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地理研究 >

2015 , Vol. 34 >Issue 9: 1755 - 1769

DOI: https://doi.org/10.11821/dlyj201509013

1978-2012年武陵山区公路通达性演化及其对经济发展的影响

  • 王武林 , 1 ,
  • 王妙妙 1 ,
  • 曹小曙 , 1, 2
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  • 1. 中山大学地理科学与规划学院,广州 510275
  • 2. 陕西师范大学交通地理与空间规划研究所,西安 710062
曹小曙（1970- ）,男,甘肃灵台人,教授,博士生导师,研究方向为交通地理与土地利用。E-mail:

作者简介：王武林（1982- ）,男,湖南邵阳人,博士研究生,研究方向为区域交通地理。E-mail:

收稿日期: 2015-03-17

  要求修回日期: 2015-06-08

  网络出版日期: 2015-09-15

基金资助

中央高校基本科研业务费专项资金（GK201303006）

国家自然科学基金项目（41171139,41130747）

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Evolution of road accessibility and its effects on economy development in Wuling Mountain Areas from 1978 to 2012

  • WANG Wulin , 1 ,
  • WANG Miaomiao 1 ,
  • CAO Xiaoshu , 1, 2
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  • 1. School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China
  • 2. Institute of Transport Geography and Spatial Planning, Shaanxi Normal University, Xi'an 710062, China

Received date: 2015-03-17

  Request revised date: 2015-06-08

  Online published: 2015-09-15

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《地理研究》编辑部
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摘要

利用通达性系数和加权平均出行时间,结合GIS网络分析和空间分析方法,探讨了1978-2012年武陵山区64个县（市、区）与武陵山区及其外围38个地级市以上城市之间通达性演化的格局和特征,并分析了2000-2012年武陵山区经济发展格局,采用柯布—道格拉斯生产函数模型,定量模拟了通达性对经济发展的影响。研究发现：1978-2000年,武陵山区通达性系数的稳定性较好,到2012年,通达性系数较小值具有向武陵山区东南部集聚的趋势。1978-2000年武陵山区的经济加权平均出行时间和人口加权出行时间的优劣程度均具有由东向西逐渐下降的“圈层式”布局的特点,到2012年,经济加权平均出行时间和人口加权平均出行时间较小值均具有向武陵山区东南部迁移的趋势,原因在于武陵山区及其外围的东部和南部城市较多且路网发展更为迅速和完善。2000-2012年,武陵山区经济发展格局相对稳定,形成了“东部和西北部强、西南部和中北部弱”的经济发展格局,但经济发展的绝对差距逐步扩大,两极分化的趋势越来越明显。2000-2012年武陵山区通达性的重要程度发生变化,通达性的优劣程度对于GDP的影响明显上升,通达性的改善在整体上较好地促进了武陵山区GDP的增长,对武陵山区经济发展的作用变得越来越重要。同时,通达性改善削弱了第一产业的发展,但对第二产业发展具有逐渐上升的正向影响,对第三产业发展的正向影响显著上升。研究充实了贫困地区交通与经济发展关系的实证和理论,对武陵山区通达性改善与经济发展具有重要的指导意义,可以为相关政策的制定提供参考依据。

关键词： 通达性; 柯布—道格拉斯生产函数; 影响; 武陵山区

本文引用格式

王武林 , 王妙妙 , 曹小曙 . 1978-2012年武陵山区公路通达性演化及其对经济发展的影响[J]. 地理研究, 2015 , 34(9) : 1755 -1769 . DOI: 10.11821/dlyj201509013

Abstract

The patterns and characteristics of accessibility evolution in 64 counties (county-level city, district) of Wuling Mountain Areas and 38 cities related to the surroundings from 1978 to 2012 are discussed. Based on the indexes of accessibility coefficient and weighted average travel time, the GIS network and space analysis are employed. Then after the pattern analysis of economic development in this region, Cobb-Douglas Production Function Model is used to simulate the impact of accessibility on economic development. The research shows that the accessibility coefficient was consistent from 1978 to 2000, but the smaller values of accessibility coefficient turned to be agglomerated towards the southeast areas from 2000 to 2012. During the period 1978-2000, both the qualities of economy weighted average travel time and population weighted average travel time showed a gradual decline from east to west, and constructed a "circling structure". However both the smaller value of economy weighted average travel time and population weighted average travel time mainly appeared in the southeast from 2000 to 2012, because of the rapid and advanced development of road networks in the eastern and southern areas. From 2000 to 2012, the patterns of economic development were relatively stable, forming an economic development pattern of "strong east and north, but weak south and central north", while the absolute gap in economic development was widening with a strong and obvious trend of polarization. At the same time, the importance of the accessibility for Wuling Mountain Areas changed. The accessibility quality had more effect on the growth of GDP, and the improvement of accessibility promoted the growth of GDP in the study area on the whole, which is more important for the local eonomic development. Meanwhile, the improvement of accessibility weakened the development of primary industry, but had a gradually increasing positive influence on the secondary industry and noticeably increasing positive influence on the tertiary industry. This paper enriches the empirical and theoretical relation between transportation and economic development in poor regions, provides reference to the formulation of relevant policies, and is instructive and meaningful to the enhancement of accessibility and economic development.

