Transcript Economies of Scale in U.S. Electric Power Generation

Economies of Scale in U.S. Electric
Power Generation
(1976)
Authors: Laurits R. Christensen and William H. Greene
Presented by: Jared Hayden
Econ 435
Overview
 Study aims to estimate economies of scale for U.S.
firms producing electric power
 Comparison between 1955 and 1970 using cross
sectional data
 Data analyzed using a translog cost function
 The paper adds and compares results to the
pioneering work on the subject done by Marc Nerlove
(1963)
1976 Context
 Electricity rates rising at “historically unprecedented rates”
 Weiss proposes idea to vertically disintegrate the industry
by separating generation from transmission and
distribution (1975)
 Weiss believed competition in generation would put
downward pressure on electricity rates
 Leads to critical question: Would significant scale
economies be sacrificed by allowing many potential
suppliers to compete in generation market?
 If so, could offset the benefits of increased competition
Need for Study
 The regulation of the U.S. electric power industry is on the firm
level
 Information on the economies of scale for firms is required to
assess the affect of such a reorganization of the industy
 This study aims to attain this information by using the
neoclassical cost function approach, as Nerlove (1963) pioneered
 Advancements in duality theory and functional form
specification between 1963 and 1976 allow a more general
model than that of Nerlove
 The study places emphasis on distinguishing economies of scale
and decreases in cost due to technical change.
 Accomplish this by using cross-sectional data on firms with same
access to plant design
 Show change over time by analyzing Nerlove’s data from 1955
and new data from 1970
Electric Power Industry
 Dominant form of electricity generation in time period was steamdriven turbines (i.e. coal plants)
 Nuclear had yet to make and impact and hydro was running out of
attractive dam sites.
 Internal combustion engines primarily employed in only peak demand
periods.
 Study limits attention to conventional steam driven plants
 Conventional plants account for 90% of sample firms’ total generation
 Study also limits sample to investor owned utilities with upwards of
$1 million in annual revenue
 Accounts for 77% of total power produced in the U.S. in 1970
Economies of Scale in
ElectricityGeneration
 It is unanimously agreed upon that economies of
scale exists in electricity generation
 Debate lies over what range the economies of scale
exists
 Hulbert (1969) estimated that economies of scale exist
all the way up to 25,000 MW
 Johnson (1960) and Nerlove (1963) concluded that
economies of scale were exhausted at a “relatively
modest firm size”
Electricity Growth1955-1970
 1955 sales to ultimate consumers: 369 billion kWh
 1970 sales to ultimate consumers: 1,085 billion kWh
 Number of firms declined slightly, so output per firm
increased threefold!
 Technology allowed firms to expand to exploit scale
economies or rapid expansion has exhausted
economies of scale??
 Need for current econometric analysis.
Modeling Neoclassical Cost Function
 Duality theory: cost and production functions which are
dual to each other.
 Chose to estimate cost function
 Input levels endogenous
 Output level and input prices exogenous
 Allows implied demand equations that are linear in
parameters and represent general production structures
 Chose translog cost function
 No restrictions on substitution possibilities
 Allows scale economies to vary with output
 Special cases of translog function can be directly compared to
Nerlove’s findings
Translog Cost Function
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Y = output
Pi’s = prices of factor inputs (K,L,F)
Yij = Yji
Homogenous of degree 1 in prices
 i.e. total cost increases proportionally
to all prices increasing by factor, holding
output constant
Implications
Derived Functions

Demand function for production factors (Shephard’s Lemma!)

