Productivity and Profitability Changes in the U.S. Electric Power Plants
during SO~2~ Trading Regime

Surender Kumar^1^

^1^Fellow, National Institute of Public Finance and Policy, New Delhi
110 067, INDIA, E-mail:
[**surender@nipfp.org.in**](mailto:surender@nipfp.org.in)
[**surenderkumarbansal@hotmail.com**](mailto:surenderkumarbansal@hotmail.com)

Abstract: We examine the productivity and profitability changes in the
US electric generating plants during the SO~2~ trading regime. Input
distance function is used to compute the cumulative Malmquist
productivity and Fisher productivity indexes. By exploiting the duality
between cost and input distance functions, we obtain a measure of
profitability, as an approximation for the Fisher productivity index. We
measure productivity and profitability changes when SO~2~ emissions are
ignored in the production technology and when these emissions appear as
bad output. We find that the productivity is higher when the bad outputs
are modeled as weakly disposable in comparison to the situation when
they are modeled as freely disposable. But we do not find any
significant difference in profitability under these alternative methods
of modeling of production technology concerning the disposability of bad
outputs.

JEL Classification Number: L5, N5, Q2, Q4

**Key Words**: Electricity Generating Plants, Productivity,
Profitability, SO~2~ Allowance Program.

**1. Introduction**

The paper aims to examine the changes in productivity and profitability
of US electric utility plants during the period of the application of
tradable permit system, known as SO~2~ allowance system. We estimate the
input distance function using a panel data on 67 electricity-generating
plants for the period 1995-2001. Malmquist productivity and its
components- technical efficiency change and technical change are
measured on the basis of the estimated parameters. Fisher Productivity
index has an interpretation in terms of Georgescu-Roegen's (1951) notion
of 'return to dollar', a measure of profitability (Althin et al., 1996).
We also use the parameters of the distance function to measure the
changes in profitability over time.

Title IV of the 1990 Clean Air Act Amendments (CAAA) establishes a
market for transferable SO~2~ emissions allowance among electric
utilities. Under this system, reduction in SO~2~ emissions are achieved
by setting a cap along with allowing the trading of marketable pollution
permits, popularly known as SO~2~ *allowances*. Here each generating
unit of the electricity industry is allocated a fixed number of
allowances each year in proportion to emissions during the 1985-87
period and is required to hold one allowance for each ton of SO~2~ it
emits. Electricity generating firms can now transfer allowance among
their own facilities, sell them to other firms, or bank them for use in
future years. Thus the flexibility provided by this program enables the
generating units to pursue a variety of compliance options to meet the
regulation obligations, including scrubber installation, fuel switching,
energy efficiency and allowance trading. Through emissions trading
electricity generating firms have the incentive to find the lowest-cost
means of achieving compliance and to reap financial rewards for
developing those means. We examine the productivity and profitability
changes of these firms during this period of trading in SO~2~
allowances.

Previous studies have tried to examine the gains from trading in
emissions in comparison to command and control alternatives such as
forced scrubbing and a uniform emission rate standard (e.g., Carlson et
al., 2000) or to judge whether there remain opportunities to reduce
abatement costs through allowance trading even after plant owners have
taken advantages of other cost reducing opportunities (e.g., Swinton,
2002; Coggins and Swinton, 1996). Fare et al. (2002) have estimated the
total cost of pollution abatement of US electric plants and compared
these estimates with the survey estimates of pollution abatement costs
incurred by power plants. Kolstad and Turnovsky (1998) have shown that
technological change has been substantially sulfur saving, which
supports the case that technical progress was responsible at least in
part for the drop in abatement costs of SO~2~ emissions. This explains
the differentials of observed prices of SO~2~ allowance and the
predicted abatement costs of these emissions. But none of these studies
have tried to examine the productivity and profitability changes during
the period when the sulfur emissions are regulated through an
environmental policy which relies on the logic of 'cap and trade' in
emissions.

Although the US electric industry has received increasing attention,
there are only a few empirical studies on productivity impacts of
environmental regulation. To the best of our knowledge, these include
Gollop and Roberts (1983) and Yaisawarng and Klien (1994). Gollop and
Roberts (1983) used the cost function framework to analyze the effects
of SO~2~ restrictions on the rate of productivity growth in the electric
power industry over the period of 1973-1979. They develop a firm
specific measure of regulatory intensity and find that emission
regulations result in significantly higher generating costs and average
rate of productivity growth reduces by 0.59 percentage points per year
due to these regulations. Yaisawarng and Klien (1994) investigated the
productivity performance of US power plants during 1985-1989 using a
framework similar to the present study. They used the data envelopment
analysis (DEA) to compute the cumulative Malmquist input-based
productivity index. They account for input used to control sulfur
emissions as well as emissions output. They find that productivity
decreased from 1985 to each of their three target years, but grew in the
last year.

The computation of profitability requires data on the prices of inputs
and outputs. Price information can be had for the desired outputs and
inputs, but for unwanted products price information does not exist. Like
that, productivity is conventionally measured by the index numbers and
the computation of index numbers is possible with the data of prices of
all outputs and inputs. With regard to prices of bad outputs Repetto et
al. (1996) suggest the need to establish market valuation for
environmental damages, so that reductions in those damages can be
credited to firm output. To get information on abatement expenditures,
surveys have been used as principal methods but their accuracy has
always been the issue of much concern. Moreover, these expenditure
estimates are unlikely to be available on yearly basis. Thus, one cannot
compute profitability directly, but can retrieve that information
indirectly using the duality theory. In this case one can compute
Malmquist productivity index using only input and output quantity data
and the duality between the input distance function and the cost
function provide a measure of profitability, namely Fisher productivity
index.

Moreover, the conventional productivity measures, by neglecting the
decrease in the SO~2~ emissions, fail to recognize that a higher
proportional increase in the production of good output was feasible with
given inputs if adequate efforts had not been made to reduce SO~2~. Thus
the conventional measures are biased because environmental compliance
expenditures by the firms lead to environmental improvements, both the
expenditure and improvement should be accounted for in the measurement
of productivity changes. An environmentally sensitive measure, when the
abatement of pollution is costly, leads to higher productivity growth
estimates for a firm because this measure is sensitive to changes in
pollution levels and credits the firms for pollution abatement
activities while the conventional measure does not. In other words, it
can be said that the environmentally sensitive measure accounts not only
for the production of marketable outputs but also for producing it with
a lower level of sulfur emissions. Therefore the Malmquist index
measured with weak disposability of bad outputs is a better indicator of
true productivity growth from the social point of view.

