I Introduction

To bridge this research gap, this study on the efficiency and productivity of RRBs has been undertaken. The study is concerned with the period of 1996-2002. In this period, RRBs underwent revolutionary changes due to the impact of overall economic liberalisation coupled with vigorous financial sector liberalisation, technological progress and the DAP of NABARD. As a result, RRBs were able to produce new services and increase the quality of their productive and organisational systems, with a corresponding effect on productivity and production costs. However, not all RRBs are able to take advantage of the new technologies. From a technological standpoint, some of them are not efficient. This study to some extent also examines factors, which influence these differences in efficiency and TFP growth.

The rest of the paper proceeds as follows. Section II sets the modelling stage with the specification of our data envelopment analysis (DEA) models for calculating the Malmquist TFP index and its three constituent components, as well as discusses the data set used for the study. In Section III, results are discussed. Section IV ends with conclusions and policy implications.

Bhattacharya et al (1997) studied the impact of the limited liberalisation initiated before the deregulation of the 1990s on the performance of Indian commercial banks. Their study covered 70 banks in the period 1986-91. The authors used advances, investments and deposits as outputs and interest expenses and operating expenses as inputs. They found public sector banks had the highest efficiency compared to private and foreign banks. However, the efficiency of public sector banks declined after 1987, private banks showed no change while foreign banks showed a sharp rise in efficiency. They did not consider technical change explicitly in the model.

While studying efficiency of Indian banks Das (1997) measured overall efficiency as well as technical, allocative and scale efficiency of PSBs during 1990 to 1996. The study concluded that there was a decline in all efficiency measures during that period. However, this study also did not explicitly measure technological progress (TFP growth) of the banks in the period.

Reddy (2005) observed that the share of public sector banks in the aggregate assets of the banking sector came down from 90 per cent in 1991 to around 75 per cent in 2004. The share of wholly government-owned public sector banks sharply declined from about 90 per cent to 10 per cent of aggregate assets of all scheduled commercial banks during the same period. Diversification of ownership has led to greater market accountability and improved efficiency.

Leeladhar (2005) pointed out that foreign banks and new private sector banks have embraced technology right from the inception of their operations and, therefore, they have adapted themselves to changes in technology easily, whereas the PSBs and old PSBs have not been able to keep pace with these developments. Added to these woes, the PSBs were also saddled with some non-viable and loss-making branches, thanks to the social banking concept thrust upon them by the regulatory authorities in 1960s.

Mohan (2005) stated that internationally, a return of 1 per cent on assets is considered as outstanding. India’s banking system in 2002 was the second most profitable in the world after that of the US. Most recent research places the optimal size of banks between $ 10 bn and $ 25 bn in the US. It is possible that technological progress as well as deregulation has resulted in a larger size being optimal than before. The average size of Indian banks in comparison to international banks is quite small, for example SBI, India’s largest bank ranks 82nd amongst the top global banks.

II Model Specifications

Even though studies from the developing country perspective on costs, efficiency and productivity of financial institutions are few, a voluminous literature is available for developed countries. There are two approaches to study productivity change: one is the parametric (econometric approach) and the other is the nonparametric approach. In the econometric approach there is a need to estimate cost, production and revenue functions, while the non-parametric approach requires the construction of index numbers by using non-parametric techniques. This study adopts the latter approach as it does not require a specific functional form for the structure of production technology, as is the case with the econometric approach. This approach is the most widely used and accepted method in measuring the efficiency of banks. Specifically, the Malmquist TFP index has been used in this study.

In the current study, we employ the non-parametric frontier method of data DEA to compute the Malmquist TFP indexes. The reasons for choosing Malmquist (1953) index over Fisher and Tornquist (1936) indexes are manifold; it also does not require price data and is capable of accommodating multiple inputs and outputs without worrying about how the inputs and outputs have been aggregated. It also does not make any restrictive value/behaviour assumptions for the economic units, such as cost minimisation or profit maximisation, as required by the Törnquist and Fisher indexes. Most importantly, this technique allows further decomposition of the Malmquist TFP index into three components: (a) shifts in production technology, (b) pure changes in technical efficiency, and (c) effects of economies of scale. The decomposition of the Malmquist TFP index is informative: the component of technological progress represents the degree of innovation potential, and the component of pure technical efficiency change reflects the potential of a banking firm to catch up with other leading benchmarks [Arcelus and Arozena 1999; Grifell-Tatje and Lovell 1999].

The original MPI assumes constant returns to scale for the production process. As a result, the original MPI typically overestimates productivity change if the production process displays decreasing returns to scale (or underestimates it for increasing returns to scale). To cope with the issue of variable returns to scale, Färe et al (1994) recommended the use of a generalised MPI that includes an additional component, called scale index to represent such an effect of economies of scale on productivity. We will also include such scale factors in our analysis. A brief mathematical account has been given below.

