From Specification,   reduction of the following standard is approximately calculated by an empirical strategy.

 IR= a+b ln (PF)+c ln (PL)+d ln(PK)+e ln (SIZE)+f ln (CRAR)+g ln (LNASST)+h ln (BR)+ i (D5) ………3


IR is interest revenue (net of income on CRR) scaled by total assets

PL is personnel expense to the total number of employees (proxy for unit price of labor)

SIZE is natural logarithm of the total assets,

LINASST is the ratio of loans to total assets,

D5 is dummy variable for total assets (one for the five largest banks, zero elsewhere),

­ denotes the natural logarithmic operator,

PF is average funding rate calculated as the ratio of aggregate interest expenses to total deposits plus borrowings (proxy for unit price of labor).

PK is other operating costs to fixed assets (proxy for unit price of capital),

CRAR is the ratio of capital to risk-weighted assets, and

BR is the number of branches to the total number of branches.

              By following an equation (3) H statistics is equals to b, c and d i.e.; H=b + c + d. When there is rise in costs mutually with an equal amount, total revenues and marginal costs are increasing while there is an increase in the input price, under perfect competition. Reducing of total revenues, marginal costs and reducing of equilibrium output are augmented by input prices, when under monopoly there is an increase in input prices. 

                                 Table: Interpretation of the Panzar-Rosse H Statistic 

H-value Interpretation
H ≤0 Monopoly or perfectly collusive oligopoly
H<1 Monopolistic competition
H=1 Perfect competition, natural monopoly in a perfectly contestable market, or sales-maximizing firm subject to a break-even constraint

 Particularly it is very interest to understand that is in cost figures how total revenues react towards variations this is the main opinion of H statistic in environment.  Banks central business is financial intermediation, first of all as a dependent variable, interest revenue is considered. The relation is a total income in the share of non-interest income is increasing, through total revenue (TR), interest revenue (IR) is restored then the revenue function’s alternative specification is evaluated where it is defined as aggregate of interest revenues and non-interest revenues. 

                To consider the bank-specific features, control variables are initiated. For aggregate demand and bank size, proxy is measured by the natural algorithm of total asset (SIZE). For the purpose of risk-return profile, the size is also controlled in comparison with the cost differences; therefore the coefficients sign that is ex ante is not definite.

                 To consider the firm-level risk, there is an integration of loan-to-total-asset (LNASST) ratios and capital to risk-weighted assets ratios (CRAR). The coefficient which is based on former differs as positive or negative which depends on high range of risk that may lead to low revenue or high revenue of bank. When the revenue of the bank becomes high due to the reason of increased loans based on the assets, the coefficient which is on later becomes positive.

              On revenues, to calculate an outcome of bank size one more proxy which is useful is signified towards total number of branches (BR) by the ratio of many bank branches and therefore possible scale economies and discovered. The above mentioned ratio becomes negative or positive based on the branch networks and the differences between those particular banks which in turn affect the bank revenue.  In banks, particularly state-owned banks are having a large branch network that is the reason in Indian context variable is very useful.

                  To decide five largest banks, an additional dummy variable D5 is used: D5 must be significant, at present oligopoly power is having link with large size 


              In the long-run equilibrium phases, banks are operated in which income should be correlated statistically with input prices. In order to test the H=0 hypothesis, ratio of net income to total assets are specified in eq (3). PR (Panzar Rosse) test and long-run equilibrium are meaningfully interpreted and the results are not discarded at the 5 percent level of the market equilibrium condition. Descriptive summary of variables as specified by the eq (3) are presented in the below table (Descriptive summary of variables (1996-2004).

Descriptive summary of variables (1996-2004):

Variable Mean Standard Deviation Minimum Maximum
Ln (SIZE) 8.870 1.415 4.054 12.919
Ln (PF) 1.920 0.272 -0.199 2.693
Ln (PL) 0.832 0.625 -0.627 3.841
Ln (PK) 5.152 0.803 2.313 7.026
Ln (CRAR) 2.379 0.658 -6.908 5.088
Ln (BR) -0.940 2.065 -5.599 2.917
Ln (Wages/ total asset) 0.192 0.655 -2.135 1.359
Ln( interest revenue) 6.465 1.361 1.764 10.341
Ln ( total revenue) 6.648 1.365 1.880 10.545


                          Descriptive summary of Variables four features are Mean, Standard Deviation, Minimum and maximum are most important. High variability is exhibited initially through both bank networks and bank size, and by the RBI rationalization policy of banks is affected.  Second, by means of interest revenues, total revenues are determined, as is obvious from the close correspondence among standard deviation and mean of two variables. Third, capital prices remain high, on average, over the period.     

                In the public sector banks operating expenses of banks are high, which results with the low variability labor costs are cheap, which is the strength of the banking system.  Total revenues and share of interest revenues are depicted in the below figures as a result of total assets in the form of percentages across bank groups. In 2002, the new private bank groups record the shares of interest revenues which are significant. 

