Vol., No.6, Dec 20, pp.2332 Comparson of the Ratng of Socal Securty Insurance Branches of Sstan and Baluchestan Provnce Based on Effcency Usng DEA and SFA Models Peymaneh ahmad pour, Nazar Dahmardeh 2, Alreza Shahrak 3 Abstract There are two general methods to evaluate the effcency of decson maker departments: Parametrc and nonparametrc methods. In ths paper, Data Envelopment Analyss (DEA), as a parametrc method and Stochastc Fronter Functon, as a nonparametrc method were used to evaluate and grade dfferent branches of socal securty nsurance n Sstan and Baluchestan provnce. To do ths, nformaton related to nput output of 2 branches of the provnce was collected for three successve years and dfferent branches were graded based on the average effcency of these two gradng methods. Fnally, usng Pared ttest, the sgnfcant dfference between the two appled methods were tested and confrmed. Key words: socal securty nsurance, Data Envelopment Analyss (DEA), Stochastc Fronter Producton Functon, effcency, ratng of branches Avalable onlne www.bmdynamcs.com ISSN: 2047703 INTRODUCTION Wth respect to the everncreasng growth of technology, extensve amount of nformaton, and development of varous servces, each economc frm needs to have necessary dynamcs all the tme to survve and compete wth other frms n one ndustry; that s why controllng and evaluatng actvtes of the frm contnuously s an nevtable necessty. Therefore, nsurance system s no excepton and needs to be evaluated n ths concern. In addton, effcency of the nsurance system s among the subjects, whch are both mportant for ther managers and supervsory system and customers. Because on the one hand, managers need to reach the hghest level of effcency to compete wth other rvals, and on the other hand customers and supervsory system know that ncreasng effcency wll always be together wth prce reducton and qualty mprovement. Generally, effcency evoluton methods of the organzatons are dvded nto two major categores of parametrc methods and nonparametrc methods. The topmost methods among the parametrc methods and nonparametrc methods are Stochastc Fronter Functon (SFA) and Data Envelopment Analyss (DEA), respectvely. Wth respect to the entty of each of the methods, they have a seres of advantages and constrants, some of whch are explaned as follows: A) Constrants of Data Envelopment Analyss (DEA) It s merely a mathematcal method that s based upon the lnear programmng. If only one of the nput and/or output s changed, t causes fundamental changes n effcency. There s no general agreement on choosng the avalable nput and output (Babae, 2006, p. 65) B) Constrants of Stochastc Fronter Functon (SFA) It s nevtable to hypothesze a producton functon for each ndustry. When the cost functon s desgned and/or estmated, t s hypotheszed that the ndustres are actng qute effcently or as Beckers and Hammond say, The only dstngushed devaton n ths methodology s the random error. Normal dstrbuton s the hypothess, whch s rather nflexble. Such a concepton calculates neffcency almost less than ts (normal) level and as Berger and Humphrey say, It causes varaton n calculatng effcency of the manufacturng ndustres. In ths paper, we have attempted to grade socal securty branches of Sstan and Baluchestan provnce and compare the obtaned results usng Data Envelopment Analyss (DEA) and Stochastc Fronter Analyss (SFA). Theoretcal Lterature of the Research Department of Industral Engneerng, Islamc Azad Unversty, Zahedan Branch, Zahedan, Iran, ahmadpour354@yahoo.com 2 Assocate Professor of Department of Economcs, Unversty of Sstan & Balochestan, Zahedan, Iran, nazar@hamoon.usb.ac.r 3 Assstant Professor, Unversty of Sstan and Baluchestan, Department of Industral Engneerng, shahrakar@hamoon.usb.ac.r
Vol., No.6, Dec 20, pp.2332 As the mportance of productvty was revealed durng recent years, several researches were carred out n ths feld n the country and abroad. We present a summary of the artcles made and researches conducted n ths feld as follows: In a research carred out by Supachet Chansarn n 2008 called Relaton of Effcency of Commercal Banks n Thaland Usng DEA Approach, the effcency of 3 commercal banks were nvestgated between 2003 and 2006 usng DEA method. In ths research, an nput, that s, number of staff and two outputs, whch are nterest ncome and other ncomes, were consdered to calculate DEA. Constant return to seale has been used for effcency calculatons. The results obtaned from the research showed that the effcency of banks wth operaton approach, whch s growng gradually, s very hgh as ther average effcency n each year was above 90%. In addton, old commercal banks tred to compete wth newly establshed nsttutes and, on