Data Envelopment Analysis In Stata - Stata: Software For .
Data Envelopment Analysis in StataChoonjoo Lee (sarang90@kndu.ac.kr)Yong--bae Ji (jyb7707@hanmail.net)YongKorea National Defense University, Republic of KoreaStata Conference DC09 (July 3030-31, 2009)DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
Outline1. Why DEA in Stata?2. The Basics of DEA3. The Stata/DEA program4. Stata/DEA Examples5. DEA Frontiers in Stata?6. ReferencesDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
1. Why DEA in Stata? Software Tools for Frontier AnalysisMethodData Envelopment AnalysisStochastic FrontierAnalysisLanguageAMPL, GAMS, Mathematica, SAS,VBASAS, Matlab, RProgramDEA Excel Solver, DEAP(v 2.1),DEAQual, DEA-Solver-Pro, EMS,FEAR, Frontier Analyst, OnFront,PIM-DEAsoft, Pioneer, WarwickDEA, MaxDEA, KonSi DEA,ISYDS(SIAD), xlDEA, LIMDEP,StoNEDStata, BSFM, Frontier(v4.1), WinBUGS,LIMDEP, StoNEDDEA Solver Online, iDEA.OnlineProgramDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
1. Why DEA in Stata? (cont.) DEA literatures by Year(2001Year(2001--2009) D/B: Science Direct, EBSCO, Google scholar, *SCI, SSCIQuery: DEA or Data Envelopment Analysis in title, key word, abstractmore to goDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
1. Why DEA in Stata? (cont.) DEA literatures by Journal(2001Journal(2001--2009)Source TitleRecord Count% of 446European J. OF Oper. Res.9320.8J. of the Oper. Res. Society378.3App. Math. and Computation368.1J. of Prod. Ana.306.7Omega-Int. of Management Sci.214.7Comp. & Oper. Research153.3Expert Systems with Applications132.9Annal of Oper. Res.102.2App. Economics102.2Int. J. of Infor. Tech. & Decision Making102.2DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
1. Why DEA in Stata? (cont.) DEA literatures by Subject(2001Subject(2001-2009)DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
1. Why DEA in Stata? (cont.) Stata is easy to use and powerful statistical software;Data Envelopment Analysis code in Stata willpromote the efficiency in data management for DEAusers and open new application areas in statisticalinference for Stata users.DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
2. The Basics of DEA(cont.) DEA ConceptPerformance(Efficiency, Productivity) InputsOutputsequipmentspace# type A laborOutputsInputsTechnology Decision Making# type B labor .?#type A customer#type B customerquality indexoper. profit .DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
2. The Basics of DEA(cont.) Assumptions to analyze the black boxlllllllEconomic Behaviors: No input, no output!(Free) DisposabilityConvexityFrontier Search: PiecePiece-wise Linear MethodScale EconomyOrientation: InputInput-based or OutputOutput-based Analysis Interpretation of DEA ResultsllllX-inefficiencyRational Choice of InputInput-Output MixesPerformance DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
2. The Basics of DEA(cont.) Terms & Notationsll( X , Y ): Input, output matrixu, v: Row vectorl λ (λ1 , ., λn )T : NonNon-negativity vectorlθ, η: Real variablel Decision Making Units(DMUs)DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
2. The Basics of DEA(cont.) Basic DEA Models: CCR, BCCOrientationPrimalmaxInputθm ins .t . θ x j X λ 0z uy j (u j )*s.t. vx j 1Oriented vX uY (u j e) 0minOrientedYλ yj*v 0, u 0, (u j freeOutputDualin sign)*m axs .t.z vx j (v j )*s.t. uy j 1vX uY (v j e) 0*v 0, u 0, (v j free in sign)*( e λ 1) *λ 0ηxj X λ 0η yj Yλ 0( e λ 1) *λ 0( )* is the additional constraint in BCC modelDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
2. The Basics of DEA(cont.) Characteristics of DEAl No assumption about InputInput-Output Functionl No limits to the number of inputs and outputsl Not required to weight restrictionsl Provide reference sets for benchmarkingl Provide useful information for inputinput-output mix decisionl n times computations for n DMUsDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
3. The Stata/DEA program User Written StataStata/DEA/DEA Descriptionl Considered the basic DEA models (CCR & BCC)l Can handle both input minimization and outputmaximization problemsl The data flow in the StataStata/DEA/DEA program¡ the input and output variables data sets required¡ the DEA options define the model¡ the “Stata“Stata/DEA”/DEA” program consists of “basic” and ““lplp”” subroutine¡ the result data sets available for print or further analysisDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
3. The Stata/DEA program(cont.) Diagram of Data flow in Stata/DEAStata/DEA programDATAStata /DEARESULTDEA OptionsData conversionDEA LoopInput &OutputVariablesdata fileLinearProgrammingFiles ofEfficiency& LambdasBasic SolutionGeneratingDEA result ReportDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
