An Analysis of the Production Function of Private-Sector Banks in India

Submitted to Dr. Kaushik BhattacharyaIndian Institute of Management Lucknow

8/7/2010

By,Anurag Arora – PGP26006

Hashim S- PGP26015Jay Prakash Musirana – PGP26018

Ravi Pathak – PGP26039Ravi Ramani – PGP26040

Sabareesh Venugopal – PGP26046Soundarya Kedarnath- PGP26057

Section A, Group 3

ContentsABSTRACT........................................................................................................................................................ 3INTRODUCTION............................................................................................................................................. 4

ECONOMIES OF SCALE................................................................................................................................. 4PRODUCTION FUNCTION............................................................................................................................. 5COBB-DOUGLAS PRODUCTION FUNCTION................................................................................................5

METHODOLOGY.............................................................................................................................................6REGRESSION MODELS ADOPTED................................................................................................................6REGRESSION METHODOLOGY..................................................................................................................... 7

Formation of Cobb-Douglas function for Banks.......................................................................7Regression models tested for Indian Domestic Private Banks (2008-09 data).............8Regression models tested for Foreign Banks in India (2008-09 data)..............................9

DATA ANALYSIS AND INTREPRETATIONS......................................................................................11RETURNS ON SCALE BASED ON SEGMENTATION OF BANKING INDUSTRY.......................13LIMITATIONS OF THE METHODOLOGY ADOPTED....................................................................................14COMPARISON BETWEEN FOREIGN AND DOMESTIC PRIVATE BANKS..................................................15

CONCLUSION............................................................................................................................................... 15REFERENCES................................................................................................................................................. 16

ABSTRACT

This project estimates the Production Function of Private Sector Banks in India from the year 2004-05 till 2008-09. We worked on a set of 4 input and 4 output variables to arrive at the best two Cobb-Douglas models for the Production function. Different combinations of input and output variables were analyzed statistically using multivariate regression on the data of 5 years. The two selected models were then analyzed for comparing Returns to Scale for different years in the Banking Industry. The study finds the results to be consistent with the erstwhile economic conditions and the economies of scale in the banking industry. Furthermore, we segmented the banking industry into small, medium and large scale banks to analyze the Returns to Scale for these segments. The results showed that small size banks have the Returns to Scale lower than the industry figure. The study also highlights the key differences in the Production Function analysis of Domestic Private Banks and Foreign Banks in India.

INTRODUCTION

Defining and measuring bank output has long been a difficult and somewhat contentious issue. This has been made even more challenging by rapid and massive changes over the past two decades in both the form of organizations and the range and features of financial instruments offered by banks. Nowadays, banks engage in a wide range of non-traditional activities such as underwriting firms’ public offerings of debt and equity securities, standby letters of credit and a variety of derivatives contracts (e.g. swaps and options). The main reason for the difficulty in measuring the output is that much of bank service output is not explicitly priced. Instead the implicit charges for financial services are bundled with interest flows between banks and their customers; on net, banks earn a positive spread between interest rates received and interest rates paid.

In 2010, the share of private sector banks increases to 30 per cent of total sector assets, from current levels of 18 per cent, while that of foreign banks increases to over 12 per cent of total assets. The share of the private sector banks (including through mergers with PSBs) increases to 35 per cent and that of foreign banks increases to 20 per cent of total sector assets.

ECONOMIES OF SCALE

Economies of scale relates to the cost advantage a business obtains from expansion. It is a long-run concept and refers to the reduction in unit cost as the facility size and usage level of other inputs increase. The common sources are purchasing (bulk buying through long-term contracts), managerial (increasing the specialization of managers), financial (obtaining lower-interest charges and having access to a greater range of financial instruments), marketing (spreading the cost of advertising over a greater range of output in media markets) and technological (taking advantage of returns to scale in the production function). Each of these factors reduces the long run average costs (LRAC) of production by shifting the short-run average total cost (SRATC) curve down and to the right. Economies of scale are also derived partially from learning by doing.

If a bank expands its scale of operations and diversifies its activities, it can reduce average costs and thereby improve spread. Thus, the bank can exploit economies of scale and scope. While banking researchers generally agree that economies of scale do exist in the industry at low levels of output, there is less agreement about whether diseconomies of scale emerge at high levels of output. Earlier studies found evidence that diseconomies of scale did occur when total banking assets exceeded roughly $10 billion. However, these results were discovered when banking companies operating in multiple states had to maintain separately capitalized, individually chartered bank subsidiaries in those states.

