THE PRODUCTIVE EFFICIENCY OF FEDERAL INSTITUTIONS OF BRAZILIAN HIGHER EDUCATION

THE PRODUCTIVE EFFICIENCY OF FEDERAL INSTITUTIONS OF BRAZILIAN HIGHER EDUCATION ABSTRACT This paper discusses an important issue in the framework of Brazilian higher education, with an emphasis on Federal Institutions of Higher Education (IFES) We examine the efficiency frontier of federal public higher education through a non-parametric method called Data Envelopment Analysis (DEA) Dynamic frontier was estimated and the Malmquist index was evaluated, determining productivity through panels Analysis used several educational administrative indicators (inputs and outputs of the productive process) provided by the institutions themselves between 2004 and 2008 The total number of IFES (49) was divided into two subsets – group A composed of 28 institutions and group B containing 21 – in order to minimize heterogeneity in the sector Estimation results for efficiency of dynamic models suggest as frontier levels with elevated efficiency scores On the other hand, productivity variations of IFES in each panel show decreased productivity for most facilities These findings demonstrate that although frontiers exhibit low inefficiency scores, the technical efficiency frontier moved to a lower level This indicates a possible deterioration of the educational product over time Keywords: IFES DEA Efficiency Frontier Higher Education RESUMO Este trabalho discute um importante ponto que faz parte arcabouỗo da educaỗóo superior brasileira, tendo como ờnfase as Instituiỗừes Federais de Ensino Superior (IFES) Examina a fronteira de eficiờncia da educaỗóo superior pỳblica federal atravộs de uma metodologia não paramétrica denominada Análise Envoltória de Dados (DEA) Foi estimada a fronteira dinâmica, bem como foi avaliado o índice de Malmquist, que verifica a produtividade atravộs de painộis A mensuraỗóo foi realizada através de alguns indicadores educacionais de gestão (os inputs e os outputs processo produtivo) fornecidos pelas próprias instituiỗừes, cujo perớodo se estendeu de 2004 a 2008 O conjunto total das IFES (49) foi dividido em dois subconjuntos o grupo A contendo 28 instituiỗừes e o grupo B contendo 21 – a fim de minimizar a heterogeneidade existente no setor Os resultados da estimaỗóo modelo dinõmico sugerem fronteiras com níveis de scores de eficiência elevados Por outro lado, a variaỗóo de produtividade das IFES em cada painel mostrou queda de produtividade para a maioria das IFES Esses resultados mostram que apesar das fronteiras apresentarem baixos scores de ineficiência, houve um deslocamento da fronteira técnica de eficiência para um nớvel inferior, indicando que pode estar havendo deterioraỗóo produto educacional ao longo tempo Palavras-chaves: IFES DEA Fronteira de eficiờncia Educaỗóo Superior Jel Codes: CO2 I23 2 INTRODUCTION Performance of Institutions of Higher Education (IFES) has been the subject of growing attention in recent years Several studies address this matter at both national and international levels Some of these apply statistical tools to measure performance, while others use non-statistical instruments These investigations use “performance indicators” (such as the proportion of students in a specific year and the cost per student) to determine efficiency in public or private IFES In order to measure their performance, IFES are treated as productive units the same as any other, that is, they require inputs to attain a certain level of output In addition, peculiarities inherent to the educational sector are considered when calculating efficiency Thus, a performance ranking is compiled to determine the optimal allocation of resources to IFES The educational sector is substantially varied It is therefore necessary to use extreme care in constructing “performance indicators” for efficiency analysis in IFES Two issues are of primary importance: first, institutions operate under different conditions and environments, which are often not simply explained Second, the educational production sector contains many inputs and outputs The question of how public resources should be allocated in higher education has led most research to focus on measuring the efficiency of public IFES In recent years several studies have aimed to measure efficiency levels and rank institutions accordingly Furthermore, every country has its own financing and resource allocation structures, which serve as a basis for assessing efficiency in higher education In Brazil, the public sector has Federal, State and Municipal faculties and universities, while private institutions may be profit or non-profit organizations According to the higher education census carried out by the Ministry of Education (MEC) in 2009, there are 2,314 IES in Brazil Distribution by administrative category indicates 90% are private institutions and 10% are public Of the latter, 38% are federal, 34% state and 28% are municipal institutions Federal Institutions of Higher Education (IFES) are mostly financed by the federal government through combined taxes established in Article 212 of the 1988 Federal Constitution Institutions also receive funds from parliamentary amendments, contracts with public and private organizations, as well as by their own funding Government resource allocation is carried out by the Secretary of Higher Education (SESu)/MEC through a resource allocation matrix aimed at favoring IFES efficiency The most common methods used for efficiency measurement in the educational field are statistical and non-statistical techniques Statistical methods are based on Ordinary Least Squares (OLS) regression for analysis of the stochastic frontier Linear programming (LP) techniques are applied to equate relations between inputs and outputs Data