Centre for Efficiency and Productivity Analysis

Working Paper Series
No. 06/2004

Title
Regulatory Reform and Economic Performance in
US Electricity Generation
Authors
Supawat Rungsuriyawiboon
Tim Coelli

Date: September 2004

School of Economics
University of Queensland
St. Lucia, Qld. 4072
Australia

Regulatory Reform and Economic Performance in US
Electricity Generation

Supawat Rungsuriyawiboon and Tim Coelli
Centre for Efficiency and Productivity Analysis
School of Economics
University of Queensland

10 September 2004

ABSTRACTIn this paper we investigate the effect of the introduction of incentive regulation upon the totalfactor productivity (TFP) growth of electricity generation companies in the United States, using
sample data on 61 firms observed over a 13-year period from 1986 to 1998. Empirical estimatesof TFP growth are obtained using three techniques: Tornqvist index numbers, a stochastic cost
frontier and a stochastic input distance function. The results obtained using the stochastic cost
frontier are discarded because they are found to differ from those obtained using the othertechniques, apparently as a consequence of violations of the required cost minimizing behavioral
assumptions, which are not uncommon in regulated industries. Tests of hypotheses regarding theeffect of regulatory reform upon TFP (using the distance function results) indicate that the
introduction of incentive regulation has not had the desired positive effect upon the economic
performance of the firms involved. In fact, in the case of these data, we find that performance isnegatively related with the introduction of the new regulatory regimes, a result that is the
opposite of the theoretical predictions.
Key words:

Incentive regulation, Total Factor Productivity Growth, Cost Frontier, Input

Distance Function, Törnqvist index

21.

Introduction
The regulation of infrastructure industries, such as electricity, gas and water supply, has

undergone substantial changes over the past few decades, with the rise in popularity of the socalled incentive regulation approaches. Changes have occurred in many countries around theworld. In countries such as the UK and Chile, a number of infrastructure industries have been
privatized, and incentive regulation regimes, such as price-cap regulation, have been
implemented. In the USA, where investor owned utilities were more the norm, the traditional
method of rate-of-return regulation is also being gradually replaced with alternative incentive
regulation regimes (eg. see Newbery, 2000).
It is widely argued that incentive regulation methods, such as price cap regulation, areexpected to provide stronger incentives for cost reduction and technological innovation (relative
to rate-of-return regulation). This is because the regulated firm is permitted to keep any “extra”
profits it may happen to earn, if it manages to reduce its costs of production at a rate greater than
the rate of allowed (real) price changes.1 However, given that many countries have only recently
introduced these incentive regulation methods, there is limited empirical evidence available for
one to assess if the benefits that are predicted by the economic theory actually eventuate inpractice.
Thus the primary motivation of this study is to see if we can find empirical evidence tosupport the hypothesis that incentive regulation methods actually have had a positive influence
upon the productivity of those US electricity supply businesses which have been exposed tothese new regulatory methods. To this end, we have compiled historical data on the generation
businesses of 61 US electricity supply utilities, observed over a 13-year period from 1986 to
1998. This group of 61 firms include some that have faced incentive regulation methods andsome that have not. Furthermore, the year in which a particular firm first faced the change inregulatory regime differs between firms. Hence, the nature of this data allows us to control for
macro-economic effects to some extent.
A secondary aim of this paper is to investigate the effect of choice of methodology upon
the productivity measures obtained. Previous studies have used a variety of methods to calculate
total factor productivity (TFP) growth and efficiency levels in infrastructure industries. For
example, see the excellent survey of the methods used in electricity industries, provided by
Jamasb and Pollitt (2002), who note the use of stochastic frontier production frontiers, costfunctions, data envelopment analysis, and Tornqvist index numbers, among others. Generally,1

See Parker (1996) for a good introductory discussion of these issues.

3each study tends to apply only one method to the data at hand. However, as some studies haveshown (eg. see the Coelli 2002 analysis of productivity growth in electricity generation inAustralia) different methods can in some cases provide quite different measures, especially whenperfect competition assumptions are violated – which is often the case in regulated industries. In
this study, we utilise three often used methods – Tornqvist index numbers, stochastic cost
frontiers and stochastic input distance functions – to calculate our productivity measures. Thisempirical analysis helps highlight the relative advantages and disadvantages of these methods,
and in particular allows us to demonstrate the degree to which the performance measures canchange when one uses different methodologies.
The outline of this paper is as follows. In the next section we describe and discuss thethree alternative performance measurement methods that we use to measure TFP growth in thisstudy. This is followed in section 3 with a brief description of the US electricity supply industry,along with a discussion of the data set used in this study. The next section provides anassessment of the influence of regulatory regime upon firm-level productivity measures, and thenconclusions follow in the final section.

2.

Methodology
The methods that are used to measure the TFP change can be roughly classified into twogroups according to the types of prices employed, i.e. market price and shadow prices. Market
prices are the actual prices that people pay for the goods and services, while shadow prices(internal prices to the firms) are derived from the shape of the underlying production technology.
Three TFP measurement approaches that are widely applied are: the Törnqvist price-based index
number, stochastic frontier analysis (SFA) and data envelopment analysis (DEA). The Törnqvist
price-based index number approach uses market prices, while the SFA and the DEA involve theestimation of a production technology, and hence the use of shadow prices derived from theshape of the estimated frontier.
The Törnqvist price-based index number approach has the advantage that it can be used
when limited data are available (e.g. aggregate industry-level data). The SFA and DEA frontier
approaches require more data (i.e. firm-level panel data), however they have the advantage thatthey allow one to identify various components of the TFP growth (such as technical change,
efficiency change and scale effects), which are often of particular interest to regulators. The SFA
approach has an advantage over the DEA approach when analyzing data in a stochastic
environment. This is because DEA typically does not attempt to take statistical noise into

4account (and consequently may provide inaccurate efficiency measures), while the parametricapproach does attempt to accommodate statistical noise and allows performing tests ofhypotheses regarding the structure of the production technology.
This study utilizes two alternative SFA approaches, i.e. cost frontier and input distancefunctions, in a TFP analysis of panel data on 61 U.S. electric utilities observed over the time
period of 1986-1998, and compares the results with those obtained using the traditional
Törnqvist price-based index number approach. The main objective is to examine the sensitivityof the estimates obtained to the choice of TFP measurement methodology, and to illustrate theimplications that these choices may have in the implementation of incentive regulation. We now
describe each of these three methods in some detail.

2.1.

The Törnqvist Price-Based Index Number (TPIN) Approach
TFP change is generally defined as the residual growth in outputs not explained by thegrowth in input use. Following Caves, Christensen and Diewert (1982), a Törnqvist TFP index
may be constructed as the ratio of a Törnqvist output index to a Törnqvist input index. The
logarithmic form of the Törnqvist TFP change index between periods t and t + 1 is defined asln (TFPi ,t +1 TFPi ,t ) =T

1 M∑ [(rmi,t +1 + rmi,t )( ymi,t +1 − ymi,t )]
2 m=1

1 K
− ∑ [(ski ,t +1 + ski ,t )(xki ,t +1 − xki ,t )]2 k =1(2-1)

where the T superscript refers to Törnqvist; i = 1,..., I indexes firms; k = 1,..., K indexes input
variables; m = 1,..., M indexes output variables; xki ,t is the log of the k-th input quantity, X ki ,t ;ymi ,t is the log of the m-th output quantity, Ymi ,t ; rmi ,t is the observed revenue share of the m-th

output; and ski ,t is the observed cost share of the k-th input.
For the single-output case, which is considered in the empirical part of this study,
equation (2-1) is rewritten asln (TFPi ,t +1 TFPi ,t ) = ( yi ,t +1 − yi ,t ) −T

1 K∑ [(ski,t +1 + ski,t )(xki,t +1 − xki,t )]2 k =1(2-2)

As noted earlier, the Törnqvist TFP index approach has the advantage that it can be used
to measure the TFP change when limited data is available. However, this approach also has someshortcomings. It requires information on both quantities and prices of outputs and inputs. In
addition, it cannot be used to decompose the TFP change measure into its components, such as5technical change (frontier shift) and technical efficiency change (catch-up), which are of broadinterest for regulators.2 This problem can be addressed by gaining access to panel data and usinga frontier technique, such as a stochastic cost frontier or a stochastic input distance function, todecompose the measured TFP growth into its components.