A production process, which employs input vector Xt to produce output vector Yt at time t, can be defined by using an output set [Shao and Shu 2002]:

Pt(Xt) = {Yt: Xt can produce Yt}. (1)

The output set Pt (Xt) is assumed to be closed, bounded and convex, and it satisfies the strong disposability of inputs and outputs [Coelli et al 1998]. The output distance function is defined on the output set as:

Dt(Xt, Yt) = min {ρ : (Yt/ρ) ∈ Pt (Xt)} (2-1) = [max {ρ : (ρYt) ∈ Pt (Xt)}]–1. (2-2) The formula in equation (2-2) indicates that the distance function

Dt is the inverse of the measure of Farrell’s output-oriented technical efficiency [Farell 1957] and it facilitates the computation of an output distance function through the methods of efficiency measurement like DEA. The value of the output distance function ranges from 0 to 1, with a higher score indicating a location closer to the boundary of the output set (i e, the production frontier).

According to Färe et al (1994), the MPI can be defined as:

M ( Xt , Y , X , Y ) =⎢×⎥

= ⎢×⎥(3)

In equation (3), the ratio outside the brackets is equal to the change of technical efficiency between time t and t + 1. In other words, it represents the change in the relative distance of the observed production from the maximum potential production. The component inside the brackets of equation (3) is the geometric mean of the two productivity indexes and represents the shift in production technologies (technical change) between timetand t + 1.

That is, technical efficiency change + t +1 t+

TEC = Dt 1(X , Y 1) (4) tt

Dt (X , Y ) Technical change

TCH= ⎡ Dt (X , Y 1) Dt (X , Y ) ⎤ (5)

Technical efficiency change (TEC) in equation (4) can be further decomposed as the product of two components – pure technical efficiency change and scale change – as follows [Fare et al 1994]:

Dt 1(X , Y 1)

Dt +1(Xt+1, Yt +1) ⎡Dt +1( t+1 t+1) Dt (Xt , Yt ) ⎤ rX , Y r

The ratio outside the brackets in equation (6) represents the pure change of technical efficiency, subject to a distance function

(D) with variable returns to scale, between time t and t + 1 and

ris denoted by PEC hereafter. In other words, Pure technical efficiency change

PEC = r(7) ttt

The component inside the brackets of equation (6) represents the effects of economies of scale on productivity and is expressed as SCH. It is noted that SCH can be readily derived by dividing TEC of equation (4) by PEC of equation (7) and would not involve its own computations of additional output distance functions. That is, scale change

SCH = TEC / PEC (8)

After incorporating equation (6) – (8) into equation (3), we obtain the complete decomposition of the MPI:

Mt (Xt , Yt , Xt+1, Yt +1)= (TCH) × (TEC)

= (TCH) × (PEC) × (SCH) (9)

Another merit of defining the MPI using the output distance function Dt is that the MPI and its corresponding components (TCH, TEC, PEC and SCH) are all calculated in an index form and have a threshold value of one. In other words, if a derived value is equal to one, it indicates that a bank’s performance remains unchanged in that performance measure. A value greater than one represents an improvement, and a value less than one indicates a decline. The product of the index components of TCH, PEC and SCH then amounts to the final MPI.

DEA is a non-parametric and linear programming-based method for calculating a Farrell-like measure of technical efficiency [Banker et al 1984; Charnes et al 1978]. Due to the computational linkage specified by equation (2-2), the optimal values obtained by the corresponding output-oriented DEA models are equal to the reciprocal of the output distance functions in computing the final MPI.

To determine the final MPI, a close examination of equations

(3) and (6) reveal that we have to compute TCH, TEC and PEC, and then derive SCH by dividing TEC by PEC. Each output distance function corresponds to one particular output-oriented DEA linear programme. Among TCH, TEC and PEC, there are six output distance functions and, thus, a total of six different DEA models have to be formulated and solved:

D (X , Y ), D (X , Y ), D (X , Y ),

D (X , Y ), D (X , Y ), and D (X , Y ).

For easy understanding, the study denotes superscripts u and v to represent the possible combinations of t and t + 1 in formulating our DEA models (i e, u, v ∈ {t, t + 1}). As a result, as an alternative of six linear programmes, the study presents only two general DEA models to compute the MPI for the banking industry of a particular bank m (where I is the number of inputs, J is the number of outputs, and N is the number of banks):

[ (X ,Y )] = max qm

Definitions and Measurement of Bank Inputsand Outputs

There are three common approaches –the intermediation, user cost and production approach (value added approaches) in measuring outputs and inputs in the banking industry. A brief description about each method has been given below.

