptions to compute point estimates. I derive sharp bounds on the Atkinson inequality index that are valid for any underlying distribution of income conditional on given fractile shares and Gini coefficients. While the bounds are too wide to reject the hypothesis that world inequality may have risen, I show that world welfare rose unambiguously between 1970 and 2006. This conclusion is valid for alternative methods of dealing with countries and years with missing surveys, alternative survey harmonization procedures, alternative GDP series, or if the inequality surveys used systematically underreport the income of the very rich, or suffer from nonresponse bias.

► Provide sharp nonparametric bounds for inequality measures based on limited data.
► Use bounds to show world welfare rose substantially between 1970 and 2006.
► World inequality may have risen or fallen between 1970 and 2006 based on the bounds.
► Conclusions robust to survey inhomogeneity and nonrandom sampling.