Efficiency in the Chinese Banking Industry

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Efficiency in the Chinese Banking Industry

Xu Yu (S1553046)

Supervisor: Dr.

Michael Koetter

PhD Student A.J. Meesters

University of Groningen

The Faculty of Economics and Business

Thesis for master IE&B

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ABSTRACT

In this paper I use the unbalanced panel data which include 36 different sized Chinese commercial banks to investigate the relationship between the bank size and the profit (cost) efficiency in the period 1999-2003 using Stochastic Frontier Analysis (SFA).For this purpose, I adopt the two-step model that is the stochastic profit (cost) frontier model and the profit (cost) inefficiency effect model. For the first step I explain the stochastic cost and profit frontier models in order to predict the value of the inefficiency on the profit and the cost. As for the second step the predicted inefficiency effects are assumed to be a function of the total asset to estimate the relationship between the bank size and the profit (cost) efficiency. Results indicate that the profit (cost) inefficiency effect is significant in the stochastic frontier profit (cost) model; the total assets significantly influence the mean of the profit (cost) inefficiency distribution, which implies that the bank size has a negative effect on the profit inefficiency and a positive effect on the cost inefficiency. In other words the large Chinese commercial banks are more efficient in profit than the small ones and the small Chinese commercial banks are more efficient in cost than the large ones.

KEYWORDS: Chinese Commercial Bank, SFA, Profit Efficiency, Cost Efficiency Bank Size

Acknowledgements

I would like to highly appreciate for Michael Koetter and A.J. Meesters’s unlimited valuable

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Since 1978 China’s economy began to transform from a centralized planning economy into at market-based economy. This transition process also accompanied the reconstruction of the bank system in order to improve the overall efficiency of the Chinese banking system. In the last more than two decades the Chinese banking system became more diversified. Before 1985 there were actually only four large state-owned banks in China which were the Commercial Bank of China (ICBC), the Construction Bank of China (CBC), the Bank of China (BOC) and the Agriculture Bank of China (ABC). After 1985 many different sized commercial banks were set up in China. For example, Bank of Communications CO. LTD., China Everbright Bank CO LTD., Hua Xia Bank etc. were established as the nationwide commercial banks. Moreover, many regional commercial banks were set up in Chinese different cities such as Shenzhen Development Bank CO., LTD 、 Guangdong Development Bank, and Shanghai Pudong Development Bank etc. Additionally a great deal of city credit unions were merged by the city cooperation banks, whose name was officially changed into the city commercial banks in 1998. Till 2005 the Chinese banking system is mainly composed of the large sized national commercial banks, the medium sized nationwide commercial banks and the small sized regional commercial banks as well as the city commercial banks. While various sized banking organizations coexist in the Chinese banking system they take on different efficiency performance.

In this paper the question to be answered is whether the bank size significantly influences the bank profit (cost) efficiency effect among 36 Chinese commercial banks over the period of 1999-2003 using stochastic frontier approach (SFA), which compares how close the individual bank is away from a best-practice efficient frontier. For this purpose I use a two-step model to test the relationship between the bank size and the profit (cost) efficiency, which include a stochastic profit (cost) frontier model and a profit (cost) inefficiency effect model. Firstly I adopt the intermediation approach1 to model the stochastic cost and profit frontier functions to obtain the profit (cost) inefficiency score for those different sized banks in China, in which

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some bank-specific variables are involved such as the financial capital, the physical capital and the labor cost as input as well as the customer loans, investment and the interbank loans as outputs. Secondly on the basis of getting the profit (cost) inefficiency score I will establish a profit (cost) inefficiency effect model to investigate whether the profit (cost) efficiency effect is significantly influenced by the bank size. Results therefore indicate that the profit (cost) inefficiency effect is significant in the stochastic frontier profit (cost) model; the relationship between the bank size and the profit (cost) inefficiency is significant, which implies that the bank size has a negative effect on the profit inefficiency and a positive effect on the cost inefficiency. In other words the large Chinese commercial banks are significantly more efficient on profit than the small ones and the small Chinese commercial banks are significantly more efficient on cost than the large ones.

As far as I know, only few studies assess the efficiency of Chinese commercial banks related to the bank size using SFA. Fu and Heffernan (2005) analyzed the cost efficiency in China’s banking sector over the period 1985-2002 using SFA. However as for the profit efficiency of Chinese banks, although Zhang, Gu etc. (2005) apply SFA to test profit efficiency of 13 Chinese commercial banks from 2000 to 20002, they focus on the difference of profit efficiency for Chinese banks with different ownership. Consequently the relationship between the bank size and the profit efficiency among these Chinese banks has not been adequately investigated. Hence this paper is valuable for supplementing the research on the relationship between the bank size and the efficiency using SFA in the Chinese banking industry.

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Ⅱ. CHINESE BANKING SYSTEM

In this section I briefly review the institutional history, regulation, and economical

environment of the Chinese banking system so as to understand the historical background of the establishment of the Chinese commercial banks.

The 1978-1984 period

From 19492 to 1978, the People’s Bank of China (PBOC) acted as both a central and commercial bank in the Chinese banking industry. Following overall economic reforms since 1978 the Chinese banking system has undergone significant changes. At the end of 1979, PBOC became a separate institution and only played a role as the central bank. During the period of 1978-1984 the primary purpose of the banking reforms in China was to adjust the existing structure and financial operations of China’s banking system. It was characterized by the separation of the key role of the central bank and the commercial bank. Four large state-owned commercial banks were set up respectively to conduct commercial banking businesses instead of PBOC. The Construction Bank of China (CBC) engaged in bank services related to urban large construction projects; the Bank of China (BOC) specialized in the international business related to the foreign trade and overseas investment; the Agriculture Bank of China (ABC) handled all rural finance in those rural areas; the Industrial and Commercial Bank of China (ICBC) dealt with the rest of the bank businesses of the PBOC. Hence a so-called two-tier banking system was established in China. During this period on the one hand PBOC did not necessarily play the primary role of a commercial bank anymore. On the other hand the detached bank businesses3 greatly affected the efficiency performance of the four large state-owned commercial banks in the following year. Furthermore the intervention of the central government also greatly influenced the management of the four large state-owned banks so that they usually can not actively pursue the profit maximization but implement the orders of the central government, which lowered the efficiency of the four

2

The people’s republic of china was founded in 1949.