average, they showed that they were more effcent than those nsttutons (Supachet Chansarn, 2008). Comparng DEA, DFA and SFA, Hjalmarsson (996) concludes that the estmated amounts for effcency n each of these models have consderable dfferences. Rest (997), who obtaned dfferent results, beleves that n case econometrc methods and lnear programmng use smlar nputs and conceptual framework, ther results do not dffer much. Berger and Mester (997) compared DFA, SFA, Fourer Flexble Functonal Form and translog form. They concluded that choosng effcencymeasurng method does not usually make any dfference n terms of the average effcency of ndustry and gradng sngle frms (Ponar). In an artcle called Apprasng and Analyss of Cost Effcency n Greek Banks Usng DEA Approach, n 2007, Fotos Pasouras, Emmanoul Sfodaskalaks & Constantn Zopounds, apprased the effcency of Greek cooperatve banks, totally 6 banks, durng 2000 to 2004. Usng DEA method, they frst apprased cost, expert and management effcences of the banks under study and then dstngushed the effectve nteror and exteror factors n the varous aboveapprased effcences usng Tobt regresson. The result obtaned from ther study ndcates that the average defcency of all the banks s 7.7. Aghajan et al. (2009) presented a theoretcal nnovaton based on the results of the earler studes usng theoretcal comparson of some of researches carred out on the applcaton of DEA n apprasng organzatons effcency. On the bass of ths, the results of the expermental researches were contrasted theoretcally and ther smlartes and dfferences were extracted. For smlartes, the followng three tems were quoted from other researchers: A) The ablty to separate the effcency apprasal of dfferent organzatonal departments through DEA B) Data Envelopment Analyss, an approprate method for apprasng effcency of organzatonal departments, and C) Effcency n terms of organzatons ownershp For dfferences, the followng three tems were quoted from other researchers: A) Excellence Model s an approprate crtera to apprase effcency B) The excellence of CCR Model to other DEA models to apprase effcency C) Type of ownershp and other dfferent results Pourkazem (2007) has nvestgated the effcency of commercal banks usng DEA and then graded them by dfferent ndces. Based on the research results n each of the banks, there are approprate supervsons wth hgh effcency. Servng these supervsons as some examples and encouragng them, one s able to prevent low effcency of the supervsons. Tranng condton of banks staff s not approprate and ther level of knowledge s as low as the dploma level. Therefore, plannng to ncrease level of knowledge of staff takes prorty n the present age that s called the Knowledge Era. Banks expenses are generally hgh. Although only deprecaton has been consdered and assets such as buldngs and goodwll have not been regarded, plannng to mprove expenses, especally staff expenses of some banks and the nteror decoraton expenses are of paramount mportance.
Vol., No.6, Dec 20, pp.2332 Nader Kazaj, n a plan called The Study and Comparson of DEAbased Interest Bankng and Interest Free Bankng System n the World n 2005 studed nterestfree bankng effcency and compared the effcency of the nterest free banks wth the nterest banks n the world. In ths study, he apprased the effcency of 46 nterest free banks and 64 nterest banks n the world n 200 usng CCR method and showed that the effcency of nterest free banks, whch are workng n a compettve envronment together wth nterest bankng banks, s more than the ones, whch are workng under the Interest Free Bankng System. Javanmard, n a research called Apprasng the Effcency of Branches Usng Consoldated Method of data analyss and DEA n 2007 attempted to nvestgate how to make an expert system through ntroducng a smart algorthm and dentfyng the effectve elements n the effcency of decson departments. After that, the proposed algorthm for vrtual bank was mplemented. The two tools of data analyss and DEA have been used to dentfy the hdden and examples among the dfferent status of staff ndces and effcency. Decson Support Systems based on Neural Network Models have been proposed to predct the effcency of branches n dfferent condtons. Abbasan and Mehregan (2007) studed productvty of producton elements usng DEA. The results ndcate that although the country s economc productvty has generally been ncreased, the overall performance of economc actvtes cannot be justfed, snce they had the consderable amounts of materal and human resources. Due to vastness of actvtes and havng a large number of employees, servce department suffers from more problems. Contnuous growth and lvelness of servce department are the major features of the