A note on testing the nested structure in multivariate regression models

In this article we propose a simple method of identifying, at an earlier stage of analysis, the nested structure among the coefficient matrices in multivariate regression models. When the limiting distribution of the estimators of the coefficient matrices are jointly normal, the Wald type statistics based on the proposed method is asymptotically a chi-squared random variable. A numerical example that arises in cointegration analysis is provided to illustrate the method and a small simulation study is provided to illustrate its effectiveness.