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SCIENTIA GEOGRAPHICA SINICA >

2018 , Vol. 38 >Issue 7: 1165 - 1173

DOI: https://doi.org/10.13249/j.cnki.sgs.2018.07.018

The Flexible Demand Analysis of Agricultural Irrigation Water Use Based on Tech-nical Efficiency and Shadow Price: Taking Heilongjiang Province for an Example

  • Zhang Xiangda ,
  • Zhu Shuai
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  • School of Public Administration, Dongbei University of Finance and Economics, Dalian 116025, Liaoning, China

Received date: 2018-01-30

  Request revised date: 2018-04-04

  Online published: 2018-07-20

Supported by

National Social Science Foundation of China(14BJL039)

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Abstract

Based on the input-output datas of agriculture in 13 cities of Heilongjiang Province from 2000 to 2015, the input-output index system was built. The input indexes included cultivated area of the crops, total power of agricultural machinery, fertilizer amount, the number of agricultural employment and water consumption for agricultural irrigation and the output indexes included agricultural output value. Then the method of stochastic nonparametric envelopment of data was introduced to build the technical efficiency model of agricultural irrigation water. Based on the measurement results, the shadow price of agricultural irrigation water was calculated with the shadow price theory. Last the empirical model of flexible demand analysis on agricultural irrigation water was established using the Shephard theory. On the basis of the above analysis, the model bulit in this paper can estimate the noise in the data of the agricultural irrigation water sample correctly and formulate the economic relations between the agricultural irrigation water and the agricultural production adopting the crop production function reasonably. Compared with 2000, in the condition of the same output, the agricultural water use inefficienint in 2015 decreased by 23.68% and the agricultural water use efficienint increased by 25.02%. The most agricultural water use efficienint of all cities in Heilongjiang Province is Harbin with 0.978 8, the least is Qiqihar with 0.685 4. The average agricultural water shadow prices of Heilongjiang Province are between 2.04-3.86 yuan/m3. But the average agricultural water shadow prices of different cities differ largely, and the range is 11.92 yuan/m3. On the condition of other inputs no change, the agricultural water consumption will decrease by 4.64%, increase by 1.10% and decrease by 0.20% respectively with each increase of 1% of agricultural water price, total agricultural output and agricultural water efficiency. Due to the shortcomings of relying on the functional form of SFA (Stochastic frontier analysis) model and ignoring the data stochastic noise of DEA (Data envelopment analysis) model, the StoNED model can better solve these problems and satisfy the the concepts and principles of SFA and DEA. The empirical model for the analysis of agricultural irrigation water elasticity demand can effectively reveal the impact mechanism of the agricultural irrigation water price and the technical efficiency to the agricultural irrigation water demand in Heilongjiang Province. The research results have important theoretical and practical significance for drawing up the agricultural water use price scientific and rational, promoting the reform of agricultural water use price and saving agricultural water resources in Heilongjiang Province.

Key words： StoNED model; agricultural irrigation water; shadow price; technology efficiency; Heilongjiang Province

Cite this article

Zhang Xiangda , Zhu Shuai . The Flexible Demand Analysis of Agricultural Irrigation Water Use Based on Tech-nical Efficiency and Shadow Price: Taking Heilongjiang Province for an Example[J]. SCIENTIA GEOGRAPHICA SINICA, 2018 , 38(7) : 1165 -1173 . DOI: 10.13249/j.cnki.sgs.2018.07.018

