1、毕业论文(设计)外文翻译（20 届）浙江科技资源空间配置效率测度与影响因素研究的外文翻译所在学院 专业班级 统计学 学生姓名 学号 指导教师 职称 完成日期 年 月 外文翻译之一Productivity Changes in Swedish Pharmacies 1980-1989：A Non-Parametric Malmquist ApproachAuthor(s)：R. FRE; S. GROSSKOPF; B. LINDGREN; P.ROOSNationality：USA；SwedishSource：The Journal of Productivity Analysis, 3, 8
2、5-101 (1992)Abstract In this article we develop a non-parametric (linear programming) approach for calculation of a Malmquist (input based) productivity index. The method is applied to the case of Swedish pharmacies.1. IntroductionThe purpose of this article is to develop an input based non-parametr
3、ic methodology for calculating productivity growth and to apply it to a sample of Swedish pharmacies. Our methodology merges ideas from measurement of efficiency by Farrell 1957 and from measurement of productivity as expressed by Caves, Christensen, and Dicwert 1982. In his classic article, “The Me
4、asurement of Productive Efficiency,” Farrell introduced a framework for efficiency gauging in which overall efficiency can be decomposed into the two component measures: allocative and technical efficiency. Technical efficiency is the reciprocal of the Shephard 1953 and Malmquist 1953 (input) distan
5、ce function, which is the key building block in the Mahnquist input based productivity index, which we use here. Caves, Christensen, and Dicwert 1982 define the input based Malmquist productivity index as the ratio of two, yet to be defined, input distance functions. When they impose overall efficie
6、ncy by Farrell 1957 and a translog structure on the distance functions, they show how the Torqvist index can be derived from the geometric mean of two Malmquist indexes. Here, no such assumptions on behavior or technology will be imposed. Instead, we allow for inefficiencies and model technology as
7、piecewise linear. Thus our Malmquist index of productivity can distinguish between changes in efficiency and changes in the production frontier. This distinction should prove useful for policy purposes.In Sweden, the retail trade of pharmaceutical products has been the responsibility of a public mon
8、opoly since 1971. In their agreement with the Swedish Government, Apoteksbolaget (the National Corporation of Swedish Pharmacies) “is responsible for ensuring that an adequate supply of drugs is maintained in the country. For this purpose, the business shall be conducted to foster opportunities for
9、taking advantage of pharmaceutical advances, while maintaining drug costs at the lowest possible level” (Act on Retail Trade in Drugs of May 27, 1970, No. 205, Sec. 4.). That is, Apoteksbolaget should meet demand while minimizing cost, which suggests that an input based productivity index using inpu
10、t distance functions is an appropriate approach. At present, Apoteksbolaget calculates the productivity of a pharmacy as the ratio between a weighted sum of four outputs and the total number of hours worked for two categories of personnel. The weights assigned to the respective outputs are assumed t
11、o - 1 -reflect differences in resource use, and in the calculation of total output aggregate, all pharmacies are assigned the same weights. Total labor input is obtained as the sum of hours worked by the two types of personnel. For each pharmacy, productivity is calculated every month by the headqua
12、rters of Apoteksbolaget in Stockholm and reported back to the pharmacy within a period of three months. The report to the pharmacy also includes comparisons with its own productivity one year earlier, as well as with the average pharmacy. The present method of calculating productivity is sensitive t
13、o the weights assigned to outputs and inputs, respectively. It also does not account for all inputs. Our sample consists of 42 group (or regional) pharmacies operating in Sweden from 1980 to 1989. These group pharmacies are a small part of the total number of pharmacies in Sweden (there were 816 pha
14、rmacies in 1989). We focus on these 42 groups pharmacies for several reasons. First, we had data on these 42 over the entire time period. Second, the fact that they are all group pharmacies (as opposed to local or hospital pharmacies) means that their responsibilities and sizes are fairly similar. T
15、hird, this sample size was computationally feasible using a PC. Relative to the method presently used by Apoteksbolaget, our method is different with respect to the degree of productivity change, as well as with respect to direction of change in some cases. For the sample as a whole we find producti
16、vity increasing in seven periods and productivity declining in two. The method presently used by Apoteksbolaget also yields progress in seven periods and regress in two. However, the important point to observe is that periods with progress/regress were not always the same using the two approaches. F
17、or example, on average our method showed regress between 1980 and 1981 and progress between 1985 and 1986. According to the Apoteksbolaget, the opposite occurred for these years. So, for a pharmacy or for the average of a group of pharmacies, the methodology suggested in this article may give quite
18、different result of productivity changes with respect to level and/or direction of changes. The method of calculating productivity and productivity changes presently used by Apoteksbolaget has many drawbacks, e.g.: (1) It assumes that the underlying pharmacy technology is of a very special form (whi
19、ch may not be an appropriate assumption for the pharmacy production technology); (2) It cannot distinguish between changes in efficiency and change in the frontier technology; (3) It cannot easily include more input variables other than labor and requires outputs to be measured in the same units; (4
