Locally Stationary Quantile Regression for Inflation and Interest Rates

Motivated by the potential time-varying and quantile-specific relation between inflation and interest rates, we propose a locally stationary quantile regression approach to model the inflation and interest rates relation. Large sample theory for estimation and inference of quantile-varying and time-varying coefficients are established. In empirical analysis of inflation and interest rates relation, it is found that the estimated functional coefficients vary with time in a complicated manner. Furthermore, the relation is quantile-specific: not only do the selected orders differ for different quantiles, but also the coefficients corresponding to different quantiles can display completely different patterns.