Introduction

At the global level, the first social economic organizations were born following the Industrial Revolution in England between 1750 and 1840, as a response to the impoverishment caused in the less favored social classes. In the middle of the 19^th century, the first credit unions emerged, which were characterized by having an alternative approach to the market economy and thus curbing the exploitation and impoverishment felt in society. In Ecuador, the first unions were born in the guilds of craftsmen, workers, merchants, employees, and employers, linked to the socialist and liberal parties as well as to the Catholic Church. The Sociedad Protectora del Obrero (Workers Protection Association)-considered the first Ecuadorian union-was founded in Guayaquil in 1919 (^{Miño, 2013}).

Within the history of unions in Ecuador and referring to the most significant events that have arisen, we can cite that in the late 1980s and early 1990s this financial sector had a decline in its growth due to the closure of some small and medium unions (^{Miño, 2013}). This same author announces that by the end of the 1990s-when the country presented one of the biggest financial crises in its history, the main event of which was the bank holiday of 1999 that brought with it the fall and closure of approximately 20 banking institutions-the general public lost confidence in the banking sector and, therefore, turned this confidence to the credit union sector, which experienced significant growth. In this situation, unions are forced to implement greater security measures and control over their assets for the tranquility of their clients and administrators. By 1999, according to data from the Federation of Savings and Credit Cooperatives (FECOAC for its acronym in Spanish), the confidence and solvency of the citizens was reflected in the increase in deposits, especially fixed-term deposits, which grew by 116% from January to June.

By 2016, Ecuador had a total of 921 credit unions registered in the 5 segments of the Financial Cooperative Sector registry¹ of the SEPS. Until 2015 Ecuador was the second country in Latin America after Brazil to have the largest number of credit unions; the credit union sector has had a great impact on economic development since approximately 66% of microcredits granted correspond to this system, thus differentiating it from the banking system.²

In the production environment of the different industrial sectors it is common to find efficiency studies based on the initial work by ^{Farrel (1957)}, same which have served as a theoretical framework for the creation of several concepts on efficiency. In this context, Technical Efficiency (TE) is considered for each Decision-Making Unit (DMU) as the maximization of the results obtained from the resources that were used. Thus, efficiency can be approached from two different directions: the first is oriented towards input variables where inputs are minimized, while DMUs remain in the frontier of production possibilities; and the second is oriented towards the maximization of the output variables given a fixed level of input variables (^{Navarro & Torres, 2006}). However, any of the approaches of the DEA analysis allows defining an efficient frontier with the leaders of the sector (^{Belmonte & Plaza, 2008}). In turn, ^{Valencia & Chediak (2008)} indicate that efficiency is based on the resulting coefficient between the products and inputs of the DMUs, with these being: companies, schools, hospitals, municipalities, or any organization that produces goods or provides a service.

Coelli et al., as cited in ^{Restrepo & Villegas (2011)} and ^{Benavides & García (2014)}, state that there are several methods that have been used to measure the efficiency of organizations, such as: econometric techniques, price indices and, presently, Data Envelopment Analysis. There are several studies on efficiency analysis in unions, exhibiting unanimity in the use of the DEA methodology to measure the efficiency of the union sector in different countries during certain periods of time and combinations of different analysis models derived from this methodology. This is evidenced by (^{Andrieş & Cocriş, 2010}; ^{Asawaruangpipop & Suwunnamek, 2014}; ^{Belmonte & Plaza, 2008}; ^{Joseph & Pastory, 2013}; ^{Lemos, Seido, & Monforte, 2007}; ^{Marrero Ancízar & Ortíz Torres, 2016}; ^{Santana Ramírea, 2015}).

^{Asawaruangpipop & Suwunnamek (2014)} used DEA to research the pure, technical, and scale efficiencies of 732 Credit Unions in Thailand. For this, they classified unions according to the segment to which they belong: professors, police, military, etc. Efficiency was assessed using the Constant Returns to Scale (CRS) and Variable Returns to Scale (VRS) models, while also presenting the average values by type of union. As a result, it was observed that under the CRS and VRS model, unions that belong to the public sector obtained the highest efficiency averages, with 90.04% and 93.43%, respectively.

