中国区域人口密度模型及经济增长的空间模式
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摘要
现代社会的人口在空间上的分布并不是随意的,而是遵循一定规律的。区域人口密度模型用于描述区域单元人口密度随着其到区域中心距离变化的变动规律。任何经济活动都离不开人的参与,人作为劳动力时是经济活动的供给方,作为消费者时又是经济活动的需求方。人口分布及其变动在很大程度上反映了经济活动的态势。考察—定时段内区域经济增长的空间模式,可以从分析人口分布的变化入手。人口密度模型拟合系数的变化反映了人口分布的变化,为探讨区域经济增长的空间模式提供了新视角。
本文从功能区域的范畴,探讨了中国13个区域的人口密度模型,然后依据人口与经济的关联性,基于人口密度模型视角探讨经济增长的空间模式,并提出空间调控对策。文章可以分为以下四部分：
第一部分(第1章、第2章和第3章)：文章的研究基础,包括研究背景、框架和目标,相关研究综述和理论基础,以及数据准备、研究方法和研究区域界定。
第二部分(第4章)：区域人口分布的空间特征分析,主要包括区域人口重心分布及其演变,区域人口空间极化及其演变,区域人口密度的空间自相关分析。
第三部分(第5章)：区域人口密度模型估计,主要包括经验模型(对数模型和平方根负指数模型)拟合的验证和拟合优度对比,基于路网距离和欧氏距离的区域人口密度模型拟合结果对比,虚拟变量对对数模型的优化,以及其他模型的优化尝试。
第四部分(第6章和第7章)：区域增长模式探讨,主要包括人口密度变动与区域经济增长空间模式的关联性分析,13个研究区域经济增长的空间模式判别与探讨,区域经济增长的空间调控对策。
文章的主要结论有：
(1)区域人口重心都不同程度地偏离区域中心,从1990至2010年,除沈阳、郑州和武汉区域外的其他10个区域的人口重心都向区域中心移动。全部研究区域的人口都存在不同程度的空间极化现象,区域中心对所在区域人口空间极化的贡献度均很大。沈阳、南京、杭州、广州、成都和西安等6个区域的人口密度呈较强的正向空间自相关,表明这些区域人口分布的空间依赖性较强,武汉区域人口密度的正向空间自相关则较弱。其他区域人口密度在目前的区域单元尺度上空间自相关并不明显。
(2)区域单元人口密度随着其到区域中心距离的增加而降低。相比平方根负指数模型,中国区域人口密度更符合对数模型分布,并且随着区域的发展,区域人口密度分布越来越符合对数模型。对数模型对均质自然环境区域和非均质自然环境区域人口密度的拟合效果并没有显著差异。运用对数模型拟合区域人口密度分布时,基于路网距离拟合的判定系数从统计意义上要大于基于欧氏距离的判定系数,路网距离较欧氏距离能更好地刻画区域人口密度分布规律。引入区域单元“是否为地级市驻地”和“山地丘陵地貌比重”两个虚拟变量能提高多数区域人口密度的对数模型拟合优度,说明这两个虚拟变量对某些区域人口密度分布的解释是有益的。对数二次模型对某些区域人口密度的拟合结果要优于对数模型,但是其局限性也非常明显,即适用性相对有限。
(3)13个研究区域的区域中心人口密度在时间序列上的增长普遍都比较大,而位于边缘的区域单元人口密度在时间序列上地变化都很小,甚至没有变化。人口密度变化所反映的区域经济增长的空间模式都较为—致。区域中心经济活动相对快速增长,临近区域中心的地区也有相对较快的增长,但边缘地区增长相对缓慢甚至停滞和负增长。这种空间上的增长差异可以概括为强向心集聚及近域扩散空间模式,但不同区域在不同时间段的向心集聚程度和扩散的空间范围存在着明显差异。
Any economic activity can not do without the participation of the people. As the labour force, people can act as the supply side of economic activities. And as the consumer, people can act as the demand side of economic activities. The trend of economic activities can be clearly reflected by population distribution and it's changes. By analyzing population distribution and its' changes, we can inspect the spatial pattern of regional economic growth condition. Regional population density model can be used to describe the regional population density and it's changes with the distance from regional center. The changes of the fitting coefficient of population density model can show the changes of population distribution, and offer a new perspective of the research on spatial pattern of regional economic growth.
According to the relationship of population and economy, this research firstly discusses thirteen regional population density models in China from the perspective of functional area. Secondly, inquiring into the spatial pattern of regional economic growth based on population density model. And then put forward a set of spatial regulation policies. This article can be divided into the following four parts:
First part (including chapter one, two, and three) introducing the research backgrounds, research framework, research objective, research bases, and a review of related researches.
Second part (chapter four) mainly discussing the spatial characteristics of regional population density distribution. The research points include the gravity centers of regional population distribution and it's changes, regional population spatial polarization and it's evolution, spatial autocorrelation analysis of regional population density.
