Socio-Eron. Plum. SC;. Vol. 23. No. 6. pp. 325-344, 1989 Printed in Great Britain

0038-0121:89 $3.00 + 0.00 Pergamon Press plc

Using Data Envelopment Analysis to

Evaluate Efficiency in the Economic

Performance of Chinese Cities?

ABRAHAM CHARNES, WILLIAM W. COOPER and SHANLING LI The University of Texas at Austin, Graduate School of Business, Austin, TX 78712-I 177, U.S.A.

(Rrcriwd April 1988)

Abstract-This paper studies the use of DEA (data envelopment analysis) as a tool for possible use in evaluating and planning the economic performance of China’s cities (28 in all) which play a critical role in the government’s program of economic development. DEA promises advantages which include the absence of any need for the assignment of weights on an a priori basis (to reflect the supposed relative importance of various outputs or inputs) when evaluating technical efficiency. It is also unnecessary to explicitly specify underlying functions that are intended to prescribe the analytical form of the relations between inputs and outputs. Finally, as is illustrated in the paper, DEA can be used to identify sources, and estimate amounts of inefficiencies in each city’s performance as well as to identify returns-to-scale possibilities in ways that seem well-suited to the mixture of centralized and decentralized planning and performance that China is currently trying to use.

PREFACE

A recent article in the U.S. press stated: “Deng changed the face of China.” It has been 7 years since China launched a new economic reform under the direction of Deng Xiaoping, the former party leader in China. The mixture of central planning and market economies that has developed in China since 1978 has resulted in increased volumes of both consumer and industrial goods. Dramatic success in industrialization has been claimed.

However, as stated in another recent article, which appeared in TIME (Nov. 1987), “The Chinese face the same difficulties that the Soviets have encountered in revitalizing inefficient urban industries. One result of an investigation published in the Guangming Dnily [a Chinese language newspaper published in Beijing] revealed that only 15% of managers surveyed believed they had been successful in carrying out the reforms. An additional 65% claimed that some changes had taken place but more improvements were needed, while 20% admitted that their operations lacked economic vitality.”

This paper seeks to assess urban economic performance of 28 key cities in China for the years 1983 and 1984 by using a mathematical programming model with related concepts called DEA (data envelopment analysis), as first presented by Charnes et al. [l] in 1978. DEA results from 1983 and 1984 data show that China did achieve dramatic changes in industry. However, with expensive investments and material costs as inputs, the output achievements may have been accompanied by hidden costs of considerable magnitude. Recent inflationary trends in some Chinese cities could be the result of these high input costs.

A recommendation from this study is to analyze carefully all information obtained from the DEA models. This can help to highlight achievements and shortcomings (in both inputs and outputs) obtained from the available empirical evidence on the performance of each city covered by the analysis. The purpose of this paper is neither criticism nor evaluation carried on from a distance. Its purpose is rather to study DEA (and like methodologies) as an approach for possible use in improving economic planning at various administrative levels in China.

tThe research for this paper was partly supported by National Science Foundation Grant SES 8520806 with the Center for Cybernetic Studies at The University of Texas at Austin. It was also partly supported by the IC* Institute at The University of Texas. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.

325

326 ABRAHAM CHAKNES ei al

PROSPECTS AND PROBLEMS IN CHINA’S MODERNIZATION

Until 1978, China’s economy was under strong central control. State planners set targets in great detail and supervised everything from the crops to be grown to the machine tools to be produced. The year 1980 brought significant changes in China’s policies and approaches to its problems. Inspired by the national goal of “four modernizations”-modernization of industries, of agricul- ture. of defense, and of science and technology-the new leadership, led by Deng Xiaoping, initiated a series of economic reforms in an effort to advance China’s economy. Principles of managerial autonomy, material incentives, the development of productive forces, and correlation between production and market demands were to be applied to both industry and agriculture.

Believing that any attempt to modernize the country must ultimately rest upon its farmers, China’s leaders first carried out reforms in the agricultural sector. In October, 1984. the leadership in China put its full weight behind a fundamental change in the urban-industrial sector wherein the previous doctrine of central control was replaced by one in which, as officially stated. .‘. . our enterprises are [to be] put to the test of direct judgement by consumers in the market place so that only the best survive.” (See the interview with Hu Qili of the Politburo of China’s Communist Party reported in AieMJ Perspectices Quarterly [2].)

While changes have been dramatic during the past 7 years of economic reform, China still faces serious problems that need to be resolved. One of the major issues, if not the major issue, is China’s huge population and the extremely nonuniform distribution of the population, industry, and other major components of the economy.

Nearly one-quarter of the world’s people live in China. The official Chinese census reported a population of 1,104,532,000 in 1985. By the end of the century, it is now estimated that the number

of Chinese will reach 1.2--l .3 billion. China’s population is not only large. An additional problem, however. is that its population density varies strikingly, with the greatest contrast being hctween the eastern half of the country and the lands of the west and northwest (see Fig. I). More than 50% of China’s land mass lies in the northwestern part of the country which contains only 5% of the total population. Exceptionally high population densities--for example, more t.han 1500 persons per square mile--occur in the lower Yangtze Valley and western Sichuan. An exceptionally high density area is the city of Shanghai which has 5092 persons per square mile. A critical question thus becomes: is such a huge and unevenly distributed population capable of becoming an economic equal of developed countries, and, if so, can this be accomplished in the near future?

As a result of economic reforms in agriculture, many farmers have become rather w,ealthy.

Contributing to this phenomenon has been a replacement of entire areas devoted to such staples as cotton and wheat in favor of cash crops, such as sugar, tobacco, hemp, and oil-bearing plants. Coincident with these changes has been a mass migration of population from farms to the cities. It is believed that more than 50 million persons have already shifted from farming to urban or rural industry. Table 1 shows that from 1980 to 1985 the urban population increased from 19.4% of the total to 36.6% while the rural population decreased from 80.6 to 63.4%.

Along with these demographic changes, capital investment in industry has continued to grow rapidly with resulting strains on energy and transportation. Between January and July 1985, for example, investment in capital construction grew 44.9% over the corresponding period in 1984. However, many projects were undertaken without adequate feasibility studies; accompanying mid-

Table I. Urban-rural uouulation m Chin& 1980-1985

Urban population Proportion Rural population Proportion YetiT (IO thousand) (%I (IO thousand) (%I

1980 19,140 19.4 79,568 80.6 1981 20,171 20.2 79.501 19.8 1982 21,154 20.8 80.387 79.2 1983 24, I26 23.5 78,369 76.5 1984 33,006 31.9 70,469 68. I 1985 38,244 36.6 66,288 63.4

Source: Almanuc LJ/ China’s Econonq 1985: 1986 [6]. Note: urban population refers to the population living in areas under the adtmmstratton

of cities and towns. Contributing to the substantial rise in urban population in 1984 was an increase in the number of towns due to an adjustment in the criterion for town status made in that year.

DEA evaluation of Chinese cities

Fig. I. Cities in this study and popuiation distribution by province. Sources: China, A Handbook; China, A C’ounfr~ Study; Population Headlines (see [3], [4], [5]). Note: Suzhou, Ningbo, Wuxi, Changzhou, and Nantong are not shown, even though included in this study, because of their proximity to Shanghai,

328 ABRAHAM CHAKNES rt al,

and long-term plans were not properly developed. Other recent phenomena of importance include the retail price hikes that have occurred, principally in the cities. This has been accompanied by resentment among urban residents over the increasing prosperity of peasants in the countryside. In an effort to help alleviate this situation, the original subsidy of $2.19 per month paid to every urban resident so as to offset the rise in food prices was raised in 1986. This, however, creates a problem of its own: maintaining agricultural demand in urban and peripheral urban areas.

China is well endowed with natural resources such as coal, iron, and oil. Coal and iron are spread widely over the country while oil is gradually being found in significant amounts in many provinces. China also possesses substantial deposits of some of the world’s more important non-ferrous minerals which are located mainly in the southwestern corner of the country. Despite these riches, their development has been handicapped by an inadequate transportation infrastructure. Further- more, although oil is abundant in the northwest, coal, iron, and steel facilities are dispersed in the south, central and southern parts of China. These locations are generally ill-positioned for supplying industry. The value of industrial output for the northwest accounts for only 3.2% of the national total, while for the southwest, central, and southern regions, the values are 5.5, 7.9 and 7.3%, respectively. As the population continues to increase, a more efficient development and positioning of various industries within the country is vitally needed.

