nach oben

Quality & Quantity

05.02.2025

Zipf and the MAUP: empirical evidence of non-parametric estimates from a mediterranean country

verfasst von: Alessandro Muolo, Michele Postigliola, Leonardo Salvatore Alaimo, Luca Salvati

Erschienen in: Quality & Quantity

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The present study investigates the rank-size relationship in Greece using data from the 2021 census. The research focuses on testing Zipf’s law across six different territorial partitions, ranging from the most aggregated administrative units (prefectures) to the most disaggregated (villages and a regular population grid). The main objective is to verify the hypothesis of the Modifiable Areal Unit Problem (MAUP) and its impact on the estimation of Zipf’s law across the whole population hierarchy—from the largest urban center to the smallest settlement in the country. The study employs mixed econometric techniques, using both fixed and adaptive splines, to capture the complexity and non-linearity inherent in the relationship between rank and population. The results indicate limited variability among the different spatial configurations, suggesting stability in the estimates and minimal impact of the MAUP. However, significant differences were observed in settlement patterns, with greater deviation from Zipf’s law in urban areas than in rural ones. These differences reflect multiple and complex population structures over spaces, possibly highlighting the presence of diverse socioeconomic dynamics. These results are relevant to the methodological and economic debate, indicating that the scale of spatial aggregation does not significantly affect the estimation of Zipf’s law in Greece. These conclusions are useful for urban and regional planning, providing a basis for better understanding the dynamics of territorial growth and development. The study contributes to the debate on the relevance of spatial specification in economic analysis and the implications of centralized (or decentralized) governance configurations.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Auerbach, F., Ciccone, A.: The law of population concentration. Environ. Plann. Urban Analyt. City. Sci. 50(2), 290–298 (2023). https://doi.org/10.1177/23998083221147139CrossRef

Aurélie, L., Martin, Z.: From Gibrat’s law to Zipf’s law through cointegration? Econom. Lett. 192, 109211 (2020). https://doi.org/10.1016/j.econlet.2020.109211CrossRef

Aurélie, L., Martin, Z.: From Gibrat’s law to Zipf’s law through cointegration? Econ. Lett. 192, 109211 (2020)CrossRef

Bergs, R.: The detection of natural cities in the Netherlands—Nocturnal satellite imagery and Zipf’s law. Rev. Region. Res. 38(2), 111–140 (2018). https://doi.org/10.1007/s10037-018-0122-6CrossRef

Bergs, R.: Spatial dependence in the rank-size distribution of cities–weak but not negligible. PLoS ONE 16(2), e0246796 (2021)CrossRef

Brakman, S., Garretsen, H., Van Marrewijk, C., Van Den Berg, M.: The return of Zipf: Towards a further understanding of the rank-size distribution. J. Reg. Sci. 39(1), 183–213 (2002). https://doi.org/10.1111/1467-9787.00129CrossRef

Brida, J.G., Alvarez, E., Cayssials, G., Mednik, M.: How does population growth affect economic growth and vice versa? An empirical analysis. Rev. Econom Polit. Sci. 9(3), 265–297 (2024). https://doi.org/10.1108/REPS-11-2022-0093CrossRef

Budde, R., Neumann, U.: The size ranking of cities in Germany: caught by a MAUP? GeoJournal 84, 1447–1464 (2019). https://doi.org/10.1007/s10708-018-9930-zCrossRef

Cai, B., Shao, Z., Fang, S., Huang, X., Tang, Y., Zheng, M., Zhang, H.: The Evolution of urban agglomerations in China and how it deviates from Zipf’s law. Geo-Spatial Inf. Sci. (2022). https://doi.org/10.1080/10095020.2022.2083527CrossRef

Calderín-Ojeda, E.: The distribution of all French communes: a composite parametric approach. Physica A 450, 385–394 (2016). https://doi.org/10.1016/j.physa.2016.01.018CrossRef

