Estimation and Inference in Short Panel Vector Autoregressions with Unit Roots and Cointegration

This paper considers estimation and inference in panel vector autoregressions (PVARs) with fixed effects when the time dimension is finite and the cross-sectional dimension is large. A Maximum Likelihood (ML) estimator based on a transformed likelihood function is proposed and shown to be consistent and asymptotically normal irrespective of the unit-root and cointegrating properties of the underlying PVAR model. This transformed framework is also used to derive unit-root and cointegration tests, based on standard chi-squared and normally distributed statistics, in panels with a short time dimension. It is shown that the standard Generalized Method of Moments (GMM) estimator, examined as an alternative to the proposed ML estimator, breaks down if the underlying time series contain unit roots. Also, the extended GMM estimator, using variants of homoskedasticity and stationarity restrictions as suggested in a univariate context, is subject to difficulties. Monte Carlo evidence suggests that the ML estimator and the tests of hypotheses and cointegration that are based on it perform well in small samples in marked contrast to the performance of GMM estimators.