CN103455727A - Technical method of urban agglomeration input and output efficiency comprehensive measurement - Google Patents

Abstract

The invention discloses a technical method of urban agglomeration input and output efficiency comprehensive measurement. The method comprises the following main steps: firstly, establishing a comprehensive index system of urban agglomeration input and output efficiency measurement, wherein the system includes a fixed first-grade index and a flexibly selected second-grade index; secondly, performing standardized processing on the input and output second-grade index; thirdly, calculating the comprehensive value of the input and output first-grade index; fourthly, calculating the initial measurement value of the urban agglomeration input and output efficiency through a data envelopment analysis (DEA) method; fifthly, correcting the initial efficiency measurement value through adopting a Bootstrap deviation correcting technology, so as to finally obtain the true measurement value of the urban agglomeration input and output efficiency. The method can quantitatively and accurately measure the urban agglomeration input and output efficiency, and can provide a scientific, objective and accurate decision basis for the development and management of urban agglomeration.

Description

A kind of group of cities input-output ratio Synthetic Measurement technical method

Technical field

The invention belongs to Urban Agglomeration Development and management review field, provided a kind of method that can accurately estimate the group of cities input-output ratio, but the effect that the method quantitative measure group of cities high density is gathered, and then be improve the input-output ratio of group of cities and formulate the decision basis that incentive policy is established science.

Background technology

Group of cities refers to that take 1 megalopolis in specific territorial scope is core, by at least 3 above big cities or Mode of Metropolitan (district), be the basic comprising unit, rely on the infrastructure network such as flourishing traffic communication and the space relative compact that forms, economic link closely, and final the realization with city and highly integrated city colony.As a complication system, the essence that Urban Agglomeration Development is grown up remains the input energy resource, obtains every output of economy, society and environment, and input-output ratio is a Scientific Indicators of objective evaluation group of cities high density compacting effect.

The group of cities input-output ratio refers in the unit interval (as 1 year), under certain production specifications, Megapolis key element resource is created or the effective value amount of value-added physical product and intellectual product and the ratio of total input (human and material resources and financial resources), is the comprehensive embodiment of effective configuration of group of cities Input Factors resource, rationally utilization and management level.For group of cities, the input-output ratio height not only mean its key element resource in effective configuration and rationally utilize state and competitiveness strong, also mean that production technology, scale concentration level and the management level of group of cities is rationally efficient.

Input-output ratio is estimated the method that needs science, and existing input-output ratio Measurement Method is mainly application data Envelope Analysis (Data Envelopment Analysis, DEA) method.At present, the DEA method has been widely used in, in estimating of single city input-output ratio, there is not yet DEA and being applied to the patent report that the group of cities input-output ratio is estimated.But, traditional DEA input-output ratio Measurement Method has self intrinsic shortcoming and deficiency, this is mainly manifested in: at first, the input-output ratio that DEA calculates is the relative efficiency estimated value between each sample of estimating of a kind of participation, and the real level of efficiency of each sample is less than or equal the DEA estimated value, the input-output ratio value that is sample is over-evaluated, it is effective that this may be judged as DEA by invalid unit, and, due to the varying in size of deviation, in the time of even may causing carrying out the efficiency comparative analysis between different units, derive a wrong conclusion; Secondly, when DEA is used for small sample set, be that to be less than 2 times of inputoutput index quantity sum (be 3 times in paper to the efficiency calculation sample size, I see that what write in document is all 2 times) time, result tends to occur that the efficiency value of most samples is 1 i.e. equal effective situation, this has also illustrated that efficiency value is over-evaluated, and this makes the efficiency discrimination of DEA reduce.Therefore, the application of DEA has comparatively strict restrictive condition, the more important thing is, the intrinsic deficiency of its method (being that efficiency is easily over-evaluated) has reduced the accuracy of DEA efficiency measure result to a certain extent, and then is difficult to provide for the user decision support of science.On the other hand, city is the system of an economy, society and environment organic composition, and the inputoutput index of DEA efficiency measure should be chosen from economy, society and three aspects of environment.Yet existingly by the DEA method, carry out Urban Efficiency while estimating at present, the output index is all to choose the economic society index, indexs such as GDP, per capita income, ignored the various indexs of relevant environment output.Obviously, this DEA measurement index system of having ignored the environment output is incomplete, and its comprehensive and authenticity of estimating result also is subject to impact to a certain extent.

