The impact of regulation on input substitution and operating cost.

Lovell, C.A. Knox

1. Introduction

Input-based regulation restricts a firm's input choices to a subset of those allowed by the structure of production technology. It follows that regulation distorts a firm's input demands and the substitutability between various input pairs. The distortion of input demands caused by rate-of-return regulation was the subject of the Averch-Johnson (1962) hypothesis, which spawned an extensive theoretical and empirical literature. The distortion of input substitutability has received less attention in the literature and is the subject of this paper. The subject is of some significance because regulation raises operating cost for fixed input prices. However, to the extent that regulation also affects input substitutability, as input prices inevitably change, the fixed-price cost consequences of regulation are dampened or magnified accordingly as regulation enhances or retards input substitutability.

Smith (1981) derived Allen-Uzawa elasticities of substitution (AUES) for a cost-minimizing firm subject to rate-of-return regulation. Nelson (1983) applied Smith's results to a translog specification of a rate-of-return regulated cost function derived by Cowing (1981) and Fuss and Waverman (1977). Nelson used U.S. electric utility data to estimate the unregulated and regulated translog cost functions and then to calculate the unregulated and regulated AUES. He found little impact on the AUES between pairs of rate base and non-rate-base inputs, but he found a large impact on the AUES between pairs of non-rate-base inputs.

Blackorby and Russell (1989) demonstrated that if the number of inputs exceeds two, or if technology cannot be characterized with constant elasticities of substitution, the AUES concept is uninformative. On the reasonable presumption that the AUES concept is as uninformative in a regulated environment as it is in an unregulated environment, this finding casts serious doubt on the value of the research cited in the previous paragraph. Blackorby and Russell also demonstrated that an alternative notion of the elasticity of substitution, due originally to Morishima (1967), is informative if the number of inputs exceeds two or if the substitution elasticities are not constant. They showed that Morishima elasticities of substitution (MES) can also be obtained from the firm's cost function and are informative in the sense that (i) they do provide a measure of the curvature of an isoquant; (ii) they do provide measures of the effects of changes in input price ratios on relative input shares; and (iii) they are equal to elasticities of input quantity ratios with respect to input price ratios. They also showed that AUES are uninformative on each of these three criteria. In a subsequent paper, Blackorby and Russell (1990) derived formuli for the MES between various pairs of non-rate-base and rate base inputs and contrasted these with the formuli for the MES between the corresponding pairs of inputs in the unregulated firm. They did not, however, attempt to sign the differences between the unregulated and the regulated MES.

At a purely analytical level it is of interest to determine if the differences between any pair of unregulated and regulated MES can be signed and, if so, which ones. We know that for a given input price structure, regulation raises operating cost by distorting input choice as regulated firms respond to regulated shadow prices of capital that are lower than true capital costs. However, if regulation also enhances input substitutability, then, as input prices change, the cost increase is dampened. Conversely, if regulation retards input substitutability, then, as input prices change, the cost increase is magnified. At an empirical level it is of interest to seek quantitative evidence first of the impact of regulation on firms' propensity to substitute between various pairs of inputs as their relative prices change but also, more important, of the impact of the input substitutability distortions on firms' operating costs.

The objective of this paper is to conduct just such a combined analytical and empirical investigation into the effect of regulation on the MES and on operating cost. The regulation we consider is the familiar rate of return regulation, and the industry we examine is the U.S. interstate natural gas pipeline industry, which was subject to rate-of-return regulation during the 1977-87 period we study.

We begin by examining unregulated and regulated MES and then conduct an analytical investigation into the differences between the two sets of elasticities. Theory does not allow us to sign the difference between any pair of MES, although it does enable us to offer conjectures on the sign of the difference between each pair of MES. Armed with these conjectures, we conduct an empirical exercise in which we estimate sets of unregulated and regulated MES in the interstate natural gas pipeline industry. Results indicate that regulation increased the willingness of firms to substitute each rate base input for our sole non-rate-base input when the non-rate-base input price increased. Regulation decreased the willingness of firms to substitute (i) between the rate base inputs and (ii) our sole non-rate-base input for each rate base input when a rate base input price increased. The finding that regulation decreased the willingness to substitute between some input pairs and increased the willingness to substitute between other input pairs suggests that the secondary substitutability impacts of regulation neither reinforced nor retarded to any significant degree the initial fixed-price impact of regulation.

Finally, we find that regulation led to an increase in operating cost of 16% on average, although we are unable to decompose this estimate into an initial fixed-price component and a secondary substitutability component.

This paper is organized as follows. In section 2 we examine the unregulated and regulated MES and exploit what little guidance theory provides to make some conjectures concerning the relationships between the unregulated and the regulated MES. In section 3 we present our empirical model, which we use to estimate the parameters of unregulated and regulated translog cost functions from which the unregulated and regulated MES are derived. In section 4 we describe our data sample. Section 5 contains our empirical analysis of the impact of regulation on input substitutability and on operating cost. Section 6 concludes.

