Economies of Scale in U.S. Electric Power Generation (1976) Authors: Laurits R. Christensen and...
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Transcript of Economies of Scale in U.S. Electric Power Generation (1976) Authors: Laurits R. Christensen and...
Economies of Scale in U.S. Electric Power Generation
(1976)Authors: Laurits R. Christensen and William H. Greene
Presented by: Jared HaydenEcon 435
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)
Overview
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
1976 Context
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
Need for Study
Dominant form of electricity generation in time period was steam-driven 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
Electric Power Industry
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”
Economies of Scale in ElectricityGeneration
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.
Electricity Growth1955-1970
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
Modeling Neoclassical Cost Function
Y = output Implications
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
Translog Cost Function
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
Scale Economies (1-elasticity of total cost with respect to output)
*positive = scale economies , negative = scale diseconomies
*natural interpretation in percentage terms
Derived Functions
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:
Translog Function Restrictions
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
6 Models
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
Estimation Procedure
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
Data
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
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
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
Grand Conclusions
Potential question: How would inclusion of modern generation mix
change the paper? (Coal, Nuclear, Natural Gas)
THE END