Inference in Cointegrated VAR Systems

This note examines the asymptotic properties of the Wald statistic in vector autoregressions (VAR) that may have unit roots. Within this framework we extend the theoretical results to nonlinear restrictions. As an example we study constraints derived from linear(ized) rational expectations models focusing on the expectations hypothesis using U.S. term structure data. For such cross-equation restrictions the statistic has a nonstandard distribution because the restrictions constrain the row space of the total impact matrix of the VAR. A Monte Carlo study is performed, and we find that the test statistic is somewhat oversized in small samples.