Spatial heterogeneity of population distribution in Poland: a geographically weighted regression approach to Zipf's law
By: Andrzej Cieślik
References
- Arendt, L & Grabowski, W 2019, ‘The role of firm-level factors and regional innovation capabilities for Polish SMEs’, Journal of Entrepreneurship, Management and Innovation, vol. 15, no. 3, pp. 11–45.
- Arshad, S, Hu, S & Ashraf, BN 2018, ‘Zipf's law and city size distribution: A survey of the literature and future research agenda’, Physica A: Statistical Mechanics and its Applications, vol. 492, no. C, pp. 75–92.
- Auerbach, F 1913, ‘Das gesetz der bevölkerungskonzentration’, Petermanns Geographische Mitteilungen, vol. 59, pp. 74–76.
- Baldwin, R, Forslid, R, Robert-Nicoud, F, Ottaviano, G & Martin, P 2011, Economic geography and public policy, Princeton University Press, Princeton.
- Bergs, R 2021, ‘Spatial dependence in the rank-size distribution of cities – weak but not negligible’, PLos One, vol. 16, no. 2, article number: e0246796.
- Bertinelli, L & Strobl, E 2007, ‘Urbanisation, urban concentration and economic development’, Urban Studies, vol. 44, no. 13, pp. 2499–2510.
- Chidlow, A, Salciuviene, L & Young, S 2009, ‘Regional determinants of inward FDI distribution in Poland’, International Business Review, vol. 18, pp. 119–133.
- Cieślik, A 2005a, ‘Location of foreign firms and national border effects: the case of Poland’, Tijdschrift voor Economische en Sociale Geografie, vol. 96, no. 3, pp. 287–297.
- Cieślik, A 2005b, ‘European integration, national border effects and the location of multinational enterprises in Poland: The case of new voivodships’, Brussels Economic Review, vol. 48, pp. 1–13.
- Cieślik, A 2007, ‘The impact of free trade agreements on Poland's foreign trade in 1992–2004’, Bank & Credit, vol. 38, no. 6, pp. 3–23.
- Cieślik, A 2013, ‘Determinants of the location of foreign firms in Polish regions: Does firm size matter?’, Tijdschrift voor Economische en Sociale Geografie, vol. 104, no. 2, pp. 175–193.
- Cieślik, A 2017, ‘Determinants of foreign direct investment in Poland: Does European integration matter?’, Collegium of Economic Analysis Annals, vol. 47, pp. 65–82.
- Cieślik, A 2018, ‘Determinants of Poland's bilateral trade volumes: Does European integration matter?’, Przedsiębiorczość i Zarządzanie, vol. 19, no. 22, pp. 23–34.
- Cieślik, A & Hagemejer, J 2011, ‘The effectiveness of preferential trade liberalization in Central and Eastern Europe’, International Trade Journal, vol. 25, no. 5, pp. 516–538.
- Cieślik, A & Misiak, T 2022, ‘Related versus unrelated variety and per employee income regional disparities: A case of Polish regions’, Miscellanea Geographica. Regional Studies on Development, vol. 26, no. 4, pp. 178–184.
- Cieślik, A & Misiak, T 2024, ‘Related and unrelated variety and convergence to technological frontier: empirical evidence for Polish regions’, European Planning Studies, vol. 32, no. 3, pp. 648–667.
- Cieślik, A & Rokicki, B 2017, ‘EU structural interventions and individual wages in Poland: Empirical evidence for 2004–2006 financial framework’, Regional Science Policy & Practice, vol. 9, no. 3, pp. 201–216.
- Cieślik, A & Ryan, M 2005, ‘Location determinants of Japanese multinationals in Poland: Do special economic zones really matter for investment decisions?’, Journal of Economic Integration, vol. 20, no. 3, pp. 475–496.
- Cieślik, A & Tarsalewska, M 2023, ‘European integration and international M&As: The case of Poland’, Journal of East-West Business, vol. 29, no. 1, pp. 26–45.
- Cieślik, A & Teresiński, J 2016, ‘Does Zipf's law hold for Polish cities?’, Miscellanea Geographica – Regional Studies on Development, vol. 20, no. 4, pp. 5–10.
- Deichmann, U & Henderson, JV 2000, ‘Urban and regional dynamics in Poland’, The World Bank Policy Research Working Paper, no. 2457.
- Deliktas, E, Onder, AO & Karadag, M 2013, ‘The size distribution of cities and determinants of city growth in Turkey’, European Planning Studies, vol. 21, no. 2, pp. 251–263.
- Duran, HE & Cieślik, A 2021, ‘The distribution of city sizes in Turkey: A failure of Zipf's law due to concavity’, Regional Science Policy & Practice, vol. 13, no. 5, pp. 1702–1719.
- Eaton, J & Eckstein, Z 1997, ‘Cities and growth: Theory and evidence from France and Japan’, Regional Science and Urban Economics, vol. 27, no. 5, pp. 443–474.
- Eeckhout, J 2004, ‘Gibrat's law for (all) cities’, American Economic Review, vol. 94, no. 5, pp. 1429–1451.
- Ellison, G, Glaeser, EL & Kerr, WR 2010, ‘What causes industry agglomeration? Evidence from co-agglomeration patterns’, American Economic Review, vol. 100, no. 3, pp. 1195–1213.