Key words： accessibility; Cobb-Douglas production function; effects; Wuling Mountain Areas

1 引言

交通基础设施及其通达性和经济社会发展之间的关系密切,国外许多学者从理论上探讨交通基础设施与经济社会之间的关系,强调了交通的作用[1-3]。Wilkie等[4-6]以刚果盆地、中国、西班牙等国家或地区为例进行实证研究,指出交通基础设施发展对资源在空间上的重新配置、经济活动的空间实现、经济结构演化等方面具有很大的影响。针对贫困地区的研究,国外学者尤其关注交通发展与贫困地区经济发展之间的关系,指出交通发展以及通达性演化在经济发展和减少贫困方面并不是万能的。相关研究包括：Bryan研究指出穿越北威尔士的公路改善工程对其边缘地区的发展而言是必要条件但不是充分条件[7];Walle探讨了越南农村公路改善对减少贫困的影响[8,9];Gibson等认为贫困地区因基础设施通道少,所以能从新的交通投资中获益较多,并以巴布亚新几内亚为例来验证这种投资的高回报率[10]。Bryceson利用埃塞俄比亚、赞比亚以及越南的调查数据,指出公路改善能扩大社会服务,但不是改善农村贫困者机动性的充分条件[11]。Barrios认为农村公路是农村基础设施的核心,对农村发展指数和收入增长产生最大的影响,通达性网络的可利用性缓解了农村的孤立状态[12]。Fan等指出公路增长的边际效益和减少贫困之间的变化很大,低等级公路每元投资比高等级公路更能促进农村和城市人口脱离贫困线[13]。Olsson以菲律宾农村为例,认为公路改善能带来广泛的直接影响和大量的间接影响[14]。类似的研究还涉及到葡萄牙的落后地区[15]、斯里兰卡[16]、中国[17]等区域。上述研究主要强调了在一定条件下交通通达性发展对经济发展或减少贫困的积极影响,但也有学者指出交通通达性发展所带来的消极影响也不容忽视：Porter研究指出尼日利亚北部区域的公路建设导致当地的人口比以前更加陷入孤立和不公的境地[18];Jacoby以尼泊尔为例,认为公路投资虽能给贫困家庭带来收益,但不能明显地减少收入的不均衡问题[19];Faber指出高速公路网络建设虽然导致了地区间运输成本下降,但也加剧了边缘地区及其城市更加边缘化[20]。
近年来,国内学者对交通与经济发展关系的研究逐步深入,研究成果主要集中在交通发展对区域空间开发和区域经济发展作用机理与作用规律,以及交通对于区域经济活动空间结构形成及二者之间的互动关系等方面[21]。金凤君等[22-26]从不同区域视角研究了交通发展与经济发展之间的关系。国内学者目前较少以贫困地区交通网络与经济发展作为研究的切入点,贫困地区的交通与区域经济发展相互关系的研究仍是较薄弱的环节。
武陵山区集革命老区、民族地区和贫困山区于一体,是中国跨省交界面大、少数民族聚集多、贫困人口分布广的集中连片特殊困难地区,也是重要的经济协作区,在中国的贫困地区中具有一定的代表性。根据2012年国务院扶贫办公布的全国连片特困地区分县名单,武陵山区共包含湖北省、湖南省、重庆市以及贵州省的64个县（市、区）,国土面积约17万km2,2012年其人口和GDP分别为3367.85万人和4439.17亿元。有鉴于此,以武陵山区为研究对象,探讨自改革开放以来武陵山区交通通达性发展演化特征,进而研究武陵山区交通通达性改善对其总体的经济发展和不同的产业发展产生何种影响,以及这种影响与其他因素如投资和劳动力相比居于何种程度,有助于加深对贫困地区交通与经济发展之间关系的认识,以充实对贫困地区交通与经济发展关系的实证和理论研究,同时也为武陵山区以及其他贫困地区的发展提供有益的参考。

2 数据来源与研究方法

2.1 数据来源

2012年6月,国务院扶贫办划定了包括武陵山区在内的11个集中连片特殊困难地区。数据处理范围涉及武陵山区及其外围的38个城市,包括湖南、湖北、贵州、重庆4个省（直辖市）及与武陵山区邻近的广西桂林市（图1）。数据来源分为两个方面：一是地图矢量化数据,扫描整理1979年中国地图出版社的《中国交通图册》[27]、1992年测绘出版社的《中国交通地图册》[28]、2000年中国地图出版社的《分省中国地图集》[29]、2013年中国地图出版社的《中国公路里程地图分册系列》[30]所涉及研究范围的地图数据,对其公路交通及城市（镇）进行矢量化处理,并根据《中国人民共和国公路工程技术标准（JTGB01-2003）》[31]规定的公路设计速度,结合区域实际和对当地若干名年老的汽车驾驶员关于车行速度的访谈,对不同年份不同类型与等级的公路赋予不同的车行速度（表1）。二是经济社会统计数据,收集了2000年和2012年武陵山区64个贫困县（市、区）和湖南、湖北、贵州、重庆以及广西桂林市共计38个地级市以上城市的经济社会统计数据。再对上述数据进行整合,建立相应的地理分析数据库。
Fig. 1 Sketch map of Wuling Mountain Areas and its peripheral areas

图1 武陵山区及其外围地区示意图

Tab. 1 Driving speeds of different grade roads

表1 不同等级公路行车速度

年份 高速公路（km/h） 国道（主要公路）（km/h） 省道（一般公路）（km/h） 县道（大道）（km/h）
1978 - 40 30 20
1990 - 50 40 30
2000 90 60 45 35
2012 100 70 50 40

