An alternative semiparametric model for spatial panel data
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An alternative semiparametric model for spatial panel data Román Mínguez1
· Roberto Basile2
· María Durbán3
Accepted: 20 September 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract We propose a semiparametric P-Spline model to deal with spatial panel data. This model includes a non-parametric spatio-temporal trend, a spatial lag of the dependent variable, and a time series autoregressive noise. Specifically, we consider a spatiotemporal ANOVA model, disaggregating the trend into spatial and temporal main effects, as well as second- and third-order interactions between them. Algorithms based on spatial anisotropic penalties are used to estimate all the parameters in a closed form without the need for multidimensional optimization. Monte Carlo simulations and an empirical analysis of regional unemployment in Italy show that our model represents a valid alternative to parametric methods aimed at disentangling strong and weak cross-sectional dependence when both spatial and temporal heterogeneity are smoothly distributed. Keywords Spatial panel · Spatio-temporal trend · Mixed models · P-splines · PS-ANOVA JEL Classification C33 · C14 · C63
1 Introduction A recent strand of the spatial econometric literature has proposed Spatial Autoregressive Semiparametric Geoadditive Models as a means of simultaneously dealing with different critical issues typically encountered when using spatial economic data; namely, spatial dependence, spatial heterogeneity and unknown functional form (Montero et al. 2012; Basile et al. 2014; Hoshino 2018). This approach combines penalized
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Román Mínguez [email protected]
1
Department of Statistics, University of Castilla-La Mancha, Avenida de los Alfares 44, 16002 Cuenca, Spain
2
Department of Industrial and Information Engineering and Economics, University of L’Aquila, Via Giuseppe Mezzanotte, Localitá Acquasanta 67100, Italy
3
Department of Statistics, University Carlos III of Madrid , Avda Universidad 30, 28911 Leganés, Madrid, Spain
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regression spline (PS) methods (Eilers et al. 2015) with standard spatial autoregressive models (such as SAR, SEM and SDM). An important feature of these models is that they make it possible to include within the same specification: (i) spatial autoregressive terms to capture spatial interaction or network effects; (ii) parametric and nonparametric (smooth) terms to identify nonlinear relationships between the response variable and the covariates; and (iii) a geoadditive term, i.e. a smooth function of the spatial coordinates, to capture a spatial trend effect, that is, to capture spatially autocorrelated unobserved heterogeneity. In this paper, we propose a new alternative model for spatial panel data. This model is based on the P-Spline spatial autoregressive model (PS-SAR), extending it to deal with spatio-temporal data when both a large cross-section and a long time series are available. With this kind of data, it is possible to estimate not only spatial trends, but also spatio-temporal tren
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