Regressor Dimension Reduction with Economic Constraints: The Example of Demand Systems with Many Goods

Stefan Hoderlein and Arthur Lewbel

No 668, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: Microeconomic theory often yields models with multiple nonlinear equations, nonseparable unobservables, nonlinear cross equation restrictions, and many potentially multicollinear 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 de- mand functions that are nonseparable in unobservables. The standard method of achieving dimension reduction in demand systems is to impose strong, empirically questionable economic restrictions like separability. In contrast, the validity of statistical methods of dimension reduction like principal components have not hitherto been studied in contexts like these. We derive the restrictions implied by utility maximization on dimension reduced de- mand 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.

Keywords: Demand System; Dimension Reduction; Marshallian demands; Separability; Testing Rationality; Nonparametric; Gasoline prices. (search for similar items in EconPapers)
JEL-codes: C14 C30 C43 D12 (search for similar items in EconPapers)
Date: 2007-06-13, Revised 2011-02-23
References: Add references at CitEc
Citations:

Downloads: (external link)
http://fmwww.bc.edu/EC-P/wp668.pdf main text (application/pdf)

Related works:
Journal Article: REGRESSOR DIMENSION REDUCTION WITH ECONOMIC CONSTRAINTS: THE EXAMPLE OF DEMAND SYSTEMS WITH MANY GOODS (2012)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:boc:bocoec:668

Access Statistics for this paper

More papers in Boston College Working Papers in Economics from Boston College Department of Economics Boston College, 140 Commonwealth Avenue, Chestnut Hill MA 02467 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Christopher F Baum ().