Elsevier

Energy

Volume 32, Issue 7, July 2007, Pages 1055-1066
Energy

Environmental production functions and environmental directional distance functions

https://doi.org/10.1016/j.energy.2006.09.005Get rights and content

Abstract

This study derives the relationship between environmental production functions and environmental directional distance functions. These two approaches make different assumptions when modeling the joint production of good and bad outputs. The environmental production function credits a producer solely for expanding good output production, while the directional environmental distance function credits a producer for simultaneously increasing production of the good output and reducing production of bad outputs. Estimates of technical efficiency and pollution abatement costs are calculated using data from coal-fired power plants. These results provide the empirical basis for comparing the environmental production function to the environmental directional distance function.

Introduction

Many studies of productivity changes have attempted to explain the source(s) of the observed slowdown in US productivity growth rates since the early 1970s. A number of hypotheses have been proposed, one being that environmental regulations impose a burden on producers.1 Since environmental regulations divert inputs to pollution abatement activities which results in reduced production of the good output, the essence of the hypothesis is pollution abatement activities require firms to employ more inputs to produce the same quantity of the good output therefore, by definition, traditional measures of productivity (see [1] for a discussion) must decline.2

Although it can be argued that the output of pollution abatement activities (i.e., reduced emissions) should be incorporated into any analysis of productivity, the effect of environmental regulations on traditional measures of productivity is also an important issue to investigate.3 Studies of the effects of environmental regulations on traditional measures of productivity compare the level of production of the good output in regulated and unregulated environments. When conducting ex post facto studies of the effects of regulations, the quantity of the good output produced in the regulated environment is the observed behavior of a producer. Hence, the challenge confronting these studies is estimating production of the good output in an unregulated environment. Only after estimating good output production in an unregulated environment is it possible to calculate the lost production of the good output associated with pollution abatement activities.

Christainsen and Tietenberg [3, pp. 373–376] specify a traditional production function in which production of the good output is a function of inputs, regulatory intensity, and time. They categorize “direct” or “indirect” effects of environmental regulations on production of the good output. Holding the technology and inputs constant, the change in production of the good output that occurs as a result of changes in regulatory intensity represents the direct effect of the regulation. Changes in production of the good output resulting from changes in scale economies, output composition of an economy, the mix of labor and non-labor inputs, and changes in traditional measures of technical progress resulting from environmental regulations are classified as the indirect effects.

The following are some of the ways in which regulatory intensity has been specified in empirical studies of order to determine the effect of environmental regulations on traditional measures of productivity: (1) pollution abatement costs (PACs), (2) emissions, and (3) number of individuals associated with regulatory activities. PACs have been estimated using surveys, engineering estimates, and models.4

Two strategies have evolved for calculating PACs. One approach involves assigning inputs to either good output production or abatement activities. Hence, we refer to this approach as the “assigned input” model. According to this approach, PACs are the costs of inputs assigned to abatement activities. The second method for calculating the association between pollution abatement activities and traditional productivity involves modeling the joint production of good and bad output production by regulated and unregulated technologies. We refer to this method as the “joint production” model. From the perspective of this method, PACs are the value of the forgone good output production associated with abatement activities.

In this study, we present a framework for comparing the traditional production function, with two functions that model the joint production of good and bad outputs. Specifically, we discuss technical inefficiency and PACs from the perspective of a traditional production function, an environmental production function, and an environmental directional distance function. Although the costs associated with pollution abatement are relatively small for the entire economy, several sectors—including electric power producers—bear a disproportionate share of these costs. Even if abatement costs are relatively small, determining the optimal policy depends on maximizing the difference between the total benefits and total costs associated with the policy.

The remainder of this study is organized in the following manner. Section 2 specifies a model of the joint production of good and bad outputs. The “environmental” production function derived in this section establishes the relationship between traditional production functions and the technology modeling the joint production of good and bad outputs. Section 3 establishes the link between environmental production functions and environmental directional distance functions, while Section 4 discusses technical inefficiency and the opportunity cost of pollution abatement activities from both perspectives. Section 5 discusses the data and empirical results, while Section 6 summarizes this study and discusses its implications.

Section snippets

The environmental technology

In this section, we formulate what we call the environmental technology. This technology incorporates weak disposability of outputs and null-jointness. The later concept essentially tells us that producing good outputs require the production of bads. Our general model can be “reduced” to the more traditional production function framework, and we identify the special conditions such an environmental production function must meet. This is useful since most existing studies investigate the

Environmental production and environmental directional distance functions

We now turn to characterize the environmental technology as functions and we start with a traditional production function. These functions will provide us with a functional representation of the environmental technology that can be estimated either parametrically or nonparametrically. For this, we need to assume that only a single good output is produced. Assuming y+, we may define the environmental production function asF(x;b)=max{y:(y,b)P(x)}.

Since P(x) is a compact set (P.2), this

Opportunity cost of environmental regulation

To evaluate and estimate the cost of environmental regulation we next introduce the unregulated technology. Following Färe et al. [4], [11], the opportunity cost of pollution abatement activities, measured by either the environmental production function or environmental directional distance function, is the difference in good output production associated with the unregulated and regulated technologies. If society was completely unregulated with respect to the environment then each firm or

Data and results

Data for coal-fired power plants from 1995 are used to solve the LP problems. The technology modeled in this study consists of one good output, net electrical generation (kWh), and two bad outputs—sulfur dioxide (SO2) and nitrogen oxides (NOx). The inputs consist of the capital stock (CS), the number of employees, and the heat content (in Btu) of the coal, oil, and natural gas consumed at the plant.11 The US

Conclusions

The goal of this study is to demonstrate alternative definitions of technical efficiency and PACs by modeling the joint production of good and bad outputs.15 Using a joint production model to model the consequences of pollution abatement activities has several advantages. First, it does not require information about pollution abatement technologies and their associated

Acknowledgments

An earlier version of this study was presented at the January 2002 ASSA meetings in Atlanta, GA. We thank Karen Smith-Vaden and two anonymous referees for helpful comments on earlier versions of this article. We also wish to thank Curtis Carlson for providing his CS and employment data. Any errors, opinions, or conclusions are those of the authors and should not be attributed to the US Environmental Protection Agency.

References (23)

  • M. Keilback

    Estimation of the value of the marginal product of emission in a country where emissions output is regulated—an empirical study

    Environ Resour Econom

    (1995)
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