The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators
Javier Alvarez, Manuel Arellano
Econometrica · 2003 · Volume 71 · Issue 4
Abstract
In this paper we derive the asymptotic properties of within groups (WG), GMM, and LIML estimators for an autoregressive model with random effects when bothTandNtend to infinity. GMM and LIML are consistent and asymptotically equivalent to the WG estimator. WhenT/N→ 0 the fixedTresults for GMM and LIML remain valid, but WG, although consistent, has an asymptotic bias in its asymptotic distribution. WhenT/Ntends to a positive constant, the WG, GMM, and LIML estimators exhibit negative asymptotic biases of order 1/T, 1/N, and 1/(2N−T), respectively. In addition, the crude GMM estimator that neglects the autocorrelation in first differenced errors is inconsistent asT/N→c>0, despite being consistent for fixedT. Finally, we discuss the properties of a random effects pseudo MLE with unrestricted initial conditions when bothTandNtend to infinity.
Keywords
Autoregressive models, random effects, panel data, within-groups, generalized method of moments, maximum likelihood, double asymptotics
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