Measuring Welfare and Inequality with Incomplete Price Information

Measuring changes in welfare, and particularly the price index, is challenging in the absence of well-measured prices covering the entire consumption basket. We propose and implement a new approach to estimate changes in income-group specific price indices and welfare using rich, but widely available, expenditure survey microdata. We build on existing work that uses Engel curves and expenditures on income-elastic goods to infer real incomes. While based on non-homothetic preferences, the price indices this approach recovers are homothetic and hence are neither theory consistent nor suitable for distributional analysis. We show that we can recover income-specific price index and welfare changes from horizontal shifts in Engel curves if preferences are quasi-separable and we focus on "relative" Engel curves. Our approach is flexible enough to allow for the non-linear Engel curves we document in the data, and for non-parametric estimation at each point of the income distribution. We implement this approach to estimate inflation and welfare in rural India between 1987/1988 and 1999/2000, and to revisit the impacts of India's trade reforms. Our estimates reveal that lower inflation rates for the rich erased the real income convergence documented by the existing literature that calculates inflation using only well-measured prices.