The first method is the intermediation approach in which bank deposits are regarded as having being converted into loans. While this approach seems to be appropriate for banks that purchase their funds in big chunks from other banks and large institutional depositors, it may not be so for the rural banks. Most rural banks provide value added services for their deposit holders, such as safekeeping of funds and other transaction services. Most importantly, accepting deposits from the vast majority of the rural population spread over widely dispersed and remote villages is an important social objective assigned to rural banks. This makes their deposits an output rather than an input and therefore the intermediation approach underestimates the overall value addition of the RRBs in serving rural India.

The second method is the user-cost approach. The user-cost approach considers an asset as an output, if the financial returns are greater than the opportunity cost of funds. Similarly, a liability item is regarded as an output if the financial costs are less than the opportunity cost. If neither of these conditions is satisfied, the assets or the liability is classified as an input [Berger and Humpherey 1992]. The user-cost approach is usually attributed to Hancock (1986). According to Hancock, user costs can be calculated for all the assets and liabilities on the balance sheet. However, an important weakness of this approach is that the assignment of assets and liability items as inputs or outputs may change with movements in interest rates and services charges.

The alternative is the production approach (value added approach) where banks are regarded as using labour and capital to produce deposits, loans and income [Mester 1987; Berger and Humpherey 1992]. Under this approach, high value creating activities such as loans, taking deposits and income are classified as outputs and measured in dollar terms, whereas labour and physical capital are classified as inputs [Wheelock and Wilson 1995].

Taking into account the advantages and disadvantages of each method, the value added (production) approach was employed, which enabled the classification of inputs and outputs based on their perceived value addition. This method turns out to be attractive as it allows differentiation between the various functions performed by banks. In analysing the functions performed by commercial banks, Bergendhal (1998) mentions five fundamental goals of efficient bank management: profit maximisation, risk management, service provision, intermediation and utility provision. David and Manole (2002) reclassified the above five functions into two broadly defined ones: profit maximisation (combining features of Bergendhal’s profit maximisation and risk management) and service provision (combining elements of service provision, intermediation and utility provision). In reality any bank operation combines the elements of the above two functions, since it is hard to imagine a bank which is not trying to produce (if not maximise) profits or establish a good rapport with its clients (service provision in terms of deposit mobilisation and making loans).

In this paper, two separate models were evaluated (both based on production approach) one with emphasis on profitability and the other with service provision. The inputs considered were interest expenses plus operational expenses excluding provisions. The three outputs considered in the first model (model I) were liquid assets, total advances and total income (interest income plus non-interest income). And the three outputs considered in the second model (model II) are liquid assets, total advance and total deposits.

The above mix of outputs and inputs were selected by considering the broader objectives such as profitability (total income; model I), service provision (deposits; model II) in addition to the usual total liquid assets and total advances as outputs with interest expenses and operating expenses as inputs. (The same approach has been followed in David and Manole (2002) and Wheelock and Wilson (1995). In the context of rural India, taking deposits (mobilising savings) from the vast mass of the population (who were dispersed in a wide area and not within the reach of capital markets to invest their savings) is an equally important function (in line with the social/national objectives) as that of giving loans (advances) to the needy; hence, both deposits and advances are considered as outputs in line with the study by David and Manole (2002) using the service approach. In both the models, advances and liquidity are taken as outputs as maintaining adequate liquidity and providing loans is an important and natural function of rural banks.

III Results of DEA

In line with the objectives of RRBs, mean efficiency is higher in service provision than in earning profits (Table 1). The average technical efficiency of all RRBs increased from 0.71 to 0.81 from 1996 to 2002 in model I (profitability), while average efficiency rose from 0.81 to 0.86 in the same period measured by model II (service). Mean efficiency in profitability also increased by about 10 per cent during 1996 to 2002 with initiatives such as the DAP and liberalisation. The efficiency of RRBs in devel-Figure 1: Technical Efficiency of RRBs by Size (Total Assets) oped regions is higher compared to less developed regions in both profitability and service provision. 0.95

0.9

0.8

Bottom quartile Lower middle quartile Top middle quartile Top quartile

0.7

0.6

Total Assets

—e—Model I (1996) —*—Model I (2002)

—D— Model II (1996) —+—Model II (2002)

Technical Efficiency Profitability Services (Model I) (Model II)

Table 2: Technical Efficiency of RRBs by Regions

Table 4: Technical Efficiency of RRBsby Banking Density of Region

Technical Efficiency

Bank Grouping based on No of Branches —+—Profit (1996) —

—Profit (2002) —,— Service (1996) —*—Service (2002)

