A Misuse of Specification Tests

TL;DR

This paper critically examines the use of model specification tests like Hausman tests, revealing they often fail to accurately determine estimator validity and that correct model specification does not guarantee unbiased estimation.

Contribution

It demonstrates that local asymptotic properties of tests do not reliably indicate estimator validity, challenging common empirical practices.

Findings

Specification tests cannot reliably detect biased estimators.

Correct model specification is neither necessary nor sufficient for unbiased estimation.

Estimation validity and model correctness are fundamentally distinct issues.

Abstract

Empirical researchers often perform model specification tests, such as Hausman tests and overidentifying restrictions tests, to assess the validity of estimators rather than that of models. This paper examines the effectiveness of such specification pretests in detecting invalid estimators. We analyze the local asymptotic properties of test statistics and estimators and show that locally unbiased specification tests cannot determine whether asymptotically efficient estimators are asymptotically biased. In particular, an estimator may remain valid even when the null hypothesis of correct model specification is false, and it may be invalid even when the null hypothesis is true. The main message of the paper is that correct model specification and valid estimation are distinct issues: correct specification is neither necessary nor sufficient for asymptotically unbiased estimation.