Estimating and testing structural changes in multivariate regressions

This paper considers issues related to estimation, inference and computation with multiple structural changes occurring at unknown dates in a system of equations. Changes can occur in the regression coefficients and/or the covariance matrix of the errors. We also allow arbitrary restrictions on these parameters, which permits the analysis of partial structural change models, common breaks occurring in all equations, breaks occurring in a subset of equations, etc. The method of estimation is quasi maximum likelihood based on Normal errors. The limiting distributions are obtained under more general assumptions than previous studies. Of special interest is the fact that substantial efficiency gains can be obtained by casting a regression affected by changes in a system even if the other equations are not affected by breaks, provided there is non-zero correlation between the errors. For testing, we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes. Structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present. We propose an algorithm for an efficient procedure to construct the estimates and test statistics. We also introduce a novel locally ordered breaks model, which allows the breaks in different equations to be related yet not occurring at the same dates.