中国是世界上水资源严重短缺的国家之一[1],按照市场经济的运行规律和水资源的商品性,短缺的水资源应该具有更高的价格。然而,由于水资源具有维持人类生存和发展的特殊属性,同时长期形成的粗放管理理念[2],导致中国水价普遍偏低,尤其是农业灌溉水价。农业作为中国用水大户,其农业灌溉用水量占到了全国总用水量的65%左右,较低的农业灌溉水价导致了农业灌溉用水的浪费和效率的低下,不利于农业水资源的可持续利用。提高农业灌溉用水效率是解决农业水资源不足的重要途径之一,尽管中国近十多年大范围推广了农业灌溉节水技术,但农业灌溉用水效率与发达国家依然存在较大的差距。黑龙江省作为农业大省,农业灌溉对于保障粮食安全稳定生产具有重要的意义,但农业灌溉水价偏低、农业水资源紧缺、农业灌溉用水效率低下等问题严重制约了黑龙江省农业的快速发展。目前,黑龙江省农田灌溉用水量占全省总用水量的比例高达85.30%,而水稻（Oryza sativa）的水粮产出比仅为0.001 5 kg/m3[3],农业灌溉水价仅为300 元/hm2（水田）,井灌区尚不收取水费[4]。此种背景下,从技术效率和农业灌溉用水价格的角度对农业灌溉用水需求进行分析,揭示农业灌溉水价和技术效率对农业灌溉用水需求的影响机制,可为科学合理的确定区域农业灌溉水价,制定区域农业灌溉用水策略提供理论依据和技术支撑。
从经济学的角度看,应将农业灌溉用水作为一种商品,通过技术效率配置,使农业灌溉用水的边际机会成本与边际收益相等,即可实现农业灌溉用水效益的最大化。为了保障粮食安全和降低农民灌溉的经济负担,中国农业灌溉水价并非按照实际灌水量收取水费,而是按照灌溉面积进行收费,这种非用水量的收费模式导致水费收益较低,不利于农业节水。已有研究表明：当水价较低且与实际灌水量无关时,节水效益将较低或不存在,不利于农民节水意识的提升[5]。为了协同农业灌溉水价、技术效率与农业灌溉用水量之间的关系,相关学者对农业灌溉用水价格、技术效率及其与农业灌溉用水之间的关系[6,7]等方面进行研究。随着农业灌溉用水价格的升高,农业用水量将呈现出下降趋势[8],而农业用水量是影响农业灌溉用水定价最敏感的因素[9]。因此,为了节约用水和保障农业用水户的收益,灌区应充分发挥农业灌溉水价改革在促进农民节约用水中的杠杆作用[10,11,12,13,14]。纵观国内外研究成果,以往研究从不同的角度分析了农业灌溉水价改革和技术效率对农业灌溉用水的影响,但多侧重于农业灌溉水价。由于地区经济发展的差异导致其研究成果的实用性各不相同,尤其是区域尺度上。同时,上述成果缺少对农业灌溉用水投入和产出效益的综合分析,缺少将农业灌溉用水价格与技术效率相结合的分析,虽然已有学者在该方面进行了相关研究,但多采用DEA或SFA模型[15,16],缺少对农业用水样本数据噪音的估计,且不易找到合理的作物生产函数来表述其经济学关系[17,18]。
因此,针对上述问题,本文从省域分析的角度出发,以中国重要的商品粮生产基地——黑龙江省为研究对象,采用随机非参数包络分析法（StoNED）,通过估算其农业灌溉用水的技术效率和影子价格,建立农业灌溉用水弹性需求分析经验模型,提出农业灌溉水价和技术效率对黑龙江省农业灌溉用水需求的影响,以期为黑龙江省科学合理的制定农业灌溉用水策略、提高农业灌溉用水效率提供理论依据和技术支撑。

1 材料与方法

1.1 研究区概况

黑龙江省位于中国东北部,介于121°11′~135°05′E,43°26′~53°33′N之间,是中国最重要的商品粮生产基地之一[19]。现辖1个副省级城市,行政区包括12个地级市、1个地区行署（图1）。据统计,2016年全省粮食总产量突破684×108kg,连续5 a粮食总产量和商品粮全国第一;用水总量为352.6×108m3,全国排名第四,其中农业用水总量为313.8×108m3,占到了用水总量的88.99%,远远超出全国水平（62.4%）,且农业灌溉用水浪费严重,灌溉水利用效率低下,仅为0.50左右,低于全国平均水平（0.53）。可见,研究黑龙江省农业灌溉用水需求,对于缓解区域紧张的用水局面具有重要意义。
Fig.1 Location of Heilongjiang Province