2.2 研究方法

2.2.1 通达性计算方法 金凤君等提出了通达性系数的概念[32],主要指各节点的总运输距离与系统内节点总运输距离平均值的比,其计算公式为：
A di = D i ∑ D i n , i = 1,2 , … , n （1）
式中：Adi为节点i的通达性系数,通达性系数说明了整个交通网络中各节点相对通达关系水平的高低。通达性系数值越小,表明其通达性越好,反之则越差。系数最小的节点,往往具有较好的通达性水平,成为网络的交通中心。根据通达性系数的定义,将总运输空间距离Di修正为总运输时间距离Ti,以此来衡量武陵山区各县级城镇节点的通达性系数,其计算公式为：
A ti = T i ∑ T i n , i = 1,2 , … , n （2）
通达性系数能很好地表明节点在整个交通网络中的地位。
加权平均出行时间（weighted average travel time）指标是一个评价节点到各经济中心的时间测度,主要由评价节点的空间区位决定,也与经济中心的实力及连接评价节点和经济中心的交通设施质量密切相关[33]。指标得分越低,表示该节点的通达性越高,与经济中心的联系越紧密。加权平均出行时间的计算公式为：
A i = ∑ j = 1 n （ T ij × M j ） ∑ j = 1 n M j （3）
式中：Ai表示节点i的通达性;Tij表示节点i通过交通网络中通行时间最短的路线到达经济中心j所花费的时间成本;Mj表示经济中心的质量（可以是GDP、就业或人口等）;n为评价系统内除i点以外的节点总数。Ai越小表明节点i在接受经济中心辐射优势越突出,分别采用GDP和人口作为加权因子,计算出经济加权平均出行时间和人口加权平均出行时间来综合衡量区域节点的通达性水平。
2.2.2 通达性与经济发展关系分析模型 柯布—道格拉斯生产函数（Cobb-Douglas production function）是经济学中使用最广泛的生产函数,是美国数学家柯布和经济学家道格拉斯共同提出来的一个著名的生产函数,经济学家经常利用统计分析来测定要素投入和产量变动之间的关系[34],经济发展是社会生产力发展的表现,生产模型选取主要的生产要素作为输入,可建立各个要素与社会产出之间的关系,为了描述交通通达性要素对经济发展的作用,采用经典的柯布—道格拉斯生产函数：
Y = A K а L β （4）
式中：Y表示产量;A是反映技术水平的正常数;K表示投入的资本量;L表示投入的劳动力;а和β表示资本产出的弹性系数和劳动力产出的弹性系数,代表了资本和劳动力在生产过程中的重要程度。
由于交通运输对于区域经济的促进作用主要体现在降低了区域交通的流通成本,节省了客货流的时间,通过通达性的改善而促进了人流、物流、信息和资金的流动,从而为经济的增长营造了良好的区位优势,国内外许多学者曾尝试将交通因素引入柯布—道格拉斯生产函数之中进行交通与经济发展关系的研究[35,36]。本文用通达性系数来反映交通通达性优劣,并将通达性系数作为一个投入变量引入到柯布—道格拉斯生产函数中,进而对式（4）进行改进,建立新的生产模型,以考察通达性格局与经济发展关系,计算公式如下：
Y = A K а L β P γ （5）
式中：P为引入的交通通达性要素,此处指通达性系数;а、β、γ分别为资本产出、劳动力产出和交通通达性要素的投入产出弹性,代表了资本、劳动力和交通通达性要素在区域经济发展中的重要程度。对式（5）两边取对数,得到区域经济总量GDP和资本、人力以及交通通达性的关系式：
lnY = lnA + а lnK + βlnL + γlnP （6）
通过多元回归分析,即可得到资本、劳动力和交通通达性的投入产出弹性系数а、β、γ,通过3个弹性值的大小即可得出3个要素在区域经济增长中发挥的作用大小。分别用固定资产投资、从业人员数、通达性系数三个指标来衡量资本、劳动力和交通通达性。

3 通达性演化

3.1 通达性系数演化

以武陵山区64个贫困县（市、区）为起始点,以武陵山区及其外围的38个城市为目的地点,根据式（2）,利用ArcGIS软件的网络分析工具,分别求得1978年、1990年、2000年、2012年4个年份武陵山区64个县级城镇节点的通达性系数（表2、图2）。1978年、1990年、2000年三个年份武陵山区的通达性系数的稳定性较好,慈利、安化、沅陵、石门、辰溪、泸溪等县（市、区）的通达性系数较小,通达性水平相对较好;石柱、丰都、正安、道真、秭归、务川、武隆、湄潭、凤冈等县（市、区）的通达性系数较高,通达性水平相对较差。到2012年,通达性系数极小值分布发生较大变化,通达性系数较小值具有向武陵山区东南部集聚的特点,隆回、新邵、泸溪、涟源、慈利、邵阳等县（市、区）的通达性系数较小,通达性水平明显变好,原因在于武陵山区东南部路网更加密集;正安、道真、务川、湄潭、凤冈、丰都等县（市、区）的通达性系数仍然较大,其通达性水平仍然较差。
Tab. 2 Accessibility coefficient in Wuling Mountain Areas from 1978 to 2012

