Tests for the error component model in the presence of local misspecification

It is well known that most of the standard specification tests are not valid when the alternative hypothesis is misspecified. This is particularly true in the error component model, when one tests for either random effects or serial correlation without taking account of the presence of the other effect. In this paper we study the size and power of the standard Rao's score tests analytically and by simulation when the data are contaminated by local misspecification. These tests are adversely affected under misspecification. We suggest simple procedures to test for random effects (or serial correlation) in the presence of local serial correlation (or random effects), and these tests require ordinary least-squares residuals only. Our Monte Carlo results demonstrate that the suggested tests have good finite sample properties for local misspecification, and in some cases even for far distant misspecification. Our tests are also capable of detecting the right direction of the departure from the null hypothesis. We also provide some empirical illustrations to highlight the usefulness of our tests.