Cost efficiency and
Credit risk
Evidence from Commercial Banks in China
Author: Fan Zhang
Student Number: 1823981
Supervisor: Dr. Aljar Meesters
University of Groningen
Cost efficiency and Credit risk:
Evidence from Commercial Banks in China
Abstract:
This paper examines the causality of cost efficiency and credit risk by extending the
framework of Berger and DeYoung (1997). Cost efficiency scores are calculated by Data
Envelopment Analysis model. Non-performing loan ratio is the indicator of credit risk.
We apply GMM dynamic panel data estimators to investigate the relationship between
cost efficiency and credit risk. Our data includes 49 Chinese commercial banks between
2001 and 2008. The findings show that there is statistical evidence of significant negative
effects of credit risk on cost efficiency. It is in accordance with the bad luck hypothesis,
according to which the accumulation of non-performing loans exerts an impact on the
deterioration of cost efficiency. The econometric results do not support the bad
management hypothesis or the skimping hypothesis. This paper suggests that the Chinese
banking industry should consequently strengthen the control of credit risk in order to
increase bank cost efficiency. Moreover, the Chinese bank management should better
utilize their resources to solve the deeply rooted problems in transition countries on the
basis of the correlation between these two factors.
JEL classification: G21; G28; C14; D21
Keywords: Chinese commercial banks; Cost efficiency; Credit risk; Data Envelopment
1. Introduction:
Many problems have been found in the banking industry for transition countries, such as inefficient management, highly concentrated risk, low profitability, unbalanced market and ownership structures and loose regulations, etc. (Lardy 1998, Park and Sehrt 2001, Fan 2003). The underdevelopment of the banking system among transition countries is manifested by the large amount of impaired loans. To a large extent, the future of banking institutions will depend on how well they can manage risks. Among various kinds of risks, credit risk is a crucial component of risk management. It is essential to the success of banks in the long run; meanwhile it is also a threat to the healthy development of transition economies if badly managed. Moreover, because of the increasing competition in financial market and gradual financial reforms in transition countries, bank managers attempt to improve their cost efficiency as well. Credit risk and cost efficiency are critical components of comprehensive banking management. As a result, bank managers are curious about how to conduct their operations in order to balance their risk behavior and efficiency management. This ability could be enhanced if the internal relations between these two factors are systematically identified.
relationship between cost control and risk behavior is clearer and then banking managers could utilize their resources allocation better, further enhancement of banking management is expected.
Considering the relationship between cost efficiency and credit risk, apparently these two topics might be largely unrelated. However, Berger and DeYoung (1997) argue that they are actually related for following reasons. Firstly, for failing banks, they tend to be inefficient or low cost efficiency and exhibit high ratios of problem loans. Even for banks which have not failed, there is a negative relationship between efficiency and problem loans. Secondly, cost efficiency is positively related to ratings of bank management, moreover management quality ratings are more strongly related to asset quality ratings, hence asset quality and cost efficiency is positively associated. This relationship is consistent for the failed banks, and suggests that the negative relationship between cost efficiency and problem loans holds for the population of banks as well as for the subset of failing banks. Thirdly, lots of studies apply the adjustment of efficiency to control asset quality by including non-performing loans in the estimation of efficiency scores, which underlines the relationship between these two factors.
This paper examines the inter-temporal relationship between cost efficiency and credit risk, which are main measure of efficiency and the main risk faced by Chinese commercial banks respectively. Moreover, this paper systematically identifies the sign of the influence and presents some evidence to assist the bank behavior in order to control credit risk, improve cost efficiency and
find the most pressing management problem for banks in China. The main research question is
developed as “What are the bi-directional relationships between cost efficiency and credit risk for Chinese commercial banks”. Extending the studies on this issue, this paper examines cost efficiency of Chinese commercial banks from 2001 to 2008. In contrast to previous studies, this paper applies a non-parametric method (Data Envelopment Analysis). And then GMM dynamic panel estimators are conducted to analyze the causality between cost efficiency and credit risk.
The contributions of this study are threefold. Firstly, there are a few papers investigating how credit risk (cost efficiency) influences cost efficiency (credit risk) in Chinese commercial banks. Nevertheless, this paper examines cost efficiency’s association with credit risk in dual ways, which is informative for this research area and for bank managers as well. Secondly, since there are few scholars who applied the Data Envelopment Analysis to examine Chinese bank efficiency. This paper tries to add more evidence to current efficiency studies as well. Thirdly, this paper applies the most recent data and wide range of Chinese commercial banks. Due to China’s gradual openness, corresponding with the modification of legal and financial infrastructure, it would be meaningful to give some updated results in order to provide more evidence in light of further reform. Including joint-stock banks and city banks, a comparison among different categories of banks are highlighted in terms of cost efficiency, credit risk and their association.
The remaining part of this paper is organized as follows. In the next section, the existing theories are reviewed; drawing up on the theoretical overview, testable hypotheses are derived. The research methodology is described in Section 3. This section starts with how to measure cost efficiency, followed by an econometric model. Section 4 includes the data collection and the descriptive statistics. Section 5 presents the results of empirical tests. Robustness test is given in Section 6. Section 7 concludes and discusses the implications of this paper.
2. Literature Review
2.1 The evolution of the Chinese banking industry
controlled bank under the Ministry of Finance. It played a role of both the central bank and a commercial bank, who took up the majority of overall industry assets and financial transactions. The initial financial reform between 1978 and 1988 focused on changing the structure and operations of the administrative banking system. During this reform, PBOC became a separate entity of the central bank and four state-owned commercial banks (SOCBs) emerged to conduct commercial banking activities. The Bank of China (BOC) specialized in transactions related to foreign trade and investment; the People’s Construction Bank of China (PCBC) mainly dealt with transactions related to manufacturing; the Agriculture Bank of China (ABC) handled transactions in rural areas; the Industrial and Commercial Bank of China (ICBC) took over the rest of the commercial transactions of PBOC. Chinese banking industry replaced the mono-bank system with a two-layered system, which separates commercial lending and central banking functions. In the early 1980s, the Chinese banking sector benefited from the financial deregulation. However, PBOC and SOCBs operated within the central economic plan and under the control of the government; they performed as a particular economic sector. Changes were made in order to tackle this problem in 1985, through giving these banks a greater scope within collecting and allocating capital. Thus specialized banks were allowed to operate beyond their designated sectors. During the 1980s, besides the important role of four stated-owned banks (Big Four) played in the banking sector, the development of regional banks was also drawn a lot of attention as the new type of financial institutions in China. Regional banks were set up in the Special Economic Zones in coastal areas, which were partially owned by local governments. Later on, an increasing number of city commercial banks were established in the other areas across China.
