測(cè)度1980-1989間瑞典制藥業(yè)生產(chǎn)率變化基于非參數(shù)的malmquist指數(shù)法-外文翻譯

1、<p>　　畢業(yè)論文(設(shè)計(jì))外文翻譯</p><p><b>　?。?0 屆）</b></p><p>　　浙江科技資源空間配置效率測(cè)度與影響因素研究的外文翻譯</p><p>　　所在學(xué)院 </p><p>　　專(zhuān)業(yè)班級(jí) 統(tǒng)計(jì)學(xué)

2、 </p><p>　　學(xué)生姓名 學(xué)號(hào) </p><p>　　指導(dǎo)教師 職稱(chēng) </p><p>　　完成日期 年 月 </p><p><b>　　外文翻譯之一</b>&

3、lt;/p><p>　　Productivity Changes in Swedish Pharmacies 1980-1989：A Non-Parametric Malmquist Approach</p><p>　　Author(s)：R. FÄRE; S. GROSSKOPF; B. LINDGREN; P.ROOS</p><p>　　Nation

4、ality：USA；Swedish</p><p>　　Source：The Journal of Productivity Analysis, 3, 85-101 (1992)</p><p><b>　　Abstract </b></p><p>　　In this article we develop a non-parametric (

5、linear programming) approach for calculation of a Malmquist (input based) productivity index. The method is applied to the case of Swedish pharmacies.</p><p>　　1. Introduction</p><p>　　The purpo

6、se of this article is to develop an input based non-parametric methodology for calculating productivity growth and to apply it to a sample of Swedish pharmacies. Our methodology merges ideas from measurement of efficienc

7、y by Farrell [1957] and from measurement of productivity as expressed by Caves, Christensen, and Dicwert [1982]. In his classic article, “The Measurement of Productive Efficiency,” Farrell introduced a framework for effi

8、ciency gauging in which overall efficiency can be d</p><p>　　In Sweden, the retail trade of pharmaceutical products has been the responsibility of a public monopoly since 1971. In their agreement with the Sw

9、edish 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 conduc

10、ted to foster opportunities for taking advantage of pharmaceutical advances, while maintaining drug costs at the lowest possible level</p><p>　　At present, Apoteksbolaget calculates the productivity of a pha

11、rmacy 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 to reflect differences in resourc

12、e 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, product<

13、;/p><p>　　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 phar

14、macies 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 hospita

15、l pharmacies) means that their responsibilities and sizes are fairly similar. Th</p><p>　　Relative to the method presently used by Apoteksbolaget, our method is different with respect to the degree of produc

16、tivity change, as well as with respect to direction of change in some cases. For the sample as a whole we find productivity increasing in seven periods and productivity declining in two. The method presently used by Apot

17、eksbolaget 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 </p><p>　　The method of calculating producti

18、vity 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 (which may not be an appropriate assumption for th

19、e 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 t

20、o be measured in the same </p><p>　　2. The productivity index</p><p>　　The production technology is defined at each period ,，to be the set of all feasible input and output vectors. If denotes an

21、 input vector at period and an output vector in the same period, then the technology is the set , where . We also model the technology by the input correspondence or equivalently by the input requirement set</p>

22、<p><b>　　(1)</b></p><p>　　The input requirement set , denotes all input vectors capable of producing outputs during period . Here we assume that is a closed convex set for all , and that

23、 there is no free lunch, i.e., . Moreover, we impose disposability of inputs and outputs, i.e., and , respectively.</p><p>　　In this article, we formalize equation (1) as a piecewise linear input requirement

24、 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 inputs in each period . These inputs are employed to

25、produce of observed outputs, , at period , and we assume that the number of observations are the same for all , i.e., .</p><p>　　The input requirement set (1) is formed from the observations as (see F

26、8;re, Grosskopf, and Lovell [1985])</p><p><b>　　(2)</b></p><p>　　where is an intensity variable familiar from activity analysis. The intensity variables serve to form technology, wh