successful and developed economc systems n today s world. Therefore, payng no attenton to the problems of ths department, ncludng low level of relatve productvty, causes deprvaton of growth opportuntes and economc development and may create al lot of socal, poltcal and cultural problems n the future. METHODOLOGY OF RESEARCH Type of Methodology The present research, n terms of procedure s known as ex post facto descrptve research, n terms of statstcs and data collectng, t s known as a documentary research, and n terms of target, t s an appled research. Socety and Sample Statstcal populaton n the present research ncludes 2 branches of socal securty n Sstan and Baluchestan provnce. In addton, number of samples concdes wth the statstcal populaton. In other words, n ths research, all the statstcal populaton s studed as a sample. Research Varables DEA and SFA models compare alternatves or branches usng the data of nput and output varables. Therefore, the grade of each branch s calculated and presented n comparson wth all other branches and based on the types of effcency. The nput varables are normally consdered those, whch are taken nto account as the producton element of the product or the presented servces of the frm under study. For nstance, labor force or producton cost, raw materal... are all approprate varables for the model, snce, usng them, servces are produced. The output varables, as ther names ndcate, are those, whch are the result of the frm s actvty. Input Varables and Producton Elements: In ths paper, studes have been conducted on the nput varables of DEA and SFA models, for nsurance ndustry and all the theores related to ths feld. The nput varables whose statstcs have been collected for all the 2 branches n queston durng three years (2007 to 2009) are as follows: Number of staff Average annual reward of staff
Vol., No.6, Dec 20, pp.2332 Average of emoluments of staff The above varables are those mportant parameters that alterng and optmzng them may drectly effectve n mprovement of effcency, productvty of staff and maxmum effcency of branches. Meanwhle, all branches have the statstcs of above parameters. Takng the above three varables as the nput varables causes all the varables and parameters effectve n ths concern are covered and used. The varables statstcs model have been collected for three years. Average of the varables wll be used for the analyss of effcency and gradng n order to rely more on the accuracy of the estmaton results. Output Varables Wth respect to the workng entty of the nsurance, the output varables are as follows: Admnstratve Expenses of branches Sum of operatng and nonoperatng ncome of branches (whch s summarzed as branches revenues n ths paper) Analyss of Informaton The collected data was analyzed usng DEA, DEAP software, SFA, and Fronter 4 software and the results obtaned from the two models were compared usng SPSS software. Gradng Socal Securty Branches of the Provnce Usng DEA To grade the branches usng ths method, the collected nformaton has been calculated usng DEAP software Varable Returns to Scale and Axs Output: Calculaton of Effcency Concernng Varable Returns to Scale and Axs Output: Effcency of labor force n branches at the state of axs output and varable returns to scale was also calculated usng DEAP software results of whch are as below: Followng table presents dfferent effcences of the 2 branches of organzaton and type of ther performance: Table () Types of effcences of dfferent branches of the provnce and type of ther performance at the state of the state of varable returns to scale and axs output Insert table here It should be noted that the type of rs performance means the ncreasng returns to scale. Regardng the above table, branches, 4, 0,, 2 were consdered as the effectve branches of the organzaton n Sstan and Baluchestan provnce and the others are fallen wthn the group of neffectve branches. The neffectve branches should know ther reference branches. Ther optmzed nput and output should be determned. Meanwhle, surplus of agents of producton s calculated for all the branches. Gradng Branches usng DEA method: To grade usng DEA, frst, one should grade the effectve branches. Several branches may be ntroduced as the effectve, even dstngushed and reference branches; however, t does not mean that all of them are n one grade as far as effcency s concerned. To grade these effectve branches, we consder the reference. As mentoned above, for neffectve branches, one or many effectve branches are ntroduces as samples. Now, each branch, whch s ntroduced as the dstngushed branch for the neffectve branches, takes the leadng poston among the whole branches, and accordngly, the second branch, the thrd branch are graded. Above ponts were about gradng effectve branches. However, neffectve branches should be graded as well so that the weakest branch s recognzed n terms of effcency and productvty and poston of each branch s dstngushed n rankng. To grade the neffectve branches, we consder the average of dfferent effcences (management, scale and techncal effcences) at varable returns to scale mode. The hgher the average effcency of each branch s, the hgher the grade of that branch wll be. Of