图1 黑龙江省位置

1.2 研究方法

1.2.1 农业灌溉用水技术效率测算的随机非参数数据包络分析法
随机非参数数据包络分析法（StoNED）是由Timor Kuosmanen于2006年提出的[20,21],该方法融合了非参数包络分析法（DEA）和随机前沿分析法（SFA）的优点,既无需设定生产函数的具体形式,也可将残差项分离为无效率项和随机误差项,同时完全忠实于DEA模型和SFA模型本身的原理,为解决农业灌溉用水技术效率的测定提供了新的思路。公式如下：
min ∑ i = 1 n θ i 2 s . t . y i = α i + β i x i + θ i ∀ i = 1,2 , … , n α i + β i x i ≤ α h + β h x i ∀ i , h = 1,2 , … , n β i ≥ 0 ∀ i = 1,2 , … , n （1）
式中, y i 为农业产出要素实测值; x i 为农业投入要素实测值; θ i 为残差项,可将其分解为无效率项 ε i 和随机误差项 δ i ,即： θ i = ε i - δ i ,当对农业灌溉用水决策单元i进行技术效率测算时,无效率项可采用以下条件均值计算[21]：
E ε i δ i = - δ i σ ˆ ε 2 σ ˆ ε 2 + σ ˆ δ 2 + σ ˆ ε 2 σ ˆ δ 2 σ ˆ ε 2 + σ ˆ δ 2 ϕ ( δ i σ ˆ δ 2 ) 1 - Φ ( δ i σ ˆ δ 2 ) （2）
式中, σ ˆ ε 2 和 σ ˆ δ 2 为无效率项 ε i 和随机误差项 δ i 方差的估计值,其公式为： σ ˆ ε 2 = ( m 3 ( 2 π ) ( 1 - 4 π ) ) 1.5 , σ ˆ δ 2 = m 2 - ( π - 2 π ) σ ˆ ε 2 。 m 2 和 m 3 可采用残差 θ i 的二阶中心距和三阶中心距表示,即： m 2 = ∑ i = 1 n ( θ i - E ( θ i ) ) 2 / n 和 m 2 = ∑ i = 1 n ( θ i - E ( θ i ) ) 3 / n ; ϕ 为标准正态密度函数, Φ 为标准正态累计分布函数。
1.2.2 农业灌溉用水影子价格估算
影子价格是由荷兰数理经济学家詹恩·丁伯根和前苏联经济学家康托罗维奇于20世纪30年代末分别提出的。其涵义是指当投入增加时对产出的影响大小,故影子价格也可称为投入的机会成本,表示投入在最优组合时所具有的潜在价值。结合1.2.1的优化结果,可采用下式计算[23]：
p x im = p y i β im exp ( ε ) （3）
式中, p x im 为农业灌溉用水决策单元i第m个投入要素的影子价格; p y i 为农业灌溉用水决策单元i产出要素的价格; β im 为农业灌溉用水决策单元i第m个投入要素生产函数中的系数; exp ( ε ) 为乘法误差,目的是在求解1.2.1优化问题和计算条件均值时,尽可能降低不同农业用水决策单元之间的异方差性[24]。由于本文主要估计农业用水的影子价格,故m指农业总用水量。
1.2.3 农业灌溉用水弹性需求分析理论
假设农业生产活动存在两大类投入要素,即：水和资金,则生产函数可采用下式表示：
y = y ( w , c ) （4）
式中,w为水的投入量,c为资金投入量。对于农业生产者,从经济学的角度看,希望投入的资本越少越好,即：
min ( P w × w + P c × c ) s . t . y = y w , c （5）
式中, P w 和 P c 分别为水和资金的价格。通过求解上述优化问题,即可得到农业生产的价值函数为： V = V ( P w , P c , y ) 。
根据Shephard理论[25],对农业生产价值函数中的农业用水求偏导,即可得到农业灌溉用水的需求函数为：
w = ∂ V ∂ P w = w ( P w , P c , y ) （6）
由此可见,农业灌溉用水需求取决于农业灌溉用水的价格、资金的投入以及农业的产出水平。事实上,农业灌溉用水技术效率（Te）在一定程度上也反映了农业灌溉用水的特征,因此将上述农业灌溉用水需求函数可改写为：
w = w ( P w , P c , y , Te ) （7）
根据已有研究成果[26,27],农业灌溉用水生产函数往往假定为对数形式,则农业灌溉用水弹性需求分析的经验模型可采用下式表示：
ln w = α 0 + α 1 × ln P w + α 2 × ln P c + α 3 × ln y + + α 4 × ln Te + μ （8）
式中, Te 可根据1.2.1求得, μ 为残差项, α 0 、 α 1 、 α 2 、 α 3 、 α 4 为常数项和各变量的系数,通过分析各变量的系数大小以及变化比率,即可得到农业灌溉用水的弹性需求特征。