Envelopment Analysis (DEA) is most adequate for efficiency studies using these techniques (LP) DEA has been increasingly used to estimate efficiency in education This is primarily because the field is composed of multiple inputs and outputs, facilitating DEA frontier estimation In addition, the non-necessity of the production function does not cause model misspecification errors in estimation Thus, the aim of this study is to estimate the efficiency frontier of federal public education to obtain the degree of productive efficiency for each federal higher Education institution (IFES), and then compile a ranking from the most to least efficient LITERATURE REVIEW ON USING DEA METHODOLOGY TO ESTIMATION EFFICIENCY IN HIGHER EDUCATION The international literature contains several studies on the efficiency of public universities in many countries, which mostly apply Data Envelopment Analysis (DEA) Ahn, Charnes & Cooper (1988), compared US higher Education institutions aimed at research using three input and three output factors Public universities achieved greater levels of efficiency than private facilities In a separate study, Rhodes & Southwick (1986), contrast the efficiency of 96 public and 54 private universities in the United States (US), applying the DEA model with five input and six output factors Results indicated that efficiency in private institutions at that time was higher than in public facilities Breu & Raab (1994) used Data Envelopment Analysis (DEA) to assess efficiency in 25 of the best US universities Their findings confirm DEA as an appropriate method for measuring efficiency in higher Education In addition, an inverse relationship was found between the pre-established ranking and that obtained with DEA SARRICO et al (1997) evaluated 90 higher Education facilities in the United Kingdom, in three categories: (i) government/society; (ii) institutions: departments, staff and students, and (iii) potential students The authors used DEA methodology to determine efficiency levels and compared these with a local ranking, the Times League Table Results achieved through DEA indicated better efficiency outcomes Førsund & Kalhagen (1999) investigated efficiency in Norwegian regional faculties in 1994, 1995 and 1996 Some institutions were found to be efficient with regard to education services, while inefficient faculties showed significant variation between inefficiency levels Additionally, productivity improved during the years studied indicating a positive productivity effect, moving the efficiency frontier to a higher level Thurlow & Field (2003) analyzed the technical efficiency of 45 British universities from 1980/81 to 1992/93 This period was chosen primarily because it represents a time of substantial changes in public financing The study recorded a significant increase in technical efficiency during this time, more pronounced between 1987/88 and 1990/91 Research by Afonso and Santos (2005) estimated efficiency of public universities in Portugal in 2003 Inputs were compiled from the number of teachers and university expenses and outputs were based on graduation rates and the number of doctorate theses Findings indicate a mean efficiency index of approximately 55.3% and 67.8%, respectively among facilities investigated Abbot and Doucouliagos (2003) studied the technical efficiency scale of Australian universities using DEA Results point to performance homogeneity for the whole university system, indicating that universities in that country operate at high efficiency levels However, the authors confirm a possibility for improved efficiency in some universities Joumady & Ris (2004) applied DEA methodology to measure efficiency differences in a group of 210 higher Education institutions from European countries, using a sample of students graduated for more than three years Three models were assessed: the first focused on the competence of educational services; the second (adjustment model) estimated Education efficiency after graduation, and the third (global model) was designed to investigate the university’s overall performance Outcomes were substantially different for all three models, that is, efficiency varied in accordance with the model used In Brazil, analytical efficiency studies of federal universities have intensified in the last decade This is mainly in light of pressure from organizations linked to higher Education through the Ministry of Education to evaluate the scope of this efficiency and its results for society as a whole Ramos and Souza (1997) analyzed the performance of federal higher education facilities using DEA and found that about 39.1% of institutions evaluated achieved maximum efficiency, while 6.5% were among the least efficient In comparison with studies from other countries, the author’s results demonstrate low efficiency during this period in public IFES Corbucci (2000) assessed MEC expenditure on federal higher Education institutions, establishing efficiency and productivity indicators between 1995 and 1998 Outcomes confirm that despite a reduction in operating costs for institutions analyzed, an increase was recorded in the number of stricto sensu graduates and post-graduates, as well as higher scientific production This indicates efficiency and productivity improvements in these institutions Faỗanha and Marinho (2001) investigated performance differences between IFES in large regions of Brazil from 1995 to 1998, using DEA to gauge efficiency Measurement also considered IFES distribution into federal, state and municipal facilities In relation to graduate teaching, findings demonstrate that private and municipal IFES achieved higher relative efficiency than state and federal facilities during the period studied However, in Postgraduate teaching, results