Solution of the above issues requires an economic planning approach that includes both short-run and long-run development strategies which are consistent with overall planning objectives and processes. For purposes of planning, China is organized as a centralized country divided administratively/geographically into 22 provinces, 5 autonomous regions, and three municipalities directly under the control of the central authorities (see Fig. 2, below). For some time, China,

People’s Republtc Of Chlna

E

Fig. 2. Administrative structure. Source: The China ~nz~e~~~e~~ Guide I984’1985 {see [lo]). Note: the number of administrative units (in parentheses) is based on 1983 statistics. Administrative regions. prefectures and leagues are shown in broken lines because they are only executive bodies of the province and autonomous regions. Street office is controlled by the region under control of the municipality.

See the Appendix for definitions and further discussion.

DEA evaluation of Chinese cities 329

following the Soviet Union, has been using the method of input-output analysis [7] as an important part of its economic planning and forecasting efforts. However, collection of the necessary data and the processes of estimation and modification of technical coefficients required by input-output analysis models are generally difficult to implement on a timely basis.

The purpose of this paper is, therefore, to explore an alternative approach which is easier to implement and which can provide the State Planning and State Economic Commissions of China with an improved ability to monitor economic activity. In addition, we seek to identify areas of potential improvement in a manner that is consistent with current trends in planning and management of China’s economic development. As noted earlier, this will be done by employing data envelopment analysis. Using 1983 and 1984 data, we will show how DEA might be used to address topics such as the following:

(1) estimation and evaluation of the relative economic efficiency of 28 key Chinese cities; (2) identification of sources and levels of economic inefficiency of each city; and (3) returns-to-scale possibilities that might be present in each city and how these potentials

might be exploited.

Our emphasis here will be on monitoring and evaluating what has been undertaken and accomplished rather than attempting to provide a comprehensive plan to be formulated in central directives. As mentioned previously, we explore DEA as an effective tool in the mixed and partially

decentralized structure used in current-day China.

INTRODUCTION TO DEA

A key concept in DEA is the choice of decision making units (DMUs) as the entities responsible for converting inputs into outputs. Evidently, the choices of outputs and inputs are also important. It is not required, however, that functional forms which relate the inputs to the outputs be specified explicitly; it is also not required that weights be assigned to any of the inputs or outputs to reflect their supposed relative importance on an a priori basis. Given the choices and the observed values of the inputs used and the outputs produced by each DMU, DEA can be used to obtain an overall measure of efficiency for each DMU. It can also be used to locate possible sources of inefficiency when departures from 100% efficiency occur. Obtained by means of mathematical models and methods like those described below (in the section, Selection of DMUs, Inputs and Outputs), efficiency results depend on the performance evidenced by all of the DMUs. Thus, 100% efficiency is achieved only if the evidence does not allow for a combination of other DMUs which will improve upon the performance of the DMU being evaluated. In other words, the efficiency measures and identification of sources of inefficiency for each DMU via DEA are obtained from relative comparisons with other DMUs either individually or in combination.

Suppose, for instance, that some DMU, designated as DMU,,, is being evaluated relative to some other DMU which produced the same amount of every output as DMUo but used smaller levels of input. DMU, would then be rated as inefficient relative to the other DMU, where differences in their inputs would represent sources and amounts of inefficiency in DMU,.

Only DMUs which are rated as 100% efficient form the bases for effecting such comparisons and evaluations in DEA. Identification of inefficiencies does not require a priori evaluation and weighting of the relative importance of different inputs. Similar comments apply to output differences and to output differences considered simultaneously-provided that no output reduc- tions or input augmentations are required to eliminate these differences. Stated differently, a DMU is said to be DEA efficient if and only if no output or input can be improved without worsening some other output or input as determined by reference to the performances recorded by other DMUs singly or in combination.

The inefficiencies discussed thus far are called “technical inefficiencies” (or waste). Another type of inefficiency is “allocative inefficiency”, which, however, necessitates the use of prices or other forms of weighting on an a priori basis. This is the case since achievement of allocative efficiency requires assessment of output and input changes along an “efficiency frontier”, where improvement in any output or input requires worsening other outputs or inputs-i.e. tradeoffs must be made in order to move along the efficiency frontier.

330 ABRAHAM CHARNES et al

The focus here will be on technical or, rather, relative technical efficiency-also called Pareto-Koopmans efficiency [8]-so that we can concentrate on possible improvements in performance without requiring prices or other a priori weights. According to Leibenstein [9], technical inefficiencies are substantial in undeveloped and even in developed economic systems and thus warrant our direct attention here. We shall also explore the issue of increasing and decreasing returns-to-scale but in a way that bypasses the problem of tradeoffs that must be made when some outputs or inputs exhibit increasing returns-to-scale while others exhibit decreasing returns-to-scale

in the same DMU.

ALTERNATIVE APPROACHES

The role of cities (and contiguous areas) in Chinese economic development planning is indicated by the following statement from The China Investment Guide [lo], p. 23 “To maximize resources it has been proposed that planned economic activities be integrated in a concerted development in and around key cities, which will gradually grow into economic zones.” Such a statement makes clear the need to examine suitable means for evaluating the performance of China’s “key cities”.

The objective of providing planners of a managed economy with some means of evaluating the efficiencies (and identifying inefficiencies) in the performance of its cities is a novel one. Approaches that might have been used as alternatives to DEA for measuring and identifying these inefficiencies need to be considered.

The use of cost--benefit analysis offers one possibility in a tradition that goes back to the 1943 publication Measuring Municipal Activities [I I]. Virtually all such studies are concerned with one-service-at-a-time situations (e.g. police, fire-fighting, etc.). There appears to be no easy way to aggregate these and other activities (e.g. manufacturing) into the kind of “overall” scalar efficiency measures that can be secured from DEA. Furthermore, the use of money (or similar weighting

systems) brings additional difficulties. To these problems can be added the danger of circularity when dealing with comprehensive planning systems such as those currently used in China.

Turning from municipal to regional analysis as yet another alternative. one finds that the focus of this literature is oriented more toward “understanding” or “predicting” economic activities in ways that are better suited to “western-style” economic systems than to the kinds of control activities that form centers of attention in China’s planning mechanisms. (See [12] for further discussion of the distinctions between control, prediction and understanding as objectives of scientific research.)

An additional shortcoming of these more standard approaches is that they provide very little help in distinguishing between efficient and inefficient activities. The statistical techniques they customarily employ result in averages or aggregates that make it difficult to identify the individual entities which are capable of effecting needed correctionst.

DEA has some potential use in closing gaps and repairing deficiencies in some of the above approaches. Schinnar, in [15], for instance, has suggested replacing the coefficients of a Leontief- type (input-output) analysis with an alternative set of efJicient values that can be derived from the dual variables of DEA. To this, Macmillan, in [16], adds the possibility of using the resulting efficiency frontier as a basis for assessing the behavior of inefficient DMUs, e.g. to test whether the behavior assumed for perfect competition is present by observing whether convergence to efficient behavior occurs.

Even with these extensions, however, something more is required to obtain a focus on the performance (efficient or not) of individual DMUs, which here are individual cities. We thus return to the DEA model and show, in detail, how it may be used in the current context.

SELECTION OF DMUs, INPUTS AND OUTPUTS

In choosing appropriate DMUs for our study, we note that certain provinces and municipalities monitored by the central government have some freedom to allocate resources within their regions (see Fig. 2). Planning decisions in these cases may be made by appropriate committees at urban, municipal, and/or provincial levels. It is therefore reasonable to consider the cities, municipalities,

tSer e.g. the use of “shift share analysis ” in [13] or the way the coefficients used in Leontief-type matrices are generally

dericed. as described in [ 141.

DEA evaluation of Chinese cities 331

and provincial capitals as representing the DMUs responsible for transforming inputs and outputs (see right-hand side of Fig. 2). In the current study, we have selected 28 cities as our DMUs; they are called “key cities” based on their importance to the economic and industrial performance of China (see Fig. 1 for their location).

Turning to the choice of inputs and outputs, it would be well to distinguish between those which are discretionary and those which are not. Inputs and outputs such as manpower and factory production are familiar examples of discretionary variables used in production economics. There are other variables, of course, such as climate or geographical area which are also important in evaluating the relative efficiency of different DMUs, although such variables cannot be varied at the management’s discretion, i.e. they are not controllable variables.

Values for the latter types of variables can be handled by altering the DEA model in various ways, as in [ 17, 181, or by adding constraints as outlined in [8] and [ 181. For purposes of simplification, however, these topics are not addressed in this paper?.

Even with the issue of non-discretionary variables set aside, the selection of inputs and outputs requires some preliminary comments. There is concern for comparability of qualities, of course, even when the “same” inputs and outputs are used. This issue canot be addressed completely in the current study, in part, due to lack of data availability. To some extent, however, the way in which selected outputs and inputs are defined allows for some differences in qualities. For instance, the mixes of light industry (textiles, electronics) and heavily industry (coal, steel, etc.) vary from one city to another. Wage rates of workers in heavy industry are higher than wage rates for workers in light industry with comparable levels of experience. Similarly, capital and technical equipment investments are more costly in heavy industry. Thus, to the extent that inputs like these are used, some of the related qualitative differences should be reflected in the DEA comparisons and evaluations.

