Specification tests for time-varying coefficient models

Time-varying coefficient models have been widely used to characterize changing relationships among economic and financial variables. The existing literature usually specifies the time-varying coefficient vector as a stationary stochastic process, a deterministic function of time, and a unit root process, respectively. In this paper, we propose two tests to distinguish these three specifications. Both test statistics follow asymptotic normal distributions under the respective null hypotheses and diverge to infinity in probability under the corresponding alternatives. To improve the finite sample performance of the tests, we propose a dependent wild bootstrap to obtain the bootstrap critical value (or P-value) and establish its asymptotic validity. Simulation studies show that our bootstrap-based tests perform reasonably well in finite samples. We apply the proposed tests to the time-varying specifications of the equity return’s predictive model, the U.S. Taylor rule, and inflation persistence, respectively. The results suggest that a unit root process is favored for the first application, whereas a deterministic function of time should be adopted for the latter two applications.