Modifiable Areal Unit Problem: the issue of determining the relationship between microparameters and a macroparameter

Keywords: Modifiable Areal Unit Problem, microparameter, macroparameter, micro-dependencies, macro-dependencies

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.

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References

Anselin, L. (1988). Spatial econometrics: method and models. Boston: Kluwer Academic Prespp.

Arbia, G. (1988). Spatial data configuration in statistical analysis of regional economics and related problems. Dordrecht: Kluwer Academic Press.

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

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.

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.

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.

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.

Bivand, R. S. (1984). Regression modeling with spatial dependence: an applica¬tion of some class selection and estimation methods. Geographical Analysis, 16(1).

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.

Bivand, R. S., Pebesma, E. J., & Gómez-Rubio, V. (2008). Applied spatial data analysis with R. New York: Springer.

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

Clif, A., & Ord, J. K. (1981). Spatial processes, models and applications. London: Pion.

Bołt, T. W., Krauze, K., & Kulawczuk, T. (1985). Aggregation of econometric models. Warszawa: PWE.

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.

Haining, R. P. (2005). Spatial data analysis. Theory and practice. Cambridge: Cambridge University Press.

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.

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.

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).

Klein, L. R. (1946). Macroeconomics and the theory of rational behavior. Econometrica, 14(2).

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)).

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.

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.

LeSage, J. P., & Pace, R. K. (2009). Introduction to spatial econometrics. Boca Raton: Wiley.

Malaga-Toboła, U. (2010). Technical infrastructure of farms and milk production efficiency. Inżynieria Rolnicza, 5(123).

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.

May, K. (1946). The aggregation problem for a one-industry model. Econometrica, 14(4).

Michna, W. (2007). Controlled and spontaneous changes in agrarian structure in various regions of the country. Warszawa: IERiGŻ-PIB.

Moran, P. A. P. (1948). The interpretation of statistical maps. Journal of the Royal Statistical Society, Series B, 10.

Nowak, P. (2018). Regional variety in quality of life in Poland. Oeconomia Copernicana, 9(3). doi: 10.24136/oc.2018.019.

Openshaw, S. (1984). The modifiable areal unit problem. Concepts and Techniques in Modern Geography, 38.

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.

Pawłowski, Z. (1969). Econometrics. Warszawa: PWN.

Paelinck, J. H. P. (2000). On aggregation in spatial econometric modelling. Journal of Geographical Systems, 2(2). doi: 10.1007/PL00011452.

Paelinck, J. H. P., & Klaassen, L. H. (1979). Spatial econometrics. Farnborough: Saxon House.

Pietrzak, M. B. (2010a). Two-stage procedure of building a spatial weight matrix with the consideration of economic distance. Oeconomia Copernicana, 1.

Pietrzak, M. B. (2010b). Application of economic distance for the purposes of a spatial analysis of the unemployment rate for Poland. Oeconomia Copernicana, 1.

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).

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.

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.

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.

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.

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.

Pietrzak, M. B. (2018b). Problem zmiennej jednostki odniesienia w przestrzennych badaniach. Toruń: Polskie Towarzystwo Ekonomiczne oddział w Toruniu.

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).

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.

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).

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.

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)).

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.

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.

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.

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).

Simionescu, M. (2016). Competitiveness and economic growth in Romanian regions. Journal of Competitiveness, 8(4). doi: 10.7441/joc.2016.04.03.

Skarżyńska, A., Goraj, L., & Ziętek, I. (2005). Methodology SGM "2002" for the typology of farms in Poland. Warszawa: lERiGŻ-PIB.

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.

Suchecka, J. (Ed.) (2014). Spatial Statistics. Methods for analyzing spatial structures. Warszawa: C.H. Beck.

Suchecki, B. (Ed.) (2010). Spatial econometrics, methods and models for spatial data analysis. Warszawa: C.H. Beck.

Suchecki, B. (Ed.) (2012). Spatial econometrics II, advanced models. Warszawa: C.H. Beck.

Szulc, E. (2007). Econometric analysis of multidimensional economic processes. Toruń: Wydawnictwo UMK w Toruniu.

Theil, H. (1965). Linear aggregation of economic relations. Amsterdam: North-Holland Publishing Company.

Tinbergen, J. (1939). Business cycles in the United States of America 1919-1932. Genewa: League of Nations.

Tobler, W. R. (1970). A computer movie simulating urban growth in the Detroit region. Economic Geography, 46.

Tobler, W. R. (1989). Frame independent spatial analysis. In M.F. Goodchild & S. Gopal (Eds.), The accuracy of spatial databases. London: Taylor &Francis.

Tvaronavičienė, M., & Razminienė, K. (2017). Towards competitive regional development trough clusters. Journal of Competitiveness, 9(4). doi: 10.7441/joc. 2017.04.09.

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.

Zeliaś, A. (Ed.) (1991). Spatial Econometrics. Warszawa: PWE.

Zieliński, Z. (1991). Linear econometric models as a tool for describing and analyzing the causal dependencies of economic phenomena. Toruń: Wydawnictwo Adam Marszałek.

Published
2019-09-30
How to Cite
Pietrzak, M. B. (2019). Modifiable Areal Unit Problem: the issue of determining the relationship between microparameters and a macroparameter. Oeconomia Copernicana, 10(3), 393-417. https://doi.org/10.24136/oc.2019.019
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Articles