- Fotheringham, AS, Brunsdon, C & Charlton, M 2003, Geographically weighted regression: the analysis of spatially varying relationships, John Wiley & Sons, Chichester.
- Fujita, M & Thisse, JF 1996, ‘Economics of agglomeration’, Journal of the Japanese and International Economies, vol. 10, no. 4, pp. 339–378.
- Gabaix, X 1999, ‘Zipf's law for cities: An explanation’, Quarterly Journal of Economics, vol. 114, no. 3, pp. 739–767.
- Gabaix, X & Ioannides, YM 2004, ‘The evolution of city size distributions’ in Handbook of Regional and Urban Economics, vol. IV, eds. JV Henderson & J-F Thisse, North-Holland, Amsterdam, pp. 2341–2378.
- Górny, A & Śleszyński, P 2019, ‘Exploring the spatial concentration of foreign employment in Poland under the simplified procedure’, Geographia Polonica, vol. 92, no. 3, pp. 331–345.
- Grabowski, W & Korczak, K 2023, ‘Identifying the envelope wages phenomenon based on LFS and SES data sets-evidence from Poland’, Economics & Sociology, vol. 16, no. 4, pp. 130–154.
- Havlin, S 1995, ‘The distance between Zipf plots’, Physica A, vol. 216, pp. 148–150.
- Henderson, V 2003, ‘The urbanization process and economic growth: The so-what question’, Journal of Economic Growth, vol. 8, pp. 47–71.
- Hill, BM 1975, ‘A simple general approach to inference about the tail of a distribution’, Annals of Statistics, vol. 3, no. 5, pp. 1163–1174.
- Jażdżewska, I 2017, ‘Spatial and dynamic aspects of the rank-size rule method. Case of an urban settlement in Poland’, Computers, Environment and Urban Systems, vol. 62, pp. 199–209.
- Josic, H & Bašić, M 2018, ‘Reconsidering Zipf's law for regional development: The case of settlements and cities in Croatia’, Miscellanea Geographica – Regional Studies on Development, vol. 22, no. 1, pp. 22–30.
- Kijek, A & Jóźwik, B 2023, ‘Income convergence: Does the catch-up process take place in Polish regions?’ in Modeling Economic Growth in Contemporary Poland (Entrepreneurship and Global Economic Growth), eds. E Bukalska, T Kijek & BS Sergi, Emerald Publishing Limited, Leeds, pp. 33–50.
- Krugman, P 1991, ‘Increasing returns and economic geography’, Journal of Political Economy, vol. 99, no. 3, pp. 483–499.
- Krugman, P 1996, ‘Urban concentration: The role of increasing returns and transport costs’, International Regional Science Review, vol. 19, no. 1/2, pp. 5–30.
- Lu, M & Wan, G 2014, ‘Urbanization and urban systems in the People's Republic of China: Research findings and policy recommendations’, Journal of Economic Surveys, vol. 28, no. 4, pp. 671–685.
- Misiak, T 2022, ‘Is the division of Western and Eastern Poland still valid? The evolution of regional convergence in Poland’, Economics and Business Review, vol. 8, no. 2, pp. 145–169.
- Moran, PAP 1950, ‘Notes on continuous stochastic phenomena’, Biometrika, vol. 37, no. 1/2, pp. 17–23.
- Moomaw, RL & Alvosabi, MA 2007, ‘Urban primacy, gigantism, and international trade: Evidence from Asia and the Americas’, Journal of Economic Integration, vol. 22, no. 2, pp. 439–460.
- Mutlu, S 1989, ‘Urban concentration and primacy revisited: An analysis and some policy conclusions’, Economic Development and Cultural Change, vol. 37, no. 3, pp. 611–639.
- Nitsch, V 2005, ‘Zipf zipped’, Journal of Urban Economics, vol. 57, no. 1, pp. 86–100.
- Nitsch, V 2006, ‘Trade openness and urban concentration: New evidence’, Journal of Economic Integration, vol. 21, no. 2, pp. 340–362.
- Paez, A, Steven, F & Wheeler, D 2011, ‘A simulation-based study of geographically weighted regression as a method for investigating spatially varying relationships’, Environment and Planning A, vol. 43, no. 12, pp. 2992–3010.
- Rosen, KT & Resnick, M 1980, ‘The size distribution of cities: an examination of the Pareto law and primacy’, Journal of Urban Economics, vol. 8, no. 2, pp. 165–186.
- Singer, HW 1936, ‘The “Courbe des populations”. A parallel to Pareto's law’, Economic Journal, vol. 46, no. 182, pp. 254–263.
- Soo, KT 2005, ‘Zipf's law for cities: A cross-country investigation’, Regional Science and Urban Economics, vol. 35, no. 3, pp. 239–263.
- Statistics Poland 2022. Available from: <
www.stat.gov.pl >. [20 May 2022]. - Zipf, GK 1949, Human behaviour and the principle of least effort: An introduction to human ecology, Adison-Wesley Press, Reading, MA.
Language: English
Submitted on: Sep 2, 2024
Accepted on: Sep 21, 2025
Published on: Apr 26, 2026
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
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© 2026 Andrzej Cieślik, published by Faculty of Geography and Regional Studies, University of Warsaw
This work is licensed under the Creative Commons Attribution 4.0 License.