Efficiency in higher education. Empirical study in public universities of Colombia and Spain

In recent decades, Iberoamerican universities have introduced new quality assessment and accountability schemes, inspired by the New Public Management (NGP) model. In this context, efficiency in the distribution of public funds and obtaining the maximum possible return are a priority. Thus, measuring efficiency in the public sector, and specifically in higher education, has become a challenge for accounting science. The objective of this work is a proposal to calculate efficiency indices with Data Envelopment Analysis (DEA) models, introducing a previous step through the Analysis of Canonical Correlation (ACC). Using this technique, the aim is to improve discrimination capacity and overcome monodimensionality and lack of reliability in the representativeness of the chosen input and output variables. The study is applied in the public universities of Colombia and Spain during the years 2015 and 2016. The results obtained demonstrate the convenience of applying this preliminary step in the multivariate analysis. This reinforces the need to explore more rigorous methodologies in stages before and after the calculation of the efficiency indices. This practice increases confidence when using the indices to formulate policies and manage resources for the sector


INTRODUCTION
In recent decades, society has increasingly demanded an increase in transparency and accountability from public organizations. In response to this, and aiming to improve quality and ensure efficient use of public resources (C. R. M. Silva & Crisóstomo, 2019), most countries have introduced new management models in their institutions, inspired by the principles of new public management (NPM) (Andrews, Beynon, & McDermott, 2019;Broucker, De Wit, & Verhoeven, 2018;Lane, 2002), introducing management techniques from the private sector.
Within this new paradigm, public higher education institutions have been pressured to improve their performance. Thus, many governments have implemented new regulations to professionalize universities in search of excellence. This market approach has fostered an interest in analyzing and comparing results between different universities, with particular emphasis on research (Mateos- González & Boliver, 2019).
However, the increase in university quality should not be linked only to the university's effectiveness, that is, achieving its objectives in terms of the number of publications, citations, or graduates (De-Juanas Oliva & Beltrán Llera, 2013;Giménez-Toledo & Tejada-Artigas, 2015), regardless of the cost or effort required. It is also important to consider efficiency, that is, the relationship between resources used and output produced, something indisputable given extreme resource constraints (Gómez-Sancho & Mancebón-Torrubia, 2005;Mateos-Gonzalez & Boliver, 2019).
In the public sector, the concepts of quality and efficiency should be inseparable. As stated by Gómez-Sancho & Mancebón-Torrubia (2005), it is hard to imagine that a high-quality university could be inefficient. Quality should also be associated with optimizing resource use, thus improving the services provided to the population and contributing to socioeconomic development (Debnath & Shankar, 2014;Tiana Ferrer, 2018).
On this background, this study aims to calculate efficiency scores using data envelopment analysis (DEA) by applying a preliminary calculation with canonical correlation analysis (CCA). Our main interest lies in multivariate methodological questions that are conducive to overcoming the unidimensionality and unreliable representativeness of the selected input and output variables, to improve the discriminatory power of efficiency analysis. The study considers Colombian and Spanish public universities in 2015 and 2016. Its key contribution is not so much the numerical results obtained (efficiency scores) for each university evaluated but the discussion of various methodological aspects arising from the evaluation process: formulation, delimitation, significance, and representativeness of inputs and outputs specific to public universities; technique selection; model evaluation; and selection of the units of analysis.
The results obtained show the convenience of using CCA in a preliminary step in multivariate analysis to provide reliability and representativeness to the variables used for efficiency calculations in the public higher education sector. Colombian universities obtain high average efficiency scores (0.7107 and 0.7911) in 2015 and 2016 along with high inefficiency scores (0.2280 and 0.3792), with a high dispersion of the input and output data used in the calculation. Spanish universities show lower average efficiency (0.6537 and 0.5865) and dispersion levels. Eleven out of 32 Colombian universities and six out of 48 Spanish universities are fully efficient, showing that data refinement and the selection of appropriate methods increase the reliability of the final results and therefore their usefulness.
This study is subdivided into four sections: the first reviews the literature on the subject of public management and efficiency in higher education; the second describes the CCA and DEA models applied in the study and the variables and units of analysis involved; the third describes and analyzes the empirical results obtained; finally, the fourth proceeds to the discussion and conclusions.

