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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/5091


    Title: 「階層大小法則」之理論探討與動態過程之模擬研究
    Other Titles: The Theoretical Derivation and the Dynamic Process Simulation of the Rank-Size Rule
    Authors: 陳心蘋
    Keywords: 動態過程模擬;階層大小法則;瑞普夫定理;吉伯特定理;自我組織臨界性;複雜系統
    Dynamic process simulation;Rank-size rule;Zipf`s Law;Gibrt`s Law;Self-organized criticality;Complex system
    Date: 2000
    Issue Date: 2007-04-18 18:27:30 (UTC+8)
    Publisher: 臺北市：國立政治大學經濟學系
    Abstract: 由於實證資料顯示瑞普夫定理(Zipf`s Law)對不同經濟結構與不同時代的國家中都市大小的分佈有共同的解釋能力，此定理已被界定為都市成長模型的基本條件。吉伯特定理(Gibrat`s law)被證明為瑞普夫定理的充份條件。它是以純統計的方法來解釋都市的階層大小法則(Rank-size rule)。本文的目的在探討一般的經濟模型與純統計觀點的吉伯特定理之間的相關性。分析結果顯示一般的經濟模型，在地區選擇機率是logit型態的假設下可推導出區域都市人口的成長率有共同的平均值與變異數。根據吉伯特定理，這個同質分配的都市成長率特性隱含了區域都市的極限分配會趨近於瑞普夫定理。在沒有logit型式的選擇機率假設下，都市極限分配的型態會受到區域居民的外佈效果和廠商的聚集經濟特性的影響。當總外佈效果趨近一共同的臨界值的情形下，都市的極限分配會趨近於瑞普夫型態。實證資料顯示冪次法則(Power law)是許多具有自我組織結構(Self-organized structure)的複雜系統(Complex system)的共同特性；而區域科學中解釋城市大小分佈的普瑞夫定理(Zipf`s law)是符合冪次法則資料中最受到頻繁討論的分佈。本文主要是以動態複雜系統中自我組織結構的角度來探討冪次法則與複雜系統的相關性以及可能影響冪次參數值的原因。並進而以動態複雜系統的特性檢視以吉伯特定理(Gibrat`s law)解釋普瑞夫定理(Zipf`s law)的充分性。研究結果顯示吉伯特定理所指出的同質的隨機成長率僅能保證冪次法則的實現；而隨時間漸緩遞減標準差的隨機成長率才能衍生出趨近瑞普夫分配的城市分佈型態。隨時間漸緩遞減標準差的隨機成長率是來自於都市成長的複雜系統中逐漸增進的潛在聯繫與階層組織相互影響的敏感度。城市間的潛在連繫與相互影響敏感度越多越高，城市間的區位利益差異越小，因此都市的成長率的差異會越小。系統中潛在連繫與敏感度增進的速度會影響冪次分佈的冪次參數值與分佈收斂的速度。
    Zipf`s law has been considered the minimum criterion for the city growth model due to its robust empirical evidence across various types of countries and dates. Gibrat`s law is proved to be the condition for the emergence of Zipf`s limit distribution by a statistical method. This paper shows that a general economic growth model with logit choice probability will converge to Zipf`s law in the steady state. The growth process derived from the gravity type optimal migrant flow is homogeneous. This implies that the gravity type optimal migrant flow has limit distribution converging to Zipf`s pattern based on Gibrat`s law. Without the assumption of discrete choice probability, the pattern of region`s limit distribution is closely related to the property of the externality effects of residents and firms. Zipf`s pattern will emerge as the limit distribution if the externalities from resident and firm converge to an asymptotic value as city size getting large. Power law has been shown to be a common feature of many self-organized complex systems, and Zipf`s law in regional science is the most famous of all these distributions. This paper shows that the assumption of homogeneity of the random growth process as assumed in Gibrat`s law will generate city size distribution as power law. However, Gibrat`s law does not necessarily generate Zipf`s limiting pattern. City distribution could possibily converge to a Zipf`s pattern limiting distribution only with a diminishing decreasing standard deviation of the random growth rate. Moreover, the value of the diminishing rate of the standard deviation of city growth rate determines the speed of the convergence and the value of the converged slope. The homogeneous random evolving process is the essential underlying feature, which generates the common power law property of many complex systems. Nevertheless, the variation of the changing rate of increased potential connections and the sensitivity of interactions among cities are the major reasons for the differences of the slopes among self-organized systems.
    Description: 核定金額：493800元
    Data Type: report
    Appears in Collections:[經濟學系] 國科會研究計畫

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