2. Unregulated and Regulated Morishima Elasticities of Substitution

Let x = ([x.sub.n], [x.sub.c]) denote a nonnegative vector of inputs, with [x.sub.n] = ([x.sub.n1], ..., [x.sub.nN],) and [x.sub.c] = ([x.sub.c1], ..., [x.sub.cM]) denoting subvectors of the non-rate-base and rate base inputs, respectively. Let w = ([w.sub.n],[w.sub.c]) denote a corresponding strictly positive vector of input prices. Denote a firm's desired level of output y [greater than] 0 and its production function f(x). The firm's unregulated cost function is

c(y,w) = [min.sub.x]{[w.sup.T]x: y [less than or equal to] f(x)} (1)

where c(y,w) is nondecreasing in y and nondecreasing, concave, and homogeneous of degree +1 in w. Shephard's lemma yields the cost-minimizing input demand equations x(y,w) = [Nabla].sub.w]C(y,w).

Blackorby and Russell (1989, 1990) showed that the Morishima elasticities of substitution,

[MES.sub.ij] (y, w) = [w.sub.i][[c.sub.ji] (y, w)/[c.sub.j] (y, w) - [c.sub.ii] (y, w)/[c.sub.i](y, w)]

= [[Epsilon].sub.ji](y, w) - [[Epsilon].sub.ii](y, w), (2)

describe the substitution possibilities for all pairs of inputs for an unregulated firm.(1) The subscripts on c(y,w) indicate partial differentiation with respect to the indicated input price(s), and [[Epsilon].sub.ji](y,w) and [[Epsilon].sub.ii](y,w) are the cross-price and own-price elasticities of input demand, respectively. The variable [MES.sub.ij](y,w) describes how the quantity of input j changes (the substitution of input j for input i) in response to a change in the price of input i. It should be clear from Equation 2 that [MES.sub.ij](y,w) and [MES.sub.ji](y,w) are not in general symmetric.(2)

Suppose that the firm faces the inverse product demand function p(y) and that rate-of-return regulation is applied to the input subvector [x.sub.c]. The regulatory constraint is

[Mathematical Expression Omitted], (3)

where [[Theta].sub.c] is the allowed user cost of capital.(3) The firm's regulated cost function is

[Mathematical Expression Omitted]. (4)

Fare and Logan (1983a) showed that [c.sup.r](y,w,p, [[Theta].sub.c]) satisfies the properties (i) [c.sup.r](y, [Lambda]w, [Lambda]p, [[Theta].sub.c]) = [Lambda][c.sup.r](y, w, p, [[Theta].sub.c]), [Lambda] [greater than] 0, and (ii) [min.sub.[Theta]c][c.sup.r](y, w, p. [[Theta].sub.c]) = c(y, w). The first property states that [c.sup.r](y, w, p, [[Theta].sub.C}) is homogeneous of degree + 1 in (w,p); unlike c(y,w), [c.sup.r](y,w,p, [[Theta].sub.c]) is not homogeneous of degree + 1 in w alone. The second property states that there exists a value of [[Theta].sub.c] (call it [Mathematical Expression Omitted]) sufficient to cause [c.sup.r](y,w, p, [[Theta].sub.c]) to coincide with c(y,w). At [Mathematical Expression Omitted] the rate-of-return constraint becomes nonbinding. Fare and Logan (1983b) also showed that [c.sup.r](y,w,p, [[Theta].sub.c]) is not necessarily concave in w.

Blackorby and Russell (1990) derived MES for a regulated firm. In our notation the regulated MES can be written as

[Mathematical Expression Omitted], (5)

[Mathematical Expression Omitted], (6)

respectively.

For pairs of non-rate-base inputs and also for pairs of rate base inputs, [MES.sub.ij] (y,w) and [Mathematical Expression Omitted] have the same structure. It is difficult to compare them, however, because (i) although they involve the same partial derivatives, they are derivatives of different cost functions and (ii) the cost functions have different properties. For a rate base input and a non-rate-base input, [Mathematical Expression Omitted] takes on a different structure than that of [MES.sub.ij](y,w), making a comparison in this case even more difficult. Nevertheless, it is possible to speculate.

Consider [MES.sub.ij](y,w) and [Mathematical Expression Omitted] for non-rate-base inputs i and j. We know that [c.sub.i](y,w) [greater than] 0 and that [Mathematical Expression Omitted]; that is, an increase in the price of a non-rate-base input raises both unregulated and regulated cost. Since c(y,w) is concave in w, [c.sub.ii](y,w) [less than or equal to] 0. Since [c.sup.r](y,w,p, [[Theta].sub.c]) is not necessarily concave in w, there is a possibility that [Mathematical Expression Omitted] and an even greater possibility that [Mathematical Expression Omitted]. Comparing the second terms in Equations 2 and 5, the latter possibility leads to the conjecture that [Mathematical Expression Omitted]. We are thus led to hypothesize that regulation reduces the willingness of firms to substitute between pairs of non-rate-base inputs. Since there is no analytical difference between the structures of Equations 2 and 5 for pairs of non-rate-base inputs and pairs of rate base inputs, we also conjecture that regulation reduces the willingness of firms to substitute between pairs of rate base inputs.