Cost Share of ith-factor input

Allen partial elasticities of substitution

Own-price elasticity of demand for ith factor of production
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Scale Economies (1-elasticity of total cost with respect to output)

*positive = scale economies , negative = scale diseconomies
*natural interpretation in percentage terms
Translog Function Restrictions
 Translog function does not impose homothetic or
homogeneity restrictions
 Homothetic: monotonic transformation of homogenous
function
 Homogenous: f(tx1 + tx2) = tk(x1 + x2)
 Can be restricted and tested statistically
 Can also restrict to being unitarily elastic by eliminating the
second order term in prices
 Homotheticity restriction:
 Homogeneity restictions:
 Unitary elasticity restriction:
6 Models
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Model A: Translog Function
Model B: Translog with homotheticity restriction
Model C: Translog with homogeneity restriction
Model D: Translog with unitary elasticity restriction
Model E: Translog with homotheticity and unitary elasticity restrictions
Model F: Translog with homogeneity and unitary elasticity restrictions
Estimation Procedure
 OLS is attractive in simplicity, but neglects information in
cost shares and multicollinearity may be a problem
 Cost shares as a multivariate regression system inadequate
as crucial cost function information is neglected
 Chose procedure of jointly estimating cost function and
cost shares a multivariate regression system
 Specify additive disturbances for each of the share equations
(assume joint normal distribution)
 Allow nonzero correlations for single firm but zero
correlations across firms (Zellner procedure)
 Delete one of the share equations from system for system to
work
Data
 Capital, Labor, and Fuel as inputs (K, L, F)
 Require prices and cost shares for 3 inputs
 Nerlove’s did not construct cost share data and mis-specified
holding companies (possibly underestimating scale economies)
 Christensen and Greene revised his work to compare results (reduced
1955 observations from 145 to 124)
 1970 data includes 114 firms and holding companies
 Used same data procedures as Nerlove with two exceptions:
 Used plant by plant fuel prices instead of state averages
 Used plant by plant labor prices instead of state averages
 Three data sets were used for each model (A-F)
 1955I, 1955II (revised), 1970
Empirical Results
Model A-1955II and 1970
• T-ratios suggest
nonhomotheticity
parameters (Yyi) and
substitution parameters (Yij)
that neither homotheticity
hypothesis nor unitary
elasticity hypothesis is
consistent with any of the
data sets
• Confirmed by table 5 by
likelihood ratio statistics (all
restricted models rejected
handily)
Estimated Elasticities
• Shows that there may be significant substitution
possibilities at the firm level
Estimated Economies of Scale
• Homogenous models
incorrectly show inexhaustible
scale economies
• Non-homogenous models show
the scale economies are being
exhausted with in the output
range of the sample
• Unitary elasticity yields a worse
fit to data, but little effect on
estimation of scale economies
• “erroneous” Nerlove model
used incorrect formula
• Shows U shape of Average Cost
Curve
1955 Average Cost Curves (Nerlove)
• Implies Nerlove
underestimated
scale economies
• Shown by
homogenous
models C and F
Estimated Economies of Scale at Firm
Level
• Can observe trend of
flattening average
cost curve
• Economies of scale
decrease as the firm
grows large
Model A Average Cost Curves (1955I,
1955II, and 1970)
Ranges of Significant Scale
Economies
Model A-No significant economies
range (1970)
*5% significance
Conclusions
 There is large range of firm size yielding constant returns to scale
 Aggregate cost related to number of firms operating in flat area of
average cost curve
 Drop in cost attributed mostly to technical change, not
exploitations of economies of scale (still some relatively small gains
from scale economies)
 1970 average cost curve downward displacement of 1955II average cost
curve
 Little correlation between cost reduction and firm growth rate
 Reducing number of generation firms may yield cost savings
 If all firms operated at minimum average cost, could save $175.1 million
(47.9% labor, 28.3% capital, 23.8% fuel)
 33 firms could produce total output that was generated by 114 firms in
1970
Grand Conclusions
 1955: scale economies available to most firms
 1970: majority of electricity generation operating on flat
portion of average cost curve
 Great scale economies at low levels of output, but average
cost curves flatten out at relatively moderate firm size
 A small number of very large firms not required for optimal
exploitation of scale economies
 Policies designed to promote competition in generation
cannot be faulted in terms of sacrificing scale economies
THE END
 Potential question:
 How would inclusion of modern generation mix change
the paper? (Coal, Nuclear, Natural Gas)