# Explaining regulatory commission behavior in the electric utility industry.

I. Introduction

A number of theoretical studies have examined regulated output price and regulatory lag as policy tools of regulatory commissions. Bailey and Coleman |6~ argue that regulatory lag mitigates the Averch-Johnson effect |4~. Wendel |20~ uses a game-theoretic model to show that regulators' and firms' strategies determine R and D expenditures and regulatory lag. Bailey |5~ argues that firms engage in R and D to earn excess profits because of regulatory lag, which is set by regulators. Assuming cost plus regulation, Sweeney |19~ argues that increased regulatory lag can retard adoption of new technologies; Sappington |18~ presents a similar argument--increasing lag induces waste. Bawa and Sibley |7~ assume that regulators directly adjust price to affect rates of return and that regulatory lag is endogenously determined as a function of the difference between the actual and fair rate of return. While we are aware of no econometric studies which explain the length of regulatory lag, a number of authors have attempted to explain the rate of return requested by the firm and that allowed by the commission. Using a recursive econometric model, Joskow |11~ finds a positive correlation between these two variables. This study was criticized by Roberts, Maddala, and Enholm |17~ for not addressing the sample selectivity bias and simultaneity issues. Hagerman and Ratchford |10~ find that both economic and political variables are significant in explaining the allowed rate of return, although the elected-versus-appointed status of the commissioners is not important. Costello |9~ obtains similar results regarding electric rates, although Primeaux and Mann |6~ find weakly conflicting evidence.

While theoretical justification exists for the use of regulatory lag as a policy tool, we believe this is the first attempt to formally model and test this aspect of regulatory commission behavior. The remainder of the paper is organized as follows. Section II presents a theoretical model of a welfare-maximizing regulator who can choose both price and the period of regulatory lag in order to meet a revenue requirement. The implication of the model is that both the optimal price and lag are dependent on a set of exogenous variables, and that lag and price changes may be used as substitutes in order to meet the firms revenue requirement. Section III presents the econometric models used to test the theory. The data and results are reported in section IV. Finally, conclusions are presented in section V.

II. Regulatory Lag and Regulated Price

Regulatory lag is defined as the time a regulatory commission requires to rule on a utility's request for a rate increase. Within the framework of a two-period model, we assume the utility, with an allowed rate |p.sub.1~, files a request for rate relief at time |t.sub.0~. At time |t.sub.1~ the commission rules on the company's request and institutes the new rate, |p.sub.2~. The first period, |t.sub.1~ - |t.sub.0~, is regulatory lag (LAG). The new set of rates is in effect at time |t.sub.2~ when the utility again files for a rate increase (and remains in effect until the new rate is enacted). Thus, |t.sub.2~ - |t.sub.1~, represents the second period.

Demand for the utility's product is represented by the function |q.sub.1~ = |q.sub.1~(|p.sub.1~, t) during the first period and |q.sub.2~ = |q.sub.2~(|p.sub.2~, t) during the second period. In both expressions, |q.sub.i~ represents the quantity demanded per unit of time and |p.sub.i~ is the price per unit, i = 1, 2. Cross elasticities of demand between the two periods are assumed to be zero.

The discounted present value of consumer surplus during the first period is written as

|Mathematical Expression Omitted~,

where ||Delta~.sub.1~ is the discount rate in the first period.

During this period, the utility's variable costs are assumed to be rising, while capital costs are fixed. The firm's discounted profits are

|Mathematical Expression Omitted~,

where

V|C.sub.1~ = the variable cost function,

|Alpha~ = the rate of increase in variable costs during the first period,

|r.sub.1~ = the price of capital during the first period,

|K.sub.1~ = the quantity of capital used during the first period.

Increases in variable costs reduce profits over time. The longer the lag the greater the erosion of profits. Apparently, this occurred in the late 1970s and early 1980s.

During the second period, discounted consumer surplus is

|Mathematical Expression Omitted~,

and discounted profit is

|Mathematical Expression Omitted~,

where the subscripts on variables used in (1) and (2) have been incremented. For simplicity we assume that variable costs are constant in period 2.