Adjustments should be made for differences in percentages between staff and white collar workers when these can affect the efficiency evaluations. However, lack of data makes it difficult, if not impossible, to check the effects of these differences, e.g. by conducting sensitivity analyses in which some inputs and/or outputs might be dropped or replaced by other inputs or outputs. Also combined here are the inputs and outputs from the three types of enterprises currently operative in China-state-owned, collective, and individual enterprises. Since we are concerned with regional or city efficiencies, it is not necessary to distinguish between “program” ( = type of enterprise) and “managerial” ( = within each type of enterprise) efficiencies. (See [20] for further discussion of the concepts “program” and “managerial” inefficiency and how DEA may be used to identify and evaluate each of them.)

Proceeding along these lines, the following were selected to be the inputs in this study:

(1) labor: number of staff and workers who are engaged in industry in a key city, exclusive of farm labor;

(2) working fund: the amount of “circulating capital” and the total annual wage bill for staff and workers; and

(3) investment: annual amount of additional monies supplied for (a) capital construction of state-owned units and (b) acquisitions of machinery and other fixed assets for collective units in cities and towns.

These input categories play important roles in China although certain simplifying assumptions are made in our analysis. For example, we assume comparability for the composition of workers and staff in each DMU so that differences in numbers for the first input (labor) reflect differences in mixes of staff and production workers. The second input conforms to reported data on the yearly capital used for wages, administration, maintenance, and other miscellaneous costs.

The third input covers funds used in large or small-scale capital projects, importation of new

tYet another alternative is to ignore the distinction between discretionary and non-discretionary variables in the initial analysis, as is done with the “weather” and “climate ” in [19], and then test further consequences of the values assumed

by these non-discretionary variables by subsequently conducting a variety of sensitivity analyses. None of this will be done here, however. The objective of this paper is to provide an illustrative analysis from which to judge whether subsequent. more realistic. developments are worth undertaking. Introduction of these additional considerations would complicate matters and cloud the presentation.

332 ABRAHAM CC~ARNES et nf.

technology, and the extension of existing enterprises in each city. It is also to be noted that the current study covers a period of only 2 years. Longer term implications from these investments may therefore not be open to evaluation. In this regard, conformance with the 5-year planning periods is not taken into account explicitly.

The three outputs to be utilized in this study are as follows:

(I) gross industrial output value: a measure of the contribution to the national economy derived from the total monetary value of the outputs produced in a key city;

(2) profit and taxes: a measure of the net contribution to the central government by the profit and taxes generated by state-owned enterprises; and

(3) retail sales: a measure of the local consumption (and investment) generated in the city, represented by total sales value of the nnal products in the local market.

The method of computing gross industrial output value in China differs from the approach used in western countries in that the value of a final product may include some duplication. For example, in place of the usual western economic approach of “net value added”, the contribution from a particular product includes the value added plus the value from earlier stages of processing. It is not possible to eliminate such duplications in the data we have available, so the best we can do is to conform to the economic indicators currently used in China and leave further refinements to subsequent studies. Profit and taxes realized in state-owned enterprises is an output of special interest to state planners, while retail sales should be of special interest as a measure of a city’s economic contribution to consumers living in that city. Naturally, there are issues of measurement as well as issues of completeness of coverage to be addressed, but these are not discussed in adequate detail in the sources we shall be using-sources such as the ~~~~~~~c ~~e~in~‘s economy

(6]--which are published periodically and from which we take the numbers basically as we find them. In any case, we employ all of the above inputs and outputs as totals rather than ratios (e.g.

Tzable 2. 19X3 Statistics

DMU No.

KAY cities GIOV

Outputs i 10,000 rmb)

P&T RS

Labor - (10,000

persons)

IIlpUtS

WF INV. (lO.OOOrmb) (10,OOOrmb)

2

4

h

9 IO I1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Shanghai Beijiig

6.7853798 2.505.984

Tianjin 2.29?,025 Shenyang 1.158.016 Wuhan 1,244. I24 Guangzhou 1.1X7.130 Harbin 638,910 Chongqing 993.23x Nan~ing 854.188 Xl‘kill 606.743 Chengdu 736.545 Changchun 454,684 Tazyuan 494.196 Dalian 842,854 Qingdao 776.285 Lanzhou 490.998 Jman 482,448 Fushun 515.237 Anshan 625.517 Kunming 382,880 S!.lZhOU 867.467

Hangzhou 830,142 Ningbo 52 I .6X4 Wuxi 869,973

Changzhou 604,715

Nantong 601,299

Yichang 145,792

Changsha 319,218

I s94.957 1.0X8.699

54s. I40 x35.745 406,947 473.600 135.939 336.165 204,909 3 17.709 190,178 605.037 86.314 239,760

I .4 I I.954 353,X96 135,327 239,360 78,357 208,188

114.365 298,112 67,) 54 233,733 78.992 1 I x.553

149,186 243,361

I 16,974 234,875 I 17.854 118.924 67,857 IS&250

114,883 101,231 173,099 130,423 74,126 123,968

65,229 262.X76

128 279 371245

242,773 184,055

86,859 194,416 55,989 127,586 37,088 224,855 11,816 24,442 31,726 169,051

483.01 I .391.736 bl6,9bl 371.95 855,509 385,433 268.23 685,584 341,941 202.02 452.7 I3 I 17,424 197 93 471,650 112,634 178.96 423,124 189,743 148.04 367,012 97,004 184.93 40x,3 I I I I I .904 123.33 251,542 91,861 116.91 305.316 91.710 129.62 295,8 I2 92.409 106.26 198,703 53.499 89.70 210,891 95.642

109.26 282.209 84.202 85.50 184,992 49,357 72.17 222,327 73,907 76.18 161,159 47,971 73.21 144,163 43,312 86.72 190,043 55.326 69.09 158,436 66.640 i7.b9 135,046 46,198 97.42 206,926 66,120 54.96 79,563 43.192 67.00 144,092 43,350 46.30 100.431 3 1,428 65. I2 96,873 28,112 20.09 50.717 54,650 69.81 117,790 30,976

Source: Almanac of China’s Econom?: 1985/1986 [6). Note: I. rmb is the Chmese monetary unit. 2. GIOV stands for gross industrial output value. 3. P & T stands for profit and taxes. 4. RS stands for retail sales. 5. WF stands for working funds. 6. INV. stands for investment.

DEA evaluation of Chinese cities 333

Table 3. 19x4 Statl\tlc\

Inputs 0ucpu1s

(10,000 rmb) L‘lbor DMU Key ( lo.oot~ WF INV.

NO. cities GIOV P&T RS persons1 (10.000 rmb) (10,000 rmb) -_

Shanghai 7,443,700 1,692.lOO 1.123.X00 487.44 I ,594.040 718,953 I

2

3 4 5 6 1 8 9

IO II I2 I3 I4 I5 I6 II IX I9 20 21 22 23 24 25 26 21 28 Changsha

Beaning 2,X17,200

359,956

TianJin 2.514.900 Shenyang 1,337,lOO Wuhan 1.377.600 Guangzhou 1,333,600 Harbin 158.941 Chongqing l.l57,572 Nanjmg 973,951 Xi’an 668.107 Chengdu 834,600 Changchun 540.428 Taiyuan 541,923 Dalian 918.508 Qingdao 849,956 Lanzhou 540,857 JillaIl 546.065 Fushun 547.122 Anahan 686.383 Kunming 450,743 Suzhou 922,512 Hangrhou 1,00X.736 Ningbo 664.434 Wuxi 1.093.882 Changzhou 709,278 Nantong 694,295 Ylchang 162,454

589,600 I

38,869

.O 16.600

201.7Y5

-375 47

443.600

72.37

566.200 ?7? 69

162,700 4 10.3Ol~ 208.82

232,900 3x7.900 lY9.99 209.700 614.500 lYl.90 102,893 2Y8,563 150.93 166,978 412.991 I SX.2.~ 166,056 294.927 1x4x 83,735 24X.680 12’ 70

128.455 X56.868 133.13 86,288 29x. I82 IOY 31 87,296 145.379 94.45

169.458 290.5 I9 II? I6 128,665 274.982 x7.54 130,638 14l.JOY 73.70 82,058 I92.074 71.64

140,122 1213.739 74.19 201.297 152.8X I 8’) 69

X9.03 I 171.l23 75.52 61,174 255,6X5 70 73

137,108 29x.717 68 IO 62.610 211.554 58 5x 97,857 214.07x 69 27 69.343 150. I42 47 Y7 38.004 256.040 67 77 12,841 29,041 2tJ.07

955,124 522,032 782.585 371,314 489,676

133,826

138.017 5 19.686

4,322

142,688 480,392 259,092 410,727 95,775 47% IO4 134.031 296,534 130,325 335.329 105,474 335,605 103.431 277.57 I 65,906 204,998 130,349 309,779 115.381 2OY.197 64.903 250,558 X6.045 181,067 52,858 158.850 52,715 203.720 76.5X0 184.676 18.686 136,273 13.424 735,282 12.365 95.712 7,454

174.73 I 13,906 I Il.573 10.502 105,075 10,317 55.384 I .x47

I. rmb is the Chinese monetary unit. 2. GIOV stands for gross industrial output value. 3. P & T stands for profit and tmcs 4. RS stands for retail sales. 5. WF stands for working funds. 6. INV. stands for investment.

per capita ratios) and rely on DEA to effect the separations needed for this comparative evaluation by means of the optimization principles used (see [18] and [21]).