2.2.

The Stochastic Cost Frontier Approach

Following Greene (1980), a translog stochastic cost frontier may be defined as follows.
K

cit = β 0 + ∑ β k wkit +
k =1

K

M
1 K K
1 M M
β kl wkit wlit + ∑ β ym ymit + ∑∑ β ym yn ymit ynit∑∑
2 k =1 l =1
2 m=1 n=1
m =1

M

K
M
1
+ ∑∑ β kym wkit ymit + β z z + β zz z 2 + ∑ β kz wkit z + ∑ β ym z ymit z + vit + uit2
k =1 m =1
k =1
m =1

(2-3)

where c is the log of total cost, C ; wk is the log of k-th input price, Wk ; z represents a timetrend variable; v is a symmetric error term (designed to capture the effects of random noise); u isan asymmetric error term (included to capture the effects of cost inefficiency); the βs are
unknown parameters to be estimated, and all other notation is as previously defined.
In this study, we follow the standard practice of assuming a normal distribution for v anda half-normal distribution for u. That is, we set v ~ N ( 0,σ v2 ) and u ~| N ( 0 ,σ u2 ) | . Given these
distributional assumptions, the parameters of this model can then be estimated using the methodof maximum likelihood. Furthermore, note that we follow the suggestion of Battese and Corra(1977), and replace the two variance parameters with the two new parameters σ 2 = σ v2 + σ u2 andγ = σ u2 / σ 2 . By doing this we can search the parameter space of γ between 0 and 1, to provide
good starting values for the iterative maximization routine which is used to calculate themaximum likelihood parameter estimates.
For the single-output and three-input case, equation (2-3) is rewritten as
3

cit = β 0 + ∑ β k wkit +
k =1

3
1 3 3
1
β kl wkit wlit + β y yit + β yy yit2 + ∑ β ky wkit yit + β z z∑∑
2 k =1 l =1
2
k =1

3
1
+ β zz z 2 + ∑ β kz wkit z + β yz yit z + vit + uit
2
k =1

(2-4)

Young’s theorem requires that symmetry restrictions are imposed so thatβkl = βlk for all k , l = 1,2,3(2-4a)and homogeneity of degree +1 in input prices requires imposition of the additional restrictions
2

See Coelli et al (2003) for further discussion.

63∑ β = 1,k =1

(2-4b)k3∑β = 0,k =1

kl

l = 1,2,3(2-4c)

3∑β = 0 ,k =1(2-4d)ky3∑β = 0.
k =1(2-4e)

kz

These restrictions can be imposed by estimating a model where the cost variable and K-1
input price variables are normalized by the K-th input price variable. Equation (2-4) can be
rewritten as
2

*
*
ckit
= β 0 + ∑ β k wkit
+
k =1

2
1 2 2
1
*
*
β kl wkit
wlit* + β y yit + β yy yit2 + ∑ β ky wkit
yit + β z z∑∑
2 k =1 l =1
2
k =1

2
1
*
+ β zz z 2 + ∑ β kz wkit
z + β yz yit z + vit + uit
2
k =1

(2-5)

*
*
where ckit
= (ckit wKit ) , wkit
= (wkit wKit ) and wlit* = (wlit wKit ) . Once the parameters of thisequation have been estimated, the parameters associated with the K-th normalizing input canthen be calculated using these estimated parameters and the restrictions in equation (2-4a) to(2-4e).
A measure of total factor productivity change (TFPCit ,t +1 ) , for each firm between any twotime periods, can be calculated by using the estimates of the coefficients of the cost frontier inequation (2-5) and the firm-level sample data. The logarithmic form of the TFPC between periodt and t + 1 for the i-th firm is defined asln (TFP1i ,t +1 TFP1i ,t ) = ln (CEi ,t CEi ,t +1 ) −1[∂ci,t +1 ∂t + ∂ci ,t ∂t ]2

1
+ [(1 − ∂ci ,t +1 ∂y ) + (1 − ∂ci ,t ∂y )]( yi ,t +1 − yi ,t )
2

(2-6)

where the three terms on the right-hand-side of equation (2-6) represents the cost efficiencychange(CEC ) , technical change (TC ) and scale efficiency change (SEC ) ,it , t +1

it , t +1

it , t +1

respectively.
The formula in equation (2-6) has been derived by exploiting Diewert’s (1976) Quadratic
Identity Lemma, following a similar derivation to that outlined for the distance function case in
Orea (2002).

This formula is quite similar to that provided in Bauer (1990), which wasalternatively derived using a differential approach. The main differences between the two sets of
TFP decomposition formula is that the technical change and scale efficiency change measures in7equation (2-6) are evaluated at the t and t+1 data points, while the Bauer (1990) formula is only
evaluated at the t data point. This difference will have minimal effect on the empirical measuresobtained in most instances.
The cost efficiency measure, (CEit ) , in equation (2-6) is the cost efficiency prediction of
the i-th firm in the t-th time period, and is calculated from the cost frontier in equation (2-5)
using the method outlined in Coelli (1996). The technical change measure, (TCit ,t +1 ) , is the meanof the technical change measures evaluated at the period t and period t + 1 data points. The scaleefficiency change measure, (SECit ,t +1 ) , relates to the change in scale efficiency, which requires
calculation of the output elasticity in period t , ∂ci ,t ∂y , and period t + 1 , ∂ci ,t +1 ∂y .
When information on input quantities is also available, the regulator can also calculate an
allocative efficiency change ( AECit ,t +1 ) component, which is equal to the difference between the(TFPC ) measure obtained from the cost frontier in equation (2-6) and the Törnqvist TFPC
index in equation (2-2). The allocative efficiency change ( AEC ) measure yields
it , t +1

it , t +1

AECit ,t +1 =

1 3
∑ [((∂cki,t ∂wk ) − ski,t ) + ((∂cki,t +1 ∂wk ) − ski,t +1 )](wki,t +1 − wki,t )2 k =1(2-7)

This AECit ,t +1 measure will be equal to 0 when the observed cost shares, ski ,t , are identical to the“efficient” cost shares, ∂cki ,t ∂wk , or when there is no change in the input price vector.
Thus, the total factor productivity change (TFPCit ,t +1 ) for each firm between any two time
periods can be decomposed into four components: the cost efficiency change (CECit ,t +1 ) ,technical change (TCit ,t +1 ) , scale efficiency change (SECit ,t +1 ) , and allocative efficiency change( AECit ,t +1 ). In the empirical part of this paper, we report two TFPC measures, one with and one
without the AEC measure included. That is,
TFPC1it ,t +1 = CECit ,t +1 + TC it ,t +1 + SECit ,t +1(2-8)

TFPC 2it ,t +1 = TFPC1it ,t +1 + AECit ,t +1(2-9).

andCost functions have been used extensively in empirical analyses of production in
infrastructure industries over recent decades3.

This has been in preference to the use of

production function estimates. This is most likely because of the ready availability of cost data;3

For example, see Burns and Weyman-Jones (1996) and references cited therein.

8

the fact that they can accommodate multiple outputs; and also because in most cases input prices
are more likely to be exogenous than the input quantities. However, the cost function approachrequires one to accept the behavioral assumption that the producer is cost-minimizing in
production. If this assumption is incorrect, perhaps because of political intervention or aregulatory bias, the duality between the cost frontier and the production frontier will be violated,leading to incorrect measures of allocative efficiency, technical efficiency, scale efficiency, andtechnical change. This issue has provided a motivation for the development of the distancefunction techniques that are discussed in the following section.

2.3.

