EVOLUTION OF THE METHODOLOGY OF TECHNICAL AND ALLOCATIVE EFFICIENCY STUDIES IN ECONOMICS: A REVIEW OF LITERATURE 1

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1 EVOLUTION OF THE METHODOLOGY OF TECHNICAL AND ALLOCATIVE EFFICIENCY STUDIES IN ECONOMICS: A REVIEW OF LITERATURE 1 R.M.A.K. Rathnayake 2 S.P.P. Amarathunge 3 ABSTRACT Effcency measurements have been a great concern of researchers wth an am to study the effcency levels of almost all economc actvtes. Emprcal estmaton and dentfyng the determnants of effcency are the major tasks n effcency analyss. The man objectve of ths study s to nvestgate major changes taken place n the methodology of techncal and allocatve effcency n economcs. The hstorcal approach s used as the methodology of ths study. There was no accepted statstcal methodology to measure economc, techncal and allocatve effcences untl the study of Farrell (1957); The Measurement of Productve effcency. In economcs, economc effcency has two components whch are referred to as techncal effcency and allocatve effcency. Techncal effcency s assocated wth the ablty to produce on the fronter soquant, whle allocatve effcency refers to the ablty to produce at a gven level of output usng the cost-mnmzng nput ratos. Few alternatve parametrc methods are avalable n lterature such as producton, cost, proft, revenue and dstance functons to analyze effcency by estmatng producton technology. The nonparametrc methodology nvolves manly the use of lnear programmng technques. Accordng to avalable lterature, t s clear that varous approaches to effcency analyss have been developed by two parallel tradtons, the econometrc method and the non-parametrc data envelopment analyss. Each of these tradtons ncorporate ts nherent merts and demerts. Fndngs of the study reveal that nput dstance functon s the best methodology for measurng allocatve effcency f nputs quanttes do not sgnfcantly vary across unts of studes. Keywords: Techncal Effcency, Allocatve Effcency, Economc Effcency 1 Ths paper s based on PhD dssertaton An Economc Analyss of Techncal and Allocatve Effcency of Paddy Farmng: A Case Study n Mahawel System H whch s to be submtted to the Department of Economcs, Unversty of Colombo, Sr Lanka. 2 R.M.A.K. Rathnayaka s a Senor Lecturer at the Department of Busness Economcs, Faculty of Management Studes and Commerce, Unversty of Sr Jayewardenepura, Sr Lanka. Emal : anandausjp@gmal.com 3 Sampath Amaratunge s a Professor at the Department of Busness Economcs, Faculty of Management Studes and Commerce, Unversty of Sr Jayewardenepura, Sr Lanka. Emal : amaratunge@sjp.ac.lk 56

2 1. Introducton Productve effcency has two components namely techncal effcency and allocatve effcency. The techncal effcency component refers to ablty to mnmze wastages by producng as much output by gven level of nputs or by usng as lttle nput to produce gven level of output. Thus, the techncal effcency can be explaned based on two alternatve arguments; an output augmentng and an nput orentaton. The allocatve (prce component) s defned as the ablty to combne resources and outputs n optmal proportons. Many researchers have pad ther attenton to defne the concept of effcency and ts components. Debreu (1951) and Farrel (1957) ntroduced a measure of techncal effcency. Based on Farrel (1957), measure of techncal effcency can be obtaned by usng nput and output quantty wthout ntroducng prces of these nputs and outputs. Techncal effcency can be decomposed nto three components such as scale effcency, congeston and pure techncal effcency. Techncal effcency s just one component of overall economc effcency. However, a frm must frst be techncally effcent n order to be economcally effcent. A frm should produce maxmum output gven the level of nputs employed n order to be techncally effcent and should use the rght mx of nputs n lght of the relatve prce of each nput n order to be allocatvelly effcent (Kumbhaker and Lovell 2000). However, there are many examples n lterature whch show the dfference between allocatve effcency and techncal effcency by usng Isoquant curve. In Fgure 01 below, observaton A utlzes two nput factors to produce a sngle output. SS/ s the effcent soquant curve estmated wth an avalable technque. Pont B on the soquant represents the effcent reference of the observaton A. The techncal effcency of a producton unt operatng at A s most commonly measured by the rato TE = OB/OA, whch s equal to one mnus BA/OB. It wll take a value between zero and one, and hence an ndcator of the degree of techncal neffcency of the producton unt. A value of one ndcates that the frm s fully techncally effcent, for nstance, the pont B s techncally effcent because t les on the effcent soquant. Allocatve effcency can be calculated f the nput prce rato represented by the slop of the socost lne, WW / n Fgure 01, s known, the allocatve effcency (AE) of a producton unt operatng at A s defned to be the rato of AE = OC/OB. Snce the dstance CB represents the reducton n producton costs that would occur f producton were to occur at the allocatvely and techncally effcent pont E, nstead of the techncally effcent, but allocatvely neffcent pont B. The total economc effcency (EE) s defned to be the rato of EE = OC/OA where the dstance CA can also be nterpreted n terms of a cost reducton. Note that the product of techncal effcency and allocatve effcency measures provdes the measure of overall economc effcency. 57