Tables 2 and 3 give the input and output data which we shall use for the 28 key Chinese cities in 1983 and 1984, respectively. The first column in both tables identifies the DMU numbers to be assigned while the second column lists the names of the 28 key cities with which these numbers are associated. Columns 3, 4 and 5 provide the amounts of the three outputs reported for each city in the Almanac of China’s Economy [6] for the indicated year. GIOV in column 3 stands for gross industrial output value, P & T in column 4 stands for profit and taxes, and RS in column 5 stands for retail sales. The last three columns list the three inputs reported for each city under the heading of labor, WF (representing working fund) and INV. (representing investment). All the outputs and inputs are in units of 10 thousand rmb (renmingbi = people’s money) except for labor which is stated in units of 10 thousand persons.

For example, in 1983, the city of Shanghai, identified as DMU 1, generated 6,785,798 x (10,000) rmb of gross industrial output, 1,594,957 x (10,000) rmb of profit and taxes, and 1,088,699 x (10,000) rmb of retail sales. The 1983 data also show that Shanghai used 483.01 x (10,000) workers, 1,397,736 x (10,000) rmb of working funds, and 616,961 x (10,000) rmb for investment. As can be seen, Shanghai increased all of its outputs and inputs in 1984 relative to 1983. It remains to be seen whether Shanghai can be regarded as DEA-efficient in either or both years relative to the performance exhibited by the other cities listed in these tables.

DEA MODELS

The model we shall use to study and evaluate the efficiency of 28 key Chinese cities derives from what is called the “CCR ratio form of DEA” [l]. Using vector--matrix notation, the following dual pair of linear programming models are the ones we shall employ. These models were originally

334 ABRAHAM CHARMS et al.

derived in [l] and further elaborated and extended in [8] and [19]:

maximize: I*’ Y, minimize: 0 - c [e’s + + eT3 ] subject to subject to

V’X, = 1 YL-s’=Y, /LTY-VTX<O ex, - Xj* - s = 0 (1)

-pT < - 6eT i,s+,s- 20 -_ \S T < - (eT.

Here. X0 and Y, are vectors with components xi0 and yrO, representing observed values of i= l,..., minputsandr=l,... , s outputs for DMU,, the DMU being evaluated. Using xi, and y, to represent the corresponding inputs and outputs for each DMU,, j = 1, . . . , n, we array these observations in the form of the associated s x n matrix of observed output values, Y, and the m x n matrix of observed input values, X. Also included in this collection ofj = 1, . . , IZ DMUs are the observed outputs and inputs for DMU,, the decision making unit to be evaluated. That is, the outputs and inputs for DMU, are included in the matrices Y and X as well as in the vectors Y, and X0.

Prescribing c > 0 as a very small (non-Archimedean) constant and defining eT as a vector of ones (of appropriate length) guarantees that all variables are constrained to be positive in the vectors pT and uT, where the superscript T defines these vectors as transposes of the corresponding column vectors pt I;, and e. Roughly speaking, therefore, the imposition of t > 0 as a requirement to be satisfied by every variable means that all inputs and outputs are to be regarded as having at least “some” positive worth, which remains unspecified.

The problem on the left in (1) may now be interpreted as follows: treating all inputs and outputs as having some positive value, the objective is to maximize a “virtual output”, defined by pTY,,, subject to the condition that the virtual input, defined by uTX,, is restricted to unit level in the first constraint and subject to the further condition that no virtual output can exceed its associated virtual input for any DMU as represented in the next set of constraints.

The vectors s +, s 3 0 in the right hand problem represent slack. The first set of constraints can therefore be equivalently represented by YE. z Y,, so that the choices of the vectors 2 3 0 yield combinations of output values formed from all DMUs that are always at least as large as the corresponding output values of DMU,,. Similarly, X1 < 0X, means that the solutions i > 0 yield combinations of inputs from other DMUs which do not exceed 0X,. Thus, the minimizing objective is achieved by scaling all the inputs by the scalar 0 to the lowest possible level that the inputs and the 1 choices allow. The name “data envelopment analysis” reflects the fact that the Y,, outputs are being enveloped from above in this manner and that the 0X, values are being enveloped from

below. It should be noted that the t > 0 values appear in the objective function of the problem on the

right, where they are defined to be so small that they will not affect the minimizing value of 0.

Further, via the duality theory of linear programming, we have

Maximum pTY, = minimum (6 - teTs+ - 6eTs - ). (2)

In fact, defining h,=O-ceTs+-cTsp, (3)

we have the condition for efficiency, given as follows: DMUo is efficient if and only if minimum h, = h,* = 1, which can occur if and only if both of the following conditions are satisfied:

(i) 8* = 1; and (4.1)

(ii) all slacks are zero. (4.2)

We can now interpret what was said earlier about the conditions for Pareto-Koopmans ( = DEA) efficiency by introducing the following formulas as first given in [l]:

x; = 0*x,-s-*

Y;= y,+s+’ (5)

where the star (*) specifies optimal values.

DEA evaluation of Chinese cities 335

Thus, if any component of s +* is positive then, as this optimum solution shows, we could increase at least one output without decreasing any other so that Yh 3 Y,, and at least one component of Y; would exceed the corresponding component of Y,. Similarly, we could have X; = X0 if and only if 8 * = 1 and all components of s -* are zero [cf. (4.1) and (4.2) above].

Managerially speaking, the formulas (5) make it possible to locate sources and amounts of inefficiency by comparing DMU,, with possibly better combinations of other DMUs using the same kinds of inputs and producing the same kinds of outputs. Geometrically these formulas make it possible to project the observed X0, Y,, values onto the efficiency surface where still further tradeoffs may be made by using the values of the dual variables obtained from the left hand problem in (1) (see the discussion in [S]).

The latter, i.e. the efficiency surface, assumes the form of a piecewise linear series of facets obtained by projecting each DMU,, i = 1, . . , n onto the efficiency facet with which it is associated and regarding it as a new DMU,, to be evaluated. In each case, a standard simplex code? will select a set of basis vectors which will maximize the virtual output for this DMU, in the problem on the left of (I)-or, in the problem on the right of (1) reduce the inputs to the lowest possible level and increase the outputs to the highest level that the constraints will allow.

The basis vectors that appear in an optimum solution, when using the simplex method, provide the means for identifying facets. This is one part of what is achieved in each of these optimizations. Another part of what can be achieved is obtained from the fact that each such optimization comes as close as the data allow to estimating the inefficiencies that may be present in each DMU. Thus, in contrast to the usual statistical averugirzg approaches obtained from a single optimization (as noted earlier in this paper), the optimization in DEA is made on each observation in a series of n optimizations, one for each DMU, (j = 1,) . , n) where each is treated as a different DMU,. Finally, the basis sets used to generate these efficiency scores in the form of the 8* values are obtained from the computer printouts so that the source of comparisons for each such evaluation can be readily identified by reference to the DMUs in the optimum basis.

We note again that nothing is required in the way of explicitly specified functional forms or u priori weights. The resulting piecewise linear efficiency surface may thus be interpreted as approximating “as closely as possible” whatever functional forms underlie the data in each segment

(see PI).

DEA RESULTS AND INTERPRETATION

Based on data from the 1984 and 1985 editions of the Almanac of China’s Economy [6], the DEA model as described earlier produced information which can be important for guiding central planners to points that need to be considered in evaluating the performances of the DMUs under

study. In order to show how this topic might be approached, our DEA analyses are divided into three parts. The first part provides information about the relative economic efficiency ratios of the 28 key cities. The second part shows how sources and amounts of inefficiency may be identified in the performance of each city. The third part examines the returns-to-scale for each of the 28 cities.