On the cost side, it is apparent that the cost structure of running a network of bank branches across multiple states should be more efficient than running a group of individually capitalized bank subsidiaries. On the revenue side, research on mega-mergers suggests that merged banks experienced higher profit efficiency from increased revenues than did a group of individual

banks, because they provided customers with higher value-added products and services. Moreover, a banking organization of a certain scale may even earn a "too-big-to-fail" subsidy due to the market's perception of de facto government backing of a megabank in times of crisis.

PRODUCTION FUNCTION

A production function is a function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs. This function is an assumed technological relationship, based on the current state of engineering knowledge.

In a general mathematical form, a production function can be expressed as:

Q = f(X1, X2, X3... Xn)Where: Q = quantity of outputX1, X2, X3... Xn = quantities of factor inputs (such as capital, labor, land or raw materials).

One formulation of the production function is as a linear function:

Q = a + bX1 + cX2 + dX3 +...Where a, b, c and d are parameters that are determined empirically.

RETURNS TO SCALE

Returns to Scale refer to changes in output resulting from a proportional change in all inputs (where all inputs increase by a constant factor). If the output increases by that same proportional change, then there are constant returns to scale (CRS). If the output increases by less than that proportional change, then there are decreasing returns to scale (DRS). If the output increases by more than that proportional change, there are increasing returns to scale (IRS). Thus the returns to scale faced by a firm are purely technologically imposed and are not influenced by economic decisions or by market conditions.

COBB-DOUGLAS PRODUCTION FUNCTION

The Cobb–Douglas functional form of production functions is widely used to represent the relationship of an output to inputs. It was proposed by Knut and Wicksell and tested against statistical evidence by Charles Cobb and Paul Douglas.

The function is: Y = AL K

Where: Y = total production (the monetary value of all goods produced in a year)L = labor inputK = capital inputA = total factor productivityα and β are the output elasticities of labor and capital, respectively. The intercept value A is a constant determined by available technology.

Output elasticity measures the responsiveness of the output to a change in levels of either labor or capital used in production, ceteris paribus. For example if α = 0.15, a 1% increase in labor

would lead to approximately a 0.15% increase in output.If α + β = 1, the production function has constant returns to scale. That is, if L and K are each increased by 20%, Y increases by 20%. If α + β < 1, returns to scale are decreasing.If α + β > 1, returns to scale are increasing.

METHODOLOGY

REGRESSION MODELS ADOPTED

We employed the Cobb-Douglas Production Function to measure the total production of banks as the output with different input factors described below. A bank’s output and input can be presented by many different variables, as opposed to a manufacturing firm which has fixed output and input parameters. We analyzed 4 different output variables for our initial analysis and these were regressed with 4 input variables. These input variables were carefully selected to take into account the possible inputs for a bank. Selection of Input Variables – We employed a 2-input variable Cobb Douglas Production

Function. A combination of 2 inputs was taken from the 4 inputs given below.

o No. of Employees – This refers to the number of people hired by the bank to run its operations. Employees are one of the inputs on which a bank’s production depends. We expect the increase in labor to translate into an increase in the output. This input can be used as the ‘Labor’ variable in the Cobb Douglas function.

o Capital – The Capital parameter signifies the monetary capital employed by the bank for carrying out the business. The Capital parameter consists of the Paid-Up Capital and the General Reserves and Surplus available, and the long term loans taken by the bank. This summed up capital would be used up by the bank for furthering its business. This input can be used as the ‘Capital’ variable in the Cobb Douglas function.

o Number of offices – Another choice of input is the No. of offices (Branches) of the Bank. This factor need not be fully factored in by ‘labor’ input, since as the no. of offices increases, the reach ability of the bank to its customers increases manifold. When the no. of employees increases, the service quality of the bank is affected.

o Capital and Deposits: This input is defined as the summation of capital (as described above) and the deposits available to the bank. This term tells us the total lending capacity of the bank, since we are taking the total cash available to the bank. This input can be used as the ‘Capital’ variable in the Cobb Douglas function.

Selection of Output Variables – We considered the following variables to be a representative of the production output of a bank

o Advances – This refers to the loans given by the bank to its customers. The data for ‘Advances’ is sourced from the Balance Sheets of various banks.

o Deposits – This refers to the deposits made by the bank’s customers. We consider deposits to be an intermediate output in the operations of banks. The data for ‘Deposits’ is sourced from the Balance sheets of various banks.

o Sum of Advances and Deposits (SAD) – Measures the cumulative sum of Advances and Deposits. This overall measure is taken since the bank bases its financial position on the deposits it has and the incomes from loans.

o Interest Income – The Interest Income is another output which shows the net

interest earned by the bank.

