GMM Estimation of Autoregressive Roots Near Unity with Panel Data

Hyungsik Moon () and Peter Phillips

No 1274, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper investigates a generalized method of moments (GMM) approach to the estimation of autoregressive roots near unity with panel data. The two moment conditions studied are obtained by constructing bias corrections to the score functions under OLS and GLS detrending, respectively. It is shown that the moment condition under GLS detrending corresponds to taking the projected score on the Bhattacharya basis, linking the approach to recent work on projected score methods for models with infinite numbers of nuisance parameters (Waterman and Lindsay, 1998). Assuming that the localizing parameter makes a nonpositive value, we establish consistency of the GMM estimator and find its limiting distribution. A notable new finding is that the GMM estimator has convergence rate n^{1/6}, slower than root{n}, when the true localizing parameter is zero (i.e., when there is a panel unit root) and the deterministic trends in the panel are linear. These results, which rely on boundary point asymptotics, point to the continued difficulty of distinguishing unit roots from local alternatives, even when there is an infinity of additional data.

Keywords: Bias; boundary point asymptotics; GMM estimation; local to unity; moment conditions; nuisance parameters; panel data; pooled regression; projected score (search for similar items in EconPapers)
JEL-codes: C22 C23 (search for similar items in EconPapers)
Pages: 54 pages
Date: 2000-09
Note: CFP 1085.
References: Add references at CitEc
Citations: View citations in EconPapers (18)

Published in Econometrica (March 2004), 72(2): 467-522

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Related works:
Journal Article: GMM Estimation of Autoregressive Roots Near Unity with Panel Data (2004)
Working Paper: GMM Estimation of Autoregressive Roots Near Unity with Panel Data (2003)
Working Paper: GMM Estimation of Autoregressive Roots Near Unity with Panel Data (2000)
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