3. The Stata/DEA program(cont.) StataStata/DEA/DEA Syntax (program code under Stata journal review) dea [, data(ata(stringstring)) iotypeiotype((stringstring)) model(model(stringstring)) lambda]DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples Example 1: Store’s efficiency case(for model verification)l Data: two inputs, two outputs, and 5 DMUs※ Data imported from Cooper et al.(2006), p.75, Table 3.7l The inputs are¡ The number of employees (Employee)¡ The floor area (Area)l The outputs are¡ The volume of sales (Sales(Sales))¡ The volume of profits (Profits)(Profits)DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples(cont.)l The data file including input and output variables※ The input and output variables are saved in files "ta3 7.csv"l A user needs to set the options as required and run thefollowing code for input orientation model deadea,, data(ata(ta3 7ta3 7)) ioiotypetype((inputinput)) model(model(ccrccr)) lambdaDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples(cont.) The Result WindowDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples(cont.)l The result file including the efficiency score and reference set Scores match with the results of Cooper et. al.(2006).DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples(cont.)l The result file including detail values for the efficiency scoreand reference set (l(lambda option)DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples(cont.) Example 2: Weapons system construction efficiencyl two inputs, three outputs, and 10 DMUs※ Data from JAA frfr(( Jane's Armour and Artillery)l The inputs are¡ Combat weight¡ Heightl The outputs are¡ PowerPower--toto--weight ratio¡ Max road speed¡ Main armament diameterDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples(cont.)l The data file including input and output variablesiotype varnameM48A3 M60 T-62 Leopard1A4 T-72 Leopard2 M1 K1 Leclerc T-90input Combat weight46 40 4140 41 55.2 54.5 51 54 46.5input Height3.124 3.27 3.332.76 2.19 2.64 2.44 2.24 2.46 2.2output Power-to-weight ratio 16 16.2 14.519.7 19 27 27 23.5 27 17output Max road speed48 48 5064 80 72 72.4 65 71 60output Main armament diameter 90 105 115105 125 120 105 105 120 125※ The input and output variables are saved in files "t4 2.csv"DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples(cont.) deadea,, data(ata(t4 2t4 2)) ioiotypetype((outputoutput)) modmodel(el(ccrccr)) lambdaDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples(cont.)l The result file including the efficiency score and reference setDEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
4. Stata/DEA Examples(cont.)l The result file including detail values for the efficiencyscore and reference set (l(lambda option)DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
5. DEA Frontiers in Stata? The Stata/DEAStata/DEA program is a new application in StataStata. DEA is a prevalent and powerful managerial tool for measuring the performance. The Stata/DEAStata/DEA program will provide Stata users with several opportunities :l No extra cost to access DEAl Flexible DEA model extension and developmentl A powerful managerial tool as well as data management, statistical analysis, andoptimization procedures The Stata/DEAStata/DEA program report's files can directly feed to other Stata routines forfurther analysis. Further Extensions to 2nd Stage Regression Analysis, DGP of DEA, StatisticalInferences of DEA, Case Specific DEA Models, and more are possible.DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
6. References Lee, C., & Ji, Y. (2009). “Data Envelopment Analysis in Stata”, underreview by the Stata Journal. Cooper, W. W., Seiford, L. M., & Tone, A. (2006). Introduction to DataEnvelopment Analysis and Its Uses, Springer Science Business Media. Charnes, A., Cooper, W. W., & Rhodes, E. (1981). "Evaluating Programand Managerial Efficiency: An Application of Data EnvelopmentAnalysis to Program Follow Through." Management Science, Vol. 27.,pp. 668668-697. Banker, R. D., Charnes, A., & Coopers, A. A. (1984). “Some Models forEstimating Technical and Scale Inefficiencies in Data EnvelopmentAnalysis”, Management Science Vol. 30, No. 9, pp.1078pp.1078-1092.DEA in Stata PDF created with pdfFactory Pro trial version www.pdffactory.com
DEA in Stata Characteristics of DEA lNo o aassumption about Inputnput--Output Function lNo limits to the number of inputs and outputs lNot required to weight restrictions lProvide reference sets for benchmarking lProvide useful information for inputnput--output mix decision ln n times computations for n DMUs o nput nput n 2. The Basic
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STATA/IC, STATA/SE, and STATA/MP. The difference is basically in terms of the number of variables STATA can handle and the speed at which information is processed. Most users will probably work with the “Intercooled” (IC) version. STATA runs on the Windows (2000, 2003, XP, Vista, Server 2008, or Windows 7), Mac, and Unix computers platform.
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