Cardesin Diaz, J.M., Araujo, J.M.: Historic Urbanization Process in Spain (1746–2013) From the Fall of the American Empire to the Real Estate Bubble. J. Urban Hist. 43(1), 33–52 (2017)CrossRef

Carlucci, M., Grigoriadis, E., Rontos, K., Salvati, L.: Revisiting an Hegemonic Concept: long-term ‘Mediterranean Urbanization’ in between city re-polarization and metropolitan decline. Appl. Spat. Anal. Policy 10(3), 347–362 (2017). https://doi.org/10.1007/s12061-016-9186-2CrossRef

Cecchini, M., Zambon, I., Pontrandolfi, A., Turco, R., Colantoni, A., Mavrakis, A., Salvati, L.: Urban sprawl and the ‘olive’ landscape: Sustainable land management for ‘crisis’ cities. GeoJournal 84, 237–255 (2019). https://doi.org/10.1007/s10708-018-9848-5CrossRef

Chen, Y.: Exploring the level of urbanization based on Zipf’s scaling exponent. Physica A 566, 125620 (2021). https://doi.org/10.1016/j.physa.2020.125620CrossRef

Chen, Y., Wang, J.: Recursive subdivision of urban space and Zipf’s law. Physica A 395, 392–404 (2014)CrossRef

Chen, L., Yu, L., Yin, J., Xi, M.: Impact of population density on spatial differences in the economic growth of urban agglomerations: the case of Guanzhong Plain Urban Agglomeration. China. Sustainability 15(19), 14601 (2023)CrossRef

Cheshire, P.C., Magrini, S.: Urban Growth Drivers in a Europe of Sticky People and Implicit Boundaries. Journal of Economic Geography 9(1), 85–115 (2009)CrossRef

Colantoni, A., Grigoriadis, E., Sateriano, A., Venanzoni, G., Salvati, L.: Cities as selective land predators? A lesson on urban growth, deregulated planning and sprawl containment. Sci. Total Environ. 545, 329–339 (2016). https://doi.org/10.1016/j.scitotenv.2015.11.170CrossRef

Corral, Á., Serra, I., Ferrer-i-Cancho, R.: Distinct flavors of Zipf’s law and its maximum likelihood fitting: Rank-size and size-distribution representations. Phys. Rev. E 102(5), 052113 (2020). https://doi.org/10.1103/PhysRevE.102.052113CrossRef

Cuadrado-Ciuraneta, S., Durà-Guimerà, A., Salvati, L.: Not only tourism: unravelling suburbanization, second-home expansion and “rural” sprawl in Catalonia. Spain. Urban Geography 38(1), 66–89 (2017). https://doi.org/10.1080/02723638.2015.1113806CrossRef

de Boor, C.: A practical guide to splines. Springer, Berlin (2001)

De Marzo, G., Gabrielli, A., Zaccaria, A., Pietronero, L.: Dynamical approach to Zipf’s law. Phys. Rev. Res. 3(1), 013084 (2021). https://doi.org/10.1103/PhysRevResearch.3.013084CrossRef

De Marzo, G., Attili, F., Pietronero, L.: Growing inequality in systems showing Zipf’s law. J. Phys. Complex. 4(1), 015014 (2023). https://doi.org/10.1088/2632-072X/acc0c1CrossRef

Di Feliciantonio, C., Salvati, L.: ‘Southern’ Alternatives of Urban diffusion: investigating settlement characteristics and socio-economic patterns in three mediterranean regions. Tijdschr. Econ. Soc. Geogr. 106(4), 453–470 (2015). https://doi.org/10.1111/tesg.12102CrossRef

Dijkstra, L., Florczyk, A.J., Freire, S., Kemper, T., Melchiorri, M., Pesaresi, M., Schiavina, M.: Applying the degree of urbanisation to the globe: A new harmonised definition reveals a different picture of global urbanisation. J. Urban Econ. 125, 103312 (2021). https://doi.org/10.1016/j.jue.2020.103312CrossRef

Duran, H.E., Cieślik, A.: The distribution of city sizes in Turkey: A failure of Zipf’s law due to concavity. Reg. Sci. Policy Pract. 13(5), 1702–1719 (2021)CrossRef