NEW PUBLIC MANAGEMENT AND EFFICIENCY IN HIGHER EDUCATION
NPM emerged at the end of the 20th century from the need to use public resources with maximum efficiency, meet citizens' demands, take advantage of the opportunities of a globalized and competitive world, and make societies more aligned with the collective will (Frey & Jegen, 2001;Agasisti & Haelermans, 2016). Thus, NPM aims to create a more efficient and effective administration in areas where a better supplier is not found, eliminating bureaucracy, adopting more rational processes, and having greater administrative autonomy (García Sánchez, 2007).
In this context, measuring public sector efficiency, specifically in higher education, becomes a challenge for accounting (A. F. Silva, J. D. G. Silva, M. C. Silva & 2017). However, measuring university efficiency is not trivial; in fact, obtaining an easy and objective measurement is one of the main problems (Moreno-Enguix, Lorente-Bayona, & Gras-Gil, 2019).
Efficiency has been a widely addressed topic in the context of private and for-profit organizations and generally implies doing things well, i.e., ensuring adequate distribution of the means utilized relative to the outcomes achieved (Álvarez, 2001). In the public sector, efficiency consists in optimizing resource use to obtain the maximum of goods and services in both quantitative and qualitative terms (Hauner & Kyobe, 2010;Mukokoma & Dijk, 2013;Peña 2008;A. F. Silva et al., 2017;Soto Mejía & Arenas Valencia, 2010).
To assess organizational efficiency, it is necessary to specify a production function reflecting the process by which the entities under evaluation transform inputs into outputs (Johnes, 2006;Kuah & Wong, 2013;A. F. Silva et al., 2017). To construct a production function for universities, their normal activities must be considered (Moncayo-Martínez, Ramírez-Nafarrate, & Hernández-Balderrama, 2020). The productive efforts of universities involve simultaneously performing several activities of different kinds (activities related to the creation of knowledge-research activities-and its dissemination through teaching, transfer, and extension activities, along with other activities that universities perform as social agents) while sharing most resources (faculty, administrative and service staff, facilities, equipment, supplies, etc.).
Like any other public organization, universities find it difficult to assign monetary values to the inputs and outputs of their production process given that they both generate multiple outputs (e.g., graduates and publications) and use multiple inputs (e.g., speakers and facilities) (Kuah & Wong, 2013).
It should be noted many of these papers focus more on the relationship between institutional inputs and outputs than on their overall performance since they compare universities by the units with best practices, based on their ability to maximize outputs given some available inputs (Johnes, 2006). The present study aims to provide a comprehensive view of both inputs and outputs -which must be relevant and significant -of the processes they engage in, by using appropriate methods, and of the results that ultimately allow the assessment and classification of the institutions. We finally aim to propose options for improvement and put forward individual and sector management policies.

CCA
A previous step before using DEA in efficiency analysis is to select the most representative variables. This step is very important since the variables used directly affect the final score. The selection of these variables seeks to obtain good discrimination between efficient and inefficient units and set a boundary that best fits the observed data. Despite their significance, few studies propose preliminary methods to construct the variables that best represent the set of inputs and outputs used for efficiency analysis (Azor Hernández, Sánchez García, & DelaCerda Gastélum, 2018;Friedman & Sinuany-Stern, 1997;Moreno Sáez & Trillo del Pozo, 2001;Sabando Vélez, & Cruz Arteaga, 2019). To optimize this process, as a previous step before using DEA, the present study applies CCA to analyze the significance and representativeness of the selected variables (inputs, outputs) to calculate efficiency scores.
CCA is a linear, multivariate statistical analysis method (Hotelling, 1935) used to identify, measure, and analyze associations between two sets of variables. While multiple regression predicts a single dependent variable from a set of independent variables, CCA facilitates the study of the interrelationships between multiple criterion variables (dependent) and multiple predictor variables (independent) (Badii & Castillo, 2007;Soto Mejía, Vásquez Artunduaga, & Villegas Flórez, 2009;Soto Mejía & Arenas Valencia, 2010). The mathematical expression of CCA is: CCA is a valuable tool in human factor research, as it involves a clear distinction between independent and dependent variables, multiple dependent variables, and the potential for multidimensional relationships between these two sets of variables.

