Practical Steps to Improve Specification Testing

Testing of null hypotheses about model parameters, with a dichotomous choice of reject or not, has come under heavy fire from many quarters of late, but the same attention has not been paid to specification tests. We outline a framework for improving specification tests that accepts the dichotomous choice of rejecting a model or not in a very small class of cases (where results are entirely uninterpretable upon rejecting the null, as in the case of underidentification), but argues for more informative testing in most cases. The Arellano (1993) version of Hausman’s (1978) specification test is one example where results can be more informative. We also provide a novel example of more informative testing in the case of White’s test of heteroskedasticity. In general, we argue that the researcher should generically not reject a model based on misspecification tests, but should describe the sensitivity of estimation or inference to potential violations of assumptions using more informative specification tests.