Segregation of Indian Banking Industry – We segregated of the Indian private banking industry into ‘Indian Domestic private Banks’ and ‘Foreign banks in India’. The need for this segregation arises because the scale of operations for a private domestic bank is much larger than scale of operations of a foreign bank in India. Many of the foreign banks have just set foot in India and they don’t have a big presence in the country yet.

REGRESSION METHODOLOGY

The methodology employed in estimating the Production function is multi-variate linear regression. In order for the linear regression to hold we take the natural logarithm of the Cobb-Douglas Production function and apply linear regression.

Let the production function be Y = AL K

Where: Y = total production (the monetary value of all goods produced in a year)L = labor inputK = capital inputA = total factor productivity

Taking log on both sides,Log Y = Log A + α Log L + β Log K

Formation of Cobb-Douglas function for Banks

We have 2 input variables to choose the ‘Labor’ variable from and 2 input variables to choose the ‘Capital’ variable from. We also have one output variable to be selected from the 4 output variables defined above. There are thus 16 combinations of Cobb-Douglas production functions.

We then applied the regression methodology on the 16 combinations by using the bank data for 2008-09. Our objective was to find those models which were able to fit the output and input data in a straight line. We rejected those models which have a ‘p-value’ corresponding to an input variable greater than 0.05, since that indicates an insignificant relationship.

The models which showed significant results while fitting the input and output data are listed below in the table along with the corresponding ‘α’ and ‘β’ values. The corresponding p-values for each coefficient are also shown in parenthesis. Explanation of statistical terms

R square: This represents the goodness of fit of a model. The R-square of the regression is the fraction of the variation in the dependent variable that is accounted for by the independent variables.

T-stat: It is the ratio of the coefficient to the standard error. P value: It represents the significance level. A ‘p-value’ of 5% or less is the generally

accepted point at which the null hypothesis is rejected. It says that there is only a 5% chance that these values fitted into the model by chance.

Regression models tested for Indian Domestic Private Banks (2008-09 data)

Case R Square Α β P-value(α)

P-value (β)

α+β

Output: Interest Income0.982550801 0.554116 0.514068 4.26E-06 6.72E-06 1.068185Input 1:Employee

Input 2:CapitalOutput: Sum of Advances & Deposits

0.968976113 0.629405 0.421238 2.64E-05 0.001072 1.050643Input 1:EmployeeInput 2:Capital

Output: Advances0.973508226 0.607138 0.487517 2.55E-05 0.000186 1.094655Input 1:Employee

Input 2:Capital

Output: Deposits0.94579181 -0.19342 1.175867 0.187725 9.85E-08 0.982451Input 1:Number of Offices

Input 2:EmployeeOutput: Advances

0.953850263 -0.30885 1.348553 0.039753 1.03E-08 1.039707Input 1:No: of OffInput 2:EmployeeOutput: Interest IncomeInput 1: Summation of Capital and DepositsInput 2: Number of employees

0.989561 0.861616

0.185377 5.03E-07 0.118248 1.046993

Output: AdvancesInput 1: Summation of Capital and DepositsInput 2: Number of employees

0.993051 0.98431 0.091359 2.73E-09 0.321592 1.07567

Output: Interest Income0.967523077 0.263061 0.821105 0.001388 2.47E-10 1.084167

Input 1:Number of Offices

Input 2:Capital

Output: Interest Income0.965092768 -0.38279 1.386763 0.004461 4.74E-10 1.003974Input 1:Number of Offices

Input 2:EmployeeOutput: Advances

0.961543406 0.312397 0.807114 0.000829 1.97E-09 1.119511Input 1:Number of OfficesInput 2:CapitalOutput: Deposits

0.961159734 0.368085 0.651488 0.005905 4.76E-05 1.019573Input 1:EmployeeInput 2:CapitalOutput: Sum of Advances & Deposits

0.951395799 -0.24382 1.249514 0.092841 2.65E-08 1.005693Input 1:Number of OfficesInput 2:EmployeeOutput: Sum of Advances &Deposits

0.957389468 0.333219 0.746038 0.000509 8.01E-09 1.079257Input 1:Number of OfficesInput 2:CapitalOutput: Deposits

0.949894537 0.351464 0.699719 0.000514 4.81E-08 1.051183Input 1:Number of OfficesInput 2:Capital

Regression models tested for Foreign Banks in India (2008-09 data)

Case R Square α ΒP -value(α)

P-value (β)

α+β

Output: Interest Income0.961655 0.34782 0.89997 2.55E-03 9.08E-09 1.2478Input 1:Employee

Input 2:CapitalOutput: Sum of Advances & Deposits

0.936269 0.49812 0.71244 2.64E-05 0.000826 1.210571Input 1:EmployeeInput 2:CapitaOutput: Advances

0.818368 0.48986 0.80667 6.30E-02 0.003882 1.29654Input 1:EmployeeInput 2:CapitalOutput: Deposits

0.936389 0.63753 0.58157 6.05E-05 1.80E-04 1.219109Input 1:No: of OffInput 2:Employee

Selection of models which fitted best with the input and output data

Out of the models which showed significant results, we selected the two best models based on R square value, Multiple Regression coefficient, t-stat and p-values.

