Tests for overidentifying restrictions in Factor-Augmented VAR models

This paper develops tests for overidentifying restrictions in Factor-Augmented Vector Autoregressive (FAVAR) models. The identification of structural shocks in FAVAR can involve infinitely many restrictions as the number of cross sections goes to infinity. Our focus is to test the joint null hypothesis that all the restrictions are satisfied. Conventional tests cannot be used due to the large dimension. We transform the infinite-dimensional problem into a finite-dimensional one by combining the individual statistics across the cross section dimension. We find the limit distribution of our joint test statistic under the null hypothesis and prove that it is consistent against the alternative that a fraction of or all identifying restrictions are violated. The Monte Carlo results show that the joint test statistic has good finite-sample size and power. We implement our tests to an updated version of Stock and Watson's (2005) data set. Our test result is further confirmed by the impulse responses of major macroeconomic variables to the monetary policy shock: the impulse responses based on the specification selected by our test are generally more plausible than those based on the specifications rejected by our test.