Bayesian Bandwidth Estimation in Nonparametric Time-Varying Coefficient Models

Bandwidth plays an important role in determining the performance of nonparametric estimators, such as the local constant estimator. In this paper, we propose a Bayesian approach to bandwidth estimation for local constant estimators of time–varying coefficients in time series models. We establish a large sample theory for the proposed bandwidth estimator and Bayesian estimators of the unknown parameters involved in the error density. A Monte Carlo simulation study shows that (i) the proposed Bayesian estimators for bandwidth and parameters in the error density have satisfactory finite sample performance; and (ii) our proposed Bayesian approach achieves better performance in estimating the bandwidths than the normal reference rule and cross–validation. Moreover, we apply our proposed Bayesian bandwidth estimation method for the time–varying coefficient models that explain Okun’s law and the relationship between consumption growth and income growth in the US. For each model, we also provide calibrated parametric forms of the time–varying coefficients.