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GMM Estimation of Autoregressive Roots Near Unity with Panel Data

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  • Hyungsik Roger Moon

    (University of Southern California)

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 Bhttacharyya 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 non-positive value, we establish consistency of the GMM estimator and find its limiting distribution. A notable new finding is that the GMM estimator is super-consistent (i.e., has convergence rate faster 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.

Suggested Citation

  • Hyungsik Roger Moon, 2000. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometric Society World Congress 2000 Contributed Papers 0913, Econometric Society.
    • Handle: RePEc:ecm:wc2000:0913
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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