In this article, we estimate the technical efficiency ratio for a sample of 24 financial institutions in Ecuador over the period 2015–2019. To do so, we first apply a non-parametric method such as the data envelopment analysis (DEA). Under variable returns to scale and output-oriented “Interest Income”, the average technical efficiency for the 24 banks is 84.26% and, under output-oriented “Other Operating Income”, the average technical efficiency is 73.22%. We find that the group of large banks has higher levels of efficiency and that there are still opportunities for improvement in the group of medium and small banks. We also estimate that 80% of Ecuadorian banks need to make potential improvements either by increasing their output or reducing their inputs, such as salary costs, to increase the efficiency. In addition, the growth of the banking sector is crucial to achieve the financial development in Ecuador, being significant the efficiency indices, which show that a 1% increase in banking efficiency could increase its size by USD 605 million. By using the random effects panel data econometric model, we demonstrate that the growth of the banking industry is mostly influenced by the concentration of deposits and taxes.

1 INTRODUCTION

The financial sector channels resources from surplus agents to deficit agents for investment, thus triggering the economy dynamics, providing the liquidity that finally translates into an increase in the level of welfare of society (Khan & Zahler, 1986). In Ecuador, in the last century the financial market has been self-regulated on the premise that free markets are more efficient. Thus, in 1994, with the General Law of Financial System Institutions (GLFSI), freedom was promoted in the banking sector, which had a very strong impact and was one of the causes of the financial debacle and bankruptcy that occurred in 1999, giving way to dollarization (Albornoz, 2009). In 2014, the GLFSI was repealed, and new rules were enacted under the Organic Monetary and Financial Code (OMFC), seeking greater control in the relationship between the national financial system and its clients, consolidating the power of the regulator and protecting the rights of users. Finally, reforms are proposed that seek the independence of the Central Bank to guarantee liquidity with bank deposits and that it responds in each of its balance sheets (Calderon, 2021). The efficient performance of the financial sector in 2019, allowed responding to the current health crisis by offering solutions to those customers with financial difficulties. It turned into a better reputation, since the financial efficiency of private banks has increased by an average of 24.96% in 2019. Likewise, the growth rate of the financial margin of private banks in the same year is 6.10% (Superintendencia de Compañías, 2020). Therefore, this image should be maintained in the future, for which banks must be proactive, transparent, and efficient. This is a major challenge because in the world companies seek to take a position in an environment of profound changes on both the supply and demand side, which accelerated in 2020 (De Quinto, 2020). Through the changes and regulations imposed over time, financial institutions in general have tended to be efficient and achieve their objectives and financial results; however, they have not yet reached optimal levels of efficiency, due to the meagre management of costs and expenses incurred by these entities.

In the banking industry, growth is explained by several variables, being efficiency levels one of the most determinant variables for its growth, which has its implications in the reduction of intermediation spreads. Particularly, in Ecuador, although it is not happening yet, nevertheless, productive sectors and regulators are hinting that this spread reduction could occur due to efficiency improvements in the banking sector.

Equally important, a clear relationship between economic growth and the development of the financial system has been evidenced. Through macroeconomic theory, Schumpeter (2003) indicates the positive relationship between the development of a country's financial system and its per capita income growth rate. Also, Goldsmith (1955) indicates a direct relationship between economic and financial development in various periods analysed.

Thus, with microeconomic theory, the relational coexistence of business or industrial growth and the development of the financial system is ratified. Ramcharran (2016) conducted an empirical estimation on efficiency in bank lending to small and medium enterprises in India, indicating a positive relationship between efficiency with the growth of the industrial sector of small and medium enterprises. Wijesiri et al. (2015) measured the efficiency of micro financial institutions in the island of Sri Lanka; indicating direct causality of efficiency with the growth of micro financial institutions.

As it is evident, through macroeconomic theories and microeconomic studies, it is possible to perform the analysis of the positive relationship between growth (global or industrial) and the development of the financial system measured through the technical efficiency studied in this article.

Therefore, studying the changes in technical efficiency (in turn, knowing the global and allocative efficiencies) of the Ecuadorian banking system is of great relevance, since it will be possible to identify and develop tools to increase the efficiency and productivity of the financial institutions that make up the Ecuadorian banking system. In fact, the optimal quantities of products and inputs in which the banks are efficient will be identified. To strengthen the contribution of this work regarding the analysis of the relationship between the industrial banking growth and the development of the financial system of the studied entities (measured through variables that allow explaining their behaviour, mainly focused on the calculated technical efficiency). Therefore, it allows us to answer the following central question: does the impact of the measurement of technical efficiency in Ecuadorian banks contribute to the growth of the banking industry? The question will lie in establishing the relationships and determinants of the growth of the banking sector in the analysed period.

The measurement of the efficiency of the banking system is developed through the efficiency analysis of the DEA model assessed by Farrell (1957). The model orientation in DEA seeks to improve efficiency indices through input and output orientation, using panel data consisting of 24 banking institutions, with a time window of 5 years (2015–2019).

The objective of this paper is to measure the efficiency of the Ecuadorian banking system, through mathematical programming methods such as data envelopment analysis (DEA), outlining a series of commonly used efficiency measures and discuss how they can be calculated in relation to an efficient technology that is generally represented by some frontier function. In the same way, the relationship between bank industrial growth and calculated technical efficiency will be determined.

The structure of this paper includes the following sections: the present introduction, a second section that will develop the literature review; in the third section the methodology and data analysis will be explained; section four analyses the results and discussion; finally, section five presents the conclusions.

2 LITERATURE REVIEW

2.1 Theoretical foundation

The microeconomic theory of production incorporates technical efficiency into the production function, considering that this shows the maximum amount of production that can be achieved with a given set of factors and a technological process (Alvarez & Crespi, 2003). Farrell (1957) decomposed the global efficiency (GE) of a firm into two components: technical efficiency (TE), defined as the capacity of a firm to obtain the maximum level of output from the optimal use of the quantities of inputs. Price or allocative efficiency (PE) refers to the firm's ability to use the different inputs in optimal proportions given their relative prices (minimises costs). Technical efficiency (TE) can only take values between 0 and 1. A score close to zero means that the company evaluated is far from the efficient isoquant and, consequently, it is a technically inefficient company. The opposite is true if the technical efficiency is close to one. Consequently, a technical efficiency of one indicates that the company is above the efficient isoquant. In turn, price (PE) or allocative efficiency also takes values between zero and one, so that if the price efficiency score is other than one, the firm under consideration is said to be price inefficient. For a given firm, overall efficiency (GE) is equal to the product of technical efficiency and price efficiency, and as with the latter, its value will be between zero and one. It is worth illustrating the distinction between technical efficiency and productivity, which are concepts that are usually used as synonyms; a firm can be technically efficient but still be able to improve its productivity by exploiting economies of scale (Keat & Young, 2004). The notion of economies of scale is only valid for firms operating on the efficient cost curve (Suescun & Misas, 1996), that is, operating on the efficient frontier. The inclusion of firms that are above the average cost curve leads to confusing economies of scale with changes in inefficiency X either due to misallocation of inputs or excessive employment (Berger & Humphrey, 1991). An alternative frontier approach is DEA, as a method that measures relative efficiency, so that the output of a business unit should be compared to a standard efficiency measure. This is achieved by constructing an efficiency frontier and comparing the results obtained from each company with this frontier, so that business units that are above this frontier will be characterised as inefficient. According to the type of returns to scale, there are two basic models for measuring the efficient frontier:

The DEA-CCR Input oriented model [15] aims to obtain the optimal set of weights (or multipliers) that maximise the relative efficiency of the unit, defined as the quotient between the weighted sum of outputs and the weighted sum of inputs, subject to the constraint that no unit can have an efficiency score greater than one using these same weights.
The DEA-BCC Input oriented model [16] is an extension of the previous DEA-CCR model with the difference that the latter introduces the assumption of variable returns to scale and the former considers constant returns to scale. Therefore, the efficiency measure is the ratio between the weighted sum of Outputs plus the constant and the weighted sum of inputs. The overall efficiency in the CCR model can be decomposed into two parts: pure technical efficiency (that of the BCC model) and scale efficiency (SE), whose magnitudes are related as follows:

SE = \frac{Global efficiency}{Pure efficiency} = \frac{CCR}{BCC}

With the use of the frontier technique, it can be determined whether the economy of scale under which a firm is operating is increasing, constant or decreasing for points resting on the frontier (Banker et al., 1984).