Further revisions and reforms were introduced during the period of 1990s. It included the establishment of three policy banks in 1994, named China Development Bank, Agricultural Development Bank and China Export-import Bank. Policy banks took over the government-directed spending functions of “Big Four” banks and handled the financing of state-invested projects related to agriculture, infrastructure and trade development. It must be mentioned that the stock market (two domestic stock exchanges in Shanghai and Shenzhen: SHSE and SZSE) in China was formed in 1990, which was significant for the Chinese financial system and it has enjoyed fast growth as well. With the development of the stock market there were some joint-stock commercial banks (JSCBs) emerging in the banking industry and three out of four SOCBs have become state-owned joint-stock banks until now.
a higher amount of non-performing loans (NPLs). Especially for SOCBs, they took over a large fraction of NPLs because they used to make lots of lending decisions upon political or other non-economic reasons, which ultimately proved to be poor lending. The non-performing loan ratio (NPL ratio) of the SOCBs was 53% in the year 1997. Chinese government took a rescue action to tackle this problem by writing off bad loans or paying off outstanding debts. Four state-owned asset management companies (AMCs) were established in 1999. They endorsed US$ 60 billion to four state-owned banks separately from the Chinese government’s reserve invested in US. The NPL ratio was reduced to 31.5% in the year 2000 in terms of SOCBs (Ma 2006).
WTO entry in 2001 heralded a new stage of reform in the Chinese banking industry. Chinese financial institutions confronted increasing competition and opportunities. Nevertheless, due to the lack of efficient corporate governance, risk management and operational mechanism, the NPL ratio of SOCBs still took up 26.12% at the end of 2002 (Zhou 2004). It was mainly attributed to the authorities since whenever SOCBs confronted financial distress, the government’s bailout plans made them feel assured. Based on the support of the government, they could invest in any project with little consideration. While the injection plans could not prevent the new NPLs after liquidating the old NPLs. In 2003, the China Banking Regulatory Commission was established as a separate regulator to oversee the banking industry. With the new reform of Chinese banking sector from 2003 to 2006, Chinese government recognized the importance and responsibility in handling NPLs; therefore, it took active measures again by injecting foreign currency reserves into main state-owned banks in order to improve their capital base in preparation for going public (Allen et al. 2007). The authorities injected US$45 billion of reserves into BOC and PCBC and US$15 billion into ICBC during 2005 (China Banking Regulatory Commission). The reason for different amounts divided among the banks was not disclosed. Afterwards ICBC, BOC and PCBC all underwent the same process of becoming publicly listed and traded in either the Hong Kong Stock exchange (HKSE) and/or SHSE. After initial public offerings, they obtained sufficient capital and each had experienced dropping ratios of non-performing loans since listing.
In contrast to the other three SOCBs, ABC kept the old format1
1
Since the restructuring and recapitalization of the other three, with the non-performing loans and NPLs Ratio declined substantially, there is news updated that ABC’s IPO has been repeatedly delayed since 2006 to give the lender time to reform its management and balance sheet, which was dented by non-performing loans to the country’s rural economy. However, it is expected to push ahead with a listing in Shanghai and Hong Kong the summer of 2010. (Financial times 2010-4-7)
Recently, it has been admitted that Chinese government plays an important role in reducing the NPLs and improving the efficiency of the Chinese banking industry. To begin with, AMCs accumulated NPLs of Big Four banks and liquidated them by asset sales, resale of loans and securitization, etc. Moreover, the assistance to SOCBs in going public was also meaningful. Chinese banks restructured their balance sheets, improved capitalization, diversified earnings, reduced costs, and gradually improved corporate governance as well as risk management. The latest reform of SOCBs and development of the banking industry have already been effective in reducing NPLs, the NPL ratio had been falling from 53% in 1997 to 9% in 2006 (Shanker et al. 2008). It evidently appears that the efficiency of Chinese commercial banks has been increased and credit risk has been decreased during the last two decades. It seems that Chinese government is good at writing off excessive NPLs aiming to avert any serious problems. However, Allen et al. (2007) argue that we shouldn’t treat this issue optimistically. Due to the lack of objective data on NPLs treated as a strategic disclosure decision of the government, the accurate amount of NPLs is underestimated. They suggest the official figures on outstanding NPLs do not include the bad loans that have been transferred from banks to AMCs, with the purpose of AMCs liquidating these bad loans. It underlies that if adding back the NPLs held by AMCs, the overall NPLs will increase significantly. In addition, they indicate that the reform takes time to conduct so that new NPLs would keep arising in SOCBs. As mentioned above, we cannot deny the reduction of NPLs by the assistance of the government, but we should also objectively treat credit risk faced by the Chinese banking sector. Moreover we should reduce non-performing loans to a normal level by further reforms and prevent them from hindering the development of banks in China.
2.2 Bank efficiency
This paper focuses on the commercial banks since the evaluation of commercial banks is different with that of trust and investment companies or policy banks (Lardy et al. 1997). Currently Chinese commercial banks are mainly comprised of 4 large state-owned commercial banks
(SOCBs)2
2
Currently, state-owned commercial banks include the Industrial and Commercial Bank of China (ICBC), the Agricultural Bank of China (ABC), the Bank of China (BOC), the People’s Construction Bank of China (PCBC) and Bank of Communications (BOCOM), the big four SOCB used by various paper are ICBC, ABC, BOC, PCBC. This paper applies the Big Four the same with previous studies.
results are mixed and datasets used are relatively old, which shed little light on current efficiency levels.