    SoB: State-owned Banks; NPVT –New Private Banks. 

    OPVT- Old Private Banks; Foreign- Foreign Banks. 

    SoB: State-owned Banks; NPVT –New Private Banks. 

    OPVT- Old Private Banks; Foreign- Foreign Banks.

         The achievement of the financial sector reforms in India is broadly divided into two phases. First generation reforms is generally labeled as 1992-99 and it is known as first phase. Potential reforms, diversification and prudential reforms are guided by the first phase. Second generation reforms are perceived during 1999 and this phase is called as second phase and by means of structural reforms implementation of financial sectors are consolidated.  Below figure shows the economic results of Indian Commercial Banks over the period of 1996-2004.  

                        Estimated value of H is always considerable as non-negative. According to the PR classification Indian banking sector is distinguished by monopolistic competition and the suggested results are observed at specific period. At the one percent level, the unit cost of funds (PF) has a positive symbol which has statistically important. And also at the conventional levels PL turned to be significant. In the explanation of interest revenues (and therefore to the H statistic), the price of funds offers highest involvement during the period of 1996-2004.    

                    The entire Control variables have positive signs and which are significant. Therefore revenues are positively related to bank size. Interest revenues are increased which allows significant capital ratios. In the below table interest revenues are showed between the periods of 1996-2004. During the second sub period H statistics are increased marginally compared to the first, while in the both sub periods H statistics are differ from both 0 and 1.      

                 During the second sub period PK coefficient is important whereas the coefficient of PF also uniformly significant across both the sub periods at the rising importance of the price of capital. Due to the two factors like manpower rationalization and increasing technological sophistication, PL turns to be insignificant particularly at the state-owned banks across the second sub period.

Estimation results for the Indian Commercial Banks: Interest Revenue, 1996-2004. 

Dependent Variable = Ln (Interest Revenue/Total Assets)
  1996-2004 Sub-period 1, 1996-99 Sub-period 2, 2000-04
  Model 1 Model 2a Model 2b
Constant -3.181 (0.140)* -3.227 (0.173)* -3.424 (0.189)*
Ln PF 0.438 (0.024)* 0.382 (0.030)* 0.449 (0.029)*
Ln PL 0.052 (0.018)* 0.086 (0.029)* -0.004 (0.024)*
Ln (SIZE) 0.979 (0.012)* 0.959 (0.014)* 0.985 (0.016)*
Ln PK 0.021


0.0007 (0.013) 0.042 (0.016)*
Ln(LNASST) 0.007 (0.006) 0.872 (0.077)* 0.002 (0.0005)
Ln (CRAR) 0.014


0.030 (0.014)** 0.021 (0.009)*
Ln (BR) -0.015(0.009) 0.026 (0.012)** 0.005 (0.012)*
D5 0.059


0.032(0.047) 0.018 (0.043)
H statistic 0.407 0.469 0.487
F-value on Wald test for H=0 149.32a 125.52a 147.96a
F-value on Wald test for H=1 316.11b 160.47b 163.09b
Adjusted R-square 0.989 0.994 0.989
Number of banks 64 64 64
Total panel observations 570 252 318

 *, ** and *** indicate statistical significance at 1, 5, and 10%, respectively 

Significantly is different from 0 to 5% level. 

Significantly is different from 0 to 5% level. 

            In current years, the bank’s non-interest revenues have raised drastically which can be distinguished. The banks like old private and state owned banks, in terms of augmenting their fee incomes leaned to insulate after their new foreign and private counterparts historically and considerable progress is made in this regard. In 1992 from a level of 8-10 percentages, the non-interest revenues share like a percentage of total revenues is doubled for the banks of public sector to 18-20 percentages at end of the year 2004.

The alternate revenue function specification can be estimated in order to get the report of non-interest revenues increasing share in total revenues. The TR (total revenue) is defined as the “aggregate of non-interest revenues plus interest revenues net of CRR income” when a dependent variable like interest revenue is replaced. In the above given table the results are displayed. For the relevant related financial services, between the regressors the interest to non-interest income ratio to account is incorporated additionally for dissimilar elasticity of demand.

Table: For the Indian Commercial Banks the estimated results: Total revenue from    1996 to 2004

