Price Dimension Reduction in Demand Systems With Many Goods
Estimation of demand systems with many goods is empirically difficult because demand functions depend, flexibly and usually nonlinearly, on the prices of all goods. The standard solution is to impose strong, empirically questionable behavioral restrictions on price elasticities via separability. This paper proposes an alternative based on applying statistical dimension reduction methods to the price vector, and deriving the resulting restrictions on demand functions that remain due to Slutsky symmetry and other implications of utility maximization. The results permit estimation of the effects of income and of prices of some goods on the demand functions for every good without imposing any separability. We illustrate the results by reporting estimates of the effects of gasoline prices on the demands for many goods.
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