Inference in Panel Cointegration Models With Long Panels

Abstract

This article presents a general likelihood-based framework for inference in panel vector autoregressive (VAR) models with cointegration restrictions. The cointegrating relationships are restricted to each cross section while the rest of the model is unrestricted. The homogeneous restriction of common cointegrating space is also considered. Asymptotic distributions of parameter estimators and the test statistics for the cointegrating rank and the homogeneous restriction are derived. The asymptotic distribution for the cointegrating rank is shown to be the convolution of the standard distribution of the trace statistic and the χ2 distribution. The homogeneous restriction test statistic is asymptotically χ2. A Monte Carlo simulation investigates the small-sample properties of the two tests. The empirical size of the test for the cointegrating rank is well above the nominal. A Bartlett-corrected test statistic is shown to have size very close to the nominal. We give an empirical example for a consumption model, including consumption, income, and inflation as well as considering the monetary exchange rate model of Groen and Kleibergen.