Inference regarding multiple structural changes in linear models with endogenous regressors

This paper considers estimation and inference within a linear model with endogenous regressors and multiple changes in the parameters at unknown times. It is shown that estimation via a Generalized Method of Moments criterion yields inconsistent estimators of the break fractions under reasonable conditions. In contrast, minimization of the Two Stage Least Squares (2SLS) minimand is shown to yield consistent estimators of the break fractions. We further establishthe consistency and asymptotic normality of the 2SLS parameter estimators in this model. We propose and derive the limiting distributions of various tests for structural change, and also propose a method for estimating the number of breaks based on these tests. The analysis covers the cases where the reduced form is either stable or unstable. Simulation evidence validates our methodology in finite samples. The methodology is illustrated via an application to the New Keynesian Phillips curve for the US.