Intercept Homogeneity Test for Fixed Effect Models under Cross-sectional Dependence: Some Insights

This paper develops a test for intercept homogeneity in fixed-effects one-way error component models assuming slope homogeneity. We show that the proposed test works equally well when intercepts are assumed to be either fixed (non-stochastic) or random. Moreover, this test can also be used to test for random effect vs. fixed effect although in the restrictive sense. The test is shown to be robust to cross-sectional dependence; for both weak and strong dependence. The proposed test is shown to have a standard χ2 limiting distribution and is free from nuisance parameters under the null hypothesis. Monte Carlo simulations also show that the proposed test delivers more accurate finite sample sizes than existing tests for various combinations of N and T. Simulation study shows that F-test is either over-sized or under-sized depending on the pattern of cross-sectional dependence. The performance of Hausman test (1978), on the other hand, is quite unstable across various DGPs; and empirical size varies from 0% to the nominal sizes depending on the structure of error variance-covariance matrix. The power of the proposed test outperforms the other two tests. It is worthwhile to mention that the power of our proposed test increases with T in contrast to that of Hausman test which is known to have no power as T→∞. An empirical illustration to examine the Kuznets’ U curve hypothesis with balanced panel data of Indian states is also provided. This empirical illustration points out the efficacy and the necessity of our robust test.