Cointegration Testing in Panel VAR Models Under Partial Identification and Spatial Dependence

This paper considers the Panel Vector Autoregressive Models of order 1 (PVAR(1)) with possibly spatially dependent error terms. We prove that the cointegration testing procedure of Binder, Hsiao, and Pesaran (2005) is not valid due to the singularity of the corresponding Hessian matrices under pure unit roots or cointegrated processes. As an alternative we propose a simple Method of Moments based cointegration test using the rank test of Kleibergen and Paap (2006) for fixed number of time observations. The test is shown to be robust to time series heteroscedasticity as well as unbalanced panels. The novelty of our approach is that we exploit the "weakness" of the Anderson and Hsiao (1982) moment conditions in the construction of the new test. The finite-sample performance of the proposed test statistic is investigated using the simulated data. The results show that for most scenarios the method performs well in terms of both size and power. The proposed test is applied to employment and wage equations using Spanish firm data of Alonso-Borrego and Arellano (1999) and the results show little evidence for cointegration.