Comparison of TFP Growth in RRBs and PSBs

Average TFP growth per annum for RRBs is 1.21 in profitability (model I) and 1.14 in service provision (model II) and for PSBs the same figures are 1.03 and 1.22 respectively (Table 6). TFP growth of RRBs in profitability was higher than in service provision, while for PSBs TFP in service provision was higher than that in profitability. These figures indicate that productivity growth measured in terms of profitability have increased significantly for RRBs, compared even to their parent PSBs in the study period (descriptive statistics of productivity growth have been given in Appendix 1). This shows that in the liberalisation period the emphasis of RRBs shifted to profitability from pure service orientation, while the hitherto emphasis on profitability of PSBs changed to service provision in rural areas. TFP growth was higher for RRBs and PSBs in developed regions than in less developed regions even from a higher base as reported in Table 1. The decomposition of TFP growth into technical change and technical efficiency change indicates that for both RRBs and PSBs contribution of technical efficiency change (catching up) is higher than technical change (technical progress). Further, the contribution of pure efficiency change is higher than scale efficiency change in technical efficiency change. Technical change (technical progress) is significantly higher for RRBs (1.03)

compared to PSBs (0.33), especially in service provision irre-Figure 1 depicts the relation between TFP growth of RRBs spective of development of region of operation (see Table 5). and PSBs derived from both model I and model II. Only the TFPs

RRBs in north and central India have high TFP growth, while growth derived from model I and model II for RRBs aresignificant RRBs located in the south and north-eastern region exhibit low positive influences on each other. The efficiency of the parent TFP growth. These figures indicate that RRBs located in backward PSB’s TFP growth does not have any significant influence on regions in terms of literacy and banking culture are picking up the TFP growth of RRBs in either in the profitability or service their productivity levels, while banks located in educationally well provision approach (top 20 RRBs in terms of TFP growth have developed regions are facing slow growth in TFP, which indicates been given in Appendix 2). convergence of efficiency in RRBs as well as PSBs across geographical regions. This is also indicated in the low level of technical Table 6: TFP Growth of RRBs by Geographical

Location, 1996-2002

change (less than one) and high level of technical efficiency change (catching up) in north-eastern and southern banks (see Table 6). Efficiency indicator North North-east East Central West South Total Banks belonging to the middle and lower quartile according

Total factor productivity growthto size of assets showed significantly high TFP growth than top RRBs-M1 1.28 1.05 1.24 1.28 1.17 1.07 1.21 and bottom quartile banks, however, these banks exhibited a low RRBs-M2 1.18 1.14 1.13 1.20 1.10 1.03 1.14

PSBs-M1 1.01 1.07 1.05 1.01 0.99 1.06 1.03

level of technical efficiency in 1996 as well as in 2002 (Table 7).

PSBs-M2 1.71 1.03 1.18 1.29 0.97 1.08 1.22This indicates that even though middle size banks showed signi-Technical change

ficant TFP growth during the study period, they have not reached RRBs-M1 1.04 1.01 1.01 1.06 1.02 1.03 1.03 RRBs-M2 1.10 0.89 1.02 1.08 1.01 0.98 1.03

the technical efficiency level of the top quartile banks. The same

PSBs-M1 1.00 0.99 1.00 0.99 1.01 1.02 1.00is true for bank groups based on the number of bank branches, PSBs-M2 0.34 0.31 0.31 0.34 0.33 0.34 0.33

but due to the paucity of space the tables are not given here. Table 8 Technical efficiency change RRBs-M1 1.23 1.04 1.23 1.21 1.14 1.03 1.17

depicts relation between TFP growth of RRBs and banking density

RRBs-M2 1.07 1.28 1.11 1.12 1.10 1.05 1.10

of the region of operation. These figures clearly indicate that banks

PSBs-M1 1.01 1.07 1.05 1.02 0.98 1.03 1.03 operating in low banking density areas showed significantly PSBs-M2 5.06 3.30 3.79 3.85 2.96 3.13 3.71 higher TFP growth than banks operating in higher banking density Pure efficiency change

RRBs-M1 1.21 1.00 1.24 1.18 1.13 1.02 1.15

regions, even though these banks showed a higher level of technical

RRBs-M2 1.05 1.15 1.05 1.06 1.07 1.03 1.06efficiency in the base year of the study period (see Table 4). These PSBs-M1 1.05 1.10 1.08 1.04 1.00 1.04 1.05

figures indicate that the location of operation of RRBs plays an PSBs-M2 2.49 1.73 1.86 1.70 1.78 1.81 1.86 Scale change

important role in productivity level as well as growth in the study

RRBs-M1 1.01 1.04 0.99 1.02 1.01 1.01 1.01period. That is, banks operating in less dense populated areas are RRBs-M2 1.03 1.11 1.06 1.05 1.02 1.02 1.04

functioning at a higher level of efficiency and exhibited high TFP PSBs-M1 0.96 0.98 0.97 0.98 0.98 1.00 0.98 PSBs-M2 2.03 1.91 2.03 2.27 1.66 1.73 2.00

growth in the study period. This clearly reveals the justification for expanding RRBs (or similar regional banks) in low banking Notes: M1: model I (profit approach); M2: model II (service approach) density regions, not only for social and equity goals but also to RRBs: regional rural banks; PSBs: public sector banks. increase the productivity and profitability of regional banks.