Duvernoy, I., Zambon, I., Sateriano, A., Salvati, L.: Pictures from the Other Side of the Fringe: Urban Growth and Peri-urban Agriculture in a Post-industrial City (Toulouse, France). J. Rural Stud. 57, 25–35 (2018). https://doi.org/10.1016/j.jrurstud.2017.10.007CrossRef

Fotheringham, A.S., Wong, D.W.: The modifiable areal unit problem in multivariate statistical analysis. Environ Plan A 23(7), 1025–1044 (1991)CrossRef

Furceri, D.: Zipf’s law and world income distribution. Appl. Econ. Lett. 15(12), 921–923 (2008). https://doi.org/10.1080/13504850600972261CrossRef

Gabaix, X.: Zipf’s law for cities: an explanation. Q. J. Econ. 114(3), 739–767 (1999a). https://doi.org/10.1162/003355399556133CrossRef

Gabaix, X.: Zipf’s Law and the Growth of Cities. Am. Econom. Rev. 89(2), 129–132 (1999b). https://doi.org/10.1257/aer.89.2.129CrossRef

Gan, L., Dong, L., Song, S.: Is the Zipf law spurious in explaining city-size distributions? Econ. Lett. 92(2), 256–262 (2006). https://doi.org/10.1016/j.econlet.2006.03.004CrossRef

Gao, H., Wu, K.: Zipf’s law and influential factors of the Pareto exponent of the city size distribution: Evidence from China. Front. Econ. China 3, 137–149 (2008). https://doi.org/10.1007/s11459-008-0006-8CrossRef

Giesen, K., Südekum, J.: Zipf’s law for cities in the regions and the country. J. Econom. Geograp. 11(4), 667–686 (2011). https://doi.org/10.1093/jeg/lbq019CrossRef

Gomez-Lievano, A., Youn, H., Cartone, L.M.A.: The statistics of urban scaling and their connection to Zipf’s law. PLoS ONE 7(7), e40393 (2012). https://doi.org/10.1371/journal.pone.0040393CrossRef

Gong, J., Shengwen, L., Xinyue, Y., Qiong, P., Sonali, K.: Modelling impacts of high-speed rail on urban interaction with social media in China’s mainland. Geo-Spatial Inf. Sci. 24(4), 638–653 (2021). https://doi.org/10.1080/10095020.2021.1972771CrossRef

González-Val, R.: Deviations from Zipf’s law for American cities: an empirical examination. Urban Stud. 48(5), 1017–1035 (2011). https://doi.org/10.1177/0042098010371394CrossRef

González-Val, R.: The Spanish spatial city size distribution. Environ. Plann B. Urban Analyt. City Sci. 48(6), 1609–1631 (2021). https://doi.org/10.1177/2399808320941860CrossRef

Grekousis, G., Manetos, P., Photis, Y.N.: Modeling urban evolution using neural networks, fuzzy logic and GIS: the case of the Athens metropolitan area. Cities 30, 193–203 (2013). https://doi.org/10.1016/j.cities.2012.03.006CrossRef

Hackmann, A., Torben, K.: The evolution of Zipf’s Law for US cities. Pap. Reg. Sci. 99(3), 841–852 (2020). https://doi.org/10.1111/pirs.12498CrossRef

Hordijk, W.: Snooker Statist. Zipf’s Law. Stats 5(4), 985–992 (2022). https://doi.org/10.3390/stats5040058CrossRef

Hsu, W.T.: Central place theory and city size distribution. Econ. J. 122(563), 903–932 (2012). https://doi.org/10.1111/j.1468-0297.2012.02518.xCrossRef

Jiang, B., Tao, J.: Zipf’s law for all the natural cities in the United States: a geospatial perspective. Int. J. Geogr. Inf. Sci. 25(8), 1269–1281 (2011). https://doi.org/10.1080/13658816.2010.510801CrossRef

