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NEYMAN’S C(α) TEST FOR UNOBSERVED HETEROGENEITY

Published online by Cambridge University Press:  01 September 2015

Jiaying Gu
Jiaying Gu*
Affiliation:
University of Illinois at Urbana-Champaign
*
*Address correspondence to Jiaying Gu, Department of Economics, University of Illinois at Urbana-Champaign, 214 David Kinley Hall, 1407 W. Gregory Dr., Urbana, Illinois 61801, MC-707, USA; e-mail: gu17@illinois.edu.
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Abstract

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A unified framework is proposed for tests of unobserved heterogeneity in parametric statistic models based on Neyman’s C(α) approach. Such tests are irregular in the sense that the first order derivative of the log likelihood with respect to the heterogeneity parameter is identically zero, and consequently the conventional Fisher information about the parameter is zero. Nevertheless, local asymptotic optimality of the C(α) tests can be established via LeCam’s differentiability in quadratic mean and the limit experiment approach. This leads to local alternatives of order n −1/4 . The scalar case result is already familiar from existing literature and we extend it to the multidimensional case. The new framework reveals that certain regularity conditions commonly employed in earlier developments are unnecessary, i.e. the symmetry or third moment condition imposed on the heterogeneity distribution. Additionally, the limit experiment for the multidimensional case suggests modifications on existing tests for slope heterogeneity in cross sectional and panel data models that lead to power improvement. Since the C(α) framework is not restricted to the parametric model and the test statistics do not depend on the particular choice of the heterogeneity distribution, it is useful for a broad range of applications for testing parametric heterogeneity.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 6 , December 2016, pp. 1483 - 1522
Copyright
Copyright © Cambridge University Press 2015 

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