Chapter 2 An Extension from Network DEA to Copula-Based Network SFA
2.6 Conclusion
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In sum, Table 1.6 and Figure 1.1 present that the mean TE is sensitive to different values of
1 and
2, depends on the presence of
, and varies with the assumptionof a single stage or multiple production stages. If
1 and
2 are given incorrect values, then the resulting TE score tends to be misleading. This suggests that the fractional parameters should be either given directly on the grounds of disaggregated data or estimated by an appropriate econometric model like the one proposed by this article. In addition, employing the copula method is necessary since it is able to account for the dependence between the production frontier and the cost frontier, characterizing the two production processes of banks.2.6 Conclusion
This essay extends the network DEA model to a copula-based network SFA model that embodies multi-stage production processes for banks under the framework of simultaneous equations. These equations are derived from economic models under the assumption of output maximization in the first stage and cost minimization in the second stage. Our model allows for correlated composite errors, which arise from two subunits of a bank that are connected in series by intermediate outputs and reflect the joint decision making for the two subunits made by bank managers. In this manner, the entire production process is no longer treated as a “black box”, as previous studies did, and the efficiency measures of different subsectors can be respectively estimated. More importantly, the fractional parameters are not required to be known, a priori, but rather can be estimated using aggregated, instead of disaggregated, data of firms - a salient feature of our model. The theoretical model can be transformed into an econometric model, consisting of 4 simultaneous equations, for the purpose of identifying the
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additional fractional parameters.
In the empirical study, deposits are treated as an intermediate output produced in the first production stage and described by the translog production frontier that is a function of some portions of labor and capital, rather than the entire employment of both inputs. This intermediate output is next viewed as an input in the second production stage, together with the remaining portions of labor and capital, to produce loans, investments, and non-interest incomes, in the context of the translog cost frontier.
Under the copula-based network SFA framework, the fractional parameters of the two inputs involved in the first stage can be estimated by relying on additional information from the cost share equations. The resulting simultaneous equations, formed by a stochastic production frontier, a stochastic cost frontier, and two cost share equations, can be consistently estimated by the ML whose likelihood function is derived by the copula methods of Lai and Huang (2013). This allows for estimating the mutual dependence among equations.
Adopting the idea of a two-step procedure, which is in essence similar to Kumbhakar and Lovell (2000), we successfully solve the convergence problem specifically for a highly non-linear simultaneous equations model. To justify this procedure, we conduct Monte Carlo simulations to show the consistency of the parameter estimates. The efficiency score of each subsector and the fractional parameters can then be assessed and identified. The knowledge of the technical efficiencies in and the resources’ allocation among different stages provides detailed information to regulatory authorities, bank managers, and industry consultants, concerning the effects of mergers and acquisitions, capital regulations, deregulation of deposit rates, removal of geographic restrictions on branching and holding company
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acquisitions, etc. on bank performance and probability of failure.
Using data of U.S. commercial banks in 2009, we demonstrate that the fractions of a bank’s labor and capital consumed in the first-stage production are estimable and equal to 0.26 and 0.68, respectively. This implies that a representative bank is apt to allocate relatively less of its workforce and more of its physical capital in the first production stage to satisfy customers’ financial needs. This intermediate output, along with the remaining inputs of labor and capital, is next used to produce three final outputs in the second production stage, which is primarily a revenue generation process. The average TE score in the first stage is equal to around 0.6717, meaning that an average bank is manufacturing around 67.17% of the best-practice bank’s output for a given input mix. The average TE measure in the second stage is equal to 0.7758, implying that an average bank should cut 28.90% of its current expenditures to reach the cost frontier. Evidence shows that the major source of inefficiency comes from the first stage, rather than the second stage. Banks are suggested to enhance their managerial ability, particularly in the first production process, in order to effectively raise output quantities for a given input mix.
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Chapter 3
Evaluating Efficiencies of Chinese Commercial Banks in the Context of Stochastic Multistage Technologies
3.1 Introduction
Following the 2008 financial crisis, the U.S. and some member nations in the European Union (EU) have experienced an economic recession for the past years. China, on the contrary, has maintained outstanding economic growth during the same period.
It became the world’s second largest economy in 2010, overtaking Japan, and is forecasted by the International Monetary Fund to be the largest economy in 2025.