27、ich here is the convex cone of observed inputs and outputs. Constant returns to scale is imposed on the reference technology, but other forms of returns to scale may be imposed by restricting the sum of the intensity var

28、iables (see Grosskopf [1986]). One may also show that satisfies the properties introduced above (see Shephard [1970] or Färe [1988]).</p><p>　　The Malmquist input based productivity index is expressed

29、in terms of four input distance functions. The first is defined as</p><p><b>　　(3)</b></p><p><b>　　Clearly,</b></p><p>　　as the following figure 1 illustrate

30、s.</p><p>　　In figure 1, the input vector belongs to the input requirement set . The distance function measures the largest possible contraction of under the condition that is feasible, i.e., . In terms

31、of figure 1, . For observation , , the value of the distance function is obtained as the solution to the linear programming problem</p><p><b>　　(4)</b></p><p>　　Note that is an ele

32、ment of the input set which implies that the distance function takes 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

33、 technically efficient à la Farrell [1957].</p><p>　　Figure 1. The input distance function.</p><p>　　We note the input distance function is the reciprocal of the Farrell technical efficien

34、cy measure, a fact which we have exploited to calculate the distance function.</p><p>　　In order to define the input based Malmquist productivity index by Caves, Christensen, and Diewert [1982], we need to r

35、elate the input output vectors at period to the technology in the succeeding period. Therefore, we evaluate the input distance function for an input output vector at period relative to the input requirement set in

36、the following period.</p><p><b>　　(5)</b></p><p>　　Again, . However, need not be feasible at , thus if equation (5) has a solution (i.e., supremum is a maximum), the value of may b

37、e strictly less than one.</p><p>　　In our data set, the observed input , is positive for each observation and each period. This together with strong disposability of inputs and constant returns to scale ensu

38、re that we can calculate the value of the input distance function (5) for , , as the solution to the linear programming problem</p><p><b>　　(6)</b></p><p>　　We note that since need

39、not be a member of the input requirement set , the value of this distance function may be strictly less than one.</p><p>　　Two additional evaluations of the input distance function are required in order to d

40、efine the productivity index. We need to evaluate observations at relative to the technologies at and . In particular,</p><p><b>　　(7)</b></p><p><b>　　and</b></p>

41、<p><b>　　(8)</b></p><p>　　The computation 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 par

42、allel to that of equation (5), and again we need only substitute for and vice versa. We note of course that since need not be feasible under the technology , the input distance function may be strictly less than one.

43、</p><p>　　Following Caves, Christensen, and Diewert [1982], we define the input based Malmquist productivity index as</p><p><b>　　(9)</b></p><p>　　Actually, our definiti

44、on is the geometric mean of two Malmquist indexes as defined by Caves, Christensen, and Diewert [1982].</p><p>　　In their work, Caves, Christensen and Diewert [1982] make two assumptions. First, they assume

45、that and equal unity for each observation and period. In the terminology of Farrell [1957], this means that there is no technical inefficiency. Second, they assume that the distance functions are of translog form with i

46、dentical second order terms. Here we follow Färe et al. [1989], and model the technology as piecewise linear and allow for inefficiencies. By allowing for inefficiencies, the productivit</p><p><b>

47、;　　(10)</b></p><p>　　where the quotient outside the bracket measures the change in technical inefficiency and the ratios inside the bracket measure the shift in the frontier between periods and as fi

48、gure 2 illustrates.</p><p>　　We denote the technology at by and at by , and note that and that is similarly defined. The two observations and are both feasible in their respective periods. We may expres

49、s the productivity index in terms of the above distances along the x-axis as</p><p><b>　　(11)</b></p><p>　　where denotes the ratio of the Farrell measure of technical efficiency and

50、 the last part is the geometric mean of the shifts in technology at and . Note that the shifts in technology are measured locally for the observation at and . This implies that: 1) the whole technology need not behave

51、uniformly, and 2) that technological regress is possible. </p><p>　　In the literature on parametric modeling of productivity growth one can find decompositions comparable to the above (see e.g., Bauer [1990]

