Heterogeneous Autoregressions in Short T Panel Data Models

This paper considers a first-order autoregressive panel data model with individual-specific effects and a heterogeneous autoregressive coefficient. It proposes estimators for the moments of the cross-sectional distribution of the autoregressive coefficients, with a focus on the first two moments, assuming a random coefficient model for the autoregressive coefficients without imposing any restrictions on the fixed effects. It is shown that the standard generalized method of moments estimators obtained under homogeneous slopes are biased. The paper also investigates conditions under which the probability distribution of the autoregressive coefficients is identified assuming a categorical distribution with a finite number of categories. Small sample properties of the proposed estimators are investigated by Monte Carlo experiments and compared with alternatives both under homogenous and heterogeneous slopes. The utility of the heterogeneous approach is illustrated in the case of earning dynamics, where a clear upward pattern is obtained in the mean persistence of earnings by the level of educational attainments.