But, over time, firms may experience changes in productivity (Parkin & Loría, 2010); and this productive improvement need not be due solely to efficiency improvements; it may be due to technical changes or to the exploitation of economies of scale or from some combination of these three factors (Battese & Coelli, 1988). The Malmquist input-oriented productivity index defined by Brown et al. (1979); Caves et al. (1982) can be written as follows:

{IPM}_{CCD}^{t} = \frac{D_{I}^{t} (X_{t}, Y_{t})}{D_{I}^{t} (X_{t + 1}, Y_{t + 1})}

Where:

$D_{I}^{t} (X_{t}, Y_{t})$ : represents the distance input of a unit in period t with respect to the efficient frontier in that period and determines the maximum reduction that should take place in the level of inputs of the unit in period t, given the level of outputs, to place it on the efficient frontier defined in period t.

Similarly, $D_{I}^{t} (X_{t + 1}, Y_{t + 1})$ represents the distance input of a unit in period t + 1 with respect to the efficient frontier of period t. It measures the proportional adjustment that should be made on the vector of inputs observed for the unit in period t + 1, given the level of outputs, in order to place said Unit on the efficient frontier of period t.

A ${IPM}_{CCD}^{t} > 1$ implies an increase in productivity, the opposite if this index is less than 1; and, if it is equal to 1 it means that there was no change in productivity. Caves et al. (1982) determine that the only source of productivity growth is technological change, whilst for Färe et al. (1994), productive change can be explained by the effect of two different components: the change in technical efficiency, or catching-up effect, and technical change. Bansal et al. (2022) propose additional indices to measure the productivity change in a system that can be represented by a dynamic network production structure such as the dynamic Malmquist-Luenberger index and dynamic sequential Malmquist-Luenberger.

The analysis of productive efficiency began in the 1950s with the works of Koopmans and Carter (1952); Debreu (1951); and Shephard (1970). Koopmans was the first to provide a definition of productive efficiency, stating that a firm that uses several inputs to produce several outputs is technically efficient if, and only if, it is impossible for it to produce more of any input without producing less of some other output or using one more input (Algeri et al., 2022).

Thus, the efficiency of the financial system is measured in terms of the mobilisation of savings from surplus-savings units and the allocation of these funds amongst surplus-deficit savings units in the economy (Obaidullah, 2005). In the literature on banking efficiency distinguishes two types of efficiency: scale efficiency and X-efficiency (Yaumidin, 2007). In recent years, countries in transition have gained a lot of attention regarding bank efficiency, because they opened their markets to foreign capital and began privatisation (Nurboja & Košak, 2017). The benefits of financial development for economic growth are remarkable; however, in many developing countries competition in banking promotes firms to improve their productivity (Liu & Li, 2022).

Studying changes in the efficiency and scale of the Ecuadorian banking system is of great relevance for developing tools to strengthen the functioning of the entities, in addition to providing the regulator, the Superintendence of Banks (SB), with information to identify inefficiencies that may be correlated with other determinants.

A brief analysis of the banking industry in Ecuador since the 1990s leads to the conclusion that the issuance of the GLFSI in 1994 allowed banks to operate with almost total freedom. Regulation was weak and it did not manage to control certain excesses (linked credits, credit standards, interest rates, etc.), which would later lead to the banking crisis of 1999, resulting in the dollarization of the economy. Later, in 2007, a struggle with the government led the latter to enact the OMFC (Código Orgánico Monetario y Financiero [COMYF], 2014) to regulate the performance of banks, strengthening the control and supervisory bodies (such as the SB); and to put an end to the excesses of the past, promoting the system of popular and solidarity economy (the cooperative sector).

The SB performs an annual classification of bank size results: into “large, medium and small” banks. This classification is obtained using a “percentile methodology” in which the key variable is the total assets of the last reported period (usually the last fiscal year). Therefore, a bank is classified as large if the total assets are greater than 36%, medium between 12% and 36% and small less than 12% of the total assets of the private banking ranking system (Superintendencia de Bancos, 2016).

Table 1 presents some average financial indicators for 2019 that the regulator publishes to diagnose the financial situation of the 24 banking entities according to size:

TABLE 1. Financial variables, on average, in USD (2019)

N	Size	Total loans	Total deposits	Operating costs	Financial margin	Operational efficiency	Financial efficiency
4	Large	4,433,721.84	4,937,631.50	348,917.57	429,841.79	79.09%	5.12%
9	Medium	1,080,010.72	1,246,375.46	79,182.41	111,365.88	72.54%	5.19%
11	Small	87,886.85	70,904.16	8372.60	92,961.22	29.37%	9.79%

Source: Own elaboration based on Superintendency of Banks.

The table above shows that small banks have better financial efficiency ratios than medium and large banks, whilst the operating efficiency of large banks is higher than that of medium and small banks.

2.2 Previous literature

Worldwide, efficiency studies have been specified in the field of X-efficiency. Berger et al. (1993) and Maudos et al. (2002) refer those economies of scale and scope generally explain less than 5% of the percentage of costs; and X-efficiency dominates the effects of returns to scale and multiple production in determining the costs of banking institutions, respectively. On the issue of efficiency produced by geographic expansion, Berger (2000) deduced that geographic expansion improves efficiency by diversifying financial products and instruments issued in different locations. On the other hand, studies by McAllister and McManus (1993); Hughes et al. (1996); Hughes et al. (2000); Demsetz and Strahan (1997); Hughes and Mester (1998) and, Cummins et al. (1999) conclude that US commercial banks found that larger financial institutions and greater geographic coverage tend to achieve better trade-offs between risk and return.

In the same global context regarding bank mergers and acquisitions, Berger (2000) theorises that merger-acquisition processes can be efficient; and it is likely that there are also dynamic efficiency effects in these processes. Altunbaş et al. (2001) estimate that eliminating scale inefficiencies would improve costs by 5%–10%, whilst eliminating X-inefficiencies would improve costs by 25%; likewise, Marín et al. (2008) find that larger entities are more efficient in banks and savings banks in Spain.

Liberalisation and rapid growth have resulted in fragile banking in Vietnam. According to Le et al. (2022) Vietnamese banks experienced a deterioration in technical efficiency in periods of liberalisation. Additionally, bank ownership influences its efficiency levels, suggesting privatisation to improve efficiency. Finally, lending and bank size have non-linear effects on the estimated efficiency levels, concluding that medium-sized banks are more efficient than large and small banks.