The Stochastic Input Distance Function Approach

Following Coelli and Perelman (1999), a translog input distance function may be defined
as follows.
Kd it = β 0 + ∑ β k xkit +
k =1

K

M
1 K K
1 M M
β kl xkit xlit + ∑ β ym ymit + ∑∑ β ym yn ymit ynit∑∑
2 k =1 l =1
2 m=1 n=1
m =1

M

K
M
1
+ ∑∑ β kym xkit ymit + β z z + β zz z 2 + ∑ β kz xkit z + ∑ β ym z ymit z
2
k =1 m =1
k =1
m =1

(2-10)

where d is the log of input distance, D ; and all other notation is as previously defined.
For the single-output and three-input case, equation (2-10) is rewritten as
3

d it = β 0 + ∑ β k xkit +
k =1

3
1 3 3
1
β kl xkit xlit + β y yit + β yy yit2 + ∑ β ky xkit yit + β z z∑∑
2 k =1 l =1
2
k =1

3
1
+ β zz z 2 + ∑ β kz xkit z + β yz yit z + vit
2
k =1(2-11)

Young’s theorem requires that symmetry restrictions are imposed so thatβkl = βlk for all k , l = 1,2,3(2-11a)and homogeneity of degree +1 in input requires imposition of the additional restrictions3∑ β = 1,k =1
3∑β = 0,k =1(2-11b)kkl

l = 1,2,3(2-11c)3∑β = 0 ,k =1ky(2-11d)3∑β = 0.
k =1kz(2-11e)9

Imposing these restrictions upon equation (2-11) yields the estimating form of the input
distance function, in which the distance term, d, can be viewed as an error term as follows
2− x Kit = β 0 + ∑ β k x*kit +
k =1

1 2 2
1
β kl x*kit x*kit + β y y it + β yy y it2∑∑
2 k =1 l =1
2

2

2
1
+ ∑ β ky x*kit y it + β z z + β zz z 2 + ∑ β kz x*kit z + β yz y it z − d it
2
k =1
k =1

(2-12)*= ( xkit xKit ) . By replacing the distance term, − d it , with a composed error term,
where xkit

vit − uit , equation (2-12) can be estimated as a standard stochastic frontier function.
The total factor productivity change (TFPCit ,t +1 ) for each firm between any two time
periods can be calculated by using the estimates of the coefficients of the input distance frontier
in equation (2-12). The logarithmic form of the TFPC between period t and t + 1 for the i-th
firm is defined asln (TFP1i ,t +1 TFP1i ,t ) = ln (TEi ,t +1 TEi ,t ) +1[∂di,t +1 ∂t + ∂di ,t ∂t ]2

1
+ [(1 + ∂d i ,t +1 ∂y ) + (1 + ∂d i ,t ∂y )]( yi ,t +1 − yi ,t )2(2-13)

where the three terms on the right-hand-side of equation (2-13) represents the technicalefficiency change (TECit ,t +1 ) , technical change (TCit ,t +1 ) and scale efficiency change (SECit ,t +1 ) ,respectively.
The formula in equation (2-13) has been derived by exploiting Diewert’s (1976)
Quadratic Identity Lemma, following a similar derivation to that outlined for the output distancefunction case in Orea (2002).
The technical efficiency measure, (TEit ) , in equation (2-13) is the technical efficiency
prediction of the i-th firm in the t-th time period, which is calculated using the method outlinedin Battese and Coelli (1988). The technical change measure, (TCit ,t +1 ) , is the mean of thetechnical change measures evaluated at the period t and period t + 1 data points. The scaleefficiency change measure, (SECit ,t +1 ) , calculates the change in scale efficiency, which requires
calculation of the production elasticity at the period t , ∂d i ,t ∂y , and period t + 1 , ∂di ,t +1 ∂y .
When information on input prices is available, the one can also calculate an allocative
efficiency change(AEC ) component, which is equal to the difference between theit , t +1(TFPC ) measure obtained from the input distance frontier in equation (2-12) and a Törnqvist
TFPC index in equation (2-2). The allocative efficiency change ( AEC ) measure yields
it , t +1

it , t +1

10

AECit ,t +1 =1 3
∑ [[((∂d ki,t ∂xk ) − ski,t ) + ((∂d ki,t +1 ∂xk ) − ski,t +1 )](xki,t +1 − xki,t )] .
2 k =1(2-14)

This AECit ,t +1 measure will be equal to 0 when the market input shares, ski ,t , equal to the shadow
input shares, ∂d ki ,t ∂xk , or when there is no change in the input quantity vector.
Thus, the total factor productivity change (TFPCit ,t +1 ) for each firm between any two time
periods can be decomposed into four components: the technical efficiency change (TECit ,t +1 ) ,technical change (TCit ,t +1 ) , scale efficiency change (SECit ,t +1 ) , and allocative efficiency change(AEC ). In the empirical part of this paper, we report two TFPC measures, one with and one
it , t +1

without the AEC measure included. That is,

TFPC 2it ,t +1 = TECit ,t +1 + TCit ,t +1 + SECit ,t +1 + AECit ,t +1(2-15)

TFPC 2it ,t +1 = TFPC1it ,t +1 + AECit ,t +1(2-16)

This input distance function approach can be viewed as a multiple output version of a
production frontier. It considers the amount by which the input set of each firm may be
proportionally contracted with the output set held fixed. The advantages of this approach are thatit avoids the problems associated with the cost function approach when cost minimization isviolated and it is much less complicated than the shadow cost function approach. In addition, it
allows one to specify multiple outputs in a primal setting and avoids the endogenous regressors
criticism that is sometimes leveled at the production frontier approach [Coelli, (2000)]. There
are increasing numbers of the studies applying this approach in analyses of infrastructureindustries [e.g. Coelli and Perelman (1999, 2000), Carrington, Coelli, and Groom (2002), andAtkinson and Primont (2002)].

3.

The U.S. Electricity Supply Industry

3.1.

Overview of the industry

For a number of decades, the U.S. electricity supply industry has been predominantly
comprised of investor-owned utilities (IOUs). These IOUs traditionally have been verticallyintegrated utilities – generating, transmitting, and distributing the electricity that they sell tocustomers living in their territories, where regulations provide them with exclusive rights to
supply electricity in their specified territory. Traditionally, an electricity customer has paid one
regulated price for electricity to a single vertically integrated utility responsible for generation,

11transmission, distribution, and marketing. Under this form of regulation, electric utilities havethe potential to exert their market power and they will receive a guaranteed profit for thegeneration of electricity. This led to strong incentives to over invest in capital as well as
operating at an inefficient level of production, which is of broad interest for regulators [e.g.,
Averch and Johnson (1962), Atkinson and Halvorson (1980), Rungsuriyawiboon and Stefanou(2003)]. This lack of efficiency incentives contributed to various legislative changes and to therecent adoption of more incentive compatible regulatory structures in some parts of the U.S.
The U.S. electricity supply industry has changed significantly in the past two decades.
This has been partly driven by a number of legislative changes. The first of note was whenCongress passed the Public Utility Regulatory Policies Act of 1978 (PURPA), which allowed
independent generators to sell their electricity to utilities at regulated rates. Then the 1992
Energy Policy Act, followed by the Federal Energy Regulatory Commission’s (FERC’s) Orders
888 and 889 in 1996, expanded the PURPA initiative by forcing utilities with transmission
networks to deliver power to third parties at nondiscriminatory cost-based rates. These policy
initiatives recognize that while electricity transmission and distribution remain natural
monopolies, competition in generation is possible with open access to transportation networks.
Policies to open markets led to new competitors in generation and marketing, with arestructuring of the industry away from the regulated, single-provider model.4
During this period of legislative changes, a movement towards incentive regulation
methods also began to gather pace.

There were relatively few applications of incentive

regulation in U.S. electric utilities in the 1980s. However, incentive regulation began to makesubstantial inroads in this industry in the early 1990s. By the end of the decade there were 28
electric utilities with some form of incentive regulation in 16 states [Sappington et al (2001)].

3.2.

Electricity industry data

The empirical analysis in this study focuses on steam electric power generation using a
fossil fuel as the primary fuel for major investor-owned utilities in the United States. This
generation source is the dominant part of the electricity industry5. Panel data on 61 electric

4

These changes have not all been implemented at the same pace in all parts of the U.S. In some States the reforms
have moved quite slowly.
5
About 61.1 percent of all the electricity supplied by the U.S. electric power industry comes from steam turbines
fired by fossil fuel. Recent figure indicate that coal-fired generation accounts for 84 percent, natural gas accounts for12.7 percent, and petroleum comprises 3.3 percent. Investor-Owned Utilities own 71 percent of the U.S. generating

12

utilities over the time period of 1986-1998 are used in the empirical analysis. A list of the electricutilities included in this study is available from the authors on request.
The primary sources of data are obtained from the Energy Information Administration(EIA), the Federal Energy Regulatory Commission (FERC), the Bureau of Labor Statistics(BLS), and the Federal Reserve Board (FRB). The data set used to obtain the TFP measurescontains measurements of firm output quantities, input quantities, input prices and costs forsteam electric power production. The definitions of these variables are summarized below.