Our approach to measure productivity and profitability changes of US
electric utility plants during the regime of SO~2~ allowance program
differs from the existing literature. Brannlund et al. (1995) have
examined the impact on the environmental regulations on firm profits in
the Swedish pulp and paper industry. They have adopted the
non-parametric programming approach and measure the impact for the cross
section data. Althin et al. (1996) have provided the theoretical
framework for measuring the changes in the productivity and
profitability of firms in terms of input distance function when the firm
is producing only the good outputs. We apply their results when the firm
is producing both good as well as bad outputs and the later are
regulated. Moreover, we take production inefficiency into account in
deriving the measure of change in elasticity of scale, a component of
profitability. This point contrasts markedly with Althin et al. since
plants generally operate on different levels of efficiency; therefore
taking the inherent inefficiency into account should provide a more
realistic measure.

There are several studies on the measurement of productivity changes in
industries, which produces good and bad outputs simultaneously during
the production process. Some of these studies have treated the bad
outputs as inputs[^1], while the others have treated them as a synthetic
output such as pollution abatement (e.g. Gollop and Robert, 1983).
Sushamamurty and Russell (2002) have pointed out that the treatment of
bad outputs as inputs is not consistent with the material balance
approach. The approach adopted by Gollop and Robert to treat the
reduction in bad output as good output creates a different non-linear
transformation of the original variable in the absence of base
constrained emission rates (Atkinson and Dorfman, 2002). Pittman (1983)
proposed to overcome this problem by treating good and bad outputs
non-symmetrically. He was of the view of measuring the maximal radial
expansion of good outputs and contraction of bad outputs. Chung et al.
(1997) has used the directional distance function to calculate
production relationships involving good and bad outputs to overcome this
problem. The disadvantage of this approach in the present context is
that it is difference based whereas the Malmquist productivity index and
Fisher index are ratio based. Therefore, following Atkinson and Dorfman
(2002) input distance function is used as an analytical tool in the
present study. It provides a radial (ratio based) measure of efficiency
which signals better performance for observations that are using lesser
quantities of inputs for the given level of outputs. This function is
less restrictive in the sense that it is not treating the bad outputs,
either inputs or pollution abatement, as good output, rather it treats
the bad outputs as an \'exogenous\' technology shifter.

The remainder paper is organized as follow: The theoretical framework of
the study is presented in Section 2. Section 3 describes the empirical
model. The data set employed in the paper is explained in Section 4. The
results of the study are discussed in Section 5. The conclusions follow
in Section 6.

**2. Theoretical Framework**

Conventionally a firm's performance is assessed by a measure of
productivity based on the estimates of production function without
considering the joint production of good output and bad outputs
(pollution loads). This results in a potentially misleading comparison
of productivity of firms producing significant amounts of undesirable
outputs, such as water and air pollution. When firms divert resources
for reducing undesirable outputs, the input/output ratios of the firm
are higher and the productivity of the plant appears lower. It is
understood that the constraints imposed by environmental regulation on
the decisions of the firm will be subsumed within an overall measure of
productivity.

Consider a firm employing a vector of inputs ***x**∈ℜ^N^~+~* to produce
a vector of outputs **y**∈ℜ^M^~+~ where *ℜ^N^~+~, ℜ^M^~+~,* are
non-negative *N*- and *M*-dimensional Euclidean spaces, respectively.
Let *P(**x**)* be the feasible output set for the given input vector
***x*** and *L(**y**)* is the input requirement set for a given output
vector ***y***. Now the technology set is defined as (Fare et al. 1994)

*T = {(**y**, **x**) ∈ ℜ^M+N^~+,~ **y**∈ P(**x**), **x**∈L(**y**) }.*
(1)

The assumptions about the disposability of outputs become very important
in the context of a firm producing both good and bad outputs. The normal
assumption of strong or free disposability about the technology implies,
*if (y~1~, y~2~ ) ∈ P(**x**)* and *0 ≤ y~1~ \* ≤ y~1~ , 0 ≤ y~2~\* ≤
y~2~ ⇒ (y~1~\*,y\*~2~ ) ∈ P(**x**)*. This means, we can reduce some
outputs given the other outputs or without reducing them. This
assumption may exclude important production processes, such as
undesirable outputs. For example, in the case of air pollution, Sulfur
dioxide (SO~2~), Nitrogen Oxides (NO~x~) and Carbon Dioxide (CO) are
regulated and the firm cannot freely dispose of them. The assumption of
weak disposability is relevant to describe such production processes.
The assumption of weak disposability implies, *if **y** ∈ P(**x**) and 0
≤*$q$ *≤ 1 ⇒* $q$***y** ∈ P(**x**)*. This means a firm can reduce the
bad output only by decreasing simultaneously the good output. Hence one
can characterize a world where there are non-priced outputs in
production that the plant manager has an interest in controlling. The
assumption of weak disposability about the production technology enables
one to consider this behavior of the firm while defining the factor
productivity. For the problem considered here it is convenient to
decompose the plant's output vector into two sub-vectors, ***y** =
(**g**, **b**)* which represent the desirable output, ***g***, and
undesirable outputs, ***b***, of the production process. The difference
between these two types of outputs is captured via the disposability
assumptions. Here it is assumed that the desirable outputs are freely
disposable and the undesirable outputs may only be weakly disposable.
That is, the firm may have to expand resources (or reduce 'good' output)
to reduce the bad outputs.

## 

## Input Distance Function 

The conventional production function defines the maximum output that can
be produced from an exogenously given input vector while the cost
function defines the minimum cost to produce the exogenously given
output. The output and input distance functions generalize these notions
to a multi-output case. The input distance function
($D_{i}(y,x))$describes "how far" an input vector is from the boundary
of the representative input set, given the fixed output vector.

Formally, the input distance function is defined as

$D_{i}^{t}\left( y^{t},x^{t} \right) = \text{ min}\left\{ \lambda:\left\lbrack \frac{x^{t}}{\lambda},y^{t} \right\rbrack \in T^{t} \right\}$
(2)

Equation (2) characterizes the input possibility set by the maximum
*equi*-proportional contraction of all inputs consistent with the
technology set (1). These functions are defined for the technology
$T^{t} =$can produce$y^{t}$, as the 'maximal' feasible proportional
contraction of the inputs. The 'mixed' periods
functions$D_{i}^{0}\left( y^{1},x^{1} \right)$and
$D_{i}^{1}\left( y^{0},x^{0} \right)$ are defined in the same manner.
The input distance functions can be used to measure the Debreu-Farrell
technical efficiency. The input distance function is homogeneous of
degree one in inputs and dual to the cost function.[^2] That is:

$C_{i}(\lbrack g,b\rbrack,w,t) = \underset{}{\underset{x}{\text{min}}\left\{ \text{wx}:D(\lbrack g,b\rbrack,x,t) \geq 1 \right\}}$
(3)

where $w$is a vector of input prices and C is a unit cost function if
the costs are minimized. This implies that the value of input distance
function would be equal to one only when the inputs are used in their
cost minimizing proportions, i.e.,

$C_{i}(\lbrack g,b\rbrack,w,t) = \frac{\text{wx}}{D}(\lbrack g,b\rbrack,x,t)$
(4)