Data and Variables
According to Gómez-Sancho and Mancebón-Torrubia (2005), it has not been possible to specify a generally accepted production function of higher education. Inputs are usually proxies of capital and labor factors. While for the labor factor there seems to be agreement on using the number of full-time equivalent faculty (Chang, Chung, & Hsu, 2012;Johnes, 2006;Laureti, Secondi, & Biggeri, 2014;Rhodes & Southwick, 1993;Sarafoglou & Haynes, 1996;Sav, 2012), in the case of capital, the approaches are sufficiently different (infrastructure, technology, operating expenses, among others) that it continues to be an open topic for discussion. Outputs in all cases are related to the results of the two main activities in universities: teaching and research (Pérez-Esparrels & Gómez-Sancho, 2011), measured, for example, by the number of graduates (Athanassopoulos & Shale, 1997;Avrikan, 2001;Laureti et al., 2014;Rhodes & Southwick, 1993) and the number of publications (Chang et al., 2012;García-Aracil, 2013;Kao & Hung, 2008;Munoz, 2016;Kuah & Wong, 2013), respectively. The conclusion is there is no definitive standard to guide the selection of inputs and outputs in assessing university efficiency (Kuah & Wong, 2013). According to Buitrago-Suescún et al. (2017), the literature reports approximately 254 inputs and 230 outputs to measure education efficiency worldwide.
In the present study, starting from the bibliometric and systemic analysis in Ramírez-Gutiérrez, Barrachina-Palanca, and Ripoll-Feliu (2019) of the existing literature within the area of efficiency in higher education, we have selected those variables (see Table 1) that have had the most impact in previous studies and were available in the databases (National System of Higher Education Institutions of Colombia -SNIES, for its initials in Spanish, and Integrated University Information System of Spain -SIIU, for its initials in Spanish) of Colombia and Spain. The study periods are 2015 and 2016.
To formulate canonical functions, the smallest number of variables is considered, i.e., five for Colombia and three for Spain (see Table 1), since the number of possible canonical random variables (canonical dimensions) is equal to the number of variables in the smallest set (Badii & Castillo, 2007).

DEA
This model, developed by Charnes, Cooper, and Rhodes (1978), is a nonparametric and deterministic procedure to assess the relative efficiency of a set of homogeneous production units. Using the number of inputs consumed and outputs produced by each unit, and by linear programming techniques, DEA constructs, from the current best practice, the efficient production frontier against which the efficiency of each unit is evaluated (Salinas-Jiménez & Smith, 1996). The conceptual foundations of DEA were laid by Farrel (1957), who defined technical (relative) efficiency as the ability to achieve certain objectives through the desirable combination of certain inputs and products (Ramos Ruiz, Moreno Cuello, Almanza Ramírez, Picón Viana, & Rodríguez Albor, 2015). Following Farrel (1957), DEA calculates efficiency from the following equation: Where: r = 1…s Subscript identifying an output j = 1…n Subscript identifying the different decision-making units (DMUs) i = 1…m Subscript identifying the input j o Subscript identifying the decision-making unit (DMU) for which the efficiency is being calculated. h j0 Efficiency of the decision-making unit (DMU) that is being calculated u r Relative weight of the output yr for the DMU j0 that is being calculated. v i Relative weight of input xi in the DMU j0 that is being calculated.
The weights obtained (U r and V i ) represent the values attributed to each input and output that provide the highest possible efficiency index to each decision-making unit (DMU). This weight combination, when applied to the rest of the DMUs must yield an efficiency indicator between 0 and 1. Thus, the objective is to find the DMUs producing the highest output levels from the lowest input levels. To do this, it maximizes the ratio of weighted outputs and weighted inputs for each DMU under consideration (Ray, 1991).

Min_θ
Subject to: Subject to: Subject to: Subject to: Source: Elaborated by the authors. Note: The BCC-O model aims to determine how much output could be obtained from the same level of inputs if all the DMUs were efficient, once the scale effects are removed.
The BCC model is designed to measure efficiency under variable returns. In this procedure, the inefficient DMUs are compared only with efficient units operating on a similar scale (Soto Mejía & Arenas Valencia, 2010). The output-oriented BCC model is the best suited to evaluate the efficiency of public universities (Ramos Ruiz et al., 2015;Visbal-Cadavid, Mendoza Mendoza, & Causado Rodríguez, 2016), as these may have different sizes in terms of the number of students, faculty, and/ or financial resources allocated, may not control their inputs, and may rely on models of state funding and budget allocation. Thus, the BCC-O model aims to determine how much output could be obtained from the same level of inputs if all DMUs were efficient, once scale effects were eliminated.

