Demand Analysis as an Ill-Posed Inverse Problem with Semiparametric Specification

Stefan Hoderlein and Hajo Holzmann ()
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Hajo Holzmann: Karlsruhe University

No 752, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: In this paper we are concerned with analyzing the behavior of a semiparametric estimator which 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 results characterizing the large sample behavior of such an estimator. In addition, in a Monte Carlo experiment we analyze the finite sample behavior of the proposed estimator. Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages, and the difficulties of an approach which leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between nonparametric instrumental variable models, and the recently emphasized issue of unobserved heterogeneity in structural models.

Keywords: Instrumental variables; Inverse problem; Nonparametric regression, Consumer Demand, Convergence rates (search for similar items in EconPapers)
Date: 2008-08-06
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: DEMAND ANALYSIS AS AN ILL-POSED INVERSE PROBLEM WITH SEMIPARAMETRIC SPECIFICATION (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:boc:bocoec:752

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