Estimation of Production Function of Public Sector Banks

Project| Estimation of Production function of Public Sector Banks | | | Contents 1. INRODUCTION3 2. Methodology4 2. 1General Approach:4 2. 2Data Collection:4 2. 3Data Processing:5 2. 3. 1Nature of Banks:5 2. 3. 2Nature of Variables:5 2. 3. 3Assumptions in the treatment of Variables:5 2. 4Data Analysis:5 2. 4. 1Objective of the Analysis5 2. 4. 2Production Function Relationship:5 2. 5Limitation8 3. Data analysis and Results9 4. Conclusion15 5. Bibliography16 1. INRODUCTIONThe structure of the banking industry has undergone sweeping changes in the past two decades. In response to heightened competition from non-bank financial firms enabled by technological progress among other factors, banks have been expanding both the scale and scope of their operations, largely through consolidations. This merger wave coincides with extensive deregulation, which has removed restrictions on product offerings and interstate banking. These changes have motivated many studies. The estimation of bank prod uctivity and returns to scale is of particular nterest because of its broad practical applications and important policy implications The Banking Sector is characterized by multiple inputs and outputs that are associated with various attributes, such as different types of deposits, loans, number of accounts, classes of employees and location of branches. Transformation in terms of moving from high operating cost, low productivity and high spread to being more efficient, productive and competitive has been an important challenge for the banking sector in India.Recent years have witnessed substantial research efforts that have been devoted to measuring the efficiency and productivity of the banking industry. However, assessment of performance of banks has been a problematic one because of the unresolved questions concerning inputs and outputs. In the absence of any coherent definitions, researchers have used a variety of inputs and outputs, mostly based on an intermediation or producti on approach. The study of the Indian banking sector is of special interest for multiple reasons.Besides being one of the fastest-growing emerging economies of the world, India has one of the largest state-owned banking systems and generates employment of around 1 million people. Secondly, the vast network of around 70,000 commercial bank branches provides the base of the finance-led growth and development process in India. Thus the issue of efficiency and productivity of banks in India is particularly important. In the aforementioned context we define productivity as a concept that involves the transformation of resources into final goods and services.Production function is a function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs. It indicates the highest output that a firm can produce for every specified combination of inputs. This function is an assumed technological relationship, based on the current state of engineering kno wledge; it does not represent the result of economic choices, but rather is an externally given entity that influences economic decision-making. Almost all economic theories presuppose a production function, either on the firm level or the aggregate level.In this sense, the production function is one of the key concepts of mainstream neoclassical theories. In micro-economics, a production function is a function that specifies the output of a firm for all combinations of inputs. 2. Methodology 1 2 3. 1 General Approach: This section describes the general approach taken for the analysis of the Production function of the Public Sector Banks (PSBs) in India. A bank for its operation takes several inputs and generates several outputs. For e. g. the typical inputs are Employees, Capital for operation, Reserve & Surplus, number of Branches, number of ATMs of a bank etc.Its output is typically the Loan (Advances), Interest Income etc. Since Multiple Regression is used so the production outp ut is taken only one at a time. Also, only two input variable at a time is used, though several regression analysis have been done for different combinations of input and output to get the most reasonable and best approximate relationship. However, a bank uses any number of variables as input simultaneously. A bank measures its performance among other parameters on how much Loan or Credit it has disbursed in a fiscal year or how much Deposit it has collected from the customers etc.Though such data in isolation may not be a true estimate of the efficiency of the business because unregulated disbursal of loans may cause Non Performing Assets (NPAs) which will lower the Retained Earning of the Bank but since the report is concerned only with the Production function of the PSBs hence no comment will be made on this aspect. Similarly how competitively the Deposits have been taken will not be a subject matter of this report. The Methodology of the report is to be first gather relevant inp ut/output data from authoritative source.The data so obtained are processed and any assumptions made for their subsequent analysis is clearly defined. In the next phase the data analysis is done wherein suitable regression technique is used to generate the relationship between the input variables and the Production output. Finally the Interpretation is done to assign the meaning to such endeavor. 