The Limit Distribution of the Estimates in Cointegrated Regression Models with Multiple Structural Changes

This paper studies the problem of estimation and inference in cointegrated regression models with multiple structural changes. Our framework is general enough to incorporate both stationary and integrated regressors. Both pure and partial structural change models are analyzed. We derive the consistency, rate of convergence and the limit distribution of the estimated break fractions. Our conditions are considerably less restrictive than those in Bai, Lumsdaine and Stock (1998) who considered the single break case in a multi-equations system, and permit a wide class of practically relevant models. We show that if the coefficients of the integrated regressors are allowed to change, the estimated break fractions are asymptotically dependent so that confidence intervals need to be constructed jointly. Methods to construct such confidence intervals are discussed. If, however, only the intercept and/or the coefficients of the stationary regressors are allowed to change, the estimates of the break dates are asymptotically independent as in the stationary framework analyzed by Bai and Perron (1998). We also show that our results remain valid, under very weak conditions, when the potential endogeneity of the nonstationary regressors is accounted for via an increasing sequence of leads and lags of their first-differences as additional regressors. Simulation evidence is presented to assess the adequacy of the asymptotic approximations in finite samples.