52、 or Nishimizu and Page [1982]).</p><p>　　Figure 2. The input based Malmquist productivity index.</p><p>　　3. Results and comments</p><p>　　The data in this study consist of annual o

53、bservations of outputs and inputs from 42 Swedish group pharmacies. The time period is 1980 to 1989. We specify four output variables and four input variables. Our four outputs: Drug deliveries to hospitals (SJHFANT); pr

54、escription drugs for outpatient care (RECFANT); medical appliances for the handicapped (FOLIANT); and over the counter goods (OTC). The first three outputs are measured in number of times. The volume of OTC is measured i

55、n 1980 prices. All</p><p>　　Four separate inputs are used: Labour input for pharmacists (ARBTFT); labour input for technical staff (ARBTTT); building services (LOKY); and equipment services (AVSK). Labour in

56、put is measured in number of hours 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 s

57、quare meters. The services flow from equipment is assumed to be proportional to the stock of equipmen</p><p>　　The number of hours worked by technical staff has decreased by 32 percent on average between 198

58、0 and 1989. On the other hand, the number of hours worked by pharmacists is almost the same in 1989 as in 1980. However, on a year to year base, we observed small changes in the average number of hours worked by pharmaci

59、sts on average. One reason for the decrease in hours worked by technical staff is that the pharmacies ceased to recruit new technical staff in the middle of the 1980’s. Another reason </p><p>　　Our estimatio

60、n of services from equipment shows an increase for the average pharmacy during the observed time period by 16 percent. We note that almost all pharmacies have changed from old to new equipment during the 1980’s and that

61、some pharmacies have been completely rebuilt. Looking at floor space we observe a decrease on average. One reason for the decrease in floor space is that the pharmacies have eliminated unnecessary space. Another reason i

62、s that new pharmacies are smaller than the old </p><p>　　On average, our statistics show a decrease over time in deliveries of drugs to hospitals. A dramatic decrease of 57 percent occurred between 1983 and

63、1984, due mainly to reorganization.</p><p>　　Prescription of drugs for outpatient care has been fairly constant over time on average. However, we observe a peak in 1983, which is due in part to an increase i

64、n the out of pocket price of prescription drugs that took place in December 1983. This increase led to an increase in sales of prescription drugs, i.e., prescription drugs that the patient should have purchased later but

65、 because of the increase in out of pocket price purchased earlier.</p><p>　　In the end of the 1970’s, medical appliances for the handicapped were introduced as new products for the pharmacy. On average an in

66、crease in sales of medical appliances took place during the 1980’s. Here, we note that the number of products for the handicapped has increased over time, which may be one reason for the observed growth in medical applia

67、nces for the average pharmacy.</p><p>　　On average sales of over the counter goods have increased by 57 percent between 1980 and 1989 measured in fixed prices. An increase in over the counter goods is in acc

68、ordance with the development policy pursued by these pharmacies during the 1980’s. The business of the pharmacies has gradually come to focus more and more on self medications. One may, however, find great variations amo

69、ng the pharmacies in the extent to which this policy has been pursued.</p><p>　　The mix of inputs and outputs has changed quite considerably during our observation period. We also note that in all years we f

70、ind differences in input mix and output mix across pharmacies.</p><p>　　Computer costs and expenditures for energy, cleaning, stationery, etc. are not included among our input variables, because the data is

71、not readily available. In addition, drugs and pharmaceuticals delivered to pharmacies have been excluded as inputs since the data is not readily available.</p><p>　　測(cè)度1980-1989間瑞典制藥業(yè)生產(chǎn)率變化：基于非參數(shù)的Malmquist指數(shù)法&

72、lt;/p><p>　　作者：R. FÄRE; S. GROSSKOPF; B. LINDGREN; P.ROOS</p><p><b>　　國(guó)籍：美國(guó);瑞典</b></p><p>　　出處：生產(chǎn)力分析，1992年第3期，85-101頁(yè)</p><p><b>　　摘要</b></p

