imat ion of A ut oregressive Root s N ear Unity wit h Panel Dat a

A bst r act This paper invest igates a generalized method of moments (GMM) approach to the est imat ion of autoregressive roots near unity with panel data. The two moment condit ions studied areobtained by const ruct ing bias correct ions to thescore funct ions under OLS and GLS det rending, respect ively. I t is shown that the moment condit ion under GLS det rending corresponds to taking theprojected scoreon the Bhat tacharya basis, linking theapproach to recent work on projected scoremethods for models with inønite numbers of nuisance parameters (Waterman and Lindsay, 1998). Assuming that the localizing parameter takes a nonpositvevalue, weestablish consistency of the GMM est imator and ønd its limit ing dist ribut ion. A notable new ønding is that the GMM est imator has convergence rate ?c slower than I ?c when the t rue localizing parameter is zero (i.e., when there is a panel unit root ) and the determinist ic t rends in the panel are linear. These results, which rely on boundary point asymptot ics, point to the cont inued di• culty of dist inguishing unit roots from local alternat ives, even when there is an inønity of addit ional data.