The following are the best two models selected:Model No Input 1 Input 2 Output

1 No. of Employees Capital Interest Income

2 No. of Employees Capital Sum of Advances and Deposits

These selected combinations are then used to determine the returns to scale for the banking industry by regressing data for all 5 years from 2004-05 till 2008-09. This same process is done separately for both Foreign and Domestic Private Banks.

Production Output for Indian Domestic Private Banks –

The Production Functions using the two models are plotted. The actual values, along with their estimated values are plotted alongside to get a feel of the closeness of regression fit performed. This is important, since the high R square value may not always be a sufficient condition for a good model.

Production Output for Foreign Banks in India -

Calculation of Returns to Scale

A regression analysis was done on the two best models selected above for 2004-05 till 2008-09. The returns to scale (α+β) is plotted as shown in the graphs below –

Model 1: We saw that the returns on scale for the banking industry for the model (Output: Interest Income, Input: Capital and employees) showed a value greater than 1 in all the 5 years we studied (2004-09)

Model 2: The second model (Output: Sum of Advances and Deposits, Input: Capital and Employees) also showed a value greater than 1 in all the 5 years we studied (2004-09)

DATA ANALYSIS AND INTREPRETATIONS

Interest plot in the figure stands for Model 1(Output is Interest Income)SAD plot in the figure stands for Model 2 (Output is Sum of Advances and Deposits)

Indian Domestic Banks –

SAD is the sum of advances a bank makes to outside entities and deposits that it receives from its customers. Interest income is the revenue it generates on advances minus the money it gives on the deposits. RBI uses CRR and SLR as tools to tackle inflation and to spur growth in the economy. An increase in SLR or CRR effectively reduces the amount that a bank can lend as advance which in turn will reduce its interest income. A decrease in the base rate to spur growth also has a tendency to reduce the interest income.

The plot of private banks can be interpreted using the above logic. During 2004 – 2005, the interest rates might be decreasing and hence we are seeing a dip in the graphs. When there has been sufficient liquidity created in the market, RBI might have started increasing the interest rates to curb excess liquidity and bring down inflation. Since the interest rates are high, the banks might see an increase in their volume of business as well as their income. So, in a year of low base rate, the net amount generated as interest on the capital employed decreases and when the base rate increases, the net interest earned increases on the same amount of capital. The sharp dip in the SAD and interest income in 2008-09 is consistent with the financial crisis of 2008. The banks did not have enough capital resources to lend and hence the sharp decline in both SAD and interest income.

The Central Government is one of the most prolific money takers from the market. Increase in Government borrowings from the market results into an increase in bond rates. Because of General elections in May 2004, the government had to halt its social sector schemes, which probably would result into a decrease in bond rates. This decrease in yield rate perhaps could be one of the many reasons why interest income for the year 2004-05 decreased for the Indian private banks. The same reasoning doesn’t apply to foreign banks since they are not much dependent on the Indian government borrowings. Based on this reasoning, we do not see a dip in the graph of the foreign banks.

The above graphs are consistent in that they in proportion to the actual base rates of RBI in the period 2004 to 2009. The central bank overnight rate in 2004 was around 4.5%; it increased in the period during 2007 – 2008 to 6% and decreased to around 3.25% in 2009.

Foreign Banks in India –

During the first half of the 2000’s, the foreign banks started to establish themselves and tried to improve their foothold in India, hence (alpha + beta ) may be less than 1 during the initial phase as captured by the graph. Since the foreign banks base inputs were low, they could expand their operations rapidly. Hence we see the slope increasing at a faster rate.

During the worldwide recession, all the banks were hit and we could see a dip in the graph around 2007 – 2008. Once the economies started recovering, the parent companies of these foreign subsidiaries might have hesitated to invest in already volatile developed markets and instead concentrated on investing in the emerging markets. The Indian foreign banks thus had larger access to lending capital. Hence we could see an increase in the returns of scale of foreign banks even when many private Indian banks saw a decline in the corresponding period.