OutputThe output variable, Yit , is represented by net steam electric power generation in
megawatt-hours, which is defined as the amount of power produced using fossil-fuel fired boilers
to produce steam for turbine generators during a given period of time.

Price and Quantity of Fuel Input
The price of fuel aggregate, W1it , is a Tornqvist price index of fuels (i.e. coal, oil, gas)
which is calculated as a weighted geometric average of the price relatives with weights given by
the simple average of the value shares in period t and t + 1 .
⎛ a fit + a fit +1 ⎞
⎟⎟
⎜
2
⎠

⎜
⎛ W1it +1 ⎞ 3 ⎛ Pfit +1 ⎞⎝⎟⎟⎟ = Π ⎜⎜⎜⎟⎜⎝ W1it ⎠ f =1⎝ Pfit ⎠

(3-1)

P Q
where a fit = 3 fit fit , Pfit is the price of the f-th fuel (i.e. coal, oil, gas), and Q fit is the∑ Pfit Q fit
f =1

consumption of the same fuel. The Törnqvist price index of fuel aggregate is converted into
multilateral Törnqvist price index to confirm the transitivity property using the EKS method
discussed in Coelli, Rao and Battese (1998, Ch 4).

capacity owned by both utilities and nonutility generators and are responsible for 74 percent of all retail sales ofelectricity (EIA 2000).

13

The quantity of fuel, X 1it , is calculated as the steam power production fuel costs divided
by the multilateral Tornqvist price index for fuels.
Price and Quantity of Aggregate Labor and Maintenance Input

The price of labor and maintenance aggregate, W2it , is a cost share-weighted Tornqvist
price index for labor and maintenance. The price of labor is a firm-level average wage rate. The
price of maintenance and other supplies is an industry-level price index of electrical supplies.
The Törnqvist price index of labor and maintenance aggregate is also converted into multilateral
Törnqvist price index using the EKS method.
The quantity of labor and maintenance, X 2it , is measured as the aggregate costs of laborand maintenance divided by the multilateral Tornqvist price index for labor and maintenance.
Data on labor and maintenance costs are calculated by subtracting fuel expenses from total steam
power production expenses.6

Price and Quantity of Capital Input

The price of capital, W3it , is the yield of the firm’s latest issue of long term debt adjusted
for appreciation and depreciation of the capital good using the Christensen and Jorgenson (1970)
cost of capital formula.
W3it = p kt [idit + sit (reit − idit ) + d − f t ](3-2)

where pkt is a price index for electrical generating plant and equipment; idit is the adjusted
corporate bond rate by firm based upon its bond ratings by Moody’s Investor Service; sit is theequity share of total capital defined as total proprietary capital (TPC) divided by the sum of total
proprietary capital and total long-term debt (TOTB); reit is the equity rate of return defined as theratio of net income to total proprietary capital; d is a depreciation rate assuming 30 years straightline depreciation; and ft the inflation rate.
The values of capital stocks are calculated by the valuation of base and peak load
capacity at replacement cost to estimate capital stocks in a base year and then updating it in thesubsequent years based upon the value of additions and retirements to steam power plant as

6These costs were not separated into labor and non-labor costs because the wide spread use of outsourcing has
made such distinctions rather arbitrary.

14

discussed in Considine (2000). The base year capacity is calculated by multiplying the price of
new generation capacity in dollars per megawatt and the base year nameplate capacity inmegawatts.
X 3it = Pcit Cit , t = 1986

(3-3)

where Pcit is the price of new generation capacity in dollars per megawatt, and Cit is thenameplate capacity in megawatts.
For the subsequent years, the values of capital stocks are calculated by
X 3it =

(1 − υ )( X 3it −1 ) pkit
+ Ait − Rit ,pkit −1

t = 1987,...,1998(3-4)

where υ denotes the depreciation rate;7 X3it is equal to the nominal stock divided by the priceindex for electrical generating plant and equipment, pkit ; Ait and Rit denote additions andretirements to steam power plant.
Cost

The total cost for steam electric power generation, Cit , is defined as the sum of the
product of input prices and quantities for aggregate fuel, aggregate labor and maintenance andcapital.
3

Cit = ∑ Wkit X kit ,
k =1

(3-5)

The final data set is a balanced panel of 61 electric utilities for the years 1986 to 1998
with a total of 793 observations. Table 1 represents a summary of the data used in this study8.
The average expenses of aggregate fuels, aggregate labor and maintenance, and capital arecalculated to be 258.79, 66.66, and 97.43 million dollars, respectively. The mean cost shares offuel, labor and maintenance, and capital account for 59, 18, and 23 percent, respectively.

4.

Empirical results

4.1

Discussion of parameter estimates

7
8

A depreciation rate of 0.033 is used.
All price indices used in this study are obtained and calculated relative to the base period 1993.

15

The data described in the previous section were used in the calculation of Tornqvist TFP indicesand also in the estimation of the cost and input distance functions described in section 2. The
maximum likelihood parameter estimates for these two functions (obtained using the computer
program described in Coelli, 1996) are listed in Table 2. The data variables used in the model
estimation were each transformed by division by their respective geometric means.

Thistransformation does not alter the performance measures obtained, but does allow one to interpretthe estimated first-order parameters as elasticities, evaluated at the sample means.
If we first focus on the estimates of the input elasticities in Table 2, we observe that the
distance function estimates of 0.574, 0.136 and 0.290 (for fuel, labor and maintenance, andcapital, respectively) differ significantly from the cost frontier estimates of 0.449, 0.361 and
0.190. These elasticities can also be interpreted as shadow shares, and hence indicate that when
TFP measures are calculated using these estimates, the two TFP measures are likely to differ forthe average firm, if the input quantities change at different rates through time. Given that
substantial labor shedding has occurred during this period, it is likely that this issue will be
important. Furthermore, we observe that the average observed shares in this data set are 0.59,
0.18 and 0.23, respectively. These shares are fairly similar to (but not identical to) the distancefunction shares, but clearly differ from the cost frontier shares. Given this observation, we
expect that the TFP growth estimates obtained using the Tornqvist index (which uses observed
shares) is likely to more closely approximate the distance function TFP measures, relative to thecost frontier TFP measures.
The reasons for the large differences that we observe between the cost frontier shares andthe other two sets of shares warrant further discussion. One possible cause of these differences
could be some type of systematic measurement error in either the input quantities or prices. For
example, in the way in which capital price is measured. This possibility cannot be discounted,
but as indicated in the previous section, we have taken great care in this regard. A second
possible culprit is that the distance function estimates suffer from some type of simultaneous
equations bias, due to an endogenous regressors problem, as discussed in Atkinson, Cornwelland Honerkamp (2003). However, given the arguments outlined in Coelli (2000) regarding theabsence of an endogeneity problem in input distance functions (when firms are shadow costminimisers), and given the fact that the distance function shares and shadow shares are fairly
similar, we do not believe that this is likely to be an issue.
We then come to the third and most likely culprit, that of the violation of the cost
minimization assumption. In infrastructure industries such as this, this assumption is unlikely to16

be appropriate, due to factors such as political and regulatory interventions. Therefore, whencost minimization is no longer applicable, duality theory will no longer apply, and hence the costelasticities cannot be assumed to equal the input shares. Thus, any TFP calculations (anddecompositions) based upon cost frontier estimates in this situation need to be treated with alarge amount of caution.9
An issue closely related to this, is the Averch-Johnston (AJ) effect, which predicts thatthe use of rate of return regulation (which is applied to most businesses in this data sample) tends
to cause the shadow price of capital to decrease and hence encourages over capitalization. From
our distance function shadow cost share of capital (0.290), we note that it closely approximatesthe observed capital share (0.23), suggesting that this is not an issue in this industry.
Alternatively, when we look at the (most likely biased) cost frontier shadow cost share of capital(0.190), we appear to obtain evidence of this AJ effect. However, given the above discussion,
one is inclined to put more weight on the distance function results, relative to these cost frontier
results.
The estimated parameters in Table 2 also provide information on scale economies andtechnical change. Using the first order coefficient of the output variable, we can calculate theelasticities of scale relative to the cost and input distance functions as
RTS = (∂c ∂y ) = −(∂d ∂y ) ,−1−1

where a value of RTS greater than one imply increasing returns to scale, while values less than
one imply decreasing returns to scale, and values equal to one indicate constant returns to scale.
From the Table 2 parameter estimates, we find RTS measures very close to one in value,indicating that the technology exhibits constant returns to scale, at the sample mean. This result
is not surprising given the results reported in past studies (e.g. see Christensen and Greene,1976).
The first order coefficients of the time trend variable in Table 2 provide estimates of theaverage annual rate in technical change. The cost frontier estimates suggest that the technology