Chen et al. (2005) consider 43 Chinese banks during the period from 1993 to 2000, they argue that the four major SOCBs are more cost-efficient than JSCBs, and CCBs show a relatively higher mean efficiency score after deregulation; in terms of bank size, the large and small banks are more efficient than the medium sized banks. While Hu et al. (2006) investigate 12 Chinese banks between 1996 and 2003; they suggest that JSCBs have higher efficiency relative to SOCBs. Although the overall efficiency has improved from 1996 to 2003, these twelve banks have lower cost and technical efficiencies after the WTO participation and lower cost efficiency after the 1997 Asian financial crisis. Fu and Heffernan (2007) examine 14 commercial banks from 1985 to 2002 and their findings support that SOCBs are less efficient than JSCBs. They also find that cost efficiency is higher during the first phase of bank reform. Furthermore, Kumbhakar and Wang (2007) analyze the impact of banking reforms on efficiency and find out JSCBs are more efficient than SOCBs between 1993 and 2002 as well. By examining bank efficiency of 28 developing nations, Berger et al. (2004) find that both domestic private banks and foreign banks are more efficient than state-owned banks. In the case of China, Berger et al. (2009) apply a parametric method to investigate the Chinese commercial banks from 1994 to 2003 and indicate that lower efficiency level of SOCBs than other counterparties. They also present higher efficiency associated with the increasing role of foreign ownership. Ariff and Can (2008) investigate cost and profit efficiency of 28 Chinese commercial banks between 1995 and 2004; they find profit efficiency levels are well below those of cost efficiency. Considering ownership and size, JSCBs appear to be more efficient than SOCBs on average and the medium-sized banks are significantly more efficient than the small and large banks, which contrasts with that of Chen et al. (2005).
2.3 Cost efficiency and credit risk
efficiency and (or) decrease credit risk. Nevertheless, which one of the two is more urgent to deal with should be determined by the clear relationship between these two factors. Ariff and Can (2008) investigate the impact of credit risk on efficiency by using loan loss provisions to gross loans as an indicator of credit risk; it appears that credit risk has negative impact on the efficiency of Chinese banks. There are some researchers examining the inter-temporal relationship between credit risk and cost efficiency in Europe and US (Berger and De Young 1997, Kwan and Eisenbeis 1997, Williams 2004, Rossi et al. 2005, Podpiera and Weill 2008, etc.). They suggest there is an impact of credit risk on cost efficiency predicted by “bad luck” and the causality from cost efficiency to credit risk explained by “bad management” and “skimping”, which will be discussed in the following paragraphs. Nevertheless, few literatures investigate the inter-temporal relationship between credit risk and cost efficiency in the case of China.
Applying the similar methodology of Berger and DeYoung (1997), there are some replicative studies described as follows. Williams (2004) carries a study on this issue in case of European banks from 1990 to 1998. The same with Berger and De Young (1997), he produces efficiency by SFA. In contrast with them, he calculates both cost efficiency and profit efficiency, and uses the ratio of loan loss provisions to total loans (LLR ratio) as a proxy of the loan quality instead of the NPL ratio. The results of this paper show that the decrease in cost efficiency and profit efficiency is related with the increase in LLR, which indicates the negative impact of efficiency on credit risk. This paper supports the bad management hypothesis. Moreover, Rossi et al. (2005) extend Williams (2004)’s work by examining banks of transition countries. However, to be different with the results of Williams (2004), they find that they could not reject the bad luck hypothesis indicating that the decreasing loan quality (higher level of LLR ratio) is related to the reductions in cost efficiency and profit efficiency. Podpiera and Weill (2008) investigate the bi-directional relationships between non-performing loans and cost efficiency as well, while they use the updated data of Czech banks between 1995 and 2002. Besides presenting the causality analysis, they aim to examine the factors which determine the banks’ failures. In terms of the methodology, they use non-performing loans as measurement of loan quality and apply SFA to obtain cost efficiency scores; furthermore they conduct the empirical research by employing GMM dynamic panel estimators. They conclude that the reduction in cost efficiency precedes the increase in non-performing loans, which confirms the bad management hypothesis.
of the environment variables. Bad loans are mostly attributed to internal factors. The findings support the bad management hypothesis.
We estimate Chinese commercial banks as an extended test of previous studies and aim to add some evidence on basis of the emerging banking market experience. This paper follows the framework proposed by Berger and DeYoung (1997) with certain adjustments suitable for Chinese commercial banks. This study only examines the first three hypotheses because our objective is to explain the relationship between cost efficiency and credit risk. Cost efficiency scores are estimated by the non-parametric method–DEA, which differentiates from previous papers. In addition, credit risk measures the loan quality of banks, which is defined by the ratio of non-performing loans to total loans.
2.4 Hypotheses:
Since the relationship between cost efficiency and credit risk is expected to be bi-directional, this paper will test three hypotheses described as follows.
Hypothesis 1: Credit risk has a significant negative impact on cost efficiency for Chinese commercial banks. (Bad luck hypothesis)
The bad luck hypothesis predicts that external resources would increase credit risk of Chinese commercial banks. Since problem loans could arise from external events (adverse economic circumstances, the stability of financial market, etc.) beyond the confines of management control, it would result in higher operating costs to recover problem loans. This conduct could correspondingly hamper cost efficiency of banks. Under the discussions of Berger and DeYoung (1997), the costs come from monitoring and controlling the quality of borrowers, the value of collateral and the related cost of default. Consequently, this hypothesis predicts that the increase in credit risk causes the reduction in cost efficiency.
Hypothesis 2a: Cost efficiency has a significant negative impact on credit risk for Chinese commercial banks. (Bad management hypothesis)
The bad management hypothesis considers the inefficiency of banks signals the poor management who may not effectively oversee loan applications. Since the low efficiency is assumed to be related with poor internal cost control and the doubtable capability to evaluate and monitor loans, it leads to an increase of problem loans. Under this hypothesis, therefore, the reduction in cost efficiency precedes the increase in credit risk. The skimping hypothesis is contrast to the bad management hypothesis, which assumes that more efficient banks are more likely to engage in skimping behavior. It indicates the resources spent on monitoring loans would have an influence on credit risk and cost efficiency simultaneously. There is a trade-off between the short-term profit and the long-term non-performing loans. Bank managers reduce the short-term operating cost in order to generate profit. Regardless of the problem of bringing problem loans, they reduce resource allocations of loan applications. Therefore, there is an illusion that banks are cost-efficient in the short-term, while it would accumulate non-performing loans in the future.
This paper proposes that the bad management hypothesis dominates the skimping hypothesis in our sample. Since bad management practices are generally more common in transition countries, they are manifested not only in excess expenditures, but also in subpar underwriting and monitoring practices that eventually lead to NPLs. Furthermore, the skimping hypothesis has a typical implication that skimping is a long-run strategy and the measure of the efficiency is more appropriate by using several years of data. However, our data has a relatively small time span.
3. Methodology
In order to analyze the inter-temporal relationship between cost efficiency and credit risk for Chinese commercial banks, DEA is applied to measure cost efficiency of the sample banks. Afterwards, the GMM dynamic panel data estimator is adopted to examine whether and how cost efficiency and credit risk affect each other.
