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DEMAND ANALYSIS AS AN ILL-POSED INVERSE PROBLEM WITH SEMIPARAMETRIC SPECIFICATION

Published online by Cambridge University Press:  04 November 2010

Stefan Hoderlein  and
Hajo Holzmann
Stefan Hoderlein*
Affiliation:
Brown University
Hajo Holzmann
Affiliation:
Marburg University
*
*Address correspondence to Stefan Hoderlein, Department of Economics, Box B, Providence, RI 02912, USA; e-mail: stefan_hoderlein@yahoo.com.
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Abstract

In this paper we are concerned with analyzing the behavior of a semiparametric estimator that corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to test for conditional normality. More importantly, we then establish how to exploit this knowledge when constructing an estimator, and we derive the large sample behavior of such an estimator. In addition, in a Monte Carlo experiment we analyze its finite sample behavior. Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages and the difficulties of an approach that leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between endogenous nonparametric regression models and the recently emphasized issue of unobserved heterogeneity in structural models.

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Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 3: SPECIAL ISSUE ON INVERSE PROBLEMS IN ECONOMETRICS , June 2011 , pp. 609 - 638
Copyright
Copyright © Cambridge University Press 2011

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