1.3 数据来源

为了从投入和产出的角度分析农业灌溉用水效率,计算农业灌溉用水的影子价格,进而揭示农业灌溉用水的弹性需求特征,本文收集了黑龙江省13个地市的2000~2015年农业生产方面的数据。通过专家咨询和相关调研,选择农作物播种面积、农机总动力、化肥施用量、农业从业人数、农业灌溉用水量作为投入指标,该5个指标全面反映了农业生产中土地、资金、化肥、劳动力和农业用水等方面的投入;选择农业产值（不包括林、牧、渔）作为产出指标,同时为了消除通货膨胀的影响,以1999年为基准年,计算农业产值。上述投入和产出指标数据分别来自于2001~2016年《黑龙江省统计年鉴》[28]。农业投入和产出指标统计分析结果如表1所示。由表1可知：不同年份黑龙江省各地市农业投入和产出指标值存在较大的差异,如：农业产值最大值约为最小值的117倍。可见,黑龙江省各地市农业灌溉用水效率也必然存在一定的差异。
Table 1 The statistic analysis results of agricultural input-output indices in Heilongjiang Province from 2000 to 2015

表1 黑龙江省2000~2015年农业投入和产出指标统计分析结果

指标 平均值 最大值 最小值 方差 中位数 标准差
农业产值指数(108元) 106.49 647.10 5.50 12919.61 70.19 113.66
农业灌溉用水量(108m3) 323.52 377.02 265.14 350.15 321.65 18.71
农业从业人数(104人) 55.60 183.73 1.50 2926.27 31.90 54.09
农机总动力(104kW) 201.63 1024.50 20.80 40590.75 134.70 201.47
化肥施用量(104t) 24.12 118.55 0.06 829.57 11.26 28.80
农作物播种面积(104hm2) 76.90 229.43 8.77 4435.37 48.95 66.60

2 结果与分析

2.1 黑龙江省农业灌溉用水技术效率测算

根据前述农业用水技术效率测算的随机非参数数据包络分析法,采用lingo11.0编写程序求解1.2.1的优化问题,计算黑龙江省2000~2015年农业灌溉用水技术效率平均无效率值 ε i 、无效率值 ε i 和随机误差 δ i 的方差估计值 σ ˆ ε 2 和 σ ˆ δ 2 、农业灌溉用水技术效率平均值以及信噪比,具体结果如表2所示。
Table 2 The measurement of agricultural irrigation water use efficient in Heilongjiang Province from 2000 to 2015

表2 黑龙江省2000~2015年农业灌溉用水效率测度结果

年份 平均无
效率值		 σˆε2 σˆδ2 σˆε2+σˆδ2 平均效
率值		 信噪比
σˆε/σˆδ
2000 0.3277 0.0561 0.0262 0.0823 0.6723 1.4624
2001 0.2706 0.0156 0.0233 0.0388 0.7294 0.8180
2002 0.2666 0.0725 0.0128 0.0853 0.7334 2.3814
2003 0.2537 0.0583 0.0184 0.0766 0.7463 1.7822
2004 0.2492 0.0210 0.0190 0.0400 0.7508 1.0530
2005 0.2233 0.0581 0.0165 0.0746 0.7767 1.8741
2006 0.2177 0.0538 0.0772 0.1310 0.7823 0.8343
2007 0.2099 0.0711 0.0726 0.1438 0.7901 0.9894
2008 0.1927 0.0950 0.0746 0.1696 0.8073 1.1283
2009 0.1831 0.0862 0.0721 0.1584 0.8169 1.0935
2010 0.1459 0.0847 0.0567 0.1414 0.8541 1.2218
2011 0.1078 0.0927 0.0589 0.1516 0.8922 1.2549
2012 0.1068 0.0909 0.0432 0.1341 0.8932 1.4497
2013 0.1066 0.0803 0.0557 0.1361 0.8934 1.2006
2014 0.1052 0.0120 0.0172 0.0292 0.8948 0.8338
2015 0.1034 0.0128 0.0152 0.0280 0.8966 0.9162
由表2可知：① 随机误差项 δ i 的方差在残差总方差 σ ˆ ε 2 + σ ˆ δ 2 中的比例较高,信噪比 σ ˆ ε / σ ˆ δ 最高值达到了2.381 4,说明收集的2000~2015年的农业投入和产出指标样本数据存在一定的误差,如果将所有的残差作为测算农业灌溉用水技术效率的依据,必然导致农业灌溉用水技术效率无效的估计值偏低,即：本文采用StoNED模型测算黑龙江省农业灌溉用水技术效率是可行的;② 农业灌溉用水技术效率无效在研究时段均较高,最大值达0.327 7（2000年）,最小值为0.103 4（2015年）,且呈现出了逐渐下降的趋势,经计算平均每年下降0.014 8,即：在相同的产出条件下,2015年农业灌溉用水技术效率无效比2000年降低了23.68 %;而农业用水技术效率有效在研究时间呈现出了稳定的上升趋势,与2000年相比,2015年农业灌溉用水技术效率有效提高了25.02%。为了进一步分析黑龙江省各地市农业灌溉用水技术效率的空间变化规律,绘制黑龙江省2000~2015年各地市农业灌溉用水技术效率的平均值柱状图（图2）。
Fig.2 The technology efficient of agricultural irrigation water use of each city in Heilongjiang Province from 2000 to 2015

