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THE EVOLUTION OF EFFICIENCY IN COSTA RICAN BANKING SYSTEM 2005-2015: EVIDENCE FROM DATA ENVELOPMENT ANALYSIS.

RESUMEN

En esta investigacion se estima el nivel de eficiencia tecnica y de escala para el sistema bancario costarricense para el periodo 2005-2015 mediante la metodologia de Analisis Envolvente de Datos (AED). Las estimaciones se realizan desde la perspectiva de rendimientos variables de escala con variables de holgura desarrollada por Banker, Charnes, y Cooper (1984) y rendimientos constantes de escala desarrollada por Charnes, Cooper, y Rhodes (1978). Los niveles de eficiencia se estiman anualmente de forma individual para cada entidad bancaria para obtener promedios para el sistema total, segmento privado y estatal. Los insumos y productos considerados el modelo fueron definidos de acuerdo al enfoque de intermediacion. Mediante la aplicacion de los modelos AED se concluye que a) no hay evidencia de mejoras en el nivel de eficiencia tecnica y de escala del sistema bancario durante el periodo analizado, b) los bancos mas eficientes fueron el Banco BCT y el Banco General, c) los bancos privados son en promedio mas eficientes que los estatales y d) los bienes de uso neto son el insumo con mayor nivel de holgura.

PALABRAS CLAVE: FRONTERA DE EFICIENCIA, EFICIENCIA TECNICA, BANCA, PROGRAMACION LINEAL, GESTION DE RECURSOS.

ABSTRACT

In this study the technical and scale efficiency of Costa Rican banking system is estimated for the 2005-2015 period, through the Data Envelopment Analysis (DEA). The estimations are within the approach of variable returns to scale with slacks developed by Banker, Charnes, and Cooper (1984) and the constant returns to scale approach developed by Chames, Cooper, and Rhodes (1978). Efficiency scores were estimated annually for each bank to get the average for state banks, private banks, and the whole system. The inputs and outputs considered in the DEA model were defined through the intermediation approach. Through the application of DEA was concluded that a) for the whole system there are no clear efficiency improvements during the period analyzed, b) the most efficient banks were Banco BCT and Banco General, c) private banks were on average more efficient than state banks and d) the goods of net use were, on average, the input with bigger slack.

KEYWORDS: EFFICIENCY FRONTIER, TECHNICAL EFFICIENCY, BANKING, LINEAR PROGRAMMING, RESOURCE MANAGEMENT.

I. INTRODUCTION

In this study is estimated the technical and scale efficiency of Costa Rican banking system for the 2005-2015 period, through the Data Envelopment Analysis (DEA). The estimations are within the approach of variable returns to scale with slacks developed by Banker, Charnes, and Cooper (1984) and the constant returns to scale approach developed by Charnes, Cooper, and Rhodes (1978). Efficiency scores were estimated annually for each bank to get the simple average for state banks, private banks, and the whole system. The inputs and outputs considered in the DEA model were defined through the intermediation approach.

The study of efficiency for the Costa Rican banking has been developed mostly with the intermediation margin approach and some financial ratios, omitting efficiency perspectives such as the technical and scale. For instance, Camacho and Mesalles (1994), estimated the efficiency levels through several margin measures for the 1987-1992 period. Loria (2013), followed the same approach for the 1988-2013 period, determining margins by currency. Finally, Villamichel (2015) follows the same method than previous authors for the period 1995-2015, nevertheless, added the analysis of the administrative expense to assets ratio.

The application of DEA to Costa Rican banking is entirely new; although, the study follows the methodological framework applied by several authors to non-financial research. Some of them are, Xirinachs (2012) who estimated bayesian DEA models for the first level of health attention in the Caja Costarricense del Seguro Social (CCSS), she found out that for the period 2004-2010 the average technical efficiency was between 83.58% and 110.29%, even some of the health areas reached super efficiency levels. Morera-Salas (2015) estimated technical efficiency of Costa Rican hospitals for the 2012-2013 period; the author concluded that 70% of hospitals had the margin to improve resources management. In an application oriented to environmental economics, Sneessens (2011), estimated technical efficiency for 37 Dos Pinos dairy bovine farms, the author concluded that the farms could reduce environmental impact by 20.6% parallel with an 18.8% cost reduction. And Segura, Loaiza, and Valverde (2015), estimated the technical efficiency of the municipal aqueducts in Costa Rica.