3. 2 Data Collection: The data for the Public Sector Banks (PSB) in India for the following variables have been collected from the Reserve Bank of India’s (RBI) official website for the fiscal 2004-05 to 2008-09: Deposits * Capital * Loans & Advances * Labour * Interest Income 3. 3 Data Processing: Nature of Banks: All the 20 Nationalised Banks including IDBI as well as all the Associate Banks of the State Bank of India have been considered for the study. Thus a total of 27 banks has been focussed from the fiscal 2004-05 to 2008-09 for their Production output vis-a-vis different inpu ts. Nature of Variables: For the Banking Sector there are few variables which are clearly treated as input variables and output (production) variables.Example includes Labour and Loan (Advances) as input variables and Interest Income as output variables. But their are variables like Deposits which are ambiguous in their treatment as either input or output. It is input because to disburse loan which is an output the bank requires deposits. It is this deposit which is finally disbursed as loan. However, Deposit is treated as Output because the performance of a Bank is measured among other parameters by how much Deposit it has been able to generate in a fiscal year. For our analysis we treat Deposits as Output/ Production variable.Assumptions in the treatment of Variables: 1. It is assumed that the cost of per unit Labour is constant and same across all banks. Thus we may take the Labour as a quantity across all banks as an input variable, without bothering about the variable wage rate for each labour i. e the Cost of Labour is a linear function of the quantity of Labour. 3. 4 Data Analysis: Objective of the Analysis The report wish to obtain the following objectives: * To establish a mathematical model of Production Function for PSBs in India. * To analyze the regression coefficients obtained vis-s-vis the PSBs’ input and output. To analyze the regression coefficients for specific banks over five years Production Function Relationship: To estimate the one variable Production output function for an economic entity the Cobb-Douglas Production Function is widely used. For the Banking industry the report establishes the relationship between the following input variables and the Production output variable: (A) For all the 20 Nationalised Banks (including IDBI) along with the Associate Banks of SBI, the following Regression Analysis is done across all the years starting from the fiscal 2004-05 to 2008-09. S.No| Input Variable1| Input Variable 2| Production Outp ut| Across Time Period| Banks| 1| Labour| Capital| Deposit| 2004-05 to 2008-09| All PSBs| 2| Labour| Capital| Advances| 2004-05 to 2008-09| All PSBs| 3| Labour| Capital| Advances + Deposit| 2004-05 to 2008-09| All PSBs| 4| Labour| Capital| Interest Income| 2004-05 to 2008-09| All PSBs| The number observations made = Number of Production Functions * Number of Fiscal Years for which the observation is made = 4*5 =20 (B) Specific to the Largest Nationalised Bank as per capital viz. State Bank of India (SBI) and the Smallest PSB as per Capital viz. State Bank of Indore (SBIndore) were taken for regression analysis separately. The merger of  State Bank of Indore, the smallest associate bank of State Bank of India (SBI), was completed in the last week of August 2010, ut for our analysis we still continue to treat its data as separate from that of SBI. S. No| Input Variable1| Input Variable 2| Production Output| Across Time Period| Bank| 1| Labour| Capital| Deposit| 2004-05 to 2008-09| S BI| 2| Labour| Capital| Advances| 2004-05 to 2008-09| SBI| 3| Labour| Capital| Advances + Deposit| 2004-05 to 2008-09| SBI| 4| Labour| Capital| Interest Income| 2004-05 to 2008-09| SBI| 5| Labour| Capital| Deposit| 2004-05 to 2008-09| SBIndore| 6| Labour| Capital| Advances| 2004-05 to 2008-09| SBIndore| 7| Labour| Capital| Advances + Deposit| 2004-05 to 2008-09| SBIndore| 8| Labour| Capital| Interest Income| 2004-05 to 2008-09| SBIndore|The number observations made = Number of Production Functions * Number of Fiscal Years for which the observation is made = 8*5 =40 3. 5. 1. 1 Multiple Regressions: For modelling and testing of multiple independent variables (or predictor variables), Multiple Regression is used. Since it is for only single dependent variable (or criterion variable) hence Multiple Regression is not a multivariate test. The model for a multiple regression takes the form:   y  =  ? 0  +  ? 1Ãâ€"1  +  ? 2Ãâ€"2  +  ? 3Ãâ€"3  + †¦.. +  ? And we wish to estimate the  ? 0,  ? 1,  ? 