表2 1978-2012年武陵山区通达性系数

年份 最小值 最大值 均值 最小值前十名县（市、区）（由小到大） 最大值前十名县（市、区）（由小到大）
1978 0.83 1.43 1 慈利、安化、沅陵、石门、辰溪、麻阳、泸溪、凤凰、溆浦、永顺 巴东、凤冈、湄潭、武隆、务川、秭归、道真、正安、丰都、石柱
1990 0.83 1.41 1 安化、慈利、石门、沅陵、溆浦、辰溪、涟源、中方、泸溪、新邵 彭水、凤冈、湄潭、武隆、务川、秭归、道真、正安、丰都、石柱
2000 0.82 1.46 1 慈利、石门、沅陵、辰溪、泸溪、涟源、麻阳、新邵、安化、凤凰 通道、思南、凤冈、湄潭、武隆、务川、正安、道真、丰都、石柱
2012 0.82 1.34 1 隆回、新邵、泸溪、涟源、慈利、邵阳、洞口、凤凰、石门、中方 鹤峰、城步、五峰、丰都、通道、凤冈、湄潭、务川、道真、正安
Fig. 2 Accessibility coefficient of Wuling Mountain Areas from 1978 to 2012

图2 1978-2012年武陵山区通达性系数

3.2 加权平均出行时间演化

根据式（3）计算武陵山区64个县（市、区）的加权平均出行时间,从经济和人口两个角度分析武陵山区加权平均出行时间的演化,考察武陵山区及其外围的38个地级市以上城市对武陵山区64个县（市、区）的经济辐射和人口辐射的演化过程及特征。
（1）以GDP来衡量一个城市的质量,武陵山区64个县（市、区）的经济加权平均出行时间格局由“圈层式”向“圈层式+局部岛状”演化,均值由1978年14.18小时下降到2012年的6.30小时,其值具有由东北向西南逐渐增大的趋势（表3、图3）,原因在于38个地级市以上城市主要位于武陵山区以东,这些城市隶属于湖南省和湖北省,经济总量大于武陵山区西部外围地区的贵州省和重庆市,武陵山区64个县（市、区）受到东部外围地区经济辐射的影响大于西部外围地区。1978年、1990年和2000年,武陵山区64个县（市、区）的经济加权平均出行时间的格局基本吻合,经济加权平均出行时间较小的为慈利、石门、安化、永顺、沅陵、辰溪等县（市、区）,由此向武陵山区西部逐渐扩大,到石柱、丰都、正安、道真、秭归、务川等县（市、区）经济加权平均出行时间达到最大值。到2012年,武陵山区的经济加权平均出行时间从小到大仍具有由东向西“圈层式”扩张的态势,但经济加权平均出行时间的最小值开始向东南部迁移,原因是武陵山区及其外围的东部和南部高速公路发展更为迅速和完善,因而受到东部和南部城市的经济辐射的影响加大,经济加权平均出行时间较小的有长阳、慈利、泸溪、石门、隆回、新邵、涟源等县（市、区）,表明这些县（市、区）受武陵山区及其外围地级市以上城市的经济辐射影响最大,与上述38个地级市以上城市的经济联系最大;凤凰—泸溪、鹤峰—五峰等县（市、区）的经济加权平均出行时间形成闭合的岛状,表明这些县（市、区）与其邻近县（市、区）的经济加权平均出行时间存在不连续性;较大的为正安、务川、道真、通道、湄潭等县（市、区）,表明这些县（市、区）受武陵山区及其外围38个地级市以上城市的经济辐射影响最小,与其经济联系最小。
Tab. 3 The economy weighted average travel time of some counties in Wuling Mountain Areas from 1978 to 2012

表3 1978-2012年武陵山区部分县经济加权平均出行时间

年份 最小值(h) 最大值(h) 均值(h) 最小值前十名县(市、区)(由小到大) 最大值前十名县(市、区)(由小到大)
1978 11.26 19.15 14.18 慈利、石门、安化、永顺、沅陵、辰溪、泸溪、保靖、麻阳、溆浦 德江、凤冈、通道、湄潭、务川、秭归、道真、正安、丰都、石柱
1990 8.85 14.59 11.12 慈利、石门、安化、永顺、沅陵、长阳、涟源、辰溪、溆浦、泸溪 通道、德江、凤冈、秭归、湄潭、道真、务川、正安、丰都、石柱
2000 7.30 12.75 9.43 石门、慈利、长阳、秭归、沅陵、泸溪、安化、辰溪、涟源、五峰 凤冈、石阡、思南、湄潭、通道、丰都、道真、正安、务川、石柱
2012 5.18 8.23 6.30 长阳、慈利、泸溪、石门、隆回、新邵、涟源、秭归、邵阳、凤凰 靖州、绥宁、思南、凤冈、城步、湄潭、通道、道真、务川、正安
Fig. 3 The economy weighted average travel time in Wuling Mountain Areas from 1978 to 2012

