Monitoring Parameter Constancy with Endogenous Regressors

This paper proposes monitoring tests for parameter change in linear regression models with endogenous regressors. We consider a CUSUM-type test based on the instrumental variable (IV) estimation, as the IV method is standard for models with endogenous regressors. In addition, we propose a test based on the residuals from the least squares (LS) estimation. We show that for a given boundary function, both tests have the same limiting distribution under the null hypothesis, whereas their powers are different. In particular, when a structural change occurs early in a monitoring period, the test based on the LS method tends to detect it more rapidly than that based on the IV method. We apply our methods to investigate the Japanese Phillips curve and show that the LS based test performs well to detect a change in 2007, while neither test finds evidence of a change after 2013.23, [12] p