Units of Analysis or DMUs
A DMU is the unit subject to efficiency measurement compared to others of its kind or typology. The DMU controls the process of transforming resources (inputs) into products. To identify the DMU, it must comply with an essential homogeneity characteristic, which is evident when it is verified that all DMUs use the same type of resource (inputs) to obtain the same type of output, albeit in different amounts (Soto Mejía & Arenas Valencia, 2010).
Thus, Colombian and Spanish public universities can be seen as production units transforming resources into products. Each institution-treated as a DMU-can be considered a multiproduct organization (Ray, 1991). This study focuses on 32 DMUs (Colombian public universities) and 48 DMUs (Spanish public universities) belonging to the public university system (SUE, for its initials in Spanish) of each country (see Table 2).  Table 3 shows the canonical correlation scores and the multivariate dimensional analysis for five independent and five dependent variables selected for the Colombian SUE and four independent and three dependent variables processed for the Spanish SUE. The most important canonical correlation index for each country is that of Function 1 (0.9078 for Colombia and 0.8779 for Spain). A significant relationship between the two sets of variables is established at the 1% level, representing the greatest possible correlation between any linear combination of independent variables (faculty, teaching quality, administrative staff, and public transfers) and any linear combination of dependent variables (graduates, postgraduates, and publications). Note that the highest coefficient of determination (canonical R 2 ) corresponds to the first pair of canonical variables (U 1 , V 1 ) (R 2 can = 0.8241 for Colombia and 0.7707 for Spain), which are high values indicating high practical significance (Badii & Castillo, 2007). These results mean 82.41% of the variability of U 1 (linear combination of dependent variables) is explained by V 1 (linear combination of independent variables). This preliminary approach demonstrates for each public university system the importance and representativeness of the selected variables and the explanatory power of the set of independent variables with respect to the set of dependent variables. Both sets of variables (inputs, outputs), specifically selected for each university system, have interdependencies with each other and a high explanatory value, which corroborates their selection as proxies to perform efficiency calculations using DEA models.

CCA Redundancy Analysis
Amount of shared variance. Table 4 shows the correlation between the first dependent canonical variable and each original dependent variable. Each correlation is interpreted as a factor loading, which identifies the value of each item's relative contribution to its canonical item. Redundancy rates. In Table 5, the canonical Function 1 for Colombia shows a percentage of 50.78%, which is high, indicating the explanatory power of the input variables (independent) in the variances of the original (dependent) output variables. For Spain, this percentage is 57.06%, showing the variables associated with Spanish universities have a high explanatory power for the variability of their original outputs (Soto Mejía et al., 2009;Badii & Castillo, 2007)  Thus, for the first canonical correlation (Function 1), the independent canonical variables explain 82.41% (Colombia) and 77.07% (Spain) of the variance of the dependent canonical variables, while the first variables predict 50.78% and 57.06% of the variance in the original dependent variables, respectively. Dependent canonical variables predict 61.62% and 74.04% of the variance in the original dependent variables, and independent canonical variables predict 73.20% and 74.12% of the variance in the original independent variables. The above shows, in percentages, all the relationships and interdependencies between the two sets of variables and their respective linear combinations, providing reliability (Azor Hernández et  Regarding independent theoretical values (canonical loadings), as seen in Table 6, the three items that significantly contribute to teaching and research activities in Colombian universities are the number of full-time faculty (prof_tce), the space available for missionary use (m2_uso_misional), and the resources transferred from the state (transfer_nacion). These variables imply high representativeness and significance as inputs and as explanatory variables for the outputs in each country.
The most significant dependent variables are degree graduates (grad_preg) and total Scopus publications (total_pub_scopus) for Colombia and postgraduates (grad_post) and total Web of Science publications (pub_wos) for Spain, consistent with previous studies (Kao & Hung, 2008;Kuah & Wong, 2013;Chang et al., 2012;García-Aracil, 2013;Munoz, 2016), as they are representative variables for teaching and research activities in universities.