Table 7: TFP Growth of RRBs by Bank Size Groups,1996-2002

Table 5: TFP Growth Per Annum of RRBs by Development of Region, 1996-2002

Total Bank Assets (RRBs) Indicator Bottom Lower Middle Top Middle Top Total Developed Medium Less Total

Quartile Quartile Quartile Quartile Total factor productivity growth

Total factor productivity growthRRBs-M1 1.22 1.22 1.10 1.21

RRBs-M1 1.22 1.20 1.29 1.13 1.21

RRBs-M2 1.17 1.11 1.10 1.14

RRBs-M2 1.13 1.14 1.16 1.12 1.14

PSBs-M1 1.02 1.03 1.05 1.03

PSBs-M1 1.04 1.02 1.02 1.04 1.03

PSBs-M2 1.32 1.16 1.07 1.22

PSBs-M2 1.13 1.35 1.19 1.22 1.22

Technical change Technical changeRRBs-M1 1.07 1.01 1.01 1.03

RRBs-M1 0.99 0.99 1.06 1.09 1.03

RRBs-M2 1.06 1.03 0.94 1.03

RRBs-M2 0.99 1.02 1.04 1.08 1.03

PSBs-M1 1.01 0.99 0.99 1.00

PSBs-M1 1.00 1.00 0.99 1.00 1.00

PSBs-M2 0.34 0.32 0.33 0.33

PSBs-M2 0.33 0.34 0.33 0.32 0.33

Technical efficiency change Technical efficiency changeRRBs-M1 1.14 1.21 1.09 1.17

RRBs-M1 1.22 1.21 1.21 1.04 1.17

RRBs-M2 1.10 1.08 1.18 1.10

RRBs-M2 1.14 1.12 1.12 1.03 1.10

PSBs-M1 1.01 1.04 1.06 1.03

PSBs-M1 1.03 1.01 1.03 1.03 1.03 PSBs-M2 3.89 3.65 3.23 3.71

PSBs-M2 3.47 3.97 3.59 3.81 3.71 Pure efficiency change

Pure efficiency changeRRBs-M1 1.12 1.20 1.08 1.15

RRBs-M1 1.19 1.19 1.21 1.04 1.15 RRBs-M2 1.07 1.04 1.09 1.06

RRBs-M2 1.11 1.07 1.06 0.99 1.06 PSBs-M1 1.03 1.06 1.08 1.05

PSBs-M1 1.05 1.04 1.04 1.06 1.05 PSBs-M2 1.99 1.80 1.57 1.86

PSBs-M2 1.73 1.95 1.76 2.00 1.86 Scale efficiency change Scale changeRRBs-M1 1.02 1.01 1.01 1.01 RRBs-M1 1.03 1.02 1.00 1.01 1.01 RRBs-M2 1.03 1.05 1.08 1.04 RRBs-M2 1.03 1.04 1.06 1.04 1.04 PSBs-M1 0.98 0.98 0.99 0.98 PSBs-M1 0.98 0.98 0.99 0.97 0.98 PSBs-M2 1.95 2.03 2.06 2.00 PSBs-M2 2.00 2.04 2.04 1.91 2.00

Notes: M1: model I (profit approach); M2: model II (service approach) Notes: M1: model I (profit approach); M2: model II (service approach) RRBs: regional rural banks; PSBs: public sector banks. RRBs: regional rural banks; PSBs: public sector banks.

RRBs-1 RRBs-2 PSBs-1 PSBs-2 RRBs-1RRBs-2

RRBs-1=.257+ .851*RRBs-2; R^2=.415 RRBs-2=.551+ .487*RRBs-1; R^2= .415 RRBs-1=1.791- .533*PSBs-1; R^2=.014 RRBs-2=1.862- .685*PSBs-1; R^2= .04 RRBs-1=1.165+ .053*PSBs-2; R^2=.045 RRBs-2= 1.127+ .02*PSBs-2; R^2= .011 RRBs-1and PSBs-1 are based on profitability (Model I) RRBs-2 and PSBs-2 are based on service (Model II)

Figure 3: Scatter Diagram of TFP Growth of RRBs by TFPThe above finding clearly reveals that development of the

Growth of PSBs, 1996-2002

region, geographical location, banking density of the region, bank size indicators such as total assets under operation and number of branches played a greater role in determining the efficiency and TFP growth of RRBs than did the efficiency of the parent PSBs.

