Modifiable Areal Unit Problem: the issue of determining the relationship between microparameters and a macroparameter
Abstract
Research background: One of the issues considered by economists such as Tinbergen (1939), Klein (1946), May, (1946), Theil (1965), Pawłowski (1969), Bołt et al. (1985) was to determine the mechanism of transition between the results of microeconomics and the theory of macroeconomics. As part of this research, Pawłowski (1969) raised the problem of establishing the relationship between microparameters and a macroparameter. In the presented article, Pawłowski's problem was expanded to include spatial economic research, where micro-dependencies and spatial macro-dependencies were analysed.
Purpose of the article: The purpose of the article is to establish the relationship between the microparameters set for SGM agricultural macroregions and the macroparameter referring to the whole area of Poland, where the parameters describe the economic dependencies regarding the impact of the size of farms in established region on their technical equipment. In the study, the economic relationships analysed in the case of individual SGM agricultural macroregions were defined as spatial micro-dependencies, and in the case of the entire area of Poland as spatial macro-dependencies.
Methods: The methodological part of the article describes the concepts of Modifiable Areal Unit Problem, causal homogeneity of spatial data, homogeneous system of sets of areal units, area and sub-areas of conclusions. The concepts of micro-dependencies and spatial macro-dependencies are presented. Basic equations allowing to determine the evaluation of the spatial macroparameter as a linear combination of spatial microparameters were also presented.
Findings & Value added: In the first stage of the study, spatial micro-dependencies were identified for subsequent SGM agricultural macroregions. In the second stage of the study, the relationship between spatial microparameters for single macroregions and the spatial macroparameter for Poland was determined. Establishing the relationship allowed to determine the macroparameter estimate for the whole area of Poland.
Keywords
Modifiable Areal Unit Problem, microparameter, macroparameter, micro-dependencies, macro-dependencies
References
- Anselin, L. (1988). Spatial econometrics: method and models. Boston: Kluwer Academic Prespp. DOI: https://doi.org/10.1007/978-94-015-7799-1
View in Google Scholar - Arbia, G. (1988). Spatial data configuration in statistical analysis of regional economics and related problems. Dordrecht: Kluwer Academic Press. DOI: https://doi.org/10.1007/978-94-009-2395-9
View in Google Scholar - Arbia, G. (2006). Spatial econometrics, statistical foundations and applications to regional convergence. Heidelberg: Springer.
View in Google Scholar - Balcerzak, A. P. (2016a). Technological potential of European Economy. Proposition of measurement with application of multiple criteria decision analysis. Montenegrin Journal of Economics, 12(3). doi: 10.14254/1800-5845.2016/12-3/1. DOI: https://doi.org/10.14254/1800-5845.2016/12-3/1
View in Google Scholar - Balcerzak, A. P. (2016b). Multiple-criteria evaluation of quality of human capital in the European Union countries. Economics & Sociology, 9(2). doi: 10.14254/207 1-789X.2016/9-2/1. DOI: https://doi.org/10.14254/2071-789X.2016/9-2/1
View in Google Scholar - Balcerzak, A. P. (2017). Digital economy in Czech Republic, Slovakia and Hungary. Measurement with TOPSIS based on entropy measure for objective weighting. In T. Loster & T. Pavelka (Eds.). The 11th international days of statistics and economics. Conference proceedings. September 8-10, 2016. Prague: Libuse Macakova, Melandrium.
View in Google Scholar - Balcerzak, A. P., & Pietrzak, M. B. (2017). Digital Economy in Visegrad Coutnries. Multiple-criteria decision analysis at Regional Level in the Years 2012 and 2015. Journal of Competitiveness, 9(2). doi: 10.7441/joc.2017.02.01. DOI: https://doi.org/10.7441/joc.2017.02.01
View in Google Scholar - Bivand, R. S. (1984). Regression modeling with spatial dependence: an applica¬tion of some class selection and estimation methods. Geographical Analysis, 16(1). DOI: https://doi.org/10.1111/j.1538-4632.1984.tb00798.x
View in Google Scholar - Bal-Domańska, B. (2016). The impact of economic crisis on convergence process-es in European Union regions. Prague Economic Papers, 25(5). doi: 10.18267/j.pep.574. DOI: https://doi.org/10.18267/j.pep.574
View in Google Scholar - Bivand, R. S., Pebesma, E. J., & Gómez-Rubio, V. (2008). Applied spatial data analysis with R. New York: Springer.
View in Google Scholar - Clif, A., & Ord, J. K. (1973). Spatial autocorrelation. London: Pion.
View in Google Scholar - Clif, A., & Ord, J. K. (1981). Spatial processes, models and applications. London: Pion.
