Measuring Welfare and Inequality with Incomplete Price Information

We propose and implement a new approach that allows us to estimate income-specific changes in household welfare in contexts where well-measured prices are not available for important subsets of consumption. Using rich but widely available expenditure survey microdata, we show that we can recover income-specific equivalent and compensating variations from horizontal shifts in what we term “relative Engel curves”—as long as preferences fall within the broad quasi-separable class (Gorman 1970; 1976). Our approach is flexible enough to allow for nonparametric estimation at each point of the income distribution. We apply the methodology to estimate inflation and welfare changes in rural India between 1987 and 2000. Our estimates reveal that lower rates of inflation for the rich erased the real income convergence found in the existing literature that uses the subset of consumption with well-measured prices to calculate inflation.