Likelihood-Based Inference in Multivariate Panel Cointegration Models

This paper presents a general likelihood-based framework for inference in panel-VAR models with cointegrating restrictions. The cointegrating relations are restricted to each cross-section while the rest of the model is unrestricted. The homogenous restriction of common cointegrating space is also considered. Asymptotic distributions of parameter estimates and the test statistics for the cointegrating rank and the homogenous restriction are derived. The distribution for the cointegrating rank is shown to be the convolution of the standard distribution of the trace statistic and the chi^2 distribution. The homogenous restriction test statistic is chi^2. 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.