The relatice economic eficiency ratio

How well each key city performed in the current economic reform in comparison with the other key cities could be one question that China’s planners might have raised. Partly to emphasize that the analysis depends on the evidence used, Charnes et al. state in [19] that: “100% relative efficiency is attained by any DMU only when comparisons with other relevant DMUs do not provide evidence of inefficiency in the use of any input or output”. Therefore, to answer this question, we separate the 1983 data from the 1984 data and let the DEA model solve the problems respectively. This use of DEA means that each DMU is to be given a maximal efficiency ratio relative to the performance of the other 27 DMUs in each period. Table 4 provides these results.

Columns 1 and 2 in Table 4 list the 28 key city DMU numbers and names. Columns 3 and 4 provide the DEA relative efficiency ratios obtained for each of these 28 cities in 1983 and 1984,

tMore efficient codes for use with DEA are available on request to the Center for Cybernetic Studies, University of Texas at Austin.

Table .i Kclauw ~fhwncy ratios of the 2X key aties (DMUs) in 1983 and 19&l

.-

Efficmcy EffiClWKy % Change DMU Key ratio ratio 1984 DMU YS

No. cltles (rn 1983) (in 1984) 1983 DMU .~

I .a000 0.00

0.7674 -0.75 0.6385 -2.93 0.507 t - 9.49 0 5471 -23.91 0.8192 - IX.10 0.4764 -5.50 0.5555 -11.19 0.6752 0.67 0 4877 - I I .0x n.6661 -7.30 0.6663 -3.66 0.4831 5.57 0.7072 -9.76 0.X46X - 15.32 as’)07 ~- t 0.02 0.6542 -4.50 1J.Y397 2.01 I 0000 n.On 0 6324 4.70 I .onno 0.00 1 .oooo 20.48 I .oooo 0.00 I .OOOO 0.00 0 99’7 --0.70 I .oooo 0.00 0 6324 IX.05 I .01100 40.04

respectively. The results are intended to provide information on how each individual city performed in comparison with other key cities in the year under consideration.

Some cities, such as Shanghai (DMU I), Anshan (DMU 19) Suzhou (DMU 21), Ningbo (DMU

23) Wuxi (DMU 24). and Nantong (DMU 26) achieved 100% DEA efficiency (efficiency ratio = 1.000) in the 2 consecutive years. It is noteworthy that these six cities have been part of the traditional industrialized base in China. However. not all well developed industrial cities achieved high efficiency ratios. Shenyang (DMU 4). the largest industrial base of Northeast China, had ratios of 0.5602 in 1983 and 0.5071 in 1984; Harbin (DMU 7). an important heavy industrial city in the north of China. had ratios of 0.5041 and 0.4764 in 1983 and 1984, while Chongqing, the biggest port on the upper reaches of the Yangtze. had ratios of 0.6255 and 0.5555 in 1983 and 1984.

Furthermore, some strategically important key cities experienced dramatic drops in their efficiency ratios from 1983 to 1984. The city of Guangzhou (DMU 6) is an example. Guangzhou, the capital of the booming southeastern province of Guangdong, has played a leading role in the process of economic reform. Many capital projects and joint ventures were set up there as a result of its superior location (just north of Hong Kong). However, DEA results show that its relative efficiency ratio dropped from I.000 in 1983 to 0.X 192 in 1984. This implies that in 1984 Guangzhou was actually falling behind some other key cities, on a relative basis, in utilizing its resources.

Another result of potential interest is that some key cities achieved tremendous improvements in their efficiency ratios over the 2 years studied. The city of Changsha (DMU 28) capital of Hunan Province in the central part of China, while not considered a pioneer in the reform effort, nevertheless increased its efficiency ratio from 0.7141 in 1983 to 1.000 in 1984.

It is of interest to explore discrepancies that might exist between our DEA results and supposedly customary observations on the performance on these cities. We use other DEA information to address this question below. As mentioned earlier, China’s industry is not uniformly distributed. Among the 28 key cities, four are substantially less developed. It is therefore not surprising to see that they appear as relatively poor economic performers in our DEA results. In Table 4, Taiyuan (DMU 13), which has a severe shortage of technical and professional workers due to its isolated location, had efficiency ratios of 0.4576 in 1983 and 0.4831 in 1984. The city of Kunming (DMU 20). which is the capital of Yunnan Province (site of the recent devastating earthquake), is inhabited by many national minorities. It had efficiency ratios of 0.6040 in 19g3 and 0.6324 in 1984, while

DEA evaluation of Chinese cities 337

the city of Lanzhou (DMU 16), which is the capital of northeastern Gansu Province, had efficiency ratios of 0.6565 in 1983 and 0.5907 in 1984 (see Fig. 1 for location of these cities/provinces).

Improving the performance of these cities is a critical issue facing China’s economic planners: it

will be addressed later in the paper. The last column in Table 4 gives the percentage change in efhciency ratios for each city from

1983 to 1984. Most cities show negative percentage changes. Does this mean that the 28 key cities’ economic performance in 1984 is worse than that in 1983? We can answer this question more easily by grouping the 2 years’ data together and treating each of the 28 key cities as a different DMU in each of the 2 years. In other words, we convert these 28 key cities into 56 DMUs with two representations for each-one for 1983 and one for 1984. Through comparisons with other DMUs, DEA can then be used to assign each DMU an optimal relative efficiency ratio by applying (1) to each of the 56 entities.

Results from proceeding in this manner are summarized in Table 5, where the names of the 28 key cities appear in column 3. The DMUs from 1 to 28 in column 1 represent the 28 key cities in 1983 while the DMUs numbered from 29 to 56 in column 4 represent these same 28 key cities in 1984. Columns 2 and 5 provide the corresponding efficiency ratios for these 56 DMUs. The last column indicates the percentage change for each city from 1983 to 1984. For example, the maximal relative efficiency ratio achieved by Beijing (DMU 2). the capital of China, was 0.6987 in 1983. Its lower 1984 efficiency value compared to 1983 in Table 4 occurs with the expansion in the number of DMUs used. In contrast, its efficiency rating for 1984 in Table 5. where it is treated as “DMU 30”, has retained the 0.7674 value as in Table 4.

We now have a different way of addressing the question of whether a city’s 1983 performance was worse than that in 1986by turning to the last column in Table 5. With the exception of two cities (Guangzhou, DMU 6 and DMU 34, and Anshan, DMU 19 and DMU 47) which have negative percentage changes, all the rest increased their relative efficiency ratios in 1984. The average change is a positive 19.4%. This is a more meaningful way of addressing the issue of whether there was a general improvement since Table 4 used two separate comparison sets, one for 1983 and one for 1984, while Table 5 combined these two sets to allow each city to be evaluated relative to the performance of all of the other cities in both years,

There is, nevertheless, something of value to be gained by using both tables. Notice, for instance, that except for Shanghai (which appears as DMU 1 and DMU 29 in Table 5) all DMUs which

fable 5. Efficiency ratios of the 56 DMUs (I983 and 1984)

% Change DMU No. Efficiency Key DMU No. Efficiency 19X4 DMU YS

(1983) ratio cities (1984) ratio 1983 DMU

I I .oooo Shanghai 29 1 .oooo 0.00 2 0.6987 Beijing 30 0.7674 9.83 3 0.6320 Tianjin 31 0.6385 1.03 4 0.4455 Shenyang 32 0.507 1 13.X.3 5 0.5043 W&an 33 0.3477 X.61 6 0.8407 Guangzhou 34 0.8192 -2.56 I 0.4012 Harbin 35 0.4764 18.74 8 0.5071 Chongqing 36 0.5555 9.54 9 0.6080 Nanjing 37 0.6752 Il.05

10 0.4361 Xi’an 38 0.4877 11.83 II 0.5242 Chengdu 39 0.6610 26.10 12 0.5758 Changchun 40 0.6663 15.72 13 0.4171 Taiyuan 41 0.4760 14.12 14 0.6426 Dalian 42 0.7072 10.05 15 0.7852 Qingdao 43 0.8468 7.85 16 0.55.40 Lanzhou 44 0.5907 6.43 17 0.5705 Jinan 45 0.6542 14 67 18 0.8368 Fushun 46 0.8871 6.00 19 0.9692 Anshan 47 0.9380 - 3.22 20 0.5360 Kunming 4X 0.6324 17.99 21 0.9346 Suzhou 49 1 .oooo 7.00 22 0.7343 Hangzhou 50 1.0000 36.18 23 0.9747 Ningbo 51 1.OOOo 2.60 24 0.9454 Wuxi 52 1.0000 5.78 25 0.9329 Changzhou 53 0.9927 6.41 26 0.9607 Nantong 54 I .oooo 4.09 27 0.4595 Yichang 55 0.9876 114.93 28 0.6353 Changsha 56 I .oooo 57.41

are 100% DEA-efficient appear so in 1984 but not in 1983. Thus, when the comparison set is expanded, it appears that improvements in efficiency occur in conformance with the government’s statement that economic performance has improved from 1983 levels. As evidence of economic achievement, China*s gross national industrial (output) value increased by 14% from 1983 to 1984. The fact that only Shanghai (DMIJ 1 and DMU 29) achieved IOOOi DEA efficiency in both 1983 and 1984 also corresponds to reports from China that Shanghai, China’s largest economic center, has been playing a pioneering role in implementing the current reforms. Finally, the last column in Table 5 indicates that Yichang (DMU 27 and DMU 55) increased its efficiency ratio by 114.9% and Changsha (DMU 28 and DMU 56) increased by 57.4%. It need not be argued that increases of this magnitude occurred, but there are reasons to believe that these key cities have contributed substantially to China’s material progress and might be studied further as models for the country’s advances in other cities. At the same time, the fact that DEA indicates significant achievements in these cities may provide central planners with reasons to inquire more deeply into factors inducing such changes.