20、) It requires a priori chosen weights for the aggregation of inputs and outputs, respectively. All of these drawbacks can be relaxed using our non-parametric methodology for calculating productivity and productivity changes.2. The productivity indexThe production technology is defined at each period
21、 , ，to be the set of all t1.,Tfeasible input and output vectors. If denotes an input vector at period and tNxRtan output vector in the same period, then the technology is the set , where tNyR S. We also model the technology by the input ,:canproduettt tSxycorrespondence or equivalently by the input
22、requirement set(1):,1.,ttttLxyST- 2 -The input requirement set , denotes all input vectors capable of producing tLytxoutputs during period . Here we assume that is a closed convex set for all , ty tLytyand that there is no free lunch, i.e., . Moreover, we impose 0if0,tttdisposability of inputs and o
23、utputs, i.e., and tttttxLyx, respectively.tttttyLyLyIn this article, we formalize equation (1) as a piecewise linear input requirement set or equivalently as an activity analysis model. The coefficients in this model consist of observed inputs and outputs. We assume that there are observations of 1,
24、.tkKinputs in each period . These inputs are employed to produce 1,.nN,ktnx1,tTof observed outputs, , at period , and we assume tkK1.mMktmy.tTthat the number of observations are the same for all , i.e., .The input requirement set (1) is formed from the observations as (see Fre, Grosskopf, and Lovell
25、 1985) ,1: 1,.KttktmmLyxzyM(2), n,.tktnN,0 ,.ktzwhere is an intensity variable familiar from activity analysis. The intensity variables ,ktzserve to form technology, which here is the convex cone of observed inputs and outputs. Constant returns to scale is imposed on the reference technology, but ot
26、her forms of returns to scale may be imposed by restricting the sum of the intensity variables (see Grosskopf 1986). One may also show that satisfies the properties introduced tLyabove (see Shephard 1970 or Fre 1988).The Malmquist input based productivity index is expressed in terms of four input di
27、stance functions. The first is defined as(3),sup0:/.tt ttiDyxxyClearly,1 ifandol f,tt ttiDyxLas the following figure 1 illustrates.In figure 1, the input vector belongs to the input requirement set . The distance tx tLyfunction measures the largest possible contraction of under the condition ,ttiyx
28、txthat is feasible, i.e., . In terms of figure 1, . /t/ttLy,0/ttiDabFor observation , , the value of the distance function is k1.K ,tkttiyxobtained as the solution to the linear programming problem- 3 -(4)1,min,tkttiDyx,1,subjec o1,. n,.0 ,.KtktktktntzyMxxNzNote that is an element of the input set w
29、hich implies that the distance function ktakes values larger than or equal to one. The value one is achieved whenever the input vector belongs to the isoquant of the input set, and hence where it is technically efficient la Farrell 1957.Figure 1. The input distance function.We note the input distanc
30、e function is the reciprocal of the Farrell technical efficiency measure, a fact which we have exploited to calculate the distance function.In order to define the input based Malmquist productivity index by Caves, Christensen, and Diewert 1982, we need to relate the input output vectors at period to
31、 the ,txyttechnology in the succeeding period. Therefore, we evaluate the input distance 1tLfunction for an input output vector at period relative to the input requirement ,txytset in the following period.1t(5)11,sup0:/.ttt t tiDxLyAgain, . However, need not be 11, fandoly ifttt ttixyy ,txfeasible a
32、t , thus if equation (5) has a solution (i.e., supremum is a maximum), the value of may be strictly less than one.ttiIn our data set, the observed input , is positive for each observation and ,1.ktnxNeach period. This together with strong disposability of inputs and constant returns to scale - 4 -en
33、sure that we can calculate the value of the input distance function (5) for , k, as the solution to the linear programming problem1.kK(6)1,min,tkttiDyx,11,1subjec o,. n,.0 ,.KtkttktkttntzyMxxNzWe note that since need not be a member of the input requirement set , ktn 1tktLythe value of this distance
34、 function may be strictly less than one.Two additional evaluations of the input distance function are required in order to define the productivity index. We need to evaluate observations at relative to the ttechnologies at and . In particular,t1(7)1 11,sup0:/t ttiDyxxLyand(8)1111,:/ttt tttiThe compu
35、tation of equation (8) is identical to that of equation (3) so that in equation (4) we need only substitute for . The computation of equation (7) is parallel to that ttof equation (5), and again we need only substitute for and vice versa. We note of ttcourse that since need not be feasible under the
36、 technology , the input 1,ttxy tLdistance function may be strictly less than one.ttiDFollowing Caves, Christensen, and Diewert 1982, we define the input based Malmquist productivity index as(9)121111,(,) .ttttti itttti yxDyxMyxActually, our definition is the geometric mean of two Malmquist indexes a
37、s defined by Caves, Christensen, and Diewert 1982.In their work, Caves, Christensen and Diewert 1982 make two assumptions. First, they assume that and equal unity for each observation and ,ttiDyx11,tttiyxperiod. In the terminology of Farrell 1957, this means that there is no technical inefficiency.