73、><p>　　在這篇文章中我們開(kāi)發(fā)了一種基于Malmquist生產(chǎn)指數(shù)的非參數(shù)(線性規(guī)劃)的計(jì)算方法。探究該方法用于瑞典制藥業(yè)的情況。</p><p><b>　　1.簡(jiǎn)介</b></p><p>　　本文的目的是為了開(kāi)發(fā)一種非參數(shù)方法計(jì)算生產(chǎn)率增長(zhǎng)的輸入模型，并將其應(yīng)用到瑞典制藥業(yè)這個(gè)樣本中。我們的方法是由法瑞爾(1957)提出的效率測(cè)度和凱夫斯

74、，克里斯坦森和迪唯爾特(1982)提出的生產(chǎn)率的測(cè)量合并而成。在他的經(jīng)典文章，“生產(chǎn)效率的測(cè)量”中，法瑞爾介紹了整體效率可以分解為兩部分組合效率的計(jì)量框架：資源配置效率和技術(shù)效率。技術(shù)效率是謝潑德(1953)和馬姆奎斯特(1953)的(輸入)距離函數(shù)的倒數(shù)，它是基于生產(chǎn)率指數(shù)的Malmquist輸入模型的關(guān)鍵構(gòu)建模塊，我們?cè)诖颂幨褂?。凱夫斯，克里斯坦森和迪唯爾特(1982)定義的基于Malmquist生產(chǎn)率指數(shù)的投入比例，將其定義為輸入

75、距離函數(shù)。當(dāng)他們把法瑞爾(1957)的整體效率和距離函數(shù)對(duì)數(shù)結(jié)構(gòu)結(jié)合，他們展示了Törqvist指數(shù)可以來(lái)自?xún)蓚€(gè)Malmquist指數(shù)的幾何平均數(shù)。在這里，沒(méi)有強(qiáng)加在行為或技術(shù)上的假設(shè)。相反，我們?cè)试S效率低下和分段線性模型技術(shù)。因此，我們的Malmquist生產(chǎn)力指數(shù)的區(qū)別在于生產(chǎn)前沿面效率的變化。這種區(qū)別證明對(duì)當(dāng)前政策目的有效。</p><p>　　在瑞典，藥品零售業(yè)從1971以來(lái)便被公共壟斷。他們?cè)?/p>

76、與瑞典政府達(dá)成的協(xié)議，Apoteksbolaget(瑞典全國(guó)性藥店)“是負(fù)責(zé)確保國(guó)內(nèi)藥品供應(yīng)充足。為此，企業(yè)應(yīng)當(dāng)利用此次契機(jī)發(fā)展自己，同時(shí)保持藥物的成本盡可能達(dá)到最低的水平”( 在1970年5月27日205號(hào)藥物零售貿(mào)易法案的第4條)。那就是，即要滿足需求又要使Apoteksbolaget成本最小化，這表明以輸入為基礎(chǔ)的生產(chǎn)力指數(shù)使用輸入距離函數(shù)是一個(gè)合適的方法。</p><p>　　目前，Apoteksbola

77、get計(jì)算一個(gè)藥房的生產(chǎn)率為四個(gè)輸出變量的和兩類(lèi)人員工作的總小時(shí)數(shù)的加權(quán)總和之間的比率。它分配的相應(yīng)的輸出量被認(rèn)為是反映了資源利用差異，并且在總產(chǎn)出的計(jì)算中所有的藥店都被分配相同的權(quán)重。通過(guò)總勞動(dòng)投入的工作時(shí)間之和得到兩種類(lèi)型的人員。對(duì)于每個(gè)藥店，生產(chǎn)力是由Apoteksbolaget在斯德哥爾摩的總部按月計(jì)算并且在三個(gè)月內(nèi)反饋給藥店。藥店的報(bào)告包括與其自己一年前的生產(chǎn)力比較，以及與其他藥店的比較。目前，計(jì)算效率的方法對(duì)于分配給輸入、輸

