Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions

Kruiniger, H.

Abstract

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.

Citation

Kruiniger, H. (2013). Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions. Journal of Econometrics, 173(2), https://doi.org/10.1016/j.jeconom.2012.11.004

• Journal Article Type: Article
• Publication Date: 2013-04
• Deposit Date: Feb 12, 2013
• Journal: Journal of Econometrics
• Print ISSN: 0304-4076
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 173
• Issue: 2
• DOI: https://doi.org/10.1016/j.jeconom.2012.11.004
• Public URL: https://durham-repository.worktribe.com/output/1466735