In another study by Luo et al. (2017) they investigate the impact of foreign bank penetration on the domestic banking sector in China. Measuring in terms of geographical proximity, they found that exposure to foreign bank branch networks was associated with higher profitability, higher efficiency, and higher non-interest income in domestic banks due to knowledge transfer from foreign banks. A similar study was conducted in Ghana examining foreign bank entry on bank efficiency scores (Ofori-Sasu et al., 2019). The results show that an immediate entry of foreign banks in the short run has a negative relationship with technical and cost efficiency scores, whereas in the long term the entry of foreign banks shows an inconsistent relationship with all three-bank efficiency scores. In this sense, it is concluded that a positive impact of foreign bank entry on bank efficiency scores depends on the form of bank efficiency considered and the interaction between the competitive banking environment and foreign bank entry.

Studies at the Latin American level are directed towards the analysis of X-efficiency and inefficiency, so Dick (1996) studies Argentinean banking with the parametric methodology Thick Frontier Approach (TFA) and shows that the X-inefficiencies of the sector. In addition, the scale elasticities indicate the existence of increasing returns in the industry. Likewise, Marín et al. (2008) determines that the average efficiency is 55%, with public banks having the lowest efficiency levels. Finally, Suescun and Misas (1996) study the efficiency of Colombian banks, showing inefficiencies of 30%.

Finally, at the national level, Mora (2017) estimates the technical efficiency of the Banking System and the Popular and Solidarity System of Ecuador between 2011 and 2016, obtaining efficiency levels above 90%. Recalde Lara (2019) analyses efficiency in the private banking sector, obtaining 100% efficiency in the three largest banks in the industry and levels below 80% in the rest of the banks. Merlo (2017), evaluates the relationship between bank scale and its efficiency in Ecuador for the period 2006–2015, observing a positive relationship between its operational scale and efficiency. According to Buenaño (2004) indicates that there are high levels of cost inefficiency in Ecuadorian banks, which are of the order of 32% on average.

There are therefore various types of research, in which at a global level, X-efficiency, geographic expansion and mergers and acquisitions studies, which contribute to a reduction in banking costs, are the most important. Latin American banking shows inefficiencies in general in studies for Colombia and Argentina; however, at present there are no records or evidence to show that efficiency levels have improved. Finally, at the national level, we find that efficiency levels are presented in the largest banks. However, in 2004, X-inefficiencies appears in the Ecuadorian banking system; thus, it is asserted that, over the years, the Ecuadorian banking system has been improving its efficiency levels, so that this study corroborates such hypothesis.

On the other hand, and with respect to the growth-efficiency relationship, Rajan and Zingales (1996) examine whether financial development facilitates growth, confirming that the development of the financial system reduces the costs of bank financing. According to Belke et al. (2015) analyse the impact of banking sector efficiency and regional growth in Europe, resulting that there is a positive relationship between banking efficiency and regional growth.

In another way, Havranek et al. (2016) analysed the relationship between bank efficiency and bank output through outputs such as loans and deposits; pointing out an inverse relationship between efficient banks and placement and deposit activities.

3 DATA AND METHODOLOGY

The databases used are those published by the Superintendency of Banks (SB), the Central Bank of Ecuador (BCE) and the Association of Private Banks of Ecuador (APBE) for the years 2015–2019. This time window is defined because Ecuador in this period went through some events that could influence banking stability such as the fall in oil prices, a huge earthquake, the change of president, a social conflict, and so forth. Being a dollarized economy, the management of financial institutions and banks should take care of liquidity and credit risk to avoid the credit cycle. All private banks operating in the Ecuadorian financial system belonging to “private commercial banking” are considered. Our sample consists of 24 banks: 4 large, 9 medium-sized and 11 small banks. Currently, these entities have the same regulations for their operation, which allows them to carry out the same activities. Therefore, the common regulatory framework in which they operate allows them to be considered as companies in the same competitive environment.

From the databases used (SB and APBE), information has been obtained on different characteristics related to the type and volume of activity carried out by the banking entities evaluated, practically 100% of the operating companies.

There are two options for calculating efficiency: parametric and non-parametric approaches. The first is a probabilistic approach and tries to separate noise from inefficiencies whilst the second is non-probabilistic and combines noise and inefficiencies (Crouhy et al., 1999).

Through the DEA (data envelopment analysis) methodology, individual technologies of the firms are captured by means of the frontier, which is constructed based on individual optimizations, thus taking advantage of individual rather than aggregate analysis. This methodology also allows the incorporation of different returns to scale, since not all firms have the same types of returns to scale. So, we measure efficiency to DEA, a nonparametric technique widely discussed and accepted in the frontier efficiency literature (He et al., 2011). One of the main advantages of this methodology is that it uses radial measures (interpretation of costs and revenues), and allows the use of external information, such as the researcher's criteria. In different analyses of the banking industry, the non-parametric DEA method was used to analyse the most appropriate risk measure when calculating bank efficiency (Louhichi & Boujelbene, 2019). One of the main advantages of using this method is that DEA is suitable for the small sample size available for this analysis (Biener & Eling, 2011).

Regarding the classic DEA models of Constant Returns to Scale (CCR), created by Charnes et al. (1978), they assume constant returns to scale, since, for increases in inputs, outputs increase proportionally. On the other hand, Variable Returns to Scale (BCC) presented by Banker et al. (1984), considers variable returns to scale, that is, for an increase in inputs, there is an increase in outputs of greater or lesser proportion.

The formulation of the BCC model to outputs is (Mora, 2017):

Min \frac{\sum_{i = 1}^{m} ν_{i} x_{i}^{(h)}}{\sum_{r = 1}^{s} u_{r} y_{r}^{(h)}}

(1)

Subject to:

\frac{\sum_{i = 1}^{m} ν_{i} x_{i}^{(j)}}{\sum_{r = 1}^{s} u_{r} y_{r}^{(j)}} \geq 1 for j = 1, 2, \dots n

ν_{i} \geq 0 i = 1, 2, \dots \dots m

u_{r} \geq 0 r = 1, 2, \dots \dots s

Where “n” is the number of companies, “m” the number of inputs; and “s” the following outputs:

$x_{i}^{(h)}$ : i^th input of the evaluated company.

$y_{r}^{(h)}$ : r^th output of the evaluated company.

$x_{i}^{(j)}$ : i^th input of the j^th company evaluated.

$y_{r}^{(j)}$ : r^th output of the j^th company evaluated.

$ν_{i}$ : Variable representing the weighting of the i^th input.

$u_{r}$ : Variable representing the weighting of the r^th output.

The function to be minimised is the technical inefficiency of the evaluated company, being the reciprocal of the technical efficiency measure. It is assumed that the evaluated company is company “h”. To obtain the integral evaluation of all the companies to be studied, a linear programme must be solved for each company (h = 1, 2 …n).