3.1 The measurement of cost efficiency by DEA model
biased efficiency measurement when the shape of the frontier is not correctly specified. On the contrary, DEA serves as a non-parametric estimator providing linear combinations connecting a set of best observations that yields a best-practice frontier. In summary, DEA has some advantages as follows. Firstly, it does not need to specify the functional form. Furthermore, it does not need any assumptions about the distribution of efficiency scores. Thirdly, DEA is more appropriate with relatively small sample size while handling multiple inputs and outputs. Unfortunately, DEA does not take data errors into account.
Chen et al. (2005) suggest that DEA is suitable for estimating cost efficiency in the case of China. They believe if the sample size is small, DEA is better to measure how well a bank performs corresponding to the best predicted performance of the banking sector. Ariff and Can (2008) confirm that DEA is more relevant when analyzing the efficiency of Chinese banks, since DEA works well with a small sample size while there is lack of the knowledge on the functional form of the frontier. Therefore, this paper applies a more appropriate estimator–DEA to Chinese commercial banks.
3.1.1 The selection of inputs and outputs
There are generally two approaches of determining inputs and outputs based on the role of a bank. One is the production model: banks act as regular corporations to run the operations that generate deposits and loans by capital and labor (Chen et al. 2005, Heffernan & Fu 2005, Berger and DeYong 1997, Berger et al. 2009). The other is the intermediation model: banks play a role of intermediary institutions using labor and capital to transform deposits into loans (Ariff & Can 2008, Hu et al. 2006, Podpiera & Weill 2008). Table 1 summarizes the literatures that apply the frontier analysis to estimate bank efficiencies. Because of the data availability, this paper applies the intermediation approach. Moreover, there are some researchers taking risk into account when calculating cost efficiency. They adjust outputs by risk factors. However, it is irrelevant for this paper since the objective is to measure cost efficiency without adjustment of risk factors in order to test the bad luck hypothesis (NPL is exogenous) and the bad management hypothesis or the skimping hypothesis (NPL is endogenous).
Since they investigate the major banks in China, the comprehensive and detailed information could be retrieved for all the banks over their investigation period.
Table 1: literature overview in parametric and non-parametric models on bank efficiency
Authors Sample Methodology Outputs Inputs
Chen et al. (2005)
China 1993-2000
DEA Loans, deposits and non-interest income
Interest expenses, non-interest expenses Ariff & Can
(2008)
China 1995-2004
DEA Loans, investments Borrowed funds, labor, capital
Hu et al. (2006)
China 1996-2003
DEA Investment s and lending Borrowed funds, labor, capital
Heffernan &Fu (2005)
China 1985-2002
SFA Total deposits, total loans, investments, non-interest income
Borrowed funds, labor, fixed assets
Berger et al. (2009)
China 1994-2003
SFA Total loans, total deposits, liquid assets, other earning assets
Interest expenses, non-interest expenses
Berger &DeYong (1997)
U.S. 1985-1994
SFA Commercial, consumer and real estate loans, transactions deposits, fee-based income
Labor and capital
Podpiera & Weill (2008)
Czech 1994-2005
SFA Total loans, and investment assets
Borrowed funds, labor, capital
For our examination, we also apply the intermediation approach which assumes that the bank collects deposits and transforms them into loans and investments by using labor and capital. Two outputs are included: total loans and total securities. Total securities represent investment assets. The inputs consist of borrowed funds, fixed assets and the number of employees. The inputs prices include funding, capital and labor price. The outputs, inputs and input prices are detailed as follows in table 2.
Table 2: Outputs and inputs prices of DEA model
Outputs Inputs Input prices
y1 : Total loans
y2 : Total securities
x1: Borrowed funds
w1: Price of borrowed funds
=interest expenses / total deposits(x1) x2: Fixed assets w2: Price of fixed assets
= operating expenses / fixed assets (x2)
x3: Number of employees w3: Price of labor
= personnel expenses / number of employees (x3)
3.1.2. DEA model
serving industry. DEA can calculate scores for technical efficiency (TE), allocative efficiency (AE) and cost efficiency (CE). Technical efficiency refers to producing a given set of outputs using the smallest number of inputs; allocative efficiency indicates minimizing the cost of producing outputs by proper selection of inputs set. The details of the efficiency theory are presented in the Appendix. Laurenceson and Qin (2008) suggest that the decision making unit (DMU) is cost efficient if it is both technically and allocatively efficient. Hence, cost efficiency is the encompassing efficiency measure and could be the ultimate determinant of the competitiveness of a bank. Cost efficiency is measured by how close the certain firm’s cost next to the best-practice firms in terms of the same amount of outputs, output prices and input prices. Following this argument, this paper applies cost efficiency as bank efficiency measurement.
After specifying the inputs and outputs, it is necessary to choose a specific DEA model. Considering the formulation of DEA model, in general, the choice is determined by the implicit returns-to-scale (RTS) properties including CRS and VRS. This study will estimate cost efficiency of banks by using a model which assumes a variable return to scale (VRS). However, our starting point is a model with constant returns to scale (CRS) and then we extend it to allow for VRS. CRS and VRS are economic concepts. CRS means the same additional amount of inputs will produce the same proportional additional amount of outputs, whereas in the case of VRS, the proportion might change.
In terms of CRS technology, the linear programming method establishes the envelopment surfaces (referred to production function or efficient frontier) determined by the DMUs. The benchmark frontier is formed by connecting the set of best practice observations, which is a linear combination of efficient banks in the sample. DEA provides a computational analysis of the relative efficiency for multiple inputs or outputs situations through evaluating each DMU and measuring its performance relative to the envelopment composed of best practice units.
We assume that there are K inputs and M outputs for each of N banks (
i
=1, 2…..N). For eachDMU, the inputs and outputs are represented by vectors X and Y respectively (K*N is the input matrix X and M*N is the output matrix Y). Coelli et al. (1998) suggest
w
i is a vector of weightsfor th
i DMU and *
i
x is the cost-minimizing vector of input quantities for the th
i DMU, given the
∗ i i x
w
x
Min
i ' , λ Subject to:−
y
i+
Y
λ
≥
0
,
x
i∗−
X
λ
≥
0
,
λ
≥
0
The total cost efficiency (CE) for the
i
thDMU would be calculated as:i i i i
x
w
x
w
CE
∗ ∗=
'
(1)Where λ is an N by 1 vector of constants, ∗
i ix
w' is the minimum cost by preference weights. And
the denominator wi∗xi is the actual cost observed. Note that the cost efficiency cannot lie outside the feasible set that ranges between zero and one. If the cost efficiency equals one, it indicates the best-practice bank in the sample and the location of that bank is on the efficiency frontier.
