Estimation of Production Function of Public Sector Banks

Project regard of drudgery influence of general celestial sp present marges Contents 1. INRODUCTION3 2. Methodology4 2. 1General Approach4 2. 2 information Collection4 2. 3Data Processing5 2. 3. 1Nature of relys5 2. 3. 2Nature of Variables5 2. 3. 3As spiritptions in the manipulation of Variables5 2. 4Data digest5 2. 4. 1Objective of the digest5 2. 4. 2 occupation Function Relationship5 2. 5Limitation8 3. Data shopping mallmary and Results9 4. Conclusion15 5. Bibliographical recordy16 1. INRODUCTIONThe structure of the hopeing industry has downstairsgone sweeping spays in the outgoing two decades. In response to heightened competition from non- bank building building financial besotteds enabled by technical progress among other divisors, banks oblige been expanding both the exfoliation and scope of their operations, by and large through consolidations. This merger wave coincides with extensive deregulation, which has removed restrictions on turnout offerings and interstate banking. These changes let motivated many studies. The estimation of bank productivity and returns to scale is of particular nterest because of its broad practical applications and important policy implications The Banking Sector is characterized by multiplex comments and rigs that atomic number 18 associated with various attributes, such as divergent types of deposits, loans, number of accounts, classes of employees and location of branches. Trans mental straination in terms of moving from graduate(prenominal) operating cost, low productivity and high spread to beingness to a greater extent efficient, productive and competitive has been an important ch aloneenge for the banking vault of heaven in India.Recent old age confound witnessed substantial question efforts that ask been devoted to measuring the aptitude and productivity of the banking industry. However, assessment of exploit of banks has been a problematic one because of the clear question s concerning inputs and takingss. In the absence of any coherent definitions, researchers have used a variety of inputs and issues, just aboutly based on an intermediation or ware approach. The study of the Indian banking sphere of influence 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 one thousand thousand people. Secondly, the vast network of around 70,000 commercial bank branches provides the base of the finance-led growing and development process in India. olibanum 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. employment hold up is a function that specifies the output of a firm, an industry, or an entire delivery for all(a) in all combinations of inputs. It indicates the highest output that a firm mess farm for every undertake combination of inputs. This function is an assumed technological consanguinity, based on the certain state of engineering knowledge it does non represent the result of frugal choices, but rather is an externally minded(p) entity that influences frugal decision-making. Almost all economic theories presuppose a proceeds function, either on the firm level or the aggregate level.In this sense, the production function is one of the anchor 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 interpreted for the compend of the ware function of the ordinary Sector Banks (PSBs) in India. A bank for its operation takes several inputs and generates several outputs. For e. g. th e typical inputs are Employees, nifty for operation, Reserve & Surplus, number of Branches, number of ATMs of a bank etceteraIts output is typically the Loan (Advances), engross Income etc. Since Multiple retroflexion is used so the production output is taken only one at a magazine. Also, only two input versatile at a time is used, though several regression digest have been done for contrasting combinations of input and output to get the most reasonable and best count on relationship. However, a bank uses any number of proteans as input simultaneously. A bank measures its performance among other parameters on how oft Loan or Credit it has disbursed in a fiscal year or how much baffle it has collected from the customers etc.Though such entropy in isolation whitethorn non be a true omen of the efficiency of the pedigree because unregulated disbursal of loans may cause Non Performing Assets (NPAs) which will everywherethrow the Retained Earning of the Bank but since t he insure is concerned only with the Production function of the PSBs indeed no comment will be make on this conniption. Similarly how competitively the puzzles have been taken will non be a subject matter of this report. The Methodology of the report is to be first gather relevant input/output data from arbitrary source.The data so obtained are processed and any boldnesss make for their consequent 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 deal the meaning to such endeavor. 3. 2 Data Collection The data for the Public Sector Banks (PSB) in India for the hobby variables have been collected from the Reserve Bank of Indias (RBI) official website for the fiscal 2004-05 to 2008-09 adheres * detonating device * Loans & Advances * excavate * pursuit Income 3. 3 Data Processing Natu re of Banks All the 20 Nationalised Banks including IDBI as advantageously as all the Associate Banks of the demesne 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 inputs. Nature of Variables For the Banking Sector there are someer variables which are clearly treated as input variables and output (production) variables.Example includes outwear and Loan (Advances) as input variables and Interest Income as output variables. that their are variables kindred 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 out garb 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 ana lysis we treat Deposits as railroad siding/ Production variable.Assumptions in the treatment of Variables 1. It is assumed that the cost of per unit fatigue is incessant and same crosswise all banks. Thus we may take the bray as a sum of money across all banks as an input variable, without bothering about the variable wage rate for each mash i. e the Cost of proletariat is a elongated function of the quantity of Labour. 3. 