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Applying Shephard's lemma to the logarithmic partial derivative appearing in 10 , we obtain the following relations:. Equation 12 is used in this study as an indicator to measure the returns to scale. The Linkage Having equations 1 - 4 and 9 - 15 at our disposal, we can now establish a "link" between the index number and parametric procedures.

This is done to cross check the consistency of TFP measurement between the two procedures. By substituting 14 into 15 and rearranging, we obtain,. A comparison between equations 4 and 17 reveals that, under the assumptions of constant returns to scale i.

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measurement errors, the rate of change in TFP i. However, if we assume that one of the conditions above does not exist, that is, the technology does not exhibit constant returns to scale i. estimate the rate of technological change. This is because the methodology cannot account for the measurement of rate of returns to scale. On the contrary, the parametric procedure can still serve the purpose as before. Nevertheless, it can be explicitly shown that if the two procedures are linked, a validation concerning the consistency of measuring the TFP growth between them is possible.

Henceforth, equation 19 will be used as the basis to measure the TFP growth and its two major components, namely, the scale and technological change effects, of the Sudanese Islamic banking sector. Econometric Specification and Data Sources 3. The cost-share S j is derived through Shephard's lemma as,. For any cost function to be sensible, it must satisfy the linear homogeneity in input prices which requires: 3. Additional regularity conditions that the cost function must satisfy in order to correspond to well-behaved production technology are monotonicity and concavity in factor prices.

For econometric estimation, the cross-equations equality and the linear homogeneity restrictions defined in 22 are imposed a priori on the translog cost function 20 , and on the cost-share equations This allows us to drop arbitrarily any one of the three 3 cost-share equations. In this study, the cost-share equation of deposits was omitted. The estimates of the coefficients of this equation are obtainable by using the parameter relationships of the. linear homogeneity restrictions, once the system of the remaining cost-share equations has been estimated.

Given this set of conditions, we chose as the estimation method the Iterative Seemingly Unrelated Regression ISUR. From equation 23 , we can obtain information on returns to scale. Finally, the growth rate of cost diminution can be obtained as. The years were chosen because they represent the transformation of the conventional Sudanese banks into full-fledged Islamic banks.

The definitions of the cost, prices, and output variables were made based on how and what banks produce 1. There are two different views on the determination of input and output variables. They are the intermediate approach and the production approach. The intermediate approach views banks as using deposits together with physical inputs to produce various types of bank assets as measured by their currency value.

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Berger and Humphrey suggest that the intermediate 1. Karlyn Mitchell and Nur M. Onvural, , Economies of Scale and Scope at Large Commercial Banks: Evidence from the Fourier Flexible Functional Form, Journal of Money, Credit and Banking, Vol. approach is best suited for evaluating firm level efficiency as in our case. The reason is that the intermediate approach is superior for measuring the importance of frontier efficiency to the profitability of the financial institution since the minimization of total costs, not just production costs, is needed to maximize profit 1.

The production approach on other hand, views bank as is using only physical inputs such as labor and capital to produce deposits and other types of bank assets. appropriate for evaluating the efficiency of the branches of financial institutions. Hence in this study, one output variable 1. Allen N. Berger and David B. Humphrey, Efficiency of financial institutions: International survey and directions for future research, European Journal of Operational Research 98 Since during the period of investigation loans that were given on the basis of interest bearing financing was forbidden by the Islamic banking system, all Sudanese banks practiced only equity financing.

As a result, the only output available w a s investments Y. While labor X1 , fixed assets X2 and core deposits X3 are treated as factor inputs, salaries and wages divided by number of employees W1 , total expenses on furniture, equipment and premises divided by their book value W2 , and rate of return on deposits divided by the total deposits W3 are the prices of X1, X2 and X3 respectively.

Empirical Results 4. Sample Statistics for the Variables and Group In Table 1 we present summary statistics for output investment , inputs labor, capital or fixed assets, and deposits and their respective prices of the average 12 Sudanese Islamic banks and each group, namely Group A, Group B and Group C. Sample Statistics of Variables: Output, Inputs and Input Prices in millions Sudan Pound, SP a, Share of each Input in Total Cost Fixed Assets S1 0.

Group A. Note: a labor is measured in terms of number of employees by the end of the respective financial year. b Panel A summarizes output, inputs, input prices and other relevant variables of the Sudanese Islamic banks for aggregate data, i. c Panel B summarizes output, inputs and input prices of the Sudanese Islamic banks for the specified groups, namely Group A, Group B and Group C. There are 40 observations in each group, i. Panel A reports the average output, inputs, input prices, share of each factor inputs in the total cost and the total cost itself along with their standard deviations, minimum and maximum values.

On the other hand, with the aim to provide a clear picture on the production structure of each group of the surveyed banks, we also report the average output, inputs and input prices of each factor inputs along with their standard deviations, minimum and maximum values. To conserve space, we will, however, highlight the variables that are extensively used in the study. First, as evident from Panel A, deposits took the lion share of the total cost of the Sudanese Islamic banks during the period.

Second, the large-size banks Group A , on average, held approximately This is shown in the Panel B of Table 1. Third, in terms of investment Y Group A banks invested the largest amount of investment worth SP million during the period. It seems from observations i and ii that there is a positive relationship between the size of fixed assets and the amount of investment made. A tentative conclusion that can be made from this observation is that the larger the bank the bigger the size of its fixed assets and investment. There are few interesting observations that can be gleaned from the table.

This is particularly true if the focus is given to the trends of productivity index i. First, with the exceptions of El Neillien Industrial Development Bank and few. observation years, the productivity index of other banks in Group A showed an increasing trend over the period. Second, in the case of Group B banks it seems and were the years where the productivity index reached its peak.

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Specifically, the index registered was larger than unity. In fact, in two banks the index was 7. For readers with high interest to know in greater details about the trends of the indexes, we also provide Figures They are attached to the paper as Appendix A. One question that remains unanswered is, what were the factors behind the several trends showed by the three groups of banks?

We will, in due course of the paper, answer the question. Sample No. Note: The overall sample size is which consisted of 10 observation years and 12 banks. The benchmark for the initial and terminal year was and , respectively. We arrange the data sets in the following order:. TFP Growth Table 3 exhibits output, total input and TFP growth rates of all Sudanese Islamic banks and the three groups, Group A the Large-size banks , Group B the Medium-size banks and Group C the Small-size banks for the period.

As can be seen from the table, irrespective of the groups, the average annual TFP growth rate for all Sudanese Islamic banks over the period was 1. More or less the same rate was recorded by the Large-size banks with TFP of 1. In the case of Medium-size banks, the TFP growth rate registered by them over the surveyed period was an exceptionally high of It is fairly obvious.

In other words, given the fact that the output growth rate was negative, banks were obliged or compelled to minimize their input costs. Indeed, judging from the input growth rate of Next, we turn our attention to the performance of the Small-size banks. In stark constrast to the case of Medium-size banks, the Small-size banks, despite experiencing a negative output growth rate during the period, have failed to minimize the input costs.

This had resulted in a negative TFP growth rate for the small-size banks. The actual reason s for variation in TFP growth rates registered by the Sudanese Islamic banks as a whole and the ones registered by the groups can only be empirically verified when the TFP growth is decomposed into scale and technological change effects. As defined before, Total Factor Productivity growth rate TFP is a substraction of total input growth rate from output growth rate or.

The advantage of decomposing the sources of TFP into scale and technological change effects is that it provides certain insights as to what lies behind this pattern of TFP growth.

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