3 FIGURE 01 Allocatve and Techncal Effcency X 2 S A W C B E W / S/ 0 X 1 Source: By the author based on lterature survey The research problem of the study s based on the followng facts. Improvng of economc effcency s the key determnant n determnng productvty of economc resources. In economc theory, achevement of both techncal and allocatve effcences s requred n order to be economcally effcent. There are dfferent approaches and methods n the theory of economcs n measurng techncal and allocatve effcency, but there s no consstency among economsts. There s a consderable number of studes n developng countres n whch methods were selected wthout proper evdence. Wthn ths context, the research problem of ths study can be stated n the followng manner; How should we select a better methodology to estmate techncal and allocatve effcences wth proper understandng of ther merts and demerts? Thus, the man objectve of the study s to nvestgate major changes taken place n the methodology of techncal and allocatve effcency n economcs. Ths study also ams at achevng the followng objectves; 1. To dentfy dfferences among alternatve approaches and methods n estmatng techncal and allocatve effcency. 2. To dentfy merts and demerts of alternatve approaches and methods n estmatng techncal and allocatve effcency. 3. To dentfy a better methodology n estmatng techncal and allocatve effcency wthn the Sr Lankan context wth specal emphass on agrculture sector. The study ams to nvestgate major changes taken place n the methodology of techncal and allocatve effcency n economcs through analyzng avalable lterature n ths feld. Hstorcal approach s used as the methodology of ths study to fulfll the aforementoned objectves. Most of the popular data bases 58

4 have been referred for the survey of lterature and the sectons of the analytcal part are dvded consderng common features of the studes conducted n ths feld. 2. Analyss and Dscusson 2.1. Measurements of Techncal Effcency Varous approaches to effcency analyss have been used by two parallel tradtons, the econometrc methods (Agner, et al., 1977, Battese, 1992) and the non-parametrc Data Envelopment Analyss (DEA) methods (Slkman, 1986, Sengupta, 1989). Bascally DEA method s based on lnear programmng technques and conssts of estmatng a producton fronter through a convex envelop curve formed by lne segments jonng observed effcent producton unt. DEA method can be known as Programmng approach. Especally t should be noted that n ths method there s no functonal form mposed on the producton fronter and there are no any assumptons made on the error term. However, both strengths and weaknesses can be seen n the Data Envelopment Theory n estmatng techncal effcency. Strengths TABLE 01 Strengths and Weaknesses of DEA Method Weaknesses -DEA can be used for multple nputs and multple outputs. -DEA doesn't requre relatng nputs to outputs. -Comparsons are subjectve. -Inputs and outputs can have very dfferent unts. -Measurement error s not consdered. -DEA does not measure "absolute" effcency. -Statstcal tests are not applcable. -Computaton of large data set s dffcult. Source: Lterature survey by the author Wth recent developments n effcency analyss, methods have been desgned to overcome some lmtatons of DEA. A determnstc fronters statstcal theory s one of such methods n effcency analyss. Smar (2003) has proposed a method to mprove the performance of FDH/DEA estmators n the presence of nose, whle Cazals et at. (2002) developed a robust none parametrc estmator. Argon (2003) developed a new none parametrc estmator of the effcency fronter based on the condtonal quntles of an approprate dstrbuton assocated wth producton process. However, ths method has not extended to cover the multvarate analyss. The second approach s the parametrc approach. It s based on econometrc estmaton of a producton fronter whose functonal form s specfed n advance. In 59

