Literature review of efficiency focused on environment-adjusted analysis

Previous study on the external operational environment and measures of efficiency based on DEA model can be broadly classified into two categories: the all-in-one approach and the two-stage approach.

The all-in-one approach first proposed by Charnes et al. (1981) includes the external operational environment variables directly in the linear programming (LP) formulation along with the traditional inputs and outputs. The external factors which are from the operational environment and indeed influence the firms’ performance are treated as the additional inputs and outputs along with the real inputs and outputs in the same LP formulation to analyze.

However, an additional input and output variables from external factors could wrongly estimate the real efficiency. If the operational environment enters the LP formulation as an input, this implies that more outputs could be produced, suggesting that the operational environment is favorable. If the operational environment enters the LP formulation as an output, this implies that more inputs are required, suggesting that the operational environment is unfavorable. This prior input or output classification is unsuitable if such external factors can not be classified appropriately, e.g. age, gender, vocation, education background, etc. It may make little sense for an external feature of the operational environment.

The two-stage approach called by Coelli et al. (1998) includes the traditional inputs and outputs in the LP formulation used to compute efficiency, which is then used as the dependent variable in a second stage regression, where the explanatory variables measure the external environment. An advantage of the two-stage approach is that the influence of the external variables on the production process can be tested in terms of both sign and significance.

the slacks and surpluses from inputs and outputs. This may bias the parameter estimates and give misleading conclusions regarding the impact of each external variable on efficiency.

The two-stage procedure does not provide a separate measure of managerial efficiency or inefficiency.

Fried et al. (1999) introduced a four-stage DEA approach to estimate the influence by the environment-adjusted variables of American hospital-affiliated nursing homes in 1993.

They used two outputs: inpatient days of skilled care and inpatient days of intermediate cares, and four inputs: registered nurses, licensed practical nurses, other personnel, and non-payroll expenses. As suggested by Fried et al., the four-stage DEA approach has some intriguing findings: First, it uses the information contained in the slacks or surpluses of the original model. Second, it does not require imposing a sign on the effect of an external variable on inefficiency. Third, it provides tests of significance of each external variable on inefficiency in each individual input (for an input-oriented model) or output dimension (for an output-oriented model). Fourth, it provides an overall effect on inefficiency for a categorical variable. Finally, it can generate a single result of firms’ inefficiency caused by managers.

The utilization of the four-stage DEA procedure can avoid the above disadvantages of the all-in-one approach and the two-stage approach. As suggested by Fried et al., this approach is not necessary to classified the external variables into additional input and output categories prior to the analysis, and information on slacks or surpluses generated by the initial model is used in the calculations. The result would rely on the conventional DEA model and efficiency estimation theory, and the influence of the external variables on each input variables can be tested. The management component of inefficiency also could be separated from the influences of the external operational environment. This approach is adopted in

this study.

Pastor (2002) also proposed his new three-stage sequence based on DEA model to evaluate the efficiency of banks in Spain, Italy, France and Germany from 1988 to 1994.

The main concept of his procedure is to find out some factors out of business operation. The external factors would indeed affect the performance of banks. The author considered that the most important of those external factors is risk which mostly results from bad loans, caused by poor management. The total bad loans were decomposed into two components:

one due to poor risk management and another due to external economic and environmental factors. The author then compared the results by controlling the bad loans to compute the efficiency scores via DEA. The conclusion indicated that the external factors do not account for the inefficiency significantly, but the bad loans caused by failed risk management do.

Although it may be much simple to define risk only as bad loans. However, the concept that separating inefficiency from managerial failure and unavoidable external factors is worthy being noticed.

Based on Fried et al. (1999), Drake and Simper (2005) and Drake et al. (2006) extended the application of the four-stage DEA procedure to respectively analyze the efficiency of United Kingdom police force and Hong Kong banking institutions excluding the influence of external environment.

Drake and Simper (2005) compare the results from police force efficiency measured by DEA and by radar approach, the wholly output based measurement, currently advocated by Home Office in the United Kingdom as a new police force performance evaluation. The performance radar approach took multiple criteria used to evaluate each regional police force

into consideration simultaneously such as numbers of reducing crimes, numbers of the criminal offenders brought to justice, promoting level of public safety, citizen satisfaction and resource usage. Because the environment may be a penalty or benefit to an individual unit that is under the evaluation, the authors attempted to purge the raw DEA scores of any impact from environmental factors outside the control of individual police force by using the slack-based environment adjusted input specification. In order to ensure the environmental factors are indeed adequately accounted for, the authors used Tobit regression to determine the external variables, and then they could measure the inefficiency excluding the influence of environment. More significantly, the authors claimed that the current radar approach advocated by Home Office of UK could produce misleading assessments of the performance of individual police force, because the radar approach assumes each police force is in the same environment. Using four-stage DEA approach proposed by Fried et al. (1999) helps to exclude the external factors for all police force, thus all police can be evaluated equally.

Drake et al. (2006) also assessed the relative technical efficiency of banking institutions operational in the Hong Kong financial market from 1995 to 2001. They used the panel data sample consisted of 413 observations to almost follow the four-stage DEA approach introduced by Fried et al. (1999), using a profit-oriented specification with revenue components as outputs and cost components as inputs. Therefore, the three inputs variables specified are employee expenses, other non-interest expense and loan loss provisions, and the three output variables specified are net interest income, net commission income and total other income. They also adopted the intermediation specification (with employees, capital, deposits as inputs and investment and loan as outputs) to assess the technical efficiency to compare the results via profit-oriented specification. Their conclusive results indicated quite clearly that the failure to incorporate slacks formally and directly into the efficiency analysis

could sometimes produce inflated and misleading indications of relative efficiency, even though the rank correlation between the two sets of results is relatively high.