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

In this paper, we present a limiting distribution theory for the break point estimator in a linear regression model estimated via Two Stage Least Squares under two different scenarios regarding the magnitude of the parameter change between regimes. First, we consider the case where the parameter change is of fixed magnitude; in this case the resulting distribution depends on distribution of the data and is not of much practical use for inference. Second, we consider the case where the magnitude of the parameter change shrinks with the sample size; in this case, the resulting distribution can be used to construct approximate large sample confidence intervals for the break point. The finite sample performance of these intervals are analyzed in a small simulation study and the intervals are illustrated via an application to the New Keynesian Phillips curve.