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Stochastic vs. deterministic frontier distance output function: Evidence from Brazilian higher education institutions

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Abstract

Using data from the Brazilian Higher Education Census and other public institutions, this study aims to obtain and compare efficiency scores from stochastic frontier analysis (SFA) and data envelopment analysis (DEA) models for 56 Brazilian federal universities for the period of 2010 to 2016. The output distance function includes financial and human resources as inputs, and teaching, research, patents and third mission activities as outputs. The research is innovative considering: (i) the estimation of SFA for Brazilian universities as whole institutions, (ii) its comparison with DEA; and (iii) the inclusion of patents and third mission variables. The findings suggest there is inefficiency in Brazilian higher education production, with a very small increase through time and with some influence from universities and environmental characteristics. Thus, consolidated traditional institutions with university hospitals tend to be more efficient than the younger ones. The values and the rank of the efficiencies are sensitive to the model/method employed, presenting highly significant although modest correlations. In general, the inclusion of third mission activities improves the efficiencies for both approaches, mainly for DEA. Hence, as advised in other international comparative analyses, caution is required when deriving management and policy recommendations from the analytical results.

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Notes

  1. Until 2016 there were 7 other universities, 4 completely new ones, and 3 others created by disaggregation. The new ones were: UFFS (in 2009), UNILA (in 2010), UNILAB (in 2010) and UFESBA (in 2013). The disaggregated ones were UFCA (in 2013, originally from UFC), UFOB (in 2013, originally from UFBA) and UNIFESSPA (in 2013, originally from UFPA).

  2. According to the recommendation of TCU (2000), the problem is how to disentangle the share of expenses incurred in the university hospitals that corresponds to teaching and research activities, in addition to the regular services provided by these hospitals. Amaral (1998 apud TCU 2000) considers that 35% of the expenses of the university hospitals can be appropriated in the cost of teaching. According to Silva et al. (2004), this proportion of 35% seems to be based on Jones and Korn (1997).

  3. Measured in R$ of year 2000, deflated by the GDP implicit index.

  4. It is important to clarify (or remember) that the Brazilian regions are very heterogeneous regarding their natural, social and economic characteristics.

  5. Decision Making Unit (DMU) in this context is a synonymous to HEI, or University.

  6. It could be considered the standard primal problem in contemporary DEA literature using VRS model and output orientation (Forsund 2018, p. 4; Thanassoulis et al. 2011, p. 1297)

  7. These procedures were developed focusing in solving specifically DEA limitations regarding outlier DMU(s).

  8. The Cobb-Douglas functional form was tested versus the complete Translog functional form (the former is nested in the latter). According to the LR test, the Translog model has a better fit.

  9. According to Coelli et al. (2005) and O’Donnell (2014), cited by Johnes (2013), endogeneity could exist, caused by correlation of the explanatory variable and the error term (eit = vi + ui). However, Coelli and Perelman (2000, apud Johnes 2013, p. 5) argue that this “bias is not a problem in an output distance function which [as here] uses a translog functional form”.

  10. PROFES presented better results than PROFEQ according to AIC and BIC criteria.

  11. Some of the recent federal universities present different years of creation and federalization, that is, they were created originally as other type of institution and worked for a time until the federal government ‘federalize’ them, that is, they became managed by the federal government. Then, both ‘year of creation’ and ‘year of federalization’ were tested in the models and only the latter presents statistical significance in the models.

  12. The sensitivity of the results was checked by using the other outputs as numeraire; results then showed the insensitivity of the change, as expected, according to Coelli and Perelman (2000) and Johnes (2013).

  13. To estimate ûit of uit, the largely used strategy is to look at the conditional distribution of uit given eit and use the conditional expectation EV(uit | eit) as an estimator of uit. The details of this procedure, following the seminal work of Jondrow et al. (1982, p. 238) and Battese and Coelli (1988, p. 392), are described and commented with details in Bogetoft and Otto (2011, pp. 217–219).

  14. Battese and Coelli (1995, p. 327) argue this assumption is a simplifying, but restrictive, condition but Gómez and Pérez (2017) found that the consideration of independent error terms results in overestimated cost efficiencies in a general magnitude lower than 5%. Because of this lower value and the novelty of this work to the Brazilian case, in the present research we chose to consider the ‘classical’ assumption of independent and identically distributed error terms to all models estimated.

  15. Johnes and Schwarzenberger (2011, p. 498) pertinently observe that in empirical applications, when sigma and gamma terms are statistically different from zero, it suggests an appropriate approach in relation to efficiency distribution.

  16. The log-likelihood function of this model is presented in the appendix of Battese and Coelli (1992).

  17. The log-likelihood function of this model is presented in the appendix of Battese and Coelli (1993).

  18. In an attempt to choose the final specification of the BC92 models, first we estimated eight models considering different outputs and only CCCHU as input. Then, the same eight models were estimated considering only PROFEQ and FUNCEQSHU as inputs and, also, the same eight models were estimated considering the three inputs. Then the results were compared by using the LR test and all models with the three inputs presented the best fit. Only then, we compared these eight models with three inputs and different outputs among themselves, and we selected the two models with the best fit.

  19. Regarding the estimation method and the software used, all DEA procedures were done using the R (2017) and the package ‘Benchmarking’ developed by Bogetoft and Otto (2018). The package ‘FEAR’ (Wilson 2008) was used to apply the Wilson (1993)’s procedures to identify potential HEI outliers to DEA analysis. The SFA estimations were done by maximum likelihood estimation using the package ‘frontier’ developed by Coelli and Henningsen (2017). It is an R version of the classical FRONTIER 4.1 software developed by Tim Coelli and presented in Coelli (1996).

  20. Only if considering the model with THIRDM.

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Funding

This work received a grant by CAPES, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brazil, from Sep 2017 to Aug 2018; and it was also supported by CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico (grant 312369/2018-2).

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Authors and Affiliations

  1. Universidade do Estado da Bahia (UNEB), Senhor do Bonfim, Brazil

    Ariel Gustavo Letti

  2. Universidade Federal do Paraná (UFPR), Curitiba, Brazil

    Mauricio Vaz Lobo Bittencourt

  3. Universitat de València (UV), Valencia, Spain

    Luis E. Vila

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  1. Ariel Gustavo Letti
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  2. Mauricio Vaz Lobo Bittencourt
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  3. Luis E. Vila
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Correspondence to Ariel Gustavo Letti.

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Letti, A.G., Bittencourt, M.V.L. & Vila, L.E. Stochastic vs. deterministic frontier distance output function: Evidence from Brazilian higher education institutions. J Prod Anal 58, 55–74 (2022). https://doi.org/10.1007/s11123-022-00636-1

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