Fare and Primont (1995) show that the shadow price for each input is
given by

$w =$$C_{i}(\lbrack g,b\rbrack,w,t)\nabla_{x}D_{i}(\lbrack g,b\rbrack,x,t)$
(5)

If one assumes that the efficiency measures over the desirable outputs
and inputs are well defined and behave as expected, the bad outputs can
be treated as exogenous shifters of the technology set similar to a time
trend or state of technology variable. The advantage of treating the bad
outputs as a shifter of technology is that it credits (penalizes) the
firms for reducing (increasing) the level of bad outputs that they
produce (Atkinson and Dorfman 2002). To emphasize the point the input
distance function is now written as:

$D_{i}\left\langle \text{g,x,}t \middle| b \right\rangle = \underset{\lambda}{\text{sup}}\left\{ \lambda:\left\langle \frac{x}{\lambda},g \middle| b \right\rangle \in T\left\langle \text{x,g},t \middle| b \right\rangle \right\}$
(6)

Assuming a single bad output, Atkinson and Dorfman have derived the
appropriate monotonocity condition for bad outputs as follows. The input
distance function is monotonically non-decreasing in inputs
$\left( \frac{\partial D_{i}}{\partial x_{n}} \geq 0 \right)$ and
monotonically nonincreasing in good outputs
$\left( \frac{\partial D_{i}}{\partial g_{m}} \leq 0 \right)$. Now
assume a single bad output and take the partial total differentiation of
the input distance function equation (6) evaluated on the frontier at a
fixed time
\[implying$D_{i}\left\langle \text{g,x},t \middle| b \right\rangle = 1$
and $\text{dt} = 0$\] to obtain

$\text{dD}_{i} = \sum_{}^{}\frac{\partial D_{i}}{\partial g_{m}}\text{dg}_{m} + \sum_{}^{}\frac{\partial D_{i}}{\partial x_{n}}\text{dx}_{n} + \sum_{}^{}\frac{\partial D_{i}}{\partial b}\text{db} = 0$

In order to keep the firm on the input distance frontier,
let$\text{dg}_{m} = 0,\forall m$ and obtain

$\frac{\partial D_{i}}{\partial b} = - \sum_{}^{}\frac{\partial D_{i}}{\partial x_{n}}\frac{\text{dx}_{n}}{\text{db}}$

With the weak disposability assumption that the disposal of bad outputs
is costly it implies that $\frac{\text{dx}_{n}}{\text{db}} \leq 0$ which
combined with the non-negativity property for inputs
$\frac{\partial D_{i}}{\partial x_{n}} \geq 0$, yields
$\frac{\partial D_{i}}{\partial b} \geq 0\text{.}$

## Malmquist Productivity Index

The Malmquist index is defined as the ratio of distance functions. This
index requires two mixed period distance function, i.e. t=1,2. The input
based Malmquist is defined as the geometric mean of two periods indexes
as suggested by Caves et al. (1982). Formally the index is defined as:

$M = \left\{ \frac{D_{i}^{0}\left( y^{0},x^{0} \right)}{D_{i}^{0}\left( y^{1},x^{1} \right)}\frac{D_{i}^{1}\left( y^{0},x^{0} \right)}{D_{i}^{1}\left( y^{1},x^{1} \right)} \right\}^{\frac{1}{2}}$
(7)

The above equation can equivalently be written as:

$M = \underset{\text{EfficiencyChange}}{\overset{\left\lbrack \frac{D_{i}^{0}\left( y^{0},x^{0} \right)}{D_{i}^{1}\left( y^{1},x^{1} \right)} \right\rbrack\text{.}}{\underbrace{}}}\underset{\text{TechnicalChange}}{\overset{\left\lbrack \frac{D_{i}^{1}\left( y^{1},x^{1} \right)}{D_{i}^{0}\left( y^{1},x^{1} \right)}\frac{D_{i}^{1}\left( y^{0},x^{0} \right)}{D_{i}^{0}\left( y^{0},x^{0} \right)} \right\rbrack^{\frac{1}{2}}}{\underbrace{}}}$
(8)

The first ratio measures the changes in the input-based measure of
Farrell technical efficiency between years 0 and 1, i.e., efficiency
changes. The geometric mean of the two ratios inside the bracket
captures the shift in technology between the two periods. This term
measures the technical change, i.e. shift in the production frontier of
the firm over time. The value of M greater (less) than unity indicates
the improvement (deterioration) over time in productivity.

## 

## Fisher Productivity Index and Profitability Changes

To introduce the Fisher productivity index, we need along with inputs
and outputs quantity variable, the inputs and outputs price vectors
namely $w^{t}$, and $p^{t}$ respectively also. The Fisher productivity
index is defined as the ratio of the Fisher ideal output quantity index
and the Fisher ideal input quantity index. Formally

$F = \left( \frac{p^{1}y^{1}}{p^{1}y^{0}}\frac{p^{0}y^{1}}{p^{0}y^{0}} \right)^{\frac{1}{2}}/\left( \frac{w^{1}x^{1}}{w^{1}x^{0}}\frac{w^{0}x^{1}}{w^{0}x^{0}} \right)^{\frac{1}{2}}$
(9)

or

$F = \left\{ \frac{p^{1}y^{1}}{w^{1}x^{1}}/\frac{p^{0}y^{0}}{w^{0}x^{0}} \right\}^{\frac{1}{2}}\text{.}\left\{ \frac{p^{0}y^{1}}{w^{0}x^{1}}/\frac{p^{1}y^{0}}{w^{1}x^{0}} \right\}^{\frac{1}{2}}$
(10)

Here $\frac{p^{0}y^{0}}{w^{0}x^{0}}$ is the Georgescu-Roegen's (1951)
notion of 'return to dollar'. The first part of equation (10) measures
the current period profitability changes whereas the second part
measures the mixed period profitability changes. For the interpretation
of the Fisher output oriented productivity index as a measure of
profitability for simplicity we assume that prices are constant, i.e.,
$w^{0} = w^{1}$and $p^{0} = p^{1}$ then equation (10) can be written as:

$\overset{\hat{} =}{F}$$\left\{ \frac{p^{1}y^{1}}{w^{1}x^{1}}/\frac{p^{0}y^{0}}{w^{0}x^{0}} \right\}$
(11)

Following the notion of 'return to the dollar', the equation (11)
implies that there is an improvement in profitability of the firm if
$\overset{\hat{}}{F}$\> 1, it is constant if
$\overset{\hat{} =}{F}$`<!-- -->`{=html}1 and there is deterioration in
profitability if the $\overset{\hat{}}{F}$\<1.