Josic, H., Bašić, M.: Reconsidering Zipf’s law for regional development: The case of settlements and cities in Croatia. Miscellanea Geographica 22(1), 22–30 (2018)CrossRef

Kazemzadeh-Zow, A., Saeed, Z.S., Salvati, L., Samani, N.N.: A spatial zoning approach to calibrate and validate urban growth models. Int. J. Geogr. Inf. Sci. 31(4), 763–782 (2017). https://doi.org/10.1080/13658816.2016.1236927CrossRef

Kim, H., Huo, X.: Locally optimal adaptive smoothing splines. J. Nonparametric. Statist. 24(3), 665–680 (2012). https://doi.org/10.1080/10485252.2012.693610CrossRef

Kinoshita, T., Kato, E., Iwao, K., Yamagata, Y.: Investigating the rank‐size relationship of urban areas using land cover maps. Geophys. Res. Lett. (2008). https://doi.org/10.1029/2008GL035163CrossRef

Kosmopoulou, G., Buttry, N., Johnson, J., Kallsnick, A.: Suburbanization and the rank-size rule. Appl. Econ. Lett. 14(1), 1–4 (2007). https://doi.org/10.1080/13504850500425675CrossRef

Lamonica, G.R., Recchioni, M.C., Chelli, F.M., Salvati, L.: The efficiency of the cross-entropy method when estimating the technical coefficients of input–output tables. Spat. Econ. Anal. 15(1), 62–91 (2020)CrossRef

Magrini, S., Gerolimetto, M., Duran, H.E.: Regional convergence and aggregate business cycle in the United States. Reg. Stud. 49(2), 251–272 (2015)CrossRef

Morelli, V.G., Rontos, K., Salvati, L.: Between suburbanisation and re-urbanisation: revisiting the urban life cycle in a Mediterranean compact city. Urban Res. Practic. 7(1), 74–88 (2014). https://doi.org/10.1080/17535069.2014.885744CrossRef

Mulligan, G.F., Partridge, M.D., Carruthers, J.I.: Central place theory and its reemergence in regional science. Ann. Reg. Sci. 48, 405–431 (2012). https://doi.org/10.1007/s00168-011-0496-7CrossRef

Niebuhr, A.: Spatial interaction and regional unemployment in Europe. Europ. J. Spat. Develop. 1(5), 26–26 (2003)

Nitsch, V.: Zipf zipped. J. Urban Econ. 57(1), 86–100 (2005). https://doi.org/10.1016/j.jue.2004.09.002CrossRef

Nota, F., Song, S.: Further analysis of the Zipf’s law: Does the rank-size rule really exist? J. Urban Managem. 1(2), 19–31 (2012). https://doi.org/10.1016/S2226-5856(18)30058-XCrossRef

Oueslati, W., Alvanides, S., Garrod, G.: Determinants of urban sprawl in European cities. Urban Stud. 52(9), 1594–1614 (2015). https://doi.org/10.2139/ssrn.2397141CrossRef

Pellegrini, G.: Proximity, Polarization and Local Labour Market Performances. Network. Spat. Econom. 2, 151–174 (2002)CrossRef

Peña, G., Sanz-Gracia, F.: Zipf’s exponent and Zipf’s law in the BRICS: a rolling sample regressions approach. Econom. Bullet. 41(4), 2543–2549 (2021)

Pérez-Campuzano, E., Guzmán-Vargas, L., Angulo-Brown, F.: Distributions of city sizes in Mexico during the 20th century. Chaos. Solit. Fract. 73, 64–70 (2015). https://doi.org/10.1016/j.chaos.2014.12.015CrossRef

Petrakos, G., Rodríguez-Pose, A., Rovolis, A.: Growth, integration, and regional disparities in the European Union. Environ Plan A 37(10), 1837–1855 (2005). https://doi.org/10.1068/a37348CrossRef

Pilgrim, C., Hills, T.: Bias in Zipf’s law estimators. Sci. Rep. 11(1), 17309 (2021). https://doi.org/10.1038/s41598-021-96214-wCrossRef