9Another possible reason for the differences in the estimates could be the result of violations of regularity
conditions. Economic theory indicates that these economic functions should satisfy certain monotonicity andcurvature conditions. A cost function should be non-decreasing and concave in input prices and non-decreasing in
output quantities, while an input distance function should be non-decreasing and concave in input quantities and non
increasing in output quantities. Tests of these conditions indicate that the concavity condition is satisfied at
approximately two thirds of observations in the distance function, while it is violated in all observations in the costfunction. This result adds further weight to our concerns about the reliability of the cost function estimates. With
regard to the monotonicity conditions, we note that these are 15 violations in the cost frontier case and six in the
distance function case. This rate of violation is quite low, indicating that this condition is satisfied at the vast
majority of observations.

17

is improving at a rate of 2.2% per year, while the distance function estimates suggest a moremodest 0.8% per year.

The latter measure is likely to be more reliable, given the above

discussion. In addition, we note that it also more closely approximates the technical change
measures reported in other studies of the US electricity supply industry (e.g. see Atkinson et al,2003).

4.2

Discussion of performance measures

Some summary measures of the TFP growth measures (and components) described in
section 2 are listed in Table 3. The mean value reported for the Tornqvist index (TPIN) is 1.518,
indicating that the average annual change in this TFP measure over this period is 1.518 percent
per year. This is quite similar to the value of 1.496 reported for the distance function case, butdiffers significantly from the value of 3.545 reported for the cost function case. The fact that thecost function measure differs from the others is not surprising given the previous discussion. In
the following discussion we will focus most attention on the distance function measures, since
they are expected to be the more reliable ones.
In looking at which components contribute most to TFP change in the distance function
section of Table 3, we observe that the major contribution is from TC (0.826%),10 followed by
TEC (0.318%), AEC (0.315) and lastly SEC (0.038%).

The large contribution from TC

conforms with most past studies of this industry (e.g. Atkinson and Primont, 2002). The nearzero contribution of SEC is not surprising, given that the estimated technology exhibits constantreturns to scale (at the sample mean).
In Table 4 we produce weighted averages of our results, where the firm-level results havebeen weighted by the output of each firm. These weighted average results are likely to give amore accurate picture of the industry-level changes over time. We note that the weighted mean
TFP growth measure is quite similar to the unweighted mean, in the case of the Tornqvist anddistance function results. However, it is interesting to observe that the weighted TC measure isalmost 40% larger than the unweighted measure, indicating that larger firms have been pushingout the frontier at a faster rate. This is perhaps due to them having greater resources devoted toresearch and development, or maybe due to these larger firms having higher growth rates and

10

It is reassuring to note that these TC measures, formed by averaging firm-level measures, are similar to thoseobtained earlier, which were derived by evaluating the time derivative at the sample means.

18

hence more opportunities to benefit from embodied technical change in new investments.
However, further research is required confirm these hypotheses.
Tables 3 and 4 also contain year-by-year averages. These annual measures indicate thedegree of volatility in the TFP growth measures. For example, in the final column of Table 4,
we see that TFP growth varies from a high of 5.598% in 1986/87 to a low of negative 1.202% in
1989/90, and from the associated TEC column, we see that most of this TFP volatility is due toTEC. These measures illustrate the degree to which exogenous factors, such as the businesscycle and climatic conditions, can affect efficiency measures. Given this, it would clearly be
prudent for an analyst to not base TFP growth measures upon only a handful of years of data,
where the danger that an unusual event could significantly affect the measures obtained.
Annual averages of the firm-level measures are reported in Table 5. There is a wealth of
information in this table. Of particular note is the degree to which TFP performance varies fromfirm to firm, from an annual average decrease of 3.858% for firm 43 to an increase of 10.758%
for firm number 2. The distribution of TFP scores is further illustrated using the frequency
distributions reported in Table 6 and Figure 1. This variability in performance is of particularinterest to us in this study. In particular, to what extent can this variation be explained bydifferent regulatory regimes?

4.3

The influence of regulation

In this section we test a number of hypotheses regarding the degree to which theregulatory regime has influenced firm-level productivity performance.

Firstly, as noted in

Sappington et al (2001), by the end of the 1990’s, 28 electric utilities in 16 different States facedsome form of incentive regulation. Of the 61 utilities included in the data set used in the present
study, 11 faced some form of incentive regulation for some part of the sample period. Details ofthese schemes are summarised in Table 7. As can be seen in this table, incentive regulation was
introduced in different States in different years.
The first hypothesis we consider is whether there was a significant difference inperformance of firms when they faced incentive regulation versus those under more traditional
forms of regulation. The means of TE, TFP1 and TFP2 for these two groups are reported underhypothesis (1) in Table 8. The null hypothesis that the means of the two groups are equal is19rejected for all three pairs of means at the 5% level of significance. In fact, for all pairs of means
reported in Table 8 this null hypothesis was rejected at he 5% level in all cases.
What is of interest is to note that those firms facing incentive regulation have lower mean
TE levels and lower mean TFP growth. This is contrary to what the theory predicts should
happen. One possible reason for this finding is that we have perhaps not accounted for particularmacro economic effects that may be making the earlier part of the 1986-1998 data period lookgood and hence given that adoption of incentive regulation methods occurred in the latter half ofthe period, our measures may be affected. To attempt to remove the effect of this possibility we
excluded the 1986-1990 data (which is the period prior to 1991, the date on which the first firmin the sample faced incentive regulation) and then re-ran the t-tests. The results, which arereported as hypothesis (2) in Table 8, come to the same set of conclusions as the first set. Hencethe macro effects issue does not appear to be crucial.
Another possible explanation of our unexpected results is that of “endogenous selection”,
in that those State regulators who decided to implement incentive regulation methods did so
because they knew that the firms in their State were not performing well and hence needed someencouragement. To test this hypothesis we took the 1986-1990 results and dived the firms into
those that would subsequently adopt incentive regulation and those that would not. The results
reported in Table 8 under hypothesis (3) confirm our suspicions. Those firms that subsequently
face incentive regulation do have lower performance during this period. This means that wecannot have much faith in the reliability of the results of hypothesis (1).
Hence we consider one final hypothesis test. In this test we focus only upon those firmsthat actually do face incentive regulation and we look at the period of three years immediately
prior to the regulatory change for that firm and compare it to the following first three years of theregulatory regime for that firm. Given that we are no longer comparing adopters and nonadopters the endogenity issue is removed. Furthermore, given that we focus on a short time
period, macro effects should also be minimised. The results of hypothesis (4) in Table 8 indicatethat performance declines following the introduction of incentive regulation, which confirms theconclusion of hypothesis (1).

Thus, in this instance, the empirical evidence suggests thatincentive regulation has not achieved the desired result.

20

5.

Conclusions

In this paper we have sought to make a number of contributions. First, we have provided
up to date information on productivity growth in fossil-fuel steam electricity generation in the
United States. Using sample data on 61 firms observed over a 13-year period from 1986 to
1998, we found that productivity has improved at the rate of approximately 1.5 percent per year
over this period. We have also calculated productivity growth for each firm in the sample,
finding that they range from a four percent annual decline for one firm to an 11 percent annual
increase for the best performing firm.
Second, we have compared and contrasted three different methods of productivity
measurement. Namely, Tornqvist index numbers, stochastic cost frontiers and input distancefunctions. We argue that the latter method is to be preferred because of its ability to deal withviolations of cost minimizing behavior (which are common in regulated industries) and because
it allows one to decompose productivity growth into various components that are of interest to
regulators (such as technical change and efficiency change).
Finally, we have used our empirical results to test various hypotheses regarding the effectof regulatory reform upon productivity. From the results of this analysis, we conclude that the
introduction of incentive regulation has not had the desired positive effect upon the economic
performance of the firms involved. In fact, in the case of these data, we find that performance isnegatively related with the introduction of the new regulatory regimes. Whether this is a resultof the failure of these regulatory methods, or a failure to properly implement the methods is an
issue that warrants further attention.