Next consider [MES.sub.ij](y,w) and [Mathematical Expression Omitted] for non-rate-base input i and rate base input j. Now we focus on the terms [Mathematical Expression Omitted] and [Mathematical Expression Omitted] in Equation 6. We know from Baumol and Klevorick (1970) and Petersen (1975) that [Mathematical Expression Omitted]; that is, tightening the regulatory constraint induces the firm to adopt an allocatively inefficient input mix, which raises the cost of producing its chosen rate of output. We also know from the same sources the direction of the misallocation: a reduction in the use of non-rate-base inputs relative to rate base inputs. Although [Mathematical Expression Omitted] is not the demand for non-rate-base input i and [Mathematical Expression Omitted] is not the demand for rate base input j, the two expressions are positively related to the respective demands. This leads us to conjecture that [Mathematical Expression Omitted] and that [Mathematical Expression Omitted]; that is, tightening the regulatory constraint induces the firm to reduce its use of (at least some) non-rate-base inputs and to increase its use of rate base inputs. In addition, the impact of the second term is lessened if, as we hypothesized above, [Mathematical Expression Omitted]. Consequently, we are led to conjecture that regulation leads to an increase in the willingness of firms to substitute (at least some) rate base inputs for non-rate-base inputs when prices of non-rate-base inputs increase.

Finally, consider [MES.sub.ji](y,w) and [Mathematical Expression Omitted] for rate base input j and non-rate-base input i. We noted above that [Mathematical Expression Omitted], and we conjectured above that [Mathematical Expression Omitted]. Consequently, both the numerator and the denominator of the second term in Equation 6 are reduced. However, if [Mathematical Expression Omitted], we are led to conjecture that regulation leads to a reduction in the willingness of firms to substitute non-rate-base inputs for rate base inputs when the prices of rate base inputs increase.

Summarizing, we conjecture that rate-of-return regulation is likely to reduce the willingness to substitute (i) between pairs of non-rate-base inputs, (ii) between pairs of rate base inputs, and (iii) a non-rate-base input for a rate base input when the price of the rate base input increases. Rate-of-return regulation is likely to enhance the willingness to substitute a rate base input for a non-rate-base input when the price of the non-rate-base input changes. If these conjectures are correct, then the first three effects reinforce the fixed-price impact of regulation on operating cost, whereas the fourth effect dampens the impact of regulation on operating cost. However, these conjectures are based on very limited theoretical guidance, and so, in the following section, we develop an empirical model capable of testing them.

3. The Empirical Model

We estimate a transcendental logarithmic (translog) cost function, as developed by Christensen, Jorgenson, and Lau (1971). The translog cost function places no a priori restrictions on returns to scale or substitution elasticities. Let [[Theta].sub.c] = ([[Theta].sub.pc],[[Theta].sub.cc]) denote a vector of the allowed user costs of transmission pipeline capital ([[Theta].sub.pc]) and compressor station capital ([[Theta].sub.cc]). Following Nelson and Wohar (1983) and Fare and Logan (1986), the translog regulated cost function is

In [c.sup.r](y, W, p, [[Theta].sub.c]

[Mathematical Expression Omitted], (7)

where i,j = {l,f,p,c} denote labor, fuel, transmission pipeline capital, and compressor station capital inputs, respectively.(4) Input cost share equations for the non-rate-base inputs and the rate base inputs are(5)

[Mathematical Expression Omitted] (8)

and

[Mathematical Expression Omitted], (9)

where

[Mathematical Expression Omitted]

and

[Mathematical Expression Omitted].

Although the regulated cost function is not homogeneous of degree + 1 in input prices, the unregulated cost function derived from it satisfies all the properties of a minimum cost function. To impose linear homogeneity in input prices on the unregulated cost function,(6) we first derive the functional form of the unregulated cost function by minimizing the regulated cost function with respect to [[Theta].sub.c]. At [Mathematical Expression Omitted]. Note that

[Mathematical Expression Omitted]. (10)

Setting [[Nabla].sub.[[Theta].sub.c]] ln [c.sup.r](y, w, p, [[Theta].sub.c]) = 0 and solving for [Mathematical Expression Omitted] yields

[Mathematical Expression Omitted], (11)

where d = [[Alpha].sub.pp] + [[Pi].sub.cc]. Substituting [Mathematical Expression Omitted] for [[Theta].sub.c] into Equation 7 gives the unregulated cost function ln c(y, w)

[Mathematical Expression Omitted], (12)

from which we obtain the parameter restrictions implied by linear homogeneity in input prices (of the unregulated cost function).