2, etc. by obtaining   ^ y1  =  b0  +  b1x1  +  b2x2  +  b3x3  + †¦..Where the  b's are termed as the â€Å"regression coefficients† and ? is the error or residual value. For 2 independent variables we fit the data for a plane. The beta values are used in measuring how effectively the predictor variable influences the criterion variable. R2, in multiple regression is the square of the measure of association which indicates the percent of overlap between the predictor variables and the criterion variable. 3. 5. 1. 2 Cobb-Douglas Production Function: The Production of an economic entity may be defined as a function of its inputs. In a general mathematical form, a production function can be defined as: P= f(X1,X2,X3,†¦Xn) Where: P = Production or output quantityX1,X2,X3,†¦Xn = Input variables such as Labour, raw material, capital etc. f() = function defining the relationship. This function may be a L inear Function of all input variables. It can also be a Product Function of all the individual variables with each variables weighted for a corresponding exponent. The Cobb-Douglas Production Function follows the latter approach and is as follows: P = A. L?. K? Where, P = Production or output quantity L = Labour (the number of employees) K = Capital (the monetary worth of all machinery, equipment, and buildings) A = Total factor productivity, a variable which accounts for effects on total output not explained by chosen inputs. ?, ? are the output elasticity of labour and capital, respectively. These values are constants. We assume ? , ? ;lt; 1 so that the firm has decreasing marginal products of labour and capital. The Multiple Regression is to be done using the Cobb-Douglas Production Function, then the said function needs to be in a the linear form. To achieve linear scale the exponential Log of the Cobb-Douglas Production Function may be taken. Thus the following function is bein g used in the report for regression: Log (P) = a0 + ? *Log(L) + ? *Log(K) Thus the Input 1= Log(L), Input 2 = Log(K) and Output = Log(P) and Model Coefficients = ? , ? 3. 5. 1. 3 Return to Scale:Returns to scale refers to a technical property of production that examines changes in output subsequent to a proportional change in all inputs (where all inputs increase by a constant factor). If output increases by that same proportional change then there are constant returns to scale (CRTS). If output increases by less than that proportional change, there are decreasing returns to scale (DRS). If output increases by more than that proportion, there are increasing returns to scale (IRS). To summarise, it is as follows: ? + ? | Returns to scale| =1| constant| ;lt; 1| decreasing| ;gt; 1| increasing| 3. 5 Limitation * The correlation between labour expense and production across banks may be limited if the business model of the bank varies.For example banks who primary operate in larger   ci ties can produce more with a smaller workforce because of greater labour utilization while labour in far flung remote branches might be under utilized and may not contribute to production that efficiently. Hence we assume a linear utilisation of labour. * This correlation is limited because as technology is increasingly substituting labour in banks so a bank with smaller workforce but superior technology can still produce more. Different PSBs may differ on this aspect of technological implementation vis-a-vis their labour. * Our analysis has restricted inputs and outputs to very few variables. There can be other variables although the report has included the most important ones for the study. * In analysis of SBI and State bank of Indore we have taken only 5 data points for 5 years. This may limit the authenticity of analysis. We have chosen only two input case to estimate the production while other inputs are collectively taken in intercept. * There is an assumption that the produc tion function follows Cobb-Douglas Production estimation. Other Production estimation methods like Olley/Pakes and Levinshon/Pertin functions are not considered. * In the regression model, we have not factored in any smoothing techniques. * In the analysis of bank over the years the data may be misleading,banks over the year may with better technology produce more with lesser input this effect will lower their economies of scale in the given analysis, this is a wrong conclusion 3. Data analysis and Results We referred the website of RBI to get the data needed for our analysis.A total of 27 banks were taken for analysis and the data for these banks from the period 2004-05 to 2008-09 have been used for the analysis. We used the Cobb Douglas Function for the models, wherein Q = A * (Input1^ ? 1) * (Input2 ^ ? 2) The production functions thus attained provides us a view of the overall sector as a whole for the following the outputs. 