A NOTE ON ESTIMATING AND TESTING FOR MULTIPLE STRUCTURAL CHANGES IN MODELS WITH ENDOGENOUS REGRESSORS VIA 2SLS
为存在内生回归变量的单一方程模型中多个结构变化的估计和检验问题提供了一个简单证明，基于标准假设，将两阶段最小二乘法的第二阶段回归转化为满足Perron和Qu（2006）假设的形式，从而直接得到断点估计的一致性和极限分布等结果。
This note provides a simple proof for the problem of estimating and testing for multiple breaks in a single equation framework with regressors that are endogenous. We show based on standard assumptions about the regressors, instruments, and errors that the second-stage regression of the instrumental variable procedure involves regressors and errors that satisfy all the assumptions in Perron and Qu (2006, Journal of Econometrics 134, 373–399) so that the results about consistency, rate of convergence and limit distributions of the estimates of the break dates, in addition to the limit distributions of the tests, are obtained as simple consequences. The results are obtained within a unified framework for various cases about the nature of the reduced form: stable, no structural changes but time variations in the parameters, structural changes at dates that are common to those of the structural form, and structural changes occurring at arbitrary dates.