Abstract
This paper examines whether rate-of return regulation alters the input quantities firms use to produce their selected output level when the corresponding input prices change, in a manner similar to the Le Chatelier principle. More specifically, would the change in a rate regulated firm’s input quantity due to a change in its input price be less price elastic than the unregulated firm’s change in the input quantity due to a change in its input price. We follow Färe and Logan (1986), Nelson and Wohar (1983) in estimating a rate regulated cost function and capital input share system of equations. Using a 1992–2000 panel of 34 US major investor-owned electric utilities, empirical results indicate that the regulated own-input price elasticities of demand for labor and fuel are less price elastic than their corresponding unregulated own-input price elasticities of demand (a Le Chatelier principle type effect). Having a fuel clause (1) reduces the firm’s willingness to substitute from fuel to either non-fuel (capital, labor) input when the price of fuel rises, and (2) enhances the firm’s willingness to substitute from non-fuel inputs to fuel when the price of non-fuel inputs rises.
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Notes
The Le Chatelier principle provides an example of the notion that in optimization models additional constraints reduce the absolute response of a decision variable to a change in a parameter.
Among the inputs capital, fuel, and labor, the quantity of capital is at times considered to be fixed (capital is thought of as a fixed input). In the data sample (which consists of 34 major US investor owned electric utilities), 31 of the 34 firms used more capital (quantity of capital measured as the capacity of the steam generation plant) over the sample period. Most of the 31 firms expanded their capacity several times over the sample period. It would be difficult to model, and obtain data for, the dynamic process of capital accumulation.
The Federal Energy Regulatory Commission regulates the sale and transmission of electric power in interstate commerce.
If one computes the second derivatives of the cost function with respect to the input quantities and the Lagrange multipliers, then uses the matrix of second derivatives to solve for ∂Lr/∂wl and ∂Fr/∂wf, one cannot determine the signs of ∂Lr/∂wl or ∂Fr/∂wf.
To impose concavity of the regulated cost function locally (at one point) in input prices, we first select an observation to normalize the independent variables: let y″, wi″, θ″, and t″ denote the value of the variables at the selected observation. Now, the independent variables used in estimating the cost function and the capital input share equation are y′ = y/y″, wi′ = wi/wi″, θ ′ = θ/θ″, and t′ = t − t″. Second, denote γij′ parameters on the interaction terms of the input prices in the regulated cost function. Concavity of the regulated cost function in input prices imposes restrictions on γij. We initially estimated the system of equations (cost function, capital input share equation) using parameter restrictions that would impose concavity of the derived unregulated cost function (in Eq. 13) in input prices. Unfortunately, some of the cost input share values were negative when imposing concavity locally and globally of the regulated cost function in input prices. Positive values of the unregulated cost input shares were obtained when imposing concavity of the regulated cost function locally in input prices.
The data sample ends in 2000 because starting in 2002, FERC no longer required electric utilities to report the number of electric department employees. There was insufficient data on several variables to include 2001 in the data sample. Several utilities in the 1990s (1) divested of their generation equipment, or (2) merged with other utilities. We excluded electric utilities that (1) were involved in mergers, (2) heavily divested of their generation equipment, or (3) could not obtain sufficient data over the sample period. We recognize that there are benefits to using plant level data (plant level data was used by Fabrizio, Rose, and Wolfram (2007)). There are several reasons the paper uses firm level data, and not plant level data. First, data on the allowed rate of return and the financial cost of capital (used to compute θ) is determined for the electric utility portion of the firm (not plant specific). There is not sufficient data to compute the financial cost of capital for each plant. Second, plant level data only provides information on the average number of employees working at each plant. The plant level data in the FERC reports does not separate the numbers of employees into full-time and part-time workers.
We are grateful to the anonymous referee for bringing forth to our attention the topics of different sources of electric power (nuclear, hydroelectric), and vertical integration. The referee informed us of studies by Kaserman and Mayo (1991), and Kwoka (2002). These studies found that electric utilities experienced benefits and cost savings from vertical integration. Many of the major US investor owned electric utilities also transport (have transmission plant) and distribute (have distribution plant) electric power. Information from the 1996 edition of the Financial Statistics of Major US Investor Owned Electric Utilities (published by the Energy Information Administration) indicates that 128 of the 140 major investor owned utilities have all three plants (steam generation, transmission, and distribution). Previous empirical studies that used data on the generation sector of the US electric utility industry, for example Gollop and Karlson (1978), Atkinson and Halvorsen (1980), Nelson and Wohar (1983), focused on electric power production via steam generation plants.
The investment tax credit is zero over the sample period. The depreciation rate of 4 % is based on the class life of the electric utility steam production plant, as determined by the modified accelerated cost recovery system. Data on the class life of the plant is obtained from the US Master Depreciation Guide (published by Commerce Clearing House 1998).
The reason for not including the fuel or labor input share equation in the system of equations that were estimated is that it was very difficult to get the system of equations to converge, when the system of equations consisted of the cost function, capital input share equation, and a non-capital input share equation. Also, the statistical package used to estimate the system of equations via a random effects model could not estimate a random effects model if the system of equations included a non-capital input share equation.
See Baltagi (1980) for detailed explanations on the derivations and decomposition of the inverse covariance matrix of the error terms.
The desired procedure here would be to obtain bootstrap estimates of the cost function parameters, and used the bootstrapped coefficients to obtain the samples for the various elasticities of demand. The authors are unaware of programs that can obtain bootstrap estimates of the parameters.
We are grateful to the referee for providing the suggestion of computing a measure of the cost of the impact of rate regulation on the own-input price elasticities of demand.
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Acknowledgments
We are grateful to Jennifer Shand and Sean Delehunt for their assistance in compiling the data sample, to participants of the Sixth North American Productivity Workshop, the 2010 Asia Pacific Productivity Conference, the journal editors and the referee for their valuable comments and suggestions. All errors are the sole responsibility of the authors.
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Granderson, G., Forsund, F. Rate of return regulation and the Le Chatelier principle. J Prod Anal 41, 263–275 (2014). https://doi.org/10.1007/s11123-012-0300-4
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DOI: https://doi.org/10.1007/s11123-012-0300-4