图3 1978-2012年武陵山区经济加权平均出行时间

（2）以人口总量来衡量一个城市的质量,考虑武陵山区及其外围38个城市的人口总数所产生的辐射影响,武陵山区64个县（市、区）的人口加权平均出行时间格局与经济加权平均出行时间格局相似,具有由“圈层式”向“圈层式+局部岛链状”演化的特征,均值由1978年的13.96小时下降到2012年的6.18小时,其值具有由东向西逐渐增大的趋势（图4、表4）,原因在于外围地级市以上城市主要位于武陵山区以东,这些城市隶属于湖南省和湖北省,人口总量大于武陵山区西部外围地区的贵州省和重庆市,武陵山区64个县（市、区）受到东部外围地区人口辐射的影响大于西部外围地区。1978年、1990年、2000年,武陵山区64个县（市、区）的人口加权平均出行时间的格局基本吻合,人口加权平均出行时间较小的为慈利、永顺、麻阳、凤凰、保靖、辰溪、沅陵、泸溪等县（市、区）,由此向武陵山区西部人口加权平均出行时间逐渐扩大,到石柱、秭归、丰都、正安、道真、务川等县（市、区）达到最大值,表明这些县（市、区）受武陵山区及其外围38个地级市以上城市的人口辐射影响较小。到2012年,武陵山区的人口加权平均出行时间大体上仍具有由东向西“圈层式”扩张的态势,最小值开始部分向东南部迁移,在其南部形成了“局部岛链状”的分布格局,人口加权平均出行时间较小的有泸溪、凤凰、隆回、花垣、中方、沅陵、洞口、新邵等县（市、区）,表明这些县（市、区）受武陵山区及其外围38个地级市以上城市的人口辐射影响最大;邵阳—隆回—洞口、中方、凤凰、泸溪、花垣等县（市、区）的人口加权平均出行时间形成闭合“岛链状”的分布格局,表明这些县（市、区）的人口加权平均出行时间与邻近县（市、区）存在不连续性;人口加权平均出行时间较大的为正安、务川、道真、城步、五峰、绥宁等县（市、区）,表明这些县（市、区）受武陵山区及其外围38个地级市以上城市的人口辐射影响最小。
Fig. 4 The population weighted average travel time in Wuling Mountain Areas from 1978 to 2012

图4 1978-2012年武陵山区人口加权平均出行时间

Tab. 4 The population weighted average travel time of some counties in Wuling Mountain Areas from 1978 to 2012

表4 1978-2012年武陵山区部分县人口加权平均时间

年份 最小值(h) 最大值(h) 均值(h) 最小值前十名县(市、区)(由小到大) 最大值前十名县(市、区)(由小到大)
1978 12.14 18.27 13.96 慈利、永顺、麻阳、凤凰、保靖、辰溪、沅陵、泸溪、石门、花垣 城步、巴东、通道、务川、新邵、道真、正安、丰都、秭归、石柱
1990 9.62 14.09 10.92 慈利、永顺、石门、辰溪、沅陵、泸溪、中方、保靖、安化、凤凰 湄潭、利川、通道、巴东、道真、务川、正安、丰都、秭归、石柱
2000 7.94 12.32 9.1533 慈利、沅陵、泸溪、石门、辰溪、花垣、麻阳、凤凰、永顺、保靖 思南、湄潭、绥宁、城步、通道、丰都、正安、道真、务川、石柱
2012 5.25 7.68 6.18 泸溪、凤凰、隆回、花垣、中方、沅陵、洞口、新邵、碧江、麻阳 靖州、湄潭、鹤峰、绥宁、五峰、城步、通道、道真、务川、正安

4 通达性对经济发展的影响

4.1 经济发展格局

2000-2012年,武陵山区县域经济获得了长足的发展,GDP保持了较快的增速,2000年武陵山区GDP总量为871.04亿元,2012年上升为4439.17亿元,第一、第二、第三产业分别从341.13亿元、265.57亿元、264.34亿元增长到1027.18亿元、1647.29亿元、1661.49亿元,经济发展格局相对稳定,形成了“东部和西北部强、西南部和中北部弱”的经济发展格局（图5）。由图5可以看出,经济发展较好的县（市、区）主要位于武陵山区东部和西北部,GDP较大的主要包括涟源、石门、新化、黔江、安化、恩施、慈利、丰都等县（市、区）,GDP较小的县（市、区）主要位于武陵山区西南部和中北部,主要包括万山、古丈、江口、道真、城步、通道、务川、石阡等县（市、区）。同时,武陵山区内部县（市、区）与县（市、区）GDP之间的绝对差距逐步扩大,两极分化的趋势越来越明显。2000年和2012年武陵山区各县（市、区）中GDP最小值和最大值均为万山区和涟源市,2000年GDP最小的万山区为1.1312亿元,与最大值涟源市的32.3522亿元相差31亿元;到2012年二者差距达到172亿元。
Fig. 5 GDP patterns in Wuling Mountain Areas from 2000 to 2012

图5 2000-2012年武陵山区GDP格局图

4.2 通达性对经济发展影响

交通通达性和资本投资在形成国民生产总值中具有重要性[34]。通达性水平与经济发展密切相关,交通的发达程度决定了各地理单元空间相互作用的广度与深度,交通的发展是改变经济活动区位的重要因素之一,在一定的经济发展阶段,交通通达性的波动与经济的波动之间具有显著的同步响应关系[37]。根据数据的可获取性,按照式（6）,选取2000年和2012年武陵山区64个县（市、区）的GDP及三次产业、固定资产投资、从业人员数以及通达性系数,通达性系数为反向指标,因而对其进行同向化处理变为通达性水平,其值越大表明交通水平越好,然后对所有数据进行标准化处理,计算得到2000年和2012年固定资产投资、从业人员数以及通达性水平的回归系数а、β和γ以及常数项（表5）。
Tab. 5 Simulation result of the impact of investment in the fixed assets, employed population and accessibility

