Journal Article

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

Arellano, Manuel, Alvarez, Javier

2003

Overview

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.

• Publisher: Blackwell Publishing Ltd,Econometric Society,Blackwell
• Subject: Autoregressive models / Bias / Consistent estimators / Distribution theory / double asymptotics / Econometric models / Econometrics / Economic models / Economic theory / Economics / Errors / Estimates / Estimation bias / Estimators / Exact sciences and technology / Generalized method of moments / Inference from stochastic processes; time series analysis / Infinity / Instrumental variables estimation / Mathematical methods / Mathematics / maximum likelihood / Maximum likelihood estimation / Methodology / Nonparametric inference / Panel data / Parametric inference / Preliminary estimates / Probability and statistics / Property / Random effects / Regression analysis / Sciences and techniques of general use / Simulation / Statistical median / Statistical variance / Statistics / Studies / Time series / Variables / within-groups