RETURNS ON SCALE BASED ON SEGMENTATION OF BANKING INDUSTRY

After the calculation of return on scale for the industry, we investigated the possibility of finding the returns to scale for small banks, medium sized banks and large banks. We conjectured that the returns of scale would be less for small sized banks when compared to the industry average and the large sized banks.

Criteria for Industry Segmentation

We took a reasonable assumption that the size of the bank depends upon the capital that a bank has. The criterion is as given below:

Small sized Banks: Capital < 1000 croresMid-sized Banks: 1000 crores < Capital < 5000 croresLarge Banks: Capital > 5000 crores.

We also thought of segmenting the banks based on their Market capitalization (used by BSE, NSE to classify banks). But since market capitalization is not related to the full capital available with the banks, we decided to classify banks on the basis of Capital with the assumption made above

Results of Regression based on segmented banks

We regressed the data on small, medium and large banks on the two best models described above for the year 2008-09. The regression was done separately for these 3 categories of banks. But probably because of the lack of adequate data, the results generated came out to be insignificant (p value > 0.05) for all models except one model on ‘Small Sized Banks’ mentioned below.

For Small sized Banks, the following model gave significant results.

Input 1 Input 2 Output R Square ValueAlpha(Input 1)

Beta (Input 2)

Employee Capital Interest 0.954543 0.26 0.66

Significance of this result:

The (α+β) value of this model comes out to be 0.92 which is less than the industry average of 1.06 for the year 2008-09. This result is significant because it shows that the returns of scale for small sized banks are less than the industry average. This result is consistent with the widely held belief that large banks enjoy operating scale advantages over small banks. We expected the (α+β) value for large sized banks to be greater than the industry average but could not validate it because the available data could not fit into the model for large banks. Segmentation of banks resulted into the large bank category not having enough data for regression and thus could not fit into the model.

LIMITATIONS OF THE METHODOLOGY ADOPTED

The estimation methodology employed may have some limitations, apart from those of the Cobb-Douglas production function. Some of them are elucidated as below -

There can be several input parameters. The Cobb-Douglas function restricts us to use only two of them as inputs at a time. Similarly, there are several parameters which can be considered as the output but the Cobb-Douglas function restricts us to use only one. In that sense, the production function thus determined is not comprehensive and is not an accurate representation of the production function of the industry.

The assumption ‘Ceteris Paribus’ (i.e. all other things being constant) is not true in strict sense because other parameters like technology keep on changing with time.

We assume that α < 1 and β < 1, so that the firm has decreasing marginal products of inputs which might not be necessarily true.

There are extraneous variables which are neither input nor output but may have an influence on output like the prevailing macroeconomic conditions.

We have not considered other production estimation methods like “Olley/Pakes” and “Levinshon/Pertin” functions to derive the production function.

We have not factored any smoothing techniques in the regression model. The monetary figures have been taken on nominal terms which do not take inflation

into account. We took data from a sample of 21 banks for our regression analysis. Although we tried

to take the sample from all categories of banks (Small, Mid-Sized, Large), it is possible that the representation of banks was not uniform.

COMPARISON BETWEEN FOREIGN AND DOMESTIC PRIVATE BANKS

Private banks have low Rural and Small city Penetration. This is almost nil in case of Foreign banks.

Foreign banks are striving to increase business by technological advances and use of value added services to win over clients in metros. Domestic Private Banks are expanding reach in tier-2 and smaller cities.

Foreign banks have higher growth rate than other banks due to rapid expansion and M&A activities (increase in buying old and new foreign banks in recent past) and also due to favorable government and central bank policies.

Consolidation is going on everywhere in the sector: example mergers such as ICICI-BoR, HDFC-CBoP, etc.

CONCLUSION

The project focused on defining production function for Private (domestic and foreign) Banks in India. We used capital, employees, number of offices and Summation of Capital and Deposits as inputs whereas Interest Income, Summation of Advances and Deposits, Advances and Deposits were taken as outputs. Regression results showed a weak linkage for the input variables ‘No. of offices’ and ‘Summation of Capital and Deposits’ with the four outputs. Out of the 4 outputs, we found that ‘Summation of Advances and Deposits’ and ‘Interest Income’ represent the production function of banks in the best way. The project indicates that there are increasing returns of scale for private banks, especially foreign banks as a trend. This is expected to continue with the current Macroeconomic Environment and new government Policy Framework.

Future Scope of Analysis - Examination of the production functions of banks in metro and non-metro/rural areas to

check profitability of operations in these areas. We can take yearly data instead of Cumulative Data for Loans and Advances. Using some other model of Production function, apart from Cobb-Douglas. Using inputs such as business done per employee or capital employed per employee.

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