图2 2000~2015年黑龙江省各地市农业灌溉用水技术效率

由图2可知：黑龙江省各地市在2000~2015年农业灌溉用水技术效率平均值相对较高,超过0.8的地市数量达到了8个,占全省的61.5%,其中：哈尔滨市农业灌溉用水技术效率最高,达到了0.978 8;齐齐哈尔市农业灌溉用水技术效率最低,为0.685 4。这与2个地市的农业发展情况有关,哈尔滨市为黑龙江省省会,农业方面投入相对较多,尤其是科技,而齐齐哈尔市地处黑龙江省西部半干旱区,水资源比较紧缺,多以旱田为主,农业投入相对较少。

2.2 黑龙江省农业灌溉用水影子价格估算

农业灌溉用水的影子价格在一定程度上反映了农业灌溉用水的供需状况[29],根据前述理论,计算黑龙江省各地市2000~2015年农业灌溉用水的影子价格,并对其进行统计分析,具体结果如图3和图4所示。
Fig.3 The shadow price statistic analysis of agricultural irrigation water use of each city in Heilongjiang Province from 2000 to 2015

图3 黑龙江省2000~2015年各地市农业灌溉用水影子价格

Fig.4 The shadow price statistic analysis of agricultural irrigation water use in Heilongjiang Province from 2000 to 2015

图4 黑龙江省2000~2015年农业灌溉用水影子价格

由图3和图4可知：① 哈尔滨市农业灌溉用水影子价格平均值最大,达到了11.92元/m3,大兴安岭地区农业灌溉用水影子价格平均值最小,仅为0元/m3,其极差达到了11.92元/m3,可见,2000~2015年,黑龙江省农业灌溉用水影子价格平均值存在较大的波动性;② 哈尔滨市（11.92元/m3）、齐齐哈尔市（11.86元/m3）、佳木斯市（11.64元/m3）和绥化市（11.72元/m3）4个地区的农业灌溉用水影子价格平均值均超过了11.50元/m3,对比其农业生产总值发现,这4个地区的农业生产总值均较高,且排名位于黑龙江省前4位,进而导致了其较高的农业灌溉用水影子价格,可见农业灌溉用水量对这4个地区农业生产的发展具有一定的限制作用,增加农业供水量对于促进其农业发展具有重要的推动作用;另外,大兴安岭地区的农业灌溉用水影子价格为零,并非说明农业灌溉用水对其农业发展不重要,而是由于大兴安岭多为林区,农业灌溉工程较少,农业灌溉多以天然降水为主,也进一步说明了农业灌溉对大兴安岭地区农业发展的重要性;③ 黑龙江省各地区2000~2015年农业灌溉用水影子价格的最小值均为0,且大兴安岭地区的平均值和最大值也为0,这主要是与黑龙江省当前的农业灌溉收费方式有关,即：非用水量的收费模式。从经济学理论上,当农民按照用水量支付水费时,水价作为一种沉没成本,不会对农民的用水行为产生边际影响。因此,只有当灌溉边际产量为0时,农民才会选择不灌溉。目前,黑龙江省灌溉方式比较落后,多采用“大水漫灌”等方式,如：绥化市、佳木斯市等,虽然“十二五节水增粮”项目投入了大量的喷滴灌设备,但由于农民思想落后和节水意识淡薄,并没有起到很好的效果,且水费价格较低,每方水价格约为 0.024元/m3。这种非用水量的收费模式和较低的农业水价必然导致农业灌溉用水的浪费。同时,已有研究表明：当市场价格不能够反映资源的稀缺程度时,通过影子价格可以更好的体现出资源的配置情况[30,31]。因此,黑龙江省应加大农业灌溉用水改革的力度,改变传统农业灌溉用水不按照用水量收费的模式,使农业灌溉水价能够充分体现出水资源在农业方面的供求状况,进而更加准确的估计和计算农业灌溉用水的影子价格,为农业水资源的配置提供科学依据。
图4反映了黑龙江省2000~2015年农业灌溉用水影子价格的变化过程。2000~2015年,黑龙江省农业灌溉用水影子价格平均值在为2.04~3.86元/m3之间波动,最大值在10.87~29.41元/m3之间波动,最小值没有波动,均为0元/m3。可见,黑龙江省农业灌溉用水影子价格的平均值和最小值波动较小,而最大值波动较大,这体现出了不同年景对农业灌溉用水供求关系的影响。