Although the DEA method has not been applied to financial economics in Costa Rica, it has been widely used in other regions. For example, Pirateque, Pineros and Mondragon (2013) use the DEA for studying the technical, cost and allocative efficiency for the Colombian banking system for the 2000-2012 period. The focus of the survey is on individual production functions to incorporate several financial inputs and outputs. The authors conclude that in the first years of 2000 decade, the efficiency levels were very low, nevertheless, in the following years, a remarkable improvement was observed, and local firms were more efficient than foreign ones.

Figueira, Nellis and Parker (2006) study the performance of several banking systems in the north and sub-Saharan Africa. The study is oriented to determine if the property of the banks is a driver of its efficiency. To reach the goal of the survey, the author employed performance ratios, stochastic frontier, and DEA method. The authors concluded that local private banks did not have higher efficiency levels compared to state banks, nevertheless, when the property of private banks was foreign was observed superior efficiency levels.

II. METHODOLOGY

The method used to estimate technical, and scale efficiency scores are the so-called DEA models, input-oriented with variable (BCC) and constant (CCR) returns to scale. Besides the efficiency levels, are estimated slack variables, which indicates the maximum reduction in the input to stay in an optimal condition. It is important to mention that the efficiency levels were estimated for each year during the period 2005-2015.

The model

The efficiency score with variables returns to scale is obtained through the following linear program.

[theta]* = min [theta]

Subject to:

[mathematical expression not reproducible]

Where, [theta]* is an optimum scalar equal or lower than 1,[lambda] is a nx 1 vector of constants, z is a matrix of inputs with as many rows as inputs and as many columns as DMUs (Decision making unit, for this study the banks), y is a matrix of outputs with as many rows as products and as many columns as DMUs.

The efficiency scores with constant returns to scale can be obtained with the same model by taking out the convexity constraint [[SIGMA].sup.n,sub.j=1] [[lambda].sub.j] = 1. According to Schuschny (2007), the total efficiency is the product of the pure technical efficiency by scale efficiency, consequently scale efficiency is obtained by the following cocient.

SE = CCR Efficiency score/BCC Efficiency score

After solving the linear program is possible to estimate the slacks in the inputs, the slacks are defined in the following way:

[s.sup.-.sub.i] = [theta]*[z.sub.i0] - [n.summation over (j=1)] [[lambda].sub.j][z.sub.ij] i = 1,2, ... , m

[s.sup.+.sub.r] = [n.summation over (j=1)] [[lambda].sub.j][y.sub.rj] - [y.sub.r0] r = 1,2,3, ... , s

Given the above definitions, the slacks in the inputs are calculated through the following linear program.

max [m.summation over (i=1)] [s.sup.-.sub.i] + [s.summation over (r=1)][s.sup.+.sub.r]

Subject to:

[mathematical expression not reproducible]

Slacks model provide information about the efficiency condition of each DMU. If the optimum scalar [theta]*=1 and [s.sup.-.sub.i] = [s.sup.+.sub.r] = 0 the DMU is strongly efficient. If [theta]*=1, but [s.sup.- .sub.i] [not equal to] 0 and [s.sup.+.sub.r] [not equal to] 0, the DMU is weakly efficient, which means the DMU is efficient, although it has the possibility to improve its score by decreasing some inputs. The results are obtained through the linear programming add-in for spreadsheets Solver. The results of scale efficiency, pure technical efficiency and slacks are presented as the simple average of all DMUs for each year for the period 2005-2015.