78、出值的權(quán)值比較敏感，且它不會(huì)對(duì)所有輸入值賦權(quán)數(shù)。</p><p>　　我們的樣本包括42組(或區(qū)域)從1980到1989在瑞典經(jīng)營(yíng)的藥店。這些組中的藥房是在瑞典的藥店總數(shù)量的一小部分(在1989年瑞典有816個(gè)藥店)。我們選取這42組藥店有如下幾個(gè)原因。首先，我們有這42組藥店在整個(gè)時(shí)期的數(shù)據(jù)。第二，事實(shí)上他們都是屬于同一組群(相對(duì)于當(dāng)?shù)厮幍昊蜥t(yī)院藥房)意味著他們的所負(fù)的責(zé)任和規(guī)模都非常相似。第三，這個(gè)樣本的適用

79、性是用由電腦計(jì)算而得的。</p><p>　　相對(duì)于目前Apoteksbolaget使用的方法，我們的方法測(cè)度生產(chǎn)率變化程度，以及在某些情況下改變測(cè)度方式有所不同。將樣本作為一個(gè)整體，我們發(fā)現(xiàn)生產(chǎn)率增長(zhǎng)七期的同時(shí)生產(chǎn)力下降兩期。目前所采用的Apoteksbolaget使用方法也會(huì)使生產(chǎn)率前進(jìn)七期同時(shí)倒退兩期。然而，最重要的一點(diǎn)是，時(shí)期的前進(jìn)或倒退并不總是使用相同的方法到達(dá)的。例如，我們的方法表現(xiàn)出在1980和19

80、81之間平均是倒退的而在1985和1986之間平均是進(jìn)步的。根據(jù)Apoteksbolaget的報(bào)告，這些年發(fā)生相反的情況。所以，一個(gè)藥店或一組藥店的平均值，在本文中提出的方法無(wú)論相對(duì)于水平或方向的變化，可能會(huì)對(duì)生產(chǎn)率變化得出截然不同的結(jié)果。</p><p>　　生產(chǎn)力和生產(chǎn)率的變化的計(jì)算方法目前大多采用Apoteksbolaget公司的方法，但有很多缺點(diǎn)，例如：(1)它假定潛在的制藥技術(shù)是一種特殊形式(并不是制藥

81、生產(chǎn)技術(shù)的一個(gè)適當(dāng)?shù)募僭O(shè))；(2)不能區(qū)分在效率和技術(shù)前沿面之間的變化；(3)它不能很容易地在同一單位中測(cè)量包括除勞動(dòng)以外的多個(gè)輸入變量和需要輸出的變量；(4)它需要一個(gè)先驗(yàn)的輸入和輸出變量集合的權(quán)重。所有這些缺點(diǎn)在使用我們的非參數(shù)方法的計(jì)算效率和生產(chǎn)率的變化中迎刃而解。</p><p><b>　　2.生產(chǎn)率指數(shù)</b></p><p>　　生產(chǎn)技術(shù)被定義在每個(gè)周期

82、，，是所有可行的輸入和輸出向量的集合。如果表示在周期的輸入向量，表示在相同周期的輸出向量，那么技術(shù)是集，其中。我們的技術(shù)模型通過(guò)輸入向量對(duì)應(yīng)或等效的輸入需求集</p><p><b>　　(1)</b></p><p>　　輸入要求的集合表示在時(shí)期內(nèi)所有的輸入向量都可產(chǎn)生輸出向量。這里我們假設(shè)是的閉凸集，但是是有條件的，例如。并且，我們可以對(duì)輸入向量和輸出向量分別進(jìn)行

83、處理，例如和。</p><p>　　本文中，我們把方程(1)作為分段線性輸入需求集或等效地作為有效分析模型。在這個(gè)模型中的系數(shù)是由輸入向量和輸出向量的觀測(cè)值組成。我們假設(shè)在每一個(gè)時(shí)期，輸入向量，的觀測(cè)值有個(gè)。這些輸入向量是用于生成在時(shí)期，輸出向量，的觀測(cè)值，同時(shí)我們假設(shè)對(duì)于所有時(shí)期的觀測(cè)值都相同，例如。</p><p>　　要求輸入集(1)可從觀測(cè)值中形成</p><p

