Testing Weak Exogeneity in Cointegrated System

This paper develops a limiting theory for Wald tests of weak exogeneity in error correction models (ECMs). It is well known that Wald statistics on cointegrated systems may involve nonstandard distribution and nuisance parameters, if $I(1)$ variables are not negligible in the statistics. To overcome this problem we construct a new statistic that takes only the $I(0)$ components of a Wald statistic into account and thus results in a valid $\chi^2$ criterion. Applying this procedure to test weak exogeneity in ECMs we obtain a simple and direct $\chi^2$ test