Then, by equating the denominator of the function to be minimised to the company, and linearizing the given constraints, an equivalent linear model results, that is, the multiplier model:

Min \sum_{i = 1}^{m} ν_{i} x_{i}^{(h)}

(2)

Subject to:

\sum_{r = 1}^{s} u_{r} y_{r}^{(h)} = 1

\sum_{i = 1}^{m} ν_{i} x_{i}^{(j)} \geq \sum_{r = 1}^{s} u_{r} y_{r}^{(h)} for j = 1, 2, \dots \dots . n

ν_{i} \geq 0 i = 1, 2, \dots \dots m

u_{r} \geq 0 r = 1, 2, \dots \dots s

The dual problem related to the previous model (2) is called the envelope model:

M á x I^{(h)}

(3)

Subject to:

\sum_{j = 1}^{n} z_{j} x_{i}^{(j)} \leq x_{i}^{(h)} for i = 1, 2, \dots \dots . m

I^{(h)} y_{r}^{(h)} \leq \sum_{j = 1}^{n} z_{j} y_{r}^{(j)} for r = 1, 2, \dots \dots . s

z_{j} \geq 0

Where:

$z_{j}$ : Variable, which represents the weighting of the j-th observed firm. The weights define a “potential” firm against which the firm “h” whose efficiency is to be defined is compared. $I^{(h)}$ : It is the optimal value, as a measure of technical efficiency. Its reciprocal measures the technical efficiency of the evaluated company, $E^{(h)} = I$ . To obtain the measures for all the companies analysed, “n” linear problems are solved. The index $E^{(h)} \leq 1$ .

A company is technically or Pareto Koopmans efficient if:

$E^{(h)} = I$
All slack variables are null.

Therefore, the formulation of the output-oriented BCC model can be rewritten as:

Min \frac{\sum_{i = 1}^{m} ν_{i} x_{i}^{(h)} + ν_{o}}{\sum_{r = 1}^{s} u_{r} y_{r}^{(h)}}

(4)

Subject to:

\frac{\sum_{i = 1}^{m} ν_{i} x_{i}^{(j)} + ν_{o}}{\sum_{r = 1}^{s} u_{r} y_{r}^{(j)}} \geq 1 for j = 1, 2, \dots n

ν_{i} \geq 0 i = 1, 2, \dots \dots m

u_{r} \geq 0 r = 1, 2, \dots \dots s

ν_{o} without restriction

Where:

$ν_{o}$ : is the scalar variable that, according to its sign, will indicate the type of return to scale of the company, as follows:

$ν_{o}$ < 0 ➔ Increasing Returns to Scale

$ν_{o}$ = 0 ➔ Constant Returns to Scale

$ν_{o}$ ˃ 0 ➔ Decreasing Returns to Scale

For the CCR model, the function is similar, the denominator of the function to be minimised of the model (4) is equal to one, and its restrictions are linearized, the model of the multipliers is obtained:

Min \sum_{i = 1}^{m} ν_{i} x_{i}^{(h)} + ν_{o}

(5)

Subject to:

\sum_{r = 1}^{s} u_{r} y_{r}^{(h)} = 1

\sum_{i = 1}^{m} ν_{i} x_{i}^{(j)} + ν_{o} \geq \sum_{r = 1}^{s} u_{r} y_{r}^{(j)} for j = 1, 2, \dots \dots . n

ν_{i} \geq 0 i = 1, 2, \dots \dots m

u_{r} \geq 0 r = 1, 2, \dots \dots s

ν_{o} Without restriction

The dual problem of (5) is the BCC of the envelope

M á x I^{(h)}

M á x I^{(h)}

(6)

Subject to:

\sum_{j = 1}^{n} z_{j} x_{i}^{(j)} \leq x_{i}^{(h)} for i = 1, 2, \dots \dots . m

I^{(h)} y_{r}^{(h)} \leq \sum_{j = 1}^{n} z_{j} y_{r}^{(j)} for r = 1, 2, \dots \dots . s

\sum_{j = 1}^{n} z_{j} = 1

z_{j} \geq 0

The choice of proxy variables for outputs and inputs is one of the most important problems to be solved in any efficiency study in the banking sector. The definition of bank output is controversial. According to (Casu & Molyneux, 2003), there are at least three approaches:

Asset approach, which considers loans and other assets as bank's outputs, whilst deposits and other liabilities as bank's inputs.
User cost approach, which considers outputs as any input that yields a higher return or a lower loss than its opportunity cost.
Value added approach, which considers all assets and liabilities of the bank as an output and any item with higher returns as the main output (Berger & Humphrey, 1994).

The production approach—not used in similar studies in the country—is used in this study because it is relevant since the income received by banks has diversified due to the high heterogeneity of products. The input variables under this approach comprise administrative and labour expenses, together with financial expenses to convert them into interest income and other operating income. Thus, according to (Pirateque et al., 2013), they classify inputs and outputs by the production approach, proposing as outputs: Interest Income and Other Operating Income; and, as inputs: Personnel Expenses, Administrative Expenses and Financial Expenses.

Table 2 shows the summary of the descriptive statistics of the variables corresponding to the sample of entities in the period studied:

TABLE 2. Descriptive statistics of the sample (in USD)

Variable	Tamaño	Outputs		Inputs
Variable	Tamaño	Interest income	Other operating income	Personal expenses	Administrative expenses	Financial expenses
Media	Large^a	427,564	25,541	92,323	217,094	113,539
	Medium^b	105,984	3956	23,516	43,075	33,170
	Small^c	12,754	583	3905	4771	3889
SD	Large	241,067	35,179	39,615	142,543	44,850
	Medium	65,484	8583	12,815	33,527	24,096
	Small	9041	788	2152	3459	3329
Minimum	Large	224,125	501	48,168	107,942	62,121
	Medium	22,728	40	7366	0	86
	Small	993	0	1181	1139	114
Maximum	Large	930,633	100,616	167,267	521,958	202,009
	Medium	245,268	48,690	46,787	150,623	92,891
	Small	38,015	3140	9263	15,656	11,671

^a Guayaquil, Pacífico, Pichincha, Produbanco.
^b Austro, Bolivariano, City Bank, Dinners, General Rumiñahui, Internacional, Loja, Machala, Solidario.
^c Procredit, Amazonas, Comercial de Manabí, Litoral, Coopnacional, Capital, Finca, Del Bank, D Miro, Desarrollo, Visiónfund Ecuador.
Source: Own elaboration.

For processing the information, the DMUs (private banks) are defined, the variables are identified, and the models are run to obtain the technical efficiency indexes, to make inferences and analyse the results at the individual level of each financial entity, and through the BCC model selected for efficiency in its maximisation version (product-oriented approach).

This measure of technical efficiency allows for econometric performance and modelling using the Balanced Panel Data methodology (Panel EGLS, Swamy and Arora component variance estimator) with random effects. Panel data is the evidence from the same cross-section or cross-section with N individuals over time, such that information is obtained for everyone, i = 1, 2, 3…N, for each point in time t = 1, 2, 3…T, given in a sample of N × T. In this paper, we work with 22 banks (cross-sectional units) and the time series is 60 months; therefore, the model will be estimated with 1320 observations in total.

By referring to a panel data model with random effects it means that the parameter is a random variable, whose realisations are the individual effects of each element composing the panel and distributed independently of $X$ . This value is different for each element and differs in each of them from a mean value.

Therefore, the resulting regression for a panel data model with random effects is:

Y_{it} = \propto + β_{1} X_{1 it} + β_{2} X_{2 it} + ε_{i} + u_{it}

(7)

So, the error term is now $w_{it} = ε_{i} + u_{it}$ , with the assumption that the variances of are uncorrelated $w_{it} = σ_{ε}^{2} + σ_{u}^{2}$ (Stata Corp., 2021).

Likewise, initially a database was structured with 24 panels, each one with 60 observations; subsequently, to obtain a balanced panel database, 2 panels containing incomplete information in the period analysed were eliminated; therefore, the worked database contemplated 22 banks (4 large, 8 medium and 10 small), with 60 observations for each institution of the variables studied in the period 2015–2019. The variable “Number of Accounts” contained incomplete information, so the imputation of these values was performed with TRAMO-SEATS, which is a seasonally adjustment technique that deals with outliers and missing values.

