A nonparametric approach to modeling cross-section dependence in panel data: Smart regions in germany

Abstract

In addition to intuitively plausible dependence structures in the time series dimension, in many applications it is reasonable to assume that there are contagion, spill-over, and repercussion effects among cross-sectional units. Modeling those structures in the systematic part of a panel regression requires both information on the underlying sources that drive the dependence and their respective range. The range allows one to define a neighborhood for each unit, a crucial concept for common methods in spatial statistics and econometrics. Furthermore, specification of a parametric regression function requires knowledge of the specific functional form of the spatial associations. However, lacking information on the sources usually leads to accepting misspecification and to including spatial error component or factor structures. As recent research reveals, the consequences of misspecification in both strategies are troubling in many cases. This paper proposes a data-driven nonparametric method for determining neighborhood as a first step. Second step nonparametric panel regressions have several benefits: (i) they allow one to test for misclassification of cross-sectional units to a wrong neighborhood in the first step; (ii) estimation is accomplished using data beyond the respective neighborhood, thus imposing less structure than parametric methods; (iii) neighborhood/location effects can be directly estimated in analogy to spatial statistics; (iv) no assumptions on functional form are required. The proposed method is illustrated with an empirical analysis of spatio-temporal patterns of high-skilled employees across German regions.