ESTIMATION OF AUTOREGRESSIVE ROOTS NEAR UNITY USING PANEL DATA

E s t i m a t i o n of Autoregressive R o o t s near U n i t y using P a n e l D a t a Hyungsik R. M o o n Department of Economics University of California, Santa Barbara Peter C.B. Phillips* Cowles Foundation for Research i n Economics Yale University This Version, July 1999 First Draft, November 1997 Abstract Time series data are often well modelled by using the device of an autore¬ gressive root that is local to unity. Unfortunately, the localizing parameter (c) is not consistently estimable using existing time series econometric techniques and the lack of a consistent estimator complicates inference. This paper devel¬ ops procedures for the estimation of a common localizing parameter using panel data. Pooling information across individuals in a panel aids the identification and estimation of the localising parameter and leads to consistent estimation in simple panel models. However, in the important case of models with con¬ comitant deterministic trends, it is shown that pooled panel estimators of the localising parameter are asymptotically biased. Some techniques are developed to overcome this difficulty and consistent estimators of c in the region c < 0 are developed for panel models with deterministic and stochastic trends. A limit distribution theory is also established and test statistics are constructed for ex¬ ploring interesting hypotheses, like the equivalence of local to unity parameters across subgroups of the population. The methods are applied to the empirically important problem of the eicient extraction of deterministic trends. They are also shown to deliver consistent estimates of distancing parameters in nonsta- tionary panel models where the initial conditions are in the distant past. In the development of the asymptotic theory this paper makes use of both sequential and joint limit approach. An important limitation in the operation of the joint asymptotics which is sometimes needed in our development is the rate condition *The authors thank the Co-Editor, Bruce Hansen, and four anonymous referees for comments on the earlier version of the paper, and Donald Andrews for helpful discussions. Phillips thanks the NSF for research support under Grant Nos. SBR 94-22922 A SBR 97-30295, and Moon gratefully acknowledges financial support from a C.A. Anderson Prize Fellowship. The paper was typed by the authors in Scientific Word 2.5.