The Determination of the allowed rate of return in a formal regulatory hearing by Paul L. Joskow

1. The Determination of the allowed rate of return in a formal regulatory hearingbyPaul L. Joskow Presented by: UgonnaNwaokwu

2. Introduction • This paper develops a simple model of the rate of return phase of a formal regulatory hearing in an effort to determine what factors affect the rate of return set by the regulatory authority. • The model presented is based in part on the author's case study of the regulation of the gas and electric industries in New York by the New York State Public Service Commission.

3. The model of the rate of return phase • The first equation is a commission decision equation, representing the allowed rate of return determination of the commission. The second equation is a firm request equation representing the request made by a firm in a given proceeding. • In making its decision, the commission must attempt to set a rate of return that is not "so low" that the firm cannot perform its service function adequately (or even remain in business) and not "so high" that the firm is being allowed earnings above the amount needed to enable it to maintain the desired level of service quality.

4. The commission decision equation • The commission arrives at its conclusion about the fair rate of return by examining the presentation of the parties, applying its own judgment concerning their relative merits, and possibly making certain adjustments because of the performance characteristics of the particular firm. Equation (1) represents this relationship: ,, J,E,) ………….. (1) where = random disturbance term, = allowed rate of return, = presentation of firm in the hearing, = presentation of intervenors, J = judgment of the commission, and E = performance characteristics of the firm: subjective judgment on the part of the commission concerning the efficiency of the particular firm (the commission may want to reward firms that performed well).

5. In specifying the commission decision equation the explanatory variables will be represented in the following way. : The presentation of the firm is represented by two variables = the allowed rate of return requested by the firm. This variable embodies the firm's assessment of its cost of capital . T = a dummy variable that equals unity if the firm presents testimony on the cost of equity capital and zero if it does not.

6. . • I : Takes on the value zero when there is no intervenor presenting rate of return testimony and it equals (1 - /) otherwise. The lower the value of the intervenor rate of return () relative to the requested rate of return of the firm, the higher the value of this variable, and vice versa. This variable will always lie between zero and one.

7. J : The judgment of the commission. It is difficult to quantify the judgment of the commission concerning the reasonableness of the firm's presentation. Two variables are included here to represent the judgment of the commission. • GED : A dummy variable, equal to one for gas rate cases and zero for electric cases, is used to investigate whether or not gas cases are treated differently from electric rate cases. • : The positive residuals calculated from the firm request equation (2) (which will be discussed presently) will be included. Equation (2) can be viewed as tracing out the average relationship between capital costs, company characteristics, and firm requests. Firms that stray above this average may be characterized as being relatively aggressive, trying to get more than the "typical" firm would request ceteris paribus. This variable is included to reflect not only the fact that the commission is concerned with which party made the rate of return recommendation (firm or intervenor) but also that it has some rudimentary notion of the appropriate relationship between observable capital costs and "reasonable" rate of return request. • E : The performance potential is also very difficult to measure. It seems that those companies the commission views as efficient tend to avoid the formal hearing process. As a result, there are not many observations on these companies. A dummy variable (E) that equals unity when the commission has commended a company for its efficiency or high quality of service and that equals zero otherwise was used to indicate the appearance of these firms.

8. In summary, the following variables are included in the com- mission decision equation: =rate of return allowed by commission, =rate of return requested by company, T = dummy variable representing presence of cost of equity testimony, I = variable representing the presence or absence of an intervenor and the degree of conflict between intervenor and firm where there is an intervenor presenting rate of return testimony, GED : dummy variable (gas = 1, electric = 0), = positive residuals calculated from equation (2), and E = dummy variable (efficient firms = 1, otherwise = 0).

9. A simple linear functional form has been chosen for estimation on the available data : =+++++++..(1)

10. The firm request equation • The request of the firm is based on a cost of capital study that it presents and adjustments that it makes in the cost of capital calculation to take account of certain characteristics of the firm or the department of the firm involved in the hearing: = (,,, ) …………(2) where = imbedded cost of debt, = firm's estimate of the cost of equity capital, = relevant adjustments for particular characteristics of the firm (gas department, outside ownership, etc.), and = random disturbance term. Equation (2) represents the "average" request firms make. Variable is for all intents and purposes, already determined and is not a center of controversy.

