Data

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j m

 

.¹⁹

3.4 Data

The data are mainly compiled from unconsolidated financial statements of BankScope, which is Fitch’s International Bank Database. We initially observe 136 Chinese commercial banks with 1088 bank-year observations over the period 2006-2013. After eliminating some samples with either missing, or negative, or extreme values, we end up with unbalanced panel data that include 74 banks with 303 bank-year observations. The data contain 6 large national commercial banks (LNCBs) with 41 observations,²⁰ 12 joint-stock commercial banks (JSCBs) with 82 observations, and 56 other city and rural commercial banks (CRCBs) with 180 observations. All nominal variables have been deflated by the consumer price index (CPI) provided by World Bank with the base year of 2005.

According to the intermediation approach, we identify two inputs, i.e., labor (



₁

X

₁) and physical capital (



₂

X

₂), and an intermediate output, i.e., deposits (Z) in the first stage. In the second stage, we define three inputs, i.e., Z,

 1  

1

 X

1, and

 1  

2

 X

2, and three final outputs, i.e., total loans (

Y

₁), investments (

Y

₂), and non-interest income

19 Berger et al. (1987) prove that the translog cost function requires some CC_jm to be positive. In the three-output case, if any two out of the three pairs of CC_jm are negative, then scope economies are confirmed.

20 LNCBs contain the Big 4 state-owned banks (SOBs), i.e., Industrial and Commercial Bank of China, Agricultural Bank of China, Bank of China, and China Construction Bank, as well as Bank of Communications and China Development Bank. Since those SOBs have been privatized in late- 2008, we here dub them LNCBs instead of SOBs. Moreover, Chinese authorities have restructured the main policy bank, i.e., China Development Bank, as a commercial bank at the end of 2008.

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(

Y

₃). Banks are assumed to exploit portions of

X

₁ and

X

₂ to generate various forms of deposits in the first stage. Deposits and the remaining parts of

X

₁ and

X

₂ are

next used to produce final outputs. The price of labor (

W

₁) is calculated as the ratio of personnel expenses to the number of full-time employees. The price of physical capital (

W

₂) is gauged by the ratio of expenses on premises and fixed assets to the total value

of premises and fixed assets. The price of deposits (

W

₃) is defined as the ratio of interest expenses to total deposits. Finally, total expenditure ( E ) is the sum of the aforementioned three items of expenditures. In order to impose the homogeneity restriction of degree one in input prices for a cost function, we arbitrarily select the price of labor as the numeraire.

Table 2.1 Descriptive statistics

Variable Name Mean Std. Dev. Minimum Maximum

Total loans* (

Y

₁) 112410 225286 51 1202173

Investments* (

Y

₂) 202175 405436 207 2244034

Noninterest income* (

Y

₃) 1069 2649 0.034 15958

Labor (

X

₁)** 44098 106905 89 478980

Physical capital* (

X

₂) 1631 3645 0.575 19046

Total customer deposits* (

X

₃) 155844 335265 131 1815292 Price of labor* (

W

₁) 0.0314 0.0121 0.0029 0.0780 Price of physical capital (

W

₂) 0.7490 0.4987 0.1074 4.7143 Price of funds (

W

₃) 0.0162 0.0045 0.0007 0.0338

Note: There are 74 sample banks with 303 bank-year observations.

*：Measured by millions of US dollars.

**：Measured by number of employees

Table 2.1 shows sample statistics for all of the above variables. During the sample period, the average value of investments of a representative bank is equal to US$202 billion, which is about twice as large as the average loans granted (US$112 billion), and

‧

the average non-interest income is equal to around US$1 billion. The average prices of labor, physical capital, and deposits are equal to US$31,400, 0.7490, and 0.0162, respectively. Note that all of the output and input variables have quite large standard deviations, indicating that the sample banks differ substantially in production scale and performance.

Table 2.2 Descriptive statistics by different types of banks Variable Name

Note: *：Measured by millions of US dollars.

**：Measured by number of employees

Table 2.2 presents the same statistics by different types of banks. LNCBs have the largest output and input quantities as expected, while their input prices are the smallest.

CRCBs show the least output and input quantities, but their inputs prices are ranked in the middle. The production scale of JSCBs is ranked next to LNCBs with the highest input prices. Moreover, LNCBs are operating on a large scale relative to the other two types of banks and may outperform the remaining types of banks since their input prices are the lowest.

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respective unknown functions.²¹ Microeconomic theory requires a cost function to satisfy some regularity conditions, in which the homogeneity and symmetry conditions can be directly imposed on (7) and (8), and the monotonicity in prices and outputs and concavity in prices can be checked after the parameters of the cost function have been estimated.²² The system functions, consisting of equations (1), (7), and (8), are estimated using the likelihood function of (13). However, the highly non-linear nature of the system equations forces us to adopt a two-step procedure that is less efficient, but computationally simpler, to execute the estimation job. The coefficient estimates are proven to be consistent, as presented below.