21

References

Atkinson, S. E. and R. Halvorson. (1980). “A Test of Relative and Absolute Price Efficiency inRegulated Utilities.” Review of Economics and Statistics 62: 81-88.
Atkinson, S.E. and D. Primont. (2002). “Stochastic Estimation of Firm Technology, Inefficiency,
and Productivity Growth Using Shadow Cost and Distance Functions.” Journal of
Econometrics 108: 203-225.

Atkinson, Scott E., C. Cornwell, and O. Honerkamp. (2003). ‘Measuring and Decomposing
Productivity Change: Stochastic Distance Function Estimation Versus Data Envelopment
Analysis,’ Journal of Business & Economic Statistics 21(2), 284-294.
Averch, H. and L. L. Johnson. (1962). “Behavior of the Firm under Regulatory Constraint.”
American Economic Review 52: 1052-1069.

Battese, George E. and G. S. Corra. (1977). “Estimation of a Production Frontier Model: With
Application to the Pastoral Zone off Eastern Australia, Australian Journal of Agricultural
Economics, 21(3), 169-179.

Battese, George E. and T. J. Coelli. (1988). “Prediction of Firm-Level Technical Efficiencies
with a Genneralized Frontier Production Function and Panel Data.” Journal of
Econometrics 38, 387-399.

Bauer, P. W. (1990a). “Decomposing TFP Growth in the Presence of Cost Inefficiency, Nonconstant Returns to Scale, and Technological Progress.” Journal of Productivity Analysis,1(4), 287-300.
Burns, P. and Weyman-Jones, T.G. (1996). “Cost functions and cost efficiency in electricity
distribution: A stochastic frontier approach.” Bulletin of Economic Research, 48(1), 4164.
Carrington, R., T. J. Coelli, and E. Groom. (2002). “International Benchmarking for Monopoly
Price Regulation: The Case of Australian Gas Distribution.” Journal of Regulatory
Economics 21(2), 191-216.

Caves, D. W., Christensen, L. R., and Diewert, W. E. (1982b). “The Economic Theory of Index
Numbers and the Measurement of Input, Output and Productivity.” Econometrica 50,
1393-1414.
Christensen, L. R. and W. H. Greene. (1976). “Economies of Scale in U.S. electric power
generation.” Journal of Political Economy 84, 655-676.
Christensen, L. R., and Jorgenson, D. W. (1970). “U.S. Real Product and Real Factor Input,
1928-1967.” Review of Income and Wealth 16, 19-50.

22

Coelli, T.J., D. S. P. Rao, and G. E. Battese. (1998) “An Introduction to Efficiency andProductivity Analysis.” Kluwer Academic Publishers.
Coelli, Tim J. (1996b). “A Guide to Frontier Version 4.1: A Computer Program for Stochastic
Frontier Production and Cost Function Estimation.” Center for Efficiency andProductivity Analysis Working Paper no. 96/07. University of New England, Departmentof Econometrics, Armidale, Australia.
———. (2000). “On the Econometric Estimation of the Distance Function Representation of a
Production Technology.” Catholic University of Louvain, Center for Operations
Research and Econometrics, Louvain-la-Neuve, Belgium, Processed.
———. (2002) “A Comparison of Alternative Productivity Growth Measures: With Application
to Electricity Generation.” In K. Fox, ed., Efficiency in the Public Sector. Boston: Kluwer
Academic Publishers.
———. (2003) “A Primer on Efficiency Measurement for Utilities and Transport Regulators.”
The World Bank, Washington, D.C.
Coelli, T.J., and S. Perelman. (1999). “A comparison of Parametric and Nonparametric Distance
Functions: With Application to European Railways.” European Journal of Operations
Research 117(2), 326-339.

———. (2000). “Technical Efficiency of European Railways: A Distance Function Approach.”Applied Economics 32(15), 1967-76.

Considine, T. J. (2000). “Cost Structures for Fossil Fuel-Fired Electric Power Generation.” The
Energy Journal, 21(2), 83-104.

Diewert, W. E. (1976). “Exact and Superlative Index Number” Journal of Econometrics 4, 115145.
Greene, William H. (1980). “On the Estimation of a Flexible Frontier Production Model.”Journal of Econometrics 13, 101-116.

Hemphill, R. C., Meitzen, M. E., and Schoech, P. E. (2003). “Incentive Regulation in Network
Industries: Experience and Prospects in the U.S. Telecommunications, Electricity, andNatural Gas Industries.” Review of Network Economics 3(4), 316-337.
Jamasb, T., and M. Pollitt. (2000). “Benchmarking and Regulation of Electricity Transmission
and Distribution Utilities: Lessons from International Experience.” University ofCambridge, Department of Applied Economics, Cambridge, U.K. Processed.
Orea, L. (2002). A Parametric Decomposition of a Generalized Malmquist Productivity Index,
Journal of Productivity Analysis, 18(1), 5-22.

23

Newbery, D. M. (2000). “Privatization, Restructuring, and Regulation of Network Utilities”
Cambridge, Massachusetts: MIT Press.
Parker, D. (1996), “Regulating the UK’s Privatised Monopolies: Theory and Practice”, Chapter 2
in Atkinson, G.B.J. (Ed.) Developments in Economics: An Annual Review, Volume 12,
Causeway Press.
Rungsuriyawiboon, S. and Stefanou, S. E. (2003). “Dynamic Efficiency Estimation: An
Application in U.S. Electric Utilities,” Centre for Efficiency and Productivity Analysis
Working Paper No. WP05/2003, School of Economics, University of Queensland,

Australia.
Sappington, D., Pleifenberger, J., Hansen, P., and Basheda G. (2001). “The State of
Performance-Based Regulation in the U.S. Electric Utility Industry.” The Electricity
Journal 14, 71-79.

24

Table 1: Data summary for 61 electric utilities over the periods of 1986-98
Variable

Units

Mean

S. D.

Output, Y(× 106 MWhr)

Maximum

13.70912.5610.499

79.7236

300.568

351.84212.8232,522.324

6(× 10 dollars)Fuel, X1

MinimumLabor and Maintenance, X2(× 10 dollars)

61.77653.3661.810

444.453

Capital, X3(× 106 dollars)955.225

877.403

9.070

3,878.295

Price Index of Fuel, W1

0.861

0.208

0.306

1.338

Price Index of Labor and Maintenance, W2

1.079

0.255

0.443

1.928

0.102

0.019

0.009

0.203

410.643376.033

25.6682,233.418

User Costs of Capital, W3
6

Total Cost, C(× 10 dollars)Note: The observed shares are 58.6% by fuel, 17.9% by labor and maintenance, and 23.5% by capital

Table 2: Parameter estimates for the cost frontier and input distance function
Model
Parameter
β0
β1
β2
β3
β11
β12
β13
β22
β23
β33
βy
βyy
β1y
β2y
β3y
βz
βzz
β1z
β2z
β3z
βyz
σ2
γ

Cost Frontier

Input Distance Function

Estimates

S.D.

t-ratio

Estimates

S.D.

t-ratio-0.270
0.449
0.361
0.190
0.267
-0.3600.093
0.525-0.164
0.071
0.966
0.028
-0.059-0.011
0.069-0.0220.002
0.038-0.0480.010-0.005
0.113
0.974