DEA: BCC-O results
Following the preliminary results obtained with CCA, two models (sets of variables) are proposed to calculate efficiency in higher education using DEA. Model 1. This method aims to perform efficiency calculations using DEA based on the representative and/or significant input and output variables explained by the results obtained from the canonical loadings shown in Table 6. Table 7 shows the descriptive details. The inferences are made for each set of universities (Colombian and Spanish) independently and to characterize their specific components, variables, data, and efficiency results, considering the aim is not to compare them but to demonstrate that the proposed method applies to the university sector of any country. Model 2. The prediction of the variables U 1 and V 1 , corresponding to the canonical Function 1, is made with a coefficient of determination of 82.4% for the Colombian SUE and 77.07% for the Spanish SUE. This study proposes transforming the input and output variables into fictitious variables, a product of the canonical Function 1, as explained in the methods and data section using CCA. The variable U 1 will be named U input , and V 1 will be V output. The prediction model for each variable is shown in Table 8.
From raw canonical coefficients and canonical correlations, and based on the most representative variables (Model 1) and transformed variables (Model 2), efficiency scores are calculated using DEA models to facilitate the analysis.  The coefficients shown for each variable, both input and output, are obtained as unrotated or raw canonical coefficients, for each set of variables (dependent and independent), and they will be the a priori weights for each input and output, leaving a single variable as the input and another as the output.
Data are processed in Stata and DEA-solver software. Figure 1 shows the aggregate results from efficient and inefficient universities. Tables 10 and 11 show the disaggregated efficiency scores for each model, method, period, and university.  Model 1 shows more efficient universities than Model 2. Its higher number of inputs and outputs limits the discriminatory power of the model, where some variables considered critical might be zero-weighted so that they do not affect relative calculations (Pedraja Chaparro, Salinas Jimenez, & Smith, 1994).
The importance of the results shown by Model 2 is that, using a single input variable and a single output variable (transformed variables), it groups items with their respective weight coefficients, using the canonical function described in the method section above. Table 15 shows that the average efficiency of Colombian universities is 0.7107 in 2015 and 0.7911 in 2016 (Model 1 BCC-O, 2015-2016; see Table 15). The average efficiency of Spanish universities, using the same model and periods, is 0.6537 and 0.5865. Table 9 lists Colombian and Spanish universities with recurring relative efficiency, these being universities with scale effects. For Colombia, they are the Francisco de Paula Santander University-Ocaña and University of the Llanos; the latter is not considered efficient by any of the recent efficiency studies conducted on Colombian public universities (García & González, 2011;Ramos Ruiz et al., 2015;Rodríguez-Varela & Gómez-Sancho, 2015;Visbal-Cadavid et al., 2016). For Spain, the consistent results of the University of La Rioja stand out, a university also deemed efficient by Parellada and Duch (2006)

ANALYSIS OF RESULTS
To complement the analysis of the efficiency scores shown in Tables 11 and 12, these are distributed in quartiles (see Table 13) for each higher education system analyzed.
In Model 1, efficiency scores are lower than in Model 2, due to the sensitivity shown in the number of inputs and outputs, and variable transformation by previous CCA weighting.
As for the Colombian university system, Table 13 shows that 37.5% of the Colombian universities went from having scores above 0.88854 in 2015 to above 0.9517 in 2016 (Model 1), which shows improved efficiency, analyzed among the last 12 universities. Universities with low efficiency scores, located in the first quartile (8 institutions) showed scores below 0.4093 in 2015 and less than 0.5925 in 2016.
Of the Spanish universities, as shown in Table 13, 25% went from having scores above 0.852 in 2015 to higher than 0.733 in 2016 (Model 1), which implies a worsening from one period to the next for universities in the last quartile. Institutions with low efficiency scores, corresponding to the first 25%, showed scores below 0.4755 in 2015 and less than 0.4275 in 2016, confirming the downward trend in efficiency scores in 2016. The efficiency scores are categorized in Table 14 to classify each public university, both in Colombia and Spain, for each model and period (2015)(2016), into the following groups: fully efficient (index = 1), highly efficient (1 > index > average), and low-efficiency or inefficient (index < average).   (unal, udea, udetol, ufpso, and ufpsc). Visbal-Cadavid et al. (2016) classified 20 Colombian universities as fully efficient in 2011, also with the BCC-O model, and five universities (unal, udea, uis, ufpso, and udist) are still in that category. García and González (2011) classified 17 Colombian universities as efficient in the period 2003-2009, with an average efficiency index of 89%, and three of those classified in the present study as fully efficient (uis, udetol, and udist) are still in the top 10. Rodríguez-Varela and Gómez-Sancho (2015), by applying variable returns, calculated efficiency scores for 2015 and found only three Colombian universities (unicord, uniatlantic, and udetol) to be fully efficient, of which only udetol appears in the classification for 2015 made in the present study, while the other two universities are considered to have low efficiency (below average).
Regarding the Spanish university system, Table 12 details the efficiency scores calculated for each university. For the year 2016, under the BCC-O method, there are only three efficient universities (UAL, URV, and UMH), which are also considered by Gómez-Sancho and Mancebón-Torrubia (2012) as efficient in research, and although they differ from those present in Model 1, this is surely due to the transformation of variables by CCA.
Although few studies have been published in the last 5 years at the level of Spanish public higher education institutions (Parellada & Duch, 2006 Table 14 shows the aggregate of the calculated efficiency scores, for each public university system (Spain and Colombia), to evaluate the methods and models used in both periods (2015,2016).
Colombian public universities show highly variable results, with high average efficiency and inefficiency scores, indicating high inequality in the public higher education system. The average efficiency score with Model 1 BCC-O was 0.7107 and 0.7911 in 2015 and 2016, respectively. The minimum efficiency was 0.1250 and 0.1568 for the same years.
Spanish public universities show low variability in the results and low average efficiency and inefficiency scores, indicating homogeneity in grouping data. The average efficiency index with Model 1 BCC-O was 0.6537 and 0.5865 in 2015 and 2016, respectively, and the minimum efficiency was 0.3083 and 0.2503.

