Inference regarding multiple structural changes in linear models estimated via two stage least squares

Bai and Perron(1998) develop methods that are designed to test for structural stability with an unknown number of break points in the sample. Their analysis is in the context of linear regression models estimated via Ordinary Least Squares(OLS). We extend Bai and Perron's framework for multiple break testing to linear models via Two Stage Least Squares(2SLS). Within our framework, the break points are estimated simultaneously with the regression parameters via minimization of the residual sum of squares on the second step of the 2SLS estimation. We establish the consistency of the resulting estimated break point fractions and obtain the standard convergence rate of break fraction estimators. Based on that convergence rate we derive the limiting distribution of the break point estimators. We prove that the break point estimator have the same limiting distribution of the arg max of two sided Brownian motion process, which is the same distribution considered by Bai and Perron(1998). We also show that various F-statistics for structural instability based on the 2SLS estimator have the same limiting distribution as the analogous statistics for OLS considered by Bai and Perron(1998). This allows us to extend Bai and Perron's(1998) sequential procedure for selecting the number of break points to the 2SLS setting. Simulation experiment and application to financial market has been implemented.