Asymptotic Distribution Theory for Break Point Estimators in Models Estimated via 2SLS

In this article, we present a limiting distribution theory for the break point estimator in a linear regression model with multiple structural breaks obtained by minimizing a Two Stage Least Squares (2SLS) objective function. Our analysis covers both the case in which the reduced form for the endogenous regressors is stable and the case in which it is unstable with multiple structural breaks. For stable reduced forms, we present a limiting distribution theory under two different scenarios: in the case where the parameter change is of fixed magnitude, it is shown that the resulting distribution depends on the distribution of the data and is not of much practical use for inference; in the case where the magnitude of the parameter change shrinks with the sample size, it is shown that the resulting distribution can be used to construct approximate large sample confidence intervals for the break points. For unstable reduced forms, we consider the case where the magnitudes of the parameter changes in both the equation of interest and the reduced forms shrink with the sample size at potentially different rates and not necessarily the same locations in the sample. The resulting limiting distribution theory can be used to construct approximate large sample confidence intervals for the break points. Its usefulness is illustrated via an application to the New Keynesian Phillips curve.