Envisaging the Intrinsic Departure from Zipf’s Law as an Indicator of Economic Concentration along Urban–Rural Gradients

Adele Sateriano, Giovanni Quaranta, Rosanna Salvia, Francisco Escrivà Saneugenio, Alvaro Marucci, Luca Salvati (), Barbara Zagaglia and Francesco Chelli ()
Additional contact information
Adele Sateriano: Independent Researcher, 00184 Rome, Italy
Giovanni Quaranta: Department of Mathematics, Computer Science and Economics, University of Basilicata, 85100 Potenza, Italy
Rosanna Salvia: Department of Mathematics, Computer Science and Economics, University of Basilicata, 85100 Potenza, Italy
Francisco Escrivà Saneugenio: Department of Geography, University of Valencia, Av. Blasco Ibanez, 46010 Valencia, Spain
Alvaro Marucci: Department of Agriculture and Forest Sciences (DAFNE), University of Tuscia, Via S. Camillo de Lellis snc, 01100 Viterbo, Italy
Luca Salvati: Department of Methods and Models for Economics, Territory and Finance (MEMOTEF), Faculty of Economics, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy
Barbara Zagaglia: Department of Social and Economic Sciences, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy
Francesco Chelli: Department of Social and Economic Sciences, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy

Land, 2024, vol. 13, issue 4, 1-15

Abstract: A rank-size rule following Zipf’s law was tested along a complete urban–rural hierarchy in Greece using 2021 census data released at different administrative levels. Testing five econometric specifications (linear, quadratic, and cubic forms, together with refined logistic and Gompertz forms) on log-transformed population numbers, deviations from the rank-size rule were assumed as an indicator of economic concentration (considering settlements, population, and activities jointly) along the density gradient in Greece. This hypothesis was verified using progressively disaggregated population numbers at (i) regional units (n = 75), (ii) ‘Kallikratis’ municipalities (n = 333), (iii) ‘Kapodistrian’ municipalities (n = 1037), and (iv) local communities (n = 6126). Econometric results were stable across geographical levels and indicate a relatively poor fit of linear specifications, the classical formulation of Zipf’s law. Quadratic specifications displayed a good fit for all territorial levels outperforming cubic specifications. Gompertz specifications outperformed logistic specifications under aggregate partitions (e.g., regional units and ‘Kallikratis’ municipalities). Quadratic specifications outperformed both logistic and Gompertz specifications under disaggregated levels of investigation (‘Kapodistrian’ municipalities and local communities). Altogether, these findings indicate the persistence of non-linear rank-size relationships estimated over a cross-section of population data at progressively detailed observational units. Such evidence enriches the recent literature on Zipf’s law, demonstrating the inherent complexity of rank-size rules tested on real data along the whole density gradient in a given country.

Keywords: rank-size rule; settlement structure; regional economics; indicators; Mediterranean (search for similar items in EconPapers)
JEL-codes: Q15 Q2 Q24 Q28 Q5 R14 R52 (search for similar items in EconPapers)
Date: 2024
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