1. Deposit 2. Advances 3. Deposit + Advances 4. Intere st Income Further, we focussed on two banks, State Bank of India and State Bank of Indore, the largest and smallest in the sector in terms of capital, to understand the applicability of the product functions attained in the above study.Here, the data across the five years in the consideration were used to obtain the production functions for each of the input-output combinations mentioned above. The results have been summarized in the Table 1 below for the four different models taken for all the banks across five years and Table 2 for all the four models for 2 specific banks: Table 1: Case| Year| Intercept| ? ( Elasticity of Labour)| ? (Elasticity of Capital) | R2| Model 1:Input1: Labour Input2: Capital Output: Deposits| 2004-05| 0. 6431| 0. 7257| 0. 2440| 0. 9596| | 2005-06| 0. 8010| 0. 5535| 0. 4239| 0. 9802| | 2006-07| 0. 8944| 0. 5655| 0. 4017| 0. 9731| | 2007-08| 1. 2448| 0. 4426| 0. 676| 0. 9707| | 2008-09| 1. 2768| 0. 3591| 0. 5694| 0. 9685| Model 2:Input1: Labour Input2: Capi tal Output: Advances| 2004-05| 1. 0543| 0. 2347| 0. 6749| 0. 8900| | 2005-06| 0. 9721| 0. 1998| 0. 7609| 0. 9372| | 2006-07| 0. 9495| 0. 3228| 0. 6367| 0. 9448| | 2007-08| 1. 2994| 0. 2608| 0. 6275| 0. 9544| | 2008-09| 1. 2154| 0. 2486| 0. 6746| 0. 9641| Model 3:Input1: Labour Input2: Capital Output: Deposits + Advances| 2004-05| 1. 2041| 0. 4583| 0. 4768| 0. 9416| | 2005-06| 1. 2145| 0. 3679| 0. 5987| 0. 9695| | 2006-07| 1. 2331| 0. 4450| 0. 5174| 0. 9662| | 2007-08| 1. 5742| 0. 3575| 0. 5422| 0. 9663| | 2008-09| 1. 5500| 0. 3101| 0. 6157| 0. 9683|Model 4:Input1: Labour Input2: Capital Output: Interest Income| 2004-05| -0. 1461| 0. 5320| 0. 4036| 0. 9584| | 2005-06| -0. 0207| 0. 2972| 0. 6656| 0. 9610| | 2006-07| 0. 0246| 0. 3640| 0. 5843| 0. 9733| | 2007-08| 0. 3381| 0. 3250| 0. 5629| 0. 9639| | 2008-09| 0. 4347| 0. 2483| 0. 6411| 0. 9711| Table 2 State Bank of India| Case| Intercept| ? ( Elasticity of Labour)| ? (Elasticity of Capital) | R2| Input1: Labour Input2: Capital Output: Deposits| -3. 03105| 0. 978999| 0. 77501| 0. 976381| Input1: Labour Input2: Capital Output: Advances| 2. 773811| -0. 31806| 0. 972634| 0. 93499| Input1: Labour Input2: Capital Output: Deposits + Advances| -0. 37579| 0. 453894| 0. 852554| 0. 64079| Input1: Labour Input2: Capital Output: Interest Income| -3. 36783| 0. 872917| 0. 74153| 0. 996843| State Bank of Indore| Case| Intercept| ? ( Elasticity of Labour)| ? (Elasticity of Capital) | R2| Input1: Labour Input2: Capital Output: Deposits| 1. 693202| -0. 37172| 1. 310855| 0. 985134| Input1: Labour Input2: Capital Output: Advances| -3. 03629| 0. 124397| 2. 214496| 0. 938827| Input1: Labour Input2: Capital Output: Deposits + Advances| 0. 119414| -0. 21134| 1. 712892| 0. 966654| Input1: Labour Input2: Capital Output: Interest Income| 5. 081366| -1. 73671| 1. 552713| 0. 993676| The macro-economic factors in India definitely affect the performance of the banks.The various parameters like inflation, GDP affect the sentiment of the market in general, while the regulatory measures taken by RBI through changing CRR, SLR, repo and reverse repo rates effect a shift in the business outlook of the bank. Since these parameters keep on changing from time to time, we decided to have separate product functions for every year. This guards us against the negative impacts making an assumption of Ceteris Paribas in determining the product functions, where we might have a few more variables. But the correlation of those factors with the performance of the banks is not the motive of this study, and hence not in its scope.Also, while analyzing the performance of the banks, we have to keep in mind that, being in the public sector, their focus is not always on profit maximizing. Rather, the goal is often carrying out the social responsibilities like providing banking facilities at places where the venture might not be profitable, and hence not a feasible for the private sector to open branches at those places. Analysis and Results for the different models Model 1: Input variables: Labour (L), Capital (K) Output variable: Deposit The first graph below captures the variation in output with respect to change in labour and the second with respect to change in capital. A strong similarity in graph indicates that labour n capital can be almost perfect substitutes. If the graphs differ then they are not good substitutesDeposit is essentially an intermediate variable, here treated as an output. As expected, we see some variation in the results across the years. An interesting observation here is that the elasticity of labour decreases along the period under study. This is in keeping with the redundant labour created by the technical innovations of the operations reducing the productivity of labour. The policies of the Public sector bank do not allow them to reduce the input of labour suddenly. Also, the higher elasticity of capital for 2008-2009 indicates the mood of the market during the recession, where the safety of t he bank deposits looked better when weighed against the risks and lower outputs of other avenues of investment.The high values of R2 point at the stability of the regression through which the production functions were attained. As the sum of Output Elasticity’s