The above approach is simplified as the assumption of CRS in order to control the size diversity in the sample. However, CRS assumption is only valid when all DMUs are operating at an optimal scale. There are several factors that may cause the banks not operating at an optimal scale, such as imperfect competition, leverage concerns and so on. Banker et al. (1984) suggest an extension of the CRS-DEA model to account for a variable return to scale. They add a convexity constraint
N
1
λ
'
=
1
to the above equation system, where N1 is an N by 1 vector of ones. This extra constraint ensures that an inefficient bank is locating on the benchmark envelopment against similar sized banks.Cost efficiency will be estimated by running the following cost minimization VRS-DEA model3
∗ i i x
w
x
Min
i ' , λ : Subject to:−
y
i+
Y
λ
≥
0
,
x
i∗−
X
λ
≥
0
,
λ
≥
0
,
N
1
λ
'
=
1
andi i i i
x
w
x
w
CE
∗ ∗=
'
(2) In view of previous studies for the Chinese banking industry, Hu et al. (2006) argue that not all the firms are operating at the optimal scale so that variable-returns-to-scale situations should be accounted for. Since the Chinese financial system is currently dominated by a large but under-developed banking system (Allen et al. 2007), perfect competition is unlikely. Thus this paper opts for the VRS-DEA model, in which VRS property loses the implicit assumption that all DMUs are operating at an optimal scale, as assumed by CRS.When estimating the VRS-DEA model, we pooled the data to calculate the cost efficiency scores. Dealing with the whole data to estimate cost efficiency is due to the limitation of our dataset. We could not calculate the cost efficiency for each bank on yearly basis since there are several banks with omitted data for certain years which might cause the incorrectly estimation of the efficient
3
frontier. In order to solve the problem, we assume the technology level of each bank is constant overtime, and then we pool the data of banks year by year to estimate the benchmark envelopment as a whole, finally the efficiency scores are obtained.
3.2 Econometric Model
For the main variables used in the econometric model, cost efficiency scores are obtained by the previous estimation applying DEA. Generally speaking, the Tobit model is superior in this case since efficiency scores lie between zero and one. However, McDonald (2009) presents the argument that goes against the use of Tobit model to efficiency scores. He argues that efficiency scores, in nature, are not censored data, but fractional data. In addition, efficiency scores do not equal to zero as long as there is at least one input to use. It is equivalent to the violation of the assumption of Tobit model, which error terms in Tobit model are compulsory to have a normal, identical and independent distribution. Any violation to the assumption of error terms leads to bias and inconsistent estimation. Therefore, this paper applies the GMM dynamic panel model estimator that could be appropriate on the basis of the argumentation mentioned above. In terms of credit risk, there are two ways of measurement applied by the scholars, which include the ratio of non-performing loans to total loans (NPL ratio) and the ratio of provision loss loans to total loans (PLL ratio). Comparing these two methods, some researchers argue that PLL ratio is affected by the management involvement. Since our second hypothesis aims to test the management performance, it is more appropriate to use NPL ratio as an indicator of credit risk to avoid the influence of management quality.
take common structure presenting in the series into account. Thus they develop the standard GMM estimator which is widely applied further on.
There are several advantages of applying the GMM estimator. Firstly, it is more efficient to grasp the unbalanced panel data structure. Secondly, GMM panel data model has the capacity to remove bank specific effects. Thirdly, it is still sufficient when there is short time series data. This paper extends the framework of Berger and DeYoung (1997) to explain inter-temporal relationship between cost efficiency and credit risk. In contrast to Berger and DeYoung (1997)’s estimation with OLS, we use the GMM dynamic panel model to estimate the equations separately, which is similar with the approach of Podpiera and Weill (2008). Since our sample just covers eight years and there are still a certain amount of omitted variables, then a compromise with our case is to use GMM panel data estimators in order to give more efficient estimation.
We specify a 2-year lag model. Our choice is motivated by the considerations as follows. The small sample of Chinese commercial banks is tested in this paper. Furthermore, the short time span and the omitting observations for certain individual banks of the investigation period are obvious for our dataset. These two facts limit the number of lags. Although the Berger and DeYoung (1997) suggest that three- and four- year lags model did not differ a lot with each other and Williams (2004) mention the European case was sensitive to the lag length, both studies show that the three-year lags models are more optimal. We admit the fact that a reasonably high number of lags are more helpful to fully capture the influences of cost efficiency (credit risk) on credit risk (cost efficiency). Nevertheless, we have to opt for two-year lags based on our dataset.
Equation 1 tests the bad luck hypothesis. Equation 2 tests the bad management hypothesis or the skimping hypothesis, which suggests a negative or a positive relationship between the two variables respectively. t i t i t i t i t i t i
CE
CE
NPL
NPL
CE
,=
α
1 ,−1+
α
2 ,−2+
β
1 ,−1+
β
2 ,−2+
ε
, (3) t i t i t i t i t i t iNPL
NPL
CE
CE
NPL
,=
α
3 ,−1+
α
4 ,−1+
β
3 ,−1+
β
4 ,−2+
ε
, (4) Where CEi,t is the cost efficiency of bank i in yeart. CEi,t−1 and CEi,t−2are the first and second lags of CE.t i
1
α ,α2,α3,α4and β1,β2,β3,β4 are the coefficients.
ε
i,t is the system error. The error term include thetwo parts, one part measures the bank-specific effect that captures the systematic differences across banks and the other part is the i.i.d. random error.
This paper emphasizes the association of a pair of variables. Therefore, compared with the framework of Berger and DeYoung (1997), we reduce three equations by eliminating capitalization; the two equations mentioned above are formulated for the causality analysis. The reduction of the equations is based on two considerations. Firstly, this paper aims to investigate the inter-temporal relationship between credit risk and cost efficiency. Capitalization is not in the research area of this paper. In addition, compared with the previous studies, our sample size is small; it makes the number of terms in the equations to be limited.
In terms of GMM model, taking first differences is a standard and widely applied practice to eliminate the correlated individual specific effects in dynamic panel data models. Then it commonly uses appropriately lagged level variables as the instruments to estimate the differenced model by GMM. However, since the information of instruments for the differenced model decreases as the series becoming more persistent, Arellano and Bover (1995) propose the use of system GMM estimator that combines the differenced equation with the level equation, which is more appropriate. Blundell and Bond (1998) also suggest that weak instruments could cause large small sample bias when we use the first differenced GMM procedure to estimate autoregressive models for moderately persistent series from short panels. They propose that the system GMM has superior properties in terms of finite-sample bias. Based on the overview of literature above, we use the system GMM for handling cross-section fixed effects.