The commission must allow the utility an opportunity to earn a fair rate of return. Financial markets determine a fair rate of return for period 1, |S.sub.1~, and for period 2, |S.sub.2~. The regulator chooses |p.sub.2~ and finally |t.sub.1~ to ensure that at least the fair return is earned for the two periods. The regulatory constraint, which requires that the utility's discounted average earned rate of return on capital over the period (|t.sub.0~ - |t.sub.2~) equals or exceeds its discounted authorized return for this period, is

|Mathematical Expression Omitted~.

We now model the behavior of a regulator who maximizes the welfare of producers and consumers. Defining welfare over the two periods as the sum of the discounted present value of the sum of consumer surplus and profits, we can write the regulator's problem as

|Mathematical Expression Omitted~,

subject to (5) satisfied as an equality.

The welfare function is clearly concave in both of the arguments |t.sub.1~ and |p.sub.2~. Thus, second-order conditions will require that the curvature of the welfare function be greater than the curvature of the fixed rate of return locus assuming that it also is concave. If these conditions are met a unique maximum will be located somewhere along the curve. The first-order conditions can be solved for the optimal values, |t*.sub.1~ and |p*.sub.2~. They will be functions of |Alpha~, |r.sub.1~, |r.sub.2~, |S.sub.1~, |S.sub.2~, |p.sub.1~, |t.sub.2~, |K.sub.1~, |K.sub.2~, ||Delta~.sub.1~, and ||Delta~.sub.2~. Social welfare may not be maximized to the extent that the political motivation of the commissioners or the firm's requested |p.sub.2~ influence |t*.sub.1~ or |p*.sub.2~, ceteris paribus.

The rate of return constraint illustrates the tradeoff between |t.sub.1~ and |p.sub.2~. If the commission waits longer to make a decision in a rate case, a higher price must be granted to offset the reduction of earnings due to increases in variable costs. The curvature of the fixed rate of return locus will depend on the response of quantity demanded to changes in price as well as the time period when the utility files a new rate case in response to changes in price by the commission. An increase in the exogenous variable |S.sub.2~ will shift the iso-rate of return locus upward. In order to meet the new constraint a commission may choose different combinations of |p.sub.2~ and |t.sub.1~. The choice variables |p.sub.2~ and |t.sub.1~ can be used as substitutes by the regulatory commission to ensure the utility earns a specific rate of return. That is, higher required rates of return may be associated with long periods of lag and large rate increases, or smaller periods of lag and smaller rate increases.

III. Econometric Models And Data

Specification Issues

Turning now to our econometric model, we explain the allowed change in revenues (AUTREV) instead of |p.sub.2~, and LAG instead of |t.sub.1~. AUTREV is actually approved by the commission, while |p.sub.2~ would have to be constructed as a weighted average based on revenues from each aggregate category, rather than as a marginal price faced by the consumer. LAG is defined simply as |t.sub.1~ - |t.sub.0~.

Three issues of econometric specification must be considered in explaining AUTREV and LAG. The first is whether these variables are jointly dependent and part of a simultaneous equations system. Testing the hypothesis of simultaneity is not feasible, since the theory of regulatory bargaining is inadequate to provide identification of such a system or a set of potential instruments. All explanatory variables affect both dependent variables based on our theory in section II. Thus, we estimate reduced form equations for LAG and AUTREV. The second issue is whether the estimators of the effects of explanatory variables on LAG and AUTREV may be subject to self-selectivity bias. A firm requests review only when the latent variable, U, measuring intensity of desire for review exceeds some threshold. We measure this intensity with the latent variable, U. Since variables describing a firm's financial health are available only in this case, the observed counterpart of U is truncated. Unless U is independent of LAG and AUTREV, we must explicitly model sample selectivity to avoid bias.

We test for sample selectivity by estimating the latent truncated variable model developed by Bloom and Killingsworth |8~. Estimated parameters which measure sample selectivity bias are highly insignificant at the .05 level using a one-tailed test.

Finally, for 78 of the 96 rate cases which comprise the data set, laws limiting the maximum lag were in effect. For these 78 cases the mean allowed lag was 256.67 days with a standard deviation of 156.29. Thus, two issues must be considered. First, LAG may be censored for some observations and hence the likelihoods derived below would have to be appropriately modified. In no case, however, was LAG equal to the statutory limit and in 19 cases LAG exceeded this limit. Conversations with state regulatory agency personnel indicated that these limits could be either exceeded without penalty, because of mutual agreement, or because multiple issues were being decided at one time. Hence, censoring is not relevant. Second, the presence of a limit may reduce LAG even if no observations are censored. To test for this possibility we included a dummy variable for the presence of a limit in estimating LAG. In all cases the coefficient associated with this dummy variable was highly insignificant. Thus, we omit this variable from further discussion.

