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 √ 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.
Moon, Hyungsik Roger and Phillips, Peter C.B., "GMM Estimation of Autoregressive Roots Near Unity with Panel Data" (2000). Cowles Foundation Discussion Papers. 1526.