4. The Natural Gas Pipeline Data

The data sample consists of 20 major interstate natural gas pipeline companies over an 11-year period from 1977 to 1987.(7) The sample covers more than 75% of total output of the major pipeline companies. The primary inputs for pipelines are fuel, labor, compressor station capital, and transmission pipeline capital. Total expenditures on fuel and labor are divided by the physical quantity of each input to obtain the prices of fuel and labor.(8) The quantity of compressor station capital is measured as the sum of the horsepower ratings of all compressor stations on the transmission pipeline. The quantity of transmission pipeline capital, measured as tons of line pipe on the transmission pipeline, is derived from the engineering relationship between the diameter and volume of steel in a pipeline. Callen (1978) showed that for a pipeline of length m and average diameter d, the quantity of pipeline capital is 0.382 [d.sup.2]m.

Following Jorgenson (1963), the user cost of capital and the allowed cost of capital are

[w.sub.c] [equivalent to] ((1 - k - [Tau]z) [multiplied by] (r + [[Delta].sub.c] + [m.sub.c] + [o.sub.c]))/(1 - [Tau]),

[[Theta].sub.c] [equivalent to] ((1 - k - [Tau]z) [multiplied by] (s + [[Delta].sub.c] + [m.sub.c] + [o.sub.c]))/(1 - [Tau]),

respectively, where k is the investment tax credit, [Tau] is the corporate tax rate, [[Delta].sub.c] is the rate of depreciation of capital, [m.sub.c] is a component for operation and maintenance, [o.sub.c] is a component for overhead, r is the financial cost of capital, s is the allowed rate of return, and z is the present value of depreciation allowances for tax purposes on a dollar's investment over the lifetime of the asset.

The output measure we use is the volume of compressor station fuel.(9) With this output measure the underlying production function has a Leontief form

y = f(x) = min(g([x.sub.nf]),f/e),

where [x.sub.nf] are the nonfuel inputs, g is a quasi-concave function, f is the volume of fuel, and e [greater than] 0 is a proportionality factor. A regulated firm selects the amount of fuel for which f/e = y and the amount of nonfuel inputs to minimize its expenditures subject to y = g([x.sub.nf]) and the regulatory constraint. Since the quantity of the fuel input is proportional to the level of output, the share of fuel in total cost does not vary with time, the allowed user cost of capital, or input prices. The system of equations to be estimated consists of a cost equation and input cost share equations for the three nonfuel inputs.

Since the input cost shares for the nonfuel inputs sum to one, in estimating the system we delete the labor cost share equation. Since the quantity of the fuel input is proportional to the level of output, neither labor nor capital can be substituted for fuel. We can only compute the [TABULAR DATA FOR TABLE 1 OMITTED] MES between (i) labor and each type of capital, (ii) each type of capital and labor, and (iii) each type of capital.

5. Empirical Analysis

Estimation

We estimate a random-effects model with a two-component error structure for each equation in the system.(10) The error structure of the disturbance term for each equation has a firm-specific and a purely random component. The firm-specific component reflects unmeasured persistent effects (e.g., terrain and management skill). The firm-specific components are assumed to be correlated across equations for each firm but not across firms. The purely random components are assumed to be correlated across equations for each firm but not across firms. The firm-specific and purely random components are assumed to be uncorrelated across equations and across firms.(11) We estimate the system using nonlinear least squares because the homogeneity restrictions on the unregulated cost function imply nonlinear restrictions on the parameters of the regulated cost function.

Table 1 provides a list of the variables used in the regression as well as the mean and the standard deviation of the variables in the model. Table 2 provides the parameter estimates that [TABULAR DATA FOR TABLE 2 OMITTED] were used to compute the unregulated and the regulated MES, and Table 3 provides estimates of the unregulated and the regulated MES averaged over the entire sample.(12)

Regulated and Unregulated Cost Functions

We check whether our estimates of the unregulated and regulated cost functions satisfy the properties of monotonicity in input prices and output and, for the unregulated cost function, concavity in input prices. The estimated unregulated cost function satisfies monotonicity in input prices and output in all 220 observations and satisfies concavity in input prices in 190 of the 220 observations. The estimated regulated cost function satisfies monotonicity in output in 215 of the 220 observations, and monotonicity in input prices in 143 of the 220 observations.