^{Xueping, Jie, & Hongxin (2011)} analyzed the efficiency of rural Credit Unions in the province of Hubei in China. This study comprised the analysis of the system of credits granted to rural houses. Fifty-four unions in total in a period of three years. To this end, they applied the CRS and VRS methods. The results showed that the evaluation carried out with the VRS model obtained greater ranges of efficiency.

^{Joseph & Pastory (2013)} carried out a study concerning the Credit Unions in three regions of Tanzania, where they employed the DEA methodology to measure the efficiency of 37 rural credit unions. The result indicates that, in average, unions were shown to be inefficient in the 3 regions of analysis, thus determining that the main reason for said inefficiency are the high operational costs.

^{Lemos et al. (2007)} applied the DEA methodology to measure the efficiency of the rural credit unions of the state of Sao Paulo, Brazil. The study determined that credit unions with a high volume of resources have achieved greater efficiency indices, considering the proportion of the total assets and the administration spending with relation to the granted volume of credits. The analysis of different cases in which the DEA methodology has been applied has allowed us to obtain a clearer vision of the work done and to establish a different and complementary approach to the studies that have been done.

^{Moreno Sierra & Rey Huertas (2017)} applied the DEA methodology to evaluate the efficiency of the credit unions in Colombia. Their analysis connected the efficiency of the credit union to the permanence and the success of the organizations. The study included two approaches: the financial approach that considers administrative expenses and social capital as inputs, and surplus as outputs; and a second approach aimed to determine the unions with the best practices where the number of associates and administrative expenses were considered as inputs, while the credit portfolio was considered an output. The final results determined that the efficiency of credit unions in Colombia is low.

The main objective of this work is to measure and analyze the relative efficiency of 18 credit unions classified within “Segment 1” in Ecuador, applying the DEA methodology. The analysis was done considering the closing financial statements of the period of 2007-2016 as base information, obtaining in this manner the annual efficiency of the same, which will make it possible for us to compare their institutional growth and their efficiency indicators.

Once the efficiency ratios of the credit unions were obtained, we were able to establish the following secondary objectives: (i) to monitor in time the capacity of each Credit Union (CU) to reach an optimal efficiency level; (ii) to offer information to the population that will help them define the best option when opening an account in a specific union; (iii) to clearly establish the input and output variables that must be adjusted (improved) so that unions can reach optimal efficiency levels.

The content of this article is organized in four sections: the first one refers to the description of the revised literature and the mathematical model to be used; section two indicates the methodology used for the collection and analysis of data; section three contains the results obtained, as well as a financial analysis; finally, we present the conclusions derived from the research. We will use different tables and graphs that show, with more clarity, the results obtained.

Methodology and data presentation

Results

The table represented below shows the efficiency result executed for the decision units in each one of the analyzed years. It should be noted that within each year, the efficiency of the different CUs has suffered variations that could be the reason behind different decisions and forms of management in each financial institution.

In the efficiency analysis of the 18 CUs during the period of 2007-2016, we can observe that in the year of 2008 there was a greater number of credit unions that were 100% efficient with a total of five of them. There is only one fully efficient credit union in the ten years of analysis, with it being CU1 (Cooperativa Juventud Ecuatoriana Progresista). The lowest number of fully efficient credit unions is equally present in several of the years of analysis (2007, 2009, 2010, and 2013) with a total of three efficient credit unions in each year. The lowest levels of efficiency that have been obtained in the analysis period were present in 2007, where two credit unions reached efficiency levels that were inferior to 50%. For this reason, the lowest efficiency average is present in this year. Similarly, there are cases where the efficiency level has had a behavior that varies greatly; such is the case of CU18, which in 2007 happened to be 100% efficient, while in 2014 it obtained the lowest level of all CUs in the analyzed period. On the other hand, we have the case of CUs 16 and 14, which maintained an efficiency level that was relatively low in the first years, but which then reached an optimal level of efficiency and maintained it until the end of the period.

Case comparison

The efficiency ratios obtained for each DMU allowed to determine the CU groups that were fully efficient and those that were less efficient. Therefore, we were able to compare these groups through the observation of the clearances presented by each variable; defining clearance as the difference between one and the efficiency ratio obtained by each Credit Union. The comparison analysis of the levels of increase or decrease of clearances will allow having a better understanding of the results.

Tables 7 and 8 show the quantities and percentages of increase or decrease that each variable must have had in order to be efficient.

