Testing for random individual and time effects using unbalanced panel data

This paper considers the problem of jointly testing for random individual a nd time effects using incomplete panel data. Standardized versions of the o ne-sided Lagrange Multiplier and the Local Mean Most Powerful tests are fou nd to have better asymptotic critical value approximations than the corresp onding nonstandardized statistics. This confirms similar results obtained f or the unbalanced one-way error component model by Moulton and Randolph (19 89). In cases where at least one of the variance components is close to zer o, the Gourieroux, Holly, and Monfort (1982) test is recommended. This repl aces the negative Lagrange Multiplier corresponding to that component by ze ro and is found to perform well in Monte Carlo experiments. All the tests c onsidered have larger power as the number of individuals (N) in the panel a nd/or the variance components increase. In fact, for typical labor or consu mer panels with large N, our Monte Carlo results show that the power of the se tests is one except for cases where the variance components comprise les s than 10 percent of the total variance. These tests are illustrated using two empirical examples.