We use the parameter estimates reported in Table 2 to test two hypotheses regarding regulation. The first test is whether rate-of-return regulation has affected transmission cost. If regulation has had no effect on transmission cost, then (i) the regulated and the unregulated cost functions coincide and (ii) the regulated and the unregulated MES coincide. We perform a likelihood ratio test of the following hypothesis:

[[Alpha].sub.p] = [[Alpha].sub.pp] = [[Alpha].sub.py] = [[Alpha].sub.pt] = [[Alpha].sub.pf] = [[Alpha].sub.p1] = [[Phi].sub.c] = [[Phi].sub.cc] = [[Phi].sub.cy] = [[Phi].sub.ct] = [[Phi].sub.cf] = [[Phi].sub.c1] = 0. (13)

Table 3. Morishima Elasticities of Substitution

 Labor Pipeline Compressor

Unregulated [MES.sub.ij]

Labor 0.3656 0.3665
 (0.1592)(*) (0.1972)
Pipeline 0.2481 0.5384
 (0.1810) (0.1750)(*)
Compressor 0.3218 0.5929
 (0.1532)(*) (0.1723)(*)

Regulated [MES.sub.ij]

Labor 0.4702 0.6501
 (0.3685) (0.3781)
Pipeline 0.2223 0.5139
 (0.2859) (0.1106)(*)
Compressor 0.2747 0.5675
 (0.2679) (0.1091)(*)

Entries in the rows and columns denote the ith and the jth inputs,
respectively. Standard errors in parentheses.

* Significant at the 5% level.

With a chi-square test statistic of 76.77, the hypothesis that regulation has had no effect on transmission cost is rejected at the 1% level. We computed the total costs for the regulated and unregulated cost functions at every observation in the sample to obtain estimates of the extent to which regulation has affected transmission costs. On average for our sample, a regulated firm produced its output level at a cost 16% higher than the minimum cost at which the firm could have produced its output in the absence of regulation.(13)

The second test is whether increasing the allowed rate of return lowers transmission cost. If increasing the allowed rate of return lowers transmission cost, then [Mathematical Expression Omitted], which would be consistent with economic theory (this test is similar to testing whether the regulatory constraint is binding over the sample period). Using Equation 10, note that

[[Nabla].sub.[Theta]c][c.sup.r](y,w,p,[[Theta].sub.c]) = [c.sup.r](y,w,p,[[Theta].sub.c]) [multiplied by] [[Nabla].sub.[Theta]c]) [lnc.sup.r](y,w,p,[[Theta].sub.c])

and that [[Nabla].sub.[Theta]c](y,w,p,[[Theta].sub.c] [less than] 0 if and only if [[Nabla].sub.[Theta]c] [lnc.sup.r](y,w,p,[[Theta].sub.c] [less than] 0. The functional form for the hypothesis [[Nabla].sub.[Theta]c] [lnc.sup.r](y,w,p,[[Theta].sub.c]) [less than] 0 is

[Mathematical Expression Omitted]. (14)

For our sample, the derivative is negative and significantly different from zero at the 5% level for 111 of the 220 observations.(14) For the remaining observations, the derivative is not significantly different from zero, with 42 observations positive and 67 observations negative. Almost all the observations for which the derivative is not negative and significantly different from zero are in the early years of our sample (1977-80).

One reason that the regulatory constraint on natural gas pipelines was not binding during the late 1970s could be the changes in the natural gas market during the period. Gas shortages in interstate markets developed in the 1970s as the market price of oil increased while the federally regulated well head price of natural gas remained virtually unchanged. The Natural Gas Policy Act was passed in 1978 to gradually deregulate the well head price of natural gas. At the same time the market price of oil increased, leading to an increase in the demand for natural gas. The FERC may have been more occupied with the consequences of the natural gas shortages and the process of natural gas deregulation than with the regulation of gas pipeline transmission fees until 1980 or 1981, when the crisis of a gas shortage had passed.

Regulated and Unregulated Morishima Elasticities of Substitution

The results reported in Table 3 indicate that all unregulated and regulated MES are positive and less than unity, most of them significantly so. Unregulated substitution possibilities are limited, and regulated substitution propensities are not much different. Turning to our conjectures, we find that regulation has led to a reduction in the willingness to substitute between the two capital inputs, as we conjectured in section 2. However, these reductions are small (5% in the case of pipeline capital for compressor station capital and 4% in the case of compressor station capital for pipeline capital), and they are not statistically significant. A possible explanation for the small difference in the willingness to substitute could come from the regulatory constraint (Eq. 3), which can be rewritten as

f(x) [multiplied by] p[f(x)] - [w.sup.T]x [less than or equal to] ([[Theta].sub.c] - [w.sub.c])[x.sub.c].

An increase in [w.sub.c] reduces the actual profit a firm earns (f(x) [multiplied by] p[f(x)] - [w.sup.T]x) and the allowable profit the regulated firm can earn ([[Theta].sub.c] - [w.sub.c])[x.sub.c] and in essence tightens the regulatory constraint. Substituting noncapital for capital instead of one type of capital for another would reduce allowable profit even further (by reducing [x.sub.c]), in essence tightening the regulatory constraint even more. The regulated firm would thus have an incentive to substitute one type of capital for another, which would suggest that regulation has had a small impact on the willingness to substitute between the capital inputs. This effect is difficult to identify, however, because the prices of the two capital inputs changed similarly during the period.(15)

Regulation has led to a somewhat larger reduction in the willingness to substitute labor for of each type of capital when the prices of capital rise, as conjectured: 10% (0.2481 to 0.2223) in the case of pipeline capital and 15% (0.3218 to 0.2747) in the case of compressor station capital, although neither reduction is statistically significant. The suggestion from the previous paragraph could be used to explain this result. When [w.sub.c] rises, regulated firms have an incentive to substitute capital for capital rather than tighten the regulatory constraint even further by substituting labor for capital. This would suggest that regulation leads to a reduction in the willingness to substitute noncapital for capital inputs when [w.sub.c] changes.