Vol., No.6, Dec 20, pp.2332 course, the neffectve branches are graded after the effectve branches. Regardng above ponts, grades of 2 branches of the organzaton are shown as the followng table: Insert table4 here
Vol., No.6, Dec 20, pp.2332 Gradng Socal Securty Branches of Provnce Usng SFA method Generally, cost functon of SFA model s as follows: ln TC lntc( q, p ), u TC Total cost q output vector q nput vector dstorton expresson and u are two separable statements wth dfferent probablty dstrbuton. u s nonnegatve random varable whch shows cost neffcency wth rregular normal dstrbuton n zero N(, ). s the random error (dstorton statement) whch may be due to the measurement error or unmportant varable whch have not been consdered n the model or may have been mposed by (out of control) external shocks to the economc departments. It has normal dstrbuton. There are doubts over the real form of fracton dstrbuton of neffcency and t seems that the expermental evdence have not presented an acceptable and sutable crteron to remove the problem. Many reasonng has been adopted based on fracton normal dstrbuton of random error; however, few reasonng has been adopted toward neffcency of dstrbuton. Among the proposed dstrbutons for the form of the neffcency fracton s logarthmc normal dstrbuton or (logarthmc) rregular normal. In addton, oneway normal dstrbuton and gamma dstrbuton have been used n the expermental studes. Musen (977) has used Wgner s exponental dstrbuton and halfnormal dstrbuton. These consequental forms show that the frms have been dstrbuted farly close to the effcency level and they wll evenly be dmnshed wth the ncrease of neffcency. In spte of ths, adoptng a robust reasonng toward a specal dstrbuton form for them would be dffcult. Econometrc estmaton of the cost functon requres selectng the form of functon. In ths paper, the functon s defned as below: ln( Tct ) LnQt 2LnP TCt u, 0 t t t s the total cost of the th branch and n the year t (total amount of personnel expenses and admnstratve costs), Qt output (here, total ncome of the branch), jt P s the output cost (cost of labor force whch s obtaned from dvdng personnel expenses to the number of personnel), u Pjt s the random error and t s the cost neffectveness. The above model has been estmated usng Fronter 4 software and the results obtaned from the estmaton are as follows: ln( Tc ) 2.09 0.75LnQ 0. 52LnP t t t Based on the results obtaned from the model, t statstc that s related to the model s varable coeffcents s sgnfcant at the level of sgnfcance of 90 percent. Summary of parameters of the model are mentoned n the followng table: Insert table5 and 6 here Lkelhood rato test wth the amount of LR=29.5 also ndcates that by takng the probablty of 95% (level of sgnfcance of percent), H 0 hypothess n whch the amount of gamma statstc s equal to zero, s rejected. Ineffcency results obtaned from the estmaton of cost functon at ths state s as follows:
Vol., No.6, Dec 20, pp.2332 Based on the result obtaned from the above model, the average of neffcency of the branches, durng the study perod, decreases from.50 n 2007 to.07 n 2009. In other words, the average of neffcency of dfferent branches of socal securty n Sstan and Baluchestan provnce has been decreasng for 3 recent years. Comparson of the Two Gradng Methods Usng Pared ttest Wth respect to the results obtaned from the two parametrc and nonparametrc models, gradng sgnfcant relaton has been studed n ths secton. To do so, frst, gradng of dfferent branches of socal securty of the provnce by the two methods s shown as below: Table (7) Gradng of dfferent branches of socal securty n the provnce by the two parametrc and nonparametrc methods Insert Table7 here Regardng the fact that two dfferent methods have been used to grade the branches, the pared t test s used to compare both methods. Results of the test are shown n the followng table: Table (8) Software output whch contrasts gradng of nsurance branches by two methods Insert table8 and 9 here Based on the results obtaned from the above experment, snce the estmated statstc t, s less than.96 at the level of sgnfcance of 95% (and the estmated Sg s 5% bgger at the confdence