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REGRESSOR DIMENSION REDUCTION WITH ECONOMIC CONSTRAINTS: THE EXAMPLE OF DEMAND SYSTEMS WITH MANY GOODS

Published online by Cambridge University Press:  16 August 2012

Stefan Hoderlein  and
Arthur Lewbel
Stefan Hoderlein
Affiliation:
Boston College
Arthur Lewbel*
Affiliation:
Boston College
*
*Address correspondence to Arthur Lewbel, Department of Economics, Boston College, 140 Commonwealth Ave., Chestnut Hill, MA 02467, USA; e-mail: [email protected].
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Abstract

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.

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 5 , October 2012 , pp. 1087 - 1120
Copyright
Copyright © Cambridge University Press 2012

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