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TESTING A CLASS OF SEMI- OR NONPARAMETRIC CONDITIONAL MOMENT RESTRICTION MODELS USING SERIES METHODS

Published online by Cambridge University Press:  05 December 2022

Jesper Riis-Vestergaard Sørensen Open the ORCID record for Jesper Riis-Vestergaard Sørensen [Opens in a new window]
Jesper Riis-Vestergaard Sørensen*
Affiliation:
University of Copenhagen
*
Address correspondence to Jesper Riis-Vestergaard Sørensen, Department of Economics, University of Copenhagen, Copenhagen, Denmark; e-mail: jrvs@econ.ku.dk.
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Abstract

This paper proposes a new test for a class of conditional moment restrictions (CMRs) whose parameterization involves unknown, unrestricted conditional expectation functions. Motivating examples of such CMRs arise from models of discrete choice under uncertainty including certain static games of incomplete information. The proposed test may be viewed as a semi-/nonparametric extension of the Bierens (1982, Journal of Econometrics 20, 105–134) goodness-of-fit test of a parametric model for the conditional mean. Estimating conditional expectations using series methods and employing a Gaussian multiplier bootstrap to obtain critical values, the test is shown to be asymptotically correctly sized and consistent. Simulation studies indicate good finite-sample properties. In an empirical application, the test is used to study the validity of a game-theoretical model for discount store market entry, treating equilibrium beliefs as nonparametric conditional expectations. The test indicates that Walmart and Kmart entry decisions do not result from a static discrete game of incomplete information with linearly specified profits.

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ARTICLES
Information
Econometric Theory , First View , pp. 1 - 32
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

Parts of this paper derive from my doctoral dissertation, completed under the guidance and encouragement of Denis Chetverikov and Jinyong Hahn. I thank Andres Santos, Rasmus Søndergaard Pedersen, the Editor, and two anonymous referees for highly constructive comments that helped improve this paper. All remaining errors are my own.

References

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