表5 固定资产投资及从业人员数与通达性的影响模拟

年份 Constant а β γ а+β+γ R2 F Sig.
2000年 GDP 0.057 0.110 0.552 0.220 0.882 0.656 36.200 0.000
第一产业 -0.221 0.016 0.560 0.156 0.732 0.677 39.744 0.000
第二产业 0.038 0.161 0.538 0.112 0.811 0.657 36.468 0.000
第三产业 -0.126 0.313 0.456 0.342 1.111 0.496 18.701 0.000
2012年 GDP 0.074 0.485 0.237 0.379 1.101 0.676 38.922 0.000
第一产业 -0.148 0.259 0.621 -0.019 0.861 0.574 25.175 0.000
第二产业 0.308 0.539 0.397 0.181 1.117 0.735 51.825 0.000
第三产业 0.142 0.831 -0.254 1.180 1.757 0.661 36.421 0.000
由表5可知,2000年和2012年GDP及三次产业的F值和显著性概率,回归方程均通过显著性检验,表明武陵山区固定资产投资、从业人员数和通达性水平三个要素可以很好地解释其对武陵山区GDP及三次产业发展的影响。回归分析的检验结果表明,将通达性水平加入到经典的柯布—道格拉斯生产函数中去,运用扩展的柯布—道格拉斯生产函数研究交通通达性对经济发展的影响具有可行性,在分析武陵山区经济发展过程和交通演化的基础上,提出通达性水平与固定资产投资和从业人员数一样,都是区域经济发展重要的影响因素,引入通达性水平,能系统地解释固定资产投资、从业人员数和通达性水平三个要素对武陵山区经济发展的综合影响,得到各要素对武陵山区经济发展的贡献率,并通过各自贡献率的比较来探讨固定资产投资、从业人员数与通达性水平在武陵山区经济发展中的联动作用及协调关系。
4.2.1 对GDP的影响 根据柯布—道格拉斯生产函数的性质,可以判断各项回归系数在武陵山区国民生产总值中的相对重要性。根据表5可知,а、β、γ分别表示固定资产投资、从业人员数以及通达性水平在形成国民生产总值中的相对重要性。
从2000年的а、β、γ的绝对值大小来看,0<а<γ<β,а、β、γ均大于0,表明固定资产投资、从业人员数以及通达性水平对GDP均存在正向的影响作用;通达性水平回归系数γ大于固定资产投资回归系数而小于从业人员数的回归系数β,表明通达性水平的重要程度要大于固定资产投资但小于从业人员数的影响,通达性水平在GDP的变化中的作用要明显强于固定资产投资,但通达性水平及固定资产投资的作用都明显小于从业人员数。а+β+γ=0.882<1,表明武陵山区GDP总量具有规模报酬递减的特征,如果忽略提高固定资产投资、从业人员数以及通达性水平,改善技术用于扩大生产规模来增加GDP是得不偿失的。
从2012年的а、β、γ的绝对值大小来看,0<β<γ<а,а、β、γ均大于0,表明固定资产投资、从业人员数以及通达性水平对GDP均存在正向的影响作用;通达性水平回归系数γ大于从业人员数回归系数β但小于固定资产投资回归系数а,表明通达性水平在GDP的变化中的作用要大于从业人员数,但通达性水平及从业人员数的作用均小于固定资产投资。2012年的а+β+γ=1.101>1,表明武陵山区GDP总量具有规模报酬递增的特点,通过提高固定资产投资、从业人员数以及通达性水平,改善技术用于扩大生产规模来增加GDP产出是有利的。
从2000年至2012年通达性水平重要程度的变化可以看出,到2012年,武陵山区通达性水平回归系数γ的值明显上升,表明其对GDP的影响明显上升。因此可以判断,2000-2012年期间,武陵山区通过改善其交通通达性水平,较好地促进了武陵山区经济的发展,交通通达性水平的改善对武陵山区经济发展的作用变得越来越重要。
4.2.2 对三次产业的影响 同理,根据柯布—道格拉斯生产函数的性质及表5中а、β、γ的值可以判断固定资产投资、从业人员数以及通达性水平在武陵山区三次产业发展过程中的相对重要性。
在对第一产业的影响方面,2000年时,0<а<γ<β,а、β、γ均大于0,表明固定资产投资、从业人员数以及通达性水平对第一产业均存在正向的影响作用,通达性水平对第一产业的影响大于固定资产投资但小于业人员数;а+β+γ=0.732<1,表明武陵山区第一产业具有规模报酬递减的特征。2012年时,γ<0<а<β,а、β均大于0而γ小于0,表明固定资产投资、从业人员数对第一产业存在正向的影响,但通达性水平对第一产业均存在负向的影响;а+β+γ=0.861<1,表明武陵山区第一产业具有规模报酬递减的特征。2000-2012年期间,通达性水平回归系数γ的值由正变负,表明其对第一产业的影响由正向影响变为负向影响,武陵山区通达性水平的改善反而逐渐削弱了第一产业的发展。
在对第二产业的影响方面,2000年时,0<γ<а<β,а、β、γ均大于0,表明固定资产投资、从业人员数以及通达性水平对第二产业均存在正向的影响作用,通达性水平对第二产业的影响小于固定资产投资与从业人员数;а+β+γ=0.811<1,表明武陵山区第二产业具有规模报酬递减的特征。2012年时,0<γ<β<а,а、β、γ均大于0,表明固定资产投资、从业人员数以及通达性水平对第二产业存在正向的影响;а+β+γ=1.117>1,表明武陵山区第二产业具有规模报酬递增的特征。2000-2012年期间,通达性水平回归系数γ的值均大于0且有所增长,表明通达性水平对第二产业的正向影响逐渐上升,武陵山区通达性水平的改善逐渐促进了第二产业的发展。
在对第三产业的影响方面,2000年时,0<а<γ<β,а、β、γ均大于0,表明固定资产投资、从业人员数以及通达性水平对第三产业均存在正向的影响作用,通达性水平对第三产业的影响大于固定资产投资但小于从业人员数;а+β+γ=1.111>1,表明武陵山区第三产业具有规模报酬递增的特征。2012年时,β<0<а<γ,а、γ均大于0而β小于0,表明固定资产投资与通达性水平对第三产业存在正向的影响,而从业人员数对第三产业发展存在负向影响;а+β+γ=1.757>1,表明武陵山区第三产业具有规模报酬递增的特征。2000-2012年期间,通达性水平回归系数γ的值由0.342增长到1.180,表明通达性水平对第三产业的正向影响显著上升,武陵山区通达性水平的改善较大地促进了第三产业的发展。