4 RESULTS AND ANALYSIS

4.1 Output-oriented technical efficiency (variable return to scale)

Table 3 illustrates the value of output-oriented technical efficiency (variable return to scale) obtained under the BCC Model. The report shows that the average technical efficiency of large banks is 98.15%, whilst that of medium and small banks is 85.46% and 84.11%, respectively. Banco del Pacifico is a large bank that, in the period analysed, showed inefficiency, particularly in 2015, because it belongs to the State, and suffered the decrease in deposits by public entities affected by the fall in oil prices. Likewise, Banco Produbanco presents inefficiencies in the group of large banks, these inefficiencies are evidenced in the years 2015, 2016, 2017 and 2018, being the only large bank that is inefficient during the years studied.

TABLE 3. Technical efficiency output-oriented (variable return to scale, VRS)

Financial entity	DMU	2015	2016	2017	2018	2019	Technical efficiency average
Banco Guayaquil	dmu1	100%	100%	100%	100%	100%	100%
Banco Pacifico	dmu2	99.26%	100%	100%	100%	100%	99.85%
Banco Pichincha	dmu3	100%	100%	100%	100%	100%	100%
Banco Produbanco	dmu4	90.89%	86.68%	86.46%	99.70%	100.00%	92.75%
Banco Austro	dmu5	72.70%	79.13%	75.79%	80.42%	90.69%	79.75%
Banco Bolivariano	dmu6	82.86%	91.04%	88.41%	90.75%	91.97%	89.01%
Banco City Bank	dmu7	98.49%	100%	100%	100%	100%	99.70%
Banco Dinners	dmu8	76.07%	75.32%	73.92%	84.80%	100%	82.02%
Banco General Rumiñahui	dmu9	66.17%	67.85%	67.91%	71.34%	74.90%	69.63%
Banco Internacional	dmu10	100%	100%	100%	100%	100%	100%
Banco de Loja	dmu11	100%	100%	100%	100%	100%	100%
Banco de Machala	dmu12	60.38%	64.20%	69.92%	72.53%	75.27%	68.46%
Banco Solidario	dmu13	72.04%	75.89%	90.69%	84.18%	79.85%	80.53%
Banco Procredit	dmu14	70.74%	80.58%	81.61%	83.13%	65.35%	76.28%
Banco Amazonas	dmu15	63.47%	76.58%	75.23%	54.42%	57.78%	65.50%
Banco Comercial de Manabí	dmu16	61.90%	58.74%	72.65%	70.60%	57.44%	64.27%
Banco Litoral	dmu17	100%	100%	100%	100%	100%	100%
Banco Coopnacional	dmu18	48.54%	53.11%	68.31%	100%	100%	73.99%
Banco Capital	dmu19	100%	83.53%	78.63%	84.68%	77.56%	84.88%
Banco Finca	dmu20	100%	100%	100%	100%	100%	100%
Banco Del bank	dmu21	86.99%	83.35%	85.89%	90.54%	77.10%	84.77%
Banco D Miro	dmu22	71.52%	71.74%	73.27%	77.51%	83.81%	75.57%
Banco Desarrollo	dmu23	100%	100%	100%	100%	100%	100%
Banco Visiónfund Ecuador	dmu24	100%	100%	100%	100%	100%	100%
Sample Average Efficiency		84.25%	85.32%	87.03%	89.36%	88.82%	86.96%

Source: Own elaboration.

Table 3 shows the evolution of the level of technical efficiency measured by the bank product-oriented model under variable returns to scale for each of the banks in each year. In the last column, the average efficiency over the analysis period 2015–2019 is reported.

Amongst medium-sized banks, the average TE is 85.46% and the banks that show technical efficiency throughout the period analysed are Banco Internacional and Banco de Loja. Small banks show, on average, a variable trend; their average technical efficiency score is in the range [48.54%– 100%].

4.2 Output-oriented efficiency of scale (variable return to scale)

Table 4 illustrates the output-oriented efficiency of scale (variable return to scale) obtained under the BCC Model. The average scale efficiency of large banks is 43.38%, whilst that of medium and small banks is 49.05% and 75.60%, respectively.

TABLE 4. Scale efficiency output-oriented (variable return to scale, VRS)

Financial entity	DMU	2015	2016	2017	2018	2019	Scale efficiency average
Banco Guayaquil	dmu1	50.85%	49.35%	45.23%	41.36%	33.95%	44.15%
Banco Pacifico	dmu2	40.68%	41.17%	40.23%	36.48%	35.45%	38.81%
Banco Pichincha	dmu3	50.00%	52.04%	44.05%	40.05%	42.10%	45.65%
Banco Produbanco	dmu4	47.36%	50.50%	47.11%	41.68%	37.94%	44.92%
Banco Austro	dmu5	52.81%	52.24%	48.68%	45.47%	37.75%	47.39%
Banco Bolivariano	dmu6	51.08%	51.67%	48.39%	43.70%	37.48%	46.47%
Banco City Bank	dmu7	35.21%	32.90%	34.29%	37.94%	29.98%	34.06%
Banco Dinners	dmu8	50.72%	52.97%	46.24%	41.41%	30.10%	44.29%
Banco General Rumiñahui	dmu9	45.09%	45.56%	42.58%	41.55%	35.18%	41.99%
Banco Internacional	dmu10	41.77%	45.19%	38.29%	37.51%	33.44%	39.24%
Banco de Loja	dmu11	100%	100%	100%	100%	100%	100%
Banco de Machala	dmu12	42.71%	41.58%	35.92%	36.81%	32.15%	37.83%
Banco Solidario	dmu13	50.50%	49.76%	50.94%	54.63%	45.22%	50.21%
Banco Procredit	dmu14	60.58%	60.77%	46.20%	46.94%	41.17%	51.13%
Banco Amazonas	dmu15	86.11%	100%	100%	95.92%	79.60%	92.33%
Banco Comercial de Manabí	dmu16	99.62%	85.49%	75.01%	76.31%	63.92%	80.07%
Banco Litoral	dmu17	100%	100%	100%	100%	100%	100%
Banco Coopnacional	dmu18	56.39%	74.48%	62.22%	100%	100%	78.62%
Banco Capital	dmu19	59.24%	54.68%	53.72%	48.89%	29.98%	49.30%
Banco Finca	dmu20	100%	100%	100%	100%	100%	100%
Banco Del bank	dmu21	44.44%	40.74%	42.79%	43.80%	33.06%	40.97%
Banco D Miro	dmu22	43.88%	40.45%	39.10%	40.47%	32.44%	39.27%
Banco Desarrollo	dmu23	100%	100%	100%	100%	100%	100%
Banco Visiónfund Ecuador	dmu24	100%	100%	100%	100%	100%	100%
Sample average efficiency		62.88%	63.40%	60.04%	60.46%	54.62%	60.28%

Source: Own elaboration.

Table 4 shows the evolution of the level of scale efficiency measured by the bank product-oriented model under variable returns to scale for each of the banks. The average efficiency over the analysis period 2015–2019 is presented in the last column.

Amongst the medium-sized banks, the average EE is 49.05% and the bank that shows scale efficiency throughout the period analysed is Banco de Loja. Small banks show an average variable trend in their average efficiency of scale, the score is in the interval [33.06%–100%].