The clearance results presented correspond to the year 2007, which was taken as an example for the explanation of the same. In this case, it is necessary to indicate that the level of projections of the variables changes for the CUs every year of the period of analysis due to the variability of the set of data. The percentage of differences shown in Table 7 has a negative sign due to the model used, same which, as explained before, is oriented towards the minimization of inputs. Thus, in the case of CU 16, for example, it needs to decrease its Operation Costs by 63.27% and its Uncollectable Funds by 36.97% to be efficient. In turn, Table 8 shows positive clearance percentages due to the increase that these variables must have so that Credit Unions can operate in the optimal frontier. It can be observed in the output projections that only two Credit Unions, 7 and 10, must increase their percentages of the Accounts Receivable variable, while their Total Deposits variable is working just fine.

Sensitivity analysis

The model was executed considering the variations proposed for each of the variables and their percentage differences presented in Table 7. Table 9 shows the efficiency variations reached by each DMU when adjusting the data. It can be observed that it is important to focus on avoiding or minimizing clearances in the input variables, especially concerning Operation Costs. The correct handling of these will significantly increase the efficiency of the sector and in each DMU.

Using this logic, the model was executed using the corresponding adjustments for each year. Table 10 shows the average efficiency results by year. The need to make adjustments in the Operation Costs and Uncollectable Funds variables is confirmed. Any effort done in the output variables will not alter the efficiency results.

Table 11 shows the variables that obtained a greater number of projections of increase or decrease in clearances for each year. For this, we considered indicating those variables that present a number of three projections and above as more effective.

We can observe from this analysis that the variables were less effective in 2010 and 2016, given that these years presented an adjustment projection in the four variables. Similarly, the years that present less projection variables are 2007 and 2008. It can be observed that the input variables were deficient throughout the period of analysis, so that it may be assumed that in order to obtain better efficiency ratios, credit unions must implement improvement plans for the reduction of operation costs, in addition to improving credit guarantee to consolidate a lower risk in the recovery of funds.

Table 12 indicates the comparison of each credit union determined as inefficient, with their efficient counterparts.

Conclusions

Once the Technical Efficiency analysis applied to the credit unions from “Segment 1” of the Ecuadorian credit union ranking in the period of 2007-2016 has been concluded through the use of the Data Envelopment Analysis (DEA), we obtained the efficiency level of the same, determining that throughout the period of analysis there was a variation in the total number of efficient CUs of each year. For example, the year in which there was a greater number of efficient DMUs was 2008, with 5 credit unions. The lowest number of efficient credit unions was 3 in the years 2007, 2009, 2010, and 2013. There is only one CU that was fully efficient throughout the 10 years of analysis, CU 1 (Juventud Ecuatoriana Progresista).

The contribution of this study allows observing the increase or decrease projections in the values of the variables so that it is possible to know the area of improvement of each CU. To this end, we have presented all the data of the result of the analysis online, where any interested party may access said information through the following link:

https://drive.google.com/drive/folders/0B_2_YW0EYyP8c0F1cjFMTnBsM28?usp=sharing

The results of this study indicate that different types of analysis can be used, and we can measure the efficiency of any type of financial institution (banks, credit unions, others) in the different segments in Ecuador. Furthermore, with the results obtained, it is possible to implement improvements in the financial management of their input and output variables so that they can optimize their resources until they are fully efficient. However, CUs must prioritize the adjustment of input variables (OC and UC) given that these changes will represent significant increases in the efficiency of each analysis unit.

One of the main causes of inefficiency in the case studies is the high level of operation costs and the loss of money in uncollectable funds, which can be improved with the proper management and use of resources, which would represent savings, in addition to the implementation of proper computer systems that may speed up the process and with it reduce the excessive personnel expenses. For the case of uncollectable funds, it is necessary to improve the warranties for the granting of credits, to coordinate, and to properly review the information of each client with the Risk Central.

Through the use of not only the CCR-I model but also the different models presented by the Data Envelopment Analysis, it is possible to carry out studies that show deeper comparisons and analyses of the results obtained with the implementation of more than one model for the same set of data and analyze the variability or sensitivity that may be obtained in the results.

In a comparison of the level of efficiency obtained for each credit union vs the size of the same, we can assert that not necessarily the biggest credit unions turn out to be the most efficient.