2.3 黑龙江省农业灌溉用水弹性需求分析

为了判别农业灌溉用水价改革对黑龙江省农业灌溉用水供求关系的影响,根据前述理论,建立农业灌溉用水量与农业灌溉用水影子价格、农业资金投入、农业产出和农业灌溉用水技术效率之间的经验模型,其中：农业资金投入采用农业生产资料价格指数表示,农业产出采用农业产值价格指数表示,均以1999年作为基准年,数据来源于2001~2016年《黑龙江省统计年鉴》[28],农业灌溉用水影子价格和农业灌溉用水技术效率由前述2.1和2.2部分获得,由于大兴安岭地区农业灌溉用水影子价格为0,不利于求自然对数,因此仅采用黑龙江省12个地市的多年平均值进行建模,采用SPSS编程计算,结果如下：
ln w = 0.6745 - 4.7489 ln P w - 0.3547 ln P c + 1.1457 ln y - 0.1895 ln Te R 2 = 0.9654
对上述经验模型各系数进行0.05水平的t检验,仅有农业生产资料价格指数的系数-0.354 7不显著,因此删除 ln P c 进行重新建模,具体结果如下：
ln w = 0.6745 - 4.6357 ln P w + 1.1045 ln y - 0.1986 ln Te R 2 = 0.9432
由上述经验模型可知：农业灌溉用水影子价格、农业产出和农业灌溉用水技术效率的的弹性系数分别为-4.635 7,1.104 5和-0.189 5,即：当其他投入保持不变的条件下,农业灌溉用水价格、农业产出和农业灌溉用水技术效率每增加1%,将分别减少农业灌溉用水量4.64 %、增加农业灌溉用水量1.10%和减少农业灌溉用水量0.20%。可见,对于黑龙江省而言,当其他基本投入保持不变的条件下,农业灌溉用水价格的改革对于节约农业水资源具有重要的意义,而农业灌溉用水技术效率的提升对于节约农业水资源效果不明显;另外,从产出的角度看,为了保障粮食安全,农业产值的增加也在一定程度上加剧了农业水资源的紧缺。这与李青等人[32]在新疆的研究结论相一致。

