Estimation of autoregressive roots near unity using panel data

Time series data are often well modeled by using the device of an autoregre ssive root that is local to unity. Unfortunately, the localizing parameter (c) is not consistently estimable using existing time series econometric te chniques and the lack of a consistent estimator complicates inference. This paper develops procedures for the estimation of a common localizing parame ter using panel data. Pooling information across individuals in a panel aid s the identification and estimation of the localizing parameter and leads t o consistent estimation in simple panel models. However, in the important c ase of models with concomitant deterministic trends, it is shown that poole d panel estimators of the localizing parameter are asymptotically biased. S ome techniques are developed to overcome this difficulty, and consistent es timators of c in the region c < 0 are developed for panel models with deter ministic and stochastic trends. A limit, distribution theory is also establ ished, and test statistics are constructed for exploring interesting hypoth eses, such as the equivalence of local to unity parameters across subgroups of the population. The methods are applied to the empirically important pr oblem of the efficient extraction of deterministic trends. They are also sh own to deliver consistent estimates of distancing parameters in nonstationa ry panel models where the initial conditions are in the distant past. In th e development of the asymptotic theory this paper makes use of both sequent ial and joint limit approaches. An important limitation in the operation of the joint asymptotics that is sometimes needed in our development is the r ate condition n/T --> 0. So the results in the paper are likely to be most relevant in panels where T is large and n is moderately large.