Finally, regulation has led to an increase in the willingness to substitute each type of capital for labor when the price of labor rises, as conjectured. These increases are relatively large: 29% (0.3656 to 0.4702) for pipeline capital and 77% (0.3665 to 0.6501) for compressor station capital. However, once again they are not statistically significant. Referring back to the regulatory constraint (Eq. 3), an increase in [w.sub.n] reduces regulated firms' profits but not their allowable profits ([[Theta].sub.c][x.sub.c]). Substituting capital for labor instead of one type of noncapital for another would increase allowable profits (by increasing [x.sub.c]), in essence relaxing the regulatory constraint and enhancing the incentive of regulated firms to substitute capital for noncapital when [w.sub.n] rises. This would suggest that regulation has had a large impact on the willingness to substitute capital for labor in response to the 10% annual increase in the price of labor that has occurred in this industry.(16)

6. Conclusions

We began this paper with a set of four conjectures concerning the directions of the impacts of rate of return regulation on input substitutability. Although theory does not provide signs for these impacts, it does provide guidance. This guidance enabled us to predict that regulation leads to a reduction in the willingness to substitute between pairs of non-rate-base inputs and between pairs of rate base inputs and of non-rate-base inputs for rate base inputs but to an increase in the willingness to substitute rate base inputs for non-rate-base inputs. Each conjecture was based on Morishima elasticities of substitution.

We tested our conjectures using a 1977-87 panel of 20 U.S. interstate natural gas pipeline companies that use labor, pipeline capital, and compressor station capital to distribute natural gas (proxied by fuel consumption) to their customers. Results are supportive of our conjectures. It appears that rate-of-return regulation has restricted the willingness to substitute between pipeline capital and compressor station capital and restricted the willingness to substitute labor for both types of capital. However, regulation has enhanced the willingness to substitute both types of capital for labor. The first effect was probably unimportant since the two capital prices varied together during the entire period. The second effect was significant during the early part of the time period, when both capital prices increased by over 20% per annum. The third effect was significant during the latter part of the time period, when the labor price increased by 10% per annum and both capital prices were falling by about 5% per annum.

Finally, we estimated that the distorting impact of regulation led to an increase in operating cost of 16% on average.(17) In dollar terms, in 1977 for example, a 16% increase in cost amounts to $265 million for the 20 firms combined. Since regulation restricted the willingness to substitute labor for capital and enhanced the willingness to substitute capital for labor, we conjecture that the 16% average cost increase was substantially higher than it would have been had input prices not varied so much. At least in this industry, the secondary substitution effects of regulation appear to have reinforced the initial fixed-price consequences of regulation.

We are grateful to Karen Bauer, Philip Budzik, Ronald Colter and Mary Streitwieser for their assistance in compiling the data sample, to Gary Biglaiser, David Guilkey, John Stewart and Helen Tauchen for their suggestions, and to the Editor and two referees for their helpful comments.

1 Blackorby and Russell (1981) showed that the MES can also be derived from the input distance function, which is dual to the cost function.

2 The MES are symmetric only if (i) there are only two inputs or (ii) the MES are constant. By contrast, the Allen-Uzawa elasticities of substitution are symmetric in all cases and can be written as

[AUES.sub.ij](y,w) = [[Epsilon].sub.ij](y,w)/[S.sub.j](y,w) = [[Epsilon].sub.ji](y,w)/[S.sub.i](y,w) = [AUES.sub.ji](y,w)

where [S.sub.i](y,w) and [S.sub.j](y,w) denote the expenditure shares of inputs i and j in total cost, respectively.

3 The rate of return to capital is the firm's earnings net of the noncapital expenditures and allowed expenditures on capital divided by the value of the capital stock. Regulators set the allowed rate of return s that the firm can earn on capital, with the allowed rate of return s assumed to exceed the financial cost of capital r. Once the regulators determine the allowed rate of return and the allowed expenditures on capital, they in essence determine an allowed user cost of capital [[Theta].sub.c], with [[Theta].sub.c] assumed to exceed [w.sub.c]. In essence, the difference between [[Theta].sub.c] and [w.sub.c] is s - r.

4 The output price, set to allow the firm to earn the allowed rate of return on the rate base, does not appear in the estimated regulated cost function because the regulatory agency determines the output price. The firm observes only a point on the demand curve, not the entire demand curve (the output price may not change when demand conditions change).

5 A detailed description of the derivation of the input share equations is available on request.

6 We do not impose the parameter restrictions implied by homogeneity of the regulated cost function in output and input prices because the output price does not appear in the regulated cost function.