In order to measure profitability of the firms, we introduce the profit
maximization problem as:

$\prod_{}^{}{= \underset{y^{t}}{\text{max}}}\left\{ p^{t}y^{t} - C^{t}(y^{t},w^{t}) \right\},t = 0,1\text{.}$
(12)

The first order condition for profit maximization, when the cost
function is differentiable, is given by:

$p_{m}^{t} = \frac{\partial C^{t}(y^{t},w^{t})}{\partial y_{m}^{t}},m = 1,\text{.}\text{.}\text{.}\text{.}\text{.}\text{.},M\text{.}$
(13)

From this equation, we get

> $$$p^{t}y^{t} = C^{t}(y^{t},w^{t})\varepsilon_{c}(y^{t},w^{t})$ (14)

since $\varepsilon_{c}(y^{t},w^{t})$is the cost elasticity of scale
(see, Fare and Primont 1995), i.e.,

$\varepsilon_{c}(y^{t},w^{t}) = \sum_{m = 1}^{M}{\frac{\partial C^{t}(y^{t},w^{t})}{\partial y_{m}^{t}}\frac{y_{m}^{t}}{C^{t}(y^{t},w^{t})}}$
(15)

Thus the 'return to dollar' is equal to the cost elasticity (from
equation (14), namely

$\varepsilon_{c}(y^{t},w^{t}) = \frac{p^{t}y^{t}}{C^{t}(y^{t},w^{t})},t = 0,1\text{.}$
(16)

Moreover, the first part of equation (10), that is the simplified
measure of change in profitability, using equations (4) and (16), can be
written as[^3]

$\overset{-}{F} = \left\{ \frac{D_{i}^{0}(x^{0},y^{0})}{D_{i}^{1}(x^{1},y^{1})}\frac{\varepsilon_{c}^{1}(y^{1},w^{1})}{\varepsilon_{c}^{0}(y^{0},w^{0})} \right\}^{\frac{1}{2}}$
(17)

This measure requires information on prices of inputs and outputs, and
in the context of bad outputs the price information is either absent or
not reliable, therefore we need a measure of scale of elasticity based
on input and output quantity only. Therefore we use the primal
input-based measure of elasticity of scale, i.e. (See Fare and Primont
1995)

$\varepsilon_{\text{Di}}(x,y) = - \sum_{m = 1}^{M}{\frac{\partial D_{i}(x,y)}{\partial y_{m}}\frac{y_{m}}{D_{i}(x,y)}}$
(18)

This is also known that
$\varepsilon_{\text{Di}}(x,y)$=$\frac{1}{\varepsilon_{c}}(y,w)$, when
$D_{i}(x,y) = 1$ (see Fare and Primont 1995, p.53), therefore, equation
(17) can be expressed as:

$\overset{-}{F} = \left\{ \frac{D_{i}^{0}(x^{0},y^{0})}{D_{i}^{1}(x^{1},y^{1})}\frac{\varepsilon_{\text{Di}}^{1}(x^{1},y^{1})}{\varepsilon_{\text{Di}}^{0}(x^{0},y^{0})} \right\}^{\frac{1}{2}}$
(19)

This equation shows that the change in 'return to dollar' can be
expressed as the square root of the product of change in efficiency and
scale elasticity. The equation (19) is true when the firms are operating
at the frontier, but in practice the value of input distance function is
generally observed greater than one, i.e. $D_{i}(x,y)$\>1. Therefore,
$D_{i}(x,y)\varepsilon_{\text{Di}}(x,y)$=-$\varepsilon_{c}(y,w)$, and
$\overset{-}{F}$can be expressed as

$\overset{-}{F} = \left\{ \frac{\varepsilon_{\text{Di}}^{1}(x^{1},y^{1})}{\varepsilon_{\text{Di}}^{0}(x^{0},y^{0})} \right\}^{\frac{1}{2}}$
(20)

Thus the change in return to dollar is the square root of the ratio of
scale elasticities over time.

## 

## 3. Empirical Model

The computation of Malmquist productivity index and thereby the change
in profitability index for US Electric Utilities requires the
computation of distance functions. The distance functions can be
computed either non-parametrically using the Data Envelope Analysis
(DEA) or parametrically. Here we adopt the parametric approach for the
computation of distance functions, the advantage of this approach is
that it is differentiable. We employ the translog form of input distance
function that is twice differentiable and flexible. The form is given by

$\begin{array}{r}
\text{ln}D_{i}^{t}(x^{t},y^{t},t) = \alpha_{0} + \sum_{n = 1}^{N}{\alpha_{n}\text{ln}x_{n}^{t}} + \sum_{m = 1}^{M}{\beta_{m}\text{ln}}y_{m}^{t} + \frac{1}{2}\sum_{n = 1}^{N}{\sum_{n' = 1}^{N}\alpha_{\text{nn}'}}\text{ln}x_{n}^{t}\text{ln}x_{n'}^{t} + \frac{1}{2}\sum_{m = 1}^{M}{\sum_{m' = 1}^{M}\beta_{\text{mm}'}}\text{ln}y_{m}^{t}\text{ln}y_{m'}^{t} \\
 + \sum_{n = 1}^{N}{\sum_{m = 1}^{M}{\gamma_{\text{nm}}\text{ln}}y_{m}^{t}\text{ln}x_{n}^{t} + \delta_{0}t + \frac{1}{2}}\delta_{\text{00}}t^{2} + \sum_{n = 1}^{N}{\gamma_{\text{nt}}t\text{ln}x_{n}^{t}} + \sum_{m = 1}^{M}{\gamma_{\text{mt}}t\text{ln}}y_{m}^{t},(\text{21})
\end{array}$To compute the parameters of equation (21), we use the
linear programming approach developed by Aigner and Chu (1968), that is

Minimize
$\sum_{k = 1}^{K}\left\{ \text{ln}D_{i}^{t}(x^{t},y^{t},t) - \text{ln}1 \right\},k = 1,2,\text{.}\text{.}\text{.}\text{.}\text{.}K\text{.}$
(22)

Subject to (i) $\text{ln}D_{i}^{t}(x^{t},y^{t},t) \geq 0$

\(ii\)
$\frac{\partial\text{ln}D_{i}^{t}(x^{t},y^{t},t)}{\partial\text{ln}y_{m}^{t}} \leq 0,m = 1,\text{.}\text{.}\text{.}\text{.}\text{.}\text{.}\text{.},i\text{.}$

\(iii\)
$\frac{\partial\text{ln}D_{i}^{t}(x^{t},y^{t},t)}{\partial\text{ln}y_{m}^{t}} \geq 0,m = i + 1,\text{.}\text{.}\text{.}\text{.}\text{.}\text{.}\text{.},M\text{.}$

\(iv\)
$\frac{\partial\text{ln}D_{i}^{t}(x^{t},y^{t},t)}{\partial\text{ln}x_{n}^{t}} \geq 0,n = 1,\text{.}\text{.}\text{.}\text{.}\text{.}\text{.}\text{.},N\text{.}$

