Spatio-temporal modelling of economic phenomena in the context of reducing the dimensions of the random field

Elżbieta Szulc

DOI: http://dx.doi.org/10.12775/EiP.2020.023

Abstract


Motivation: Clear spatial diversity and high variability in time of economic phenomena and the fact that they show dependencies in space and time dimensions, as well as the spatio-temporal dependencies, lead to the consideration of the phenomena in terms of random fields. On the other hand, applying methods and tools from the field of multidimensional stochastic processes called random fields is difficult due to the specificity of the economic data, in particular to a low number of the observations in space. Hence, there arises the problem of the reduction of the dimensions (especially the space dimension) of the random fields which define economic phenomena.

Aim: The aim of the paper is to discuss a model that will reflect the structure of spatial connections and dependence in the spatio-temporal process, while reducing the dimension of space as a non-random argument of the random field. As a result, the set of N time series will be analysed. Therefore, we build a multiple-equation model of autoregressive character with a spatial structure of dependence. In the paper we discuss the advantages and cognitive values of such an approach to the study of economic phenomena in spatio-temporal terms.

Results: The empirical example concerns the unemployment rate in Poland across provinces (NUTS2) in the period from January 2011 to April 2019. The data create spatio-temporal series which is the realisation of the two-dimensional random field. The model building strategy is based on a vector autoregressive (VAR) specification, where there are as many time series as the provinces. The study shows that the use of the concept of the conditional, with regard to space dimension, random field simplifies the econometric analysis of the spatio-temporal process under consideration without losing the accuracy of the description of his basic properties.


Keywords


spatio-temporal process; random field; model with spatial structure of dependence

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References


André, M., Dabo-Niang, S., Soubdhan, T., & Ould-Baba, H. (2016). Predictive spatio-temporal model for spatially sparse global solar radiation data. Energy, 111. doi:10.1016/j.energy.2016.06.004.

Anselin, L. (1988). Spatial econometrics: methods and models. Dordrecht: Kluwer Academic.

Arbia, G. (1989). Spatial data configuration in statistical analysis of regional economics and related problems. Dordrecht: Kluwer Academic.

Arbia, G. (2006). Spatial econometrics: statistical foundations and applications to regional convergence. Berlin: Springer.

Arbia, G., & Prucha, I.R. (2013). Editorial. Spatial Economic Analysis, 8(3).

Arbia, G., Espa, G., & Giuliani, D. (2013). Conditional vs. unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms’ distribution in Milan (Italy). Journal of Geographical Systems, 15(1). doi:10.1007/s10109-012-0163-2.

Arbia, G., Espa, G., & Quah, D. (2008). A class of spatial econometric methods in the empirical analysis of clusters of firms in space. Empirical Economics, 34(1). doi:10.1007/s00181-007-0154-1.

Arbia, G., Espa, G., Giuliani, G.D., & Mazzitelli, A. (2010). Detecting the existence of space-time clusters of firms. Regional Science and Urban Economics, 40(5). doi:10.1016/j.regsciurbeco.2009.10.004.

Bennett, J.R. (1979). Spatial time-series analysis: forecasting and control. London: Pion.

Bronars, S.G., & Jansen, D.W. (1987). The geographic distribution of unemployment rates in the U.S.: a spatial-time series analysis. Journal of Econometrics, 36(3). doi:10.1016/0304-4076(87)90002-9.

Case, A.C. (1991). Spatial patterns in household demand. Econometrica, 59(4). doi:10.2307/2938168.

Case, A.C., Rosen, H.S., & Hines, J.R. (1993). Budget spillovers and fiscal policy independence: evidence from the states. Journal of Public Economics, 52(3). doi:10.1016/0047-2727(93)90036-S.

Christakos, G. (2017). Spatiotemporal random fields: theory and applications. Amsterdam: Elsevier.

Cliff, A.D., & Ord, J.K. (1973). Spatial autocorrelation. London: Pion.

Conley, T.G. (1999). GMM estimation with cross sectional dependence. Journal of Econometrics, 92(1). doi:10.1016/s0304-4076(98)00084-0.

Conley, T.G., & Ligon, E.A. (2002). Economic distance and cross-country spillovers. Journal of Economic Growth, 7. doi:10.1023/A:1015676113101.

Conley, T.G., & Topa, G. (2002) Spatio-economic distance and spatial patterns in unemployment. Journal of Applied Econometrics, 17(4). doi:10.1002/jae.670.

Dahl, C.M., & Gonzalez-Rivera, G. (2003a). Identifying nonlinear components by random fields in the US GNP growth: implications for the shape of the business cycle. Studies in Nonlinear Dynamics & Econometrics, 7(1). doi:10.2202/1558-3708.1123.