11. One problem remains in specifying this equation for estimation. The firm's assessment of the cost of equity that we observe already includes, in many cases, these adjustments for firm characteristics. The firm request then reduces to a simple identity: =α + β where αand βare the proportions of debt and equity in the firm's capital structure, is the imbedded cost of debt, and is the estimated cost of equity capital adjusted for these risk characteristics. The request equation (2) would then be the following in linear form: = + + + +

12. Data on the firm's overall calculated cost of equity are not available in general from the proceedings and it is treated as an omitted variable in this analysis where the omitted variable is assumed to be uncorrelated with the variables remaining. The request equation to be estimated is therefore based on observable debt costs, and specified in linear form it becomes: = + + + + ….(2) = the imbedded cost of debt, = dummy variable taking on the value unity when the request is from a firm that is a gas department of a of a combination company and zero otherwise, and OOD = dummy variable taking on the value unity when the request is from a company without its own capital structure and zero otherwise.

13. Equations (1) and (2) make up the behavioral model of the rate of return phase. This model is a two-equation recursive system: =+++++++..(1) = + + + + ….(2)

14. A priori discussion of the coefficients • : coefficient should be positive. The requested rate of return should be positively associated with the cost of debt. • () : coefficient should be positive. It reflects the risk premium gas departments of combination companies give to themselves. • (OOD) : coefficient should be negative. If the cost of capital testimony based on the capital structure of a more risky parent company is to be considered at all by the commission, the firm must request a lower rate of return than would be indicated by the cost of capital calculation.

15. Signs and magnitudes for the coefficients of the linear commission decision equation (1) • () : The coefficient < 1 implies that the commission increases the allowed rate of return by less than the increase in the company's request. We would expect to be between zero and unity, since we do not expect the commission to allow the full amount of a firm's incremental request: 0 < < 1 • (T): The sign of this coefficient should be positive, since the cost of capital testimony represents more evidence in support of the company request and be- cause some commissioners have expressed their desire for such testimony . • (I) : The sign of this coefficient should be negative. Intervention should lower the allowed rate of return. If it does not, many people have been wasting time and money . • (GED) : The sign of this coefficient should be negative, reflecting the commission's attitude that the rates of return requested by gas companies have been unreasonably increased due to inclusion of an erroneous risk premium. • () : The sign of this coefficient should be negative. Firms that make requests that are relatively "aggressive" should have their requests cut more than firms on or below this boundary . • (E) : The sign of this coefficient should be positive if the commission gives higher rates of return to companies with good records and should be zero if it treats these companies as it does all others.

16. Data • The data come from twenty rate cases involving major gas or electric companies decided by the New York State Public Service Commission during the period 1960-1970.

17. Empirical results • Both equations of the model were fitted by ordinary least squares. The results for equation (2) are reported first: • The estimated coefficients all have the expected signs and all except are significant at the 5-percent level. The coefficients and indicate the adjustments gas departments of combination companies and gas companies with outside capital structures make relative to their calculated historic cost of debt. • The estimates indicate that, ceteris paribus, an increase of one percentage point in the imbedded cost of debt will lead to an increase of 0.64 percentage points in the firm's request. Gas departments of combination companies will tend to add a premium of 0.44 percentage points to their requests. Firms with outside capital structures will tend to discount their request by 0.33 percentage points relative to other types of firms with the same calculated cost of capital

18. All coefficients have the expected sign and all of them except the coefficient of the efficiency variable (E) are significant at the 5-percent level. The coefficient is greater than unity and is highly significant, while the constant term is negative although only significant at the 10-percent level.

19. Conclusion • The model of the rate of return phase presented indicates that although capital costs are a signficant basic component of the allowed rate of return, exactly what the commission will allow is determined by the size and relative reasonableness of the firm's request, the presence or absence of intervenors, the type of firm making the request, and the judgment of the commission. • There is no set legal rule for how the rate of return should be calculated, but once the firm's request is made, the type of firm determined, the presence of intervenors established, etc., we can predict, using equation (1), what the allowed rate of return will be. • In addition, the rate of return phase may be used to give compensation to firms for losses incurred because of regulatory lag and inflation. In an inflationary world, higher than normal rates of return may be allowed as a method of anticipating inflation and to forestall the immediate return of a firm for a rate increase. • Finally, the results indicate that statistical techniques can be of help in evaluating legal decision processes.

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