Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions
研究了面板AR(1)模型中自回归参数ρ的准极大似然估计方法，证明其在任意初始条件和异方差下仍一致，并分析了估计量的渐近性质与有限样本表现。
In this paper we show that the Quasi ML estimation method yields consistent Random and Fixed Effects estimators for the autoregression parameter ρ in the panel AR(1) model with arbitrary initial conditions and possibly time-series heteroskedasticity even when the error components are drawn from heterogeneous distributions. We investigate both analytically and by means of Monte Carlo simulations the properties of the QML estimators for ρ. The RE(Q)MLE for ρ is asymptotically at least as robust to individual heterogeneity and, when the data are i.i.d. and normal, at least as efficient as the FE(Q)MLE for ρ. Furthermore, the QML estimators for ρ only suffer from a ‘weak moment conditions’ problem when ρ is close to one if the cross-sectional average of the variances of the errors is (almost) constant over time, e.g. under time-series homoskedasticity. However, in this case the QML estimators for ρ are still consistent when ρ is local to or equal to one although they converge to a non-normal possibly asymmetric distribution at a rate that is lower than N 1/2 but at least N1/4. Finally, we study the finite sample properties of two types of estimators for the standard errors of the QML estimators for ρ, and the bounds of QML based confidence intervals for ρ.