Estimating restricted structural change models

This paper considers issues related to multiple structural changes, occurring at unknown dates, in the linear regression model when restrictions are imposed on the parameters. This includes, for example, the important special case where different nonadjacent regimes are the same. The estimates are constructed as global minimizers of the restricted sum of squared residuals and we provide an extension of the algorithm discussed in Bai and Perron [2003b, Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18, 1-22] to efficiently compute them. We show that the estimates of the break dates have the same asymptotic properties with or without the restrictions imposed; that is, in large samples, there is no efficiency gain from imposing valid restrictions as far as the estimates of the break dates are concerned. Of course, efficiency gains occur for the other parameters of the model. Simulations show that in small samples, all parameters are more efficiently estimated using the restrictions. We also consider tests of the null hypothesis of no structural change. These are also more powerful when the restrictions are imposed. A Gauss code for all the procedures discussed in this paper is available from the authors.