We now wish to return to the question of why the last column in Table 4 has negative percentage changes using Tabie 5 to identify some of the sources. In Table 4, due to the separation of 2 years’ data, DMUs in 1983 and DMUs in 1984 are evaluated separately. While the gaps between effzcient cities and inefficient cities in 1983 are not large, the gaps widened in 1984. In other words, the efficiency surface formed by efficient DMUs is further away from inefficient DMUs in 1984. As a result, the relative efficiency ratios of inefficient cities in 1984 declined from those in 1983.

Two related issues are brought to the fore in this manner. First, as the economic reform progresses, the key cities will gairl more managerial freedom and autonomy. This might cause some of the key cities to go further ahead, resulting in an even less uniform d~stributiou of economic deveiopment in the country. Second, since the DEA model only identifies refukwl~ efficient DMUs; how can we improve those cities that are already DEA-efficient? We address these two problems in the next two parts of this section.

In addition to providing values of the relative effciency ratios, DEA also makes it possible to identify sources and estimate levels of inefficiency for each DMW. In Table 4, we found that the city of Guangzhou (DMU 6) experienced a decline in its efficiency ratio in 1984. In order to examine possible reasons for this decline, we examine further the DEA results for Guangzhou in 1983 and 1984. This is done via Tables 6 and 7. From both Tables 3 and 6 we find that the city of Guangzhou achieved an efficiency ratio of 1.000 in 1983. The row labeled Facet in Table 6 lists the DMUs which form the basis (in the linear programming solution) that optimizes the efftciency ratio of the DM‘CJ being evaluated. Thus, the set consisting of DMU 6, DMU 1, and DMU 21 forms a basis (in the mathematical sense) that provides a subset of ejicient DMIls from which Guangzhou’s efficiency is to be evaluated.

The government believes that Guangzhou improved its economic performance by investing in many large projects and joint ventures. However, at least for the years covered in our study, this hypothesis may be called into question by turning to the shadow price of INV. which is virtually zero (see the intersection of the last column and last row in Table 6). In other words, the value

labie 6. DEA T-CSU~!S for the city of Guangzhotl @MU 61 in 1984

DM&’ q@iciency = 1.m FaC& 6 1 21 Lambda = I .oon 0.000 0.000

Value Value if OUtpUtS mrasured efficient Slack value Dual value

GlOV 1,187,130.0 t,187,130.0 0.0 0,1342E-10 P&T 190.178.0 190.1?8.0 0.0 O.lOIOE-OS RS 6Os.037.0 605,u37.0 0.0 0,1825E-05

lllpUtS

Labor 179.0 179.a 0.0 0.6323E-02 WF 423,124.0 423.124.0 0.0 0,3887E-06 INV. 189,743.O 189,743.O 0.0 O.l389E-09

DEA evaluation of Chinese cities 339

Table 7. DEA results for the city of Guangzhou (DMU 6) in 1984

DMlT &ciency = 0.8192 Facet: 23 22 26 Lambda = 0.084 1.250 0.871

V&K Value if Outputs measured etlic1ent Slack value Dual value

GIOV 1,333,600.0 I ,920,928. I 587328. I 0.0 P&T 209,700.O 209,700.O 0.0 0.2549E-06 RS 614,500.O 624.500.0 0.0 0. I246E-05

Inputs

Labor 181.9 149.0 0.0 0.3932E-02 WF 480,392.O 393557.3 0.0 0.59258-06 INV. 259.092.0 25.052.7 187,206.3 0.0

of incrementing INV. as a contribution to improved efficiency in 1983 is zero for all practical

purposes. Guangzhou (DMU 6), with an optimum efficiency ratio of 0.8192 in 1984, is DEA-inefficient.

Its sources of inefficiency are identified in Table 7. In the output category, we find the GIOV (gross industrial output value) has a slack value of 587,328.l in units of 10,000 rmb. This means that the optimal GIOV should have been 1,920,928.1, which is the sum of the value measured plus the slack [see expression (5), which gives the optimal solution of output asY; = Y, + s+*].

In a similar fashion, the inefficient inputs can be found under Inputs in Table 7. The input of INV. (investment), for example, has a slack value of 187,206.3. Using the efticiency value of 8* = 0.8192 shown at the top of Table 7, the value if efficient can be obtained from expression (5): XA = 0*X, - s -*. The result is seen to be 0.8192 x 259,092.O - 187,206.O = 25,052.7. The other two outputs (P & T and RS) require no adjustment while the other two inputs (labor and WF) have no slack so that their values, if efficient, are obtained simply as 0.8 192 x 4839.0 and 0.8 192 x 18 1.9,

respectively. Returning to INV., we find that a large discrepancy exists between actual usage and the value

needed to achieve efficiency. As a further check, we find that the dual of INV. remains as it was in Table 6. This implies that the input INV. played little role in both 1983 and 1984. These results indicate that the city of Guangzhou could not achieve efficiency as a result of inefficient usage of its three inputs, particularly investment. Allowance needs to be made, however, for the fact that the current study covered a 2 year period while investments undertaken in Guangzhou may need a much longer period to generate their benefits. On the other hand, a characterization of Guangzhou as being efficient because of these investments, as the government believes, needs to be scrutinized since current evidence indicates that this belief rests on extrapolations that may not be valid.

It is not the case that the dual variable values are limited to use in inefficient cities. For example, Shangai was evaluated as being 100% DEA-efficient in both 1983 and 1984. Nevertheless, the value of the dual variable for WF (working funds) remained at (or, really, very near) zero in both years. This means that further additions to working capital in Shanghai would have contributed virtually nothing to its efficiency.

What about dual variable values for cities that are not efficient? For example, Fushun (DMU 18) has a high (in fact, the highest) dual variable value for WF in both 1983 and 1984. This means that incrementing its WF value will contribute to improving its efficiency at a rate that exceeds what can be obtained by incrementing other inputs after efficiency has been achieved.

Other information, such as ratios of the dual variables, can be used to explore substitution and transformation possibilities between inputs and outputs along the efficiency frontier. We do not undertake this development here, however, and simply refer readers to [8] where the mechanics as well as the theory for accomplishing this task are set forth in full detail.

Returns-to-scale

The above analysis does not exhaust the information obtainable from DEA. Providing another illustration, we turn to the issue of returns-to-scale.

Note first that returns-to-scale possibilities become ambiguous unless efficiency is assumed. That

340 ABKAHAM CHARNES cl al

is, as in economics, the attainment of efficiency must be assumed or some structure used to obtain it. In the current case, we use the Charnes et al. [l] projection formulas given by (5) for this purpose. We elect this course so as to ensure conformance with the requirement of movement along an efficiency frontier-as distinguished from securing improvements by merely eliminating technical inefficiencies.

A second issue concerns whether returns-to-scale possibilities are to be examined at individual DMU levels or at various levels of aggregations. The use of production function approaches typically involve the use of industrial aggregates that can produce problems in transforming back to the underlying DMUs. Notice, for instance, that the presence of particular DMUs with decreasing returns-to-scale is not inconsistent with an overall finding of increasing returns-to-scale in an industry function. In DEA, however, the orientation is toward each DMU rather than to aggregates formed from them. However, information from (z/l DMUs is utilized as each DMU, optimization is undertaken [via (l)]. Hence, our identifications are directly applicable to each DMU

in ways that bypass the difficulties and shortcomings of an aggregate analysis (see [22] for a discussion of these difficulties).

There remains yet another difficulty in that the usual treatment of returns-to-scale involves only a single output or a cost function with associated prices or relative weights to be specified a priori.

Extensions to the case of multiple outputs and multiple inputs (of interest here) may cause problems if some outputs exhibit increasing returns-to-scale while others exhibit decreasing returns-to-scale.