0.012
0.022
0.030

-22.055
19.99811.983

0.010
0.017
0.018

24.49534.655
7.671

0.128
0.110

2.095
-3.287

0.047
0.042

-2.516
3.041

0.169

3.111

0.041

-0.266

0.006
0.012
0.025
0.031

155.078
2.400-2.337-0.343

0.008
0.014
0.018
0.017

-128.787-1.676-3.034-0.252

0.002
0.001
0.008
0.011

-10.455
1.458
4.756-4.453

0.002
0.001
0.005
0.004

5.015
1.456
1.346
1.466

0.002
0.007
0.008

-2.297
16.177122.552

0.256
0.574
0.136
0.290
-0.1180.127-0.009-0.011-0.1160.125-0.976-0.023-0.056-0.004
0.060
0.008
0.001
0.006
0.007
-0.013
0.006
0.110
0.979

0.002
0.007
0.009

3.195
15.175112.813

Log likelihood
function

200.651220.574

LR test of the
one-sided error

207.896190.514

25

Table 3: Annual average TFP change measures (unweighted)*
Cost Frontier Model
Year

Input Distance Model

TPIN
CEC

TC

SEC

AEC

TFPC1

TFPC2

TEC

TC

SEC

AEC

TFPC1

TFPC2

86-87

6.631

6.455

1.652

0.146

2.001

8.253

10.255

6.550

0.083

-0.078-0.281

6.555

6.274

87-88

1.575

1.962

1.888

0.042

2.615

3.892

6.507

0.083

0.270

0.199

1.068

0.552

1.620

88-89

4.003

2.748

2.073

0.250

1.477

5.071

6.548

2.574

0.469

0.063

0.569

3.106

3.675

89-90

-2.570-4.401

2.062-0.165-0.371-2.504-2.874-3.2940.598-0.0490.454-2.745-2.29190-91-2.287-2.0522.109-0.0621.971-0.006

1.966-3.550

0.695

0.012

0.764

-2.843-2.079

91-92

0.999

0.096

2.208

-0.069

1.222

2.235

3.457

0.443

0.792

-0.006-0.265

1.228

0.963

92-93

0.109

-0.9222.273-0.282

1.156

1.069

2.225

0.131

0.880

-0.243-0.725

0.768

0.043

93-94

1.767

0.012

2.361

0.114

0.421

2.486

2.907

0.387

0.977

0.070

0.530

1.434

1.964

94-95

0.428

-0.8172.467-0.032

1.008

1.617

2.626

-1.0061.076-0.059

0.279

0.010

0.290

95-96

2.377

0.089

2.514

-0.120

0.362

2.483

2.845

1.223

1.170

-0.127

0.129

2.266

2.396

96-97

3.488

0.702

2.451

0.498

0.516

3.651

4.167

0.956

1.325

0.501

0.372

2.782

3.154

97-98

1.696

-0.961

2.500

0.244

0.128

1.783

1.912

-0.686

1.572

0.171

0.890

1.057

1.947

Mean

1.518

0.243

2.213

0.047

1.042

2.503

3.545

0.318

0.826

0.038

0.315

1.181

1.496

* All measures are in percentage terms.

Table 4: Weighted annual average TFP change measures
Cost Frontier Model
Year

Input Distance Model

TPIN
CEC

TC

SEC

AEC

TFPC1

TFPC2

TEC

TC

SEC

AEC

TFPC1

TFPC2

-0.126-0.330

5.929

5.598

86-87

5.867

5.641

2.099

-0.049

2.169

7.692

9.861

5.516

0.539

87-88

1.465

1.378

2.367

0.023

2.567

3.768

6.335

0.316

0.673

0.020

0.447

1.010

1.457

88-89

2.108

0.452

2.532

0.055

1.104

3.038

4.142

1.043

0.830

-0.023

0.076

1.849

1.926

89-90

-1.416-3.6622.541-0.040-0.059-1.161-1.220-2.662

0.948

0.016

0.496

-1.698-1.20290-91-1.133-1.4972.605-0.002

2.028

1.105

3.133

-2.543

1.023

0.033

0.547

-1.486-0.939

91-92

1.227

1.431

2.702

0.007

2.886

4.139

7.025

0.186

1.089

0.048

-0.199

1.322

1.123

92-93

1.557

-1.7232.752-0.020-0.344

1.009

0.665

0.528

1.213

-0.017-0.376

1.724

1.348

93-94

1.040

-0.027

2.835

0.019

1.538

2.827

4.365

-0.192

1.325

0.006

0.169

1.139

1.308

94-95

0.864

-0.805

2.982

0.029

1.273

2.206

3.479

-0.814

1.406

0.006

0.360

0.598

0.958

95-96

3.371

0.475

3.090

0.012

0.613

3.577

4.189

1.760

1.523

0.020

-0.217

3.303

3.086

96-97

2.156

-0.699

3.105

0.121

0.812

2.527

3.339

0.583

1.662

0.168

-0.864

2.414

1.550

97-98

1.624

-0.852

3.116

0.125

0.373

2.390

2.762

-0.242

1.896

0.095

0.224

1.749

1.973

Mean

1.561

0.009

2.727

0.023

1.246

2.760

4.006

0.290

1.177

0.021

0.028

1.488

1.516

26

Table 5: Average TFPC Decomposition by Firm (in Percentage)
Cost Frontier Model

Input Distance Model

Firm

TPIN
TFPC

CEC

TC

SEC

AEC

TFPC1

TFPC2

TEC

TC

SEC

AEC

TFPC1

TFPC2

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61

0.683
11.175-0.047
2.877
0.285
1.758
0.098
0.827
0.337
-0.152
1.971
1.934
1.615
-0.960
0.569
1.854
2.529
1.907
2.601
9.341
1.121
3.318
2.017
0.593
2.447
-0.337
1.475
2.848
3.222
0.906
2.017
0.784
2.415
-0.392
0.861
1.627
0.147
-0.826-0.532
0.918
2.023
1.727
-3.943
2.556
1.674
2.915
-0.580
1.433
2.191
3.498
1.679
1.521
2.079
4.422
0.785
-1.966
0.102
2.115
0.418
0.582
1.539

-0.3288.650-2.192
1.652
0.530
1.533
-0.333-0.203-0.615-1.0791.238-0.2320.758-2.175-0.578
0.084
1.252
0.325
1.033
5.622
0.212
1.704
1.806
1.026
0.549
-0.866-1.3660.909
1.211-0.146
0.001
0.294
1.959
-0.556-1.4020.278
0.710-1.146-2.6800.588-0.719-0.806-3.8911.526
0.559-1.245-1.569
0.580
1.608
0.582
0.446
-0.7870.135
3.449-0.067-2.953-0.0490.200-0.755-0.072
0.596

2.247
0.756
2.892
1.319
1.281
2.649
1.065
1.996
1.882
0.710
0.979
3.493
1.424
0.847
3.209
3.172
1.659
2.064
3.026
3.032
2.905
2.491
0.636
-0.562
3.042
1.023
4.921
2.568
3.376
2.443
2.813
1.082
0.953
1.169
3.106
1.685
2.359
1.911
3.683
0.500
4.718
4.174
2.891
1.142
2.234
4.742
1.568
2.788
0.297
4.079
1.246
3.509
2.626
1.881
-0.152
2.268
1.641
4.284
3.620
1.488
2.149

0.050
0.663
-0.045-0.023-0.243-0.089
0.086
0.029
0.020
0.058
-0.0780.018
0.028-0.175-0.023
0.015
0.056
0.073
0.203
0.288
0.014
-0.0980.373
0.182-0.254-0.0120.018
0.045-0.037
0.066
0.109
0.060
0.006
0.047
-0.080
0.106
0.329
0.005
0.051
0.115
-0.0070.106-0.8330.336
0.015-0.0720.084-0.012
0.199
0.171
0.010
0.018
-0.0320.082
0.103-0.121
0.333-0.037-0.012
0.478
0.102

1.227
1.153
0.578
0.117
1.307
2.413
0.624
0.984
0.736
-0.447
0.253
1.338
0.615
-0.605
2.022
1.458
1.001
0.550
1.690
-0.341
2.123
0.811
0.862
0.094
0.907
0.461
2.056
0.702
1.371
1.419
0.875
0.697
0.537
1.041
0.724
0.972
3.167
1.468
1.541
0.374
1.930
1.740
2.041
1.078
1.184
0.479
0.530
1.935
-0.046
1.657
0.031
0.871
0.875
1.162
-0.904
1.077
1.776
2.340
2.289
1.307
1.351