Third part (chapter five) evaluates the regional population density. Firstly, doing fitting test and comparing the fitting goodness of the empirical models that are logarithmic models and the square root of negative exponential models. Secondly, comparing the fitting results of regional population density model based on street network distance and euclidean distance. Thirdly, discussing the fitting effects of importing dummy variables. Lastly, trying some other models to see the fitting results.
Fourth part (including chapter six, and seven) discussing the regional growth patterns. Firstly, the part analyzing the changes of regional population density and the spatial pattern of regional economic growth. Secondly, discriminating and discussing the spatial pattern of the economic development in thirteen regions. Lastly, putting forward a set of spatial regulation policies.
The main conclusions of the article are as follows:
(1) The gravity centers of regional population all deviate from regional centers in different degrees. From1990to2010, all the regional population gravity centers moved to regional centers except Shenyang, Zhengzhou, and Wuhan. All of the regional population exists the phenomenon of spatial polarization in different degrees. Regional centers makes a great contribution to population spatial polarization. Six regions'population density show a strong positive spatial autocorrelation, such as Shenyang, Nanjing, Guangzhou, Hangzhou, Chengdu, and Xi'an. This states that there is great spatial dependence of regional population in these regions. However, the population density in Wuhan shows relatively less positive spatial autocorrelation. Other regions do not show any spatial autocorrelation.
(2) Regional population density declines with the increasing distance from the region center. Comparing with the square root of negative exponential model, logarithmic model is more suitable to Chinese regional population density. When using logarithmic model to analyze the distribution of regional population density, the determination coefficient based on street network distance is higher than the determination coefficient based on euclidean distance. This means street network distance can be better suited to describe the regional population density than euclidean distance. By introducing dummy variables, such as wether prefecture level city or not, the proportion of mountainous and hilly landform, the fitting results become better. Therefore, the two dummy variables are beneficial to describe the distribution of population density. The fitting results of Logrithtic-Quadratic model are better than logarithmic model, but the applicability is limited.
(3) All the economic development patterns reflected by the population density model of the thirteen regions are nearly the same. The economic develops faster in regional center, areas near the regional center grows relatively faster than other places. However, the marginal areas develops too slowly, even shows negative growth trend. This shows the spatial difference of regional growth. That is strong agglomeration and near place spatial diffusion pattern, which are greatly different in spatial scale during different periods.
本文从功能区域的范畴,探讨了中国13个区域的人口密度模型,然后依据人口与经济的关联性,基于人口密度模型视角探讨经济增长的空间模式,并提出空间调控对策。文章可以分为以下四部分：
第一部分(第1章、第2章和第3章)：文章的研究基础,包括研究背景、框架和目标,相关研究综述和理论基础,以及数据准备、研究方法和研究区域界定。
第二部分(第4章)：区域人口分布的空间特征分析,主要包括区域人口重心分布及其演变,区域人口空间极化及其演变,区域人口密度的空间自相关分析。
第三部分(第5章)：区域人口密度模型估计,主要包括经验模型(对数模型和平方根负指数模型)拟合的验证和拟合优度对比,基于路网距离和欧氏距离的区域人口密度模型拟合结果对比,虚拟变量对对数模型的优化,以及其他模型的优化尝试。
第四部分(第6章和第7章)：区域增长模式探讨,主要包括人口密度变动与区域经济增长空间模式的关联性分析,13个研究区域经济增长的空间模式判别与探讨,区域经济增长的空间调控对策。
文章的主要结论有：
(1)区域人口重心都不同程度地偏离区域中心,从1990至2010年,除沈阳、郑州和武汉区域外的其他10个区域的人口重心都向区域中心移动。全部研究区域的人口都存在不同程度的空间极化现象,区域中心对所在区域人口空间极化的贡献度均很大。沈阳、南京、杭州、广州、成都和西安等6个区域的人口密度呈较强的正向空间自相关,表明这些区域人口分布的空间依赖性较强,武汉区域人口密度的正向空间自相关则较弱。其他区域人口密度在目前的区域单元尺度上空间自相关并不明显。
(2)区域单元人口密度随着其到区域中心距离的增加而降低。相比平方根负指数模型,中国区域人口密度更符合对数模型分布,并且随着区域的发展,区域人口密度分布越来越符合对数模型。对数模型对均质自然环境区域和非均质自然环境区域人口密度的拟合效果并没有显著差异。运用对数模型拟合区域人口密度分布时,基于路网距离拟合的判定系数从统计意义上要大于基于欧氏距离的判定系数,路网距离较欧氏距离能更好地刻画区域人口密度分布规律。引入区域单元“是否为地级市驻地”和“山地丘陵地貌比重”两个虚拟变量能提高多数区域人口密度的对数模型拟合优度,说明这两个虚拟变量对某些区域人口密度分布的解释是有益的。对数二次模型对某些区域人口密度的拟合结果要优于对数模型,但是其局限性也非常明显,即适用性相对有限。
(3)13个研究区域的区域中心人口密度在时间序列上的增长普遍都比较大,而位于边缘的区域单元人口密度在时间序列上地变化都很小,甚至没有变化。人口密度变化所反映的区域经济增长的空间模式都较为—致。区域中心经济活动相对快速增长,临近区域中心的地区也有相对较快的增长,但边缘地区增长相对缓慢甚至停滞和负增长。这种空间上的增长差异可以概括为强向心集聚及近域扩散空间模式,但不同区域在不同时间段的向心集聚程度和扩散的空间范围存在着明显差异。
Any economic activity can not do without the participation of the people. As the labour force, people can act as the supply side of economic activities. And as the consumer, people can act as the demand side of economic activities. The trend of economic activities can be clearly reflected by population distribution and it's changes. By analyzing population distribution and its' changes, we can inspect the spatial pattern of regional economic growth condition. Regional population density model can be used to describe the regional population density and it's changes with the distance from regional center. The changes of the fitting coefficient of population density model can show the changes of population distribution, and offer a new perspective of the research on spatial pattern of regional economic growth.
