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The Time Series and Cross‐Section Asymptotics of Dynamic Panel Data Estimators
Author(s) -
Alvarez Javier,
Arellano Manuel
Publication year - 2003
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00441
Subject(s) - estimator , mathematics , autocorrelation , autoregressive model , asymptotic distribution , infinity , series (stratigraphy) , asymptotic analysis , statistics , combinatorics , mathematical analysis , paleontology , biology
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/(2 N − 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.