Essays on functional coefficient models

This dissertation is composed of three essays on functional coefficient models (also referred to as varying-coefficient models) in the time series context. The first essay proposes two estimators for a functional coefficient model with discontinuities in the coefficient functions. One is based on the weighted residual mean squared error, which works well only if the conditional error variance is continuous. The other estimator is based on the local Wald test statistics which is applicable even if the conditional error variance contains discontinuities. In the second essay, we introduce a new model – the semiparametric transition model, and propose an iterative estimation procedure which is based on the straightforward application of (local) least squares. Simulations demonstrate that the proposed estimation provides precise estimates for many types of transition functions. The third essay proposes an estimator for a functional coefficient model with endogenous variables. In contrast to the existing functional coefficient IV literature, our estimator is adapted to the case that coefficients are functions of an endogenous variable. To illustrate the utility of our approach, we provide an empirical example based on the relationship among the hourly wage rate, education level, and work experience.