Heterogeneous autoregressions in short T panel data models

Abstract

This paper considers a first-order autoregressive (AR) panel data model with individual-specific effects and heterogeneous AR coefficients defined on the interval $(-\mathrm{1,1}]$, thus allowing for some of the individual processes to have unit roots. It proposes estimators for the moments of the cross-sectional distribution of the AR coefficients, assuming a random coefficient model for the AR 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. Small sample properties of the proposed estimators are investigated by Monte Carlo experiments and compared with a number of alternatives, both under homogeneous and heterogeneous slopes. It is found that a simple moment estimator of the mean of heterogeneous AR coefficients performs very well even for moderate sample sizes, but to reliably estimate the variance of AR coefficients, much larger samples are required. It is also required that the true value of this variance is not too close to zero. The utility of the heterogeneous approach is illustrated in the context of earnings dynamics.