According to the relationship of population and economy, this research firstly discusses thirteen regional population density models in China from the perspective of functional area. Secondly, inquiring into the spatial pattern of regional economic growth based on population density model. And then put forward a set of spatial regulation policies. This article can be divided into the following four parts:
First part (including chapter one, two, and three) introducing the research backgrounds, research framework, research objective, research bases, and a review of related researches.
Second part (chapter four) mainly discussing the spatial characteristics of regional population density distribution. The research points include the gravity centers of regional population distribution and it's changes, regional population spatial polarization and it's evolution, spatial autocorrelation analysis of regional population density.
Third part (chapter five) evaluates the regional population density. Firstly, doing fitting test and comparing the fitting goodness of the empirical models that are logarithmic models and the square root of negative exponential models. Secondly, comparing the fitting results of regional population density model based on street network distance and euclidean distance. Thirdly, discussing the fitting effects of importing dummy variables. Lastly, trying some other models to see the fitting results.
Fourth part (including chapter six, and seven) discussing the regional growth patterns. Firstly, the part analyzing the changes of regional population density and the spatial pattern of regional economic growth. Secondly, discriminating and discussing the spatial pattern of the economic development in thirteen regions. Lastly, putting forward a set of spatial regulation policies.
The main conclusions of the article are as follows:
(1) The gravity centers of regional population all deviate from regional centers in different degrees. From1990to2010, all the regional population gravity centers moved to regional centers except Shenyang, Zhengzhou, and Wuhan. All of the regional population exists the phenomenon of spatial polarization in different degrees. Regional centers makes a great contribution to population spatial polarization. Six regions'population density show a strong positive spatial autocorrelation, such as Shenyang, Nanjing, Guangzhou, Hangzhou, Chengdu, and Xi'an. This states that there is great spatial dependence of regional population in these regions. However, the population density in Wuhan shows relatively less positive spatial autocorrelation. Other regions do not show any spatial autocorrelation.
(2) Regional population density declines with the increasing distance from the region center. Comparing with the square root of negative exponential model, logarithmic model is more suitable to Chinese regional population density. When using logarithmic model to analyze the distribution of regional population density, the determination coefficient based on street network distance is higher than the determination coefficient based on euclidean distance. This means street network distance can be better suited to describe the regional population density than euclidean distance. By introducing dummy variables, such as wether prefecture level city or not, the proportion of mountainous and hilly landform, the fitting results become better. Therefore, the two dummy variables are beneficial to describe the distribution of population density. The fitting results of Logrithtic-Quadratic model are better than logarithmic model, but the applicability is limited.
(3) All the economic development patterns reflected by the population density model of the thirteen regions are nearly the same. The economic develops faster in regional center, areas near the regional center grows relatively faster than other places. However, the marginal areas develops too slowly, even shows negative growth trend. This shows the spatial difference of regional growth. That is strong agglomeration and near place spatial diffusion pattern, which are greatly different in spatial scale during different periods.
引文
[1]Clark,C.. Urban Population densities[J]. Journal of the Royal Statistical Society,1951,114 (4):490-496.
[2]Mills, E. S., Tan, J. P.. A Comparison of Urban Populaiton Density Functions in Developed and Developing Countries[J].1980,17 (3):313-321.
[3]Mills, E. S.. Studies in the Structure of the Urban Economy[M]. Baltimor:Johns Hopkins University,1972.
[4]Muth, R.. Cities and Housing[M]. Chicago:University of Chicago,1969.
[5]Casetti, E. Spatial Analysis:Perspectives and Prospect[J].Urban Geography,1993, (14):526-537.
[6]Wang F, Guldmann JM. Simulating urban population density with a gravity-based model[J]. Socio-Economic Planning Sciences,1996,30(4):245-256.
[7]Tanner J. Factors affecting the amount of travel[J]. Road Research Technical Paper NO 51, London:HMSO, 1961.