Ultimately, inefficient banks can improve their performance by learning from those institutions that show better scores; Banco Guayaquil, in the case of large banks; El Banco de Loja amongst the medium-sized ones, and Banco del Litoral, Banco de Desarrollo and Banco Visión, amongst the smallest, by making better use of costs (i.e., staff costs, administrative costs and interest paid).

4.3 Reference sets and technical efficiency

This section provides the results obtained regarding the variable returns to scale (VRS). The efficiency values show which of the twenty-four (24) banking institutions achieve some level of efficiency relative to the most efficient frontier. Table 5 shows the DEA efficiency values and benchmark sets for each DMU over the entire analysis period.

TABLE 5. DEA efficiency values and reference sets for each DMU

Banking institution	DMU	2015		2016		2017		2018		2019
Banking institution	DMU	Frec	Peer group	Frec	Peer group	Frec	Peer group	Frec	Peer group	Frec	Peer group
Banco Guayaquil	dmu1	4	dmu1, dmu14, dmu20	2	dmu1	4	dmu1, dmu7, dmu20, dmu24	1	dmu1, dmu7, dmu20, dmu24	3	dmu1, dmu7, dmu23, dmu24
Banco Pacifico	dmu2	2	dmu1, dmu2, dmu3, dmu7, dmu8	1	dmu2, dmu3, dmu7	0	dmu1, dmu3, dmu7, dmu9	1	dmu2	1	dmu2, dmu3, dmu7
Banco Pichincha	dmu3	3	dmu1, dmu3, dmu7, dmu13	2	dmu3, dmu7	4	dmu3, dmu7	1	dmu3, dmu7, dmu24	2	dmu3, dmu7, dmu24
Banco Produbanco	dmu4	1	dmu4, dmu7, dmu8	3	dmu4, dmu7, dmu11, dmu14	1	dmu1, dmu3, dmu4, dmu7, dmu9, dmu24	2	dmu4, dmu7, dmu24	3	dmu4, dmu7, dmu24
Banco Austro	dmu5	0	dmu7, dmu9, dmu12, dmu13	0	dmu4, dmu7, dmu9, dmu14	0	dmu7, dmu9, dmu22	0	dmu6, dmu7, dmu9	0	dmu1, dmu4, dmu7, dmu9, dmu11
Banco Bolivariano	dmu6	0	dmu1, dmu2, dmu3, dmu8, dmu9	0	dmu1, dmu4, dmu7, dmu9	0	dmu1, dmu3, dmu7, dmu9	2	dmu4, dmu6, dmu7, dmu11	1	dmu4, dmu6
Banco City Bank	dmu7	8	dmu7, dmu13, dmu20, dmu21	14	dmu7	12	dmu7, dmu23	10	dmu7	9	dmu7
Banco Dinners	dmu8	5	dmu8	1	dmu8	1	dmu8	2	dmu8	1	dmu8
Banco General Rumiñahui	dmu9	5	dmu7, dmu9	6	dmu7, dmu9	7	dmu9	4	dmu9	6	dmu9
Banco Internacional	dmu10	0	dmu7, dmu9, dmu12, dmu18	0	dmu7, dmu9, dmu14, dmu24	0	dmu7, dmu9, dmu15, dmu22	0	dmu7, dmu9, dmu22	0	dmu7, dmu9, dmu22
Banco de Loja	dmu11	2	dmu11	2	dmu11	1	dmu11	2	dmu11	2	dmu11
Banco de Machala	dmu12	4	dmu7, dmu12	4	dmu7, dmu12	0	dmu7, dmu9, dmu20, dmu22	0	dmu8, dmu9, dmu22	0	dmu9, dmu22, dmu23
Banco Solidario	dmu13	4	dmu13	0	dmu7, dmu9, dmu12, dmu14	0	dmu7, dmu21, dmu22	0	dmu7, dmu22, dmu23	0	dmu7, dmu9, dmu22
Banco Procredit	dmu14	2	dmu14	7	dmu14	2	dmu14	2	dmu14	2	dmu14
Banco Amazonas	dmu15	0	dmu9, dmu18, dmu20, dmu23	0	dmu7, dmu9, dmu14, dmu24	3	dmu15	1	dmu15	0	dmu1, dmu16, dmu20
Banco Comercial de Manabí	dmu16	0	dmu8, dmu11, dmu20, dmu21, dmu23	0	dmu7, dmu12, dmu23, dmu24	2	dmu16	2	dmu16	4	dmu16
Banco Litoral	dmu17	0	dmu12, dmu21, dmu23	0	dmu7, dmu12, dmu23, dmu24	0	dmu7, dmu21, dmu22, dmu23	0	dmu7, dmu14, dmu22, dmu23	0	dmu9, dmu14, dmu16, dmu22, dmu23
Banco Coopnacional	dmu18	3	dmu18	0	dmu7, dmu14, dmu22, dmu24	0	dmu7, dmu14, dmu15, dmu20, dmu23	1	dmu18	1	dmu18
Banco Capital	dmu19	0	dmu21, dmu23	0	dmu21, dmu22, dmu23	0	dmu16, dmu22, dmu23	0	dmu16, dmu22, dmu23	0	dmu16, dmu22, dmu23
Banco Finca	dmu20	5	dmu20	1	dmu20	4	dmu20	2	dmu20	2	dmu20
Banco Del bank	dmu21	6	dmu21	2	dmu21	3	dmu21	1	dmu21	0	dmu7, dmu22, dmu23
Banco D Miro	dmu22	1	dmu21, dmu22	3	dmu22	7	dmu22	6	dmu22	7	dmu22
Banco Desarrollo	dmu23	6	dmu23	4	dmu23	5	dmu23	4	dmu23	6	dmu23
Banco Visiónfund Ecuador	dmu24	0	dmu23	6	dmu24	3	dmu24	4	dmu7, dmu24	4	dmu24

Source: Own elaboration.

With respect to benchmark sets, it is observed that not all inefficient DMUs have the same benchmarks (reference sets). Inefficient DMUs can improve their performance by using the best practices of their peers to transform efficiently their inputs into outputs. Specifically, inefficient DMU's should adopt the benchmark policies and techniques of their peers in the production of services. Interestingly, in this study amongst the large inefficient DMUs only one large efficient DMU is compared to Banco Pichincha.

The results in Table 6 obtained by proposing the assumption of variable returns to scale (VRS) and output oriented in the two scenarios of production of financial income and other operating income, keeping the input variables (Personnel Expenses, Administrative Expenses and Financial Expenses) unchanged.

TABLE 6. Results obtained from the assumption of variable returns to scale (VRS), output oriented

Banking institution	DMU	Depending on interest income production	Depending on the production of other operating revenues
Banking institution	DMU	Technical efficiency	Technical efficiency
Banco Guayaquil	dmu1	100%	100%
Banco Pacifico	dmu2	99.85%	91.96%
Banco Pichincha	dmu3	100%	100%
Banco Produbanco	dmu4	79.98%	91.43%
Banco Austro	dmu5	64.71%	79.55%
Banco Bolivariano	dmu6	80.19%	88.31%
Banco City Bank	dmu7	99.70%	49.24%
Banco Dinners	dmu8	78.32%	79.16%
Banco General Rumiñahui	dmu9	68.27%	65.63%
Banco Internacional	dmu10	100%	87.00%
Banco de Loja	dmu11	100%	100%
Banco de Machala	dmu12	68.46%	51.12%
Banco Solidario	dmu13	77.23%	69.78%
Banco Procredit	dmu14	75.20%	71.45%
Banco Amazonas	dmu15	54.81%	65.50%
Banco Comercial de Manabí	dmu16	64.27%	37.51%
Banco Litoral	dmu17	92.39%	100%
Banco Coopnacional	dmu18	73.57%	68.78%
Banco Capital	dmu19	84.88%	35.14%
Banco Finca	dmu20	100%	100%
Banco Del bank	dmu21	84.77%	33.54%
Banco D Miro	dmu22	75.57%	35.48%
Banco Desarrollo	dmu23	100%	56.62%
Banco Visiónfund Ecuador	dmu24	100%	100%
Average Sample Efficiency		84.26%	73.22%

Source: Own elaboration.

