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Faculty of Economics

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Smith, R. J., Hahn, J. and Newey, W. K.

Neglected heterogeneity in moment condition models

Journal of Econometrics

Vol. 178(1) pp. 86-100 (2014)

Abstract: The central concern of this paper is parameter heterogeneity in models specified by a number of unconditional or conditional moment conditions and thereby the provision of a framework for the development of apposite optimal m-tests against its potential presence. We initially consider the unconditional moment restrictions framework. Optimal m-tests against moment condition parameter heterogeneity are derived with the relevant Jacobian matrix obtained in terms of the second order own derivatives of the moment indicator in a leading case. GMM and GEL tests of specification based on generalized information matrix equalities appropriate for moment-based models are described and their relation to optimal m-tests against moment condition parameter heterogeneity examined. A fundamental and important difference is noted between GMM and GEL constructions. The paper is concluded by a generalization of these tests to the conditional moment context and the provision of a limited set of simulation experiments to illustrate the efficacy of the proposed tests.

Keywords: GMM,GEL,Unconditional moments, Conditional moments, Score and LM tests, Information matrix equality

JEL Codes: C13, C30

Author links: Richard Smith  

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