Financial liberalization and banking efficiency: evidence from Turkey

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.

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:

$$ h_j =\frac{\sum\limits_{r=1}^s {u_r y_{rj} } }{\sum\limits_{i=1}^m {v_i x_{ij} } } $$

(1)

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:

• 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.

• 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:

$$ \begin{array}{ll} \hbox{Maximize }h_k =\frac{\sum\limits_{r=1}^s {u_r y_{rk}}} {\sum\limits_{i=1}^m {v_i x_{ik}}} &(2)\\ \hbox{subject to }\frac{\sum\limits_{r=1}^s {u_r y_{rj}}}{\sum\limits_{i=1}^m {v_i x_{ij}}}\leq 1\quad \hbox{for}\, j=1 \ldots \, {n} &(3) \end{array} $$

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

$$ \begin{array}{lll} \hbox{Max }q\\ \quad\hbox{s.t.} &\sum\nolimits_j {\lambda _j x_{ij} +s_i^- =(1-w_i q)x_{ij_0}} & (4)\\ &\sum\nolimits_j {\lambda _j y_{rj} -s_i^+ =(1-w_r q)y_{rj_0 } } &(5) \end{array} $$

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

$$ \begin{array}{lll} \hbox{Max} &\sum\nolimits_i F_i^- s_i^- + \sum\nolimits_i F_r^+ s_r^+ &(6)\\ \hbox{s.t.} &\sum\nolimits_j {\lambda_j x_{ij} +s_i^- =(1-w_i q)x_{ij_0}} &(7)\\ &\sum\nolimits_j {\lambda_j y_{rj} -s_i^+ =(1-w_r q)y_{rj_0}} &(8) \end{array} $$

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

$$ \begin{array}{lll} \hbox{Max} &q=\sum\nolimits_r {u_r y_{rj_0} +\Omega_1 -\Omega_2} &(9)\\ \hbox{s.t.} &\sum\nolimits_r {u_r y_{rj} -\sum\nolimits_i {v_i x_{ij} } +\Omega_1 -\Omega_2 } \leq 0 &(10)\\ &\sum\nolimits_i {v_i x_{ij_0 } =1} &(11) \end{array} $$

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

$$ \begin{array}{lll} \hbox{Min/Max} &\Omega_1 -\Omega_2 &(12)\\ \hbox{s.t.} &q^\ast =\sum\nolimits_r {u_r y_{rj_0} +\Omega_1 -\Omega_2} &(13)\\ &\sum\nolimits_r {u_r y_{rj} -\sum\nolimits_i {v_i x_{ij} } +\Omega_1 -\Omega_2 } \leq 0 &(14)\\ &\sum\nolimits_i {v_i x_{ij_0 } =1} &(15) \end{array} $$

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