5 结论与讨论

通过分析武陵山区64个县城节点到武陵山区及其外围38个地级市以上城市的通达性演化的特征,简要分析了武陵山区64个贫困县（市、区）的经济发展格局,并利用柯布—道格拉斯生产函数,探讨了武陵山区交通通达性对GDP及三次产业的影响。主要研究结论如下：
（1）就通达性而言,武陵山区通达性的演化表现出较稳定的继承性和一定程度变化性。1978-2000年以及2012年通达性系数极值分布有所不同,研究指出了1978年、1990年、2000年以及2012年通达性较好和较差的县（市、区）。同理,利用加权平均出行时间,分析了武陵山区1978-2012年通达性格局的演变,指出武陵山区经济加权平均出行时间由“圈层式”向“圈层式+局部岛状”演化,其值具有由东北向西南逐渐增大的趋势,东北部通达性水平优于西南部,到2012年,经济加权平均出行时间最小值有向东南部移动的趋势;而人口加权平均出行时间具有由“圈层式”向“圈层式+局部岛链状”演化的特征,其值具有由东向西逐渐增大的趋势,东部通达性水平优于西部;整体而言武陵山区通达性优劣程度具有由东向西逐渐下降的“圈层式”布局的特点,到2012年,人口加权平均出行时间也有向东南部移动的趋势。
（2）2000-2012年武陵山区县域经济发展格局相对稳定,形成了“东部和西北部强、西南部和中北部弱”的经济发展格局,经济发展较好的县（市、区）主要位于武陵山区东部和西北部;同时,武陵山区内部县（市、区）与县（市、区）GDP之间的绝对差距逐步扩大,两极分化的趋势越来越明显。
（3）通达性水平与经济发展密切相关。对于GDP而言,2000-2012年武陵山区通达性水平的优劣程度GDP的影响明显上升,2000-2012年期间,武陵山区通过改善其交通通达性水平,较好地促进了武陵山区经济的发展,交通通达性水平的改善对武陵山区经济发展的作用变得越来越重要。在三次产业方面,2000-2012年,武陵山区通达性水平对第一产业的影响由正向影响变为负向影响,通达性水平的改善反而逐渐削弱了第一产业的发展;2000-2012年,武陵山区通达性水平对第二产业发展具有逐渐上升的正向影响,武陵山区通达性水平的改善逐渐促进了第二产业的发展;2000-2012年,武陵山区通达性水平对第三产业的正向影响显著上升,武陵山区通达性水平的改善较大地促进了第三产业的发展。
对于武陵山区而言,经济发展和交通改善是必然的趋势。首先要加快完善交通主通道的建设,加快形成连接重庆、武汉、长沙、贵阳等中心城市的综合运输通道;其次是完善区域内的交通网络,加快交通主通道联络线、通县公路、县际断头路公路以及农村公路的建设,扩大路网覆盖面,优化路网结构。

The authors have declared that no competing interests exist.

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俞勇军, 陆玉麒. 交通投资与经济发展的关系及其区域效应评价方法研究. 人文地理, 2005, 20(1): 27-31.交通投资与经济发展的内在关系一直没有公认的结论.大家普遍同意交通条件是经济发展的重要支 撑要素之一.交通投资只有在生产条件充足的情况下,才会促进经济发展.但交通投资并不是越多越好,而是必须与生产投资保持适当比例.交通投资对交通条件改 善的区域影响较为复杂,不同的范围有不同的影响.通达性是目前进行交通网络影响评价最为常用的手段.通达性指标有时间通达性、经济潜能和日通达性.不同的 通达性指标从不同的角度对交通网络区域效应进行评价.本文旨在对我国主要交通设施区域影响的评价研究起抛砖引玉的作用.

