Likelihood Based Inference for amic Panel Data Models

This paper considers maximum likelihood (ML) based inferences for dynamic panel data models. We focus on the analysis of the panel data with a large number of cross-sectional units and a small number of repeated time-series observations for each cross-sectional unit. We examine several different ML estimators and their asymptotic and finite-sample properties. Our major finding is that when data follow unit-root processes, the ML estimators have singular information matrices. This is not a non-identification problem because the ML estimators are still consistent. Nonetheless, the estimators have nonstandard asymptotic distributions and their convergence rates are lower than N1/2. For this reason, the sizes of the Wald unit-root tests are severely distorted even asymptotically, and they reject the unit-root hypothesis too often. However, following Rotnitzky, Cox, Bottai and Robins (2000), we show that likelihood ratio (LR) tests for unit root follow mixtures of chi-square distributions. Our Monte Carlo experiments show that the LR tests are much better sized than the Wald tests, although they tend to slightly over-reject the unit root hypothesis in small samples. It is also shown that the LR tests have good finite-sample power properties