Multiscale Comparison of Nonparametric Trending Coefficients

This paper proposes a novel framework to test for slope heterogeneity between time-varying coefficients in panel data models. Our test not only allows us to detect whether the coefficient functions are the same across all units or not, but also determines which of them are different and where these differences are located. We establish the asymptotic validity of our multiscale test. As an extension of the proposed procedure, we show how to use the results to uncover latent group structures in the model. We apply our methods to test for heterogeneity in the effect of U.S. monetary shocks on 49 foreign economies and itself. We find evidence that such heterogeneity indeed exists and we discuss the clustering results for two groups.