3 结论与讨论

3.1 结论

本文采用随机非参数包络分析法（StoNED）,通过估算黑龙江省农业灌溉用水的技术效率和农业灌溉用水的影子价格,提出了基于技术效率和农业灌溉水价的农业灌溉用水弹性需求经验模型,并对黑龙江省农业灌溉用水进行了弹性需求分析,主要结论如下：① 黑龙江省农业灌溉用水技术效率无效在研究时段相对较高,但呈现出了逐年下降的趋势,平均每年下降0.014 8,在相同的产出条件下,2015年农业用水技术效率无效比2000年降低了23.68%;而农业灌溉用水技术效率有效在研究时段呈现出稳定的上升趋势,与2000年相比,2015年农业灌溉用水技术效率有效提高了25.02%;黑龙江省各地市在2000~2015年农业灌溉用水技术效率相对较高,其中：哈尔滨市的农业灌溉用水技术效率最高,达到了0.978 8;齐齐哈尔市的农业灌溉用水技术效率最低,为0.685 4;② 黑龙江省农业灌溉用水影子价格平均值在2.04~3.86元/m3之间波动,最大值在10.87~29.41 元/m3之间波动,最小值没有波动,均为0元/m3;黑龙江省各地市农业灌溉用水影子价格平均值存在较大的波动性,其极差达到了11.92元/m3,其中：哈尔滨市农业灌溉用水影子价格平均值最大,达到了11.92元/m3,大兴安岭地区农业灌溉用水影子价格平均值最小,仅为0.00 元/m3;③ 当其他投入保持不变的条件下,黑龙江省农业灌溉用水价格、农业产出和农业灌溉用水技术效率每增加1%,将分别减少农业灌溉用水量4.64%、增加农业灌溉用水量1.10%和减少农业灌溉用水量0.20%,农业灌溉水价的改革对于节约农业水资源的利用具有重要的意义。

3.2 讨论

本文将随机非参数包络分析法（StoNED）、影子价格理论、弹性需求分析理论相结合,对黑龙江省农业灌溉用水时空变化特征进行了定量研究,论文的局限在于仅分析了农业机械总动力、农业从业人口、化肥施用量等投入要素对农业灌溉用水技术效率的影响,而农民受教育的程度、灌溉技术、种植结构等因素也会影响农业灌溉用水的水平。优点在于将统计学理论、经济学模型与农业实际问题相结合,解决了农业用水样本数据的噪音估计、不同农业投入产出要素之间经济学关系的合理表述等问题,可为农业灌溉用水价格的制定提供更好的理论依据。选择采用其他主流研究方法DEA模型[3]和SFA模型[33]进行对比分析,发现：尽管研究方法和研究区域不同,且StoNED模型融合了DEA模型和SFA模型的优点,但在研究结果上均有一定的相似性。进一步研究发现,这些研究在进行投入产出分析时,均选用了相似的指标,如：农机总动力、农业从业人数等。因此,至少在2个方面需要进一步研究：第一,研究方法虽然不同,但在揭示农业灌溉用水技术效率变化特征方面具有一定的相似性,不同方法之间的差异体现在什么地方?第二,投入和产出指标相似是否是造成研究结果相似的主要原因。如果进一步在投入指标中补充农民受教育程度、灌溉技术、种植结构等因素,StoNED模型可以较好的处理多指标样本数据的噪音估计问题,其它模型在忽略该问题的条件下是否也会得到相似结论,这也是值得下一步开展研究的地方。同时,定性投入指标的量化问题,如：农民受教育程度、灌溉技术水平等定性指标的量化问题也是当前需要解决的问题。当然StoNED模型也存在一些不足之处,如：参数估计比较复杂、无效率项分布形式的假设问题等。因此,将多种方法进行组合研究也许是更为有效和合理的做法。

The authors have declared that no competing interests exist.

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Fujimoto, Takao, Perera B B. Upeksha P. Eisenberg's duality in homogeneous programming, Shephard’s duality and economic analysis[J]. Metroeonomica, 2017, 68(4):816-832.Abstract This note is to reintroduce to the reader Eisenberg's symmetric duality theorem in homogeneous programming problems as a useful tool in economic analysis, and thereby to pay a due tribute to him for one of his mathematical contributions. His duality result has been almost in oblivion during the development of Shephard's duality theory between cost and production, and has seldom been mentioned in the literature about the dualities concerning Shephard's distance function, Luenberger's benefit function and directional distance functions proposed by many authors. We show that from Eisenberg's duality it is possible to derive in a systematic way these dualities so far obtained. We also present a further extension of the duality for generalized directional distance functions. In addition, we explain the relationships between the duality theorem of linear programming and that of homogeneous programming, and show how to apply the latter in those economic models in which linear programming has been utilized.

DOI

[26]
Okadera T, Watanabe M, Xu K.Analysis of water demand and water pollutant discharge using a regional input-output table: An application to the City of Chongqing, upstream of the Three Gorges Dam in China[J]. Ecological Economics, 2006, 58(2):221-237.

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王文浩, 曹红霞, 蔡焕杰. 灌溉水价与灌区灌溉用水量关系研究[J]. 灌溉排水学报, 2013, 32(1):82-85.

