Estimation and Welfare in Large-Scale Demand Systems
In this thesis, I study large-scale demand systems with a focus on characterizing sufficient statistics (welfare-relevant average elasticities) and how allowing for large unstructured heterogeneity affects both welfare and estimation.
In Chapter 1, I make three main contributions. First, I introduce a highly flexible class of demand systems that generalizes the most popular specification in trade and macroeconomics settings. Within this class, I show that we can characterize welfare using a (potentially time- and sample-varying) average elasticity together with an auxiliary aggregate that can be calculated using readily observable data. Second, I introduce a flexible parametric demand system (GSA translog) and adapt recently developed causal machine learning techniques to estimate the key parameters of the demand system. This estimation strategy allows for product-specific price sensitivity parameters without imposing strong ex-ante restrictions on cross-sectional patterns on which products are more or less elastically demanded. Third, I implement my new method to revisit the entry/exit adjustment problem which has been widely studied using a constant elasticity of substitution framework. My new model uncovers a novel interaction between product life-cycle patterns and welfare calculations; products that exit are systematically more elastically demanded (on exit) relative to entering goods (on entry). This result is driven in part by the recently documented pattern that (at the barcode level) products are systematically more popular on entry than they are on exit.
In Chapter 2, I revisit the identifying assumptions for the popular heteroskedasticity-based identification strategy. While there has been significant attention paid to the statistical assumption of uncorrelated error terms, I turn the focus to the structural assumption of a single common elasticity parameter across groups. I show using Monte Carlo simulations that even minor violations of the common elasticity assumption can lead to extreme divergence between the underlying distribution of price sensitivities and the point estimates yielded by heteroskedasticity-based regression methods. Notably,unlike with linear methods (OLS and IV regression), with the heteroskedasticity-based method when the statistical assumptions hold but there is underlying variation in the product-specific price sensitivities the point estimate is not a weighted average of the underlying parameter values. To test the empirical relevance of this finding, using US trade data I compare heteroskedasticity-based point estimates to set-identification ranges for product-specific elasticities which rely on the same statistical assumptions but do not impose the problematic cross-sectional restriction. I find that in all product categories, the pooled point estimate is outside the set-identified range for some of the included products. The empirical pattern that I find is the point estimate is systematically higher (more elastic) than the set-identified ranges for each product, which provides an explanation for the pattern in the empirical literature whereby heteroskedasticity-based estimates are systematically higher than other estimation techniques.