Modeling and testing smooth structural changes with endogenous regressors

Modeling and detecting parameter stability of econometric models is a long standing problem. Most existing estimation and testing methods are designed for models without endogeneity. Little attention has been paid to models with endogeneous regressors, which may arise in many scenarios in economics. In this paper, we first consider a time-varying coefficient time series model with potential time-varying endogeneity. A local linear two stage least squared estimation is developed to estimate coefficient functions. The consistency and asymptotic normality of the estimator are derived. Furthermore, a nonparametric test is proposed to check smooth structural changes as well as abrupt structural breaks with possibly unknown change points in regression models with potential endogeneity. The idea is to compare the fitted values of the unrestricted nonparametric time-varying coefficient model and the restricted constant parameter model. The test has an asymptotic N(0,1) distribution and does not require any prior information about the alternatives. A simulation study highlights the merits of the proposed estimator and test. In an application, we estimate the New Keynesian Phillips Curve for the US nonparametrically and find strong evidence against its stability.