38、Second, they assume that the distance functions are of translog form with identical second order terms. Here we follow Fre et al. 1989, and model the technology as piecewise linear and allow for inefficiencies. By allowing for inefficiencies, the productivity index can be decomposed into two compone
39、nts, one measuring change in efficiency and the other measuring technical change or equivalently change in the frontier technology. Equation (9) can be rewritten as- 5 -(10)1211111 1,(,) ,ttttttti i itttti DyxyxDyxMyx where the quotient outside the bracket measures the change in technical inefficien
40、cy and the ratios inside the bracket measure the shift in the frontier between periods and t1as figure 2 illustrates.We denote the technology at by and at by , and note that ttS1t1tSand that is similarly defined. The two observations ,:,0tttttSxyLy1and are both feasible in their respective periods.
41、We may express the t 1,ttproductivity index in terms of the above distances along the x-axis as(11)1211, ,0tttti bafMyxdecwhere denotes the ratio of the Farrell measure of technical efficiency 0baand the last part is the geometric mean of the shifts in technology at and . Note ty1tthat the shifts in
42、 technology are measured locally for the observation at and . This implies that: 1) the whole technology need not behave uniformly, and 2) that technological regress is possible. In the literature on parametric modeling of productivity growth one can find decompositions comparable to the above (see
43、e.g., Bauer 1990 or Nishimizu and Page 1982).Figure 2. The input based Malmquist productivity index.3. Results and commentsThe data in this study consist of annual observations of outputs and inputs from 42 Swedish group pharmacies. The time period is 1980 to 1989. We specify four output variables a
44、nd four input variables. Our four outputs: Drug deliveries to hospitals (SJHFANT); prescription drugs for outpatient care (RECFANT); medical appliances for - 6 -the handicapped (FOLIANT); and over the counter goods (OTC). The first three outputs are measured in number of times. The volume of OTC is
45、measured in 1980 prices. All pharmacies change the same output price for a given product.Four separate inputs are used: Labour input for pharmacists (ARBTFT); labour input for technical staff (ARBTTT); building services (LOKY); and equipment services (AVSK). Labour input is measured in number of hou
46、rs worked. Absence from work due to sickness, holiday, education, etc., is excluded. The flow of building services is assumed to be proportional to the floor space available, measured in square meters. The services flow from equipment is assumed to be proportional to the stock of equipment. By assum
47、ption, we have restricted changes in the stock of equipment to be either positive or unchanged, except when a pharmacy is completely rebuilt. As a proxy for the services flow from the stocks of equipment, we use annual depreciation of pharmacy equipment measured in 1980 prices. However, since we onl
48、y allow for nonnegative changes in stocks of equipment, our series of annual depreciation measured in constant prices only shows increasing or unchanged values. Our main justification for making this assumption is that actual S. GROSSKOPF; B. LINDGREN; P.ROOS国籍：美国;瑞典出处：生产力分析，1992 年第 3 期，85-101 页摘要在这篇文章中我们开发了一种基于 Malmquist 生产指数的非参数( 线性规划)的计算方法。探究该方法用于瑞典制药业的情况。1.简介本文的目的是为了开发一种非参数方法计算生产率增长的输入模型，并将其应用到瑞典制药业这个样本中。我们的方法是由法瑞尔(1957)提出的
