GMM estimation of autoregressive roots near unity with panel data

Hyungsik Roger Moon, Peter C.B. Phillips

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

This paper investigates a generalized method of moments (GMM) approach to the estimation of autoregressive roots near unity with panel data and incidental deterministic trends. Such models arise in empirical econometric studies of firm size and in dynamic panel data modeling with weak instruments. The two moment conditions in the GMM approach 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 takes 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 √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.

Original languageEnglish
Pages (from-to)467-522
Number of pages56
JournalEconometrica
Volume72
Issue number2
DOIs
Publication statusPublished - 2004 Mar 1

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Panel data
Generalized method of moments
Moment conditions
Generalized method of moments estimator
GLS detrending
Deterministic trend
Firm size
Convergence rate
Weak instruments
Dynamic panel data
Local alternatives
Unit root
Limiting distribution
Econometrics
Bias correction
Data modeling
Nuisance parameter
Panel unit root

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Cite this

Moon, Hyungsik Roger ; Phillips, Peter C.B. / GMM estimation of autoregressive roots near unity with panel data. In: Econometrica. 2004 ; Vol. 72, No. 2. pp. 467-522.
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GMM estimation of autoregressive roots near unity with panel data. / Moon, Hyungsik Roger; Phillips, Peter C.B.

In: Econometrica, Vol. 72, No. 2, 01.03.2004, p. 467-522.

Research output: Contribution to journalArticle

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