show asymmetry in relative efficiency between IFES studied In his doctorate thesis, Belloni (2001) evaluated the productive efficiency performance of 33 Brazilian federal universities using DEA methodology In contrast to results obtained by Ramos and Souza (1997), only of the 33 federal universities investigated were considered technically efficient The author determined that constant returns to scale did not apply in the case of public federal universities Estimates were therefore performed according to the DEA-BCC model, with variable returns to scale Finally, Oliveira and Turrioni (2005) assessed the relative efficiency of Federal Institutions of Higher Education (IFES) Inputs and outputs were constructed using indicators from the Federal Accounting Tribunal (TCU) The CCR – DEA model considered constant returns to scale A total of 19 federal higher education institutions were evaluated, of which were found to be technically inefficient The results of Ramos and Souza (1997) and Belloni (2001) are in contrast to those of Oliveira and Turrioni (2005), possibly owing to the application of a model with constant returns to scale METHODOLOGY PROCEDURES 3.1 Data Envelopment Analysis - DEA DEA methodology (Data Envelopment Analysis) was developed by Charnes, Cooper and Rhodes (1978) This type of analysis generalizes the measurements of Dantzig (1951) and Farrel (1957), aiming to measure the productive efficiency of production units with multiple outputs and inputs in order to obtain an indicator satisfying Koopmans concept of efficiency DEA estimation is performed non-parametrically, measuring the efficiency of decision making units (DMU) observed and comparing them among themselves to achieve a relative efficiency indicator This method uses DMUs as the best practices observed to construct an empirical production frontier known as an efficient frontier 3.1.1 SBM DEA The slack-based DEA model (SBM) was introduced by Tone (1997, 2001) and contains two assumptions: i Measurement is constant regarding the measurement unit of each input and output item ii Measurement decreases monotonically at each input and output slack In order to estimate DMU efficiency with the SBM model, the following fractionated problem is defined for (PL) at λ , s − , s + ( SBM ) m − ∑i =1 si xio m ρ= λ ,s− ,s+ s − ∑i =1 s i+ y ro s subjecto to x o = Xλ + s − 1− (1) y o = Yλ − s + λ ≥ 0, s − ≥ 0, s + ≥ − The model assumes that X ≥ If xio = , then the expression si xio is excluded However, if yio ≤ , the positive number is very small so that expression si+ yro is disadvantageous The ρ value of the objective function satisfies the first assumption since the numerator and denominator are measured in the same unit for each expression of this function In addition, the objective − + function value falls following increases at si and si when other terms remain constant; due to the second assumption Furthermore, ≤ ρ ≤ The SMB model can be defined by input oriented, output oriented and non-oriented structures Only the output oriented structure will be dealt with here, defined by the equation below: ( SBM − O ) ρ O* = min+ λ ,s subjecto to 1 s + ∑ s r y ro s i =1 x o = Xλ 1+ ( 2) y o = Yλ − s + λ ≥ 0, s + ≥ 3.1.2 Panel data DEA: The Slack-Based Malmquist Index In the case of Panel Data, linear programming DEA methodology may be applied ((input-oriented or output-oriented) to calculate the Malmquist Index The aim is to measure the productivity variation and decomposition of this productive change in the technical and technical efficiency alteration A more detailed examination of the Malmquist productivity index is given in the equation below: ( ( ) ) ( ( ) ) δ ( x , y ) δ ( x , y )  MI =  o o ⋅ o o   δ ( xo , y o ) δ ( xo , y o )  ( 3) ( ) ( ) ( ) ( ) 1 2 2 Where, MI is composed of four terms: δ ( xo , yo ) , δ ( xo , y o ) , δ ( xo , y o ) and δ ( xo , y o ) The first two are related to measurement in the same time period with t = or t = , while the latter two are used for intertemporal comparison Thus, if MI > technical efficiency improved; MI = signifies no change in production technology; MI < shows a gain in production technology The output oriented SMB Malmquist index is defined by the following equation: [ SBM − O] ( ) m   δ s ( x o , y o ) t = 1 + ∑ψ i  ψ ,λ m i =1   subjecto to x ot ≥ X s λ n (1 + ψ i ) y iot = ∑ y sij λ j ( i = 1, , q ) ( 4) j=1 L ≤ eλ ≤ U λ ≥ 0,ψ ≥ 3.1.3 Dynamic SBM DEA Measuring intertemporal efficiency through DEA has been increasingly studied in recent years The first approach was window analysis (Klopp, 1985), followed by Fare et al (1994) who incorporated the Malmquist Index in DEA structure Sengupta (1995) and Fare and Grosspkof (1996) were the first to develop the dynamic DEA model Sengupta determined the dynamic efficiency of Farrell’s structure by varying capital input in relation to input price changes over time In contrast, Fare and Grosspkof proposed a dynamic production frontier using an intermediate output that interconnects production processes for each year Figure Structure of Dynamic DEA Source: Dynamic DEA: A slacks-based measure approach Based on the Fare and Grosspkof model, Tsutsui and Tone (2008) employed a dynamic DEA structure using carry-over variables to estimate the production frontier over several time periods Additionally, frontier estimation is carried out with a non-radial model, that is, a slack-based model known as the Dynamic SBM (DSBM) Its structure is shown in the figure above The distinguishing factor separating Dynamic DEA from other DEA forms is the existence of a transition connecting the periods over time Carry-overs, called links, can be categorized as: Desirable (good) – desirable links are treated as outputs and the value of the link is the restricted