Using the concept of most productive scale size (MPSS), as introduced by Banker in [23], we can achieve some success without confronting the latter difficulties. We proceed as follows: suppose that (111 outputs exhibit increasing returns-to-scale. We can augment the inputs to take advantage of this situation without having to assign weights or other measures of relative importance to the d@erent outputs and inputs used, provided that we augment all inputs in the same proportion. That is. we can continue to augment production until constant returns-to-scale are achieved, or, if in a region of decreasing returns-to-scale. we can use this same approach to decrement production (in all outputs) until constant returns-to-scale are achieved (see [24] for the treatment to be used when “alternate optima” are present).

Furthermore. the data for determining the returns-to-scale situation is already available from the 1 values that were previously discussed in association with Tables 6 and 7. For, as Banker has shown in [23], a value of Xi., 2 1 indicates increasing, constant, or decreasing returns.

Referring to the i. (lambda) values in Table 6. we find, for example, that Guangzhou was at constant returns-to-scale (and 100% DEA efficiency) in 1983. In 1984. however, the lambda values sum to a value exceeding unity. Hence, the increment in all of Guangzhou’s outputs from 1983 to 1984 brought it into a region of decreasing returns-to-scale.

Since Guangzhou was also technically inefficient in 1984, it must first be brought onto the efficient frontier by using the Charnes et al. projection given by (5). It may then be brought out of this region by reducing all inputs by some appropriate factor, k > 0. Allowance must be made, of course, for the fact that all such movements need not occur on the same efficiency facet. Hence, different adjustment constants, k, may be required en route to bringing Guangzhou back into a region of constant returns-to-scale. Although we do not pursue this topic here. we do need to note that movement from one facet to another will be associated with changes in the optimal sets of basis vectors. This information is available, as required, by simple recourse to the usual computer codes for sensitivity analysis in linear programming.

To be sure, there may be reasons for having Guangzhou remain in one of the regions of decreasing returns, but this would require supplementary information such as “price“ vs “cost”

for justification. As previously discussed, this was also true for movement along an efficiency frontier to effect input substitutions or input-to-output transformations. In any case, we can thus use information generated from DEA not only to determine the states of increasing and decreasing returns but also to indicate ranges of behavior that are possible before price and cost information is required.

Another question to be addressed is how valid the i, values may be for indicating the regions of returns-to-scale behavior. A full-scale field investigation is obviously beyond the scope of what is possible here, but at least a start can be made by checking for plausibility as well as for other properties such as stability.

DEA evaluation of Chinese cities 341

Table 8. Returns-to-scale of the 28 kev cities

DMU NO.

-. I 2 3 4 5 6 7 x 9

IO II I2 I3 14 I5 16 I7 18 19 20 21 22 23 24 25 26 27 28

1983

Increasing returns I;a,< I

0.887

0.858 0.639

0.262 0.829

0.268 0.610 0.710

0.308

0.915

0.129 0.750

Key cities

Shanghai Beijing Tianjin

Shenyang Wuhan

Guangzhou Harbin Chongqing

Nanjing Xi’an

Chengdu Changchun Taiyuan Dalian Qingdao Lanzhou Jinan Fushun

Anshan Kunming Suzhou Hangzhou

Ningbo Wuxi Changzhou Nantong Yichang Changsha

Constant returns ZL, = I 1.000

I.000

I .ooo

1.000

I.000

1.000 I.000 I.000 1.000

Decreasing returns ZA,>l

2. I38 I.195 I.481 I .640

I.415

1.026 1.047

Constant returns Z)., = I

1.000

1.000

I.000 I.000 1.000 1.000

1 .ooo

1.000

I984

Increasing returns “A, < I

0.881

0.492 0.935

0.266 0.850 0.855

0.603

0.686

0.244

Decreasing returns ZI;> I

3.367 I.453 1.622 I .226 2.204 1.058 I s99 I .020

I.368 I.072

I .023

Note: in the Banker, Charnes, and Cooper (BCC) model [25], the sum of the lambda values used in Banker [23] is represented by a newly defined variable.

Using the qualities of increasing vs decreasing and constant returns, the results portrayed in Table 8 seem remarkably consistent. Our knowledge of city behavior with respect to efficiency and returns-to-scale is limited by the general lack of attention paid to this topic in the regional and urban economic literature. However, it is at least plausible to believe that Shanghai has moved to

MPSS while Beijing has moved to a region of decreasing returns-to-scale if only because Shanghai is an economic center while Beijing is politically oriented.

While many regions are forging ahead with economic reforms, Hubei Province (see Fig. I) has been relatively slow to react in this regard. Due to serious managerial and technical problems, there existed a big gap between this region and other, more advanced regions. Wuhan (DMU 5), the capita1 of Hubei Province, had efficiency ratios of 0.7199 in 1983 and 0.5071 in 1984 (see Table 4). Moreover, Table 8 indicates that for these 2 years, the city of Wuhan remained in the region of decreasing returns-to-scale. Hence, any plans for expansion must consider whether and to what extent this phenomenon needs to be accounted for.

Finally, if we check the returns-to-scale value for the city of Yichang (DMU 27), we find that it has the lowest XI7 value for increasing returns-to-scale (see Table 8). Yichang, an important port on the Yangtze river, is a newly built industrial base. Since DEA indicates that the city has a large returns-to-scale potential, a useful proposal to China’s economic planners might be to switch development from Wuhan to Yichang.

CONCLUSION

The current paper reports the results of research into possible uses of DEA as a tool for

monitoring the performance of 28 cities whose economic activities constitute important compo- nents of China’s economic development planning effort. At its most elementary level, we showed how DEA could be used to identify technical inefficiencies and related waste in the economic activities of each city. As Leibenstein [9] notes, these wastes can be very important and probably offer more prospects for economic improvement than can allocative or other types of inefficiency in developing countries such as China. More can certainly be done; nevertheless, any improvement is welcome in a country like China which is trying to hasten the pace of its economic development.

Employing Banker’s MPSS concept [23], we have illustrated how DEA can be used to exploit

342 ABRAHAM CHARNB et 01.

further possibilities for expansion or contraction, after technical efficiency is attained, as long as such increases and decreases are feasible for all inputs within each city. One possible extension would involve exploiting returns-to-scale possibilities in which resources might be diverted from one city to another in order to obtain more than proportionate increases in overall totals. This would involve extending DEA to include more comprehensive planning models with the use, possibly, of goal programming models as described in [26] and with machinery for effecting tradeoffs as in the eco-demographic planning models described in [27].

The need for extending the time intervals to be considered so that they coincide with the time units used in other parts of the economic development plan (e.g. 5 years) has already been noted. This still concentrates only on economic factors, however. Clearly, other outputs should be considered in evaluating the performance of urban centers. Cities are, after all, places in which people live and enjoy themselves as well as places where they work and produce for others. In this regard, see [28] for the examples of kinds of quality-of-life outputs that can be used and how such outputs can be keyed to country programs affecting several of these outputs simultaneously (see also 1291).

6, 7. 8.

9. 10. il.

12.

13.

14. 15.

16.

17.

18.

19.

20.

21.

22. 23. 24.

25.

26.

27.

28. 29.

30.