Dahl, C.M., & Gonzalez-Rivera, G. (2003b). Testing for neglected nonlinearity in regression models: a collection of new tests based on the theory of random fields. Journal of Econometrics, 114(1). doi:10.1016/s0304-4076(02)00222-1.

de Luna, X., & Genton, M.G. (2004). Spatio-temporal autoregressive models for U.S. unemployment rate. In J.P. LeSage, & R.K. Pace (Eds.), Spatial and spatiotemporal econometrics. Amsterdam: Elsevier. doi:10.1016/s0731-9053(04)18009-2.

de Luna, X., & Genton, M.G. (2005). Predictive spatio-temporal models for spatially sparse environmental data. Statistica Sinica, 15(2).

Elhorst, J.P. (2010). Dynamic models in space and time. Geographical Analysis, 33(2). doi:10.1111/j.1538-4632.2001.tb00440.x.

Elhorst, J.P. (2012). Dynamic spatial panels: models, methods, and inferences. Journal of Geographical Systems, 14 (1). doi:10.1007/s10109-011-0158-4.

Elhorst, J.P. (2014). Spatial econometrics: from cross-sectional data to spatial panels. Heidelberg: Springer.

Epperson, B.K. (2000). Spatial and space-time correlations in ecological models. Ecological Modelling, 132(1–2). doi:10.1016/s0304-3800(00)00305-7.

Giacomini, R., & Granger, C.W.J. (2004). Aggregation of space-time processes. Journal of Econometrics, 118(1–2). doi:10.1016/s0304-4076(03)00132-5.

Guyon, X. (1995). Random fields on a network: modelling, statistics and applications. New York: Springer.

Haggett, P., Cliff, A.D., & Frey, A. (1977). Locational analysis in human geography. London: Edward Arnold.

Haining, R. (1990). Spatial data analysis in the social and environmental sciences. Cambridge: Cambridge University Press.

Ippoliti, L., Romagnoli, L., & Arbia, G. (2013). A Gaussian Markov random field approach to convergence analysis. Spatial Statistics, 6. doi:10.1016/j.spasta.2013.07.005.

Jenish, N., & Prucha, I.R. (2009). Central limit theorems and uniform laws of large numbers for arrays of random fields. Journal of Econometrics, 150(1). doi:10.1016/j.jeconom.2009.02.009.

Knopov, P.S. (1999). Markov fields and their applications in economics. Journal of Mathematical Sciences, 97(2). doi:10.1007/bf02366382.

Nummelin, E. (2000). Large deviations of random vector fields with applications to economies. Advances in Applied Mathematics, 24(3). doi:10.1006/aama.1999.0668.

Pfeifer, P.E., & Deutsch, S.J. (1980). A three-stage iterative procedure for space-time modelling. Technometrics, 22(1). doi:10.2307/1268381.

Pietrzak, M.B. (2010). Application of economic distance for the purposes of a spatial analysis of the unemployment rate for Poland. Oeconomia Copernicana, 1(1). doi:10.12775/oec.2010.005.

Przybycin, Z. (1992). Zastosowanie pól losowych w ekonomicznych modelach przestrzennych. Katowice: AE w Katowicach.

Quah, D. (1993). Empirical cross-section dynamics in economic growth. European Economic Review, 37(2–3). doi:10.1016/0014-2921(93)90031-5.

Statistics Poland. (2019). Local data bank. Retrieved 22.06.2019 from https://bdl.stat.gov.pl.

Szulc, E. (2006). Specification of the dynamic model with the spatial structure of connections. Dynamic Econometric Models, 7.

Szulc, E. (2008). Modelowanie dynamicznego procesu ekonomicznego z przestrzenną strukturą zależności. In: J. Pociecha (Ed.), Modelowanie i prognozowanie zjawisk gospodarczych. Kraków: UE w Krakowie.

Topa, G. (2001). Social interactions, local spillovers and unemployment. Review of Economic Studies, 68(2). doi:10.1111/1467-937x.00169.

Vega, S.H., & Elhorst, J.P. (2014). Modelling regional labour market dynamics in space and time. Papers in Regional Science, 93(4). doi:10.1111/pirs.12018.

Zieliński, Z. (2002). Ekonometryczne modele pól losowych: postawienie problemu, podstawowe pojęcia i określenia, wytyczne kierunków badań. In Z. Zieliński, Analiza ekonomicznych procesów stochastycznych: pisma wybrane. Toruń: UMK.








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