The sample, sources, and variables

All data required to calculate efficiency levels was annual and was gotten from the General Superintendency of Financial Institutions of Costa Rica website (SUGEF by its initials in Spanish), the data was taken from the balance sheet and income statement in financial analysis format for 12 private banks and 4 state banks.

The variables selected as inputs and outputs were defined according to the intermediation approach employed by Benston, Hanweck and Humphrey (1982), Murray and White (1983), H.Y Kim (1986), M. Kim (1986), and Mester (1997). The following table shows the way in which the inputs and outputs were elaborated (2).

There is the possibility of no homogeneity in the results, nevertheless the DMUs are not classified into homogeneous groups due to by grouping, the sample size can be reduced and consequently the discriminatory power of the models will be diminished. Zhu (2014), suggests that the number of DMUs should be two or three times the number of inputs and outputs together to avoid a power reduction in the models. Then, to analyze more homogeneos results is applied the the Modified Thompson Tau (MTT) statistic for determining outliers. The MTT statistic is given by:

[tau] = [delta](n-1)/[square root of n][square root of n-2+[[delta].sup.2]]

Where n is the sample size and S is [delta] t-student distribution with [alpha]=0.05 and n-2 freedom degrees. An outlier is any efficiency score [theta] associated to a [DELTA] that is bigger than [phi] *[tau] , where [[DELTA].sub.i] = [absolute value of [[theta].sub.i] - [bar.[theta]]] and [phi] is the standard deviation of the sample (see appendix 4). The outliers are taken out from the simple average for the aggregate banking system.

III. RESULTS

Efficiency scores

The application of DEA methodology to Costa Rica banking system reflects several important facts to highlight. The results of CCR model for the period 2005-2015 points out that private banks were more efficient than state banks, being above of the average of the system. The gap between the state and private banks is from 2007 to 2009, after that period the efficiency average for both groups of banks followed a similar trend, as a consequence of the high increase of state banks efficiency during 2012 and 2013, as can see observed in the chart 1.

The chart 1 shows a suggestive behavior of efficiency levels during the financial crisis period, in which both groups of banks decreased its scores, state banks in a more accelerated way than private banks. Nevertheless, the chart is very suggestive is not possible state a formal causal relation.

Regarding the individual CCR scores, it is important to mention that the ranking is led by two small banks, Banco General and Banco BCT. The CCR model works assuming constant returns to scale; this means that not necessarily big banks as BAC San Jose or Banco Nacional can reach efficiency levels by its size. The ranking shows that the only one state bank above of a 0.80 score is the Banco Credito Agricola de Cartago, the rest of them occupy the latest positions (see Appendix 1).

From the variable returns to scale perspective, the results show the opposite situation than CCR, starting 2008 until 2014 the average efficiency of state banks is higher than private banks, even reaching three consecutive years the maximum score of 1 as can be observed in Chart 2. This situation suggests that there is a substantial effect of the scale efficiency on the total technical efficiency scores.

The individual BCC results show another reality of efficiency levels for Costa Rican banks, as already stated by the DEA theory, all BCC scores are bigger than CCR. The ranking is led by Banco BCT, Banco General, BAC San Jose, and Davivienda from the private side. Something new in this ranking is that includes the two state banks that reached the maximum score of efficiency, Banco Nacional and Banco Popular (see Appendix 2).

According to Chapin and Schmidt (1999), a DMU has two ways to be inefficient. First, it produces the output with more inputs than necessary or even being on the variable returns to scale efficiency frontier; the DMU provides a smaller or larger output than the efficient scale.Under that situation, the ratio of output produced per input is not maximized, the point in which is maximized is where CRS and BBC intersect, it means efficiency scale is 1.

For the period analyzed was observed that state banks were the DMUs with bigger scale inefficiencies, as was noticed in BCC results, state banks presented the maximum efficiency score of 1 for several periods reaching higher scores than CCR. Nevertheless, they are not minimizing the inputs because of scale inefficiencies. The central gap is observed during the 2006-2012 period in which reached a minimum level of 0.73. The private counterparty presented more stable result for the whole time, reaching a minimum level of 0.91 in 2010 and 2015, as can be observed in Chart 3.

