Rank-Based Optimal Tests for Random Effects in Panel Data

cCentER, Tilburg University, and dDépartement de Mathématique, Universite ́ Libre de Bruxelles. We consider the problem of detecting unobserved heterogeneity, that is, the problem of testing the absence of random individual effects in a n × T panel. We establish a local asymptotic normality property (with respect to intercept, regression coefficient, scale parameter σ2, and the parameter of interest σ2u, for fixed density f1), when n tend to infinity and T is fixed. This result allows for developing asymptotically optimal parametric procedures for σ2u under spec-ified densitiesf1. The pseudo-Gaussian tests (optimal under Gaussian densities but valid under non-Gaussian ones) are investigated. Rank-based versions of the optimal parametric procedures are also provided. These tests are locally asymp-totically optimal at correctly specified innovation densities. The limiting distri-bution of our test statistics is obtained both under the null and under sequences of contiguous alternatives. A local asymptotic linearity property is establishe