اثرات جانبی حسابداری در اندازه گیری رشد بهره وری: اندازه گیری هزینه بهره وری ملکوئیست

This paper starts with the basic premise: that conventional measures of productivity growth—often used as a measure of corporate performance—which ignore external or social output, are biased. We then construct an alternative productivity growth measure using activity analysis which integrates the externality/social output into a generalized productivity measure reflecting social responsibility. This method is very general and could be applied to gauge corporate social responsibility. We provide an application to US agriculture to demonstrate the approach: we show that conventional measures of productivity are biased upward when production of negative externalities (or bad) outputs is increasing. Conversely, this same measure of productivity is biased downward when externalities in production are decreasing.

The purpose of this paper is to demonstrate how one of our most fundamental measures of performance—namely productivity growth—can be amended to account for nontraditional outputs, such as negative and positive externalities or other social outputs. The measure we propose, the Malmquist cost productivity measure (MCP) is a measure of total factor productivity that can readily integrate multiple outputs and is easily estimated. In order to make our proposed measure concrete, we illustrate its use with an application to the issue of performance in the agricultural sector when accounting for environmental degradation. Given the trend toward ‘corporate’ farming in the US, this provides a somewhat unusual, but we think relevant, example of measuring ‘corporate’ social performance, where our focus is on environmental responsibility. More generally concerns about environmental degradation have prompted the adoption of measures that would internalize externalities in production. The measures taken, ranging from command and control policies such as regulation to more market oriented policies such as issuing tradable pollution permits, were aimed at preventing the use of the environment as a medium whereby undesirable (or bad) outputs could be freely disposed. This has required that models of production be extended to accommodate joint production of “goods” and “bads”. Early contributors included Shephard (1970) and Shephard and Färe (1974). Initial studies were more geared towards a comparative evaluation of environmental performance of decision making units (DMUs) within a static framework. Literature on production frontier construction is extended and modified to measure environmental performance in addition to capturing efficiency at the decision making unit (DMU) level. The two competing approaches, stochastic frontier estimation and data envelopment models, while determining the technology to be used as a basis for constructing different measures of DMU performance, they shared equal responsibility in providing means of measuring environmental performance. As a result, empirical applications on the measurement of environmental performance have flourished from both strands. For example while Reinhard et al. (1996) used a stochastic production frontier approach to construct environmental efficiency indexes at the farm level, Ball et al. (1994) and Tyteca (1997) adopted the data envelopment analysis to measure the environmental performance. Yet Reinhard et al. (1997) used both approaches on the same data set to “analyze the strengths and weaknesses of the two methods in computing the comprehensive environmental efficiency scores”. Comparative studies such as Reinhard et al. (1997)’s confirmed the theoretically expected results. Since stochastic production frontiers contain a random error, which attribute some of the deviations from the frontier to uncontrollable chance events (and/or measurement errors), they have generated higher environmental efficiency scores than those measured by DEA, which is a deterministic technique that attributes all the deviations from the best practice to inefficiency. Nevertheless, these studies also showed that although the magnitude of environmental efficiency scores are different, both approaches generate very similar results in ranking DMU’s with respect to environmental performance and that the difference in efficiency scores obtained from alternative approaches is a matter of scaling. Stochastic production frontier models and DEA models also differed in their construction of the best practice technology. While DEA models satisfy monotonicity and curvature restrictions by construction without imposing a parametric structure on the technology, these restrictions can not be imposed in stochastic production frontier models when flexible functional forms are specified. Although the ability to test for the satisfaction of the theoretical restrictions considered to be a strength of SPF models, tests of monotonicity restrictions often time revealed that substantial number of observations violated this restriction. This further complicates the measurement issues in environmental performance by introducing specification errors. Hence, many studies that focused on measuring the cost of reduced disposability and the environmental performance of producers (see, for example, Färe et al., 1986, Färe et al., 1989a, Färe et al., 1989b, Färe et al., 1996, Tyteca, 1996, Tyteca, 1997, Zaim and