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large state-owned commercial banks. The 1985-1992 period

This period was characterized by the deregulation process and the diversity of the bank institutions. The four large state-owned commercial banks changed their business from the detached bank businesses to the diversified ones. In 1985, the four large state-owned commercial banks were allowed to provide the loan and deposit services in all sectors. Meanwhile many different sized commercial banks owned by shareholders of state-owner enterprises and regional organizations were established so as to stimulate market competition and facilitate the development of an efficient banking system. Among them some are regional commercial banks owned by local governments, local enterprises, and households such as Shenzhen Development bank, Guangdong Development bank, the Citic Industrial Bank, the Bank of Communications, China Merchants Bank, China Everbright Bank and Hua Xia Bank; some are rural credit cooperatives under the supervision of ABC in rural areas; others are urban credit cooperatives in cities.

1993 to present period

Numerous banking reforms have already been progressively implemented since 1993. The main aim of these reforms was to create a sustainable competitive and sound commercial banking system for the four state-owned banks and other forms of commercial banks can coexist. The major banking reforms were the establishment of three policy banks4 in 1994 and the city commercial banks in 1995. Consequently a so-called open and competitive three-tier banking system was formed, namely central bank, commercial banks and policy banks. On the one hand, the three policy banks mainly afforded the policy loans from the four state-owned banks. In this case the four large state-owned banks haven’t executed the policy loans from central government but can totally act as the commercial banks. Additionally the city commercial banks have injected vigor into the Chinese banking system. According to the statistic data issued by the PBOC in 2000, the expanding speed of the city commercial bank was 34.7%, which was much higher than that of the four large state-owned banks (12.4%).

4

Three policy banks are the development bank of china , the import and export bank of china and agricultural development bank of china

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They merged former local urban credit cooperatives in1995.All the city commercial banks used the same shareholding ownership structure owed by regional enterprises and were restricted geographically within their own localities. The efficiency of medium and small sized commercial banks also can improve during this period largely due to the closed relationship with their shareholders as well as better financial and policy support from the regional governments and enterprises.

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Commission was established. Its main function is to supervise and authorize all commercial banks, hereby ensuring that Chinese commercial banks can develop and compete in an orderly and legal banking system.

Nowadays for Chinese banking industry there is a diversified, competitive and multi-tie system including the PBOC as the central bank, the four large state-owned banks as backbone, the joint-stock commercial banks as growth engines and the local commercial banks as

complementarities.

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Ⅲ. THEORETICAL BACKGROUND

Ⅲ.1 profit efficiency and cost efficiency

There are two important concepts about the bank efficiency related to my study, which are the cost efficiency and the alternative profit efficiency. The cost efficiency measures how close a bank’s actual cost is to the minimum cost at which it produces the same volume of outputs under the same conditions. Its economic objective is to minimize cost incurred. It is assumed that the input markets are perfectly competitive and banks are price takers. Thus the input price W is exogenous when a bank demands input quantity X. In transforming inputs into outputs, equity, Z, is considered as an alternative to finance outputs (Hughes and Mester 1993).In this case the transformation function of a bank is expressed by T(X, Y, and Z) as the restriction for the cost minimization problem during transforming input into output production, in which Y is explained as the output quantity. The total cost of a bank is depicted by TC(Y, W).

The cost minimization problem is written as

TC(Y, W) =Min∑ (W*X) s.t.T(X, Y, Z) =0 (1) x

The Lagrangian function is expressed as

LC=∑ (W*X)-λT (·) (2)

I take first derivatives with respect to input x and the multiplier λ. After setting all of these equal to zero and solving for X, the optimal input demand function is obtained as Xi*=Xi*(Y, W, Z) (3)

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TC*= Min∑ (W*X(Y, W, Z)) =TC*(Y, W, Z) (4)

On the basis of the functional form of the minimum cost, the cost efficiency (CE) is estimated as the ratio between the minimum cost and actual cost incurred. Cost efficiency ranges from 1 to infinity and equals one for the best-practice efficient bank. It implies that a bank could save in cost of (1-CE) percent given the same vector of outputs.

Secondly in recent years, some economists introduce a new concept to measure the bank profit efficiency, namely the alternative profit efficiency5 in their literatures. Berger and Mester (1997) explain it when it only takes the output level into account instead of the output price in order to produce the maximal profits for a bank. Its advantages are that it not only consider the management factor in pricing decisions but also some non-price factors, such as quality of banking services, portfolio mix. I adopt an alternative profit function developed by Humphrey and Pulley (1997) to estimate the alternative profit efficiency. It is assumed that due to the imperfect competition of the output markets banks take as given the output quantity Y and the input price W to maximize the profits by adjusting the output price P and the input quantity X. Therefore there is a pricing power on the output side. Banks maximize the profit restricted by a technology constraint and pricing opportunity set.

Max ∏=P’Y-W’X s.t.T(X, Y) =0 and H (P, Y, W, Z) =0 (5) p,x

Where ∏ present the profit, T(·) presents the technology constraint and H(·) present the pricing opportunity set.

The corresponding Lagrangian function can be expressed as

L∏=P’Y-W’X –λT(.) –θH(·) (6)

After solving simultaneously for P and X the optimal output prices and input quantities can be written as

P*=P*(Y, W, Z) (7) X*=X*(Y, W, Z) (8)

Substitute (7) and (8) into the profit function and yields the maximum profit function ∏=P*(Y, W, Z)’Y-W’ X*(Y, W, Z) = ∏*(Y, W, Z) (9)

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The maximum profit is subject to the given the input price, the output quantity and equity. The alternative profit efficiency (APE) is the ratio of the actual profits incurred to the maximum profit. This measure takes on a value between 0 and 1 (fully efficient). For example a APEj equal to 0.85 means that a bank is losing 15% profit respect to the best practice profit bank6.

Ⅲ.2 Literature about Chinese bank efficiency

In Chinese banking context there are insufficient studies on the efficiency of the different sized banks. The main reason why the literature is so lacking is data problems. The Chinese banking industry is very opaque in terms of accessibility of their financial information. They often are not required by the regulators to issue their financial statements to the public. Furthermore the applied accounting system is different across these banks and years, which make it very difficult for outsiders to analyze this industry (Berger, Hasan &Zhou, 2005).