nterval of 95%), t s confrmed that there s a dfference between gradng branches usng DEA and SFA. CONCLUSION AND DISCUSSION One of the characterstcs of parametrc and nonparametrc performance apprasal models s gradng dfferent frms, whch follow the dentcal performance. Each of these models attempts to apprase the effcency of economc frms usng dfferent methods. DEA apprases performance of frms usng optmzaton methods and SFA model does t usng regresson methods. Dealng wth dfferent ssues, such models sometmes offer dentcal results and sometmes offer dfferent results. In ths research, t s confrmed that there s a sgnfcant dfference between the results obtaned from both models; however, t s not dscussed that whch model has more authentc results, whch may be the subject of a new research. REFERENCES Abbasan, Ezatollah and Nader Mehregan, Measurng Producton Elements Productvty of the Country s Economc Departments usng DEA Method, Economc Research Magazne, 2007, p 5376 Mohammad, Al and Somayeh Mohammad Hosenzadeh, Applcaton of AHP/DEA Consoldated Approach n Gradng Insurance Agences, Economc,پژوهشنامه 2006, p 28304 Moshr, Saed and Mehd Rezvan, Effect of Applyng Communcaton and Informaton on the Effcency of Iran s Ar Servces Industry, No 26, 2006, p 24 Emam Mebod, Al, Prncples and Measurement of Effcency and Productvty (Scentfc Appled), Second Edton, Insttute of Studes and Commercal Researches, 2005 Azar, Adel and Alreza Motaman, Measurement of Effcency n Manufacturng Companes by Data Envelopment Analyss (DEA), Scentfc and Research Bmonthly of Shahed Unversty, No 8, 2004 Mehregan, Mohammad Reza, Research n Operaton, 2003 Leftwtch, Rchard H, Costs Systems and Allocaton of Manufacturng Resources, Translated by Mrnezam Sajjad, Tehran, Alameh Tabatabae Unversty, 382 Pourkazem, Mohammad Hosen and Komars Hedar, The Use of DEA n Evaluaton of Effcency n Thermal Power Plants of the Country, Modares, Sprng 2002 Kazem, Productvty and Its Analyss n Organzatons, Frst Edton, Tehran, Samt Publcatons 2002 Samet, Morteza and Mohammad Al Rezvan, The Study of Effcency n Iran s State Unverstes Usng DEA Method, Economc Research Magazne, No 59, 200, p 747 Salvatore, Domnque, Theory and Mcroeconomcs Issues, Translated by Hasan Sobhan, Tehran, Ney Publcaton, Nneteenth Edton, 200 Tabban, Mohammad, Macroeconomcs, Tehran, Research Insttute n Programmng and Development, 2000, p 37, 372, 373
Parameter Busness Management Dynamcs Vol., No.6, Dec 20, pp.2332 Nader Kazaj, Mahmoud, Study the Effcency of Interest Free Bankng and Comparng Interest Free Banks wth Interest Banks n the World, MA Thess, Iran s Bankng Insttute, 2005 Arman, Mohammad Hosseng, Performance Apprasal of Agrculture Bank Branches n Isfahan Provnce wth Phase DEA Approach, MA Thess of Industral Management, Alameh Tabatabae Unversty, 2004 Abedfar, Pezhman, Apprasal of Techncal Effcency of Iran s Bankng Industry, MA Thess, Alameh Tabatabae Unversty, 2000 Dadras, Mohammad Ramtn, Techncal Effcency Apprasal n Iran s Cement Industry, MA Thess, Alameh Tabatabae Unversty, 999 Dadras, Javad, Techncal Effcency Measurement n Iran s Sugar Industry, MA Thess, Alameh Tabatabae Unversty 999 No 2 3 4 5 6 7 8 9 0 2 Scale Effcency 0.963 0.775 0.763 0.883 0.882 0.882 0.899 Average 0.98 Effcency Source: Fndngs of research Management Effcency 0.90 0.790 0.625 0.944 Techncal Effcency 0.963 0.775 0.763 0.804 0.697 0.552 0.899 0.869 Type of Effcency Table (4): Grades of dfferent branches of the provnce n terms of effcency usng DEA method Grade Branch 2 9 3 2 4 52 5 04 6 3 7 6 8 7 9 8 Source: Researcher s Calculatons Table (5) Estmaton of parameters of Stochastc Fronter Model T value Coeffcent Varables 6.35 2.09 α 0 Fxed Coeffcent 3.06 0.75 α Ln(Q) 7.7 0.52 α 2 Ln(p)
Vol., No.6, Dec 20, pp.2332.8 0.043 Sgma.96 0.28 Gama 69.6 Log lkelhood 29.5 LR Test 2.7 Average of neffcency of all branches wthn 5 years Table (6) Average of neffcency of dfferent branches of socal securty n the provnce wthn 3 recent years Branch 2007 2008 2009 Average neffcency of 3 years Gradng branches based on effcency.3.03.00.05 3 2.6.04.0.07 4 3.29.07.02.3 7 4.2.05.0.09 6 5.2.03.0.05 3 6.2.03.0.05 3 7.8.04.0.08 5 8.35.08.02.5 8 9.07.0.00.03 2 0 3.87.45.0 2.4 0.05.0.00.02 2 2.47.28.07.6 9 Insert table7 here Branch Gradng By DEA Gradng By SFA 3 2 4 4 3 6 7 4 5 6 5 4 3 6 3 3 7 8 5 8 9 8 9 2 2 0 5 0 5 2 3 9 Table8 Pared Samples Statstcs Mean N Std. Devaton Std. Error Mean Par DEA 4.5833 2 2.3432.66809 SFA 5.0833 2 2.90637.83900
Vol., No.6, Dec 20, pp.2332 Mean Std. Devaton Table9 Pared Samples Test Pared Dfferences Std. Error Mean 95% Confdence Interval of the Dfference Lower Upper t Df Sg. (2 taled) Par DEA SFA.50000 2.87623.83030 2.32747.32747.602.559