7 For the time period of our sample, a major pipeline company is defined as one that transported more than 50 billion cubic feet in each of the three previous years (or in the case of a new firm on the projected volume for the next three years). The primary reason the data sample stops in 1987 is because a large portion of the data on pipeline companies was available only for that time period. The last year for which data could be obtained to compute the financial cost of capital by firm was 1987.

8 Over the period 1977-87, expenditures on natural gas for compressor station fuel accounted for 93.25% of total expenditures on compressor station fuel by all the major pipeline companies. For the companies in the sample, expenditures on natural gas for compressor station fuel accounted for 85.16% of total expenditures on compressor station fuel.

9 The ideal output measure for natural gas transmission is the sum across all shipments of the volume times the distance transported. The FERC does not require firms to report this information for all types of shipments. A more detailed description of the variables and the data sources is contained in the appendix.

10 We estimated a random-effects model instead of a fixed-effects model for the following reasons. First, the random-effects model provided a more accurate description of the production technology (more plausible estimates of scale economies) and thus a more accurate description of the elasticities of substitution. Second, estimating the fixed-effects model would significantly reduce the degrees of freedom on the model, making it difficult to consistently estimate the fixed-effects model (there would be 55 parameters to estimate using 220 observations).

11 For detailed explanations on the derivation and decomposition of the inverse covariance matrix of the error terms, see Baltagi (1980) and Prucha (1984).

12 The following pairs of variables are not interacted in order to lessen the effects of multicollinearity: [[Theta].sub.pc] with [[Theta].sub.cc], [[Theta].sub.pc] with [w.sub.cc], and [[Theta].sub.cc] with [w.sub.cc], where [w.sub.pc] and [w.sub.pc] are the user costs of compressor capital and pipeline capital, respectively. The output price p does not appear on the right side of Equation 7 because the regulated firm does not observe the entire market demand curve for output. The regulated firm observes only the output price determined by the regulators (a point on the market demand curve) that enable the firm to earn the allowed rate of return s on capital.

13 The percentage by which cost increases due to regulation decreases from 54.8% in 1977 to 7.1% in 1979 and 2.91% in 1982, then increases to 8.5% in 1984 to 38.7% in 1987. In the absence of regulation, Mississippi River would experience the smallest percentage reduction in cost (3.27%), whereas Trunkline would experience the largest percentage reduction in cost (44.14%).

14 We could also test whether the estimated direction of the effect of regulation is consistent with economic theory by computing the Lagrange multiplier on the regulatory constraint. If rate-of-return regulation is binding, then the Lagrange multiplier, [[Lambda].sub.2], should be between zero and one. For the translog cost function, the multiplier is

[[Lambda].sub.2] = -([c.sup.r]/[x.sub.c]) [[Nabla].sub.[Theta]c][lnc.sup.r](y,w,p,[[Theta].sub.c]).

The multiplier [[Lambda].sub.2] is between zero and one and significantly different from zero for the 111 observations for which the derivative [[Nabla].sub.[Theta]c][lnc.sup.r](y,w,p,[[Theta].sub.c]) is negative and significantly different from zero. The observations for which [[Lambda].sub.2] is not significantly different from zero are the same observations for which the derivative [[Nabla].sub.[Theta]c][lnc.sup.r](y,w,p,[[Theta].sub.c]) is not significantly different from zero.

15 Mean prices of transmission pipeline capital and compressor station capital increased by 20.7% and 22.7% per annum during 1977-81, then declined by 4.8% and 5.0% per annum during 1981-87, respectively. The mean price of labor increased by 9.4% per annum during 1977-81 and by 10.0% per annum during 1981-87.

16 We computed and listed the regulated and unregulated Allen-Uzawa elasticities of substitution in Appendix Table 1 to determine whether our conjectures about the impacts of regulation on the elasticities of substitution apply to the Allen-Uzawa elasticities. The results indicate that regulation leads to a 7% reduction in the willingness to substitute between the capital inputs and a 12% reduction (0.8984 to 0.7950) in the willingness to substitute labor for pipeline capital. Regulation leads to a 67% increase (0.5011 to 0.8378) in the willingness to substitute labor for compressor station capital. Note that the Allen-Uwaza elasticities are symmetric, whereas the Morishima elasticities of substitution are asymmetric.

17 This estimate of 16% is similar to Courville's (1974) estimate of an 11.4% increase in the cost of electric power generation due to regulation.

18 Over the period 1977-87, expenditures on natural gas for compressor station fuel accounted for 93.25% of total expenditures on compressor station fuel for all the major pipeline companies. For the companies in the sample, expenditures on natural gas for compressor station fuel accounted for 85.16% of total expenditures on compressor station fuel.

19 Data on the horsepower ratings of compressor stations and the diameter of pipelines after 1980 come from the Cost of Pipeline and Compressor Station Construction under Non-Budget Certificate Authorization (U.S. Department of Energy, various years) and the Cost of Pipeline and Compressor Station Construction under Natural Gas Act Section (7c) (U.S. Department of Energy, various years).