[8]Sherratt G. A model for general urban growth. In Management Sciences:Models and Techniques, Churchman C W, Verhulst M, Eds. Oxford:Pergamon Press,1960.
[9]McDonald, J.,Bowman, H.. Some Test of Alternative Urban Population Density Functions[J] Journal of Urban Economics,1976, (3):241-252.
[10]Kau J B., Lee C F. The functional form in estimating the density gradient:An empirical investigation[J]. Journal of the American Statistical Association,1976,71(354):326-327.
[11]Kau J. B., Lee C.F., Chen R.C..Structural Shifts in Urban Population Density Gradients:An Empirical Investigation[J].Journal of Urban Economics,1983,13 (3):364-377.
[12]Suits, D., Mason, A., Chan, L. Spline Functions Fitted by Standard Regression Methods[J].Review of Econonimcs and Statistics,1978,60:132-139.
[13]Anderson J..Cubic Spline Urban Density Functions[J].Journal of Urban Economics,1982,12:155-167.
[14]Anderson, J..The Changing Structure of a City:Temporal Changes in Cubic Spline Urban Density Patterns[J] Journal of Regional Science,1985,25:413-425.
[15]Brueckner, J..Testing a Vintage Model of Urban Growth [J]. Journal of Regional Science,1981,21:23-36.
[16]Brueckner, J..A Switching Regression Aanalysis of Urban Population Densities[J] Journal of Urban Economics,1986,19:174-189.
[17]Johnson, S., Kau, J.Urban Spatial Structure:An Analysis with a Varying Coefficient Model [J] Journal of Urban Economics,1980,7:141-154.
[18]Zheng,X. Metropolitan Spatial Structure and its Determinants:A Case Study of Tokyo[J].Urban Studies, 1991,28:87-104.
[19]Small, K. A., Song, S..Population and Employment Densities:Structure and Change[J].Journal of Urban Economics,1994,36 (3):292-313.
[20]Heikkila,E.P., Gordon,P., Kim,J., et al.What Happened to the CBD-Disance Gradient?Land Values in a Polycentric City[J].Environment and PlanningA,1989,21:221-232.
[21]McDonald J F, Prather P J. Suburban employment centres:the case of Chicago[J]. Urban Studies,1994, 31(2):201-218.
[22]Griffith D A. Modelling urban population density in a multi-centered city[J]. Journal of Urban Economics, 1981,9(3):298-310.
[23]Wang F. Modeling Commuting Patterns in Chicago in a GIS Environment:A Job Accessibility Perspective[J].Professional Geographer,2000,52 (1):120-133.
[24]Gordon,P., Richardson, H., Wong, H..The Distribution of Population and Employment in A Polycentric City:the Case of Los Angeles[J].Environment and Planning A,1968,18:161-173.
[25]Forstall, R.L., Greence, R.P..Defining Job Concentration:the Los Angeles Case[J].Urban Geography,1968, 18:705-739.
[26]Giuliano,G., Small, K.A..Subcenters in the Los Angeles Region[J].Regional Science and Urban Economics, 1991,18:163-182.
[27]周春山,许学强.广州市人口空间分布特征及演变趋势分析[J].热带地理,1997,17(1)：53-60.
[28]Wang F., Zhou Y X.. Modeling urban population densities in Beijing 1982-1990:Suburbanization and its causes[J].Urban Studies,1999,36 (2):271-287.
[29]沈建法,王桂新.90年代上海中心城人口分布及其变动趋势的模型研究[J].中国人口科学,2000,(5)：45-52.
[30]冯健.杭州市人口密度空间分布及其演化的模型研究[J].地理研究,2002,21(5)：635-646.
[31]谢守红,宁越敏.广州市人口密度分布及演化模型研究[J].数理统计与管理,2006,25(5)：518-522.
[32]李俊莉,王慧,曹明明.西安市人口的分布变动研究[J].人文地理,2005,20(1)：121-125.
[33]张岸,齐清文.基于GIS的城市内部人口空间结构研究——以深圳市为例[J].地理科学进展,2007,26(1)：95-105.
[34]高向东,吴文钰.20世纪90年代上海市人口分布变动及模拟[J].地理学报,2005,60(4)：637-644.
[35]Parr J B. The Form of the Regional Density Function[J].Regional Studies,1985,16(6):535-546.
[36]Parr J B.. A Population Density Approach to Regional Spatial Structure[J], rban Studies,1985,22 (4): 289-303.
[37]冯健,周一星.近20年来北京都市区人口增长与分布[J].地理学报,2003,58(6)：903-916.
[38]吴文钰,马西亚.1990年代上海人口密度模型及演变[J].市场与人口分析,2007,13(2)：40-47.
[39]王法辉.基于GIS的数量方法与应用[M].姜世国,滕骏华,译.北京：商务印书馆,2011.
[40]王法辉,金凤君,曾光.区域人口密度函数与增长模式：兼论城市吸引范围划分的GIS方法[J].地理研究,2004,23(1)：97-103.