DISCUSSION AND CONCLUSIONS
Higher education has been facing challenges, not only in terms of its contribution to the generation and dissemination of knowledge to society but also in its use of limited resources to generate and disseminate knowledge. Challenges for this and the coming decades, such as internationalization and mobility, the empowerment of Ibero-American identity, and university social responsibility, are only possible if combined with a strengthening of university autonomy, governance, and funding through accountability, along with efficiency and effectiveness in resource use. Thus, to be efficient and to appear as such -in terms of quality and excellence -to citizens and governments, is a challenge that has been raised by applying NPM methods to all kinds and categories of universities.
This study has sought to apply efficiency measurement to the Colombian and Spanish public higher education institutions, entering a field of research with all its complexities related to the very nature of this type of organization, which performs multiple activities, with multiple shared resources, to deliver multiple results.
Thus, the relevant contribution of the present study has been to put forth a specific method to specify a production function that can be applied in higher education, delving into the typology and quantification of relevant inputs and outputs and the mathematical description of their relationship.
For this purpose, CCA was used as a multivariate analysis method. CCA has been little used in this field but is useful to give significance and representativeness to the variables considered in order to calculate relative efficiency using DEA models. This study confirms the usefulness of this method in higher education systems in one or more countries (Wolszczak-Derlacz & Parteka, 2011;Rodríguez-Varela & Gómez-Sancho, 2018;Agasisti & Wolszczak-Derlacz, 2015).
The results obtained allow us to contrast some hypotheses previously put forth about the number of universities classified as efficient with each method and model. With the BCC method, efficient DMUs always exceed those obtained with CCR (Ramos Ruiz et al., 2015;Visbal-Cadavid et al., 2016).
As for higher education systems for each country, there is a close relationship with context and public policy. In Colombia, inequality stands out in terms of resources vs. products, as it has a higher number of efficient universities than Spain but a greater difference between efficient and inefficient universities. In Spain, there is greater data homogeneity, with lower and more clustered efficiency scores and a smaller difference between efficient and inefficient universities.
Other results on the efficiency of Colombian and Spanish higher education institutions differ significantly from the results obtained in this study, mainly due to methodological and sample aspects (delimitation of inputs and outputs of university activity, selection of the technique and evaluation model, and selection of the sample and periods). This corroborates the difficulty in making such comparisons (Gómez-Sancho & Mancebón-Torrubia, 2012) and reinforces the great criticisms made of the homogenizing classifications that have prevailed since the beginning of the century.
Another contribution of this study lies in demonstrating that, even with independent and not necessarily related systems of public higher education in Ibero-America, a preliminary step of analysis can be performed with CCA to provide representativeness to the input and output variables necessary to calculate efficiency using DEA models. At this preliminary step, CCA can transform variables to reduce their number and generate a priori weightings, thereby improving their ability to discriminate and providing more accurate, reliable, and meaningful scores.
The most important conclusion is that, when addressing efficiency measurement in higher education, special care should be taken when selecting variables, methods, periods, and units to be evaluated. The stated objective should always be kept in mind, allowing comparability of resource management, improvement plans, and monitoring strategies. Therefore, this study highlights alternative research paths for efficiency measurement in higher education, as a public management priority.