Testing a Class of Semi- or Nonparametric Conditional Moment Restriction Models using Series Methods

Jesper R.-V. Soerensen
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Jesper R.-V. Soerensen: Department of Economics, University of Copenhagen, Denmark

No 20-04, Discussion Papers from University of Copenhagen. Department of Economics

Abstract: This paper proposes a new test for a class of conditional moment restrictions whose parameterization involves unknown, unrestricted conditional expectation functions. Examples of such conditional moment restrictions are conditional mean independence (leading to a nonparametric significance test) and conditional homoskedasticity (with an otherwise unrestricted conditional mean) and also arise from models of single-agent discrete choice under uncertainty and static games of incomplete information. The proposed test may be viewed as a semi-/nonparametric extension of the Bierens (1982) 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 resulting test is shown to be asymptotically correctly sized and consistent. A simulation study applies the procedure to test the specification of a two-player, binary-action static game of incomplete information, treating equilibrium beliefs as nonparametric conditional expectations.

Keywords: Omnibus specification testing; Semiparametric; Conditional moment restrictions; Conditional expectation; Series estimation; Bootstrap; Cramér-von Mises distance. (search for similar items in EconPapers)
JEL-codes: C01 C14 (search for similar items in EconPapers)
Date: 2020-08
New Economics Papers: this item is included in nep-ecm and nep-ore
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