Group of cities is a complicated entity consisted of a plurality of cities, has obtained huge economic society output on its basis of significantly dropping in human and material resources and financial resources, but also to urban ecological environment, has brought huge pressure simultaneously.Therefore, the group of cities input-output ratio is estimated and must be carried out Synthetic Measurement based on economy, society and three aspects of environment, its input-output ratio is estimated and is estimated more complicated than single city input-output ratio, require higher efficiency measure precision and accuracy simultaneously, therefore need to carry out Improvement and perfection to traditional DEA efficiency measure method, thereby make to estimate result, can provide more scientific decision-making foundation for development and the management of group of cities.

Summary of the invention

The present invention is directed to the group of cities input-output ratio and estimate this technical matters, carry out Improvement and perfection by the DEA method that existing input-output ratio is estimated, thereby overcome now methodical deficiency, realized to group of cities input-output ratio science, objective, estimate accurately.

Characteristics of the present invention are:

At first the DEA method of existing input-output ratio being estimated is improved.Existing inputoutput DEA efficiency measure index system is only considered the economic society output and has been ignored degradation under environmental quality and polluted output, so efficiency measure can not reflect the output situation comprehensively.Secondly, for the intrinsic deficiency of DEA method, the input-output ratio value of sample is over-evaluated, and the present invention introduces the Bootstrap deviation correcting technology and raises the efficiency precision and the accuracy of estimating.By introduce the environmental pollution output in DEA efficiency measure index system, can estimate the input-output ratio of sample comprehensively, can overcome by the Bootstrap deviation correcting technology deficiency that DEA efficiency is over-evaluated, realize thus comprehensive, scientifical to the group of cities input-output ratio, estimate accurately.

Suppose to estimate the input-output ratio value of M group of cities in a certain year, each group of cities is an efficiency measure sample, each sample has identical inputoutput index, is provided with the K kind and drops into index and L kind output index, and method of the present invention comprises the following steps:

1, build the comprehensive index system that the group of cities input-output ratio is estimated, comprise fixing first class index and the corresponding two-level index that can select flexibly.Wherein, one-level drops into index and comprises capital elements, natural resources key element, Informatization Element and manpower key element, and one-level output index comprises economic society output and environmental pollution output, obviously, and K=4 here, L=2.Choose flexibly according to the availability of estimating needs, data the two-level index that can collect concrete data again below 6 one-level inputoutput indexs.For example, under the Informatization Element first class index, can select the two-level index such as group of cities user of local telephone service number, group of cities mobile phone user's number, can select the two-level index such as wastewater discharge, discharge amount of exhaust gas of group of cities under environmental pollution output first class index.

2, the two-level index of inputoutput carried out to standardization.While under first class index, only having 1 two-level index, this two-level index does not need standardization; When 2 or 2 above two-level index are arranged under first class index, to carry out standardization to two-level index, by functional transformation, its numerical value is mapped to certain numerical value interval.Concrete, comprise the following steps:

(1) be that index request " is the bigger the better " (as GDP) for the forward index, adopt upper limit measure of merit, computing formula is:

${\mathrm{\δ}}_m=\frac{v_m}{v_{\max }}\×100,m=\mathrm{1,2},...,M---\left(1\right)$

(2) be index request " the smaller the better " (as the two-level index of environmental pollution output) for the negative sense index, adopt floor effect to estimate, computing formula is:

${\mathrm{\δ}}_m=\frac{v_{\min }}{v_m}\×100,m=\mathrm{1,2},...,M---\left(2\right)$

In formula (1) and (2), δ _mbe the value after the standardization of m group of cities inputoutput two-level index, 0<δ _m≤ 100; v _mit is the original value of the inputoutput two-level index of m group of cities; v _maxfor the maximal value in M group of cities inputoutput two-level index original value; v _minfor the minimum value in M group of cities inputoutput two-level index original value.