In the first step, the 4 equations are estimated by the non-linear iteratively seemingly unrelated regression (NISUR). Since the composed errors of equations (1) and (7) are treated as if the single disturbances in this step have mean values of zero, the constant terms of the two equations are apt to be biased, but the remaining slope

21 The Fourier flexible cost function may be an alternative choice - which has been applied by, e.g., Mitchell and Onvural (1996), Berger and Mester (1997), Berger et al. (1997), Altunbaş et al. (2000, 2001a, b), Williams and Gardener (2003), Kraft et al. (2006), Beccalli and Frantz (2009), Feng and Serletis (2009), and Huang et al. (2011a, b), to mention a few - to examine banking efficiencies. Recall that our econometric model is highly non-linear, making the convergence of the likelihood function very difficult. We thus do not select it as our empirical model.

22 The property of concavity in prices can be expressed as:

1 11 0

‧

step, those estimated



and slope parameters are viewed as given and the constant terms and parameters embedded in the distributions of

v

’s and

u

’s, i.e.,



, and



, are estimated with respect to (13) by the quasi-maximum likelihood, where only (1) and (7) are considered. Theoretically, viewing the estimated



and slope parameter estimates as given in the second step may induce the variances of the error terms to be heteroskedastic via the estimation errors. This results in consistent parameter estimates, while the corresponding estimated standard errors are inconsistent.

We suggest computing the sandwich-form for the covariance matrix of the estimators, which give rise to the correct standard errors (White, 1982).

Table 2.3 Parameter estimates of the production frontier

Variable Parameter Estimates Standard Errors



1 0.3459*** 0.0304

23 We perform Monte Carlo simulations to confirm our claim. The results are available from the authors upon request.

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Variable Parameter Estimates Standard Errors

constant -0.9723*** 0.0818

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parameters, only those estimates in the cost frontiers are shown there. Moreover, these estimates of the cost function satisfy the regularity conditions required by the microeconomic theory.²⁵ The tables reveal that most of the parameter estimates reach at least the 10% significance level, implying that the estimation results are reasonable.²⁶

Table 2.3 shows that the estimates of



₁ and



₂ are equal to 0.35 and 0.49, respectively, indicating that an average bank utilizes 35% and 49% of its workforce and capital in the first production process to produce deposits. This intermediate output, along with the rest of labor (65%) and capital (51%), is exploited to produce final outputs in the second process. Input capital is allocated almost evenly between processes, while less than one half of labor is involved in the first production process.

The findings can be justified by the fact that the first stage is a fund collection process, where various types of depositing procedures require the use of computers and storage equipment and hence tend to be capital intensive. In addition, banks are committed to provide safe and convenient banking services in this stage, which also requires the use of some form of capital goods - for example, branches, security systems, information systems, etc. Thus, both production stages depend equally on the use of capital.

The second production process aims at revenue generation, where various funds

convergence for the likelihood function, we ignore the interaction terms between time trend and all explanatory variables, such as outputs and factor prices, in an attempt to reduce the number of parameters to be estimated.

25 The signs of the partial derivatives of the cost function with respect to input prices are found to be positive for all observations, supporting the monotonicity conditions. The marginal costs of Y2 and Y3 are also found to be positive for all observations, while a few observations fail to have positive marginal costs for Y1. As for the concavity conditions, we uncover that some of the observations do not satisfy the condition of H3<0, whereas the vast majority of the observations are congruent with conditions H10 and H20. We thus claim that our estimation results are acceptable and suitable for further investigation.

26 The standard errors of



₁^,



₂^,



₁^,



₂^{, and}



and the two constant terms are yielded by the sandwich-form estimators.

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gathered in the first stage are transformed into loans, investments, and off-balance sheet activities. The major sources of revenue received by banks are interests and capital gains from loans and investments, respectively, as well as fees and commissions. These activities are frequently exposed to default and investment risks. To avoid possible losses incurred by unexpected risks, banks have to hire professionals for planning and scrutinizing. For example, loan officers collect information about loan applicants’

financial status and credit conditions in order to correctly make decisions on whether to accept or reject granting loans to these applicants. Moreover, banks are involved in other financial services, like financial planning, wealth management, and off-balance sheet activities, so as to provide customized financial products and maintain good customer relationships. Appropriate engagement in non-traditional activities may reduce the idiosyncratic risk of bank operations and sustain solid client relationships via more active interaction. All these business items consume large amounts of workforce in the second production process.

