The distance decay effect and spatial reach of spillovers

Journal of Geographical Systems (2024) 26:265–289 https://doi.org/10.1007/s10109-024-00440-5 ORIGINAL ARTICLE The distance decay effect and spatial reach of spillovers J. Paul Elhorst1 · Ioanna Tziolas1 · Chang Tan1 · Petros Milionis1 Received: 31 March 2023 / Accepted: 6 April 2024 / Published online: 18 May 2024 © The Author(s) 2024 Abstract This paper quantifies and graphically illustrates the distance decay effect and spatial reach of spillover effects derived from a spatial Durbin (SD) model with parameterized spatial weight matrices. Building on attributes of the concept of spatial autocorrelation developed by Arthur Getis, we adopt a distance-based negative exponential spatial weight matrix and parameterize it by a decay parameter that is different for each spatial lag in this model, both of the regressand and of all regressors. The quantification and illustration are applied to the spatially augmented neoclassical growth framework, which we estimate using data for 266 NUTS-2 regions in the EU over the period 2000–2018. We find distance decay parameters ranging from 0.233 to 2.224 and spatial reaches ranging from 700 to more than 1500 km for the different growth determinants in this model. These wide ranges highlight the restrictiveness of the conventional SD model based on one common spatial weight matrix for all spatial lags. Keywords Regional economic growth · Growth spillovers · Regional proximity · Distance decay JEL Classification C21 · C23 · O47 · R12 * J. Paul Elhorst Ioanna Tziolas Chang Tan Petros Milionis 1 Department of Economics, Econometrics and Finance, Faculty of Economics and Business, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands 13 Vol.:(0123456789) 266 J. P. Elhorst et al. 1 Introduction As the world economy becomes increasingly integrated, there is growing evidence that economic growth is correlated across space. This pattern is clearly visible in the data, and although it is increasingly recognized in empirical studies (Moreno and Trehan 1997; López-Bazo et al. 2004; Ertur and Koch 2007; Ramajo et al. 2008), there is no consensus in the literature on the magnitude and the spatial reach of observed growth spillovers. This lack of consensus is highlighted in a recent article by Rosenthal and Strange (2020) whose title raises the pressing question: “How close is close.” Their answer draws on a range of research on agglomeration effects in economics and regional science, yet without providing a clear research methodology on how to estimate spillover effects. To address this question, we propose a novel approach to determine growth spillovers within the spatially augmented neoclassical growth framework. This approach draws on the work of Arthur Getis regarding the concept of spatial autocorrelation, which we “translate” into present-day spatial econometrics, and the methodology of Tan (2023) to parameterize the spatial weight matrix with a different parameter for each determinant that captures the rate at which interactions between economies decay in terms of distance. Our contribution is to introduce a novel approach to quantify and visualize the spillover effects of each determinant based on distance, while considering the uncertainty associated with the parameter estimates, including the distance decay parameter that defines the accompanying spatial weight matrix. We illustrate the power of this approach by estimating spillover effects in GDP per capita growth for EU NUTS-2 regions over the period from 2000 to 2018. There is extensive work in the literature that has tried to estimate the magnitude of growth spillovers. Early work on spillovers used regional dummies (Easterly and Levine 1997) or control variables that are averaged across nearby countries (Ades and Chua 1997). Moreno and Trehan (1997) are among the first to use a spatial econometric model to empirically test whether growth spillovers work through the regressand, the error term and/or the income regressor. At that time, they labeled the coefficient of the spatially lagged regressand, which reflects per capita growth in neighboring economies, as a spillover effect. More recent work has used various approaches to measure spillovers at the sub-national level and analyze their spatial reach (Bottazzi and Peri 2003; Funke and Niebuhr 2005; Rodríguez-Pose and Crescenzi 2008). There is also an extensive body of literature on spillovers between urban areas (Glaeser et al. 1992; Henderson et al. 1995). While this literature has provided empirical evidence regarding the existence of growth spillovers, the results regarding their magnitude are inconclusive (Funke and Niebuhr 2005; Ramajo et al. 2008; Benos et al. 2015; Márquez et al. 2015). One reason is that these authors have either used indirect ways to account for growth spillovers, such as the trade-off between national growth and greater regional equality in economic outcomes (Gardiner et al. 2011), or have attempted to estimate growth spillovers directly, using econometric specifications and spatial weight matrices which impose restrictions on the extent of distance decay and the corresponding spatial reach of spillovers. 13 The distance decay effect and spatial reach of spillovers 267 Our analysis avoids these problems by linking the magnitude of growth spillovers to distance and allowing the rate of distance decay to differ per growth determinant. We illustrate the indirect or spillover effects of each growth in terms of distance, slope, magnitude and level of significance. In addition to the existence and importance of spillover effects consistent with previous studies, our findings confirm substantial variations in their magnitudes due to differences in the rate of distance decay between growth determinants. These findings complement previous studies in the literature on regional economic growth based on the spatially augmented versions of the neoclassical growth model (López-Bazo et al. 2004; Ertur and Koch 2007, 2011; Elhorst et al. 2010). The setup of this paper is as follows. In Sect. 2 we link our approach to attributes of the concept of spatial autocorrelation developed by Arthur Getis. In Sect. 3 we present the spatially augmented neoclassical model of economic growth and its empirical model in the form of a spatial Durbin (SD) model that we use for our analysis. In Sect. 4 we introduce the parameterizations of the spatial weight matrices and show their relationship with the direct and spillover effects of the growth determinants in the SD model. In Sect. 5 we describe the data, report and discuss the estimation results, plot the spillover effects for the different growth determinants and examine the robustness of the results to changes in the model specification. Finally, Sect. 6 concludes. 2 Arthur Getis: the concept of spatial autocorrelation In a survey article to the Handbook of Applied Spatial Analysis (Fischer and Getis 2010), Arthur Getis summarizes the developm (...truncated)