\(v\)
$\sum_{n = 1}^{N}{\alpha_{n} = 1,}\sum_{n' = 1}^{N}\alpha_{\text{nn}'} = \sum_{n = 1}^{N}\gamma_{\text{nm}} = 0,n,n' = 1,\text{.}\text{.}\text{.}\text{.}\text{.}\text{.}\text{.},N$

\(vi\)
$\alpha_{\text{nn}'} = \alpha_{n'n},\beta_{\text{mm}'} = \beta_{m'm},n,n' = 1,\text{.}\text{.}\text{.}\text{.}\text{.}\text{.}\text{.},N,m,m' = 1,\text{.}\text{.}\text{.}\text{.}\text{.}\text{.},M$

Where K denotes the number of observations. The restrictions in (i)
ensures that the value of input distance function is greater than or
equal to one as the logarithm of this function are restricted to be
greater than or equal to zero. Restriction in (ii) enforces the
monotonocity condition of non-increasing of input distance function in
good outputs, whereas the restriction in (iii) and (iv) enforces that
the input distance function is non-decreasing in bad outputs and inputs
respectively. Restriction (v) and (vi) impose the homogeneity and
symmetry conditions respectively as required by the theory.

The Malmquist index includes total factor productivity changes due to
technical change and technical efficiency changes, to the exclusion of
production scale effects (Orea, 2002). The calculation of the growth
rate in the Malmquist index in equation (8) was carried out as follows:

$\text{ln}M = \left\lbrack \text{ln}D_{i}^{0}(x^{0},y^{0}) - \text{ln}D_{i}^{1}(x^{1},y^{1}) \right\rbrack - \frac{1}{2}\left\lbrack \frac{\partial\text{ln}D_{i}^{1}(x^{1},y^{1})}{\partial t} + \frac{\partial\text{ln}D_{i}^{0}(x^{0},y^{0})}{\partial t} \right\rbrack$
(23)

This equation provides a meaningful decomposition of $\text{ln}M$into
changes in technical efficiency and technical changes. The negative sign
of the second term transforms technical progress (regress) into positive
(negative) value. This decomposition has the same structure as the
traditional input-oriented Malmquist productivity index introduced by
Caves et al. (1982).

**4. Data**

Since we are interested in the productivity and profitability effects of
controlling SO~2~ emissions under the Allowance program since 1995 to
2001, we restricted our attention to electricity generating plants for
which each generating unit had a minimum installed nameplate generating
capacity of 25 megawatts.[^4] We exclude from our sample plants, which
have missing data or reporting errors in a specific year. The
deterministic linear programming is sensitive to outliers, to minimize
the effects of outliers; we first examined the ratios of each of output
to each input and compared their descriptive statistics across periods.
If we observed any abnormality for any plant for a specific year, we
excluded that plant from our data set. Thus our balanced panel data
consist of 67 electric generating plants for the years 1995-2001.

The process of fossil-fueled electricity generation typically uses three
conventional inputs; namely, fuel, labor and capital to produce
electricity and emissions of sulfur dioxide. The data come primarily
from two government agencies- the Federal Energy Regulatory Commission
(FERC) and the US Environmental Protection Agency (EPA). These agencies
have over the years provided the public with access to data concerning
regulated utilities and pollution. The FERC maintains an online database
of FERC Form 1 for the years 1994 to the present. The Form 1 provides
annual information of electricity production activities at the plant
level. The EPA maintains an emissions database for all major US
pollution sources. Its Aerometric Information Retrieval System (AIRS)
database is the source of SO~2~ data for the years 1995 to the present.
The 1990 CAAA required all affected power plants to install continuous
emission monitoring system (CEMS) by 1995. Consequently, all SO~2~ data
from 1995 on are CEMS stack readings.

In summary, our data set consists of a balanced panel of 67 steam
electric utility plants operating during 1995-2001. Variables in the
dataset include net generation, fuel input, labor and capital. We employ
total net generation in million kilowatt-hours (kWh), fuel in 10^12^
British thermal units (BTUs) of heat content to neutralize the
heterogeneous nature of coal as well as to allow for different type of
fuel inputs. Labor is measured as the annual average number of
employees. Capital is measured in 1996 million dollars. We use this
measure of capital rather than the installed nameplate capacity because
we are interested not only in the generating capacity of a plant, but
also the extent to which the plants have invested in equipment to reduce
SO~2~ emissions. The descriptive statistics are provided in Table 1.

**5. Results**

The input distance function in (21) is estimated with and without
pollutant outputs. This allows us to examine the importance of the
inclusion of environmental effects of production activities in our
analysis of productivity and profitability changes. In Table 2 the
estimated parameters for a deterministic distance function following the
approach described in Section 3 are presented. Both models, when SO~2~
is considered (model1) and when SO~2~ is ignored (model2) yield first
order coefficients on inputs that have signs consistent with economic
theory. That is the positive signs of inputs with respect to the input
distance function indicate that the value of the function is
non-decreasing with respect to inputs, i.e., as inputs are used more
efficiently a firm becomes closer to the frontier. The distance
functions satisfy the regulatory conditions on good outputs and
convexity on inputs and bad outputs for average values of the
explanatory variables.

As described earlier the input distance function serves as an
input-based measure of technical efficiency, the yearly average value of
this function in both the models are presented in Table 3. We observe
that the efficiency scores when SO~2~ emissions are ignored are lower in
comparison to the situation when this pollutant is considered. It
reveals that the potential to increase the production of electricity
with the given bundle of input decreases as the power plants are not
allowed to freely dispose off the emissions of sulfur dioxide. On
average the performance of these electricity producing firms ranges from
0.695 to 0.813, revealing that 19 to 30.5 percent of the current
conventional inputs can be saved by improving managerial style and
reorganization to the best observed practice. It is also observed that
under both the situations, the average efficiency scores are decreasing
continuously. The difference in technical efficiency under these two
alternative formulations of production technology remains constant up to
1999 and it starts to increase after that.

Tables 4 and 5 present the average Malmquist productivity and Fisher
productivity indexes. In these tables we present also the components of
Malmquist productivity indices, viz., technical efficiency changes and
technological changes. (Results by plants are available from the
author). Here it should be noted that Malmquist index represent an
aggregate measure of 'true' productivity changes over time rather than a
theoretical change, as it takes into account changes in technical
efficiency over time also. Our methods of computing the productivity
changes and its components as well as profitability changes reflected by
the Fisher productivity look at marginal changes between adjunct
periods. Recall that index values greater (less) than one denote
improvements (deterioration) in the relevant performance. Here we have
calculated all the indices for both cases: when SO~2~ is ignored and
when of SO~2~ is considered as bad output in the production process.

When the technology is modeled assuming that power plants can dispose
off the emissions of sulfur dioxide without incurring extra costs for
the given level of electricity, as is conventionally done, the Fisher
index shows profitability declines through 1996 to 2001 (Table 5). The
Malmquist productivity index has value less than unity for all the study
years in comparison to the adjunct years. The decomposition of the
Malmquist index reveals that technical efficiency change index has value
less than one in all the years, except 2000 when it is almost equal to
one. Which implies that technical efficiency is declining over the study
period. The technological change index has value less than one through
out the study period. The changes in the technical efficiency change
index and technological change index explain the variation in the
Malmquist productivity index.