3, calculate the comprehensive scores of 6 inputoutput first class index.While under first class index, only having 1 two-level index, the numerical value of this two-level index is the comprehensive scores of this first class index; When 2 or 2 above two-level index are arranged under first class index, the standardization two-level index value obtained based on the 2nd step also adopts weighted average method to calculate the comprehensive scores of corresponding first class index, and the weight calculation of each two-level index such as takes at the power method.If m group of cities has n two-level index, δ under certain input (or output) first class index _mibe the standardized value on i the two-level index of m group of cities under this first class index, m the comprehensive scores x of group of cities on this input (or output) first class index _m(or y _m) be:

$x_m\left(y_m\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{n}\&times;{\mathrm{\&delta;}}_{\mathrm{mi}},i=\mathrm{1,2},...,n---\left(3\right)$

4, using the comprehensive scores of 6 first class index that the 3rd step obtains as input-output data, utilize the DEA method to calculate the preliminary measure value of each group of cities input-output ratio, formula is as follows:

$\left\{\begin{array}{c}\min (\mathrm{\&theta;}-\mathrm{\&epsiv;}(\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{s}^{-}+\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{s}^{+}))\\ s.t.\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_{\mathrm{mk}}{\mathrm{\&lambda;}}_m+s^{-}=\mathrm{\&theta;}{x}_k^m,k=\mathrm{1,2,3,4}\\ \underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{y}_{\mathrm{ml}}{\mathrm{\&lambda;}}_m-s^{+}=y_l^m,l=\mathrm{1,2}\\ {\mathrm{\&lambda;}}_m\&GreaterEqual;0,m=\mathrm{1,2},L,M\end{array}\right.---\left(4\right)$

In formula (4), x _mk(x _mk0) be that m group of cities drops into the comprehensive scores on index, y k one-level _ml(y _ml0) be the comprehensive scores of m group of cities on l one-level output index; The overall efficiency index (abbreviation efficiency) that θ (0<θ≤1) is m group of cities inputoutput, its concentrated expression group of cities to the configuration of Input Factors resource, utilize level and scale concentration level; ε is non-Archimedes's dimensionless; λ _m(λ _m>=0) be the weight variable, be used for judging the returns to scale situation of group of cities; S ^-(S ^->=0) be slack variable, mean that group of cities reaches the input amount that DEA effectively need to reduce; S ⁺(S ⁺>=0) be surplus variable, mean that group of cities reaches the quantum of output that DEA effectively need to increase.

When there is optimum solution in formula (4), be θ _m=1 o'clock, show that m group of cities operates on the Optimal Production leading surface, the output of this group of cities has reached efficiency optimization for input; Work as θ _m, show that the efficiency of m group of cities inputoutput is invalid at<1 o'clock.θ _mvalue more approach 1, mean that the efficiency of m group of cities inputoutput is more approaching effectively, on the contrary more away from effectively.

So far, use DEA method primary Calculation to go out the efficiency value of M group of cities inputoutput.

5, introduce the Bootstrap deviation correcting technology of estimating for the nonparametric distance function, the preliminary efficiency measure value of the group of cities inputoutput θ that the 4th step is obtained _mthe raw sample data formed is carried out duplicate sampling and numerical simulation, and a large amount of analog samples that produce are carried out to the DEA efficiency calculation, calculates thus preliminary efficiency value θ _mestimate deviation, thereby realize θ _mcorrection, obtain final true measure value.Concrete, comprise the following steps:

(1) the preliminary measure value θ based on M group of cities input-output ratio _m, utilize the Bootstrap method, from θ _m(m=1,2 ..., the random efficiency value sample θ ' that M) middle generation scale is M _1b, θ ' _2b..., θ ' _mb, wherein, b is for being used the b time sampling of Bootstrap method.