Dependant Variable = In (Total Revenue/Total Assets)
       1996-2004 Sub-period 1,1996-99 Sub-period 2, 2000-2004
  Model 3 Model 4a Model 4b
Constant -2.820(0.143)* -2.896(0.184)* -3.003(0.189)*
In PF 0.367(0.024)* 0.375(0.031)* 0.367(0.030)*
In PL -0.024(0.019) 0.082(0.029)* 0.024(0.023)
In PK 0.025(0.012)** -0.0009(0.012) 0.053(0.017)*
In(SIZE) 0.982(0.011)* 0.965(0.015)* 0.981(0.016)*
In(LNASST) 0.006(0.005) 0.866(0.079)* 0.0009(0.005)
In (CRAR) 0.013(0.0007)*** 0.031(0.015)** 0.018(0.008)*
In (BR) -0.023(0.009)* 0.018(0.012) -0.004(0.012)
In (interest income/ non-interest income) -0.065(0.017)* -0.111(0.022)* -0.075(0.020)*
D5 0.055(0.036) 0.033(0.049) 0.026(0.042)
H statistic 0.0368 0.456 0.444
F-value on Wald test for H=0 128.04a 113.55a 132.91a
F-value on Wald test for H=1 377.16b 161.19b 207.93b
Adjusted R-square 0.990 0.994 0.989
Total Panel observations 570 252 318
Number of banks 64 64 64

 At 1, 5 and 10%, the *, ** and *** indicates the statistical significance respectively

Significantly a different from 0 at 5% level

Significantly b different from 0 at 5% level 

              The earlier findings are explained in the above given table. The H statistic value is lower when compared to the earlier but it is positive for the entire period and confirms the monopolistic free entry equilibrium presence. Similar to that of earlier model, during the second sub period the second most contribution is made to the H statistic by the capital price. Throughout the first sub period the contribution of labor price is significant but when moved to the second sub period it is insignificant.  But the second sub period can turn into significant with the help of bank size, capital adequacy and control variables for the whole period that is, similar to that of the earlier, the magnitudes are of same order approximately.

A negative sign is shown on a particular interest in case of interest to non-interest income ratio.  When the fee incomes of a bank are increasing, the bank’s interest income falls in an era of benevolent interest rates economically and this finally makes on government securities higher treasury incomes. For this reason, the interest to non-interest income ratio became lesser probably. By means of higher total revenues, the declining of ratio is linked. In the second sub period, the marginal decline in H statistic is signified by the sub period analysis. Like in earlier specification many variables of control maintain their significance as well as sign. During the second sub period, the raising importance of capital cost is revealed by the analysis that relies on sub periods, in affecting the H statistic. 

Table: For the Indian Commercial Banks the estimated results: Interest revenue by Type of Bank in the period 1996 to 2004. 

  Public Sector Banks New Private & Foreign Banks
Constant -1.298(0.253)* -3.664(0.325)*
In PF 0.161(0.023)* 0.507(0.042)*
In PL 0.059(0.025)** -0.013(0.039)
In PK 0.004(0.015) -0.006(0.029)
In (SIZE) 0.821(0.023)* 0.981(0.030)*
In (LNASST) 0.001(0.003) 0.967(0.124)*
In (CRAR) 0.062(0.016)* 0.012(0.014)
In (BR) 0.168(0.026)* -0.010(0.031)
H statistic 0.224 0.488
F-value on Wald test for H=0 40.60a 61.54a
F-value on Wald test for H=1 487.25b 67.80b
Adjusted R-square 0.991 0.969
Number of banks 27 20
Total panel observations 243 174

 At 1, 5 and 10%, the statistical significance is indicated as *, ** and *** respectively

Significantly a different from 0 at 5% level

Significantly b different from 0 at 5% level

                 The weighted least squares (WLS) approach can be utilized for re-estimating the baseline specification (3). Here, in a particular year the banks weigh the observations with respective asset shares. The procedure of WLS is well suitable instinctively for capturing the representative banks behavior through offering high weight in case of bigger banks. Many variables contain counter instinctive signs and no extra significant insight is given by the results. Mainly for a cross country framework, the methodology of WLS is most suitable.

For various Latin American countries, the Levy Yeyati and Micco in the year 2003 in their study of bank competition reported, based on that across the countries the number of reporting banks vary. In support of dissimilar types of banks the results will be estimated.  The foreign as well as new private banks related business orientation is specially given and these two banks are grouped as one for the whole sample period in order to estimate the baseline model. The contribution of funds price is highest for the H statistic followed by the labor price in case of public sector banks which is clearly illustrated in the above table.

To H statistic, the funds price forms the most significant contribution in case of other group of banks.  In influencing the H statistic, the resultant high wage bill as well as in public sector banks the huge manpower is considered as most important because this is intuitive.  For public sector banks, the CRAR is concerned as the main which signify that for foreign banks the capital adequacy is not a key concern. When compared the foreign and private bank groups with the public sector group, the H statistic in terms of magnitudes is higher for foreign as well as private banks. The values of H statistic are dissimilar significantly from 0 and 1.

        The approximation in the table below also informs that a statistical importance for the group of public sector bank is shown by the price of both capital and labor. Since previous, for the public sector bank the capital adequacy and branch network amongst the control variables were considered significant. On the income ratio of interest to non-interest variable, the negative sign present may involve the rising importance of other incomes as well as non-interest treasury as a part of banks total income. Same as earlier(seen in table above), even though these magnitudes are reasonably lower, the H statistics magnitude practices the same order that is larger for private and foreign banks as compared to the public sector banks.