China’s economic performance was originally fostered by its business model of being the global manufacturing factory, but now the model has fundamentally changed into targeting economic growth through its own vast domestic market. Stable and continuous growth of consumption expenditure, large amounts of domestic and foreign investments, and huge net exports are all regarded as the main factors contributing to the country’s shining economic record. By end-2013, its gross domestic product (GDP) hit RMB 56.88 trillion,13 or more than twice as much as in 2006 (RMB 21.63 trillion), with an average growth rate of around 10% per year.
China’s quick economic growth appears to be sustainable due to its substantial supply of credit. Its financial system is mainly dominated by the banking sector that provides liquidity to the physical economic chain, because its captial market is rather limited and ineffective (Allen et al., 2012). Total asssets of the banking industry
13 The data are taken from the National Bureau of Statistics of the People’s Republic of China.
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amounted to RMB 151 trillion in 2013, or 12.69% higher than the previous year (RMB 134 trillion).14 The main source of loanable funds for business activities comes from domestic major commercial banks, i.e., large commercial banks and joint-stock commercial banks. The market share of these major banks in the entire banking sector was roughly 61% in 2013. Thus, it is meaningful to thoroughly investigate such a large-scale banking system with respect to its production processes and performance.
While many works have applied either a parametric stochastic frontier approach (SFA) or non-parametric data envelopment analysis (DEA) to investigate Chinese banks’ technical efficiencies, only several works, e.g. Matthews (2013), Wang et al.
(2014), Avkiran (2015) and Zha et al. (2015), utilize network DEA to evaluate the performance of Chinese banks. Network DEA, initiated by Färe and Grosskopf (2000), enables one to divide the whole production process of a firm into various divisions and to gauge the division-specific efficiencies, instead of the overall efficiency. On the contrary, conventional DEA and SFA, which treat the entire production process as a
“black box”, are suitable for measuring the efficiency of a single operational process, where firms are assumed to hire multiple inputs to manufacture multiple outputs. The omission of interrelated activities among subunits of a firm may hinder one from correctly measuring the performance of individual sectors and that of the firm as a whole.
To deal with the above difficulty, the current paper extends network DEA to network SFA, which allows for explicitly splitting the internal operation of a bank into deposit gathering and loan expansion stages and then measures the technical efficiency
14 See the annual reports of the China Banking Regulatory Commission (CBRC).
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of each production stage within the bank. We apply the new model to assess the technical efficiency of Chinese banks and compare the performances among different forms of banks for the following reasons.
First, the dilemma of whether to identify deposits as an input or an output can be resolved by network SFA. According to the intermediation approach, banks are financial intermediaries that gather deposits from depositors and grant loans to demanders. Therefore, deposits are classified as one type of input by this approach.
However, the production approach views banks as providers of financial services. Since deposits are the major item of financial services, they are considered as an output variable. This disparity leads to distinct efficiency estimates. Holod and Lewis (2011), thus, propose using network DEA and treat deposits as an intermediate product in the first stage, while the same product is viewed as an input in the second stage. In this manner, the inconsistency problem about the role of deposits can be avoided.
Second, our network SFA model enables us to explore the distribution of resources among subunits even though disaggregate data are not available. The fractions of inputs exploited by different stages can be estimated with the available aggregate data, which is the usual case faced by researchers. Conversely, those fractional parameters fail to be identified under the framework of network DEA, but have to be given by some ad hoc methods (Kao and Hwang, 2010; Holod and Lewis, 2011; Avkiran, 2015). Even more, Wang et al. (2014) in their network DEA work technically treat labor plus fixed assets as the inputs totally consumed in a single production process without considering the fractional issues. In the similar study of Zha et al. (2014), the entire deposit as the intermediate product is totally consumed in the subsequent production process.
Obviously, it is quite unreasonable that no labor and fixed assets are used in the other
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related production processes in the empirical studies. Therefore, this is an important feature of our network SFA, because almost all existing databanks offer accounting entries on the basis of an entire bank, instead of individual divisions (subunits) of a bank. Viewed from this angle, the current paper is likely to fill the gap in the network DEA literature.