Among the limited research about different sized Chinese bank efficiencyBerger, Hasan and Zhou (2005) estimate the cost efficiency of 38 Chinese banks, including the large four state-owned banks, 11 national shareholding commercial banks, 16 small city commercial banks, 6 joint venture banks and 2 solely foreign-owned banks from 1994 -2003 using SFA. They suggest that four large banks and the small joint-equity banks are more efficient in cost than the medium-sized joint-equity banks. For four large state-owned banks this may be due to accounting practices or subsidies on the cost side for state-owned institutions. Additionally Chen, Skully and Brown(2005) examines the cost efficiency of 43 Chinese banks over the period 1993 to 2000 using the non-parametric DEA cost approach. The goal of this analysis is to identify the change in Chinese banks’ efficiency following the program of deregulation initiated by the government in 1995. Results show that the large state-owned banks and smaller banks are more efficient than medium sized Chinese banks.

On the other hand, some studies found the different conclusion. For example Berger, Hasan and Zhou (2006) depict that the profit efficiencies of four large state-owned banks are relatively low due to too much poor loan for these banks. According to the annual report of PBOC in 2005 the ratio of bad loan of state-owned banks was 9.5 percent and that of

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joint-stock commercial banks stood at 3.1 percent. Additionally Hu, Chen and Su (2006) analyses the efficiency of China’s banks using the data envelopment analysis (DEA) about twelve banks in China during the period of 1996 to 2003. There are twelve banks including the four state-owned specialized banks, three policy-related banks and five nationwide joint-equity commercial banks. Their empirical findings are that small-sized banks have higher cost

efficiencies than large-sized banks. Furthermore Kumbhakar and Wang (2005) find that the Large Four are less efficient than small joint-equity bank in cost using an input distance function approach. Wei and Wang (2000) argue that the profit efficiency of large stated-owed banks is low between large stated-owned banks (62.39%) and newly smaller founded banks (84.59%). The result of Zhao, Zhong, & Jiang (2001) is also consistent with the above findings.

Given the mixed evidences on the efficiency of different sized banks I find that there is no research on the direct relationship between the bank efficiency and the bank size. Hence in my paper I will set up a two-step model to test the relationship between them. And I attempt to answer this question: how does the size determine the profit (cost) efficiency for these different sized Chinese commercial banks?

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Ⅳ. METHDOLOGY

Many approaches have already been applied to measure the bank efficiency. There are two main approaches to measure the efficiency of individual banks, which are the stochastic frontier approach (SFA) and Data envelopment analysis (DEA).I compare the difference between them as follows:

DEA SFA

Type non-parametric

methodology

Parametric methodology

Application Method linear programming

techniques

maximum-likelihood estimates

Assumption all deviation from the

frontier are due to

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inefficiency asymmetric distribution) and random error (a symmetric distribution )

Advantage No restrictions on the

functional form of the production relationships

between inputs and

outputs, and does not require imposition of any distributional assumption on inefficiency term.

*a number of

well-developed statistical tests to investigate the validity of the model specification – tests of significance for the inclusion or exclusion of factors, or for the

functional form.

*A variable which is not relevant is included, it will have a low, or even zero, weighting in the

calculation of the efficiency scores,

*allows the decomposition of deviations from

efficient levels between ”noise“ (or stochastic shocks) and pure inefficiency

Disadvantage It can be extremely

sensitive to variable selection and data errors

Production function estimation, which relies

heavily on the ex ante specification of the

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In recent year the stochastic frontier approaches (SFA) has become a significant method in measuring the bank efficiency. In my study I adopt SFA to analyze the efficiency of different sized Chinese banks. It was firstly and independently introduced by Aigner, Lovell &Schmidt (1977), Meeusen & van den Broeck (1977) and Battese & Corra (1977). Then SFA had been applied widely to analyze the banking efficiency in many prior literatures such as Aigner et al.(1977), Ferrier &Lovell (1990), Bauer at el. (1993), Kwan &Eisenbeis (1996), Berger & Mester(1997), Kumbhakar & Lovell (2000) and Clark & Siems (2002).

There are two reasons why I use SFA to measure the bank profit (cost) efficiency in my study. This method can provide the firm-specific efficiency estimates and so the different efficiency performance between these individual banks can be compared. Also it decomposes the error terms into white noise and the profit (cost) inefficiency which allows us to distinguish between the inefficiency and other random errors in the estimation of the efficiency

scores(Bauer et al.,1998). As for the application of SFA there are two assumptions. One is the nonnegative inefficiency term with an asymmetric truncated-normal distribution due to heterogeneity across banks (Kumbhakar and Lovell, 2000) and another is the random errors term with a symmetric standard normal distribution due to measurement problems. Based on the above-mentioned assumptions, SFA allows us to estimate how close is between the best efficiency and the actual cost (profit) efficiency for those different sized individual banks.

In this part I set up a two-step model to test the relationship between the bank size and the profit (cost) efficiency using SFA. For the first step I use the stochastic cost and profit frontier models to predict the mean of the inefficiency on profit (cost). And for the second step the predicted inefficiency effects are assumed to be a function of the total assets by regressing the efficiency score on the total assets.

Ⅳ.1 Model specification

The stochastic profit (cost) frontier model and the profit (cost) inefficiency effect model In my study I adopt the alternative profit efficiency7 proposed by Berger &Mester (1997) to

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investigate the profit efficiency of those different sized Chinese commercial banks. I scale the profit before tax and the input price by the price of labor in order to guarantee linear

homogeneity of the profit function (Kuenzle 2005).

I define a stochastic frontier profit model in Cobb-Douglas form following Kumbhakar and Lovell (2000) which is given by

Ln(∏it/ W3it)=β0 +β1ln(Y1it )+ β2ln(Y2it )+ β3ln(Y3it )+ β4ln(W1it/ W3it)+ β5ln(W2it/ W3it )+

β6ln(Zit )+lnV it -lnU it

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∏it represents the profit before tax produced by the ith bank in year t ;

Y1it represents the total customer loans by the ith bank in year t ;

Y2it represents the investment by the ith bank in year t;

Y3it represents the interbank loans by the ith bank in year t;

W1it represents the price of financial capital by the ith bank in year t ;

W2it represents the price of physical capital by the ith bank in year t ;

W3it represents the price of labor by the ith bank in year t ;

Z it represents the equity by the ith bank in year t

βj represents the unknown scalar of parameters to estimate(j=0,1 …6)

V it represents the random error of measurement and other uncontrollable factors affecting the

output and the input variables. It is assumed to identically distributed (i.i.d.) normal random variables with mean zero and constant variance (σv2) and independent of the U it and the

explanatory variable. V it can be either positive or negative. In other words, V it either increase

or decrease the profit level from the efficient frontier.

