  This paper considers a first-order autoregressive panel data model with
individual-specific effects and heterogeneous autoregressive coefficients
defined on the interval (-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 autoregressive (AR) coefficients, assuming
a random coefficient model for the autoregressive coefficients without imposing
any restrictions on the fixed effects. It is shown 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 case of earnings dynamics.