When the SO~2~ emissions are considered in the production technology, we
observe that the movements in the Malmquist productivity index and its
components are in the same direction as they are when the production
technology assumes that pollution can be thrown away without incurring
any cost. Unlike Malmquist index, the Fisher index has lower values for
all the study years when the disposal of SO~2~ is costly in comparison
to the situation when the disposal of sulfur dioxide emissions is free
and in both the situations its value is less than one and declining over
time. The comparison of technical efficiency change and technological
change under alternative production technologies reveals that when the
pollution is modeled as bad output in the production process the
electricity generating plants observe high technical efficiency change
and technical change in comparison to the production process when SO2 is
assumed to be freely disposable in the production process.

Managi et al. (2002) takes the ratio of productivity index measures
under weak and strong disposability of bad outputs as a measure of
productivity index of environmental outputs. We extend this concept to
the measures of profitability also. The ratio of profitability under
weak and strong disposability of bad outputs measures the change in
profitability due to changes in the environmental outputs. Table 6
presents the ratios of Malmquist productivity and Fisher productivity
index under these alternative production technologies concerning the
disposability of bad outputs. This table shows that the index of
environmental productivity is greater than one through out the study
period, crediting the firms for the efforts taken on pollution
abatement. But the environmental profitability figure is less than one
in the first two years and it becomes greater than one for the next
three years and again it becomes less than one in the last year, i.e. we
are not observing a consistent trend in environmental profitability. To
measure whether the environmental productivity and environmental
profitability figures are different from one we apply the various
non-parametric tests (Table 7). From these non-parametric tests it is
clear that the environmental productivity figures are statistically
different from one, but the figures of environmental profitability are
not different from one for the whole sample. But when these tests are
applied for yearly figures, it was found that environmental productivity
statistically differs from one during 1998-2001 and environmental
profitability statistically differs from one only in 1999-2000.

At the annual mean level, we observe that the difference in productivity
and profitability under alternative production technologies concerning
the disposability of bad output is very low. This low level of
difference under weak and strong disposability conditions in
productivity and profitability can be explained by the fact that the US
electricity industry is under regulation since decades and making
environmental compliance efforts by investing in abatement technologies.
Therefore, the modeling of these firms under the assumption of free
disposability of bad outputs may be biased and it reduces the difference
in productivity and profitability under alternative production
technologies (Fare et al., 2002).

**6. Conclusion**

In this paper, we have developed and illustrated an analytical framework
for calculating plant specific productivity and profitability measures.
A distinguishing feature of this framework is that it provides two-piece
of information simultaneously. It describes the structure of production
technology, and it provides measures of productivity and profitability
for each producer. The major advantage of this framework is that it does
not require price information for measuring productivity and
profitability of producer.

We estimated productivity and profitability changes for a sample of 67
electricity-generating plants during the years 1995 to 2001, the period
of SO~2~ allowance system. We have done this by employing the input
distance function, and then computing Malmquist and Fisher indexes in
the conventional way ignoring the production of SO~2~ emissions and
considering them as bad output in the production process. We have found
that during this era of market-based regulation, productivity and
profitability is declining under both the production technology
situations. It is observed that when the emissions of sulfur are
included, the productivity of the electricity-producing firms is
slightly higher in comparison to the situation when it is measured in
conventional way, crediting the firms for their abatement efforts.
Moreover, it is observed that gap in profitability due to environmental
regulations does not manifest symmetry of any form.

**Acknowledgement**

This research was completed when the author was a Visiting Scholar at
the Department of Agricultural and Consumer Economics, University of
Illinois at Urbana-Champaign. The author wishes to thank Professors
Madhu Khanna and M.N. Murty, for their valuable comments on an earlier
draft of this paper and encouragement, also acknowledges the financial
support provided by the Environmental Economics Overseas Fellowship
Committee, under the World Bank Aided Environmental Management Capacity
Building Project in India for this visit. Helpful comments were provided
by the two anonymous referees and the editor of the journal and the
participants of 12^th^ conference of the European Association of
Environmental and Resource Economists at Bilbao (Spain).

### References

Aigner, D. J. and S. F. Chu (1968), "Estimating the industry production
function", *American Economic Review* 58, 826-39.

Althin, R., R. Fare and S. Grosskopf (1996), "Profitability and
productivity change: an application to Swedish pharmacies", *Annals of
Operations Research*, 66, 219-230.

Atkinson,S.E. and R.H. Dorfman (2002) \"Bayesian measurement of
productivity and efficiency in the presence of undesirable outputs:
crediting electric utilities for reducing air pollution\", Department of
Economics, University of Georgia, Athens.

Boggs, R.L. (1997) *Hazardous Waste Treatment Facilities: Modeling
Production with Pollution as Both an Input and an Output*. Unpublished
Ph.D. dissertation, University of North Carolina, Chapel Hill.

Brannlund, R., R. Fare and S. Grosskopf (1995), "Environmental
Regulation and Profitability: An Application to Swedish Pulp and Paper
Mills", *Environmental and Resource Economics* 6, 23-36.

Carlson, C., D. Burtraw, M. Cropper, and K. L.Palmer (2000), "Sulfur
Dioxide Control by Electric Utilities: What Are the Gains from Trade?"
*Journal of Political Economy* 108(6), 1292--1326.

Caves, D.W., L.R. Christensen and W.E. Diewert (1982), "The economic
theory of index numbers and the measurement of input, output, and
productivity", *Econometrica*, 50, 1993-40.

Chung, Y., R. Fare and S. Grosskopf (1997), \"Productivity and
undesirable outputs: a directional distance function approach\",
*Journal of Environmental Management* 51, 229-240.

Coggins, J.S. and J.R. Swinton (1996), "The price of pollution: a dual
approach to valuing SO~2~ allowances," *Journal of Environmental
Economics and Management* 30, 58-72.

Cropper, M.L. and W.E. Oates (1992) "Environmental Economics: A Survey",
*Journal of Economic Literature* XXX:2 (June), 675-740.

Fare, R. and S. Grosskopf and C.A.K. Lovell (1994), *Production
Frontiers*, Cambridge University Press, Cambridge.

Fare, R.; S. Grosskopf and C. Pasuraka (2002), "Estimating pollution
abatement costs: a comparison of 'stated' and 'revealed' approaches",
paper presented at the Second World Congress of the Association of
Environmental and Resource Economists held at Monterey, CA, during June
23-27.

Fare, R. and D. Primont (1995), *Multi-Output Production and Duality:
Theory and Applications*, Kluwer Academic Publishers, Netherlands.