access to not less than that observed Comparative scarcity of these links is considered inefficiency; for instance, profit Undesirable (bad) – undesirable links are considered inputs Their value is limited and cannot exceed recorded value Comparative excess of these links is seen as inefficiency; for example, loss and default Discretionary (free) – this link can be freely manipulated by the DMU and its value may increase or decrease from that observed Deviance in relation to actual value is not directly reflected in efficiency evaluation, although continuity between the two periods explained in the next period exerts an indirect effect on the inefficiency score Non-discretionary (fix) – in this case, the link is beyond DMU control, and its value fixed at an observed level This link also indirectly affects the efficiency score through the continuity between the two time periods 3.1.3.1 Production Possibility Set Let n DMUs ( j = 1, , n ) during T time periods ( t = 1, , T ) , where each time period has m inputs ( i = 1, , m) , p non-discretionary (fixed) inputs ( i = 1, , p ) , s outputs ( i = 1, , s ) andd r non-discretionary (fixed) outputs ( i = 1, , r ) In addition, (discretionary) inputs xijt ( i = 1, m ) , (non-discretionary) inputs xijtfixo ( i = 1, p ) , (discretionary) outputs yijt ( i = 1, s ) and non-discretionary outputs yijtfixo ( i = 1, r ) represent DMU values j and time period t respectively Carry-overs are symbolized into four categories z good , z free , z bad , z fix In order to identify time period (t), DMU (j) and item (i), for example, the notation zitfree : free ( i = 1, , free; j = 1, n; t = 1, , T ) , denoting all link free values observed until time period T, is used { } { } { } { } , {z } , {z } fixo fixo good bad Thus, the production possibility set { xit } , xit , { yit } , yit , zit , zit defined by: free it fix it is n xit ≥ ∑ xijt λtj , j =1 n xitfixo = ∑ xijtfixo λtj , j =1 n yit ≤ ∑ yijt λtj , j =1 n yitfixo = ∑ yijtfixo λtj , j =1 n zitgood ≤ ∑ z ijtgood λtj , j =1 n ( i = 1, , m; t = 1, , T ) ( i = 1, , p; t = 1, , T ) ( i = 1, , s; t = 1, , T ) ( i = 1, , r; t = 1, , T ) ( i = 1, , ngood ; t = 1, , T ) zitbad ≥ ∑ zijtbad λtj , ( i = 1, , nbad ; = 1, , T ) zitfree : free , ( i = 1, , nfree; t = 1, , T ) j =1 n zitfix ≥ ∑ zijtfix λtj , ( i = 1, , nfix; t = 1, , T ) λtj ≥ , ( j = 1, , n; t = 1, , T ) j =1 n ∑λ j =1 t j = 1, ( 5) ( t = 1, , T ) t n Where λ j ∈ ℜ ( t = 1, , T ) is the intensity vector for time period t, and ngood , nfree , nfix are the bad, free and fix links, respectively The last restriction corresponds to the variable returns to scale hypothesis In the absence of this restriction, a model with constant returns to scale is proposed To the right of the above equations, variables assume positive values; on the left are the vector intensity variables The continuity of carry-over links between time period t and t+1 is guaranteed by the following condition: n n j =1 j =1 ∑ zijtα λtj = ∑ zijtα λtj+1 ( ∀i; t = 1, , T − 1) ( 6) Where α is the standard symbol for good, bad, free and fix links This restriction is essential to the dynamic model as it connects activities between time periods t and t+1 using these equation for production, we can express the DMU o (o = 1, , n) as follows: n xiot = ∑ xijt λtj + sit− , j =1 n xiotfixo = ∑ xijtfixo λtj , j =1 n yiot ≤ ∑ yijt λtj − sit+ , j =1 n yiotfixo = ∑ xijtfixo λtj , j =1 n good ziot = ∑ zijtgood λtj − sitgood , j =1 ( i = 1, , m; t = 1, , T ) ( i = 1, , m; t = 1, , T ) ( i = 1, , s; t = 1, , T ) ( i = 1, , r; t = 1, , T ) ( i = 1, , ngood ; t = 1, , T ) n bad ziot = ∑ zijtbad λtj + sitbad , j =1 n ziotfree = ∑ zijtfree λtj + sitfree , j =1 n ziotfix = ∑ zijtfix λtj , ∑λ j =1 t j ( i = 1, , nfree; t = 1, , T ) ( i = 1, , nfix; t = 1, , T ) j =1 n ( i = 1, , nbad ; = 1, , T ) ( t = 1, , T ) = 1, ( 7) λtj ≥ , sit− ≥ , sit+ ≥ , sitgood ≥ , sitbad ≥ e sitfree : free ( ∀i, t ) − + good bad free Where sit , sit , sit , sit e sit are the slack variables denoting input excess, output deficit, link deficit, link excess and link deviance, respectively 3.1.3.2 Objective Function and Efficiency { } { } { } { } { } { } − + good bad free Global efficiency evaluation of a DMU o (o = 1, , n) having λt , st , st , st , st , st can be done through structures input oriented, output oriented and non-oriented variables We will only address output orientation, given the definition of the research model Output oriented global efficiency τ o* with good link is represented by:  s + + ngood sitgood 1 T t  ∑ wi sit + ∑ good = max w +  ∑ T t =1  s + ngood  i =1 τ o* i =1 z iot    ( 8) + Subject to equations ( 6) and ( ) , where wi is the weight for i and satisfies condition: s ∑w i =1 + i ( 9) =s This objective function is an extension of the output oriented SBM model It deals with output inefficiencies including the link (good), which functions as an essential evaluation goal Undesirable inefficiency links are also calculated within the objective function, in the same manner as output inefficiencies However, undesirable links are not outputs; they only connect the two consecutive time periods as per equation ( 6) In equation ( 8) , each period within the brackets refers to the efficiency of period t measured by slacks relative to the outputs and link, equal to the unit when all are equivalent to zero In addition, the right side of the equation ( 8) is the weighted average of efficiency gains over time, required to be greater than or equal to Thus, once global efficiency is defined, by reciprocity, output global efficiency will be between and −* +* good * bad * free* Using the optimal solution λt* , st , st , st , st , st , defines dynamic efficiency { } { } { } { } { } { } output oriented τ ot as: * τ ot* = 1+ good *  s + +*  ngood s  ∑i =1 wi siot + ∑i =1 iotgood  , s + ngood  z iot  ( t = 1, , T ) (10) ( ) * Therefore, output oriented global efficiency during period τ ot ( ) is a harmonious mean for efficiencies of periods τ ot , demonstrated as follows: 1 = * τ ot T wt ∑ * t =1 τ ot T (11) EFFICIENCY MEASUREMENT AND RESULT ANALYSIS 4.1 DMU Selection A set of 49 institutions are considered in order to calculate efficiency in federal public higher education IFES not included in the estimation are: Federal University Foundation of São Francisco, Federal University of Recôncavo da Bahia, Federal University Foundation ABC, Federal University Foundation of Pampa, Technological Federal University of Paraná, Federal University Foundation of Grande Dourados These were not included due to insufficient temporal dimension with the period analyzed Federal Institutions for Higher Education (IFES) demonstrate a high degree of heterogeneity, making calculation of the production frontier complex Irrespective of the approach (statistical or nonstatistical), estimated models should incorporate the differences between institutions These variances can be determined from various standpoints (resources received, number of enrolled students, courses, among others) However, a large university with many areas of knowledge in both research and outreach programs demonstrates a significant difference in this sector when compared with institutions focused largely on graduation Groups placed in the first phase were determined by analyzing three indicators The first is the total number of graduate students enrolled The final two indicators are detailed in statistics compiled by the National Council for Scientific and Technological Development (CNPq): i) the faculty to research ratio, and ii) total investment in scholarships and research These two groups are estimated as follows: Table Reference Group of Institutions GROUP I University-Code University-Code 01 UFRJ 15 UFF 02 UFRGS 16 UFPB 03 UFMG 17 UFLA 04 UFPE 18 UFG 05 UFSC 19 UFSM 06 UNB 20 UFAM 07 UFC 21 UFRPE 08 UFV 22 UFU 09 UFPR 23 UFAL 10 UFBA 24 FURG 11 UFSCAR 25 UFPEL 12 UFPA 26 UFES 13 UNIFESP 27 UFMT 14 UFRN 28 UFMT Source: MEC/INEP/DEED Preparation: Author GROUP II University-Code University-Code 01 UFRRJ 15 UFERSA 02 UFMS 16 UFTM 03 UFS 17 UFVJM 04 UFMA 18 UFSJ 05 UFPI 19 UNIFAP 06 UFT 20 UNIFAL 07 UFOP 21 UFCSPA 08 UNIR 09 UFJF 10 UFRA 11 UNIFEI 12 UFAC 13 UFRR 14 UNI-RIO 10 4.2 Model Definition The concept of efficiency is related to the use and allocation of resources Thus, in order to obtain reliable estimates in efficiency calculation, it is essential to use indicators that consistently represent the characteristics of the educational production function Outputs and inputs selected to measure the efficiency of Federal Institutions for Higher Education (IFES) in the present study were based on the main outputs and inputs used in various studies in recent decades, as well as the reality of the Brazilian federal higher education system These are as follows: Output Educational outputs can be defined as a function of services offered by Institutions of Higher Education (IFES) The following variables were therefore defined as outputs for this study:  Graduate/Undergraduate students (GSR)  CAPES/MEC Concept for Postgraduation (CAPES - The Brazilian Federal Agency for the Support and Evaluation of Pós-Graduate Education) Input Educational inputs may be defined as variables enabling services to be offered by the IFES In the present study, the following variables were defined as inputs:  Curent cost/student equivalent  Full-time student/teacher equivalent  Full-time student/staff equivalent  Teacher Qualification Index Once DMUs are defined and the model selected, the period of analysis for efficiency measurement is determined Criteria for establishing the period were based on the availability of data for indicators used in this research As such, the analysis period chosen is 2004 to 2008 Variables used in this study were primarily obtained from the following organizations:  The Ministry of Education (MEC), through the website:  National Institute of educational Studies and Research (INEP), on the website 4.3 Efficiency Estimation and Results Analysis The model aimed to measure efficiency considering several indicators related to IFES administration Estimations were performed using DEA Solver Professional software version 7.0 In this model, two analyses were conducted The first sought more robust results with regard to IFES homogeneity, estimating the efficiency frontier of IFES in two groups: Group A (IFES considered large); Group B (IFES viewed as small) The second estimated the Panel data DEA • Estimation Group A In Dynamic DEA estimation, a discretionary carry-over variable was introduced to link the time periods Each term in the estimation represents a period with the inclusion of a link, that is, term refers to 2004 including the carry-over, with the same procedure for the other terms Table below shows findings for the period 2004=>2008 Table IFES Group A 11 2004=>2008 12 Rank IFES Overall Score UFAM 1 UFBA 1 UFCG 1 UFF 1 UFLA 1 UFMG 1 UFMT 1 UFPA 1 UFPB 1 UFPEL 1 UFRGS 1 UFRJ 1 UFRPE 1 UFSCAR 1 UFSM 1 UFU 1 UFV 1 UNIFESP 19 UFRN 0,92 20 UFPE 0,91 21 UFC 0,88 22 UFES 0,88 23 FURG 0,87 24 UFSC 0,86 25 UFAL 0,86 26 UFPR 0,85 27 UFG 0,85 28 UNB 0,84 Source: Estimates of the research Preparation: Author Term1 1 1 1 1 1 1 1 1 1 0,93 0,84 0,82 0,91 0,89 0,87 0,84 0,79 0,87 Term2 1 1 1 1 1 1 1 1 1 0,94 0,90 0,81 0,88 0,90 0,83 1 0,79 0,82 Term3 1 1 1 1 1 1 1 1 1 0,99 0,86 0,94 0,90 0,83 0,94 0,83 0,90 0,82 Term4 1 1 1 1 1 1 1 1 1 0,87 0,91 0,85 0,83 0,89 0,67 0,78 0,87 0,84 Term5 1 1 1 1 1 1 1 1 1 0,89 0,91 0,84 0,84 0,90 0,81 0,83 0,91 0,84 In dynamic analysis of the