From the individual perspective can be highlighted that the Banco General and Banco BCT, were the only banks that operated under optimum scale for the whole period analyzed, it means for the 11 years the CCR and BCC results were 1. From the state side the, the most efficient bank is the Banco Credito Agricola de Cartago with an average of 0.94 occupying the position 10 in the ranking. Followed by Banco Popular ranked 12, Banco Nacional ranked 13 and Banco de Costa Rica in the position 15 out of 16 DMUs (See Appendix 3).

Slack variables

The analysis of slack variables shows several facts, the use of slacks allowed to determine that for the period studied six out of sixteen banks accomplish the strong efficiency condition; it means they do not need any input reduction to reach the efficiency frontier, they have achieved a Pareto optimal condition. These institutions are Banco Nacional de Costa Rica, Banco Popular y de Desarrollo Comunal, BAC San Jose, Banco BCT, Banco General and Davivienda. It is important to mention that these six institutions achieved the strong efficiency condition under variable returns to scale. Although, some of them are scale inefficient. A remarkable fact is the outstanding performance of Banco BCT and Banco General, which for the whole period studied were on the technical and scale efficiency frontier with no slacks in their inputs.

The results indicate the goods of net use as the input with more possibilities to be reduced; this fact is more visible in private banks than state banks, seven out of nine banks with slacks are private. Nevertheless, the maximum reduction in goods of net use for the period analyzed is shown by Banco Credito Agricola de Cartago with 22% followed by Citibank with 17%.

Regarding staff expense, is observed that the inefficiency is present more in private banks that state banks, Citibank and Banco Promerica are the ones that could implement staff reduction, of 16% and 13% respectively, to reach efficiency frontier. State banks do not arrive at a possible reduction of 5%. Regarding the deposits reduction, is remarkable that the output of the model should not be read literally as the deposits frequently work like funding for loans. Consequently, instead of a deposits reduction could be interpreted as the best management of deposits. The slack in deposits could be used to generate more revenue by increasing credit or generating more investments. For the Costa Rican banking system was not observed significant slacks in deposits for the period analyzed.

IV. CONCLUSIONS

First is important to highlight that the conclusions must be read carefully as the DEA models are not able to capture drivers of efficiency such as management strategy, special projects or similars. In general, no clear trend shows significant improvements in the efficiency of the whole banking system during the period analyzed. Although, it was possible to determine that private banks were, in average, more efficient than state banks. This fact means private banks were more talented to produce credit and investments with less staff expense, deposits, and property plant and equipment.

For the period analyzed, private banks were, in average, more efficient than state banks under constant returns to scale. Under variable returns to scale, state banks reached high-efficiency levels. Nevertheless, this fact is offset by scale inefficiencies; wich means state banks do not operate on the optimal production plant size. Regarding efficiency scores, the Banco BCT and Banco General present the higher ones for constant returns to scale, variable return to scale and scale efficiency with no slacks so that they can be classified as the most efficient banks for the 2005-2015 period.

It was determined that the goods net use was the input with the bigger slacks, this means the banks out of the efficiency frontier have more property, plant, and equipment than the required to produce the output levels they present. Regarding staff expense and deposits, the first presents slacks in seven banks; nevertheless, just Banco Credito Agricola de Cartago and Citibank were higher than 5%. In the case of the latest, there is no evidence of inefficiencies.

V. REFERENCES

Banker, R., Charnes, A., & Cooper, W. (1984). Some models for estimating technical and scale inefficiencies in Data Envelopment Analysis. Management Science, 30(9), 1078-1092. https://doi. org/10.1287/mnsc.30.9.1078

Camacho, E., & Mesalles, L. (1994). Margen de intermediacion y enciencia en el sistema bancario costarricense. Columbus: Ohio State University.

