Chapter 4 Does Financial Regulation Affect the Profit Efficiency and Risk of Banks? Evidence
3. Literature Review
4.1 The Profit Efficiency Model
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Hughes and Moon (1995) and Hughes and Mester (1998) thus stress the importance of analysing the impact of efficiency on risk and capital. They observe a positive relationship between risk and the level of capital (and liquidity), perhaps signalling regulators’ preference for capital as a means of restricting risk-taking activities but a negative relationship between inefficiency and bank risk-taking.
4. Methodology and Framework
The study first use a profit model of DEA and Z-score to investigate efficiency and risk from China commercial bank point of view. Then, we then use Tobit regression model to study the relationship between the financial regulation and the efficiency of bank and OLS method to study the relationship between the financial and the risk of bank.
4.1 The Profit Efficiency Model
There are mainly two approaches in evaluating the efficiency of financial institutions.
The first approach is the financial indicators analysis. This method does not reflect the value of management and conceal the long-term operational problem (Sherman and Gold, 1985).
The second approach is economic efficiency analysis, which includes two methodologies; one is parametric and the other is nonparametric. For examples, stochastic frontier approach (SFA), thick frontier approach (TFA) and distribution-free approach (DFA) are parametric, and data envelopment analysis (DEA) and free disposal hull (FDH) are nonparametric. Two most commonly adopted methods, SFA for parametric and DEA for nonparametric, have their own advantages and disadvantages. The SFA method can test hypotheses statistically and construct confidence intervals allowing for random errors. The effects of statistical noise or measurement errors can be distinguished from random errors. Researchers, however, may lose some flexibility in model specification. On the other hand, the DEA method cannot separate the statistical noise or the measurement errors from random errors. Researchers need not to assume the functional form relating inputs to outputs. Thus, the relative efficiency scores obtained from DEA may be subject to the effects from the uncontrollable factors.
DEA uses linear programming method to construct a piecewise linear surface or frontier over the investigated data. DEA searches for points with the lowest unit cost for any given output, and connecting those points to form the efficiency frontier. Any company not on the frontier is considered inefficient. A numerical coefficient is assigned to each firm, defining its relative efficiency (between 0 and 1) in comparison with efficient peers.
In this study, we use profit efficiency to measure the efficiency of banks. Most of the studies over the 1990s have concentrated mainly on estimates of cost efficiency (Berger, Hunter and Timme, 1993; Resti, 1997). Subsequently, bank efficiency studies have been
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criticized for ignoring the revenue and profit side of banks' operations. Profit efficiency is a more inclusive concept than cost efficiency, because it takes into account the cost and revenue effects of the choice of the output vector, which is taken as given in the measurement of cost efficiency.
4.1.1 Model Description
Consider an industry producing m outputs from n inputs. An input–output bundle (x,y) is considered feasible when the output bundle y can be produced from the input bundle x. The technology faced by the firms in the industry can be described by the production possibility set
T = {(x,y)：y can be produced from x}.………(1)
In the single output case, one can conceptualize the production function
f(x) = max y：(x,y) ∈T . ……….(2)
In the multiple output case, frontier of the production possibility set is the production correspondence F(x,y) = 1.
The method of Data Envelopment Analysis introduced by Charnes et al. (1978) and further extended to non-constant returns technologies by Banker et al. (1984) provides a way to construct the production possibility set from an observed data set of input–output bundles without assuming a functional form of the production technology.
Suppose that (xj,yj) is the input–output bundle observed for firm j (j = 1,2,. . . ,N). Clearly, these input–output bundles are all feasible. Then the smallest production possibility set satisfying the assumptions of convexity and free disposability that includes these observed bundles is can be measured under alternative assumptions on the choice variables.
For a commercial firm, both inputs and outputs are choice variables and the only constraint would be the feasibility of the input–output bundle chosen. For such a firm, the criterion of efficiency is profit maximization. At input and output prices w and p, respectively, the actual profit of the firm producing the output bundle y0 from the input bundle x0 is
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Π . The maximum profit feasible for the firm is
T
In any empirical application, the maximum profit may be obtained as
x
The profit efficiency of the firm is measured as
*
This measure is also bounded between 0 and 1 except in the case where the actual profit is negative while the maximum profit is positive. In that case δ is less than 0. If the maximum profit is negative as well, δ exceeds unity.
4.1.2 Data and Definition
Previous studies have classified Chinese banks as state-owned banks, joint-stock banks, city and rural banks, and foreign banks according to the bank established. This classification method may not play the function of regulatory policies on risk prevention. Banks should be classified in accordance with the operating status. Furthermore, Chinese banks deemed to be systemically important banks (large bank) will be required to meet capital adequacy ratios of 11.5 percent, while other banks (small and medium banks) will be held to a 10.5 percent minimum. This also means that the regulatory requirements for systemically and non-systemically important banks in the future will be the difference.