Pili, S., Grigoriadis, E., Carlucci, M., Clemente, M., Salvati, L.: Towards sustainable growth? A multi-criteria assessment of (Changing) Urban Forms. Ecol. Ind. 76, 71–80 (2017). https://doi.org/10.1016/j.ecolind.2017.01.008CrossRef

Platonova, D., Jankava, A.: Description of land fragmentation in Latvia and its prevention opportunities. Rural Sustainabil. Res. 28(1), 1–8 (2013)

Rastvortseva, S.N., Manaeva, I.V.: Zipf’s law for russian cities: analysis of new indicators. Econom. Region 16(3), 935–947 (2020). https://doi.org/10.17059/ekon.reg.2020-3-20CrossRef

Reggiani, A., Peter, N.: Did Zipf anticipate spatial connectivity structures? Environ. Plann. b. Plann. des. 42(3), 468–489 (2015). https://doi.org/10.1068/b120012pCrossRef

Rodriguez-Pose, A., Fratesi, U.: Between development and social policies: the impact of European Structural Funds in Objective 1 regions. Reg. Stud. 38(1), 97–113 (2004). https://doi.org/10.1080/00343400310001632226CrossRef

Rozenfeld, H.D., Rybski, D., Gabaix, X., Makse, H.A.: The area and population of cities: new insights from a different perspective on cities. Am. Econom. Rev. 101(5), 2205–2225 (2011). https://doi.org/10.1257/aer.101.5.2205CrossRef

Saint Onge, J.M., Hunter, L.M., Boardman, J.D.: Population growth in high-amenity rural areas: does it bring socioeconomic benefits for long-term residents? Soc. Sci. q. 88(2), 366–381 (2007)CrossRef

Salvati, L.: The ‘Sprawl Divide’: comparing models of urban dispersion in mono-centric and polycentric Mediterranean cities. Europ. Urban. Region. Stud. 23(3), 338–354 (2016). https://doi.org/10.1177/0969776413512843CrossRef

Salvati, L., Carlucci, M.: Land-use structure, urban growth, and periurban landscape: a multivariate classification of the European cities. Environ. Plann. b. Plann. des. 42(5), 801–829 (2015). https://doi.org/10.1068/b120029pCrossRef

Salvati, L., Carlucci, M.: Patterns of sprawl: The socioeconomic and territorial profile of dispersed urban areas in Italy. Reg. Stud. 50(8), 1346–1359 (2016). https://doi.org/10.1080/00343404.2015.1009435CrossRef

Salvati, L., Ferrara, A., Chelli, F.M.: Long-term growth and metropolitan spatial structures: An analysis of factors influencing urban patch size under different economic cycles. Geografisk Tidsskrift-Danish J. Geograp. 118(1), 56–71 (2018a)CrossRef

Salvati, L., Zambon, I., Chelli, F.M., Serra, P.: Do spatial patterns of urbanization and land consumption reflect different socioeconomic contexts in Europe? Sci. Total Environ. 625, 722–730 (2018b). https://doi.org/10.1016/j.scitotenv.2017.12.341CrossRef

Salvia, R., Quaranta, G., Rontos, K., Cudlin, P., Salvati, L.: Investigating metropolitan hierarchies through a spatially explicit (local) approach. ISPRS Int. J. Geo Inf. 12(8), 315 (2023)CrossRef

Schluter, C.: On Zipf’s law and the bias of Zipf regressions. Empiric. Econom. 61(2), 529–548 (2021). https://doi.org/10.1007/s00181-020-01879-3CrossRef

Serra, P., Vera, A., Tulla, A.F., Salvati, L.: Beyond urban-rural dichotomy: exploring socioeconomic and land-use processes of change in Spain (1991–2011). Appl. Geogr. 55, 71–81 (2014). https://doi.org/10.1016/j.apgeog.2014.09.005CrossRef