4. Data
The whole dataset contains the information on the variables of balance sheets, income statements and other specified disclosed information of 49 Chinese commercial banks during the period from 2001 to 2008. It consists of 4 SOCBs, 11 JSCBs and 34 CCBs, total 258 observations. The main source for bank specific information is the BankScope Database. Whenever BankScope doesn't provide enough information or there are some questionable values, we collect and double check the data from other official sources such as annual report of commercial banks. All nominal data was converted to real terms using the GDP deflator.
This paper excludes the rural commercial banks and other financial institutions since they occupy comparably fewer assets among the banking industry relative to our sample. We also exclude policy banks and International trust and investment corporations since these financial institutions have different functions, and they are overseen under different regulations in comparison with commercial banks. Therefore, the sample is comprised of 49 commercial banks that occupied the majority assets among Chinese banking industry.
The investigation period and the sample are chosen primarily because of the data availability, which the Chinese commercial banks data is insufficiently disclosed to the public. Furthermore, China’s entry into the WTO in 2001 marked the beginning of a new era. Between 2001 and 2008, Chinese banking sector had recovered from the Asian financial crisis of 1997 and was not completely influenced by the global financial crisis occurred around 2008. We assume that the sample used in this paper could not be affected by financial crises so that it can objectively investigate the inter-temporal relationship between cost efficiency and credit risk.
force supply makes the labor force relatively cheap in China. From Panel B, the inputs and outputs show the tendency of increase from 2001 to 2008, along with the gradual development of the Chinese banking industry and new entrants into Chinese commercial banks. For the funding price and capital price, there is a small amount of increase during the 8 year-period. On the contrary, labor price exhibits the decreasing tendency across this period.
Table 3: Descriptive statistics for variables used for calculating the cost efficiency scores
Outputs, inputs and input prices : Panel A
Loan Security Deposit
Fixed asset Employee number Funding price Capital price Labor price Mean 423378 233143 693454 10778 33982 0.0239 0.742 0.164 Maximum 4425280 3205977 8710492 112641 441883 0.1789 2.959 0.456 Minimum 2359 2839.5 1508.7 5033 1890 0.0057 0.127 0.053 Std. Dev. 869436 559425 1488289 23664 84387 0.0172 0.363 0.066
Outputs, inputs and input prices : Panel B
2001 2002 2003 2004 2005 2006 2007 2008 Loan 113242 78244 159328 96961 140550 1534868 1631769 2688877 Security 40462 25544 43136 38215 78006 759086 730273 988391 Deposit 162823 128102 258218 159991 236088 2529986 2908079 3901248 Fixed asset 2192 1959 4826 4113 5077 60356 65475 64616 Employee no. 5023 3237 7996 5743 8789 95478 107754 187657 Funding price 0.016 0.016 0.021 0.018 0.017 0.017 0.028 0.022 Capital price 0.48 0.40 0.50 0.58 0.58 0.35 0.24 0.60 Labor price 0.18 0.15 0.16 0.21 0.16 0.11 0.09 0.10
Table 4: Descriptive statistics for variables used for the GMM dynamic panel data model
Panel A: Cross-sectional Overall SOCB JSCB CCB CE 0,74 (0,18) 0,81 (0,12) 0,81 (0,14) 0,69 (0,20) NPL 0,07 (0,10) 0,14 (0,11) 0,06 (0,06) 0,06 (0,12) Observations 258 30 80 148 Panel B: Time-series 2001 2002 2003 2004 2005 2006 2007 2008 CE 0,66 (0,11) 0,74 (0,14) 0,75 (0,17) 0,71 (0,17) 0,69 (0,22) 0,75 (0,17) 0,77 (0,20) 0,83 (0,16) NPL 0,13 (0,09) 0,14 (0,09) 0,14 (0,20) 0,11 (0,17) 0,06 (0,04) 0,04 (0,04 0,03 (0,02) 0,02 (0,01) Observations 14 19 24 34 44 48 47 28
high as 18%, indicating substantial differences among the banks in our sample. Falling in the same category of individual banks, SOCBs and JSCBs generally have the same mean cost efficiency scores with a little bit higher variation for JSCBs. However, the CCBs have lower cost efficiency but exhibit higher variability among the sub-samples. The comparison among different categories of Chinese commercial banks is inconsistent with the previous studies as there is almost the same cost efficiency for SOCBs and JSCBs. For the non-performing loan ratio, it indicates the mean ratio of NPL is 7% with greater variation of 10%. Among the different types of ownership in Chinese commercial banks, SOCBs are characterized with relatively high NPL ratio of 14%, which is consistent with the situation of the banking industry in China, more than twice as those of JSCBs or CCBs. During the years after the WTO entry, interesting features of the dataset are the increase of cost efficiency scores and the decrease of the NPL ratio, which are corresponding to the substantial changes in the cost efficiency and small variations of the NPL ratio. It is worthwhile to mention that the NPL ratio of either 2001 or 2003 is seven times more than that of the year 2008.
5. Empirical results
Equations (3) and (4) are estimated for Chinese commercial banks using the data from 2001 to 2008. The estimation follows the GMM dynamic panel data model which could grasp the panel data structure and yield consistent estimates. Based on previous literature and the feature of our sample, we distribute the equal lags for both specifications and then make independent estimation for each equation. The behavior of the Chinese banking industry is determined by a significant relationship between the dependent variable and the lagged coefficients of the explanatory variables. Subsequently, we re-estimate the equations for different categories of Chinese commercial banks4. Table 5 and Table 6 display the results for the inter-temporal relationship between cost efficiency (CE) and credit risk (NPL) in terms of the overall sample and sub-samples. The diagnostics of all estimations comprise a Sargan test on over-identifying restrictions. As we can see from the results displayed in the last row of table 5-8, the reported J-statistic is simply the Sargan statistic. By using it to construct the Sargan test of over-identifying restriction5
4
Due to the data limitation, the “Big Four” state-owned banks are insufficient to estimate using GMM panel model. This paper just presents the results of the JSCBs and CCBs.
, it never rejects the validity of the instruments.
