Estimation and Inference in Unstable Nonlinear Least Squares Models (Final)

Abstract

In this thesis, we extend Bai and Perron's (1998, Econometrica, pp. 47-78) method for detecting multiple breaks to nonlinear models. To that end, we consider an unstable univariate nonlinear least squares (NLS) model with a limited number of parameter shifts occurring at unknown dates. In our framework, the break-dates are simultaneously estimated with the parameters via minimization of the residual sum of squares. Using nonlinear asymptotic theory, we derive the asymptotic distributions of both break-point and parameter estimates and propose several instability tests. We also present simulation results that validate our procedure. Our method is useful for estimating and testing nonlinear macroeconomic models with multiple unknown breaks. As an empirical illustration, we explore the relationship between our model and smooth transition models in the context of a US interest rate reaction function. Unlike previous studies, our model can nest nonlinearities and breaks. We provide evidence for at least two breaks while allowing for smooth transition within each regime, before and after a break.