First, the average technical efficiency in both the financial income and other operating income production scenarios is 84.26% and 73.22% respectively, although there are some differences between the corresponding efficiency values. For example, seven DMUs are efficient in the financial income production scenario, whilst six DMUs are efficient in the case of production of other operating income. Subsequently, there is evidence of a significant difference between the two sets of technical efficiency values. Defining 𝜇𝐼𝐹 y 𝜇O𝐼 as the average efficiency derived from the financial income and other operating income results, respectively, the following hypotheses were designed:

H_{o} : μ_{IF} = μ_{OI}

H_{1} : μ_{IF} \neq μ_{OI}

In Table 7, the Student's t-test shows that, for a significance level of 5%, there is a statistically significant difference between the mean technical efficiency, calculated with financial income, and that calculated with other operating income. It is also corroborated by the lower value of the correlation coefficient (0.47), whose results show that the use of either of the two output variables has a direct impact on the measurement of the technical efficiency of DMUs.

TABLE 7. Student's t-test for two samples assuming unequal variances

Statistics	Variables (outputs)
Statistics	Interest income	Other operating income
Mean	0.842562917	0.732159583
Variance	0.020993864	0.055191252
Remarks	24	24
Degrees of freedom	38
Statistic t	1.959533712
p-value**	0.057415774
Critical value of t (two - tailed)	2.024394164
Significance level	0.05
Correlation coefficient	0.47112158
Determination coefficient R^2	0.2219555
R^2 adjusted	0.186590
SE	0.130678

Note: (*) significant at 1%; (**) significant at 5% and (***) significant at 10%.
Source: Own elaboration.

With the results obtained, we contrasted the technical efficiency coefficients with Kenyan financial institutions whose results show an average efficiency of 50.6% in the two scenarios (output variables), both in financial income and gross loan portfolio production, with 89% and 78% of the financial institutions efficient in each scenario respectively. The t-test shows that there are no statistically significant differences between the two sets of efficiencies, which allows clarifying that, based on these findings, there is not enough evidence to show that changing the output variables would lead to a significant change in DMU efficiency on average (Ochola, 2016). Likewise, in the case of the Chilean banking system, an overall average efficiency of 85.74% is evident (Cofré et al., 2019). For the Bolivian Financial System, commercial banks obtained better efficiency levels between 79.9% and 83.3% (Rosales & Gutiérrez, 2019). Following to Jiménez-Hernandez et al. (2019) in their estimates of technical efficiency show that average efficiency levels vary widely amongst Latin American countries, with values ranging from 95.3% for Chile to 29.4% for Nicaragua. Argentine banks 47.5% are efficient banks under constant and variable returns (Seffino & Maldonado, 2016).

In contrast, in Table 6, the results show that the average efficiency for the Ecuadorian banking system is 84.26% and 73.22% for the output variables interest income and other operating income respectively, evidencing the existence of 29% and 25% of efficient banking institutions in each of these 2 scenarios. The t-test demonstrates statistically significant differences between the two sets of efficiencies, which concludes that there is sufficient evidence to show that changing the output variables leads to a strong change in the average efficiency of the DMUs.

The efficiency levels obtained in this study for Ecuadorian banks are lower compared to those shown by Haro and Poaquiza (2022) for the case of cooperatives. Frontier Efficiency Analysis software calculated higher levels of technical efficiency under the argument that regulation is less severe than in the case of banks, and shows that those cooperatives that did not subscribe to regulation have an average efficiency of 91.33%, whilst already regulated entities have an average of 94.18%.

4.4 Econometric growth-efficiency modelling

From the theoretical framework described in the Section 2.2, the following econometric model has been developed, which adequately adjusts to the economic and financial situation between 2015 and 2019.

Following (Diallo, 2017), who determined the econometric specification of banking industry growth, as:

β {IG}_{i} = β_{0} + β_{1} CI (k) + β_{2} II (j) + β_{3} S (j, k) + β_{4} FD (j) + β_{5} ER (k) + β_{6} C (j, k) + u_{j, k}

(8)

Where:

$β {IG}_{i}$ = Banking Industry Growth.

$CI$ = Country Indicators.

$II$ = Industry Indicators.

$S$ = Size.

FD

= Financial Dependence is measured by HHI Deposits (concentration of deposits or deposits in the 22 financial institutions), which is calculated using the Herfindahl-Hirschman Index (Romero et al., 2020):

\sum_{i = 1}^{n} {\frac{q_{i}}{Q}}^{(2)} = \sum_{i = 1}^{n} S_{i}^{(2)}

Where:

$q_{i}$ = Individual bank market share.

$Q$ = Total market share of the banking sector.

$S_{i}$ = Market share of the i-th banking unit of analysis.

$n$ = Total number of analysis entities.

The HHI of Deposits is expressed as financial dependence since banks subsist on the placements and deposits they register from their clients.

$ER$ = Efficiency Rate.

$C$ = Controls.

Within the theory of industrial organisation, it is possible to approximate a causal relationship of the growth of the banking industry and suggests for the case of omitted variables that the financial sector can use to explain its growth, to approximate with proxy variables, and reduce the distortion due to endogeneity (Gujarati & Porter, 2010).

Thus, in reference to equation (8), we have the following proxy variables, applied for the present study:

TA = β_{0} + β_{1} GDP + β_{2} HHI D + β_{3} NA (- 1) + β_{4} TE + β_{5} TCF (- 2) + u_{j, k}

(9)

Where:

$TA$ = It is a proxy of Banking Industry Growth, specified by Total Assets in USD.

$GDP$ = It is a proxy of Country Indicators, measured by the Ecuadorian Gross Domestic Product at constant 2007 prices.

$HHI D$ = It is a proxy of Financial Dependence, measured by HHI Deposits (concentration of deposits or deposits in the 22 financial institutions) and calculated using the Herfindahl-Hirschman Index.

$NA$ = It is a proxy of Size, measured by the actual number of accounts registered in the 22 financial institutions studied.

$TE$ = It is a proxy of Efficiency Rate, specified by the Technical Efficiency indicator. In this study, it is calculated by DEA, which includes the Interest Income and Other Operating Income as output variables, and Personnel Expenses, Administrative Expenses and Financial Expenses as input ones.

TCF

= It is a proxy of Controls, regarding to the value attributable to the costs set by the State, the Superintendence of Banks, and the regulatory entities, and it refers to Taxes, Contributions and Fines.

TA = - 3043955 + 605787.9 (TE) + 5853810 (HHI D) + 0, 000286 (GDP) + 1.519 (NA) + 1.826 (TCF)

(10)

Consequently, through the results presented, we have that the growth of the banking industry, denoted by the cumulative Total Assets of the 22 banks analysed, is determined by the direct relationship of: the technical efficiency of each bank; the concentration of bank deposits; GDP; the number of accounts or size lagged one period (the lag is explained by the adjustment that the banking institution takes to establish by the incremental of accounts opened in the institution); taxes, contributions and fines, or controls lagged two periods (the lag is explained by the adjustment in which banking institutions take time to implement measures imposed by regulators).

