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This research aims to explore the effects and detection methods of model misspecification while using maximum likelihood techniques.

March 1, 1983Econometrica3,758 citations

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Maximum Likelihood Estimation of Misspecified Models

HWHalbert White

Key Points

This research aims to explore the effects and detection methods of model misspecification while using maximum likelihood techniques.
Examined consequences of model misspecification in maximum likelihood estimation.
Utilized quasi-maximum likelihood estimator (QMLE) and information matrix for analysis.
Proposed robust statistical tests for valid inference in misspecified models.
QMLE converges to a well-defined limit but may not be consistent for all parameters.
Standard statistical tests become invalid under misspecification conditions.
Proposed general statistics provide robust methods for drawing inferences.

Abstract

This paper examines the consequences and detection of model misspecification when using maximum likelihood techniques for estimation and inference. The quasi-maximum likelihood estimator (QMLE) converges to a well defined limit, and may or may not be consistent for particular parameters of interest. Standard tests (Wald, Lagrange Multiplier, or Likelihood Ratio) are invalid in the presence of misspecification, but more general statistics are given which allow inferences to be drawn robustly. The properties of the QMLE and the information matrix are exploited to yield several useful tests for model misspecification.

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Maximum Likelihood Estimation of Misspecified Models

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