Tables 9 and 10 reveal that there is an ongoing process of convergence of efficiency of RRBs in both profitability as well as service provisioning, as reflected in the high growth of TFP in banks with less base year technical efficiency and low growth of TFP in bank with high base year technical efficiency during the DAP and liberalisation periods. Banks that have least efficiency showed the highest TFP growth and banks that have the highest efficiency in initial years exhibited the least TFP growth during 1996 to 2002.

The technical efficiency of rural banks is higher in service provision than in the parent public sector banks. The efficiency of rural banks is higher in economically and socially developed regions as well as in low banking density regions. Rural banks

Table 8: TFP Growth of RRBs by Banking Density of Region,

showed significant economies of scale in terms of assets and number

1996-2002

of branches under each bank. Total factor productivity growth

Bank Groups Based on Bank Density

of rural banks is higher in profitability than service provision

(Population Per Branch) Parameter Bottom Lower Middle Top Middle Top Total Quartile Quartile Quartile Quartile Table 10: Initial Level of Technical Efficiency by TFP Growth(Service)

Total factor productivity growth TFP (Service) Growth of RRBs between 1996 and 2002

RRBs-M1 1.20 1.15 1.20 1.28 1.21 Technical Efficiency Lower Upper

RRBs-M2 1.11 1.10 1.11 1.20 1.14

1996 (Profit) Least Middle Middle Upper TotalPSBs-M1 1.02 1.03 1.05 1.02 1.03 PSBs-M2 1.33 1.09 1.02 1.40 1.22

Least 7 10 13 18 48 Technical change Lower middle 9 12 15 12 48 RRBs-M1 1.06 1.03 1.02 1.03 1.03 Upper middle 14 10 14 10 48 RRBs-M2 1.04 1.01 1.03 1.04 1.03 Upper 18 16 6 8 48 PSBs-M1 1.00 1.01 1.00 1.00 1.00

Total 48 48 48 48 192

PSBs-M2 0.33 0.34 0.31 0.32 0.33

Technical efficiency change Appendix 1: Descriptive Statistics of TFP GrowthRRBs-M1 1.14 1.12 1.18 1.23 1.17 and Its Components RRBs-M2 1.08 1.09 1.08 1.15 1.10

Bank Group Minimum Maximum Mean Std Deviation PSBs-M1 1.02 1.02 1.05 1.03 1.03 PSBs-M2 4.00 3.17 3.30 4.34 3.71

TFP growthPure efficiency change RRBs (M1) 0.556 2.767 1.242 0.297 RRBs-M1 1.12 1.12 1.18 1.20 1.15 RRBs (M2) 0.646 2.197 1.156 0.225 RRBs-M2 1.04 1.07 1.05 1.07 1.06 PSBs (M1) 0.823 1.266 1.031 0.065 PSBs-M1 1.03 1.03 1.08 1.06 1.05 PSBs (M2) 0.456 5.003 1.449 1.190

PSBs-M2 1.84 1.77 1.66 2.07 1.86

Technical change RRBs (M1) 0.652 1.351 1.043 0.138

Scale efficiency change RRBs (M2) 0.663 1.410 1.038 0.129

RRBs-M1 1.01 1.00 1.00 1.03 1.01

PSBs (M1) 0.938 1.120 1.003 0.038

RRBs-M2 1.04 1.02 1.03 1.08 1.04

PSBs (M2) 0.274 0.542 0.333 0.053 PSBs-M1 0.99 0.99 0.98 0.97 0.98

Technical efficiency changePSBs-M2 2.17 1.79 1.98 2.10 2.00 RRBs (M1) 0.499 2.517 1.198 0.283 RRBs (M2) 0.687 2.282 1.117 0.193

Notes: M1: model I (profit approach); M2: model II (service approach) PSBs (M1) 0.808 1.130 1.029 0.052

RRBs: regional rural banks; PSBs: public sector banks.

PSBs (M2) 0.841 17.132 4.558 4.203 Pure efficiency changeTable 9: Initial Level of Technical Efficiency by TFP Growth (Profit) RRBs (M1) 0.498 2.567 1.184 0.286 RRBs (M2) 0.679 1.975 1.069 0.162

TFP (Profit) Growth of RRBs between 1996 and 2002 PSBs (M1) 0.808 1.187 1.051 0.066 Technical Efficiency Lower Upper PSBs (M2) 0.854 6.519 2.206 1.565 1996 (Profit) Least Middle Middle Upper Total Scale efficiency change

RRBs (M1) 0.818 1.357 1.015 0.071 Least 3 6 11 28 48 RRBs (M2) 0.866 2.282 1.047 0.111 Lower middle 8 11 18 11 48 PSBs (M1) 0.888 1.030 0.981 0.043 Upper middle 11 17 13 7 48 PSBs (M2) 0.984 3.256 2.125 0.712 Upper 26 14 6 248 Total 48 48 48 48 192

