A Unified Approach to Estimating Demand and Welfare

Stephen J. Redding, David E. Weinstein

NBER Working Paper No. 22479
Issued in August 2016, Revised in March 2017
NBER Program(s):International Trade and Investment

Measuring aggregate price and welfare movements is central to international and macro economics. Existing approaches assume constant preference parameters for each good, which rules out demand shocks for individual goods. However, micro data display substantial shifts in expenditure shares conditional on prices, highlighting the empirical relevance of demand shocks. We develop a unified approach that allows for these demand shocks for individual goods, while preserving a money-metric utility function that can be used for comparisons of welfare over time. We implement our approach for one of the most widely-used preference structures in economics: constant elasticity of substitution (CES) preferences. We derive a unified price index that is exact for these preferences, allows for product entry/exit, demand shocks for individual goods, and nests all major existing economic and statistical approaches. We show that abstracting from demand shocks introduces a “consumer-valuation bias,” which is analogous to the well-known “substitution bias,” and results in a substantial overestimate of the increase in the cost of living over time. We develop a new “reverse-weighting” estimator for the elasticity of substitution between goods, which we use to derive upper and lower bounds for the true elasticity that permit set identification regardless of the correlation between demand and supply shocks.

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Document Object Identifier (DOI): 10.3386/w22479

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