84、><b>　　(2)</b></p><p>　　其中是一個(gè)強(qiáng)度變量與有效分析中相似。強(qiáng)度變量是技術(shù)的形式，它是觀察到的輸入和輸出向量的凸錐。規(guī)模收益不變是基于基準(zhǔn)技術(shù)，但其他形式的規(guī)模收益可以基于限制強(qiáng)度變量之和。也可以表明滿足以上介紹的屬性。</p><p>　　基于生產(chǎn)率指數(shù)的Malmquist輸入向量是由四個(gè)輸入向量的距離函數(shù)表示的。他定義為</p

85、><p><b>　　(3)</b></p><p>　　顯然，如下面的圖1所示。</p><p>　　在圖1中，輸入向量屬于輸入需求集。在可行的情況下，距離函數(shù)測(cè)量了的最大可能的收縮，例如。就圖1而言，。對(duì)于觀察的，，距離函數(shù)的值為線性規(guī)劃模型的解</p><p><b>　　(4)</b></

86、p><p>　　注意是一個(gè)元素的輸入集，這意味著距離函數(shù)的值大于或等于1。當(dāng)輸入向量屬于輸入集合的等產(chǎn)量曲線時(shí)便實(shí)現(xiàn)了價(jià)值，因此它是技術(shù)上的有效α。</p><p>　　圖1. 輸入向量距離函數(shù)</p><p>　　我們注意到輸入距離函數(shù)是法瑞爾技術(shù)效率測(cè)度的倒數(shù)，所以我們利用距離函數(shù)計(jì)算技術(shù)效率。</p><p>　　為了確定輸入向量基于凱夫斯

87、，克里斯坦森和迪唯爾特(1982)提出的Malmquist生產(chǎn)率指數(shù)，我們需要在期的輸入輸出向量與后續(xù)時(shí)期的技術(shù)相關(guān)。因此，我們?cè)u(píng)價(jià)對(duì)于在期的輸入輸出向量的輸入距離函數(shù)與之后時(shí)期的輸入需求集相對(duì)應(yīng)。</p><p><b>　　(5)</b></p><p>　　此處，。然而，向量不需要在期適用，因此如果方程(5)有一個(gè)解(例如，上確界最大)，的值會(huì)嚴(yán)格小于1。<

88、;/p><p>　　在我們的數(shù)據(jù)集中，輸入向量在每個(gè)時(shí)期的每個(gè)觀測(cè)值都是正值。這把處理后的投入向量與規(guī)模收益不變相結(jié)合以確保我們能計(jì)算, 的輸入距離函數(shù)(5)的值，作為線性規(guī)劃模型的解。</p><p><b>　　(6)</b></p><p>　　我們發(fā)現(xiàn)自從不必為輸入需求集中的一員，距離方程的值會(huì)嚴(yán)格小于1。</p><p

89、>　　輸入距離函數(shù)需要兩個(gè)額外的評(píng)估為了確定生產(chǎn)率指數(shù)。我們需要評(píng)估t+1期的觀測(cè)值與t期和t+1期的技術(shù)相對(duì)應(yīng)。特別是，</p><p><b>　　(7)</b></p><p><b>　　和</b></p><p><b>　　(8)</b></p><p>　　

90、方程(8)的計(jì)算與方程(3)相同，所以在方程(4)中我們只需要用代替。方程(7)的計(jì)算與方程(5)相似，所以我們也只需用代替，反之亦然。我們當(dāng)然要注意，因?yàn)椴恍枰谙驴尚?，輸入距離函數(shù)會(huì)嚴(yán)格小于1。</p><p>　　接著凱夫斯，克里斯坦森和迪唯爾特(1982)的研究，我們定義基于Malmquist的生產(chǎn)率指數(shù)為</p><p><b>　　(9)</b></