U it represents the nonnegative profit inefficiency term by the ith bank in year t. It is assumed to

identically distributed (i.i.d.) truncated-normal (at zero) random variables and constant variance (σu2) as well as independent of the V it. U it only decrease profit level.

Secondly I introduce the stochastic cost frontier model in the similar way. The Stochastic Cost Frontier function in Cobb-Douglas form proposed by Battese and Coelli’s (1992, 1995) can be written as follows

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Ln(TC it/ W3it)=β0 +β1ln(Y1it )+ β2ln(Y2it )+ β3ln(Y3it )+ β4ln(W1it/ W3it)+ β5ln(W2it/ W3it)+

β6ln(Zit )+lnV it +lnU it (11)

Where

TC it represents the total cost by the ith bank in year t.

Uit represents the nonnegative cost inefficiency term by the ith bank in year t. It is assumed to

identically distributed (i.i.d.) truncated-normal (at zero) random variables and constant variance (σu2) as well as independent of the V it. It only increases cost level.

V it represents the random error of measurement and other uncontrollable factors affecting the

output and the input variables. It is assumed to identically distributed (i.i.d.) normal random variables with mean zero and constant variance (σv2) and independent of the U it and the

explanatory variable. It either increase or decrease cost level from the efficient frontier, which means that V it either increase or decrease the cost level from the efficient frontier.

In order to keep linear homogeneity in input prices, there is a restriction for the Stochastic Cost Frontier function, which is the sum of the βj parameters (i.e. the coefficients on input prices), must be equal to one.

Finally, following the model of Battese and Coelli(1995) I use the inefficiency effects models to estimate the direct relationship between profit (cost) inefficiency effect and the total assets, which is defined by

uit =δ0 + δ1 ln(total assets) it (12)

Where

uit represents the mean of inefficiency effects Uit. And Uit is assumed to be independently (but

not identically) distributed non-negative random variables. For the i-th bank in the t-th period Uit is truncated at 0 of N (uit, σu)-distribution.

δ: unknown scalar parameters to be estimated

Ⅳ.2 Methodological Analyse

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stochastic profit (cost) frontier function using the maximum-likelihood (ML) method8 in order to analyze how the independent variables influence on the profit before tax, the total cost. On the other hand I adopt the ML method to obtain the value of σ2 and γ so as to measure all deviations deriving from either normal random errors or inefficiency factor. Battese and Corra (1977) proposed a log-likelihood function in terms of two variance parameters,

σ2 =σu2 +σv2 and γ=σu2 /σ2 . The γ presents the share of inefficiency in the overall residual

variance. Its value ranges from zero to one. A value of zero means that the deviations from the frontier are entirely due to random errors; while a value of one means that all deviations are due to inefficiency factor

By calculating the maximum of the log-likelihood function the ML estimates of β, σ2 and γ can be obtained. Computer program FRONTIER Version 4.1 can be used to obtain the ML estimates for the parameters of the stochastic profit (cost) frontier model. For this program there are three-step estimation procedures. The first step involves ordinary least-squares (OLS) estimates of all β-parameters in equation 10 and 11.All β estimators with the exception of the intercept will be unbiased. The second step processes a two-phase grid search of values of γ between zero and one by evaluating the likelihood function. During this course the values of β0

and σ2are adjusted in terms of the COLS formula9 and the rest of the β- parameter is estimated by the OLS. And the third step conducts final maximum-likelihood (ML) estimates by selecting suitable starting values from the second step in the iterative procedure using the Davidson-Fletcher-Powell (DFP) Quasi-newton method. Finally approximate standard errors of the ML estimators are obtained from the direction matrix in the final iteration of DFP procedure (Coelli, 1996).

Secondly I introduce the one-sided generalized likelihood-ratio test under both the null and alternate hypotheses as following in order to estimate whether either the stochastic frontier function or the traditional average response function without the profit (cost) inefficiency effect is an adequate representation of the data according to the likelihood-ratio formula10 following

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Maximum-likelihood method is a popular statistics method used for fitting a mathematical model to some data. Modeling real world data by estimating maximum likelihood offers a way of tuning the free parameters of the model to provide a good fit.

9

See Coelli, Prasada Rao and Battese(1997) page 188-189 for more details

This scaling implies an estimation of coefficients for PF and PL with the restriction that the sum of these coefficients is equal to one (Kuenzle 2005).

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by Battese and Corra (1977)

H011 :γ=0 , which means there are no profit(cost) inefficiency effects in the stochastic profit

(cost) frontier model. In other words all deviation comes from random noise.

H1 :γ>0, which means the residual variation is due to the profit (cost) inefficiency effect in

order to judge whether the profit(cost) inefficiency effects are significant in the stochastic frontier profit ( cost) model.

Thirdly I predict the profit (cost) efficiency for the individual bank using the results from ML estimates. In practice the value of U it is unobservable. In this case Battese and Coelli(1988)

advice that the best predictor for exp(-U it) is the conditional expectation of exp(-U it )given ei

=V it -U it for profit frontier model which is defined by

Profit EFF it =E (exp (-U it)| ei ) (13)

The value of the efficiency ranges from 0to1. 1 reflects that individual bank is fully profit efficient.

As for the stochastic cost frontier model the cost efficiency is the conditional expectation exp (U it) given ei =V it +U it, which is defined by

COSTEFF it =E (exp (U it) | ei ) (14)

The value of the cost efficiency ranges from 1 to infinity. Similarly 1 represents the highest cost efficiency level.

Lastly for the inefficiency effect model the value of δ-parameter can be obtained by maximizing the log-likelihood function12 of this model using ML method. Then the relationship between bank size and profit (cost) inefficiency can be obtained.

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Ⅴ. DATA

In my paper I use the unbalanced panel data which include 36 Chinese commercial banks and 180 observations (35 missing) in the 1999-2003 period .The reason why I choose this period is

the null and alternative hypotheses.

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This hypothesis can be tested by the Wald statistic in FRONTIER Version 4.1, which calculates the ratio of the estimate of γ to its estimated standard error. However for this test one-sided test should be adopted to test this hypothesis due to the non-negative value of γ.