5 ths approach, the Stochastc Fronter method s the most popular and also t s referred to as composed error model, the Stochastc Fronters method has the advantage of takng nto account the random error and the neffcency component specfc to every plantaton. The Stochastc Fronters producton method was proposed for the frst tme by Agner (1977) and Meeusen, and Broeck (1977). By followng dfferent parameterzatons such as those of Battese and Corra (1977), Battese et.al (1998), and Battese (1992), the lkelhood functon of the model defned by the equaton: y f ( x, ) v u f ( x, ) where, v s the two-sded nose component, and u s the nonnegatve techncal neffcency component of the error term. The nose component v s assumed to be ndependently and dentcally dstrbuted and symmetrc, dstrbuted ndependently of u. Thus the error term v u s not symmetrc, snce u 0. Assumng that v and u are dstrbuted ndependently of x. The two approaches, econometrc and DEA use dfferent technques to envelope data more or less tghtly n dfferent ways. In so dong they make dfferent adaptaton for random nose and flexblty n the structure of producton technology. It s these two dfferent adaptatons that generate strengths and weaknesses of the two approaches. 1. The econometrc approach s stochastc, and thus attempts to dstngush the effects of nose from the effects neffcency. The programmng approach s non-stochastc, and lumps nose and neffcency together and calls the combnaton neffcency. 2. The econometrc approach s parametrc, and confounds the effects of msspecfcaton of functonal form wth neffcency. The programmng approach s nonparametrc and less prone to ths type of specfcaton error. Even though the methodology of Stochastc Fronter s hghly used n techncal effcency analyss, t also comprses both strengths and weaknesses. 60

6 TABLE 02 Strengths and Weaknesses of Stochastc Fronter Method Strengths Weaknesses -Ablty of usng stochastc error term for advance analyss -Ablty of conductng statstcal tests -Fronter methodology can be used to measure absolute effcency -Analyzng of a large set of data s very easy -In many studes the choce of the functonal form appears to be arbtrary -Most researchers do not nvest much tme and effort n choosng a partcular dstrbutonal form -The Stochastc Producton Fronter approach s suted only for sngle-output technologes -Sample sze should be a large one for more accuracy of results. Source: Lterature survey by the author Methods for Identfyng Techncal Effcency Determnants Ths secton s specally focused to dscover the methods related wth Stochastc Fronter Producton Functon. Accordng to lterature, generally, two approaches used n analyzng the determnants of techncal effcency from a stochastc fronter producton functon can be dentfed. The frst s called the twostep approach; frst the Stochastc Fronter Producton functon s estmated to determne techncal effcency ndcators. Next, ndcators thus obtaned are regressed on explanatory varables that usually represent the frm s specfc characterstc, usng the ordnary least square (OLS) method. Ths two-step approach has been used by authors such as Ptt and Lee (1981), Kalrajan (1981), Parkh and shah (1995), and Belhassen (2000) n ther relevant studes. The major drawback wth the two-step approach resdes n the fact that, n the frst step, neffcency effects (uj) are assumed to be ndependently dstrbuted. In the second step, however, the techncal effcency ndcators thus obtaned are assumed to depend on certan number of factors specfc to the frm, whch mples that the (uj) are not dentcally dstrbuted unless all the coeffcents of the factors consdered happen to be smultaneously null. Kumbhakar (1991) and Refschneder and Stevenson (1991) developed a model n whch neffcency effects are defned as an explct functon of certan factors specfc to the frm, and all parameters are estmated n one step usng the maxmum lkelhood procedure. By followng ths second approach Huang and Lu (1994) developed a non natural Stochastc Fronter Producton functon, n whch the techncal neffcency effects are a functon of a number of factors specfc to the frm and of nteractons among these factors and nput varables ntroduced n the fronter functon. Battese and Coell (1995) also proposed a Stochastc Fronter Producton functon for panel data n whch techncal neffcency effects were 61

