The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators

Javier Alvarez and Manuel Arellano ()

Econometrica, 2003, vol. 71, issue 4, pages 1121-1159

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 both T and N tend to infinity. GMM and LIML are consistent and asymptotically equivalent to the WG estimator. When T/N→ 0 the fixed T results for GMM and LIML remain valid, but WG, although consistent, has an asymptotic bias in its asymptotic distribution. When T/N tends 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 as T/N→c>0, despite being consistent for fixed T. Finally, we discuss the properties of a random effects pseudo MLE with unrestricted initial conditions when both T and N tend to infinity. Copyright The Econometric Society 2003.

Date: 2003
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Working Paper: The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators (1998)
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