91、p><p>　　實(shí)際上，我們的定義是凱夫斯，克里斯坦森和迪唯爾特(1982)定義的兩個(gè)Malmquist指數(shù)的幾何平均。</p><p>　　在他們的文章中，凱夫斯，克里斯坦森和迪唯爾特(1982)做了兩個(gè)假設(shè)。第一，他們假設(shè)和在每個(gè)時(shí)期的觀測(cè)值相等。在法瑞爾(1957)的術(shù)語(yǔ)中，這意味著沒(méi)有技術(shù)效率。第二，他們假設(shè)距離函數(shù)是相同二階對(duì)數(shù)的形式。這里我們遵循法爾特奧(1989)，且建模的技術(shù)為

92、分段線性并且允許低效率。因?yàn)樵试S低效率，生產(chǎn)力指標(biāo)可以分解為兩個(gè)部分，一是測(cè)量效率的變化和其他是測(cè)量技術(shù)的變化或在前沿面上技術(shù)的等價(jià)變化。方程(9)可以改寫(xiě)為</p><p><b>　　(10)</b></p><p>　　此處外部商值在技術(shù)效率低下改變時(shí)的等級(jí)測(cè)量和在期和期之間前沿面轉(zhuǎn)換時(shí)內(nèi)部等級(jí)比率的測(cè)量如圖2所示。</p><p>　　

93、我們用表示期的技術(shù)，用表示期的技術(shù)，并且標(biāo)注且有相同的定義。兩個(gè)觀察向量和在其各自的時(shí)期都是有效的。我們可以表示生產(chǎn)率指數(shù)在沿x軸的距離條件為</p><p><b>　　(11)</b></p><p>　　其中表示法瑞爾的技術(shù)效率測(cè)量比，最后一部分是和在技術(shù)變化的幾何平均。值得注意的是，技術(shù)的變化是在和的觀察值是局部測(cè)量得到的。這意味著：1)整體技術(shù)不需要表現(xiàn)一致

94、，和2)，技術(shù)退步是可能的。</p><p>　　文獻(xiàn)中生產(chǎn)率增長(zhǎng)的參數(shù)模型可以找到一個(gè)分解與上述相媲美。</p><p>　　圖2.基于Malmquist生產(chǎn)率指數(shù)的輸入模型</p><p><b>　　3.結(jié)果和意見(jiàn)</b></p><p>　　這項(xiàng)研究中輸入輸出向量的數(shù)據(jù)是由42組瑞典藥店每年的觀測(cè)數(shù)據(jù)組成，時(shí)間跨

95、度為1980年到1989年。我們指定了四個(gè)輸入變量和四個(gè)輸出變量。四個(gè)輸出變量為：醫(yī)院交付的藥物(SJHFANT)；門(mén)診治療的處方藥(RECFANT)；殘疾人的醫(yī)療器械(FOLIANT)；和貨架上的藥物(OTC)。前三個(gè)輸出變量是以次數(shù)測(cè)度。OTC的容量是以1980的價(jià)格計(jì)算的。所有藥店對(duì)于一個(gè)給定產(chǎn)品輸出價(jià)格的變化都相同。</p><p>　　四個(gè)輸入向量分別是：藥劑師的勞動(dòng)投入(ARBTFT)；技術(shù)人員的勞動(dòng)

96、投入(ARBTTT)；房屋設(shè)備(LOKY)；和器械設(shè)備(AVSK)。勞動(dòng)投入是以小時(shí)工作測(cè)度。由于生病，假期，和教育等因素導(dǎo)致的未能工作除外。房屋設(shè)備的流量被假設(shè)在地上的可用空間的比例用平方米來(lái)測(cè)度。器械設(shè)備的流量被假設(shè)為對(duì)設(shè)備的庫(kù)存比例。由假設(shè)，我們限制改變?cè)O(shè)備的庫(kù)存是正的或不變，除非一個(gè)藥店是完全重建。作為器械設(shè)備流量庫(kù)存的代表，我們使用1980價(jià)格測(cè)量制藥設(shè)備的年折舊。然而，因?yàn)槲覀冎辉试S在庫(kù)存設(shè)備非負(fù)的變化，所以我們系列中每年的