Table 2.5 Parameter estimates of the production frontier with bank dummies Variable Parameter Estimates Standard Errors



1

‧

Note: *** denotes significance at the 1% level.

Table 2.6 Parameter estimates of the cost frontier with bank dummies

Variable Parameter Estimates Standard Errors

constant -1.4898*** 0.3382

Note: ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.

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Our sample banks are established to serve different groups of customers and hence may distribute distinct ratios of labor and capital between processes. Given that there are three forms of banks, i.e., LNCB, JSCB, and CRCB, we define two dummy variables, DJSCB and DCRCB, corresponding to the latter two types of banks and re-estimate equations (1), (7), and (8).

Tables 2.5 and 2.6 report the estimation results. Again, most of these estimates attain at least the 10% significance level. These estimates help us to calculate the fractional parameters for the three types of banks, with the results shown in Table 2.7.

Evidence is found that each type of bank allocates no more than 31% of workers in the first step, in which JSCB and CRCB assign similar ratios of labor. Conversely, each type of bank allocates more than one half of capital stock in the first step, in which JSCB and CRCB again assign similar ratios of capital (59% and 55%). LNCBs allocate 25% (73%) of labor (capital) in the first process, which deviates somewhat from the other two types of banks. Note that LNCBs are huge banks and own branches nationwide. Our estimation outcomes suggest that LNCBs employ a larger part of their tangible assets to fulfill the fund collection process. The network SFA enables us to estimate fractional parameters, which shed light on the resource allocation among various operational stages in different forms of Chinese banks.

Table 2.7 Estimates of fractional parameters by types

LNCB JSCB CRCB All sample banks



1 0.25 0.30 0.31 0.35



2 0.73 0.59 0.55 0.49

The test for the null hypothesis that both coefficients of DJSCB and DCRCB equal zero is decisively rejected at the 1% level of significance with 4 degrees of freedom,

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based on the likelihood ratio test statistic of 37.02. This confirms that the model with bank dummies is more relevant than otherwise to describe banks’ production processes.

Therefore, we shall use the parameter estimates in Tables 2.5 and 2.6 to measure technical efficiencies for the two production stages, denoted by TE1 and TE2, respectively.²⁷

Table 2.8 Average TE scores by types

TE

1

TE

₂

Mean Std. Dev. Mean Std. Dev.

LNCB 0.4451 0.0992 0.6134 0.1320

JSCB 0.7143 0.0671 0.7231 0.0693

CRCB 0.6423 0.1438 0.6922 0.0886

All sample banks 0.6351 0.1463 0.6899 0.0967

According to Table 2.8, the average value of TE1 in the first production stage is equal to 0.6351 with a standard deviation of 0.1463, meaning that a representative bank produces around 64% of the best practice bank’s output, employing the same level of inputs. This bank has to increase its intermediate output by 36% to hit the production frontier with its current input mix. The average score of TE2 in the second stage is equal to 0.6899 with a standard deviation of 0.0967, implying that an average bank can save about 31% of its current production cost for the given level of outputs, provided it is producing on the efficient frontier.

Table 2.8 also shows average TE scores of different bank types. JSCBs are found to be the most efficient in both production stages, having mean TE1 and TE2 scores of

27 It is noteworthy from Table 7 that the three estimates of ₁ (₂) for different forms of banks are all less (larger) than those in Table 3 without distinguishing bank types, implying that estimates of ₁ and

2 in Table 3 are apt to be biased.

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0.7143 and 0.7231, respectively. Those banks can produce the highest level of deposits under a given level of inputs and entail a minimum cost to produce a given level of outputs, followed by CRCBs (0.6423 and 0.6922), while LNCBs have the worst managerial abilities (0.4451 and 0.6134) in both stages. Chinese banks are found to be more technically efficient in the second stage than in the first stage, which means that the sample banks should concentrate on improving their first-stage production, particularly LNCBs. Wang et al. (2014) also point out the similar finding that Chinese banks should improve the operational efficiency in the first deposit producing sub-stage so that overall performance can be greatly improved. There could be an array of factors explaining the poorer performance of LNCBs, i.e., objectives other than cost minimization, higher market power, overstaffing, and less developed risk management.

Our results are consistent with Ariff and Can (2008), Fu and Heffernan (2008), Du and Girma (2011), and Asmild and Matthews (2012), who yield the same efficiency ranking by ownership. However, our model allows for investigating the internal performance of different subsectors, whereas theirs cannot estimate efficiency for banks of different sectors.