5
Table 5: The result of the GMM estimation for cost efficiency as the dependent variable
GMM dynamic panel model estimates in cost efficiency Equation (3)
Overall sample JSCB CCB CE(t-1) 0.21 (0.226) 0.647 (0.456) 0.763*** (0.263) CE(t-2) 0.56** (0.275) 0.871* (0.497) -0.273 (0.255) NPL(t-1) -0.104*** (0.038) 0.741 (0.804) -0.003 (0.103) NPL(t-2) -0.105** (0.051) -1.115** (0.505) -0.131 (0.099) Year2004 0.053 (0.036) 0.182* (0.104) -0.069* (0.035) Year2005 0.009 (0.026) 0.051 (0.069) -0.012 (0.029) Year2006 0.013 (0.019) 0.041 (0.054) 0.015 (0.036) Year2007 0.009 (0.018) 0.069 (0.048) 0.061 (0.049) Year2008 0.031** (0.013) 0.037* (0.02) 0.048 (0.033)
Total panel (unbalanced) observations 108 47 46
Periods included 5 5 5
Cross-sections included 34 11 21
Instrument rank 14 11 12
J-statistic 9.287.930 0.364100 3.252.474
The set of instruments comprise of dynamic and level instruments, which are lagged dependent and independent variables from 3 up to the lag 4 for each period and untransformed period dummies. The table reports coefficients with standard errors in parentheses. (*), (**), (***) denote estimates significantly different from zero at the 10%, 5% and 1% levels, respectively.
increase in NPLs causes the decrease in cost efficiency, which indicates that Chinese commercial banks suffer from bad luck. Consequently, the strong statistical evidence is found which shows that an increase in credit risk causes a decrease in cost efficiency.
Table 6: The result of the GMM estimation for NPL as the dependent variable
GMM dynamic panel model estimates in cost efficiency Equation (4)
Overall sample JSCB CCB NPL(t-1) 0.153 (0.13) 0.579 (0.059) 0.109 (0.107) NPL(t-2) 0.028 (0.118) -0.172 (0.077) -0.001 (0.068) CE(t-1) 0.124 (0.084) -0.019 (0.023) 0.019 (0.045) CE(t-2) 0.049 (0.076) 0.077 (0.049) 0.01 (0.030) Year2004 0.028* (0.011) 0.016 (0.01) 0.011 (0.008) Year2005 0.036*** (0.021) 0.028** (0.012) 0.031*** (0.007) Year2006 0.043** (0.015) 0.008* (0.005) 0.012* (0.007) Year2007 0.015** (0.007) 0.015* (0.007) 0.009** (0.003) Year2008 0.007 (0.005) 0.009* (0.004) 0.001 (0.003) Total panel (unbalanced)
observations 108 47 46
Periods included 5 5 5
Cross-sections included 34 11 21
Instrument rank 14 11 12
J-statistic 4.346 2.029 5.529
The set of instruments comprise of dynamic and level instruments, which are lagged dependent and independent variables from 3 up to the lag 4 for each period and untransformed period dummies. The table reports coefficients with standard errors in parentheses. (*), (**), (***) denote estimates significantly different from zero at the 10%, 5% and 1% levels, respectively.
efficiency variables are all insignificant, the signs of the coefficients are positive. Overall, the NPL equation could not give a conclusion upon whether the bad management hypothesis dominates the skimping hypothesis for the data set as a whole or vice versa.
Separate estimations of Equations (3) and (4) were carried out for the different types of commercial banks in this paper. Because there are just 4 SOCBs in China, it is insufficient to run the GMM estimation. Therefore, we just examine JSCBs and CCBs. However, the statistical relationships are relatively weak. From table 5, there is some evidence that the second lagged NPL is negatively significant at 5% level. It suggests that the increase in credit risk causes the decrease in cost efficiency. We find the weak negative relationship between cost efficiency and credit risk, which implies that the bad luck hypothesis cannot be rejected for JSCBs. For CCBs, the signs of the coefficients on lagged NPL are all negative, but there are no statistical relationships among them. Table 6 shows the results of sub-sample tests of the Equation (4), all the lagged coefficients on the explanatory variables are statistically insignificant. Considering the signs of the coefficients, JSCBs present mixed results among two lagged values, while CCBs exhibit the positive sign the same as the overall sample. For Chinese commercial banks at a different bank-type level, the estimation of inter-temporal relationship between cost efficiency and credit risk gives no evidence to support neither the bad management hypothesis nor the skimping hypothesis. And there is some weak evidence for JSCBs to support the bad luck
hypothesis.
In summary, the data suggests that the inter-temporal relationship between cost efficiency and the NPL ratio (an indicator of credit risk) does not run in both directions for Chinese commercial banks during the period from 2001 to 2008. Our results support the bad luck hypothesis, which predicts that when loans become past due or non-accruing, the related operating costs increase because of the difficulties in dealing with problem loans. There is no evidence of the bad management hypothesis as the relationship between the NPL ratio and the lagged values of cost efficiency is positive but insignificant. Chinese commercial banks also do not show any evidence that the reduced cost efficiency will foster an increase in the NPL ratio tested by the skimping hypothesis. In the other words, our findings give no statistical support for the bad management hypothesis or the skimping hypothesis.
hypothesis in European transition economies. The evidence from Chinese commercial banks is partially consistent with Berger and DeYoung (1997) that support the causality from non-performing loans to cost efficiency and does not support that cost efficiency is granger cause of non-performing loans. However, the findings are inconsistent with William (2004) and Podpiera and Weill (2008) who support the bad management hypothesis. The different results of this paper with the previous studies might be caused by the difference of the sample countries, the use of the Bankscope data and the different proxies for credit risk.
6. Robustness test
To begin with, we transform the cost efficiency scores estimated by the VRS-DEA model into the CRS-DEA model. The findings of the bad luck hypothesis are robust to the change of efficiency measures. As presented in table 7, when we estimate cost efficiency by the CRS technique instead of the VRS model as the efficiency measure, the relationship between cost efficiency and the lagged non-performing loan ratio has a negative sign; the first and second lags of NPL are all significant at 5% and 1% level, respectively. Changing the technique of cost efficiency measure does not yield any significant evidence for the estimation of Equation (4). There are still positive but insignificant coefficients on lagged cost efficiency, which implies that the bad management hypothesis or the skimping behavior is irrelevant of the measurement of cost efficiency as well.