Although no evidence has been found on the lag of one period on the variable Number of Accounts; and of two periods on the variable Taxes, Contributions and Fines, used in this study, it can be stated that the included lags refer to:

Procedures.
Adjustment and coupling to the increase in financial demand (opening of new bank accounts).
Implementation of established laws and regulations, which take some time to be put into effect.

These determinants constitute increases in intertemporal banking development, since the financial institution that obtains greater demand and adapts to new regulatory controls adjusts to grow in the future, in this case in the short term (between 1 and 2 months).

As Table 8 illustrates, all the variables used in the model are individually statistically significant at 1%, 5% and 10%. Likewise, the variables are significant, and explain according to the ( $\bar{R^{2}}$ ) 58.51% of the growth of the banking industry.

TABLE 8. Results of coefficients, significance, and indicators of the econometric growth-efficiency model

Dependent variable: TA
Variable	Coefficient	SE	t-Statistic	Prob.
TE*	605787.9	105134.4	5.762034	0.0000
HHI D**	5853810.0	2886654.0	2.027888	0.0428
GDP*	0.000286	6.03E-05	4.752215	0.0000
NA(−1) *	1.519418	0.040492	37.52377	0.0000
C*	−3043955.0	915640.7	−3.324399	0.0009
TCF(−2) ***	1.826247	1.074307	1.699930	0.0894
Effects specification
			SD	Rho
Cross-section random			182344.2	0.5253
Period random			25129.78	0.0100
Idiosyncratic random			171491.7	0.4647
Weighted statistics
R-squared	0.585076	Mean dependent var		197314.9
Adjusted R-squared	0.583442	SD dependent var		374264.6
S.E. of regression	241555.2	Sum squared residual		7.41E+13
F-statistic	358.1600	Durbin-Watson stat		0.324570
Prob(F-statistic)	0.000000
Unweighted statistics
R-squared	0.750871	Mean dependent var		1615640.0
Sum squared residual	1.86E+15	Durbin-Watson stat		0.013220

* Significant at 1%;
** Significant at 5%;
*** Significant at 10%.
Source: Own elaboration.

The model has no specification errors, since by means of the Breusch-Pagan tests and the Hausman test, it was determined that the regression should be modelled with balanced panel data with random effects. Likewise, to check the validity of the model, the non-existence of heteroscedasticity, multicollinearity and autocorrelation is evidenced.

5 CONCLUSIONS AND RECOMMENDATIONS

The aim of this paper is to evaluate the efficiency levels of 24 banks in Ecuador from 2015 to 2019 under two performance scenarios—financial income and other operating income—as well as to assess the potential improvement of financial institutions according to their size: large, medium and small.

In both sceneries, an average technical efficiency value of 84.26% and 73.22% is obtained, respectively. It implies that changing the output variable ceteris paribus the input variables do affect the average technical efficiency value. A t-test of differences between the mean scores confirmed this result; the correlation analysis between the technical efficiencies of the banks for the two cases analysed gives raise to the same evidence. When analysing the technical and scale efficiency of the Ecuadorian banking system for the period 2015–2019 five banks manage to achieve overall efficiency. This is the case of the following banks: Guayaquil, Loja, de Desarrollo and Visionfund, being these entities, the ones taken as benchmarks for the remaining banking institutions that require making improvements in term of costs. The main source of inefficiency is related to scale (see Table 4), with a scale efficiency index of around 60% lower than that of the previous period 2011–2016, when it reached 95.46%, suggesting that banking performance in this period was affected by the abovementioned events.

Regarding the potential improvement for each inefficient entity, the results show that inefficient banks in both scenarios can improve their performance by learning from a large benchmark bank. Similarly, in the input target values, it is highlighted that those efficient entities have their target values equal to the actual value, and when comparing in the two scenarios the emerging trends of the actual and target values, these are the same. The student's t-test, at the 5% significance level, shows that there is a statistically significant difference between the average target value in the financial income and other operating income scenarios.

The main limitation of this study is the use of a deterministic and non-parametric DEA. In addition, considering the availability of complete information in the database of the Superintendence of Banks, we used the total number of banks regardless of their size, which led to the evaluation by groups to show whether large size is synonymous of efficiency, and conversely, whether smaller size implies inefficiency. In addition, it would have been appropriate to compare cost efficiency by constructing an efficiency frontier with all entities, but due to data limitations (number of employees per entity), this was not possible and, therefore, a result for the three size groups is presented.

A competitive market structure, although ideal, does not match the reality of the banking industry in Ecuador which, despite the implications of the inefficiency of these entities evidenced by this research, shows that large banks are more likely to increase their output by providing financial services to excluded individuals and SMEs through technology.

Therefore, it is recommended that financial institutions in Ecuador improve their efficiency through optimal use of resources with respect to inputs, given that, on average, low efficiency characterises most institutions. With this, there are great possibilities for inefficient banks to have opportunities for improvement, taking as a reference those institutions that have developed in the efficient field.

According to Charnes et al. (1978) and Banker et al. (1984), those entities with indices that are far from 100% are inefficient. In our research, more than 80% of the Ecuadorian banking entities can be considered inefficient which invokes the intervention of the regulator, who also receives the interference of the business sector that pressures the resilience of the banking system through the deepening in the levels of financial intermediation also expanding financial inclusion.

Finally, by applying a random effects panel data regression, we find that the growth of the Ecuadorian banking sector in the period 2015–2019 is determined by financial development; that is, the higher the efficiency of financial institutions, the higher the probability of growth. In other words, for 1% increase in banking efficiency would imply a growth of USD 605 million in their assets. The banking system in Ecuador is probably one of the most regulated economic sectors, the role of intermediation in the economic cycle, business dynamics and the payments chain is fundamental; therefore, efforts to improve liquidity management and risk management in the sector are essential. Whilst this analysis revealed inefficiencies in most banks, they still have room to compete for greater cost efficiency.

Open Research

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Volume29, Issue2

April 2024

Pages 2011-2029

Are Ecuadorian banks enough technically efficient for growth? A clinical study

Abstract

1 INTRODUCTION

2 LITERATURE REVIEW

2.1 Theoretical foundation

2.2 Previous literature

3 DATA AND METHODOLOGY

4 RESULTS AND ANALYSIS

4.1 Output-oriented technical efficiency (variable return to scale)

4.2 Output-oriented efficiency of scale (variable return to scale)

4.3 Reference sets and technical efficiency

4.4 Econometric growth-efficiency modelling

5 CONCLUSIONS AND RECOMMENDATIONS

Open Research

DATA AVAILABILITY STATEMENT

REFERENCES

Citing Literature

References

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Are Ecuadorian banks enough technically efficient for growth? A clinical study

Abstract

1 INTRODUCTION

2 LITERATURE REVIEW

2.1 Theoretical foundation

2.2 Previous literature

3 DATA AND METHODOLOGY

4 RESULTS AND ANALYSIS

4.1 Output-oriented technical efficiency (variable return to scale)

4.2 Output-oriented efficiency of scale (variable return to scale)

4.3 Reference sets and technical efficiency

4.4 Econometric growth-efficiency modelling

5 CONCLUSIONS AND RECOMMENDATIONS

Open Research

DATA AVAILABILITY STATEMENT

REFERENCES

Citing Literature

References

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