REFERENCES A. Charnes, W. W. Cooper and E. Rhodes. Measuring the efficiency of decision making units. Eur. J. Dpn. Res. 2, 429444 (1978). Qili Hu. Capitalism has no patent on the market. Nen Perspect. Quart. 5, 7--11 (1988). Yuan-Li Wu (Ed.). China, A Handbook. Praeger, New York (1973). F. M. Bunge and Rinn-sup Shinn (Eds). China, a Country S’rudy. United States Government, Washington, D.C. (1978). United Nations Economic and Social Commission. Populali~~~ Headfine.s, Vol. 63. United Nations Economic and Social Commission for Asia and the Pacific, Bangkok (1980). Muqiao Xue (Ed.). Almanac qfC%iizn’s Eeonom~ f98S/J986. Modern Cultural Company Limited, Hong Kong (1986). W. Leontief. Studies in the Structure of rhe American Economy. Oxford University Press, New York (1953). A. Charnes, W. W. Cooper, B. Golany, L. Seiford and J. Stutz. Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. J. Economet. 30, 91-107 (1985). 11. Leibenstein. Beyond Economic Man. Harvard University Press, Cambridge. Mass. (1976). China International Economic Consultants Inc. The Chinu lncesrment Guide. Z984jl985. Longman, London (1984). C. Ridley and H. A. Simon. Measuring ‘~un~eipu~ Activities. International City Managers Association, Chicago, Ill. f1943). A. Charnes, W. W. Cooper, D. B. Learner and F. Y. Phillips. Management science and marketing management. J. Mktng 49, 93-10s (1985). H. S. Perloff, E. S. Dunn, E. E. Lampard and R. F. Muth. Regions. Resources and Economic Growth. Johns Hopkins University Press. Baltimore, Md (1960). II. B. Chenery and P. G. Clark. Intermediute Economics. Wiley. New York (1959). A. P. Schinnar. Frameworks for social accounting and monitoring of invariance, efficiency and heterogeneity. Center for Development Planning, Erasmus University, The Hague, The Netherlands (1980). W. D. Macmillan. The estimation and application of multi-regional economic planning models using data envelopment anaiysis. Pap. Reg. Sci. Ass. 60, 41-57 (1986). R. D. Banker and R. Morey. Data envelopment analysis for exogenousiy fixed inputs and outputs. Mgmt Sci. 32, 1613m-1727 (1986). R. D. Banker, A. Charnes, W. W. Cooper, J. Swarts and D. Thomas. An introduction to data envelopment analysis and their uses. In Research in Governmental and Nonprofit Accounting. JAI Press, Greenwich, Conn. In press. A. Charnes. T. Clark, W. W. Cooper and B. Golany. A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the U.S. Air Force. In Ann& ~~~~e~u~~o~.~ Research (Edited by R. Thompson and R. M. Thrall), Vol. 2, pp. 95-112 (1985). .A. Charnes, W. W. Cooper and E. Rhodes. Data envelopment analysis as an approach for evaluating program and managerial efficiency-with an illustrative application to the program follow through experiment in U.S. public school education. Mgmr Sci. 27, 6688697 (1981). A. Charnes and W. W. Cooper. Preface to topics in data envelopment analysis, In Annals of Operation Research (Edited by R. Thompson and R. M. Thrall), Vol. 2. pp. 59-94 (1985). K. Sato. Producrion Funcrions and Aggregation. North-Holland, Amsterdam, The Netherlands (1975). R. D. Banker. Estimating most productive scale size in data enveiopment analysis. Eur. J. Opir. ipes. 17, 3544 (1984). R. D. Banker and R. M. Thrall. Returns to scale in data envelopment analyses. Working paper. Carnegie-Mellon University, School of Urban & Public Affairs, Pittsburgh, Pa (1989). R. D. Banker, A. Charnes and W. W. Cooper. Some models for estimating technical and scale efficiencies in data envelopment analysis. Mgm! Sci. 30, 107881092 (1984). W. F. Bowlin, A. Charnes and W. W. Cooper. Efficiency and effectiveness in DEA: an illustrative application to base maintenance activities in the U.S. Air Force. In Cosr Benejt Analysis (Edited by 0. A. Davis). Carnegie-Mellon University, Pittsburgh, Pa. In press. A. P. Schinnar. A multidimensional accounting model model of demographic and economic planning interactions. E&v. Pfann. 8, 455-475 (1976). N. E. Terleckyj. Improvements in the Quality of Life. National Planning Association, Washington, D.C. (1975). A. Charnes, W. W. Cooper and G. Kozmetsky. Merasuring, monitoring and modelling quality of life. Mgmt Sci. 1% 1172-1188 (1973). F. M. Kaplan, J. M. Sobin and J. S. Service. Encyclopedia of China Today, 3rd edn. Harper & Row, New York (1981).

DEA evaluation of Chinese cities 343

APPENDIX

Local Government in China:t Structure and Dejinitions

OVERALL STRUCTURE

Local government in China consists of all levels of political authority below the central level. The highest levels of local government are directly responsible to the central authorities. These include the governing organs of the country’s 21 provinces, five autonomous regions, and the three centrally administered municipalities of Beijing, Shanghai, and Tianjin. Below these levels, political authority continues to be arranged in a hierarchical fashion, with each level responsible to the next level directly above it.

Local government in China functions according to two basic premises: first, local authorities are responsible for meeting the obligations presented to them by the next higher level of government. Second, local authorities can develop their own programs as long as these do not jeopardize or conflict with the plans of the next higher level. Economic requirements as set by the central authorities include contributions of food, industrial products, and profits from various enterprises.

Once centrally determined responsibilities are met, provincial authorities are urged to develop and implement their own plans for industry, agriculture, communications, medical delivery,

education, and research, and to do so in ways that conform with national standards and goals. This same pattern continues down the organizational hierarchy, with each level working to fulfill its requirements and quotas, developing its own plans, and establishing targets for the level below. The Communist Party, meanwhile, decides upon the overall framework and the social and political direction of local activity.

Local governments also provide important initiatives in fostering cultural and sports activities. They provide facilities for research and the exchange of technical information, and arrange

work-study relationships between schools and units of production. They can carry out construction projects for roads, housing, and public buildings, and are involved in the development of mass transportation. They administer health clinics and child-care facilities, and furnish social services, such as housecleaning and food preparation, as needed at the grass-roots levels. As these activities expand and affect larger areas, they are absorbed by a higher level. Such transfers often lead to tensions or conflicts between levels of administrative authority, since such decisions may result in removing the use of the fruits of local activity from the hands of local authority. The resolution of the tension between local and central authority occupies a major area of focus of the Chinese political system.

LOCAL GOVERNMENT UNITS

Provinces

Including Taiwan, China has 22 provinces. The province is a key level in economic planning, and comprises a large and relatively complex organization. Prior to the Cultural Revolution, Party and government formed two essentially separate and parallel bureaucratic organizations. In the mid-1970s as at other levels of local government, the provincial revolutionary committees fell under the leadership of provincial Party committees. In 1979, however, province-level revolutionary committees were abolished, signalling a return to the more defined divisions of administration in effect prior to 1966. Provincial governments are empowered to create special departments to suit their own particular needs, such as a department of river transport in a province with numerous waterways, or a department of nationalities affairs where there is a significant minority population. many large industrial enterprises and mines are administered at the provincial level.

Autonomous regions

Autonomous regions are large areas-geographically equivalent to provinces-that are inhabited predominantly by minority peoples. They have the same basic responsibilities as the provincial governments in economic affairs, but, in line with national policy toward minorities, are

tTaken from [30].

344 A~~RAHAM CHARNES cl ul

organizationally focused more toward language, culture, and relationships between the local people and the Han Chinese groups that have immigrated into their regions.

Prefectures. The traditional level of administration has lost most of its significance in China, and no longer seems to have any clear-cut function. Prefectures fall between the provincial and the siun or county level. In the main, prefectures function as a convenient administrative division for minority peoples who occupy areas larger than counties but smaller than provinces.

Central!)~ administered cities (or municipulities)

Three of China’s largest and most important cities, Beijing, Shanghai, and Tianjin, are not subject to provincial governments, but are on the same administrative level as the provinces and autonomous regions. These cities are particularly important as economic, political. and cultural centers, and their activities in these spheres inevitably have national implications. Since their populations are so large, they are treated as governmental; their Party committees are responsible

directly to central authorities.

Proz>inciuliJl-governed nnrnicipalities

This level of government includes all of China’s large cities except Beijing, Shanghai, and Tianjin.

Municipalities are particularly important as primary links for economic coordination. The structure and division of labor on administrative bodies in the municipalities also reflect an attempt to link urban industry with suburban agriculture and industry, and to achieve the close coordination of school, factory, and farm that characterizes the educational system. Municipal governments are also active in providing mass transportation. coordinating research and technical innovation, and planning construction and housing activities.

Municipal gol~ernmtwt. All of China’s large cities are subdvided into smaller, more manageable units of government. The largest cities, with populations of over 50,000, may be divided into urban districts; then into street offices; and further into residents’ committees (or lane committees) and even into building committees.

Urban districts. In the largest cities, urban districts resemble small municipal governments in planning and coordinating industrial activity within the district. District authorities may also play a role in pollution control and resource recycling and in providing an administrative framework for exchange of research and technological information. Urban districts can contain well over 100,000 people. They have a local people’s congress, Party congress, and a Party committee.

Street offices. The street olhce is the lowest level of the formal urban governmental structure. It elects a Party committee and apparently, in some instances, a congress. Its size varies between 35.000 and 70.000 people. or 7500~ IS.000 families. Street offices are important in the administration of public security and civil law. and in providing day care and primary and secondary school education in the neighborhood. Street offices often assist in starting and running small urban agricultural activities. Women are notably active at the street-office level of government.

COUIZ ties

The county, or xiun, is similar in size and population to a county in the U.S. It has a county congress responsible for collecting grain allocations from the communes; for schools; and for managing local water control and transport facilities. County governments run food production or consumer needs. County governments run food processing, cement, fertilizer, and tool manufacturing plants, and similar enterprises in coordination with the communes.

Township (= towns). The township, or xiung, does not play an important part in local government except in areas where minority peoples live. Elsewhere, they have largely been replaced by communes.

Mzmicipulities under county gor~ernment ( = rilluges). These are small cities or urban villages that frequently serve as the seat of xiun or cotnmune government and/or as the center of local industrial and commercial activity. They can vary in size from 1000 to 50,000 people. Their own Party committees are subordinate to those of the county.