David Atkin, MIT on A New Engel on the Gains from Trade. Measuring the gains from trade and their distribution is challenging. Recent empirical contributions have addressed this challenge by drawing on rich and newly available sources of microdata to measure changes in household nominal incomes and price indices. While such data have become available for some components of household welfare, and for some locations and periods, they are typically not available for the entire consumption basket. In this paper, we propose and implement an alternative approach that uses rich, but widely available, expenditure survey microdata to estimate theory-consistent changes in income-group specific price indices and welfare. Our approach builds on existing work that uses linear Engel curves and changes in expenditure on income-elastic goods to infer unobserved real incomes. A major shortcoming of this approach is that while based on non-homothetic preferences, the price indices it recovers are homothetic and hence are neither theory consistent nor suitable for distributional analysis when relative prices are changing. To make progress, we show that we can recover changes in income-specific price indices and welfare from horizontal shifts in Engel curves if preferences are quasi-separable (Gorman, 1970; 1976) and we focus on what we term “relative Engel curves”. Our approach is flexible enough to allow for the highly non-linear Engel curves we document in the data, and for non-parametric estimation at each point of the income distribution. We first implement this approach to estimate changes in cost of living and household welfare using Indian microdata. We then revisit the impacts of India’s trade reforms across regions.