Georgescu-Roegen, N. (1951), "The aggregate linear production function
and its applications to von Neumann's economic model." In Koopmans, T.
(ed). *Activity Analysis of Production and Allocation*. Wiley, New York,
98-115.

Gollop, Frank M., and Mark J. Roberts (1983), "Environmental regulations
and productivity growth: the case of fossil-fueled electric power
generation." *Journal of Political Economy,* 91, 654--74.

Haynes, K.E., S. Ratick, W.M. Bowen and J. Cummings-Saxton (1993)
"Environmental Decision Models: U.S. Experience and a New Approach to
Pollution Management", *Environment International* 19, 261-75.

Haynes, K.E., S. Ratick and J. Cummings-Saxton (1994) "Toward a
Pollution Abatement Monitoring Policy: Measurements, Model Mechanics,
and Data Requirements", *The Environmental Professional* 16, 292-303.

Kolstad, Charles D., and Michelle H. L. Turnovsky (1998), "Cost
functions and nonlinear prices: estimating a technology with
quality-differentiated inputs", *Review of Economics and Statistics,*
80, 444--53.

Managi, S., J.J. Opaluch, D. Jin. And T.A. Grigalunas (2002)
\"Environmental regulations and technological change in the offshore oil
and gas industry: rethinking the Porter hypothesis\", Department of
Environmental and Natural Resource Economics, University of Rhode
Island, Kingston, Rhode Island, Working paper.

Murty, M.N. and Surender Kumar (2003), *Environmental and Economic
Accounting for Indian Industry*, New Delhi: Oxford University Press
(forthcoming).

Orea, L. (2002), "Parametric decomposition of a generalized Malmquist
productivity index", *Journal of Productivity Analysis*, 18, 5-22.

Pittman, R.W. (1981), "Issues in Pollution Control: Interplant Cost
Differences and Economies of Scale", *Land Economics* 57:1 (February),
1-17.

Pittman, R.W. (1983), \"Multilateral productivity comparisons with
undesirable outputs\", *The Economic Journal* 93, 883-891.

Reinhard, S., C.A.K. Lovell and G. Thijssen (1999), "Econometric
Estimation of Technical and Environmental Efficiency: An Application to
Dutch Dairy Farms", *American Journal of Agricultural Economics* 81:1
(February), 44-60.

Repetto, R., D. Rothman, P. Faeth and D. Austin (1996), "Has
Environmental Protection Really Reduced Productivity Growth", World
Resource Institute, Washington DC.

Sushamamurty, M. and R. Russell (2002) \"On modeling pollution
generating technologies\", University of California, Riverside.

Swinton, J.R. (2002), "The Potential for Cost Savings in the Sulfur
Dioxide Allowance Market: Empirical Evidence from Florida", *Land
Economics*, 78(3), 390-404.

Yaisawarng, S, and D.J. Klein (1994), "The effects of sulphur dioxide
controls on productivity change in the U.S. electric power industry",
*Review of Economics and Statistics*, 96, 447-60.

Table 1 Descriptive Statistics of the Variables Used in the Study

+------------+-----------+-----------+---------+---------+-----------+
|            | El        | SO~2~     | Labor   | Capital | > Heat    |
|            | ectricity | (tons)    |         | (       | > (10^12^ |
|            | (10^6^    |           |         | Million | > BTU)    |
|            | kWh)      |           |         | \$)     |           |
+------------+-----------+-----------+---------+---------+-----------+
| 1995       |           |           |         |         |           |
+------------+-----------+-----------+---------+---------+-----------+
| Mean       | 2946.31   | 24481.61  | 138.5   | 230.34  | 38.5      |
+------------+-----------+-----------+---------+---------+-----------+
| Maximum    | 13595.7   | 145577    | 419     | 1598.47 | 233       |
+------------+-----------+-----------+---------+---------+-----------+
| Minimum    | 117.5     | 309       | 31      | 17.23   | 1.74      |
+------------+-----------+-----------+---------+---------+-----------+
| Std. Dev.  | 2822.60   | 31933.65  | 97      | 257.59  | 39.17     |
+------------+-----------+-----------+---------+---------+-----------+
| 1996       |           |           |         |         |           |
+------------+-----------+-----------+---------+---------+-----------+
| Mean       | 3489.75   | 26322.32  | 136.75  | 216.87  | 40.27     |
+------------+-----------+-----------+---------+---------+-----------+
| Maximum    | 26631.2   | 180590.8  | 405     | 1570    | 212       |
+------------+-----------+-----------+---------+---------+-----------+
| Minimum    | 165.3     | 335.4     | 29      | 17.2    | 2.42      |
+------------+-----------+-----------+---------+---------+-----------+
| Std. Dev.  | 4178.76   | 35979.34  | 97.48   | 231.68  | 38.81     |
+------------+-----------+-----------+---------+---------+-----------+
| 1997       |           |           |         |         |           |
+------------+-----------+-----------+---------+---------+-----------+
| Mean       | 3230.74   | 28330.03  | 127.55  | 304.27  | 42.89     |
+------------+-----------+-----------+---------+---------+-----------+
| Maximum    | 16009.8   | 183797    | 392     | 3218.24 | 218       |
+------------+-----------+-----------+---------+---------+-----------+
| Minimum    | 145.5     | 107       | 29      | 17.07   | 2.18      |
+------------+-----------+-----------+---------+---------+-----------+
| Std. Dev.  | 3090.25   | 37988.25  | 88.29   | 555.58  | 40.66     |
+------------+-----------+-----------+---------+---------+-----------+
| 1998       |           |           |         |         |           |
+------------+-----------+-----------+---------+---------+-----------+
| Mean       | 3154.08   | 30193.88  | 138.51  | 216.95  | 47.16     |
+------------+-----------+-----------+---------+---------+-----------+
| Maximum    | 10904.3   | 167623.5  | 746     | 1520.93 | 217       |
+------------+-----------+-----------+---------+---------+-----------+
| Minimum    | 171.8     | 786.9     | 29      | 16.86   | 3.99      |
+------------+-----------+-----------+---------+---------+-----------+
| Std. Dev.  | 2727.40   | 35155.93  | 131.59  | 234.42  | 40.77     |
+------------+-----------+-----------+---------+---------+-----------+
| 1999       |           |           |         |         |           |
+------------+-----------+-----------+---------+---------+-----------+
| Mean       | 3085.06   | 26221.09  | 131.16  | 206.86  | 44.27     |
+------------+-----------+-----------+---------+---------+-----------+
| Maximum    | 11275.6   | 119655.6  | 717     | 1502.59 | 231       |
+------------+-----------+-----------+---------+---------+-----------+
| Minimum    | 7.09      | 185.2     | 31      | 17.10   | 3.99      |
+------------+-----------+-----------+---------+---------+-----------+
| Std. Dev.  | 2548.49   | 30323.26  | 111.68  | 220.48  | 39.68     |
+------------+-----------+-----------+---------+---------+-----------+
| 2000       |           |           |         |         |           |
+------------+-----------+-----------+---------+---------+-----------+
| Mean       | 3554.68   | 24498.22  | 121.64  | 220.55  | 44.74     |
+------------+-----------+-----------+---------+---------+-----------+
| Maximum    | 14516.1   | 156037    | 384     | 1467.02 | 231       |
+------------+-----------+-----------+---------+---------+-----------+
| Minimum    | 310.8     | 503       | 31      | 18.06   | 4.41      |
+------------+-----------+-----------+---------+---------+-----------+
| Std. Dev.  | 2947.51   | 30460.54  | 84.41   | 232.23  | 39.94     |
+------------+-----------+-----------+---------+---------+-----------+
| 2001       |           |           |         |         |           |
+------------+-----------+-----------+---------+---------+-----------+
| Mean       | 3245.73   | 24410.58  | 131.66  | 206.14  | 44.49     |
+------------+-----------+-----------+---------+---------+-----------+
| Maximum    | 10595.03  | 135934.9  | 532     | 1443.16 | 201       |
+------------+-----------+-----------+---------+---------+-----------+
| Minimum    | 250.4     | 783.1     | 31      | 19.28   | 3.28      |
+------------+-----------+-----------+---------+---------+-----------+
| Std. Dev.  | 2598.45   | 28471.66  | 103.96  | 213.85  | 38.68     |
+------------+-----------+-----------+---------+---------+-----------+