[Wang Wenhao, Cao Hongxia, Cai Huanjie.Relationship between irrigation water price and consumption. Journal of Irrigation and Drainage, 2013, 32(1):82-85.]

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中国统计局. 黑龙江统计年鉴(2001-2016)[M]. 北京:中国统计出版社,2001-2016.

[National Bureau of Statistics. Heilongjiang statistical yearbook(2001-2016). Beijing: China Statistics Press,2001-2016. ]

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Wang W, Xie H, Zhang N et al. Sustainable water use and water shadow price in China’s urban industry[J]. Resources Conservation & Recycling, 2016, 128:489-498.China is faced with a serious water shortage problem, and industrial sector is a major water consumer. How to improve the efficiency of industrial water use is extremely important for sustainable use of water in China. This paper applies a global non-radial directional distance function (GNDDF) to measure the green use efficiency of industrial water (GUEIW) incorporating undesirable outputs during 2004鈥2012. We calculate the two components of GUEIW named economic efficiency of industrial water (ECEIW) and economic efficiency of industrial water (ENEIW), and the shadow price of industrial water to explore the bias between the actual prices and the shadow ones. The results show that the GUEIW shows a W type curve over the study period, and its growth is mainly driven by the ECEIW. The regional heterogeneity of the GUEIW is significant. The eastern region of China enjoys the highest GUEIW, while the central region suffers the poorest performance in the GUEIW. The western region has the largest internal gap of the GUEIW. The actual prices of industrial water in all the provinces are much lower than the shadow ones, and appropriate increase in the industrial water price is helpful to raise the GUEIW. Some policy implications are also suggested.

DOI

[30]
Ilak P, Rajšl I, Krajcar S et al. The impact of a wind variable generation on the hydro generation water shadow price[J]. Applied Energy, 2015, 154(15):197-208.

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Zhao J, Ni H, Peng X et al. Impact of water price reform on water conservation and economic growth in China[J]. Economic Analysis & Policy, 2016, 51:90-103.Water pricing has been used as an effective method of conserving water and optimizing water allocation. However, little is known about how to set a rational and efficient water price and how water pricing impacts economic growth. In this paper, we address this challenge by using the SICGE model, a dynamic general equilibrium model for China that is augmented by a total water constraint module. We also include a water subdivision module that allows for substitution between various water sources. These extensions facilitate a comprehensive estimate of the impact that various water price reforms have on water conservation and economic growth. The modeling results confirm that an increase in the water price will lead to a decline in total water usage, a better water use structure, and enhanced water use efficiency. We conclude with a comparison of multiple scenarios that suggests an optimal water price system.

DOI

[32]
李青, 陈红梅, 王雅鹏. 基于面板VAR模型的新疆农业用水与农业经济增长的互动效应研究[J]. 资源科学, 2014, 36(8):1679-1685.新时期以"绿洲灌溉农业"为特征的新疆各地区农业的快速发展与农业用水比重必须下降的现实,使得探讨两者之间的相互关系尤为重要。本文基于1997-2011年新疆15个地州(市)面板数据,建立了农业用水量与农业经济增长的面板VAR模型,考察农业用水与农业经济增长的互动效应。研究结果表明:1新疆三个区域的农业用水和农业经济增长之间存在长期协整关系;2北、东、南疆的农业用水对农业经济增长的推动效应有明显差异,其中北疆地区农业经济增长效应最大,其次为东疆,再次为南疆;3农业经济增长对农业用水量的变化产生的效应南疆最明显,其次为北疆,东疆用水结构较为稳定,农业用水量变动最小。因此,依据各地农业用水与农业增长的短期与中长期因果关系建立科学灌溉制度与水资源政策,依靠节水技术,才能有效提高农业综合效益。

[Li Qing, Chen Hongmei, Wang Yapeng.The interactive effect of agricultural water and agricultural economic growth in Xinjiang. Resources Science, 2014, 36(8):1679-1685.]

[33]
黎红梅, 陈惠敏. 中国粮食技术效率与灌溉用水效率交互影响——基于省区面板数据的SFA-SEM分析[J]. 系统工程, 2013, 31(5):121-126.

[Li Hongmin, Chen Huimin.The interaction effect on grain technical efficiency and irrigation efficiency. Systems Engineering, 2013, 31(5):121-126.]

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