(2) calculate analog sample (x ^* _mb, y _m), wherein:

x ^* _mb=(θ _m／θ′ _Mb)x _m，m=1，2，L，M (5)

(3) utilize the DEA method of formula (4) to calculate each analog sample (x ^* _mb, y _m) efficiency value θ ^* _mb, m=1,2 ..., M.

(4) repeating step is (1) one (3) B time, obtains a series of efficiency value θ ^* _mb, b=1,2 ..., B.The value of B is larger, and the result of calculation of efficiency value is more accurate, and degree of confidence is larger, due to the complicacy that the group of cities input-output ratio is estimated, requires B to be at least 1000.

(5) calculate the preliminary measure value θ of group of cities input-output ratio _minclined to one side mistake Δ θ, formula is:

$\mathrm{\&Delta;\&theta;}=B^{-1}\underset{b=1}{\overset{B}{\mathrm{\&Sigma;}}}{{\mathrm{\&theta;}}^{*}}_{\mathrm{mb}}-{\mathrm{\&theta;}}_m---\left(6\right)$

(6) calculate the rectify a deviation final true measure value θ of revised group of cities input-output ratio of Bootstrap _m ^t, formula is:

${{\mathrm{\&theta;}}_m}^t={\mathrm{\&theta;}}_m-\mathrm{\&Delta;\&theta;}=2{\mathrm{\&theta;}}_m-B^{-1}\underset{b=1}{\overset{B}{\mathrm{\&Sigma;}}}{{\mathrm{\&theta;}}^{*}}_{\mathrm{mb}}---\left(7\right)$

So far, complete the correction to preliminary efficiency measure value, solved the problem that simple application DEA method efficiency value is over-evaluated, obtained the true measure value of group of cities input-output ratio.

The invention has the advantages that:

1, input-output ratio is estimated more flexible.In the efficiency measure comprehensive index system, first class index immobilizes, and two-level index is chosen flexibly according to estimating needs, data availability etc.

2, input-output ratio is estimated more comprehensively.Added environmental pollution output index in the efficiency measure index system, thereby built complete efficiency measure index system, made efficiency measure more comprehensive.

3, input-output ratio estimate more accurate.On the basis of traditional DEA efficiency measure, by organic introducing Bootstrap deviation correcting technology, DEA efficiency measure value is revised, overcome inherent shortcoming and the deficiency of traditional DEA method, obtain thus more real group of cities input-output ratio value.

The accompanying drawing explanation

The process flow diagram that accompanying drawing is the inventive method.

Embodiment

For the content of the inventive method more clearly is described, characteristics and advantages, choose the sample that 23 (being M=23) Urban Agglomerations are estimated as the group of cities input-output ratio, respectively: city groups in the Yangtze Delta, Cluster of Pearl River Delta, Beijing-Tianjin Ji group of cities, city group of Shandong peninsula, the Chengdu-Chongqing group of cities, the Western Coast of Taiwan Straits group of cities, the Liaodong Peninsula group of cities, Central Henan Urban Agglomeration, Wuhan Urban Agglomeration, long strain pool group of cities, Hu Bao Hubei Province group of cities, Jinzhong City's group of cities, N-B-Q-F City Cluster, Guanzhong Urban Agglomeration, the long group of cities of Harbin-to-Dalian, the Yinchuan Plain group of cities, ring Poyang Lake group of cities, the middle regions of the Yunnan Province group of cities, group of cities in Guizhou Province, the Lan Baixi group of cities, wine is praised beautiful group of cities, Yangze river and Huai river group of cities and Northern Slope of Tianshan Mountains group of cities.

23 Urban Agglomerations of take are basis the input-output data of 2007, use the DEA method tentatively to estimate the input-output ratio of group of cities, use again the Bootstrap deviation correcting technology rectified a deviation and revise preliminary efficiency measure value, thereby obtain the final true measure value of input-output ratio.Specific embodiment of the invention comprises the following steps:

1, build the comprehensive index system that input-output ratio is estimated.First class index comprises fixing 4 input indexs and 2 output indexs, according to the availability of data, chooses altogether 12 two-level index simultaneously, as shown in Table 1 below.Input-output data according to 23 groups of cities of 12 two-level index collections in 2007.

