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ANALYZING THE RANDOM COEFFICIENT MODELNONPARAMETRICALLY

Published online by Cambridge University Press:  26 October 2009

Stefan Hoderlein ,
Jussi Klemelä  and
Enno Mammen
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Abstract

Linearity in a causal relationship between a dependentvariable and a set of regressors is a commonassumption throughout economics. In this paper weconsider the case when the coefficients in thisrelationship are random and distributedindependently from the regressors. Our aim is toidentify and estimate the distribution of thecoefficients nonparametrically. We propose akernel-based estimator for the joint probabilitydensity of the coefficients. Although this estimatorshares certain features with standard nonparametrickernel density estimators, it also differs in someimportant characteristics that are due to the verydifferent setup we are considering. Mostimportantly, the kernel is nonstandard and derivesfrom the theory of Radon transforms. Consequently,we call our estimator the Radon transform estimator(RTE). We establish the large sample behavior ofthis estimator—in particular, rate optimality andasymptotic distribution. In addition, we extend thebasic model to cover extensions, includingendogenous regressors and additional controls.Finally, we analyze the properties of the estimatorin finite samples by a simulation study, as well asan application to consumer demand using Britishhousehold data.

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Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 3 , June 2010 , pp. 804 - 837
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

We have received helpful comments from seminarparticipants in Copenhagen, Göttingen, Frankfurt,Mannheim, Oberwolfach, UCL, Northwestern, and Wien(ESEM), as well as from Jim Heckman and ArthurLewbel. We would like to thank two referees for avery careful check of the paper and for veryhelpful suggestions. In particular, we would liketo thank one of the referees for comments andhints to references on spherical kernel densityestimators. Financial support by LandesstiftungBaden-Württemberg's Eliteförderungsprogramm isgratefully acknowledged.

References

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