Unlike other studies, this study used bank assets as a classification standard from the financial risk and differential regulatory perspective. We adopted 1 trillion23 as a standard and divided Chinese banks into two categories: large and small banks. Our research data are from the Bankscope, the CBRC and the financial statements published by commercial banks. They are unbalanced data24. Appendix Table A4-1 lists the number of sample banks. Appendix Table A4-2 lists the proportions of sample banks’ assets. The study covers a period of 8 years between 2004 and 2011. In late 2006, the State Council, China’s cabinet, released a regulation giving foreign banks a five-year grace period from 2007 to comply with the 75% limit25. The
23 As the former China Banking Regulatory Commission chairman Liu said, the bank’s assets more than 1 trillion will be treated as a large bank.
24 The number of large banks and small banks are listed in Appendix Table A1. The proportion of large and small bank assets is listed in Appendix Table A2.
25 On 11 December 2006, the Regulation on the Administration of Foreign-funded Banks (issued by the State Council) and related implementing rules (issued by the CBRC) came into force. A five-year grace period for foreign banks to comply with China’s 75% loan-deposit ceiling will expire on Dec. 31, 2011.
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regulation between China domestic banks and foreign banks is different. Therefore, foreign banks were excluded from the original sample.
The DEA-based method requires bank inputs and outputs whose choice is always an arbitrary issue (Berger and Humphrey, 1997). There are many ways to define and categorize input and output variables in banking literatures, and in this study we adopt the intermediation approach26 (Subhass and Abhiman, 2010; Dasa and Ghosh, 2009; Taufiq, 2008; Lin, 2002;
Shen and Chen, 2008) to define the input and output of financial institutions. The intermediation approach may be superior for evaluating the importance of frontier efficiency for the profitability of financial institutions, since the minimization of total costs, and not just production costs, is needed to maximize profits (Iqbal and Molyneux, 2005).
Two inputs are considered – deposits and fixed assets. The prices of the first two inputs are respectively—cost of deposits, measured by average interest paid per rupee of deposits and cost per unit fixed assets as measured by non-labor operational cost per rupee amount of fixed asset. On the output side, we use two variables—investments and loans. It is fairly standard in the literature. The associated price indicator for the two output measures are average interest earned per rupee of investment and average interest earned per rupee of loan and advances, respectively. Table 4-2 lists the definitions of input and output variables27.
Table 4-2 Definitions of input and output variables
Variable Variable name Description
Fixed assets The sum of physical capital and premises Input
Funds Total deposits plus total borrowed funds Price of fixed assets Operating expenses divided by the fixed
assets Input price
Price of funds Interest expenses on customer deposits plus other interest expenses divided by the total funds
Total loans Total of short-term and long-term loans Output
Investment Includes short and long term investment Price of loans Interest income on loans divided by total
loans Output price
Price of investment Other operating income divided by investments
26 The intermediation approach was suggested by Sealey and Lindley (1977). It views bank as an intermediator of financial services and assumes that banks collect funds (deposits and purchased funds with the assistance of labor and capital) and transform these into loans and other assets. The intermediation approach is preferred over the production approach, first proposed by Benston (1965) because it suits the nature of the banking industry more than the production approach.
27 Please refer to the footnote 19 on page 33.
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financial ratios (e.g. the ratio of nonperforming loans to total loans, the ratio of provisions for nonperforming loans to total assets, etc.). These variables have been criticized by the empirical literature because the ratio method is not based on any theoretical basis, and even in its most elaborated form, the ratios method does not take into account the impact of diversification on risk.Therefore, we will use the Z-score measure to assess the bank risk and to overcome the shortcomings of the ratios method. This comprehensive measure takes into account both risks related to banking business and the degree of coverage of these risks by the capital (Goyeau and Tarazi, 1992). According to Beck, Demirgüç-Kunt, and Levine (2010), “if profits are assumed to follow a normal distribution, it can be shown that the z-score is the inverse of the probability of insolvency”, because “z indicates the number of standard deviations that a bank’s return on assets has to drop below its expected value before equity is depleted and the bank is insolvent”.
The Z-score indicator can be estimated using the probability of default extracted from Roy (1952) and developed by Goyeau and Tarazi (1992). The probability of default is the probability that losses exceed the equity, or when the net worth becomes negative (Roy, 1952;
Boyd and Graham, 1988). This may be written as:
Probability of default = Prob (π<−E)
It is possible to calculate different indicators of banking risks depending whether we divide the two terms of the inequality by the equity or by the total assets.
In this study, dividing by the value of assets results in an indicator in terms of return on assets. It provides an indicator Z , which allows separating explicitly the risk effect from the risk coverage of the bank capital. The probability of default can be written as:
) is the indicator of fragility.