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that Chinese commercial banks become stable after the Asian financial crisis in 1997.

The basic data source is the balance sheet and income statement in Bankscope, whenever Bankscope can’t provide enough information or has questionable values, I gather the data from other official data sources, such as Almanac of China’s finance and each individual bank’s website. Those banks whose required information was not available from any of these sources were excluded. Also the central bank, the specialized governmental credit bank, the

non-banking credit institution, the export–import banks are excluded from the data I provide because those banks and institutions are greatly influenced on by the policy from the central government.

All Chinese commercial banks involved in my survey are categorized into three different sized groups that are large, medium and small banks in terms of the total assets. Bank size is defined based on the total assets (inflation adjusted to the base year 2003) of the bank at year 2003.According to the proportion of the assets of individual banks among the total assets of 36 Chinese commercial banks, I sort the similar proportion into the one bank group. In the table 1 it is reflected that the four large state-owned commercial banks form a distinct large group ,whose assets account for 72% of total assets of 36 Chinese commercial banks; the medium bank group includes 11 Chinese commercial banks such as the Bank of Communications CO.LTD., China Merchants Bank CO.LTD., China Citic Bank etc., whose assets account for 25% of total assets of 36 Chinese commercial banks; the small bank group represents 21 Chinese commercial banks such as Shenzhen Commercial Bank, Tianjin City Commercial Bank and Ningbo Commercial Bank etc., whose assets account for 4% of total assets of 36 Chinese commercial banks.

Table 1: The Distribution of Different Sized Chinese Commercial banks in 2003

the distribution of different sized chinese commercial banks

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For the definition of the input and the output, I adopt the intermediation approach that already applied in many literatures about the bank efficiency. There are two dependent variables and six independent variables for the stochastic profit and cost frontier functions. I introduce them respectively as following.

Dependent variables

The dependent variables involved are the total cost and the before tax profit. The total cost (TC) measured by the sum of interest expense and other operating expenses which are recorded in the banks income statement. And the before tax Profit (∏) is recorded in the banks income statement.

Independent variable

The independent variables13 in my study comprise three input prices (the price of financial capital, the price of physical capital and the price of labor), three outputs (the total customer loan, the investment and the interbank loan) and one control variable (equity). To obtain the input price proxies, most studies (e.g. Altunbas et al. (2001), Lang and Welzel (1996)calculate input prices per bank. For an individual bank, I interpret the price of inputs as follows:

The price of financial capital (W1) is measured by the formulation

(Interest expense / total deposit) x100

The price of physical capital (W2) is measured by the formulation

(Other operating expenses/fixed assets) x100

The price of labor (W3) is measured by the formulation

(Total assets/ personnel expenses) x100

As for the three outputs, the customer loan (Y1) is measured by all loans to customers

including non-bank entities and other banks from balance sheet. The investment (Y2) is

measured by the sum of the long-term investment and short-term investment. And the interbank loan (Y3) is measured by the sum of the deposit with other banks and deposits with

central bank.

In the end I include equity (Z) as a control variable in my study following Mester (1996) and

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Altunbas et al. (2000).In transforming the inputs into the outputs, equity can be an alternative of funding source for loans for banks (Hughes and Mester, 1993). Additionally equity can be used to adjust the risk preference across banks. For example for the cost side if the leader of a bank is more risk-averse than another leader of another bank he should hold a higher equity Finally, in the Chinese banking system the insolvency of banks is great because of the high proportion of non-performing loans. Moreover the insolvency risk of a bank depends on the equity available to absorb losses. So the difference of insolvency risk reflects the bank’s costs through the risk premium that the bank has to pay in order to borrow funds (Berger and Mester 1997)

In table 2 I present the summary statistics for the variables involved in my study. Table 2: The Descriptive Statistics of Dependent Variables and Independent Variables

N Minimum Maximum Mean Std. Deviation Skewness Statistic Statistic Statistic Statistic Statistic Statistic Std. Error

∏ 172 -66 43218 2910.478 6451.317 3.849 0.185 TC 169 1.6 156480 14809.10 31282.302 2.699 0.187 Y1 174 2.4 3372000 297820.1 638238.45 2.698 0.184 Y2 129 -31 2309500 106239.3 342942.72 4.832 0.213 Y3 151 100.1 980110 76719.66 164612.59 3.019 0.197 W1 166 0 0.883 0.045 0.098 6.337 0.188 W2 169 0.137 6 0.858 0.833 4.040 0.187 W3 180 0.02 0.093 0.043 0.013 1.482 0.181 Z 173 -133210 236220 24118.78 54583.939 2.274 0.185 Valid N 128

∏: Before Tax Profit TC: Total Cost Y1: Customer Loan Y2: Investment

Y3: Interbank Loan W1: The Price of Financial Capital W2: The Price of Physical Capital W3: The Price of Labor Z: Equity

Unit in RMB million

Ⅵ Ⅵ Ⅵ

Ⅵ. EMPIRICAL RESULTS AND DISCUSSION

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relationship between the bank size and profit (cost) efficiency using profit (cost) inefficiency effect model.

Ⅵ.1 The case of profit model LLR Test

In this part I test the H0 :γ=0 which means the residual variation is due to the random error Vi

and alternative H1 :γ>0 which means the residual variation is due to the profit inefficiency

effect so as to judge whether the profit inefficiency effects are significant in the above-mentioned stochastic frontier profit model.

The result of the estimates of the parameters of the stochastic profit frontier and profit inefficiency effect model are presented in table 3

Table 3

Stochastic profit frontier

Variable Parameter Coefficients Standard-error T-ratio Customer loan Beta 1 0.098 0.126 _0.778 Investment Beta 2 0.031 0.096 0.326 Interbank loan Beta 3 2.157 0.426 _5.059* The price of financial capital Beta 4 -35.222 2.455 _-14.348* The price of physical capital Beta 5 22.544 2.436 _9.253* Equity Beta 6 0.407 0.090 _4.543* Total assets δ1 -0.942 0.216 _-4.358* Variance parameters Gamma _0.595 Sigma square 0.092

Stochastic Profit Frontier Model OLS Log

likelihood

function 6.271 -0.531

LR test _13.603*

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In table 3 I present one-sided Log Likelihood Ration Tests (LLR) of the OLS versus that of the frontier profit model. The value of the log-likelihood function for the full stochastic profit frontier model is 6.271 while the value of the log-likelihood function for the OLS fit is -0.531, which is less than that for the full frontier model. Then the one-side generalized

likelihood-ration test for the absence of the profit inefficiency effect from the frontier is 13.603. This value is reported as the LR test of the one-sided error in table3. It is significant because it is larger than 7.045 which is the 5% critical value for the degrees of freedom 314 from the Table 1 of Kodde and Palm (1986). Consequently the LLR tests results indicate that I can reject the null hypothesis of no profit inefficiency effects and accept an alternative hypothesis with stochastic profit inefficiency term in this model.