View in Google Scholar - Bołt, T. W., Krauze, K., & Kulawczuk, T. (1985). Aggregation of econometric models. Warszawa: PWE.
View in Google Scholar - Furková, A., & Chocholatá, M. (2017). Interregional R and D spillovers and regional convergence: a spatial econometric evidence from the EU regions. Equilibrium. Quarterly Journal of Economics and Economic Policy, 12(1). doi: 10.24136/eq.v12i1.1. DOI: https://doi.org/10.24136/eq.v12i1.1
View in Google Scholar - Haining, R. P. (2005). Spatial data analysis. Theory and practice. Cambridge: Cambridge University Press.
View in Google Scholar - Hlaváček, P., & Siviček, T. (2017). Spatial differences in innovation potential of central European regions during post-transformation period. Journal of International Studies, 10(2). doi:10.14254/2071-8330.2017/10-2/4. DOI: https://doi.org/10.14254/2071-8330.2017/10-2/4
View in Google Scholar - Horská, E., Moroz, S., Poláková, Z., Nagyová, Ľudmila, & Paska, I. (2019). Evaluation of interaction between chosen indicators of development of regions in Ukraine. Equilibrium. Quarterly Journal of Economics and Economic Policy, 14(2). doi: 10.24136/eq.2019.016. DOI: https://doi.org/10.24136/eq.2019.016
View in Google Scholar - Kiselitsa, E. P., Shilova, N. N., Liman, I. A., & Naumenko, E. E. (2018). Impact of spatial development on sustainable entrepreneurship. Entrepreneurship and Sustainability Issues, 6(2). doi: 10.9770/jesi.2018.6.2(28). DOI: https://doi.org/10.9770/jesi.2018.6.2(28)
View in Google Scholar - Klein, L. R. (1946). Macroeconomics and the theory of rational behavior. Econometrica, 14(2). DOI: https://doi.org/10.2307/1905362
View in Google Scholar - Kljucnikov, A., Sobekova-Majkova, M., Vincurova, Z., Gailiuniene, M., & Kiausiene, I. (2018). The insolvency of SMEs within the perspective of the Central European region. Transformations in Business & Economics, 17( 2(44)).
View in Google Scholar - Kuc, M. (2017a). Is the regional divergence a price for the international convergence? The case of Visegrad group. Journal of Competitiveness, 9(4). doi: 10.7441/joc.2017.04.04. DOI: https://doi.org/10.7441/joc.2017.04.04
View in Google Scholar - Kuc, M. (2017b). Social convergence in Nordic countries at regional level, Equilibrium. Quarterly Journal of Economics and Economic Policy, 12(1). doi: 10.24136/eq.v12i1.2. DOI: https://doi.org/10.24136/eq.v12i1.2
View in Google Scholar - LeSage, J. P., & Pace, R. K. (2009). Introduction to spatial econometrics. Boca Raton: Wiley. DOI: https://doi.org/10.1201/9781420064254
View in Google Scholar - Malaga-Toboła, U. (2010). Technical infrastructure of farms and milk production efficiency. Inżynieria Rolnicza, 5(123).
View in Google Scholar - Markhaichuk, M., & Zhuckovskaya, I. (2019). The spread of the regional intellectual capital: the case of the Russian Federation. Oeconomia Copernicana, 10(1). doi: 10.24136/oc.2019.005. DOI: https://doi.org/10.24136/oc.2019.005
View in Google Scholar - May, K. (1946). The aggregation problem for a one-industry model. Econometrica, 14(4). DOI: https://doi.org/10.2307/1906910
View in Google Scholar - Michna, W. (2007). Controlled and spontaneous changes in agrarian structure in various regions of the country. Warszawa: IERiGŻ-PIB.
View in Google Scholar - Moran, P. A. P. (1948). The interpretation of statistical maps. Journal of the Royal Statistical Society, Series B, 10. DOI: https://doi.org/10.1111/j.2517-6161.1948.tb00012.x
View in Google Scholar - Nowak, P. (2018). Regional variety in quality of life in Poland. Oeconomia Copernicana, 9(3). doi: 10.24136/oc.2018.019. DOI: https://doi.org/10.24136/oc.2018.019
View in Google Scholar - Openshaw, S. (1984). The modifiable areal unit problem. Concepts and Techniques in Modern Geography, 38.
View in Google Scholar - Openshaw, S., & Taylor, P. J.. (1979). A million or so correlation coefficients: three experiments on the modifiable areal unit problem. In N. Wrigley (Ed.). Statistical methods in the spatial sciences. London: Pion.
View in Google Scholar - Pawłowski, Z. (1969). Econometrics. Warszawa: PWN.