The network SFA model permits us to consider the interactions of internal production processes within a firm and measures each division’s performance. Hence, the model offers more insightful and detailed information useful for bank managers, business consultants, and regulators. Moreover, it might be interesting to explore the correlation between TE1 and TE2, which gives additional information on the potential link between the two production processes. The simple correlation coefficient is calculated as 0.64, suggesting that a higher first-stage score of TE1 is accompanied by a higher second-stage score of TE2. One is led to infer that a more technically efficient first-stage operation tends to foster a more cost efficient second-stage operation and

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vice-versa. This finding appears to be reasonable in that an efficient first-stage production helps generate more deposits that are utilized in the second stage as one of the inputs. This implies that the bank can either increase output quantities in the first stage without reducing the input mix, or employ deposits in the second stage at a lower price, or both, causing a positive correlation between the two stages’ technical efficiencies.

Figure 2.2 Average efficiency scores over time for all sample banks

Figure 2.2 displays the average efficiency measures of TE1 and TE2 over the sample period 2006-2013 for all sample banks. The average TE2 is higher than the average TE1. Their difference is relatively large before 2009, with the largest gap in 2008²⁸ and a sharp drop afterwards. The mean TE1 shows a secular upward trend, which declines in 2008. The mean TE2 fluctuates across time without a clear trend.

28 The gap between TE1 and TE2 in 2008 may be exacerbated due to the fact that deposits of JSCBs and CRCBs are greatly crowded out by those of LNCBs during the 2008 global financial crisis. Depositors may have withdrawn their money from JSCBs and CRCBs to put into the relatively safer LNCBs. This results in a decline of efficiency during the deposit generation production stage for all sample banks.

0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75

2006 2007 2008 2009 2010 2011 2012 2013

All Sample Banks

TE1 TE2

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Although technical efficiency in the first stage is lower than in the second stage, its managerial ability enhances over time, and the mean TE2 appears to be stagnated.

Barros et al. (2011) find that technical efficiency in the Chinese banking sector improved over the period 1998-2008. However, they fail to identify which production stage is the driver pushing up this sector’s performance.

Figure 2.3 Average efficiency scores over time for LNCBs

By segregating each type of commercial banks, the results of TE1 and TE2 over the sample period for the various commercial banks are obviously dissimilar. Figure 2.3 presents the average efficiency measures of TE1 and TE2 during the sample period 2006-2013 for the large national commercial banks (LNCBs), in which the average TE2

is higher than the average TE1. The mean TE1 greatly improves with the trend from around 0.30 in 2006 to around 0.50 in 2013. The mean TE2 fluctuates around 0.60.

Compared to the other two types of commercial banks, the issue of too big to fail may occur in the case of the China banking industry, because LNCBs absorbed large amounts of deposits from the other two types of banks in the face of the 2008 global financial crisis, thus contributing to their improvement of TE1 performance.

0.1 0.2 0.3 0.4 0.5 0.6 0.7

2006 2007 2008 2009 2010 2011 2012 2013

LNCB

TE1 TE2

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Figure 2.4 Average efficiency scores over time for JSCBs

Figure 2.4 illustrates the average efficiency measures of TE1 and TE2 over the sample period 2006-2013 for the joint stock commercial banks (JSCBs). Most average TE1 and TE2 are around 0.7, with the average TE2 outperforming the average TE1 during the periods between 2007 and 2008 and between 2012 and 2013. However, technical efficiency in the first stage is higher than that in the second stage in 2006 and for the years 2009-2010.

Figure 2.5 Average efficiency scores over time for CRCBs

0.5 0.55 0.6 0.65 0.7 0.75 0.8

2006 2007 2008 2009 2010 2011 2012 2013

JSCB

TE1 TE2

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

2006 2007 2008 2009 2010 2011 2012 2013

CRCB

TE1 TE2

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Figure 2.5 depicts the average efficiency measures of TE1 and TE2 over the sample period 2006-2013 for the city and rural commercial banks (CRCBs). China’s government released favorable policies to relax access barriers and to encourage domestic and foreign financial institutions to enter the rural financial markets in 2003-2006 so that sufficient funds can be provided to rural distracts that need them so as to bolster their development. Evidence shows that CRCBs succeeded at absorbing deposits from rural households and rural enterprises through the evidence that the mean TE1 improves from 0.55 in 2006 to 0.7 in 2013 during the first deposit generation process. We also observe that TE1 for CRCBs decreases as the 2008 global financial crisis erupted. Depositors may have believed that LNCBs are too big to fail and thus took actions to withdraw money from JSCBs and CRCBs to put into LNCBs. Finally, TE1 for LNCBs outperforms those of JSCBs and CRCBs.

Regarding the efficiency of the revenue generation process, evidence reveals that the highest TE2 took place in 2007, but appears stagnated around 0.7 thereafter. In 2007,

Regarding the efficiency of the revenue generation process, evidence reveals that the highest TE2 took place in 2007, but appears stagnated around 0.7 thereafter. In 2007,

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