Appendix

The data sample consists of 20 major interstate natural gas pipeline companies over an 11-year period from 1977 to 1987. All data, unless otherwise indicated, come from Statistics of Interstate Natural Gas Pipeline Companies (U.S. Department of Energy 1977-1987). The primary inputs for pipelines are labor, fuel, compressor station capital, and pipeline capital. Total expenditures on fuel and labor are divided by the physical quantity of each input to obtain the prices of fuel and labor.(18) The quantity of compressor station capital is measured as the sum of the horsepower ratings of all compressor stations on the transmission pipeline. Callen (1978) showed that for a pipeline of length m and average diameter d, the quantity of pipeline capital is .382 [d.sup.2]m.(19)

Following Jorgenson (1963), the user cost of capital and the allowed user cost of capital are

[w.sub.c] [equivalent to] ((1 - k - [Tau]z) [multiplied by] (r + [[Delta].sub.c] + [m.sub.c] + [o.sub.c]))/(1 - [Tau])

[[Theta].sub.c] [equivalent to] ((1 - k - [Tau]z) [multiplied by] (s + [[Delta].sub.c] + [m.sub.c] + [o.sub.c]))/(1 - [Tau]),

where k is the investment tax credit, [Tau] is the corporate tax rate, [[Delta].sub.c], is the rate of depreciation of capital, [m.sub.c] is a component for operation and maintenance, [o.sub.c] is a component for overhead, r is the financial cost of capital, s is the allowed rate of return, and z is the present value of depreciation allowances for tax purposes on a dollar's investment over the lifetime of the asset. Data on the investment tax credit and the corporate tax rate come from the U.S. Masters Tax Guide (Commerce Clearing House, various years). We follow the method of Hazilla and Kopp (1986) in computing z. The allowed rate of return for each firm comes from the National Association of Regulatory Utility Commissioners (1973-1988) and the Capitalization-Rate of Return Report, a company report (Texas Eastern Transmission Corporation 1991).

The financial cost of capital is a weighted average of the after-tax cost of debt capital ([r.sub.b]) and the cost of equity capital ([r.sub.e]), where the weights are the fraction of the rate base financed by debt and equity capital, respectively. Statistics on interest payments and the dollar amount of the rate base financed by debt and equity capital come from the Financial Performance of U.S. Interstate Pipeline Companies (Natural Gas Supply Association 1989). The cost of equity capital, computed using the capital asset pricing model, is

E([r.sub.e]) = [r.sub.f] + [Beta](E([r.sub.p]) - [r.sub.f]),

where [r.sub.f] is the expected return on a risk free asset, E([r.sub.p]) is the expected return on a market portfolio, and [Beta] is a firm's beta coefficient. The risk-free rate and the risk premium (E([r.sub.p]) - [r.sub.f]) for every year come from the annual Federal Reserve Bulletin and Ibbotson and Sinquefield (1989). Beta coefficients for each firm by year come from the Value Line Investment Survey (Value Line Publishing 1977-1987).

The compute [m.sub.c], transmission labor and compressor station fuel expenses are subtracted from the total operation and maintenance expenses of the transmission plant. The remaining operation and maintenance expenses are for compressor station capital, pipeline capital, and measuring and regulating stations. These remaining operation and maintenance expenses are allocated to capital by the total value of the capital stock to obtain [m.sub.c]. To compute [o.sub.c], overhead expenses are defined as the sum of expenses for the following accounts: customer, clearing, customer service and information, sales, and administrative and general. Wages and salaries, along with pensions and benefits, are netted out from overhead expenses to obtain nonlabor overhead expenses. Nonlabor overhead expenses are multiplied by the ratio of the value of the transmission plant to the value of the total plant in order to allocate a portion of the expenses to the transmission plant. Nonlabor overhead transmission expenses are then multiplied by the ratio of expenditures on capital to the value of the transmission plant to obtain [o.sub.c].

The ideal output measure for natural gas transmission is the sum across all shipments of the volume times the distance transported. The FERC does not require firms to report this information for all types of shipments. Published records from FERC include the amount of gas transported but not the distance transported. Pipeline maps show the complete and complex layout of most systems as well as receiving and delivery points, but there is no supplementary information available on the total volume of gas received or sold at each point. The output measure that we use, the volume of compressor station fuel, is based on the technology of transporting natural gas. The amount of compressor station fuel required to produce output y is directly related to the amount of gas transported and the distance transported.

Table A1. Allen-Uwaza Elasticities of Substitution

 Labor Pipeline Compressor

Unregulated

Labor 0.8984 0.5011
Pipeline 0.8984 1.0405
Compressor 0.5011 1.0405

Regulated

Labor a a
Pipeline 0.7950 0.9468
Compressor 0.8378 0.9648

a According to Smith (1981), comparative static properties of the
regulated cost function imply that these elasticities are zero.

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