With respect to the estimated stochastic frontier profit function I note that γ (the share of inefficiency in the overall residual variance) is 0.595 which means γ-value is close to 1.It is in line with our claim that the profit inefficiency is significant in the stochastic frontier profit function.

Correlation

Then I investigate the correlations between the dependent variable and the independent variables. While few show insignificant correlation, many variables are significantly related. For instance, as shown in table 3. Specifically at the 5% significance level (T-ratio is 1.96) the correlation between the customer loans (Y1) and PBT is statistically insignificantly (0.778).The correlation between the investment (Y2) and PBT is not significant (0.326) .The correlation between the interbank loans (Y3) and PBT is strongly significant (5.059). The correlation between the price of financial capital (W1) and PBT is also statistically significant (-14.348). The correlation between the price of physical capital (W2) and PBT is strongly significant (9.253). And the correlation between the equity (Z) and PBT is strong significant (4.543).

Overall increasing the interbank loans, the price of physical capital and the equity can lead to higher profits, which are significantly correlated to the PBT while increasing the financial capital results in lower PBT and their correlation is also significant. However the customer loan and investment are positively correlated with PBT but correlation is very low and not

14

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significant.

As for the estimate for δ, the coefficient of the ln (total assets) variable in the profit inefficiency effect model is significantly negative, which means the total asset is an important factor to significantly influence the mean of the profit inefficiency distribution. These results indicate that the total assets significantly influence the mean of the profit inefficiency

distribution .The profit inefficiency effects of larger Chinese commercial banks tend to be smaller. Similarly the inefficiency effects of smaller Chinese commercial banks will be larger. In other words the larger Chinese banks have high values of the profit efficiency whereas the smaller Chinese banks have low values of the profit efficiency.

Descriptive Statistics on PE

Next, I turn to the mean profit efficiency score. In table 4 I report a few summary of descriptive statistics on profit efficiency scores for the 36 different sized Chinese bank.

Table 4: The Descriptive Statistics of the Profit Efficiency

PE 103 0.346 0.977 0.829 0..161 -1.168 0..238

Valid N 103

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Figure 1: The Scatter Plot Average Profit Efficiency and Average Asset

Scatter Plot Average Profit Efficiency and Average Asset 1999-2003

0 0.5 1 1.5

0 1E+06 2E+06 3E+06 4E+06 5E+06

Average Asset A v e r a g e P r o f i t E f f i c i e n c y 系列1

Descriptive Statistics of Three Bank Groups

In section 2 I will go into the difference in efficiency performance among three different sized bank groups in more depth. In table 5 I report the descriptive summary of three different sized Chinese banks in terms of their assets.

Table 5: Summary of Descriptive Statistics on PE for Three different sized Chinese banks

Large 11 0.965 0.977 0.971 0.004 0.196 0.661

Medium 48 0.836 0.973 0.924 0.031 -1.388 0.343

Small 44 0.346 0.969 0.689 0.158 0.003 0.357

Valid N 11

The results demonstrate that the value of the mean of the profit efficiency for the large bank group is highest; for the medium bank group it is closed to that of the large one; and for the small bank group it is lowest. Overall my results suggest that the large banks are able to exploit their size advantage on the profit side than the small one. A possible explanation is that the dominance of the four state –owned banks may allow them to reap gains from price leadership.

In summary I conclude that the large Chinese banks appear more efficient than the small one on the profit efficiency side.

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LLR Test

In this part I analyze the cost efficiency among the 36 different sized Chinese commercial banks in the similar way.

In this case I test the H0 :γ=0 of residual variation due to the random error Vi and

alternative H1 :γ>0 of the residual variation due to the cost inefficiency effect in which to

judge whether the cost inefficiency effects are significant in the stochastic frontier cost model. The result of the estimates of the parameters of the stochastic cost frontier and cost

inefficiency model are presented in table 6 Table 6

Stochastic cost frontier

Variable Parameter Coefficients Standard-error T-ratio

Customer loan Beta 1 0.378* 0.064 _5.913

Investment Beta 2 -0.070 0.055 _-1.282

Interbank loan Beta 3 -0.013 2.130 _-0.610

The price of financial capital Beta 4 36.170 45.703 _0.791 The price of physical capital Beta 5 -34.216 36.164 -0.946 Equity Beta 6 0.451 0.068 6.673 Total assets δ1 0.366 0.116 _3.166* Variance paremeters Gamma 0.934 Sigma square 0.053

Stochastic Cost Frontier Model OLS Log likelihood

function

38.284 29.464

LR test _17.640*

* means significant at 5% level Dependent variable: Total Cost (TC)

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OLS fit is 29.464, which is less than that of the full frontier model. Then the one-side generalized likelihood-ration test for the absence of the cost inefficiency effects from the frontier is 17.640. This value is reported as the LR test of the one-sided error in the table 4.It is significant because it is larger than 7.045 which is the 5% critical value for the degrees of freedom 3 from the Table 1 of Kodde and Palm (1986). Consequently the LLR tests results indicate that I can reject the null hypothesis of no cost inefficiency effects and accept an alternative hypothesis with stochastic inefficiency term in these models.

Regarding the estimated stochastic frontier cost function I note that γ (the share of cost inefficiency in the overall residual variance) is 0.934 which significantly close to 1, which is in line with the claim that stochastic inefficiency effect is significant in the stochastic frontier cost function.

Correlation

Furthermore I estimate the correlation between the total cost and independent variables at 5% significant level. The correlation between the customer loans (Y1) and the total cost is much significant (5.913). The correlation between the investment (Y2) and the total cost is insignificant (-1.282). The correlation between the interbank loans (Y3) and the total cost is not significant (-0.610). The correlation between the price of financial capital (W1) and the total cost is quite insignificantly (0.791). The correlation between the price of physical capital (W2) and the total cost is not significantly (-0.946). And the correlation between the equity (Z) and the total cost is also strongly significant (6.673). Overall the customer loan and the equity are positively related to the total cost with significant correlation whereas the price of financial capital is insignificant positively related to the total cost. On the contrary the investment, the interbank loan and the price of physical capital are negatively correlated to the total cost. However this correlation is low.