Third, since China’s overall economic position is turning more and more important around the world, it is worth investigating whether or not its banking industry efficiently allocates resources in each operational stage. Although several previous works, e.g., Kao and Hwang (2010), Holod and Lewis (2011), Yang and Liu (2012), and Matthews (2013), Wang et al. (2014), Avkiran (2015) and Zha et al. (2015), have employed network DEA in order to account for inter-sector linkages to gauge production efficiency, DEA is deterministic and is not immune from the influence of random shocks.15 We generalize network DEA into network SFA, as the latter allows for the use of aggregate data to estimate fractional parameters of inputs hired in distinct sectors and divisional efficiency for Chinese banks. The resulting efficiency estimates tend to be free of data noise (O’Donnell and Coelli, 2005). In addition, since different forms of banks vary in their sizes and business goals, they may allocate different fractions of inputs among subsectors. We thus estimate fractional parameters and compare the technical efficiency for different types of banks. This should help us to gain further insight into banks’ performance by unveiling the “black box” of a bank’s operational procedure.
15 It is noteworthy that DEA does not require specifying a specific functional form that characterizes firms’ production process, while SFA does.
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The rest of the paper is organized as follows. Section 2 briefly reviews the literature. Section 3 develops an economic model describing a bank’s multistage production processes that lead to the network SFA model. A copula-based likelihood function is then introduced, which embodies the two-stage production processes, on the one hand, and permits us to jointly estimate the production and cost frontiers, on the other. Section 4 defines relevant variables and displays their descriptive statistics.
Section 5 presents the main findings of the empirical results, while the last section concludes the paper.
3.2 Literature Review
During the past two decades, China has undertaken a series of fundamental reforms and restructured its core financial environments by removing so-called protective umbrellas in regulations and enforcing comprehensive government monitoring, market discipline, and corporate governance. A lot of attention has picked up, because the ongoing financial liberalization and related reforms and transformation are regarded as potential factors that have stimulated China’s impressive financial market development (Jiang et al, 2013). A clear and overall picture on the evolution of Chinese banking system during the period 1978-2008 can be obtained in the studies of Jiang et al. (2009) and Huang and Fu (2013). The impact of economic reforms and deregulation on efficiency in this industry has been widely studied by, e.g., Fu and Heffernan (2007), Kumbhakar and Wang (2007), Jiang et al. (2009), and Barros et al.
(2011).
Interest has recently been focused on the ownership-performance nexus of Chinese banks. Most of the previous findings suggest that state-owned banks (SOBs)
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underperform joint stock banks (JSBs). Early SOBs are usually criticized not driven by profit-oriented objective under government intervention which forces them hiring excess staffs for the retired military officers and offering excess lending to state-own enterprises without considering risk management. Fu and Heffernan (2008) find that joint-stock banks have higher X-efficiency than state-owned banks over the period 1985-2002. Berger et al. (2009) examine the cost and profit efficiency of 38 Chinese banks during the period 1994-2003 and conclude that the 4 large stated-owned banks are the least efficient, while foreign banks are the most efficient. Du and Girma (2011) examine the productivity growth and cost efficiency of Chinese banks during 1995-2001 and also find that joint-stock banks outperform state-owned banks. Similarly, Kumbhakar and Wang (2007), Ariff and Can (2008), Lin and Zhang (2009) and Asmild and Matthews (2012) confirm the inferiority of state-owned banks to other types of banks.
However, after a series of reforms and transformations of SOBs by stripping off large amounts of NPLs, engaging ownership reforms, performing public listing in Shanghai and Hong Kong stock exchanges to induce strict corporate governance and strategic alliance with foreign companies to absorb global management skill and experience, recent studies, e.g. Yao et al. (2008) and Zhu et al. (2014), provide some interesting but opposite conclusions that the operations of JSBs are not necessarily superior to those of SOBs. In fact, the obvious advantage of SOBs in the bank-based economy is their strong national wide physical branch networks which seem to surpass the aforementioned side effect in SOBs and finally enhance their operation efficiency.
Hence, the inconsistent results regarding to the ownership issue should verified with more relevant data and more advanced powerful method.
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There exist many studies on Chinese banks’ efficiency that apply different methods and obtain mixed results. Some of them employ SFA, e.g., Kumbhakar and Wang (2007), Fu and Heffernan (2007, 2008, 2009), Yao et al. (2007), Berger et al.
(2009, 2010), Jiang et al. (2009, 2013), Chen and Yang (2011), Du and Girma (2011), Huang and Fu (2013), Tan and Floros (2013), and Dong et al. (2014). Others examine Chinese banks’ efficiency using non-parametric techniques, i.e., DEA, as in Chen et al.
(2005), Ariff and Can (2008), Yao et al. (2008), Luo and Yao (2010), Barros et al. (2011), Asmild and Matthews (2012), Matthews (2013), Dong et al. (2014), and Zhu et al.