23 group of cities input-output ratio measurement index systems of table 1

2, the two-level index in his-and-hers watches 1 carries out standardization.X ₃, y ₁and y ₂all there are 3 two-level index, respectively it is carried out to standardization.Wherein, x ₃and y ₁two-level index be all the forward index, carry out standardization with formula (1); y ₂two-level index be the negative sense index, carry out standardization with formula (2).

3, calculate the comprehensive scores of 6 first class index of inputoutput.Wherein, x ₁, x ₂and x ₄1 two-level index is respectively arranged, and its comprehensive scores directly adopts the numerical value of two-level index; x ₃, y ₁and y ₂comprehensive scores adopt the weighted average method of formula (3) to calculate, because these 3 first class index respectively have 3 two-level index, therefore, the weight of each two-level index is 1/3.With x ₃for example, its comprehensive scores is:

$x_3=\frac{1}{3}\&times;{\mathrm{\&delta;}}_3+\frac{1}{3}\&times;{\mathrm{\&delta;}}_4+\frac{1}{3}\&times;{\mathrm{\&delta;}}_5---\left(8\right)$

In above formula, δ ₃, δ ₄, δ ₅to x ₃two-level index v ₃, v ₄, v ₅carry out the data after standardization.In like manner, calculate y ₁and y ₂comprehensive scores.

So far, obtain the concrete numerical value of 6 inputoutput first class index of 23 groups of cities.

4, utilize the DEA method of formula (4) to calculate the input-output ratio of each group of cities, obtain the preliminary measure value θ of 23 group of cities input-output ratios _m, result is as shown in table 2.

23 groups of cities of table 2 are estimated result at the input-output ratio of 2007

5, utilize the Bootstrap deviation correcting technology, to the preliminary measure value θ of 23 group of cities input-output ratios _mrevised, setup parameter B=2000, calculate inclined to one side mistake Δ θ and final true measure value θ here _m ^t, result is as shown in table 2.

As shown in Table 2, the group of cities input-output ratio measure value θ after the Bootstrap correction _m ^tnearly all than preliminary measure value θ _mlow, effectively (θ _m=1) group of cities becomes invalid (θ as ring Poyang Lake group of cities, city group of Shandong peninsula etc. _m<1).Generally, the efficiency of 23 group of cities inputoutput after the Bootstrap correction is lower, this is significantly to over-evaluate tendency because the efficiency value that directly adopts traditional DEA method to obtain exists, effectively overcome this deficiency of DEA method after the Bootstrap correction, reacted truly the input-output ratio level of each group of cities.In addition, although θ _mand θ _m ^tdeposit difference numerically, but see on the whole, the two has all reflected the variation tendency of similar group of cities input-output ratio, simultaneously, the height ranking results of each group of cities input-output ratio does not change basically yet, the group of cities input-output ratio that this explanation introducing Bootstrap deviation correcting technology is estimated is reliable and effective, has reacted truly the input-output ratio level of each group of cities.

Can be found out by above-mentioned concrete case study on implementation, apply method of the present invention, by introducing environmental pollution output index, build comprehensive index system, make the group of cities input-output ratio estimate more comprehensive; After carrying out the correction based on the Bootstrap deviation correcting technology by the efficiency value that traditional DEA method is calculated, can access more real group of cities input-output ratio value, realize thus group of cities input-output ratio quantitative measure more accurately, and then science, objective, decision-making foundation accurately can be provided for the development and management of group of cities.

Claims (6)

1. a group of cities input-output ratio Synthetic Measurement technical method is characterized in that comprising the following steps:

(1) build the comprehensive index system that the group of cities input-output ratio is estimated, comprise fixing first class index and the two-level index of selecting flexibly;

(2) two-level index of inputoutput carried out to standardization;

(3) calculate the comprehensive scores of inputoutput first class index;

(4) utilize DEA DEA method to calculate the preliminary measure value of group of cities input-output ratio;

(5) utilize the Bootstrap deviation correcting technology, preliminary measure value is revised, thereby obtain the final true measure value of group of cities input-output ratio.