Chapin, A., & Schmidt, S. (1999). Do mergers improve efficiency? Evidence form deregulated rail Freight. Journal of Transport Economics and Policy, 33(2), 147-162. Retrieved from http:// www.jstor.org/stable/20053802

Charnes, A., Cooper, W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444. https://doi.org/10.1016/03772217(78)90138-8

Figueira, C., Nellis, J., & Parker, D. (2006). Does Ownership Affect the Efficiency of African Banks? Journal of Developing Areas, 40(1), 38-63. https://doi.org/10.1353/jda.2007.0004

Loria, M. (2013). El sistema financiero costarricense en los ultimos 25 anos: estructura y desempeno. San Jose: Academia de Centroamerica. Retrieved from http://www.academiaca.or.cr/wp-content/uploads/2014/03/MOMOGRAFIA-1-Loria-CARTA2-final.pdf

Morera-Salas, M. (2015). Analisis de eficiencia relativa de hospitales publicos de Costa Rica. Poblacion y Salud en Mesoamerica, 12(2), 1-16. https://doi.org/10.15517/psm.vl2i2.17220

Pirateque, J., Pineros, J., & Modragon, L. (2013). Eficiencia de los Establecimientos Bancarios: una Aproximacion Mediante Modelos DEA. Bogota: Banco de la Republica de Colombia. Retrieved from http://www.banrep.gov.co/sites/default/files/publicaciones/archivos/be_798.pdf

Schuschny, A. (2007). El metodo DEA y su aplicacion al estudio del sector energetico y las emisiones de CO2 en America Latina y el caribe. Santiago: Comision Economica para America Latina. Retrieved from http://repositorio.cepal.Org//handle/11362/4752

Segura, R., Loaiza, K., & Valverde, K. (2015). Evaluacion de la eficacia relativa de los acueductos municipales en Costa Rica. San Jose: Universidad de Costa Rica.

Sneessens, I. (2011). Eficiencia ambiental y eficiencia economica de las fincas lecheras de la cooperativa Dos Pinos Costa Rica. (Master Thesis, , Centro Agronomico Tropical de Investigacion y Ensenanza, Turrialba, Costa Rica). Retrieved from http://repositorio.bibliotecaorton.catie. ac.cr/handle/11554/7777

Villamichel, P. (2015). Analisis de los 20 anos de competencia en el sector bancario costarricense. San Jose: Programa Estado de la Nacion. Retrieved from http://estadonacion.or.cr/files/biblioteca_virtual/021/economia/VillamichelBancaC3.pdf

Xirinachs, Y. (2012). Frontera eficiente de produccion en el primer nivel de atencion de salud: modelo DEA ajustado por metodos bayesianos. (Doctoral Thesis, Universidad de las Palmas de Gran Canaria, Gran Canaria, Espana). Retrieved from http://acceda.ulpgc.es/handle/10553/10283

Zhu, J. (2014). Quantitative models for performance evaluation and benchmarking. Massachusetts: Springer.

APPENDIX
APPENDIX 4

OUTLIERS (INEFFICIENT DMUS)

                     CCR MODEL

2005    2006   2007   2008     2009   2010

BCAC    BCAC   BCAC   BCR      BCR    BCR
        BAC    BCR    CATHAY   BNCR   Citibank
               BPDC

                     CCR MODEL

2005    2011       2012   2013       2014       2015

BCAC    BNC.R      BNCR   LAFISE     Citibank   PRIVAL
        Citibank   BCR    Citibank   LAFISE     LAFISE
        BCR

                       BCC MODEL

2005    2006   2007   2008     2009        2010

BCAC    BCAC   BCAC   LAF1SE   PROMERICA   PROMERICA
                      CATHAY               Citibank
                      BCR

                       BCC MODEL

2005    2011       2012        2013       2014       2015

BCAC    Citibank   LAF1SE      LAFISE     LAFISE     LAFISE
        IMPROSA    PROMERICA   Citibank   Citibank   Citibank
                   IMPROSA                           BCAC