With regard to the estimate for δ, the coefficient of the ln (total assets) variable in this stochastic frontier cost model for the cost inefficiency effects is significantly positive (3.166). These results indicate that the total assets significantly influence the mean of the cost

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efficiency while the smaller Chinese commercial banks will have low values of the cost efficiency effects.

Descriptive Statistics on CE

Next, I turn to the mean cost efficiency score. In table 7 I present a few summary of descriptive statistics on cost efficiency scores for the different sized Chinese bank group.

Table 7: The Descriptive Statistics of the Cost Efficiency

CE 102 1.030 2.840 1.452 0.418 1.382 0.239

Valid N 102

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Figure 2: Scatter Plot Average Cost Efficiency and Average Asset

Scatter Plot Average Cost Efficiency and Average Asset 1999-2003 0 1 2 3 0 100000 0 200000 0 300000 0 400000 0 500000 0 Average Asset A v e r a g e C o s t E f f i c i e n c y 系列1

Descriptive Statistics on of Three Bank Groups

In section 2 I will go into the difference in efficiency performance among three different sized bank groups in more depth.

Table 8: Summary of Descriptive Statistics on CE for Three Different Sized Chinese Banks

large 11 1.550 2.840 2.266 0.387 -0.327 0.661

medium 48 1.060 2.240 1.460 0.320 0.933 0.343

small 43 1.030 2.100 1.234 0.220 1.944 0.361

Valid N (listwise) 11

In table 8 I report that the descriptive summary of the cost efficiency of three different sized Chinese banks. The results show that the value of the mean cost efficiency of the large bank group is highest; for the small bank group it is lowest; for the medium bank group is closed to that of the small one. Overall my results suggest that the small banks are more efficient than the large banks on the cost side.

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small banks are more efficient on the cost side rather than the profit side. I provide some possible explanations regarding above-mentioned results. According to the theory of

microeconomics15 profit is the difference between total revenue and total cost, although the cost of large banks is inefficient it is still efficiency on the profit side due to the huge total revenue they obtain. In terms of data published by the PBOCin 2003 the revenue of the four largest state-owned commercial banks accounts for 70% of total revenue of all Chinese

commercial banks. On the other hand the possible reason why the large banks demonstrate low cost efficiency is that the large banks in the Chinese banking system were built on the basis of the planned economy system they must be affected by these policies of the central government. They had to go on to implement their policy lending in response to the pressure from the central and local governments which lead to a great deal of the bad loans in the large banks. Consequently the large banks must suffer this burden of the bad loans that lead to low

efficiency in the cost side. For example according to the published data by the Chinese central bank in 2007 for four national banks, namely ABC, PCBC, BOC, ICBC, their balance of the bad loan is RMB 1061 billion and the rate of the bad loan is 8.2%. On the contrary for twelve smaller joint-equity commercial banks, such as Shanghai Pudong Development Bank, China Everbright Bank and Guangdong Development Bank etc., their balance of the bad loan is RMB 100.42 billion and the rate of the bad loan is 2.78%.In contrast the small banks show cost efficiency, which probably because the small banks do not have huge the bad loans, adopt the advanced technology and flexible management. Especially with the development of these internet banks and the present of the electronic business of bank, the small banks can take full advantage of the advanced technology to speed up the financial innovation. Whereas the strong points of the large banks that are many business branches and more employees will become their weak points because the traditional management methods must fall into disuse during the high-tech times. However the small banks still can not outperform the large banks in the profit side because they have a small market share, the limited capital which lead to the limited revenue. Also the small banks restricted by late setting-up, few business branches and market reputation are short of the powerful capability of organizing deposit to some extent which limit the small banks develop their businesses further.

15

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Ⅶ Ⅶ Ⅶ

Ⅶ. CONCLUSION

In this paper I investigate the relationship between the bank size and the profit (cost) efficiency among 36 different sized Chinese commercial banks between1999 to 2003 using SFA. I adopt the two-step model which one is the stochastic profit (cost) frontier model and another one is the profit (cost) inefficiency effect model. The results indicate that the profit (cost) inefficiency effect is significant in the stochastic frontier profit (cost) model; the total assets significantly influence the mean of the profit(cost) inefficiency distribution ,which implies that the bank size has a negative effect on the profit inefficiency and a positive effect on the cost inefficiency. In other words the large Chinese commercial banks are more efficient in profit than the small ones and the small Chinese commercial banks are more efficient in cost than the large ones.

Furthermore there are some limitations in my paper. Due to the restriction of availability of data I just analyze the efficiency performance of some of all Chinese commercial banks. The results I obtained can not present the overall trend of the bank efficiency in the Chinese

banking system. Additionally in my study I just build up the relationship between the bank size and the profit (cost) inefficiency effect. Actually other factors also greatly affect the profit (cost) efficiency. In my future research I will combine the influence of other factors such as

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REFERENCE

Aigner, D., Lovell, C. A. K. and Schmidt, P. (1977), “Formulation and Estimation of Stochastic Frontier Production Models”, Journal of Econometrics, Vol. 6, pp. 21-37

Altunbas, Y., L. Evans and P. Molyneux (2001), “Bank Ownership And Efficiency”, Journal of Money, Credit, and Banking 33(4), 926–54.

Altunbas, Y., Liu, M., Molyneux, P., Seth, R.(2000),“ Efficiency and risk in Japanese banking”, Journal of Banking and Finance 24, 1605-28.

Battese, G. E. and Corra, G. (1977), “Estimation of A Production Frontier Model: With Application To The Pastoral Zone of Eastern Australia. Australian Journal of Agricultural Economics 21, 169–179.

Battese G.E. and Coelli, T.J. (1992), "Frontier Production Functions, Technical Efficiency and Panel Data: With Application to Paddy Farmers in India", Journal of Productivity Analysis, 3(1/2), 153-169

Battese,G..E., and Coelli T.J.(1993), “A Stochastic Frontier Production Function Incorporating a Model for Technical Inefficiency Effects’, Working Papers in Econometrics and Applied Statistics, NO69, Department of Econometrics, University of New England, Armidale.

