Identification testing via sample splitting -- an application to Structural VAR models

Abstract: In this article, a novel identification test is proposed, which can be applied to parameteric models such as Mixture of Normal (MN) distributions, Markow Switching(MS), or Structural Autoregressive (SVAR) models. In the approach, it is assumed that model parameters are identified under the null whereas under the alternative they are not identified. Thanks to the setting, the Maximum Likelihood (ML) estimator preserves its properties under the null hypothesis. The proposed test is based on a comparison of two consistent estimators based on independent subsamples of the data set. A Wald type statistic is proposed which has a typical $\chi^2$ distribution. Finally, the method is adjusted to test if the heteroscedasticity assumption is sufficient to identify parameters of SVAR model. Its properties are evaluated with a Monte Carlo experiment, which allows non Gaussian distribution of errors and mis-specified VAR order. They indicate that the test has an asymptotically correct size. Moreover, outcomes show that the power of the test makes it suitable for empirical applications.