7 specfed n terms of explanatory varables, ncludng a tme trend to take nto account changes n effcency over tme. The one step approach has snce been used by such authors as Ajbefun (1996), Coell and Battese (1996), Audbert (1971), Battese and Sarfaz (1998), and Lyubov and Jensen (1998) n ther respectve studes to analyze the factors affectng the techncal effcency/neffcency of agrcultural producers. Accordng to avalable crtcsm, one-step approach s less crtczed by researchers especally at the statstcal level Measurements of Allocatve Effcency Allocatve effcency s the second component of overall economc effcency. Allocatve effcency s not hghly addressed by researchers when compared wth techncal effcency. Accordng to the avalable lterature, t s clear that, there are three alternatve approaches n allocatve effcency analyss. I. Computaton of an allocatve effcency ndex through margnal value product and margnal factor cost (prce) of resources II. Computaton of allocatve effcency through estmaton of the cost functon or mplct cost functon III. Computaton of allocatve effcency through estmaton of the nput dstance functon Allocatve effcency ndex s the rato between margnal value product and margnal factor cost of a resource. Ths s the smplest method of analyzng allocatve effcency of factor nputs. There are two man drawbacks of ths methodology. The frst drawback s that, ths method can be appled to analyze only ndvdual allocatve effcency of factors and there s no way of measurng overall allocatve effcency. The second drawback s that the nterrelatonshp among the factors of producton s not consdered by ths method n estmatng allocatve effcency. Onah, Kuye and Idong (2008), Suresh and Keshava Reddy (2006), Ogundar (2008) are some of the researchers who have appled ths methodology for allocatve effcency analyss. The ssues of allocatve and cost effcency measurements through cost functons were addressed by Schmdt and Lovell (1979), who has descrbed how one could estmate a Cobb-Douglas Stochastc Cost Fronter and then use dualty to derve the mplct producton fronter. Wth these two fronters, one could then measure cost effcency and techncal effcency, and calculate allocatve effcency resdually. Schmdt and Lovell (1979) ntroduced the Cost Fronter method and t was extended to the very flexble translog functonal form by varous authors, such as Greene (1980) and Schmdt (1984). These new methods avoded the restrctons ntrnsc n the Cobb-Douglas functonal form, but at the cost of ntroducng consderable complexty to the modelng exercse. 62