frontier during the entire intertemporal trajectory, around 64% of IFES were located on the efficiency frontier, while 22% were below it and 14% were both on and below the efficiency frontier When analyzing the dynamic frontier over the whole intertemporal trajectory 2004=>2008, about 64% of IFES were on the efficiency frontier, making them part of the efficient set, while 36% were below it and therefore placed in the inefficient group In addition, the following 10 institutions were not part of the dynamic frontier, making up the inefficient set: FURG, UFAL, UFC, UFES, UFG, UFPE, UFPR, UFRN, UFSC and UNB The UNB recorded the highest inefficiency level during the intertemporal trajectory with an overall score of 0.84 The advantage of obtaining an intertemporal frontier is the inclusion of input and output behavior in efficiency scores during the time period analyzed, generating a more robust efficiency frontier Another fact for analysis is that the dynamic efficiency frontier is situated above the efficiency score at 0.80 This indicates that IFES from group A have a relatively high frontier in relation to the overall score Finally, the graph below shows the technical dynamic efficiency frontier for this set of IFES Figure IFES Group A: Frontier Dynamics 13 Source: Estimates of the research Preparation: Author Following dynamic analysis of efficiency frontiers, we examined the decomposition of productivity change, technical and technical efficiency alterations over time It is therefore necessary to consider panel analysis The table below displays the panel obtained during time period analysis Table Decomposition of the Malmquist Index (2004=>2008) IFES FURG UFAL UFAM UFBA UFC UFCG UFES UFF UFG UFLA UFMG UFMT UFPA UFPB UFPE UFPEL UFPR UFRGS UFRJ UFRN UFRPE UFSC UFSCA R UFSM Índex Change Pure Efficiency Índex Change Scale Efficiency Índex of Malmquist 0,92 0,77 1 1,09 0,91 1,09 1,15 0,87 1,04 1 1,26 1,17 0,98 1,06 0,98 0,95 1,01 0,91 0,97 0,95 0,87 0,87 0,91 0,94 0,86 0,98 0,98 1,02 0,82 0,85 0,90 0,87 0,89 0,99 0,94 0,91 0,84 0,74 0,95 0,95 0,87 0,83 1,02 0,99 0,85 1,02 1,02 0,82 1,07 1,05 0,85 0,95 0,97 0,89 0,92 0,97 0,97 0,95 0,95 14 UFU 0,96 UFV 1,04 UNB 0,98 UNIFE SP Source: Estimates of the research Preparation: Author 0,98 0,94 0,94 0,94 0,98 0,92 0,98 0,98 In this panel (2004=>2008), UFAM, UFMT and UFRPE maintained their constant productivity with, with an index equal to the unit UFF, UFMG, UFPE and UFPEL increased their productivity during the panel, with UFPE achieving the best index (1.09) In relation to the 20 IFES with reduced productivity, UFAL recorded the worst result, with an index of 0.74 Decomposition of the Malmquist Index in the above table demonstrates that the loss of productivity in Group A IFES is due to the effect of scale efficiency change, known as the displacement effect Approximately 82% of IFES obtained a scale efficiency change index lower than Consequently, the production frontier shifted to a lower level during the panel (2004=>2008) • Estimation Group B The dynamic efficiency frontier (DSBM) was then determined in order to obtain more robust efficiency frontier scores for IFES in group B Table below shows findings for the period 2004=>2008 Table IFES Grupo B Ran DMU Overall Score UFAC 1 UFCSPA 1 UFERSA 1 UFJF 1 UFMS 1 UFPI 1 UFRA 1 UFRR 1 UFRRJ 1 UFSE 1 UFT 1 UFTM 1 UFVJM 1 UNIFAL 1 UNIFAP 1 UNIRIO 17 UFMA 0,9 18 UFOP 0,9 19 UNIFEI 0,9 20 UFSJ 0,8 21 UNIR 0,8 Source: Estimates of the research Preparation: Author 2004=>2008 Term1 Term2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0,9 0, 1 0,6 0, 0,7 0, Term3 1 1 1 1 1 1 1 1 0, 0, 0, Term4 1 1 1 1 1 1 1 1 0, 0, 0, Term5 1 1 1 1 1 1 1 1 0,97 0,80 0,78 A discretionary carry-over variable was once again introduced in Dynamic DEA analysis to link the time periods Intertemporal trajectory of the efficiency frontier indicated that about 76% of IFES were on the efficiency frontier during the entire trajectory, 24% were both on and below the efficiency frontier during the entire trajectory In analysis of overall score results, universities were not part of the dynamic frontier: UFMA, UNIFEI, and UNIR, with UNIR registering the highest degree of intertemporal inefficiency with an overall score of 0.78 15 The graph below illustrates the dynamic frontier of the overall score Only 3IFES are below the frontier and outside of the efficient group Another point to be analyzed is that the dynamic efficiency frontier is above the efficiency score of 0.78, indicating that IFES in group B have a relatively high frontier in relation to the overall score Figure IFES Group B: Frontier Dynamics Source: Estimates of the research Preparation: Author In order to examine the dynamic productivity, a panel analysis was performed using the Malmquist Index The following table displays the panels obtained during periods evaluated Tabela Decomposition of the Malmquist Index (2004=>2008) IFES UFAC UFCSPA UFERSA UFJF UFMA UFMS UFOP UFPI UFRA UFRR UFRRJ UFSE UFSJ UFT UFTM UFVJM UNIFAL UNIFAP UNIFEI UNIR Índex Change Pure Efficiency Índex Change Scale Efficiency 1,20 0,93 0,84 0,86 0,95 2,63 1,12 1,35 1,16 0,77 1,22 1,61 1 1 0,97 1,03 Índex of Malmquist 0,77 1,12 0,93 0,88 0,54 0,65 0,64 0,95 0,88 0,93 0,86 0,96 0,88 0,88 0,91 0,95 0,59 0,99 0,81 0,93 1,04 0,86 0,83 1,43 0,73 0,86 1,11 0,88 0,72 1,54 0,88 0,88 0,91 0,95 0,59 0,96 0,84 16 UNIRIO 0,94 Source: Estimates of the research Preparation: Author 0,83 The panel (2004=>2008) indicates that IFES UFERSA, UFSE and UNIRIO maintained constant productivity with an index equal to the unit Only UFCSPA, UFMS, UFRA, UFRRJ and UFSJ increased their productivity during the panel, with UFSJ achieving the best index of 1.54 The total amount of IFES with reduced productivity was high; approximately 