4 Data Analysis Objective of the Analysis The report wish to obtain the following objectives * To prove a mathematical model of Production Function for PSBs in India. * To goatvas the regression coefficients obtained vis-s-vis the PSBs input and output. To analyze the regression coefficients for specific banks over tail fin eld Production Function Relationship To estimate the one variable Production output function for an economic entity the Cobb-Douglas Production Function is wide used. For the Banking industry the report establishes the relationshi p 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 time from the fiscal 2004-05 to 2008-09. S.No Input Variable1 Input Variable 2 Production outturn across Time Period Banks 1 Labour smashing Deposit 2004-05 to 2008-09 All PSBs 2 Labour swell 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 do = Number of Production Functions * Number of fiscal Years for which the observation is made = 4*5 =20 (B) unique(predicate) to the Largest Nationalised Bank as per capital viz. raise 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 ofState Bank of Indore, the small est 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 sidetrack Across Time Period Bank 1 Labour Capital Deposit 2004-05 to 2008-09 SBI 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 SBIndoreThe 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 interrogation of multiple independent variables (or predictor variables), Multiple Regression is used. Si nce it is for only hit dependent variable (or criterion variable) hence Multiple Regression is not a multivariate test. The model for a multiple regression takes the form y=? 0+? 11+? 22+? 33+ .. +? And we wish to estimate the? 0,? 1,? 2, etc. by obtaining y1=b0+b1x1+b2x2+b3x3+ ..Where thebs are termed as the regression coefficients and ? is the error or residual nurse. For 2 independent variables we fit the data for a plane. The beta set are used in measuring how gear upively 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 variable s such as Labour, raw material, capital etc. f() = function defining the relationship. This function may be a linear 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 charge of all machinery, equipment, and buildings) A = Total factor productivity, a variable which accounts for set up on total output not explained by chosen inputs. ?, ? are the output cinch of turn over and capital, mentionively. These set are constants. We assume ? , ? lt 1 so that the firm has decreasing marginal products of motor 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 being used in the report for regression Log (P) = a0 + ? *Log(L) + ? *Log(K) Thus the Input 1= Log(L), Input 2 = Log(K) and outturn = Log(P) and Model Coefficients = ? , ? 3. 5. 1. 3 Return to ScaleReturns 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 increase returns to scale (IRS). To summarise, it is as follows ? + ? Returns to scale =1 constant lt 1 decreasing gt 1 change magnitude 3. 5 Limitation * The correlation between labour expense and production across banks may be l imited if the trade model of the bank varies.For example banks who primary operate in larger cities can produce more with a smaller workforce because of greater labour use of goods and services while labour in far flung remote branches might be under utilized and may not contribute to production that efficiently. because 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 fewerer 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 genuineness of analysis. We have chosen only two input graphic symbol to estimate the production while other inputs are collectively taken in intercept. * There is an hypothesis that the production 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 equipment casualty conclusion 3. Data analysis and Results We referred the website of RBI to get the data essential for our analysis.A total of 27 banks were taken for analysis and the data for these banks from the conclusion 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 function s thus achieve provides us a view of the overall celestial sphere as a whole for the following the outputs. 1. Deposit 2. Advances 3. Deposit + Advances 4. Interest 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 shape were used to obtain the production functions for each of the input-output combinations mentioned above. The results have been summarized in the board 1 down the stairs 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 ? ( press stud of Labour) ? ( picnic of Capital) R2 Model 1Input1 Labour Input2 Capital turnout 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. 401 7 0. 9731 2007-08 1. 2448 0. 4426 0. 676 0. 9707 2008-09 1. 2768 0. 3591 0. 5694 0. 9685 Model 2Input1 Labour Input2 Capital 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 3Input1 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. 9683Model 4Input1 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 R BI through ever-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 incessantly 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 variab les Labour (L), Capital (K) Output variable Deposit The first graph below captures the diversity 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 consummate(a) substitutes. If the graphs differ then they are not good substitutesDeposit is essentially an ordinary variable, here treated as an output. As expected, we see some variation in the results across the years. An elicit 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(prenominal) elasticity of capital for 2008-2009 indicates the mood of the market during the recession, where the safety of the 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 Elasticitys 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 incriminate 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 spy 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), capital (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 Specific banks State bank of India and State b ank 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 ideal graphs of the analysis . All the graphs of the analysis are habituated below.We must flier 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 belowThe 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 alphaand 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 given year whereas SBIs have shown increasing s cale of economy (gt1) 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 sexually attractive 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 look-alike of input. It was also ob served that sum of output elasticitys 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 *