Test for the Error Component Model in the Presence of Local Misspecification

It is well known that most of the standard speci¯cation tests are not valid when the alternative hypothesis is misspeci¯ed. This is particularly true in the error component model, when one tests for either random e®ects or serial correlation without taking account of the presence of the other e®ect. In this paper we study the size and power of the standard Rao's score tests analytically and by simulation when the data is contaminated by local misspeci¯cation. These tests are adversely a®ected under misspeci¯cation. We suggest simple procedures to test for random e®ects (or serial correlation) in the presence of local serial correlation (or random e®ects), and these tests require ordinary least squares residuals only. Our Monte Carlo results demonstrate that the suggested tests have good ¯nite sample properties for local misspeci¯cation, and in some cases even for far distant misspeci¯cation. 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.