of Inputs (Labor and Capital) as ? +? value is close to unity, it implies that the Indian Public sector banks are in Economies of Scale. This is consistent with the earlier economic researches which imply the banking sector in general is in Economies of Scale (Increasing returns to scale). Model: 2 Input variables: Labour (L), capital (K) Output variable: Advances Here, again, we see that the R2 values are high indicating higher stability in the production functions. An interesting phenomenon that can be noticed in these results is in the relative stability of all three parameters across the years.The relative variation of the coefficients across the years is relatively low. Model: 3 Input variables: Labour (L), capita l (K) Output variable: Deposit Advances Here, again, we see that the R2 values are high indicating higher stability in the production functions. An interesting phenomenon that can be noticed in these results is in the relative stability of all three parameters across the years. The relative variation of the coefficients across the years is relatively low. The economies of scale ? +? value is again close to unity and signifies that for all the different outputs there is an increasing scale of return. Model: 4 Input variables: Labour (L), capital (K) Output variable: Interest IncomeAgain, we see a clear trend of declining elasticity of labour across the years, validating the observation made in case 1. The relatively higher elasticity of capital in 2008-09 indicates the stability and optimization of performance of the Indian banks in turbulent global scenario. For each of the banks under study, the income under both the heads, Interest and other, showed a steady rise. Analyzes for Spe cific banks: State bank of India and State bank of Indore All the above mentioned four models of input and output parameters where analyzed for State bank of India and State Bank of Indore for period of 5 Years . The below graphs are a couple of sample graphs of the analysis . All the graphs of the analysis are attached below.We must note a very interesting trend in the economies of scale (ie the sum of alpha n beta) in our result. The economy of scale for almost all the cases in the initial four analysis is slightly less than or almost equal to 1 but it is greater than 1 both for SBI and State bank of Indore respectively. This means that when we look at the overall sector the banks of larger size have almost proportionally large output as compared to their input but both in SBI and State bank of Indore the increase in output is disproportionally larger compared to increase in input. The Data used for the analysis and detailed regression analyses are attached below:The complete set of graphs created for all the models are as well attached below: 4. Conclusion The study focused on modeling the Production Function for public sector banks. The regression curves obtained from all the banks that were considered for production functions for Deposits, Advances, sum of Deposits and Advances and interest income. The coefficient of variation was above 90% in most of the cases which reinforces the assumption that the level of capital and labour count significantly explains the variation in output level. The sum of ? and ? , the parameters of the system, is nearly unity. This indicates that the industry has a production which exhibits constant returns to scale.For the analysis done on individual banks (SBI and State bank of India), the values of negative value of alpha  and beta indicate that the increase in labour or capital (as the case may) decreases the overall output of the bank. We have seen constant or slightly decreasing economies of scale across banks in any gi ven year whereas SBIs have shown increasing scale of economy (;gt;1) over the years. To explore this issue further we had done a few more regression for some more banks for 5 years (5 data points). The analysis has thrown up very interesting conclusion, the economy of scale fluctuates by huge degree across various banks and overall it is negative. This happens when the bank is already utilizing more than the needed labour or capital for its given capacity and any further increase in it decreases the overall production .It can be concluded from this analysis that although overall it may not be desirable to have a large size bank, it is desirable to increase the size of both SBI and State bank of Indore as here the incremental return will outmatch the incremental investment as they have economies of scale greater than unity. Our results have been consistent with the previous research findings which state that banking industry has economies of scale i. e. output more than doubles with doubling of input. It was also observed that sum of output elasticity’s of factor inputs (? +? ) was greater for certain banks like SBI and State bank of Indore. 5. Bibliography * Microeconomics, 7th Edition. Robert S. Pindyck, Daniel L. Rubenfield, Prem L. Mehta. * http://en. wikipedia. org/wiki/Banking_in_India *