Taskin, 2000, Ball et al., 2002a, Ball et al., 2002b and Ball et al., 2002c) stayed within DEA framework. More recently, a large number of studies have been devoted to measuring the effects of environmental regulation on productivity growth. The results of these studies almost unanimously suggested that regulations retard productivity growth (see for example see for example Denison, 1979, Havemann and Christainsen, 1981, Gray, 1987 and Robinson, 1995). Such a conclusion was inevitable since these studies have only concentrated on cost increasing aspects of regulatory policies without giving any credit to regulatory outcome—reduced bads and hence reduced marginal damage. As Ball et al., 2002a, Ball et al., 2002b and Ball et al., 2002c point out, measures of productivity growth that ignore joint production of good and bad outputs and the restrictions on disposability of bad outputs will overstate the “social benefits” of production. They call for a revised measure of productivity growth that captures the cost associated with environmental externalities. This issue has been addressed within a “production” framework with the development of the Malmquist–Luenberger productivity index (see Chung et al., 1997, Ball et al., 2001 and Hailu and Veeman, 2001). The objective of the present study is to derive an alternative measure of productivity growth within a “cost” framework, which we term the Malmquist cost productivity (MCP) index, which extends Diewert’s (1992) cost function technique by allowing for bads. We believe that the MCP measure represents an attractive alternative to the Malmquist–Luenberger index of productivity for several reasons. First, since it is augmented with price information on inputs as well as information on quantities of inputs and outputs it contains almost the same information as a traditional Tornqvist-type productivity indicator. Second, since the cost structure of an industry is a fundamental determinant of cost-effective production decisions, a cost framework as used in MCP is a desirable foundation for representing production patterns and analyzing the productive contributions of both good and bad outputs and inputs to production. Finally, the underlying activity analysis framework produces technically more feasible linear programming problems, which reduce the number of infeasible solutions as compared to linear programming problems that are required for the computation of Malmquist–Luenberger index of productivity. In constructing our MCP index, we rely on activity analysis which conveniently allows us to model joint production of good and bad outputs, thereby putting due emphasis on the characteristics of production with negative externalities. The basic building blocks of our approach are as follows. First, we explicitly account for joint production of good and bad outputs. Second, our representation of technology reflects restrictions on the disposability of bad outputs. This implies that the reduction of bad outputs is possible either by reducing the production of good outputs given a fixed level of inputs (where some inputs must be diverted from the production of goods to the reduction of bads) or by increasing input use (again to reduce bad outputs) while maintaining the same level of production of good outputs. Notice that in either case the reduction of bad outputs is achieved by increased cost to the producer, since the environment ceases to be a free factor of production with a positive marginal benefit to the producer.1 Finally, we assume that bad outputs are always produced when good outputs are produced, thereby ruling out production of good outputs with no environmentally detrimental impacts. In addition we do not have to introduce separability between good and bad outputs in our framework, in contrast to Fernandez et al. (2002). The paper unfolds as follows: Section 2 introduces the MCP index and its decomposition into efficiency change and technical change components. In Section 3, we apply the proposed index to a state-by-year panel recently made available by the US Department of Agriculture’s (USDA) Economic Research Service. Section 4 concludes.

This paper suggests a procedure for measuring productivity growth in the presence of externalities (or other social outputs). The absence of price data for most externalities or social outputs is a limiting factor in measuring productivity growth using conventional growth accounting and index number approaches. Our procedure allows us to model joint production of good output and the external effect without requiring data on (shadow) prices of the externality. This allows us to specify a practical measure of enhanced productivity which can be used as a benchmark for corporate social behavior. Here we focused on environmental responsibility, but the general technique could be adapted to other social outputs. As an illustration, we provide an application using a state-by-year panel of the US agricultural sector which includes data on environmental risk due to pesticide leaching and runoff. More specifically, we show that measures of productivity growth that ignore bad outputs are biased upward when the production of bads is increasing. Conversely, when the environmental risks associated with production are decreasing, this same measure understates the social benefits of production and, hence, productivity growth.