[41]Wang F. Regional density functions and growth patterns in major plains of China,1982-1990[J]. Papers in Regional Science,2001,80(2):231-240.
[42]孙铁山,李国平,卢明华.基于区域密度函数的区域空间结构与增长模式研究——以京津冀都市圈为例[J].地理科学,2009,29(4)：500-507.
[43]Leibenstein, H..Economic Backwardness and Economic Growth [M].Wiley:New York,1957.
[44]Keynes, J. M..Some Economic Consequence of a Declining Population[J].Eugenics Review,1937,29 (1):13-17.
[45]Hansen, A..Progress and Declining Population[J].American Economic Review,1939,29 (1):1-15.
[46]Simon, j..The Ultimate Resource[M].Princeton, New Jersey:Princeton University Press,1981.
[47]库兹涅茨.现代经济增长[M].北京：经济科学出版社,1989.
[48]陆玉麒.人口移动与区域经济格局变动[J].地理研究,1990,9(1)：42-46.
[49]刘毅,张建梅,程慧.人口增长对经济增长的影响作用分析——对广东改革开放以来的实证检验[J].经济问题探索,2007,(10)：177-182.
[50]王桂新,陈冠春.中国人口变动与经济增长[J].人口学刊,2010, (3)：3-9.
[51]Barkley D.L., Henry M.S., Bao S.. Identifying "Spread" Versus "backwash" Effects in Regional Economic Areas:A density functions approach[J].Land Economics,1996,72, (3):336-357.
[52]黄永斌,白永平,李建豹.基于区域密度函数的兰-西城市区域人口聚散研究[J].地域研究与开发,2011,30(5)：30-35.
[53]汤韵,梁若冰.台湾都会区人口空间变动模式及其原因探析——基于区域人口密度函数的分析[J].华侨大学学报(哲学社会科学版),2011, (4)：38-44.
[54]Ravenstein E. G..The Laws of Migration[J].Journal of the Statistical Society of London,1885,48 (2):167-235.
[55]Lee, E. S..A theory of migration[J].The statistical study of human population,1966,3(1):47-57.
[56]Herberle R..The Causes of Rural-Urban Migration a Survey of German Theories[J].American Journal of Sociology,1938,43 (6):932-950.
[57]Kuznets,S., Murphy,J.T..Modern economic growth:Rate, structure, and spread[M]. New Haven:Yale University Press,1966.
[58]Kuznets,S..Economic growth and income inequality[J].The American economic review,1955,45 (1): 1-28.
[59]Leibenstein,H..Allocative efficiency vs."X-efficiency"[J].The American Economic Review,1966,56 (3)-.392-415.
[60]Nelson,R.R..An evolutionary theory of economic change[M]. Harvard University Press,1982.
[61]Rosenstein-Rodan,P.N..Problems of industrialisation of eastern and south-eastern Europe[J]. The Economic Journal,1943:202-211.
[62]Nurkse,R..Problems of capital formation in underdeveloped countries[J].1966.
[63]Myrdal,G..Economic Theory and Under-Development Regions[M]. Gerarld Duckworth,1957.
[64]Perroux F. Economic space:theory and applications[J]. The Quarterly Journal of Economics,1950,64(1): 89-104.
[65]Friedmann J, Miller J. The urban field[J]. Journal of the American institute of Planners,1965.31(4):312-320.
[66]崔功豪,魏清泉,刘科伟.区域分析与区域规划[M].北京：高等教育出本社,2006.
[67]许学强,周一星,宁越敏.城市地理学[M].北京：高等教育出版社,2000.
[68]殷江滨,李郇.中国人口流动与城镇化进程的回顾与展望[J].城市问题,2012,(209)：23-29.
[69]Esteban,J.M.,Ray,D..On the measurement of polarization[J]. ECONOMETRICA-EVANSTON ILL-,1994, 62:819-819.
[70]Esteban,J., Ray, D..On the measurement of polarization [J].Econometrica,1994,62:819-851.
[71]Wolfson, C. When inequalities diverge[J].American Economic Review,1994,84:353-358.
[72]Kanbur,R., Zhang,X..Which regional inequality? The evolution of rural-urban and inland-coastal inequality in China from 1983 to 1995[J]. Journal of Comparative Economics,1999,27:686-701.
[73]郭腾云.近50年来我国区域经济空间极化的变化趋势研究[J].经济地理,2004,24(6)：743-747.
[74]Shannon,C.E..A mathematical theory of communication[J]. ACM SIGMOBILE Mobile Computing and Communications Review,2001,5(1):3-55.
[75]Theil,H.. Principles of econometrics[J].1971.
[76]Hirschman,A.O..National power and the structure of foreign trade[M].Univ of California Press,1980.
[77]朱沁夫,李昭,杨樨.用地理集中指数衡量游客集中程度方法的一个改进[J].旅游学刊,2011,26(4)：26-29.
[78]Wang Y Q, Tsui K Y. Polarization orderings and new classes of polarization indices[J]. Journal of Public Economic Theory,2000,2(3):349-363.
