A two step procedure for testing partial parameter stability in cointegrated regression models
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Citation (published version)Mohitosh Kejriwal & Pierre Perron & Xuewen Yu, 2020. "A Two Step Procedure for Testing Partial Parameter Stability in Cointegrated Regression Models," Boston University - Department of Economics - Working Papers Series WP2020-011, Boston University - Department of Economics.
Kejriwal and Perron (2010, KP) provided a comprehensive treatment for the problem of testing multiple structural changes in cointegrated regression models. A variety of models were considered depending on whether all regression coefficients are allowed to change (pure structural change) or a subset of the coefficients is held fixed (partial structural change). In this note, we first show that the limit distributions of the test statistics in the latter case are not invariant to changes in the coefficients not being tested; in fact, they diverge as the sample size increases. To address this issue, we propose a simple two step procedure to test for partial parameter stability. The first entails the application of a joint test of stability for all coefficients as in KP. Upon a rejection, the second conducts a stability test on the subset of coefficients of interest while allowing the other coefficients to change at the estimated breakpoints. Its limit distribution is standard chi-square. The relevant asymptotic theory is provided along with simulations that illustrates the usefulness of the procedure in finite samples.