Sokołowski, D., Jażdżewska, I.: Zipf’s Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns. Bullet. Geograp. Socio-Econom. Series. 53(53), 147–156 (2021). https://doi.org/10.2478/bog-2021-0028CrossRef

Soo, K.T.: Zipf’s Law for cities: a cross-country investigation. Reg. Sci. Urban Econ. 35(3), 239–263 (2005). https://doi.org/10.1016/j.regsciurbeco.2004.04.004CrossRef

Sun, X., Yuan, O., Xu, Z., Yin, Y., Liu, Q., Wu, L.: Did Zipf’s Law hold for Chinese cities and why? Evidence from multi-source data. Land Use Policy 106, 105460 (2021). https://doi.org/10.1016/j.landusepol.2021.105460CrossRef

Van Der Burg, A.J., Dieleman, F.M.: Dutch urbanization policies: from ‘compact city’ to ‘urban network.’ Tijdschr. Econ. Soc. Geogr. 95(1), 108–116 (2004). https://doi.org/10.1111/j.1467-9663.2004.00297.xCrossRef

Wan, G., Zhu, D., Wang, C., Zhang, X.: The size distribution of cities in China: Evolution of urban system and deviations from Zipf’s law. Ecol. Ind. 111, 106003 (2020). https://doi.org/10.1016/j.ecolind.2019.106003CrossRef

Wang, Q.A.: Principle of least effort vs. maximum efficiency: deriving Zipf-Pareto’s laws. Chaos. Solitons. Fract. 153, 111489 (2021). https://doi.org/10.1016/j.chaos.2021.111489CrossRef

Wei, J., Zhang, J., Cai, B., Wang, K., Liang, S., Geng, Y.: Characteristics of carbon dioxide emissions in response to local development: Empirical explanation of Zipf’s law in Chinese cities. Sci. Total Environ. 757, 143912 (2021)CrossRef

Wrenn, D. H., & Irwin, E. G. (2012). How do land use policies influence fragmentation? An econometric model of land development with spatial simulation. Environmental economics, (3, Iss. 4), 82–96.

Wu, Y., Jiang, M., Chang, Z., Li, Y., Shi, K.: Does China’s urban development satisfy Zipf’s law? A multiscale perspective from the NPP-VIIRS nighttime light data. Int. J. Environ. Res. Public Health 17(4), 1460 (2020). https://doi.org/10.3390/ijerph17041460CrossRef

Xu, Z., Harriss, R.: A Spatial and Temporal Autocorrelated Growth Model for City Rank—Size Distribution. Urban Studies 47(2), 321–335 (2010). https://doi.org/10.1177/0042098009348326CrossRef

Yang, L., Ding, M., Hong, Y., Wang, X.: Estimating functions and derivatives via adaptive penalized splines. Commun. Statist. Simulat. Comput. 50(7), 2054–2071 (2019). https://doi.org/10.1080/03610918.2019.1594894CrossRef

Zambon, I., Serra, P., Sauri, D., Carlucci, M., Salvati, L.: Beyond the ‘Mediterranean city’: socioeconomic disparities and urban sprawl in three Southern European cities. Geografiska Annaler: Series B. Human. Geograp. 99(3), 319–337 (2017). https://doi.org/10.1080/04353684.2017.1294857CrossRef

Zambon, I., Benedetti, A., Ferrara, C., Salvati, L.: Soil Matters? A multivariate analysis of socioeconomic constraints to Urban expansion in mediterranean Europe. Ecol. Econ. 146, 173–183 (2018). https://doi.org/10.1016/j.ecolecon.2017.10.015CrossRef

Titel: Zipf and the MAUP: empirical evidence of non-parametric estimates from a mediterranean country
verfasst von: Alessandro Muolo
Michele Postigliola
Leonardo Salvatore Alaimo
Luca Salvati
Publikationsdatum: 05.02.2025
Verlag: Springer Netherlands
Erschienen in: Quality & Quantity
Print ISSN: 0033-5177
Elektronische ISSN: 1573-7845
DOI: https://doi.org/10.1007/s11135-025-02061-6