View in Google Scholar - Paelinck, J. H. P. (2000). On aggregation in spatial econometric modelling. Journal of Geographical Systems, 2(2). doi: 10.1007/PL00011452. DOI: https://doi.org/10.1007/PL00011452
View in Google Scholar - Paelinck, J. H. P., & Klaassen, L. H. (1979). Spatial econometrics. Farnborough: Saxon House.
View in Google Scholar - Pietrzak, M. B. (2010a). Two-stage procedure of building a spatial weight matrix with the consideration of economic distance. Oeconomia Copernicana, 1. DOI: https://doi.org/10.12775/OeC.2010.004
View in Google Scholar - Pietrzak, M. B. (2010b). Application of economic distance for the purposes of a spatial analysis of the unemployment rate for Poland. Oeconomia Copernicana, 1. DOI: https://doi.org/10.12775/OeC.2010.005
View in Google Scholar - Pietrzak, M. B. (2012). The use of a spatial switching regression model in the analysis of regional convergence in Poland. Ekonomia i Prawo, 11(4). DOI: https://doi.org/10.12775/EiP.2012.040
View in Google Scholar - Pietrzak, M. B. (2013). Interpretation of structural parameters for models with spatial autoregression. Equilibrium. Quarterly Journal of Economics and Economic Policy, 8(2). doi: 10.12775/EQUIL.2013.010. DOI: https://doi.org/10.12775/EQUIL.2013.010
View in Google Scholar - Pietrzak, M. B. (2014a). Redefining the modifiable areal unit problem within spatial econometrics: the case of the scale problem. Equilibrium. Quarterly Journal of Economics and Economic Policy, 9(2). doi: 10.12775/EQUIL.2014.014. DOI: https://doi.org/10.12775/EQUIL.2014.014
View in Google Scholar - Pietrzak, M. B. (2014b). Redefining the modifiable areal unit problem within spatial econometrics, the case of the aggregation problem. Equilibrium. Quarterly Journal of Economics and Economic Policy, 9(3). doi: 10.12775/EQUIL. 2014.021. DOI: https://doi.org/10.12775/EQUIL.2014.021
View in Google Scholar - Pietrzak, M. B. (2014c). The modifiable areal unit problem: analysis of correlation and regression. Equilibrium. Quarterly Journal of Economics and Economic Policy, 9(4). doi: 10.12775/EQUIL.2014.028. DOI: https://doi.org/10.12775/EQUIL.2014.028
View in Google Scholar - Pietrzak, M. B. (2018a). The composition of agricultural macroregions in Eastern Poland - an empirical example of the Aggregation Problem. In M. Papież & S. Śmiech (Eds.). The 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena. Conference proceedings, Cracow: Foundation of the Cracow University of Economics.
View in Google Scholar - Pietrzak, M. B. (2018b). Problem zmiennej jednostki odniesienia w przestrzennych badaniach. Toruń: Polskie Towarzystwo Ekonomiczne oddział w Toruniu. DOI: https://doi.org/10.24136/eep.mon.2018.1
View in Google Scholar - Pietrzak, M. B., Balcerzak, A. P., Gajdos, A., & Arendt, Ł (2017). Entrepreneurial environment at regional level: the case of Polish path towards sustainable socio-economic development. Entrepreneurship and Sustainability Issues, 5(2). doi: 10.9770/jesi.2017.5.2(2). DOI: https://doi.org/10.9770/jesi.2017.5.2(2)
View in Google Scholar - Pietrzak, M. B., & Ziemkiewicz, B. (2017). The use of random fields in the modifiable areal unit problem. In M. Papież & S. Śmiech (Eds.) The 11th professor Aleksander Zelias international conference on modelling and forecasting of socio-economic phenomena. Conference proceedings. Cracow: Foundation of the Cracow University of Economics. DOI: https://doi.org/10.24136/eep.wp.2016.1
View in Google Scholar - Pietrzak, M. B., & Walczak, D. (2014). The analysis of the agrarian structure in Poland with the special consideration of the years 1921 and 2002. Bulgarian Journal of Agricultural Science, 20(5).
View in Google Scholar - Reiff, M., Surmanová, K., Balcerzak, A. P., & Pietrzak, M. B. (2016). Multiple criteria analysis of European Union agriculture. Journal of International Studies, 9(3). doi: 10.14254/2071-8330.2016/9-3/5. DOI: https://doi.org/10.14254/2071-8330.2016/9-3/5
View in Google Scholar - Raszkowski, A., & Bartniczak, B. (2018). Towards sustainable regional development: economy, society, environment, good governance based on the exampleof Polish regions. Transformations in Business & Economics, 17(2(44)).