Table 7: The result of the GMM estimation for Equation (3) and (4), where cost efficiency is estimated by the CRS-DEA model
Equation (3) CECRS Equation (4) NPL
CECRS(-1) 0.539 (0.288) 0.103 (0.091) CECRS(-2) 0.579 (0.367) 0.013 (0.022) NPL(-1) -0.093** (0.036) 0.421 (0.269) NPL(-2) -0.189*** (0.052) -0.176 (0.159) Year2004 0.085 (0.059) 0.029** (0.014) Year2005 0.014 (0.031) 0.044*** (0.012) Year2006 0.042* (0.023) 0.015* (0.009) Year2007 0.036 (0.024) 0.016*** (0.004) Year2008 0.082*** (0.027) 0.005 (0.004) Total panel (unbalanced)
observations 111 111
Periods included 5 5
Cross-sections included 36 36
Instrument rank 14 14
J-statistic 5.183 2.743
The set of instruments comprise of dynamic and level instruments, which are lagged dependent and independent variables from 3 up to the lag 4 for each period and untransformed period dummies. The table reports coefficients with standard errors in parentheses. (*), (**), (***) denote estimates significantly different from zero at the 10%, 5% and 1% levels, respectively. CECRS is short for cost efficiency scores calculated by CRS-DEA model.
Table 8: Robustness tests for the optimal number of lags
Number of lags on right-hand-side of model
1 lag 2 lags 3 lags
Equation(3) Bad luck NPL(t-1) -0.095** (0.038) -0.104*** (0.038) -0.778 (0.683) NPL(t-2) -0.10494** (0.051) -0.014 (0.056) NPL(t-3) -0.023 (0.071) Equation(4) Bad management versus Skimping CE(t-1) 0.098 (0.067) 0.124 (0.084) -0.089 (0.095) CE(t-2) 0.049 (0.076) 0.128 (0.102) CE(t-3) -0.009 (0.025)
7. Conclusion and implications
This paper applies GMM dynamic panel estimators to investigate the inter-temporal relationship between cost efficiency and credit risk for 49 Chinese commercial banks between 2001 and 2008. The identification of the causality among these two factors could offer some inference of the bank behavior of the Chinese banking industry. The results of this research have provided some evidence upon the association of cost efficiency and credit risk from the emerging banking market experience.
The causality analysis of this paper supports the bad luck hypothesis. The results provide the statistical evidence that credit risk has a significant negative impact on cost efficiency for Chinese commercial banks, which suggests the exogeneity of nonperforming loans triggers the inefficiency of Chinese banking industry. It underlines that bank managers spend more time on monitoring and handling problem loans due to the high non-performing loans level; therefore they possibly pay more attention to administer the loan quality and reduce the diligence in cost efficiency management. We find no evidence of the bad management hypothesis or the skimping hypothesis. Therefore, we could not conclude that either the poor managed bank tends to have more problem loans or Chinese banking managers characterized as the skimping behavior. For the sub-samples categorized by different types of Chinese commercial banks, JSCBs provide some evidence that there is an inverse relationship between credit risk and cost efficiency supporting the bad luck hypothesis. Moreover, the remaining findings of sub-samples do not yield any significant evidence in favor of our main hypotheses. By conducting the robustness tests, the results are robust to the change of efficiency measures. Moreover, the overall sample is insensitive to the number of lags.
obtained the data of several banks for a shorter time span, which would influence on the cost efficiency estimation and the number of lags included in the econometric model.
There are some implications based on the results of this paper. Since our data provides the obvious evidence of the bad luck hypothesis which suggests that the high level of credit risk is generated by external events such as financial shocks, environmental conditions, the level of national stability, etc. Those events attribute to the decrease in cost efficiency. In terms of implications for economic or regulatory policy for Chinese commercial banks, the evidence underlines that bank inefficiency in the Chinese financial market is primarily related to external factors in lieu of internal factors (inside management control). For banks regulators, supervisors and managers, they should adopt more sophisticated measures of bank performance via controlling the banks’ exposures to external events. For instance, they could reduce banks’ exposure to the uncontrollable events by increasing the diversification of loan portfolios, the application of new risk management skills and the promotion of foreign ownership or mergers, etc. In addition, since the deterioration of cost efficiency recorded in Chinese commercial banks could be partially ascribed to credit risk; when measuring the cost efficiency, perhaps we had better to consider the controllability of non-performing loans so that cost efficiency would be improved by removing the costs caused by bad luck rather than managerial inefficiency.
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Appendix:
The theory of efficiency
Measuring the performance of firms involves converting inputs (capital, labor, etc.) into outputs (goods, services, etc.). One of the superior measurements of the performance of the firms is efficiency. Debreu (1951) defines the efficiency as the degree to which the use of the inputs to produce the outputs matches the optimal use of the inputs to produce the outputs. Farrell (1957) used an empirical example of the efficiency in the agricultural sector to show how distance functions can be used in a practical way. Farrell (1957) is viewed as the originator of microeconomic efficiency measurement. He proposes that the productive efficiency of any firm consisting of two components: technical efficiency and allocative efficiency. Technical efficiency reflects the firm’s ability to achieve maximal outputs from a given set of inputs. While allocative efficiency can be measured by the use of inputs in optimal proportion if information on prices is available, that is to say, allocative efficiency reflects the position at which the firm selects the inputs to produce a given set of outputs at minimum cost (the input prices are given). Farell (1957) suggested that production or cost efficiency can be measured empirically against the idealized frontier isoquant. The technical efficiency can be combined with allocative efficiency to measure cost efficiency and profit efficiency. If prices are taken into account, the equilibrium of cost minimization or profit maximization suggests efficiency achievement.
over OR. OP is smaller or equal to OR, so the ratio is smaller or equal to one, where one means fully cost efficient.
In the same vein, measure the efficiency from the perspective of the output orientation. Assume that a single input (x) is available to produce two outputs (y1 and y2). In figure 1b, the isoquant ZZ’ represents the production frontier. Output-orientated technical efficiency is equal to the ratio 0A/0B. If prices of these outputs are given as P3 and P4, one can obtain the line DD’ using the price ratio, every point on this line generates the same amount of profit. The production curve ZZ’ is tangent by the line DD’ at point B’ implying profit efficiency Suppose the producer fails in setting the production to B’ instead of B. the producer is still technical efficient while the allocation of the outputs is inefficient. Similar to the discussion mentioned above, point C which has the same proportion of y1/ x and y2/ x is still located on the line DD’. AE is measured by the ratio of 0B/0C. TE and AE could be combined to measure Profit efficiency (PE) by multiplying output oriented TE and AE.
