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This paper considers the unbalanced two-way error component model studied by Wansbeek and Kapteyn (1989). Alternative analysis of variance (ANOVA), minimum norm quadratic unbiased and restricted maximum likelihood (REML) estimation procedures are proposed. The mean squared error performance of these estimators are compared using Monte Carlo experiments. Results show that for the estimates of the variance components, the computationally more demanding maximum likelihood (ML) and minimum variance quadratic unbiased (MIVQUE) estimators are recommended, especially if the unbalanced pattern is severe. However, focusing on the regression coefficient estimates, the simple ANOVA methods perform just as well as the computationally demanding ML and MIVQUE methods and are recommended.

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This paper derives several Lagrange Multiplier tests for the unbalanced nested error component model. Economic data with a natural nested grouping include firms grouped by industry; or students grouped by schools. The LM tests derived include the joint test for both effects as well as the test for one effect conditional on the presence of the other. The paper also derives the standardized versions of these tests, their asymptotic locally mean most powerful version as well as their robust to local misspecification version. Monte Carlo experiments are conducted to study the performance of these LM tests.Panel data, Nested error component, Unbalanced data, LM tests,

a b s t r a c tThis paper considers a panel data regression model with heteroskedastic as well as serially correlated disturbances, and derives a joint LM test for homoskedasticity and no first order serial correlation. The restricted model is the standard random individual error component model. It also derives a conditional LM test for homoskedasticity given serial correlation, as well as, a conditional LM test for no first order serial correlation given heteroskedasticity, all in the context of a random effects panel data model. Monte Carlo results show that these tests along with their likelihood ratio alternatives have good size and power under various forms of heteroskedasticity including exponential and quadratic functional forms.