2. the Measurement Method of group of cities input-output ratio according to claim 1, it is characterized in that in step (1), fixing first class index comprises that 4 one-levels drop into index and 2 one-level output indexs, wherein, one-level input index comprises capital elements, natural resources key element, Informatization Element and manpower key element; One-level output index comprises economic society output and environmental pollution output.Choose flexibly according to the availability of estimating needs, data the two-level index that can collect concrete data again below these first class index.

3. the Measurement Method of group of cities input-output ratio according to claim 1, is characterized in that in step (2), and the method for the two-level index of inputoutput being carried out to standardization is as follows:

(1), while only having 1 two-level index under first class index, this two-level index does not need standardization;

(2), while 2 or 2 above two-level index being arranged under first class index, for the forward index, adopt formula:

Adopt formula for the negative sense index:

Wherein, δ _mbe the value after the standardization of m group of cities inputoutput two-level index, 0<δ _m≤ 100; v _mit is the original value of the inputoutput two-level index of m group of cities; v _maxfor the maximal value in M group of cities inputoutput two-level index original value; v _minfor the minimum value in M group of cities inputoutput two-level index original value.

4. the Measurement Method of group of cities input-output ratio according to claim 1, is characterized in that in step (3), and the method for calculating inputoutput first class index comprehensive scores is as follows:

(1), while only having 1 two-level index under first class index, the numerical value of this two-level index is the comprehensive scores of this first class index;

(2) while 2 or 2 above two-level index being arranged under first class index, the two-level index value based on after standardization also adopts weighted average method to calculate the comprehensive scores of corresponding first class index, and the weight calculation of each two-level index such as takes at the power method, and formula is:

Wherein, x _m(y _m) be the comprehensive scores of m group of cities on certain input (output) first class index, δ _mibe the standardized value on i the two-level index of m group of cities under this first class index, n means that m group of cities has n two-level index under this input (output) first class index.

5. the Measurement Method of group of cities input-output ratio according to claim 1, it is characterized in that in step (4), utilize the DEA method to calculate the preliminary measure value method of group of cities input-output ratio to be: using the comprehensive scores of first class index as the input-output data of DEA, utilize formula:

Wherein, x _mk(x _mk0) be that m group of cities drops into the comprehensive scores on index, y k one-level _ml(y _ml0) be the comprehensive scores of m group of cities on l one-level output index; θ (0<θ≤1) is the preliminary measure value of m group of cities input-output ratio; ε is non-Archimedes's dimensionless; λ _m(λ _m>=0) be the weight variable; S ^-(S ^->=0) be slack variable; S ⁺(S ⁺>=0) be surplus variable.

6. the Measurement Method of group of cities input-output ratio according to claim 1, is characterized in that in step (5), utilizes the Bootstrap deviation correcting technology finally to obtain the true measure value method of group of cities input-output ratio as follows:

(1) utilize the Bootstrap method, from the preliminary efficiency measure value θ of M group of cities _m(m=1,2 ..., the random efficiency value sample θ ' that M) middle generation scale is M _1b, θ ' _2b..., θ ' _mb, wherein, b is for being used the b time sampling of Bootstrap method;

(2) calculate analog sample (x ^* _mb, y _m), wherein:

x ^* _mb=(θ _m／θ′ _Mb)x _m，m=1，2，L，M (5)

(3) utilize the DEA method of formula (4) to calculate each analog sample (x ^* _mb, y _m) efficiency value θ ^* _mb, m=1,2 ..., M;

(4) repeating step is (1) one (3) B time, obtains a series of efficiency value θ ^* _mb, b=1,2 ..., B, require B>=1000.

(5) calculate preliminary efficiency measure value θ _minclined to one side mistake Δ θ, formula is:

(6) calculate the rectify a deviation final true measure value θ of revised group of cities input-output ratio of Bootstrap _m ^t, formula is:

。

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