[79]吴庆平.巧用SPSS进行单边t检验[J].丽江学院学报,2011,30(5)：16-18.
[80]段平忠.1978年以来我国地区差距形成过程中人口流动的影响分析[J].中国人口·资源与环境,2008,18(5)：27-33.
[81]Solow,R.M..A Contribution to the Theory of Economic Growth[J]Quarterly Journal of Economics, 1956,70(2):203-223.
[82]Solow,R.M..Technical and the Aggregate Production Function[J].Review of Economic Studies, 1957,39(3):327-345.
[83]Swan,T.W..Economic Growth and Capital Accumulation[J].Economic Record,1956,32:334-361.
[84]Nelson,R.R..A Theory of the Low Level Equilibrium Trap[J].American Economic Review, 1956,46(2):894-908.
[85]Rosenstein-Rodan,P.N..Problems of Industrialization of Eastern and South-Eastern EuropefJ].Economic Journal,1943,53(l):43-50.
[86]Leibenstein,H..General efficiency Theory and Economic Development[M].London:Oxford Univeristy Press,1978.
[87]Nurkes,R.International Problems of Economic Development[J].American Economic Review,1952, 5(1):64-73.
[88]Nurkse,R..Problems of Capital Formation in Underdeveloped Countries[M].London:Oxford Univeristy Press,1952.
[89]陈雯,段学军,陈江龙,等.空间开发功能区划的方法[J].地理学报,2004,59(增刊)：53-58.
[90]Christensen,N.L., Bartuska,A.M., Brown,J.H.,et al.The report of the Ecological Society of America Committee on the scientific basis for ecosystem management.Ecological Applications[J]. Ecological Applications,1996,6(3):665-691.
[91]Franklin,J.F..Preserving biodiversity:Species,ecosystems, or landscapes[J].Ecological Applications, 1993,3:202-205.
[92]Wang,X.H.,Chen,X.Y..Applications of Miyawaki method to the construction of Shanghai urban ecological environment[J].Shanghai Environ Sci,1999,18(2):10-104.
[2]Mills, E. S., Tan, J. P.. A Comparison of Urban Populaiton Density Functions in Developed and Developing Countries[J].1980,17 (3):313-321.
[3]Mills, E. S.. Studies in the Structure of the Urban Economy[M]. Baltimor:Johns Hopkins University,1972.
[4]Muth, R.. Cities and Housing[M]. Chicago:University of Chicago,1969.
[5]Casetti, E. Spatial Analysis:Perspectives and Prospect[J].Urban Geography,1993, (14):526-537.
[6]Wang F, Guldmann JM. Simulating urban population density with a gravity-based model[J]. Socio-Economic Planning Sciences,1996,30(4):245-256.
[7]Tanner J. Factors affecting the amount of travel[J]. Road Research Technical Paper NO 51, London:HMSO, 1961.
[8]Sherratt G. A model for general urban growth. In Management Sciences:Models and Techniques, Churchman C W, Verhulst M, Eds. Oxford:Pergamon Press,1960.
[9]McDonald, J.,Bowman, H.. Some Test of Alternative Urban Population Density Functions[J] Journal of Urban Economics,1976, (3):241-252.
[10]Kau J B., Lee C F. The functional form in estimating the density gradient:An empirical investigation[J]. Journal of the American Statistical Association,1976,71(354):326-327.
[11]Kau J. B., Lee C.F., Chen R.C..Structural Shifts in Urban Population Density Gradients:An Empirical Investigation[J].Journal of Urban Economics,1983,13 (3):364-377.
[12]Suits, D., Mason, A., Chan, L. Spline Functions Fitted by Standard Regression Methods[J].Review of Econonimcs and Statistics,1978,60:132-139.
[13]Anderson J..Cubic Spline Urban Density Functions[J].Journal of Urban Economics,1982,12:155-167.
[14]Anderson, J..The Changing Structure of a City:Temporal Changes in Cubic Spline Urban Density Patterns[J] Journal of Regional Science,1985,25:413-425.
[15]Brueckner, J..Testing a Vintage Model of Urban Growth [J]. Journal of Regional Science,1981,21:23-36.
[16]Brueckner, J..A Switching Regression Aanalysis of Urban Population Densities[J] Journal of Urban Economics,1986,19:174-189.
[17]Johnson, S., Kau, J.Urban Spatial Structure:An Analysis with a Varying Coefficient Model [J] Journal of Urban Economics,1980,7:141-154.
[18]Zheng,X. Metropolitan Spatial Structure and its Determinants:A Case Study of Tokyo[J].Urban Studies, 1991,28:87-104.
[19]Small, K. A., Song, S..Population and Employment Densities:Structure and Change[J].Journal of Urban Economics,1994,36 (3):292-313.
[20]Heikkila,E.P., Gordon,P., Kim,J., et al.What Happened to the CBD-Disance Gradient?Land Values in a Polycentric City[J].Environment and PlanningA,1989,21:221-232.