**Table 2 Translog Input Distance Function Coefficients**

  -------------- --------- ----------- ----------- ----------- -----------
  Variable       Model1    Model2      Variable    Model1      Model2

  Electricity    -0.523    -0.508      x1\*x3      0.010       0.019
  (y1)                                                         

  SO~2~ (y2)     -0.056    .           x2\*x3      -0.014      -0.012

  Labor (x1)     0.560     0.477       y1\*x1      -0.009      -0.011

  Capital (x2)   0.091     0.101       y1\*x2      0.004       0.003

  Heat Input     0.349     0.423       y1\*x3      0.005       0.008
  (x3)                                                         

  Time (t)       -0.075    -0.096      y2\*x1      -0.013      .

  y1^2^          0.032     0.028       y2\*x2      0.008       .

  y2^2^          -0.003    .           y2\*x3      0.005       .

  x1^2^          0.085     0.073       y1\*t       0.022       0.021

  x2^2^          -0.016    -0.011      y2\*t       0.0004      .

  x3^2^          -0.052    -0.066      x1\*t       0.003       0.0003

  t^2^           -0.009    -0.008      x2\*t       -0.001      -0.0003

  y1\*y2         -0.005    .           x3\*t       -0.002      0.00001

  x1\*x2         -0.013    -0.004      Intercept   3.240       2.927
  -------------- --------- ----------- ----------- ----------- -----------

Note: Model1: SO~2~ is considered.

Model1: SO~2~ is ignored.

**Table 3 Values of Input Distance Function.**

Note: $D_{i}(x,y)$\*: SO~2~ is considered,$D_{i}(x,y)$\*\*: SO~2~ is
ignored.

**Table 4 Values of Productivity and Profitability Index Numbers when
SO~2~** is considered.

  -------------- -------------- -------------- -------------- --------------
  Year           Efficiency     Technical      Malmquist      Fisher Index
                 Change         Change         Index          

  1996           0.958          0.954          0.914          0.855

  1997           0.960          0.961          0.923          0.834

  1998           0.948          0.970          0.920          0.851

  1999           0.981          0.979          0.961          0.815

  2000           1.013          0.986          0.999          0.814

  2001           0.985          0.994          0.979          0.763
  -------------- -------------- -------------- -------------- --------------

**Table 5 Values of Productivity and Profitability Index Numbers when
SO~2~** is ignored.

  -------------- -------------- -------------- -------------- --------------
  Year           Efficiency     Technical      Malmquist      Fisher Index
                 Change         Change         Index          

  1996           0.956          0.952          0.910          0.867

  1997           0.958          0.958          0.918          0.851

  1998           0.950          0.965          0.917          0.846

  1999           0.968          0.973          0.943          0.815

  2000           1.005          0.979          0.984          0.748

  2001           0.976          0.986          0.962          0.783
  -------------- -------------- -------------- -------------- --------------

Table 6 Environmental Productivity and Profitability Changes.

  ----------------------- ----------------------- -----------------------
  Year                    Environmental           Environmental
                          Productivity            Profitability

  1996                    1.005                   0.986

  1997                    1.006                   0.980

  1998                    1.003                   1.006

  1999                    1.019                   1.000

  2000                    1.015                   1.088

  2001                    1.017                   0.974
  ----------------------- ----------------------- -----------------------

### Table 7 Values of Various Non-Parametric Tests.

+-----------------------+-----------------------+-----------------------+
| ##                    | ### Envir             | ### Enviro            |
| # Non-Parametric Test | onmental Productivity | nmental Profitability |
+-----------------------+-----------------------+-----------------------+
| ### Mean              | ###                   | ###                   |
+-----------------------+-----------------------+-----------------------+
| ### t-test            | ### 3.54(0.0004)      | ### 0.583(0.56)       |
+-----------------------+-----------------------+-----------------------+
| ### Anova F-test      | ### 12.52(0.0004)     | ### 0.340(0.56)       |
+-----------------------+-----------------------+-----------------------+
| ### Median            | ###                   | ###                   |
+-----------------------+-----------------------+-----------------------+
| ###                   | ### 3.35(0.0008)      | ### 0.996(0.32)       |
| Wilcoxon/Mann-Whitney |                       |                       |
+-----------------------+-----------------------+-----------------------+
| ### Med. chi-square   | ### 7.84(0.005)       | ### 0.000(1.00)       |
+-----------------------+-----------------------+-----------------------+
| ###                   | ### 7.46(0.006)       | ### 0.005(0.94)       |
|  Adj. Med. Chi-square |                       |                       |
+-----------------------+-----------------------+-----------------------+
| ### Kruskal-Wallis    | ### 11.21(0.0008)     | ### 0.994(0.32)       |
+-----------------------+-----------------------+-----------------------+
| ### van der Waerden   | ### 12.73(0.0004)     | ### 1.020(0.31)       |
+-----------------------+-----------------------+-----------------------+

### Note: values in parentheses are the probabilities.

[^1]: Cropper and Oates (1992); Pittman (1981); Haynes et al. (1993,
    1994), Boggs (1997); Reinhard et al. (1999), Murty and Kumar (2003)
    etc.

[^2]: For the properties of input distance function; See Fare and
    Primont (1995).

[^3]: ^3^$\overset{-}{F}$and F will not in general be equal since
    $\overset{-}{F}$ omit mixed period terms.

[^4]: Since only the units whose nameplate generating capacity is
    greater than 25 megawatts are covered under the Allowance program.