Abstract
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.
Highlights
The random error component model introduced by Balestra and Nerlove (1966) was extended by Lillard and Willis (1978) to include serial correlation in the remainder disturbance term
It could be argued that a more e±cient testing procedure could be based on the estimation of a general model that allows for both serial correlation and random e®ects, and could test the hypothesis of no-serial correlation and no-random e®ects as restrictions on this general model
In this paper we have proposed some simple tests, based on ordinary least squares (OLS) residuals for random e®ects in the presence of serial correlation, and for serial correlation allowing for the presence of random e®ects
Summary
The random error component model introduced by Balestra and Nerlove (1966) was extended by Lillard and Willis (1978) to include serial correlation in the remainder disturbance term. The second case occurs when the alternative is underspecied in that it is a subset of a more general model representing the DGP, i.e., -0 1⁄2 -0: This happens, for example, when both serial correlation and individual e®ects are present, but are tested separately (one at a time). It turns out that the contaminated non-centrality parameter3(»; ±) may increase or decrease the power depending on the conguration of the term »0JÃÁ¢°±: The problem of overtesting occurs when multi-directional joint tests are applied based on an overstated alternative model. RSä has the same asymptotic null distribution as that of RSà based on the correct specication, thereby producing an asymptotically correct size test under locally misspecied model. If this condition is true, RSà is an asymptotically valid test in the local presence of Á
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