Notes: M1: model I (profit approach); M2: model II (service approach) RRBs: regional rural banks; PSBs: public sector banks.

during the liberalisation period. Banks located in economically developed as well as low banking density regions exhibited significantly higher productivity growth. Overall there is a convergence of efficiency of rural banks during the study period. There is no influence of parent public sector banks on the efficiency and productivity growth of rural banks. The decomposition of productivity into technical progress and technical efficiency

Appendix 2: Top 20 RRBs in Terms of TFP Growth in Profitability and Service Provision

RRB Name TFP (P) TFP (S) Parent State Growth Growth Bank

Top 20 RRBs TFP growth (profitability)

Patliputra Gramin Bank 2.77 1.68 PNB Bihar Saran Kshetriya Gramin Bank 2.07 1.52 CBI Bihar Alwar Bharatpur Gramin Bank 2.05 1.32 PNB Rajasthan Shivpuri Guna Kshetriya Gramin Bank 1.90 1.33 SBI MP Parvatiya Gramin Bank 1.89 1.97 SBI HP Samastipur Kshetriya Gramin Bank 1.87 1.11 SBI Bihar Raigarh Kshetriya Gramin Bank 1.80 1.44 SBI Chhattisgarh(MP) Baitarani Gramin Bank 1.80 1.11 BOI Orissa Sri Ganganagar Kshetriya Gramin Bank 1.78 1.31 SBBJ Rajasthan Dhenkanal Gramin Bank 1.76 1.61 IOB Orissa Kutch Grameena Bank 1.75 2.20 Dena Gujarat Bareilly Kshetriya Gramin Bank 1.75 1.30 BOB UP Bastar Kshetriya Gramin Bank 1.74 0.85 SBI Chhattisgarh(MP) Allahabad Kshetriya Gramin Bank 1.73 1.38 BOB UP Subansiri Gaonlia Gramin Bank 1.69 1.09 UBI Assam

(United) Dewas Shajapur Kshetriya Gramin Bank1.63 1.22 BOI MP Pratapgarh Kshetriya Gramin Bank 1.63 1.47 BOB UP Damoh Panna Sagar Kshetriya

Gramin Bank 1.62 1.50 SBI MP Kapurthala Firozpur Kshetriya

Gramin Bank 1.60 1.18 PNB Punjab Rushikulya Gramin Bank 1.60 1.39 Andhra Orissa Top 20 RRBs TFP growth (service) Kutch Grameena Bank 1.75 2.20 Dena Gujarat Bundelkhand Kshetriya Gramin Bank 1.52 2.06 SBI MP Parvatiya Gramin Bank 1.89 1.97 SBI HP Golconda Gramin Bank 1.32 1.93 SBH AP Patliputra Gramin Bank 2.77 1.68 PNB Bihar Mizoram Rural Bank 1.15 1.67 SBI Mizoram Dhenkanal Gramin Bank 1.76 1.61 IOB Orissa Basti Gramin Bank 1.48 1.60 SBI UP Gorakhpur Kshetriya Gramin Bank 1.29 1.53 SBI UP Saran Kshetriya Gramin Bank 2.07 1.52 CBI Bihar Nagaland Gramin Bank 1.39 1.51 SBI Nagaland Damoh Panna Sagar Kshetriya

Gramin Bank 1.62 1.50 SBI MP Pratapgarh Kshetriya Gramin Bank 1.63 1.47 BOB UP Shahajahanpur Kshetriya Gramin bank 1.48 1.46 BOB UP Etawah Kshetriya Gramin Bank 1.32 1.44 CBI UP Raigarh Kshetriya Gramin Bank 1.80 1.44 SBI Chhattisgarh(MP) Pithoragarh Kshetriya Gramin Bank 1.43 1.44 SBI Uttaranchal(UP) Farrukhabad Gramin Bank 1.53 1.42 BOI UP Rushikulya Gramin Bank 1.60 1.39 Andhra Orissa Allahabad Kshetriya Gramin Bank 1.73 1.38 BOB UP

Appendix 3: Descriptive Statistics of Inputs and Outputsin 2002 and 1996

(In Rs lakh at 1996 prices)

Mean	Minimum	Maximum	Std Deviation
Net loan 6088 (3444) 174 (39) Liquid assets 8381 (3812) 461 (302) Deposits 15452 (7227) 450 (245) Total income 1929 (771) 67 (43) Interest expenses 1155 (543) 30 (25) Operating expenses 506 (371) 36 (28) Profit/loss 212 (-297) -719 (-2424)	42391 (24827) 6044 (3695) 64988 (40501) 7382 (4989) 62561 (35317) 11125 (5961) 8620 (5267) 1492 (792) 4366 (2951) 825 (460) 2438 (1543) 402 (293) 1977 (1038) 368 (458)