(2014). Appendix B. briefly outlines recent studies applying those two methods to probe the Chinese banking industry.
Although those approaches are well-established for measuring efficiency scores, they fail to identify the specific sources of inefficiency embedded in multistage production processes within an organization. To account for this multistage system, Färe and Grosskopf (2000) propose the network DEA model to gauge the overall performance and individual subsectors’ performance of an organization. Many applications and extensive discussions on this model can be found by Lewis and Sexton (2004), Prieto and Zofío (2007), Avkiran (2009), Bogetoft et al. (2009), Chen (2009), Chen et al. (2009), Kao (2009, 2014), Tone and Tsutsui (2009, 2014), Kao and Hwang (2008, 2010), Vaz et al. (2010), Holod and Lewis (2011), Yang and Liu (2012), Lewis et al. (2013), Matthews (2013), Wang et al. (2014), Avkiran (2015), and Zha et al.
(2015), to mention a few. Note that SFA plays no role in this area, which is the main concern of the current paper.
Network DEA is able to decompose all the production processes into a set of subsectors and accounts for internal linkage among those subsectors, whereby some
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outputs of a subunit are regarded as inputs of other subunits. In order to gain further insights into the technical efficiency at each stage, the model requires the availability of disaggregated data specific to inputs employed by different stages. If disaggregated data are unavailable, then one has to estimate the fractions of inputs consumed in each production process. This appears to be difficult to achieve in the context of DEA - e.g.
Holod and Lewis (2011) provide a novel idea to solve the deposit dilemma in the context of network DEA, but they are forced to simplify their model into a single production stage due to the lack of disaggregate data. To deal with this problem, Kao and Hwang (2010) treat the information technology (IT) budget as a shared input by two serial production processes, where the fractions of this budget used are subjectively restricted to be between 0.6 and 0.9. In this paper we propose an economic model that leads to the network SFA framework, characterizes the multistage network production processes, and estimates the fractions of shared inputs used by each production stage.
We attempt to establish a simultaneous equations model that describes the multistage production processes of a firm and allows for dependence among the composed errors of different stages. In this manner, the technical efficiency of each subsector can be evaluated.
To estimate the simultaneous equations model, we suggest employing the copula methods introduced by Sklar (1959), which are a useful tool to handle in a flexible way the co-movement between markets, risk factors, and other relevant variables studied in finance. Copula methods have been widely used in the field of finance - see, for example, Longin and Solnik (2001), Yang et al. (2009), and Steven and Ng (2009).
Several recent studies in the area of SFA have considered the dependence structure between composed errors, e.g. Smith (2008), Shi and Zhang (2011), Carta and Steel (2012), Lai and Huang (2013), Tsay et al. (2013), and Amsler et al. (2014). The salient
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feather of Lai and Huang (2013) is that the composed errors of different equations are correlated with each other. The employment of copula methods assists in deriving the joint distribution from the margins of several error components under a specific copula function. Lai and Huang (2013) apply the Gaussian copula to derive a likelihood function that is later maximized to yield parameter estimates of interest. They also stress that a biased estimator of technical efficiency may be produced if the dependency component is ignored.
3.3 Model Specifications 3.3.1 The Theoretical Model
We assume that banks operate within two stages, i.e., deposit gathering and loan expansion, where parts of inputs, such as labor and capital, are utilized in the first stage to produce the intermediate product, deposits, which is one of the inputs in the second stage and used to produce final financial products, i.e., loans, investments, and non-interest income, together with the remaining parts of labor and capital. Figure 2.1 draws a general network system for the banking industry.
Figure 2.1 The network System for banking industry
‧
where g(.) is the production function,v
11
~
N
(0,
v2) denotes the statistical noise, andu
11
~ N
(0,
u2)
is technical inefficiency term. Variablesv
1 andu
1 are conventionally assumed to be mutually independent. It is worth noting that plays a pivotal role that connects the sequence of the two production processes and distributes resources between stages. Estimating the logarithmic production function of (1) alone is incapable of identifying all of its unknown parameters, including . The identification of requires adding additional information, to be discussed shortly.Banks are assumed to minimize their production cost
PC
*
in the second stage, where they utilize the remaining fractions of labor and capital, as well as the entire intermediate output (deposits) to produce multiple outputs Y.17 The minimized costBanks are assumed to minimize their production cost