[21]McDonald J F, Prather P J. Suburban employment centres:the case of Chicago[J]. Urban Studies,1994, 31(2):201-218.
[22]Griffith D A. Modelling urban population density in a multi-centered city[J]. Journal of Urban Economics, 1981,9(3):298-310.
[23]Wang F. Modeling Commuting Patterns in Chicago in a GIS Environment:A Job Accessibility Perspective[J].Professional Geographer,2000,52 (1):120-133.
[24]Gordon,P., Richardson, H., Wong, H..The Distribution of Population and Employment in A Polycentric City:the Case of Los Angeles[J].Environment and Planning A,1968,18:161-173.
[25]Forstall, R.L., Greence, R.P..Defining Job Concentration:the Los Angeles Case[J].Urban Geography,1968, 18:705-739.
[26]Giuliano,G., Small, K.A..Subcenters in the Los Angeles Region[J].Regional Science and Urban Economics, 1991,18:163-182.
[27]周春山,许学强.广州市人口空间分布特征及演变趋势分析[J].热带地理,1997,17(1)：53-60.
[28]Wang F., Zhou Y X.. Modeling urban population densities in Beijing 1982-1990:Suburbanization and its causes[J].Urban Studies,1999,36 (2):271-287.
[29]沈建法,王桂新.90年代上海中心城人口分布及其变动趋势的模型研究[J].中国人口科学,2000,(5)：45-52.
[30]冯健.杭州市人口密度空间分布及其演化的模型研究[J].地理研究,2002,21(5)：635-646.
[31]谢守红,宁越敏.广州市人口密度分布及演化模型研究[J].数理统计与管理,2006,25(5)：518-522.
[32]李俊莉,王慧,曹明明.西安市人口的分布变动研究[J].人文地理,2005,20(1)：121-125.
[33]张岸,齐清文.基于GIS的城市内部人口空间结构研究——以深圳市为例[J].地理科学进展,2007,26(1)：95-105.
[34]高向东,吴文钰.20世纪90年代上海市人口分布变动及模拟[J].地理学报,2005,60(4)：637-644.
[35]Parr J B. The Form of the Regional Density Function[J].Regional Studies,1985,16(6):535-546.
[36]Parr J B.. A Population Density Approach to Regional Spatial Structure[J], rban Studies,1985,22 (4): 289-303.
[37]冯健,周一星.近20年来北京都市区人口增长与分布[J].地理学报,2003,58(6)：903-916.
[38]吴文钰,马西亚.1990年代上海人口密度模型及演变[J].市场与人口分析,2007,13(2)：40-47.
[39]王法辉.基于GIS的数量方法与应用[M].姜世国,滕骏华,译.北京：商务印书馆,2011.
[40]王法辉,金凤君,曾光.区域人口密度函数与增长模式：兼论城市吸引范围划分的GIS方法[J].地理研究,2004,23(1)：97-103.
[41]Wang F. Regional density functions and growth patterns in major plains of China,1982-1990[J]. Papers in Regional Science,2001,80(2):231-240.
[42]孙铁山,李国平,卢明华.基于区域密度函数的区域空间结构与增长模式研究——以京津冀都市圈为例[J].地理科学,2009,29(4)：500-507.
[43]Leibenstein, H..Economic Backwardness and Economic Growth [M].Wiley:New York,1957.
[44]Keynes, J. M..Some Economic Consequence of a Declining Population[J].Eugenics Review,1937,29 (1):13-17.
[45]Hansen, A..Progress and Declining Population[J].American Economic Review,1939,29 (1):1-15.
[46]Simon, j..The Ultimate Resource[M].Princeton, New Jersey:Princeton University Press,1981.
[47]库兹涅茨.现代经济增长[M].北京：经济科学出版社,1989.
[48]陆玉麒.人口移动与区域经济格局变动[J].地理研究,1990,9(1)：42-46.
[49]刘毅,张建梅,程慧.人口增长对经济增长的影响作用分析——对广东改革开放以来的实证检验[J].经济问题探索,2007,(10)：177-182.
[50]王桂新,陈冠春.中国人口变动与经济增长[J].人口学刊,2010, (3)：3-9.
[51]Barkley D.L., Henry M.S., Bao S.. Identifying "Spread" Versus "backwash" Effects in Regional Economic Areas:A density functions approach[J].Land Economics,1996,72, (3):336-357.
[52]黄永斌,白永平,李建豹.基于区域密度函数的兰-西城市区域人口聚散研究[J].地域研究与开发,2011,30(5)：30-35.
[53]汤韵,梁若冰.台湾都会区人口空间变动模式及其原因探析——基于区域人口密度函数的分析[J].华侨大学学报(哲学社会科学版),2011, (4)：38-44.
[54]Ravenstein E. G..The Laws of Migration[J].Journal of the Statistical Society of London,1885,48 (2):167-235.
[55]Lee, E. S..A theory of migration[J].The statistical study of human population,1966,3(1):47-57.
