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.
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Notes
- 1.
In the context of panel (or longitudinal data) a cross-sectional unit i at time point t is indexed by it. We consider a (vector valued) random process \(Y =\{ Y _{n_{it}}\}_{n\in \mathcal{N}}\). For the sake of simplicity, the following considerations refer to a given time period t, as we will not discuss forms of cross-section dependence varying in the time dimension. However, the proposed non-parametric approach allows for such cases, for example spatio-temporal processes by simultaneous smoothing over n = (longitude, latitude, time).
- 2.
The respective goals in those two strands of literature may differ significantly as suggested by the respective discussions of theory and applications in Kauermann, Haupt, and Kaufmann (2012).
- 3.
Employees liable for social security insurance, who have at least 11 years of schooling and a degree.
- 4.
Note that the estimation of Eq. (11) is based on cross-section data, where only information in the initial and final time period is employed. The a priori selection of t = 0 and t = T, respectively, may have a crucial impact on the outcome. We will not discuss such sources of non-robustness in this study.
- 5.
For the sake of brevity we will not discuss issues of neglected heterogeneity induced by spatial association due to spill-over and repercussion effects between German regions here.
- 6.
In the present case of high-skilled employees in German regions the corresponding log t regression reveals no evidence in favor of global convergence on any reasonable significance level.
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Haupt, H., Schnurbus, J. (2015). A Nonparametric Approach to Modeling Cross-Section Dependence in Panel Data: Smart Regions in Germany. In: Stemmler, M., von Eye, A., Wiedermann, W. (eds) Dependent Data in Social Sciences Research. Springer Proceedings in Mathematics & Statistics, vol 145. Springer, Cham. https://doi.org/10.1007/978-3-319-20585-4_15
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