1.969
10.068
0.655
2.948
1.568
4.093
0.818
1.823
1.287
-0.311
2.139
3.279
2.210
-1.502
2.608
3.271
2.967
2.462
4.263
8.942
3.130
4.098
2.815
0.646
3.337
0.145
3.573
3.522
4.550
2.363
2.923
1.437
2.918
0.660
1.624
2.069
3.398
0.769
1.054
1.204
3.991
3.474
-1.834
3.004
2.808
3.425
0.084
3.356
2.103
4.832
1.702
2.739
2.729
5.412
-0.115-0.805
1.925
4.447
2.852
1.895
2.848

3.196
11.221
1.232
3.064
2.875
6.505
1.443
2.807
2.024
-0.759
2.393
4.617
2.825
-2.107
4.630
4.729
3.968
3.012
5.952
8.600
5.253
4.909
3.677
0.740
4.244
0.606
5.630
4.225
5.920
3.782
3.798
2.133
3.456
1.701
2.348
3.041
6.565
2.238
2.595
1.578
5.921
5.215
0.207
4.082
3.991
3.904
0.614
5.291
2.057
6.489
1.733
3.610
3.604
6.574
-1.019
0.272
3.701
6.787
5.141
3.202
4.199

-1.0528.322-1.496
0.480
0.143
0.711
-0.440-0.315-0.508-1.091
0.235
1.635
0.610
-2.943-0.3850.417
1.013-0.190
0.972
2.740
0.013
2.033
1.375
0.161
1.210
-1.406-0.250
0.608
1.839
0.240
0.254
-0.2271.865-0.253-0.5980.111
0.249-0.672-0.5910.394
0.676-0.603-3.9821.053
0.649-0.285-1.627
1.263
1.716
2.726
0.067
0.080
0.628
3.723
-0.140-1.5530.382
0.598-0.790-0.736
0.321

0.789
0.769
1.282
1.280
-0.215
0.693
0.634
0.957
1.110
0.552
1.117
1.091
0.885
1.411
1.593
1.001
0.892
0.663
1.118
-0.072
1.188
0.154
0.798
0.139
1.145
1.327
2.343
1.096
1.037
0.851
0.667
1.102
-0.098-0.3931.039
1.031-0.048-0.188
1.140
0.514
1.047
2.443
0.814
0.284
1.178
2.104
0.830
0.985
-0.143
0.286
1.046
1.257
1.131
-0.5170.810
1.097-1.138
1.808
1.155
0.386
1.104

0.068
-0.095-0.118-0.005-0.168-0.080
0.043
0.034
0.031
0.130
-0.058
0.007
0.029
0.029
-0.029
0.067
0.075
0.159
0.063
0.815
0.006
-0.1790.108
0.280-0.292-0.051
0.015
0.052
0.045
0.030
0.147
0.049
0.052
-0.048-0.099
0.115
0.275
0.009
-0.0010.051
0.009-0.182-0.7390.221-0.034-0.095
0.087
0.006
0.164
0.153
0.046
0.019
0.027
0.190
0.120
-0.0540.410-0.058
0.050
0.360
0.039

1.002
1.762
0.323
1.111
0.521
0.419
0.000
0.157
-0.1190.570
0.643-0.8340.077
0.606-0.6020.247-0.074
1.280
0.427
5.795
-0.0891.266-0.2940.009
0.359-0.176-0.6281.074
0.262-0.2440.943-0.032
0.556
0.308
0.532
0.007
-0.3350.094-1.068-0.081
0.277
0.082
0.048
0.643
-0.1451.197
0.692-0.848
0.417
0.068
0.519
0.162
0.216
0.762
-0.001-1.4210.370-0.249
0.029
0.588
0.055

-0.1958.996-0.3321.755-0.239
1.324
0.237
0.677
0.633
-0.409
1.293
2.733
1.525
-1.503
1.179
1.485
1.979
0.632
2.153
3.484
1.206
2.008
2.282
0.580
2.062
-0.130
2.108
1.755
2.921
1.121
1.068
0.924
1.819
-0.694
0.342
1.257
0.476
-0.850
0.548
0.959
1.731
1.658
-3.906
1.558
1.793
1.724
-0.710
2.255
1.737
3.164
1.159
1.356
1.786
3.396
0.790
-0.510-0.346
2.347
0.415
0.010
1.463

0.807
10.758-0.009
2.867
0.281
1.743
0.237
0.834
0.514
0.161
1.936
1.899
1.602
-0.897
0.577
1.732
1.905
1.911
2.580
9.279
1.117
3.274
1.988
0.590
2.421
-0.306
1.480
2.829
3.183
0.877
2.011
0.892
2.375
-0.386
0.874
1.264
0.141
-0.757-0.520
0.878
2.009
1.739
-3.858
2.201
1.648
2.921
-0.018
1.406
2.154
3.232
1.678
1.518
2.002
4.158
0.789
-1.931
0.023
2.098
0.444
0.598
1.518

Mean

1.518

0.243

2.213

0.047

1.042

2.503

3.545

0.318

0.826

0.038

0.315

1.181

1.496

27

Table 6: Distribution of Average Total Factor Productivity Change
TFPC1

TFPC2

Total Factor
Productivity
Change(%)

TPIN
Approach
Number of
Firms

Cost Frontier
Approach
Number of Firms

Input DistanceApproach
Number of Firms

Cost Frontier
Approach
Number of Firms

Input DistanceApproach
Number of Firms< -2.0

1

0

1

1

1

-2.0-0.0

9

5

11

2

8

0.0-2.0

31

18

36

10

34

2.0-4.0

19

29

12

25

15

4.0-6.0

1

7

0

16

1

6.0-8.0

0

0

0

5

0

8.0-10.0

1

1

1

1

1

> 10.0

1

1

0

1

1

Table 7: Incentive Regulation of U.S. Electric Utilities in the Sample Data
No

Name

State

Period1991-1995
1998-2002
1998-2002
1998-2003
1997-2001
1995-1999
1991-1993
1995-2000
1995-1997
1997-2000
1997-1998
1997-2001
1993-1996
1996-2002
1995-2001

6

Niagara Mohawk Power

NY

7
8
25
26
34

Central Illinois Light
Central Illinois Public Service
Southern California Edison
Tampa ElectricCentral Maine Power

IL
IL
CA
FL
ME

35

Consolidated Edison -NY

NY

46
52
54

Montana Power
Public Service of Colorado
Rochester Gas & Electric

MT
CO
NY

59

Union Electric

MOType of Plans
Revenue cap
Rate freeze
Price cap
Price cap
Price cap
Rate freeze
Revenue-per-customer cap
Price cap
Revenue-per-customer cap
Rate case moratorium
Price cap
Rate case moratorium
Revenue cap
Rate case moratorium
Rate freeze

Table 8: Tests of hypotheses regarding the effects of regulatory regime*
PeriodIncentive
Regulation

TE

TFP1

TFP2

(1) H0 = means between adopters and non-adopters during 1986-98 are equivalent
no
0.842
1.205
1.539
1986-1998
yes
0.715
1.103
1.380
(2) H0 = means between adopters and non-adopters during 1991-98 are equivalent
no
0.841
1.200
1.531
1991-1998
yes
0.715
1.103
1.380
(3) H0 = means between adopters and non-adopters during 1986-90 are equivalent
no
0.854
1.296
1.588
1986-1990
yes
0.793
1.154
1.415
(4) H0 = means between 3 year before and after adoption for all IR adopters are equivalent
before
0.805
1.301
1.431
various
after
0.759
1.126
1.398
* All differences were found to be significant at the 5% level.

28

Figure 1: Distribution of Average Total Factor Productivity Change
Distribution of Average TFPC2 by Firm

Distribution of Average TFPC1 by Firm
40

40

35

35
TPIN TFPCTPIN TFPC2

30

Cost TFPC1
Distance TFPC1

25
20
15
10

Num ber of Firm s

N u m b er o f F irm s

30

Cost TFPC2
25

Distabce TFPC2

20
15
10

5

5

0
<-2

-2-0

0-2

2-4

4-6
TFPC1 (%)

6-8

8-10

>10

0
<-2

-2-0

0-2

2-4

4-6

TFPC2 (%)

6-8

8-10

>10