Abstract
This paper examines the banking efficiency in a pre- and post-liberalization environment by drawing on the Turkish experience by using DEA. The paper also investigates the scale effect on efficiency. Our findings suggest that liberalization programs were followed by an observable decline in efficiency. Another finding of the study is that the Turkish banking system had a serious scale problem during the study period. The second part of our analysis relied on econometric methods and found that one major reason for such system-wide efficiency decline has been the growing macroeconomic instability of the Turkish economy in general and financial sector in particular.
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Notes
Later, Grifell-Tatje and Lovell (1997) employed a different specification and reached to the opposite conclusion.
Due to some changes in the banking regulations in Turkey after 1994 resulting from a heavy financial crises that significantly affected the banking practice, we did not include later years in our study.
Multi-stage application of DEA is not new, although it is not used in the context of present study. See, for example, Pastor (1999, 2002) and Maudos and Pastor (2003) for multi-stage DEA application to banking efficiency. Pastor (1999) proposed a new sequential DEA procedure to break down the main indicator of banking risk into two components (internal and external) to get a risk-adjusted efficiency measurement. Pastor (2002) developed a three-stage sequential DEA technique applied to the decomposition of risk into its internal and external components to obtaine efficiency measures adjusted for risk and environment. Maudos and Pastor (2003) used a two-stage DEA model to analyze cost and profit efficiency and to compare in both commercial and savings banks of Spain. All these new applications enriched the results and provided additional information about banking efficiency.
Bauer et al. (1998) provide a detailed comparison of methods used in measuring the efficiency of financial institutions.
We would like to thank Allen Berger and anonymous referee for the suggestion.
The number of banks under investigation ranged from 29 in 1976 and 1977 to 53 in 1990.
Detailed results of each model are available from the authors.
Graphs are available from the authors for interested readers.
As noted at the outset a key objective of the 1980 reforms was to raise efficiency of the banking system. Prior to 1980 banks were engaged in non-price competition as interest rates on deposits and loans were controlled which led to the expansion of bank branch networks. Following the 1980 reforms, which lifted interest rate controls and other restrictions on financial intermediation there was a slowdown in branch expansion. This situation did not last long and after mid-1980s banks started to expand their branch networks again as they were making easy profits from government securities. Bank employment never declined. The fact that banking sector restructuring started after the November 2000 and February 2001 crises and the introduction of a major stabilization program seems to confirm our interpretation of the sources of inefficiency and the scale problem: as long as they made easy profits banks would not restructure to increase their efficiency.
A common problem in time series analysis is the serial correlation where the residuals are correlated with their own lagged values. We have tested the specified model for serial correlation by using the Durbin–Watson test and found that the model has serial correlation problem. We employed the simplest and most widely used model, the first (and second)-order autoregressive model to deal with serial correlation issue. We should note that when employing an AR model, the estimated coefficients, coefficient standard errors, and t-statistics may be interpreted in the usual manner, but if one is interested in the results involving residuals should be careful because they differ from those computed in OLS settings, which is not the case in present study.
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Appendices
Appendix A
Let us start with the relatively simple fractional programming formulation of DEA. Assume that there are n DMUs to be evaluated. Each consumes different amounts of i inputs and produces r different outputs, i.e. DMUj consumes x ij amounts of input to produce y rj amounts of output. It is assumed that these inputs, x ij , and outputs, y rj , are non-negative, and each DMU has at least one positive input and output value. The productivity of a DMU can then be written as:
In this formulation, v i and u r are the weights assigned to each input and output. By using mathematical programming techniques, DEA optimally assigns the weights subject to the following constraints:
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The weights for each DMU are assigned subject to the constraint that no other DMU has an efficiency greater than 1 if it uses the same weights implying that efficient DMUs will have a ratio value of 1.
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The derived weights, u and v are not negative.
The objective function of DMUk is the ratio of the total weighted output divided by the total weighted input:
v i ≥ 0 for i = 1.... m, and u r ≥ 0 for r = 1 ..... s
This is a simple presentation of a basic DEA model.
Charnes et al. (1978) employed the optimization method of mathematical programming to generalize the single output/input technical efficiency measure to the multiple output/multiple input case by constructing a single virtual output to single virtual input relative efficiency measure. This is the principal form of the DEA model and is known as the CCR ratio model.
The characteristics of the CCR ratio model is the reduction of the multiple output /multiple input situation, for each DMU, to a single virtual output and a single virtual input ratio. For a given DMU this ratio provides a measure of efficiency, which is a function of multipliers (Charnes et al. 1978). The objective is to find the largest sum of weighted outputs of DMUk while keeping the sum of its weighted inputs at the unit value, thereby forcing the ratio of the weighted output to the weighted input for any DMU to be less than or equal to one.
It is possible to create and estimate models that provide input-oriented or output-oriented projections for both constant returns to scale and variable returns to scale envelopments. An input-oriented model attempts to maximize the proportional decrease in input variables while remaining within the envelopment space. On the other hand an output-oriented model maximizes the proportional increase in the output variables while remaining within the envelopment space. Models utilized in this study are formulated as:
CCR First Stage
λ i ≥ 0; j = 1.... 50; q ≥ 0; i = 1.... 4; r = 1.... 3
where x ij and y rj are the ith input and rth output level for DMUj. λ j is the weight of DMU in the facet for the evaluated DMU. w i and w r are priorities. s i and s r are slacks corresponding to input and output respectively ( ≥ 0). j 0 is the DMU being assessed. For input minimization model w i is set equal to 100percent, while w r is set equal to 0, implying that the input reduction is targeted while keeping output unchanged. For output maximization models, the reverse is true.
CCR Second Stage
λ i ≥ 0; j = 1.... 50; q ≥ 0; i = 1.... 4; r = 1.... 3
where F − i and F + r are priorities. In this application, F − i is \({\frac{1}{\bar{X}_i}}\) where \({\bar{X}_i}\) is the mean value of x ij , and F + r is \({\frac{1}{\bar{Y}_r}}\), where \({\bar{Y}_r}\) is the mean value of y ij .
Under input minimization and variable returns to scale conditions, Warwick Windows DEA software solves the following BCC models:
BCC First Stage
u r , v i , Ω1, Ω2 ≥ 0
By letting q * be the optimal value of q in the above model, the minimum and maximum limit of the Ω range is obtained by solving the second stage.
BCC Second Stage
u r , v i , Ω1, Ω2, ≥ 0
where u r is the weight of the rth output and v i is the weight of ith input for DMUj. Ω1 and Ω2 are the distance from frontier facet.
Annex B
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Denizer, C.A., Dinc, M. & Tarimcilar, M. Financial liberalization and banking efficiency: evidence from Turkey. J Prod Anal 27, 177–195 (2007). https://doi.org/10.1007/s11123-007-0035-9
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DOI: https://doi.org/10.1007/s11123-007-0035-9