REGRESSOR DIMENSION REDUCTION WITH ECONOMIC CONSTRAINTS: THE EXAMPLE OF DEMAND SYSTEMS WITH MANY GOODS
研究了在具有非线性方程、不可分离不可观测变量和多重共线性特征的经济模型中，如何应用统计降维技术，并以多商品需求系统为例，推导了效用最大化对降维需求系统的约束，以及结构边际效应的识别和估计。
Microeconomic theory often yields models with multiple nonlinear equations, nonseparable unobservables, nonlinear cross equation restrictions, and many potentially multicolinear covariates. We show how statistical dimension reduction techniques can be applied in models with these features. In particular, we consider estimation of derivatives of average structural functions in large consumer demand systems, which depend nonlinearly on the prices of many goods. Utility maximization imposes nonlinear cross equation constraints including Slutsky symmetry, and preference heterogeneity yields demand functions that are nonseparable in unobservables. The standard method of achieving dimension reduction in demand systems is to impose strong, empirically questionable economic restrictions such as separability. In contrast, the validity of statistical methods of dimension-reduction such as principal components has not hitherto been studied in contexts like these. We derive the restrictions implied by utility maximization on dimension-reduced demand systems and characterize the implications for identification and estimation of structural marginal effects. We illustrate the results by reporting estimates of the effects of gasoline prices on the demands for many goods, without imposing any economic separability assumptions.