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[Yu Yongjun, Lu Yuqi.Studies on the relation between transport investment and economic development and regional impacts of transport improvement. Human Geography, 2005, 20(1): 27-31.]The link between transport investment and economic development is so complicate that there is no received conclusion of it. This study indicates that three sets of necessary conditions must be present to allow economic development to take place. The first condition is the presence of underlying positive economic externalities, such as agglomeration and labor market economics, the availability of a good quality labor force. The second conditions are investment factors which relate to the availability and scales of funds for the investment, and its location, the network effects, and the actual timing of the investment. The third constitutes are political factors, which are related to the broader policy environment within which transport decision must be taken. These three necessary conditions individually will have little or no impact on development. Even if they are combined on a pair-wise basis their effect will be limited. The relation between transport investment and other investments must be taken into account, because they are competitive each other. We use models to conclude that the transport investment must keep appropriate proportion with product investment to realize optimal economic development. If the equilibrium of them is broken, government must adjust investment to enhance the weak one. Accessibility is a common approach to measure the regional impact of a new transport infrastructure. Accessibility involves a combination of two elements: location on a surface relative to suitable destination, and the characteristics of the transport network or networks linking points on that surface. There is a wide variety of indicators to measure accessibility. We select three indicators that respond to different conceptualizations. The first one is weighted average travel times. The weighted average travel time between each node and all urban agglomerations is calculated taking as weight the mass of the centers. The second one is economic potential, which is a gravity-based measure model. According to this model, the level of opportunity between two nodes is positively related to the mass of the destination and inversely proportional to some power of the distance between both nodes. The indicator measures the economic potential of each place in each of the scenarios considered and the changes in potential caused by the new infrastructure. The third one is daily accessibility indicator, which consists of calculating the amount of population that can be reached from a node within a certain travel time limit. The time limit is usually established in 3 to 5 hours, so that it is possible to go and return within the day and carry out an activity at the visit location. The three indicators handle the distance (travel time) in a different way that the economic potential indicator has distance decay and others has not.

[36]
沈航, 田小勇. 交通运输对区域经济增长影响的实证研究. 武汉理工大学学报: 交通科学与工程版, 2012, 36(4): 795-798, 803.为了实证研究运输对区域经济增长的影响,构建包含交通因素的柯布道格拉斯模型,以2009年底全国各省份第二产业劳动力、资本以及各省交通运输要素作为投入,以2009底年各省份的第二产业GDP作为产出,对拓展的柯布-道格拉斯模型进行回归分析,验证该模型的合理性,进而利用该模型定量地分析交通运输对区域经济增长的贡献,结果显示资本是经济增长最重要的影响因素,交通运输和劳动力要素亦显著影响区域经济的增长.

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[Shen Hang, Tian Xiaoyong.Empirical research on the impact of transportation on regional economy development. Journal of Wuhan University of Technology: Transportation Science & Engineering, 2012, 36(4): 795-798, 803.]In order to analyze transportation′s impact on regional economy development,the extended Cobb-Douglas Function is established which includes transportation factor.The labor,capital and transportation factor of each province in 2008 are regarded as input while the GDP of secondary industry of each province is regarded as output,then analyzes the rationality of the extended model,and calculate transportation′s contribution to economy development by the established model,and the result indicates that capital is the most important factor contributing to economy growth,transportation and labor factor also impact economy growth significantly.

[37]
刘海隆, 包安明, 陈曦, 等. 新疆交通可达性对区域经济的影响分析. 地理学报, 2008, 63(4): 428-436.采用Cobb-Douglas生产函数模型,结合GIS空间分析的方法,分析了交通可达性在区域经济发展中对投资绩效的影响,以及定量模拟了交通可达性在经济发展中的作用。研究结果表明,当交通可达性满足某一经济水平时,区域经济发展主要取决于投资的规模,但当交通可达性小于与之对应的经济水平时,它对投资绩效具有明显的制约作用。同时在一定经济发展阶段,交通可达性的波动与经济的波动之间具有显著的同步响应关系。另外,新疆的交通可达性具有明显的局部分异特征,总体水平较低,通过万元GDP增长所需交通耗费分析进一步表明,这种分异特征与经济分布特征相一致。因此,分析交通可达性对研究区域经济具有重要意义,对稳定、谐调、平衡发展区域经济,划分主体功能区提供有力的依据。

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[Liu Hailong, Bao Anming, Chen Xi, et al.The effect of transport accessibility on regional economic performance. Acta Geographica Sinica, 2008, 63(4): 429-436.]Development of transport,as one of the most important causes of changing economic activity and location advantages,is essential to economy development.The purpose of this paper,is to analyze the effect of transport accessibility on regional economy.Cobb-Douglas production function modeling,spatial analysis and network analysis in ArcGIS have been used to analyze this connection.Cobb-Douglas production function(Y = A Ka Lb,Y = Income,K=Capital,L=Labor,A=Technology,a and b are positive parameters)is used to reflect mutual relation between investment and output.It has been applied to many fields such as industry,energy sources,regional economic programming and agricultural management.Accessibility is a basic index which is used to describe traffic cost.Accessibility is one of the main reasons to cause spatial difference of regional economy,because it can reflect the degree of convenience from one place to another using certain traffic system and the economic activity and location advantages at one place on a large scale.Macroeconomic development can be seen as output of social capital investment.As part of social capital investment,infrastructure construction is very important to the regional economic development.In order to analyze the effect of transport accessibility on investment performance in regional economy and its weight in the economic growth,the authors adopted Cobb-Douglas production function and its regression modeling to constructe a homeostasis equation based on the relationship between investment(transport access

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