View in Google Scholar - Rogalska, E. (2018). Multiple-criteria analysis of regional entrepreneurship conditions in Poland. Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(4). doi: 10.24136/eq.2018.034. DOI: https://doi.org/10.24136/eq.2018.034
View in Google Scholar - Rollnik-Sadowska, E., & Dąbrowska, E. (2018). Cluster analysis of effectivenessof labour market policy in the European Union. Oeconomia Copernicana, 9(1). doi: 10.24136/oc.2018.008. DOI: https://doi.org/10.24136/oc.2018.008
View in Google Scholar - Semenenko, I., Halhash, R., & Sieriebriak, K. (2019). Sustainable development of regions in Ukraine: before and after the beginning of the conflict. Equilibrium. Quarterly Journal of Economics and Economic Policy, 14(2). doi: 10.24136/eq.2019.015. DOI: https://doi.org/10.24136/eq.2019.015
View in Google Scholar - Shuyan, L., & Fabuš, M. (2019). Study on the spatial distribution of China's outward foreign direct investment in EU and its influencing factors. Entrepreneurship and Sustainability Issues, 6(3). doi: 10.9770/jesi.2019.6.3(16). DOI: https://doi.org/10.9770/jesi.2019.6.3(16)
View in Google Scholar - Simionescu, M. (2016). Competitiveness and economic growth in Romanian regions. Journal of Competitiveness, 8(4). doi: 10.7441/joc.2016.04.03. DOI: https://doi.org/10.7441/joc.2016.04.03
View in Google Scholar - Skarżyńska, A., Goraj, L., & Ziętek, I. (2005). Methodology SGM "2002" for the typology of farms in Poland. Warszawa: lERiGŻ-PIB.
View in Google Scholar - Smékalová, L., Janíček, P., Škarka, M., Kozák, V. (2015), Spatial Concentration of the Cohesion Policy Projects in Nationally Delimitated Intervention Areas: The Case of the Czech Republic and Poland, Economics and Sociology, 8(2), pp. 211-226. DOI: 10.14254/2071-789X.2015/8-2/15. DOI: https://doi.org/10.14254/2071-789X.2015/8-2/15
View in Google Scholar - Suchecka, J. (Ed.) (2014). Spatial Statistics. Methods for analyzing spatial structures. Warszawa: C.H. Beck.
View in Google Scholar - Suchecki, B. (Ed.) (2010). Spatial econometrics, methods and models for spatial data analysis. Warszawa: C.H. Beck.
View in Google Scholar - Suchecki, B. (Ed.) (2012). Spatial econometrics II, advanced models. Warszawa: C.H. Beck.
View in Google Scholar - Szulc, E. (2007). Econometric analysis of multidimensional economic processes. Toruń: Wydawnictwo UMK w Toruniu.
View in Google Scholar - Theil, H. (1965). Linear aggregation of economic relations. Amsterdam: North-Holland Publishing Company.
View in Google Scholar - Tinbergen, J. (1939). Business cycles in the United States of America 1919-1932. Genewa: League of Nations. DOI: https://doi.org/10.2307/1232097
View in Google Scholar - Tobler, W. R. (1970). A computer movie simulating urban growth in the Detroit region. Economic Geography, 46. DOI: https://doi.org/10.2307/143141
View in Google Scholar - Tobler, W. R. (1989). Frame independent spatial analysis. In M.F. Goodchild & S. Gopal (Eds.), The accuracy of spatial databases. London: Taylor &Francis.
View in Google Scholar - Tvaronavičienė, M., & Razminienė, K. (2017). Towards competitive regional development trough clusters. Journal of Competitiveness, 9(4). doi: 10.7441/joc. 2017.04.09. DOI: https://doi.org/10.7441/joc.2017.04.09
View in Google Scholar - Walczak, D., & Pietrzak, M. B. (2016). Analysis of agrarian structure in Poland in 1921 and 2002 based on the example of selected districts. In M. H. Bilgin, H. Danis, E. Demir & U. Can (Eds.). Business challenges in the changing economic landscape. Proceedings of the 14th Eurasia Business and Economics Society conference. Cham: Springer. DOI: https://doi.org/10.1007/978-3-319-22596-8_33
View in Google Scholar - Zeliaś, A. (Ed.) (1991). Spatial Econometrics. Warszawa: PWE.
View in Google Scholar - Zieliński, Z. (1991). Linear econometric models as a tool for describing and analyzing the causal dependencies of economic phenomena. Toruń: Wydawnictwo Adam Marszałek.
View in Google Scholar
Downloads
Download data is not yet available.