Testing for common breaks in a multiple equations system

Abstract

The issue addressed in this paper is that of testing for common breaks across or within equations. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that some subsets of the parameters (either regression coe cients or elements of the covariance matrix of the errors) share one or more common break dates, with the break dates in the system asymptotically distinct so that each regime is separated by some positive fraction of the sample size. Under the alternative hypothesis, the break dates are not the same and also need not be separated by a positive fraction of the sample size. The test considered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Also of independent interest, we provide results about the consistency and rate of convergence when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as the number of parameters in the model. Simulation results show that the test has good nite sample properties. We also provide an application to various measures of in ation to illustrate its usefulness.