[56]Herberle R..The Causes of Rural-Urban Migration a Survey of German Theories[J].American Journal of Sociology,1938,43 (6):932-950.
[57]Kuznets,S., Murphy,J.T..Modern economic growth:Rate, structure, and spread[M]. New Haven:Yale University Press,1966.
[58]Kuznets,S..Economic growth and income inequality[J].The American economic review,1955,45 (1): 1-28.
[59]Leibenstein,H..Allocative efficiency vs."X-efficiency"[J].The American Economic Review,1966,56 (3)-.392-415.
[60]Nelson,R.R..An evolutionary theory of economic change[M]. Harvard University Press,1982.
[61]Rosenstein-Rodan,P.N..Problems of industrialisation of eastern and south-eastern Europe[J]. The Economic Journal,1943:202-211.
[62]Nurkse,R..Problems of capital formation in underdeveloped countries[J].1966.
[63]Myrdal,G..Economic Theory and Under-Development Regions[M]. Gerarld Duckworth,1957.
[64]Perroux F. Economic space:theory and applications[J]. The Quarterly Journal of Economics,1950,64(1): 89-104.
[65]Friedmann J, Miller J. The urban field[J]. Journal of the American institute of Planners,1965.31(4):312-320.
[66]崔功豪,魏清泉,刘科伟.区域分析与区域规划[M].北京：高等教育出本社,2006.
[67]许学强,周一星,宁越敏.城市地理学[M].北京：高等教育出版社,2000.
[68]殷江滨,李郇.中国人口流动与城镇化进程的回顾与展望[J].城市问题,2012,(209)：23-29.
[69]Esteban,J.M.,Ray,D..On the measurement of polarization[J]. ECONOMETRICA-EVANSTON ILL-,1994, 62:819-819.
[70]Esteban,J., Ray, D..On the measurement of polarization [J].Econometrica,1994,62:819-851.
[71]Wolfson, C. When inequalities diverge[J].American Economic Review,1994,84:353-358.
[72]Kanbur,R., Zhang,X..Which regional inequality? The evolution of rural-urban and inland-coastal inequality in China from 1983 to 1995[J]. Journal of Comparative Economics,1999,27:686-701.
[73]郭腾云.近50年来我国区域经济空间极化的变化趋势研究[J].经济地理,2004,24(6)：743-747.
[74]Shannon,C.E..A mathematical theory of communication[J]. ACM SIGMOBILE Mobile Computing and Communications Review,2001,5(1):3-55.
[75]Theil,H.. Principles of econometrics[J].1971.
[76]Hirschman,A.O..National power and the structure of foreign trade[M].Univ of California Press,1980.
[77]朱沁夫,李昭,杨樨.用地理集中指数衡量游客集中程度方法的一个改进[J].旅游学刊,2011,26(4)：26-29.
[78]Wang Y Q, Tsui K Y. Polarization orderings and new classes of polarization indices[J]. Journal of Public Economic Theory,2000,2(3):349-363.
[79]吴庆平.巧用SPSS进行单边t检验[J].丽江学院学报,2011,30(5)：16-18.
[80]段平忠.1978年以来我国地区差距形成过程中人口流动的影响分析[J].中国人口·资源与环境,2008,18(5)：27-33.
[81]Solow,R.M..A Contribution to the Theory of Economic Growth[J]Quarterly Journal of Economics, 1956,70(2):203-223.
[82]Solow,R.M..Technical and the Aggregate Production Function[J].Review of Economic Studies, 1957,39(3):327-345.
[83]Swan,T.W..Economic Growth and Capital Accumulation[J].Economic Record,1956,32:334-361.
[84]Nelson,R.R..A Theory of the Low Level Equilibrium Trap[J].American Economic Review, 1956,46(2):894-908.
[85]Rosenstein-Rodan,P.N..Problems of Industrialization of Eastern and South-Eastern EuropefJ].Economic Journal,1943,53(l):43-50.
[86]Leibenstein,H..General efficiency Theory and Economic Development[M].London:Oxford Univeristy Press,1978.
[87]Nurkes,R.International Problems of Economic Development[J].American Economic Review,1952, 5(1):64-73.
[88]Nurkse,R..Problems of Capital Formation in Underdeveloped Countries[M].London:Oxford Univeristy Press,1952.
[89]陈雯,段学军,陈江龙,等.空间开发功能区划的方法[J].地理学报,2004,59(增刊)：53-58.
[90]Christensen,N.L., Bartuska,A.M., Brown,J.H.,et al.The report of the Ecological Society of America Committee on the scientific basis for ecosystem management.Ecological Applications[J]. Ecological Applications,1996,6(3):665-691.
[91]Franklin,J.F..Preserving biodiversity:Species,ecosystems, or landscapes[J].Ecological Applications, 1993,3:202-205.
[92]Wang,X.H.,Chen,X.Y..Applications of Miyawaki method to the construction of Shanghai urban ecological environment[J].Shanghai Environ Sci,1999,18(2):10-104.