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banks, which may be a preferable measure for regulators and business consultants who attempt to gauge the costs and benefits to society from distinct policies to the conventional inefficiency measure based on a production frontier. It is known that a production function is suitable for a single output case without using the information on input prices which are key variables affecting the decision on inputs hiring. Therefore, the applying of cost frontier is recommended due to diversifying financial products banks provide (Huang,Chiang and Chen; 2011). Different from previous studies, we apply the SFA (SFA) to investigate the relationship between cost efficiency and CSR index that is compiled from EIRIS database.5
3. Methodology
3.1 Translog cost function
Unlike parametric methods, non-parametric DEA does not allow for random error term in the model. That is, DEA presumes that there is no measurement error, no inaccuracies related to accounting figures. Following Battese and Coelli (1995), we apply parametric approach, the SFA, to gauge cost efficiency scores, which allows for random error and identifies the environmental factors related to cost efficiency by a single-step. The SFA assumes the existence of composed errors. One of them is a non-negative random variable, representing technical inefficiency. This one-sided error is assumed to have one of the following distributions: half-normal, truncated normal, exponential, and gamma distribution. The other is a two-sided error with a normal distribution. Cost efficiency measures the distance between a bank’s actual costs and the efficient cost frontier. The estimated bank cost inefficiency is referred to as the difference between observed costs and predicted minimum costs for a given scale and mix of outputs, input prices and other country-level explanatory variables. ( Battaglia et al., 2010). However, when taking cross-country comparisons into consideration, it is worth to note that environmental heterogeneity among countries play an important role on the determination of efficiency level. Country-specific factors, such as economic development can influence heavily on the level of technical efficiency. (Fries and Taci, 2005). Thus,
5 EIRIS is one of the largest independent SRI research organisations worldwide. Its core business is undertaking research into corporate environmental, social and governance (ESG) management and performance. It provides global coverage, offering data on more than 80 research areas for some 2,800 companies in Europe, North America and Asia Pacific.
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the translog cost function is expressed as:
yijt = α + X′ijtβ + Z′jtγ + vijt+ uijt and εijt = vijt+ uijt (1)
where yijt is the (log) total cost of bank i in country j at period t, X′ijt is a vector of (log)outputs and of input prices, Z′jt is the vector of country level variables for country j at period t. Notation ε is the composite error term, where v is the two-sided normally distributed error with mean zero and a constant variance, capturing random error, and uijt > 0 is the technical inefficiency term.
The translog cost function is often used in the banking and finance literature to estimate the marginal costs of production and the output elasticities of input demand for banks. The following specific form is transformed from general form of the translog cost function [equation (1)].
lnTC = lnTC∗+ ε
Where lnTC is the natural logarithm of the actual expenditure, lnY𝑗 and ln𝑊𝑖 are the ith logarithmic output quantities and the jth logarithmic input prices, respectively. In order to satisfy the requirement of a cost function, we hereby standardize the input price of W1 to add first order homogenous condition into the functional form, i.e., TC, W2, and W3 will be normalized by dividing W1. 6
6 Although we select W1 as the standardized variable, W2 or W3 can be alternatively chosen.
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3.2 CSR hypothesis
As we stated in Chapter 2, the effect of CSR on corporate financial performance is controversial. The mixed result might be explained by the motives of a firm to conduct CSR. Therefore, here we propose three hypothesis.
Hypothesis 1. For altruistic CSR bank, CSR negatively affects efficiency.
The altruism motive indicates that banks conduct CSR initiatives for their own sake, thereby negatively affecting efficiency.
Hypothesis 2. For strategic CSR bank, CSR positively affects efficiency.
The strategic CSR banks are inclined to pursue profit maximization by enhancing their reputation and brand names through activities which include environment protection, charity behavior, integrity to customers, and maintenance the right for employees. According to Benabou and Tirole (2010), this perspective demonstrates win-win vision of CSR and they believe that strategic CSR involves taking a socially responsible position to strength market position to increase profit.
Hypothesis 3. Greenwashing CSR exhibits no obvious effect on efficiency.
Greenwashing refers to the disingenuous act of banks to spin their products and policies as environment-friendly, such as presenting cost cuts as reductions in resource use (Frankental, 2001).
3.3 Economies of scale (SE)
When estimating the cost function, the issue of scale economies is worth assessing. If economies of scale do exist, then firms can take actions to expand the production scale in order to decrease their long-run average costs. However, if the reverse is true, reducing operation scale may help to lower down long-run average costs. The definition of SE is expressed as:
SE= 𝐶
∗(𝑌,𝑊)
∑3𝑗=1𝑌𝑗𝐶𝑗∗(𝑌,𝑊)
Here 𝑇𝐶∗(𝑌, 𝑊) is the translog cost function, and 𝑇𝐶𝑗∗(𝑌, 𝑊) denotes the partial derivative of 𝑇𝐶∗ with respect to the jth output. If SE > (<) 1, then increasing (decreasing) returns to scale presents. If SE = 1, then constant returns to
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scale prevails, meaning that the current production scale of the bank is optimal.
3.4 Cost efficiency
The ratio of the cost inefficiency for the i-th bank, relative to the potential cost, defined by the frontier function, given the output vector, xi, is used to define the cost efficiency of i-th bank:
CE𝑖 = 𝐶𝑖∗
𝐶𝑖 = exp (X′ijt𝛽)
exp (X′ijt𝛽+𝑢𝑖)= exp (−𝑢𝑖) (2) Where Ci* is minimum cost and Ci is actual cost. The equation 2 is a measurement of cost efficiency, of which the value is equal or less than one after the ratio is reciprocal. Finally, we will apply cost efficiency method to analyze the difference of cost efficiency in distinct regions.