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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月5日

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  • Alessandro Muolo,
  • Michele Postigliola,
  • Leonardo Salvatore Alaimo,
  • Luca Salvati

摘要

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.