Note: Figures in parenthesis are for the year 1996.

growth indicated that technical efficiency change contributed more to productivity growth than technical progress in both rural banks and parent PSBs, however, comparatively contribution of technical progress is higher for rural banks than parent PSBs. There is a justification for opening new banks in low banking density regions as efficiency and productivity growth of rural banks in these areas is high. There is also a case for mergers and enlargement of the asset base as well as the number of branches under each rural bank as there exist economies of scale.

rr;

Email: aareddy12@email.com

References

Arcelus, F J, P Arozena (1999): ‘Measuring Sectoral Productivity across Time and across Countries’, European J Operational Res, 119(2), pp 254-66.

Banker, R D, A Charnes, W W Cooper (1984): ‘Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis’, Management Sci, 30(9), pp 1078-92.

Bergendhal, G (1998): ‘DEA and Benchmarks – An Application to Nordic Banks’, Annals of Operations research, Vol 82, pp 233-49.

Berger, A N, D B Humpherey (1992): ‘Measurement and Efficiency Issues in Commercial Banking’ in Z Griliches (ed), Output Measurement in the Service Sector, The University of Chicago Press, Chicago, pp 245-300.

Bhattacharya, Arunava, C A K Lovell, Pakaj Sahay (1997): ‘The Impact of Liberalisation on the Productive Efficiency of Indian Commercial Banks’, European Journal of Operations Research 98, pp 332-45.

Charnes, A, W W Cooper, E Rhodes (1978): ‘Measuring the Efficiency of Decision-Making Units’, European J Operational Res, 2(6), pp 429-44.

Coelli, T, D S P Rao, G E Battese (1998): An Introduction to Efficiency and Productivity Analysis, Kluwer Academic Publishers, Norwell, MA. Das, Abhiman (1997): ‘Technical, Allocative and Scale Efficiency of Public

Sector Banks in India’, RBI Ocasional Papers, 18, June-September.

David, A G, V Manole (2002): ‘Determinants of Commercial Bank Performance in Transition: An Application of Data Envelopment Analysis’, International Monetary Fund, Working Paper No 146, WP/02/146, Washington.

Färe, R, S Grossskopf, M Norris, Z Zhang (1994): ‘Productivity Growth, Technical Progress, and Efficiency Change in Industrialised Countries’, American Economic Rev, 84(1), pp 66-83.

Farrell, M J (1957): ‘The Measurement of Productive Efficiency’, J Royal Statistical Society, Series A, 120, pp 253-90. Ghosh (1992): Reducing Rural Poverty and Accelerating India’s Economic Growth, Salt Lake, Calcutta, India. Grifell-Tatje, E, C A K Lovell (1999): ‘A Generalised Malmquist Productivity Index’, Top 7:1, pp 81-101. Hancock, D (1986): ‘A Model of the Financial Firm with Imperfect Asset and Deposit Elasticities’, Journal of Banking and Finance, 10, pp 37-54.

Leeladhar (2005): ‘Contemporary and Future Issues in Indian Banking’, speech delivered to Kanara Chamber of Commerce and Industry, Mangalore, March 11.

Malmquist, S (1953): ‘Index Numbers and Indifference Surfaces’, Trabajos de Estatistica, 4, pp 209-42.

Mester, L (1987): ‘Efficient Production of Financial Services: Scale and Scope Economics’, Business Review of Federal Reserve Bank of Philadelphia, January/February, pp 15-25.

Mohan, R T T, S C Ray (2002): ‘Productivity and Efficiency at Public and Private Banks in India’, Indian Institute of Management, Working Paper Series 11, Ahmedabad, India.

Mohan, R T T (2005): ‘Bank Consolidation Issues and Evidence’, Economic and Political Weekly, Vol 40, March 19, pp 1151-59. Shao, B B M, W S Shu (2002): ‘Productivity Breakdown of the Information Technology Industries across Countries’, Arizona State University, memo. Reddy A (2004): ‘Banking Sector Liberalisation and Efficiency of Indian Banks’, ICFAI Journal of Bank Management, May, pp 115-38.

Reddy, Y V (2005): ‘Banking Sector Reforms in India: An Overview’, Address at the Institute of Bankers of Pakistan, Karachi, May 18. Tornquist, L (1936): ‘The Bank of Finlands Consumption Price Index’, Bank

of Finland Monthly Bulletin, 10, pp 1-8.

Wheelock, D C, P W Wilson (1995): ‘Evaluating the Efficiency of Commercial Banks: Does our View of What Banks Do Matter?’ Federal Reserve Bank of St Louis Review, July/August.