                  SCALE EFFICIENCY

2005      2006   2007   2008   2009   2010

BAC       BAC    BCAC   BCR    BCR    CATHAY
CATHAY           BCR    BCAC   BNCR   BCR
                 BPDC

                  SCALE EFFICIENCY

2005      2011     2012   2013         2014     2015

BAC       PRIVAL   BNCR   BCR          PRIVAL   PRIVAL
CATHAY    BNCR     BCR    CATHAY       CATHAY   BCR
          BCR             SCOTIABANK            BNCR
                                                SCOTIABANK
                                                CATHAY

Source: own elaboration.


DOI: http://dx.doi.org/10.15517/rce.v34i2.27303

Recibido: 14/08/2016

Aprobado: 16/11/2016

Andres Salas-Alvarado (1)

(1) Investigador independiente, Centro Corporativo el Cafetal edificio C; Codigo Postal 40703; Costa Rica; andres.salas.a@gmail.com

(2) The changes in the chart of accounts implemented in 2008 do not affect the results for the 2005-2007 period due to the models are based on aggregate accounts not in speficic items, the re-classification of sub-accounts does not modify the inputs and outputs as aggreagated items.

Caption: APPENDIX 1 AVERAGE TECHNICAL EFFICIENCY COSTA RICAN BANKS 2005-2015 INPUT-ORIENTED CONSTANT RETURNS TO SCALE

Caption: APPENDIX 2 AVERAGE TECHNICAL EFFICIENCY COSTA RICAN BANKS 2005-2015 INPUT-ORIENTED VARIABLE RETURNS TO SCALE

Caption: APPENDIX 3 AVERAGE SCALE EFFICIENCY COSTA RICAN BANKS 2005-2015 INPUT-ORIENTED

Caption: CHART 1 TECHNICAL EFFICIENCY COSTA RICAN BANKING SYSTEM 2005-2015 INPUT-ORIENTED CONSTANT RETURNS TO SCALE

Caption: CHART 2 TECHNICAL EFFICIENCY COSTA RICAN BANKING SYSTEM 2005-2015 INPUT-ORIENTED CONSTANT RETURNS TO SCALE

Caption: CHART 3 SCALE EFFICIENCY COSTA RICAN BANKING SYSTEM 2005-2015 INPUT-ORIENTED

Caption: CHART 3 SLACKS COSTA RICAN BANKING SYSTEM 2005-2015 INPUT-ORIENTED
TABLE 1

SAMPLES

Type                    Bank             Sample

State Bank         Banco Popular        2005-2015
State Bank     Banco Credito Agricola   2005-2015
State Bank      Banco de Costa Rica     2005-2015
State Bank         Banco Nacional       2005-2015
Private Bank        BAC San Jose        2005-2015
Private Bank            BCT             2005-2015
Private Bank           Cathay           2005-2015
Private Bank         Davivienda         2005-2015
Private Bank       Banco General        2007-2015
Private Bank       Banco Improsa        2005-2015
Private Bank        Banco Lafise        2005-2015
Private Bank      Banco Promerica       2005-2015
Private Bank        Privai Bank         2010-2015
Private Bank         Scotiabank         2005-2015
Private Bank          Citibank          2005-2015
Private Bank            CMB               2015

Source: own elaboration.

TABLE 2

VARIABLES

Output    Loans         Loans with aging <= 90 days

                        Loans with aging > 90 days
                        and legal collection

          Investments   Investments in securities

Input     Labour        Staff expenses

          Capital       Goods of net use

                        Short term deposits
                        (Interest bearing)

                        Long term deposits
                        (Interest bearing)

          Deposits      Current account deposits
                        (Interest bearing)

                        Short term deposits
                        (Non-Interest bearing)

                        Other short term liabilities
                        with the public (Non-Interest
                        bearing)

                        Other long term liabilities
                        with the public (Non-Interest
                        bearing)

Source: own elaboration.
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Date:Jul 1, 2016
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