Identification and inference in moments based analysis of linear dynamic panel data models

Abstract

We show that Dif(ference), see Arellano and Bond (1991), Lev(el), see Arellano and Bover (1995) and Blundell and Bond (1998), or the N(on-)L(inear) moment conditions of Ahn and Schmidt (1995) do not separately identify the parameters of a first-order autoregressive panel data model when the autoregressive parameter is close to one and the variance of the initial observations is large. We construct a new set of (robust) moment conditions that identify the autoregressive parameter irrespective of the variance of the initial observations. These robust moment conditions are (non-linear) combinations of the System (Sys) and A(hn-)S(chmidt) moment conditions. We use them to determine the maximal attainable power under the worst case setting which results in a quartic root convergence rate. It is identical for the AS and Sys moment conditions so assuming mean stationarity does not improve power in worst case settings. We compare the maximal attainable power under the worst case setting with the lower envelopes of power curves of different GMM test procedures. These power envelopes show the smallest rejection frequencies of these test procedures. The power envelope of the K(leibergen) L(agrange) M(ultiplier) statistic of Kleibergen (2005) coincides with the maximal attainable power curve under the worst case setting so the KLM statistic is efficient when the autoregressive parameter equals one which it also is for smaller values of the autoregressive parameter. Our results extend to other values of the autoregressive parameter for which identification fails when the variance of the individual specific effects becomes large.