97、折舊以不變價(jià)格計(jì)算測(cè)量，只顯示了增加或不變值。提出這個(gè)假設(shè)的主要理由是實(shí)際中多年使用的設(shè)備比會(huì)計(jì)記期的時(shí)間長(zhǎng)很多。為了滿足會(huì)計(jì)的要求，我們假定設(shè)備只能提供八年的服務(wù)。</p><p>　　在1980到1989年之間技術(shù)人員的投入工作小時(shí)平均減少了32%。另一方面，藥劑師的勞動(dòng)投入時(shí)間在1989年和1980年幾乎沒(méi)有什么變化。然而，與之前一年相比，我們發(fā)現(xiàn)藥劑師的平均工作小時(shí)平均有了小的變化。一方面的原因是技術(shù)人員

98、的工作時(shí)間減少，藥店在19世紀(jì)80年代中期便停止招募新的技術(shù)人員。另一方面的原因是一些技術(shù)人員已經(jīng)培訓(xùn)成為藥劑師。這種技術(shù)人員的培訓(xùn)始于19世紀(jì)80年代初期。</p><p>　　我們對(duì)機(jī)械設(shè)備服務(wù)的估計(jì)顯示，在觀察時(shí)期內(nèi)藥店的機(jī)械設(shè)備服務(wù)平均增加了16%。我們發(fā)現(xiàn)幾乎所有的藥店在19世紀(jì)80年代把舊的設(shè)備換成了新的，并且一些藥店已經(jīng)完全重建了。就地上的可用空間來(lái)說(shuō)，我們發(fā)現(xiàn)其平均在減少。一方面地上可用空間減少的

99、原因是藥店取消了不必要的空間。另一方面的原因是新的藥店比舊的要小。</p><p>　　平均來(lái)說(shuō)，我們的數(shù)據(jù)顯示藥品交付醫(yī)院的時(shí)間減少了。主要由于重組的原因，在1983年至1984年期間大幅減少了57%。</p><p>　　門(mén)診的處方藥隨時(shí)間變化基本不變。然而，我們發(fā)現(xiàn)在1983年出現(xiàn)一個(gè)頂峰，這部分的主要原因是在1983年12月自費(fèi)的處方藥價(jià)格上漲。這次上漲導(dǎo)致了處方藥銷(xiāo)量的增加，比如

100、，病人本應(yīng)該在之后購(gòu)買(mǎi)的處方藥由于自費(fèi)費(fèi)用的上漲便提前購(gòu)買(mǎi)了。</p><p>　　在19世紀(jì)70年代末，殘疾人醫(yī)療器械作為醫(yī)藥的新產(chǎn)品。在19世紀(jì)80年代，醫(yī)療器械的銷(xiāo)量平均增長(zhǎng)了。在這里，我們發(fā)現(xiàn)殘疾人的醫(yī)療器械產(chǎn)品的數(shù)量隨著時(shí)間的增加而增加，這可能是一般藥店的醫(yī)療器械數(shù)量增長(zhǎng)的一個(gè)原因。</p><p>　　以1980年至1989年的不變價(jià)格計(jì)算，藥柜上的藥品銷(xiāo)量平均增加了57%。在

101、19世紀(jì)80年代藥柜上的藥品增加與藥店所推動(dòng)的政策發(fā)展相對(duì)應(yīng)。藥店里的業(yè)務(wù)逐漸越來(lái)越關(guān)注自我的藥物治療。然而，其中一個(gè)可能是政策已經(jīng)實(shí)行對(duì)藥店有巨大的影響。</p><p>　　在我們的觀察期內(nèi)輸入和輸出向量的組合發(fā)生了相當(dāng)大的變化。我們也注意到全部年份中，我們發(fā)現(xiàn)輸入向量的組合與輸出向量的組合在藥店的差異。</p><p>　　能耗，清潔，辦公用品等的成本與支出的計(jì)算都不包括在我們的輸入