76% were from group B with UNIFAP recording the lowest result of 0.59 Decomposition of the Malmquist Index in the table above demonstrates that, as in group A IFES, loss of productivity for those in group B was mainly due to the effect of scale efficiency change Approximately 91% of institutions obtained a scale efficiency change index of less than Consequently, displacement in the production frontier to a lower level occurred during the panel (2004=>2008) CONCLUSIONS The present study sought to analyze Brazilian Federal Institutions for Higher Education (IFES) using a non-parametric method to measure their technical efficiency A model was applied to determine the maximum educational product obtained by each institution investigated, given that the product is a function of educational resources This study addresses the educational production function, demonstrating its specificity and the indicators that may be used to compile educational inputs and outputs The DEA methodology is then defined in order to carry out technical efficiency estimations for IFES A literature review was also performed regarding DEA application in education economics After consolidation of methodological procedures, IFES in the federal public higher education sector were defined to allow for efficiency frontier estimations based on the proposed model Estimations were therefore made based on a total set of IFES comprising 49 institutions, divided into two subsets (group A – 28 institutions; group B – 21 institutions) to minimize heterogeneity in the sector Results of efficiency frontier estimations for IFES in the first subset (group A) demonstrated that, Estimation of the dynamic frontier indicated that 64% of IFES were on the efficiency frontier, whereas about 36% were placed below it Moreover, the introduction of the student equivalent carry-over proved to be a good proxy to determine the increase or decrease in productivity during the period analyzed With regard to the dynamic frontier IFES group B, a mean of 76% universities were on the efficiency frontier for the entire intertemporal trajectory, while about 24% were under it As in group A, the Introducing the student equivalent carry-over proved to be a good proxy to determine the increase or decrease in productivity during the period analyzed It is important to note that the intertemporal efficiency frontiers of the federal public higher education sector for IFES in groups A and B can be considered plausible for both the current financial structure and the actual resource allocation model for these institutions On the other hand, the Malmquist Productivity Index showed reduced productivity for most facilities Examining the decomposition of this index confirms displacement of the frontier to a lower level This suggests that the technical efficiency frontier of federal public higher education decreased to a lesser level during the period analyzed This situation demonstrates that the educational product of IFES has deteriorated over time, in agreement with findings when analyzing the evolution of resources allocated to IFES That is, a reduction in funds for IFES may compromise performance with respect to their educational product In addition, some nationally significant institutions did not achieve efficiency scores compatible with the resources they received However, in order for these results to corroborate the true situation in federal public higher education, it is necessary to analyze the outcome for each IFES separately and subsequently make observations regarding causes and inefficiencies relative to productivity loss 17 In conclusion, we hope that the academy and institutions examined here, as well as SESu/MEC and ANDIFES (The National Association of Directors of Federal Higher Education Institutions) examine these results with a view to their use as an aid in discussing the politicies periodically adopted for the sector REFERENCES ABBOT, M; DOUCOULIAGOS, C The Efficiency of Australian Universities a Data Envelopment Analysis Economics of Education Review, v 22, p 89–97, 2003 AFONSO, A; SANTOS, M Students and Teachers A DEA Approach to the Relative Efficiency of Portuguese Public Universities Technical University of Lisbon, series Working Papers n 2005/07, 2004 AHN, T.; CHARNES, A.; COOPER, W Some statistical and DEA evaluations of relative efficiencies of public and private institutions of higher learning Socio-Economic Planning Sciences, v 22, n 6, p 259-269, 1988 BELLONI, J A Uma Metodologia de Avaliaỗóo da Eficiờncia Produtiva de Universidades Federais Brasileiras Tese (Engenharia de Produỗóo), Programa de Pús-Graduaỗóo em Engenharia de Produỗóo, Universidade Federal de Santa Catarina, 2000 BRASIL República Federativa Brasil Constituiỗóo da Repỳblica Federativa Brasil: Art 212 Brasớlia Senado, 1988 BREU, T.M; RAAB, R.L Efficiency and Perceived Quality of the Nation’s ‘Top 25’ National Universities and National Liberal Arts Colleges: An Application of Data Envelopment Analysis To Higher Education Socio-Economic Planning Science, v.28, p.33-45, 1994 CHARNES, A; COOPER, W.W; RHODES, E.Measuring the efficiency of DMUs European Journal of Operational Research, v 2, p 429–44, 1978 CHARNES, A; COOPER, W W Measuring the Efficiency and Productivity of Decison Manking Units European Journal of Operational Research, vol 3, p 339-338, 1979 COOPER, W W; SEIFORD, L M; TONE, K A Comprehensive Text with Models, Applications, References and DEA-Solver Software New York: ed Spring, 2007 CORBUCCI, P R As Universidades Federais: Gasto, Desempenho, Eficiência e Produtividade IPEA, texto para discussão 752 Disponível em: Acesso em: mar 2009 DANTZING, G B.Maximization of a linear function of variables subject to linear inequalities In T.C Koopmans (ed.), Activity