Abstract
In this paper, we show that the cointegration testing procedure of Binder et al. (Econom Theory 21:795–837, 2005) for Panel Vector Autoregressive model of order 1, PVAR(1) is not valid due to the singularity of the hessian matrix. As an alternative we propose a method of moments based procedure using the rank test of Kleibergen and Paap (J Econom 133:97–126, 2006) for a fixed number of time series observations. The test is shown to be applicable in situations with time-series heteroscedasticity and unbalanced data. The novelty of our approach is that in the construction of the test we exploit the “weakness” of the Anderson and Hsiao (J Econom 18:47–82, 1982) moment conditions. The finite-sample performance of the proposed test statistic is investigated using simulated data. The results indicate that for most scenarios the method has good statistical properties. The proposed test provides little statistical evidence of cointegration in the employment data of Alonso-Borrego and Arellano (J Bus Econ Stat 17:36–49, 1999).
Highlights
In this paper, we consider the cointegration testing problem for Panel VAR model of order 1 with a fixed time dimension
For lower values of N the test tends to be undersized for T = 3 and oversized for T = 7.27 In the effect stationary case τ does not play substantial role and only affects the V matrix, but we can still observe that higher value of τ is associated with slightly lower power
We study the properties of the standard Anderson and Hsiao (1982) moment conditions in a PVAR(1) for cointegrated processes
Summary
We consider the cointegration testing problem for Panel VAR model of order 1 with a fixed time dimension. We extend that result to multivariate setting and argue that the cointegration testing procedure of Binder et al (2005) is not valid due to the singularity of the corresponding expected hessian matrix. To the best of our knowledge, in the fixed T dynamic panel data (DPD) literature no feasible method of moments (or least-squares) alternative to likelihood based cointegration testing procedures is available. This procedure cannot provide inference that is uniform over the parameter space, as the asymptotic distribution of the test depends on the properties of the initial condition. In the Monte Carlo section of this paper, we investigate the finite sample properties of the proposed procedure. Rank-based cointegration testing procedure is formally introduced in Sect.
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