Battese,G..E., and Coelli T.J.(1995), “ A Model for Technical Inefficiency Effects in A Stochastic Frontier Production Function for Panel Data”, Empirical Economics,20,325-332

(33)

Battese, G. and Corra, G. (1977), “Estimation of a production frontier model: With application to the pastoral zone of Eastern Australia”, Australian Journal of Agricultural Economics 21, 169{79}.

Bauer, P. W., Berger, A. N., Ferrier, G. D.and Humphrey D. B. (1998), “Consistency Conditions for Regulatory Analysis of Financial Institutions: A Comparison of Frontier Efficiency Methods”, Journal of Economics and Business 50, 85–114.

Bauer, P. W., Berger, A. N. and Humphrey, D. B. (Eds.)(1993), “Efficiency And Productivity Growth In U.S. Banking, New York7 Oxford University Press, pp. 386– 413

Berger, A.N., Hasan, I. and Zhou, M.(2005), “Ownership, Financial Liberalization, and Efficiency of Chinese Banks”, working paper

Berger, A.N., Hasan, I. and Zhou, M. (2006), “Bank Ownership And Efficiency In China:What Will Happen In The World’s Largest Nation? “,Working paper

Berger, A. N. and Mester, L. J. (1997),”Inside the Black Box: What Explains Differences in the Efficiencies of Financial Institutions?” Journal of Banking and Finance, vol. 21, 895–947

Chen. X., Skully, M. and Brown, K. (2005), “Banking Efficiency in China: Application of DEA to Pre-and Post –Deregulation Eras:1993-2000”, China Economic Reviews 16 229-245

Clark, J.A. and Siems, T.F. (2002), “ X-Efficiency in Banking: Looking Beyond the Balance Sheet, Journal of Money, Credit and Banking, Vol. 34, 4, November, 987-1013.

(34)

Coelli, T.J., Prasada Rao, D.S. and Battese, G.E. (1997), “An Introduction to Efficiency and Productivity Analysis”, Kluwer Academic Publishers, Boston.

Ferrier, G.D.,and Lovell,C.A.K.(1990), “Measuring Cost Efficiency in Banking: Econometric and Linear Programming Evidence”, Journal of Econometrics, Vol. 46, pp. 229-245.

Fu ,X. and Heffernan, S. (2005), "Cost X-efficiency in China's Banking Sector", Cass Faculty of Finance Working Paper ,WP-FF-14-2005

Hughes, J. and Mester, L. J. (1993), “A Quality and Risk Adjusted Cost Function for Banks: Evidence on the ‘Too-Large-to-Fail-Doctrine’. Journal of Productivity Analysis 4, 292–315.

Hu, J., Chen, C. and Su, Y.(2006), “Ownership Reform and Efficiency of Nationwide Banks in China”, working paper, Institute of Business and Management, National Chiao Tung University (Taiwan),Washington College of Law, American University, USA

Humphrey, D. B., and Pulley, L. B.(1997), “Banks’ Response to Deregulation: Profits, Technology and Efficiency”, Journal of Money, Credit and Banking 29:73–93.

Kodde, D.A., and Palm, F.C. (1986), “Wald Criteria for Jointly Testing Equality and Inequality Restrictions”, Econometrics 50, 1243-8

Koetter, M., Fiorentino, E.and Karman ,A.(2006), ”The Cost Efficiency of German Banks: A Comparison of DEA and SFA Methodologies” , Bundesbank Discussion Paper Series No. 2, 10/2006,

Kuenzle, M. (2005). Cost efficiency in network industries: Application of stochastic frontier analysis, Universität Zürich.

(35)

University Press.

Kumbhakar, S. C., and Wang, Hung-Jen. (2005).“Estimation of Growth Convergence Using a Stochastic Production Frontier Approach.”, Economics Letters 88, 300-05.

Kwan, S.H. and Eisenbeis, R.A.(1996), “An Analysis of Inefficiencies in Banking: A Stochastic Cost Frontier Approach”, Federal Reserve Bank of San Francisco,

Economic Review, 2.

Lang, G. and Welzel, P. (1996),”Efficiency and Technical Progress in Banking: Empirical Results for A Panel of German Cooperative banks”, Journal of Banking & Finance 20(6), 1003–23

Meeusen, W. and J.van den Broeck (1977), ‘Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error’, International Economic Review, Vol. 18, pp. 435-444.

Mester, L. J.(1996), “A study of bank efficiency taking into account risk-preferences”, Journal of Banking and Finance 20, 1025-1045.

Sealey, C. W. and Lindley, J. T. (1977), “Inputs, Outputs, and a Theory of Production and Cost and Depository Financial Institutions”. The Journal of Finance 32, 1251– 1265.

Wei, J. and Wang, L. (2000), “The Non-Parametric Approach to the Measurement of Efficiency: The Case of China Commercial banks”, Journal of Financial Research, 3, 88–96.

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Zhang, C., Gu F., and Di, Q. (2005), “Study on measurement of profit efficiencies of

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APPENDIX

1. The correlation between the dependent variables and the independent variables under the two-step model

Y1 Y2 Y3 W1 W2 Z TA

∏ + + +* -* +* +*

TC +* - - + - +*

PIE -*

CIE +*

∏: Before Tax Profit TC: Total Cost Y1: Customer Loan Y2: Investment

Y3: Interbank Loan W1: The Price of Financial Capital W2: The Price of Physical Capital Z: Equity PIE : Profit Inefficiency Effect CIE: Cost Inefficiency Effect TA:Total Asset

* means significant at 5%

2. Descriptive Statistics of the profit efficiency score

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bank19 5 .818 .890 0.856 .032360 -0.375 0.913 bank20 3 .554 .710 0.646 .081682 -1.361 1.225 bank21 4 .466 .721 0.580 .121744 0.312 1.014 bank22 4 .508 .773 0.680 .117191 -1.701 1.014 bank23 3 .655 .790 0.712 .069907 1.230 1.225 bank24 4 .587 .914 0.704 .144177 1.675 1.014 bank25 4 .543 .615 0.588 .033160 -1.130 1.014 bank26 5 .500 .969 0.616 .199316 2.142 0.913 bank27 2 .346 .539 0.443 .136472 . . bank28 1 .424 .424 0.424 . . . Valid N (listwise) 1

3. Descriptive Statistics of the cost efficiency score

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Efficiency in the Chinese Banking Industry