Analysis of Production and Allocation, New York :Wiley, 1951 FARE, R; GROSSKOPF, S Intertemporal production Frontiers: with dynamic DEA Norwell: Kluwer, 1996 FAÇANHA, L O; MARINHO, A Instituiỗừes de Ensino Superior Governamentais e Particulares: Avaliaỗóo Comparativa de Eficiờncia IPEA, texto para discussóo n 813, 2001 Disponível em: Acesso em: jan 2010 18 FARE, R; GROSSKOPF, S.; LINDGEN, B.; ROOS, P Productivity change in swedish hospitals: A Malmquist output index approach 1994 Apud COOPER, W W; SEIFORD, L M; TONE, K A Comprehensive Text with Models, Applications, References and DEA-Solver Software New York: ed Spring, 2007 FARRELL, M.The Measurement of Productive Efficiency Journal of the Royal Statistical Society, Series A, 120, Part 3, 253-290, 1957 FLEGG, A T; ALLEN D.O; FIELD K & THURLOW, T.W Measuring the Efficiency and Productivity of British Universities: An Application of DEA and the Malmquist Approach University of the West of England, Department of Economics, series Discussion Papers n 304, 2003 FORSUND, F R; KALHAGEN, K, O Efficiency and Productivity of Norwegian Colleges Oslo University, Department of Economics, series Memorandum n 11, 1999 GOTO, M; NENOMOTO, J Measurement of Dynamic Efficiency in Production: An Application of Data Envelopment Analysis to Japanese Electric Utilities Journal of Productivity Analysis, vol 19, n 2-3, p.191-210, 2003 GOTO, M; NENOMOTO, J Dynamic data envelopment analysis: modeling intertemporal behavior of a firm in the presence of productive inefficiencies Economics Letters, vol 64, n 51–56, 1999 Instituto Nacional de Estudos e Pesquisas Educacionais (INEP) Censu da Educaỗóo Superior: 2004 Brasớlia, 2009 Disponớvel em: Acesso em: 10 fev 2010 JOHNES, G; JOHNES, J International Handbook on the Economics of Education Edward Elgar Publishing Ltd Cheltenham, UK Northampton, MA, USA 2004 Cap 16, p 613-627 JOUMADY, O; RIS, C Performance in European Higher Education: A Non-Parametric Production Frontier Approach Journal of Education Economics, ed, p 189-205, 2005 KOOPMANS, T C An Analysis of Production as an Efficient Combination of Activities In T C Koopmans, ed., Activity Analysis of Production and Allocation, Cowles Commission for Research in Economics, Monograph No 13 New York: Johon Wiley and Sons, Inc 1951 KLOPP, G The Analysis of the efficiency of production system with multiple inputs and outputs University of Illinois at Chicago Industrial and Systems Engineering College, 1985 Mc MILLAN, M; Datta, D The Relative Efficiencies of Canadian Universities: A DEA Perspective Canadian Public Policy, v 24 (4), p 485-511, 1988 MALMQUIST, S Index numbers and indifference surfaces Trabajos de Estatistica 1953 4, 209–42 OLIVEIRA, C E M; TURRIONI, J B Avaliaỗóo de Desempenho de Instituiỗừes Federais de Ensino Superior Através da Analise por Envoltória de Dados (DEA) In ENGEP 2005 PIRES, J S Dal Bem Proposta de Modelo de Orỗamento Baseado em Desempenho Acadờmico para as Universidades Públicas Estado Paraná Tese (Tese em Engenharia de Produỗóo) Programa de Pús-Graduaỗóo em Engenharia de Produỗóo, Universidade Federal de Santa Catariana, Florianópolis, 2001 19 RHODES, E L.; SOUTHWICK, L Determinants of efficiency in public and privates universities Working Paper, School of Environmental and Public Affairs Indiana University Blomington IN 47407, USA 1986 SAMPAIO DE SOUZA, M DA C; STOSIC, B D Technical Efficiency of the Brazilian Municipalities: Correcting Non-Parametric Frontier Measurements for Outliers Journal of Productivity Analysis, vol 24, n 2, p 157-181, 2005 SARRICO, C S Data envelopment analysis and university selection Journal of the Operational Research Society, v 48, p 1163-1177, 1997 SCHWARTZMAN, J As Teorias Da Universidade Brasileira Disponível em: http://www.schwartzman.org.br/simon/teorias.htm Acesso em 11 Out 2008 SCHWARTZMAN, J Um sistema de indicadores para as universidades brasileiras In: SGUISSARDI, V (org.), Avaliaỗóo Universitỏria em Questão Campinas, Autores Associados, 1997 SENGUPTA, J K Persistence of dynamic efficiency in Farrell models Applied Economics, vol 29, p 665–671, 1997 SENGUPTA, J K A dynamic efficiency model using data envelopment analysis International Journal of Production Economics, vol 62, p 209-218, 1999 SENGUPTA, J K Nonparametric efficiency analysis under uncertainty using data envelopment analysis International Journal of Production Economics, vol 95, p 39–49, 2005 SOUZA, H R.; RAMOS F.S Performance Evaluation in The Public Sector: An Application of Efficiency Measures to Brazilian Federal Higher Education Institutions Tenth World Productivity p 430-450, 1997 SHEPHARD, R Cost and Production Functions Princeton University Press, Princeton, New Jersey, EUA 1953 TONE, K.; TSUTSUI, M A Slacks-based Measure of Efficiency in Data Envelopment Analysis Research Reports, Graduate School of Policy Science, Saitama University and subsequently published in European Journal of Operational Research 130 p.498-509, 2001 TONE, K; TSUTSUI, M Dynamic DEA: A slacks-based measure approach Omega, vol 38, p.145156, 2010 WONG, Y; BEASLEY, J Restricting Weight Flexibility in DEA Journal of Operational Research Society, v 41, p 829-835  ... higher Education through the Ministry of Education to evaluate the scope of this efficiency and its results for society as a whole Ramos and Souza (1997) analyzed the performance of federal higher. .. consistently represent the characteristics of the educational production function Outputs and inputs selected to measure the efficiency of Federal Institutions for Higher Education (IFES) in the present... (2005) assessed the relative efficiency of Federal Institutions of Higher Education (IFES) Inputs and outputs were constructed using indicators from the Federal Accounting Tribunal (TCU) The CCR –