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.

翻译：本文提出了一种新颖的框架，用于检验面板数据模型中时变系数之间的斜率异质性。我们的检验不仅能够检测系数函数在所有单元间是否相同，还能确定哪些单元存在差异以及这些差异的位置。我们建立了多尺度检验的渐近有效性。作为所提方法的扩展，我们展示了如何利用结果揭示模型中的潜在分组结构。我们将该方法应用于检验美国货币政策冲击对49个外国经济体及其自身影响的异质性。我们发现存在此类异质性的证据，并讨论了两个分组的聚类结果。