8 Drect estmaton of the Cost Fronter may not be much approprate and practcal n some cases, for nstance, n a stuaton such as; 1. When there s no dfference n nput prces among frms 2. When there s a systematc devaton from cost mnmzaton behavor n the ndustry; for example when poltcal, unon or regulatory factors cause shadow prces to devate from market prces n a systematc way. In ths stuaton, the dualty between the cost and producton functons break down, and the resultng bas n the cost fronter estmates wll make the cost effcency calculaton and decomposton based as well (T. Coell, S. Sngh, E. Flemng, 2003) Bascally there are two solutons; Implct Cost Fronter and Input Dstance Functon could be dentfed n lterature for the aforementoned ssues. Implct Cost Fronter s the drect estmaton of the prmal producton technology, and then dervaton of the mplct cost fronter; for example, Bravo-Ureta and Reger (1991) estmated a Cobb-Douglas stochastc producton fronter, and then derved the mplct cost fronter. Ths also has been crtczed by many researchers. One partcular contradcton n the Bravo- Ureta and Reger (1991) approach s that a producton functon s estmated assumng that the nput quanttes are decson varables. Another weakness of the Bravo-Ureta and Reger (1991) approach s that the use of the Cobb-Douglas functonal form, whch s a restrctve functonal form. That s, t mposes untary elastctes of substtuton and constant producton elastctes across all frms. In the emprcal exercse n ths paper we fnd that the more flexble translog functonal form s not a statstcally sgnfcant mprovement over the Cobb-Douglas functonal form. Although these weaknesses are reflected by the method ntroduced by Bravo- Ureta and Reger (1991), t s beng wdely used n effcency analyss. Input Dstance Functon s another soluton ntroduced by T. Coell, S. Sngh, E. Flemng n The specalty of the Input Dstance Functon can be summarzed n the followng aspects. 1. Prces of nputs that vary across the frms are not needed for ths approach. 2. Ths s a strong soluton for systematc devatons from cost mnmzaton behavor. 3. It does not suffer from smultaneous equatons bas when frms are cost mnmzng frms or shadow cost mnmzng frms. 4. The Input Functon Approach can be used even for multple products. 3. Conclusons Varous approaches to techncal effcency analyss have been used by two parallel tradtons, the non-parametrc Data Envelopment Analyss (DEA) and econometrc methods. DEA method can be used for the researches assocated wth multple nputs and multple outputs but t s not a sutable method f the focus s an advanced statstcal analyss, because ths does not allow statstcal sgnfcant tests of parameters. The second approach s the parametrc approach. It s based on econometrc estmaton of a producton fronter whose functonal form s specfed 63

9 n advance. In ths approach, the Stochastc Fronters method s the most popular. It s also referred to as composed error model ; the Stochastc Fronter method has the advantage of takng nto account the random error and the neffcency component specfc to every plantaton. Ablty of measurng absolute effcency and ablty of applyng hypotheses are the man advantages of ths approach. Stll, there are few lmtatons of ths methodology assocated wth multple nput and multple output problems. Researchers have to be very careful n specfyng a correct functonal form for the fronter, snce a wrong functonal from generates totally naccurate results. Allocatve effcency s the second component of overall economc effcency. Accordng to the avalable lterature, t s clear that there are three alternatve approaches n allocatve effcency analyss; allocatve effcency ndex method, cost and mplct cost functon method and nput dstance functon method. If the prces of goods and nputs are vared across study unts, frst two methods can be appled and nput dstance functon method s much applcable when prces of goods and nputs are not sgnfcantly vared across the study unts. There s no sgnfcant ssue n selectng an approach n estmatng the techncal effcency n Sr Lanka. DEA method can be appled for comparatve effcency analyss and ths s especally powerful for multple nputs and outputs problems. The econometrc approach could be used f the functonal form s very clear. Ths method s very sutable for advanced statstcal analyss of economc effcency. The researcher has a great role n selectng a method for estmatng allocatve effcency. For nstance, paddy s the man agrcultural product n Sr Lanka. There are two rrgaton systems; major (Mahawel systems) and mnor n Sr Lankan paddy sector. Input dstance functon s the best method for estmatng allocatve effcency n major rrgaton systems, snce nput usages and prce of output are not sgnfcantly vared across households. Cost functon approach s better for estmatng allocatve effcency n mnor rrgaton systems of paddy snce nputs usages and prces are sgnfcantly vared across households. References Agner, D.J., Lovell, C.A.K. and Schmdt, P., (1977). Formulaton and Estmaton of Stochastc Fronter Producton Functon Models, Journal of Econometrcs, 6: pp Ajbefun, I.A., Battese, G.E. and Daramola, A.G., (1996). Investgaton of Factors Influencng the Techncal Effcences of Smallholder Croppers n Ngera, CEPA Workng papers, No. 10/96, Department of Econometrcs, Unversty of England, Armdale, pp. 19. Al, M. and Chauudhry, M.A., (1990). Inter-regonal farm effcency n Paktan s Panjab: a Fronter Producton Functon study, Journal of Agrcultural Economcs, 41: pp

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