Econometric Models Explaining LAG

Since we can expect LAG to be non-normally distributed, we examine families of failure time models which incorporate such distributions. Recent failure time studies include those of unemployment duration |11~, career length |2~, and duration of terrorist incidents |3~. The problem of estimating regulatory lag is a natural application of time to failure analysis.

Table I characterizes our failure time data. The first column breaks down the length of regulatory lag into ten equal intervals. Column two shows the number of rate cases decided in each interval. Columns three and four indicate the percent of cases not yet decided and the hazard, respectively. The hazard is the probability that the regulatory commission will end the period of regulatory lag at any time during the interval, conditional upon not having reached a decision at the beginning of the interval. The hazard is generally increasing throughout time, implying that the longer the period of regulatory lag, the more likely a decision will be rendered immediately. Note that only six percent of all decisions are made in less than four months (112.8 days) and only eight percent take longer than 13 months (394.8 days).

Several different densities have been used to describe failure time data. The most common are the Weibull and exponential distributions. The exponential regression model assumes a constant hazard rate, an assumption which is obviously inappropriate based on the empirical hazard. The Weibull model allows for a monotonic hazard, either increasing or decreasing, and seems more appropriate for this application. However, the empirical hazard is clearly non-monotonic. In this paper we reject the exponential model and report the results of two different proportional hazards models, the Weibull model and the polynomial hazard model, which allows for a non-monotonic hazard. We also examine the effects of modelling unobserved heterogeneity. The likelihoods for these models are provided in the Appendix.

Data

Definitions, means, and standard deviations of the variables used to explain LAG and AUTREV for our sample of electric utility rate hearings are presented in Table II. For the variables which influence the commission's choice of t and p in (6) we employ a dummy variable indicating that interim rate relief was granted (INTERIM), the length of time between previous rate adjustments (PREFILE), and the utility's requested rate increase (REQREV). As a measure of |S.sub.2~, we employ the authorized rate of return for the upcoming period (AROR). We utilize the rate of growth in variable costs (INFL) to measure |Alpha~, and the utility's ratebase (RATEBASE) to measure |K.sub.1~. As political variables we employ the size of the commission's budget (BUDGET), the commissioner's appointed status (APPOINT), and the length of commissioner's terms (TERM). There is little evidence of serious correlation among the explanatory variables. Most simple correlations coefficients are less than .2 in absolute value. The only exception is that between REQREV and RATEBASE, which is .67.

Our sample consists of 96 rate cases, which comprised all electric utility rate cases from 1980-84, with non-missing data for our selected covariates as reported in the Annual Report of Utility and Carrier Regulation published by the National Association of Regulatory Commissioners (NARUC) |14~. The 1980-84 interval was selected for consistency with our theory, since every rate action reported by the NARUC during this period was a request for higher rates. The data are available from the authors upon request. We first examine the hypothesized relationships between the explanatory variables and LAG.

AROR. The rate of return authorized by the commission for the upcoming period signifies the opportunity cost of increasing the length of regulatory lag. The larger the opportunity cost the shorter the expected LAG.

BUDGET. On the one hand, the larger the annual budget of the commission the better able and more quickly they should be able to perform their rate review. On the other hand, we might expect commissions with larger budgets to be more thorough in their investigation, which would lead to larger periods of regulatory lag. Overall, we have no strong expectations for this variable.

INFL. If LAG is used as a policy tool we would expect that in times of high growth rates in a company's variable costs, LAG should be short. Only in this way will the company have a realistic opportunity to earn their authorized rate of return.

INTERIM. We expect that the granting of interim rate relief will cause the commission to lengthen LAG, since at least partial compensation has been provided.

PREFILE. Joskow |11~ has argued that one of a regulatory commission's objectives is to minimize conflict and criticism. During the rate hearing, the commissioners often receive negative publicity for allowing rate increases. Hence, the commission may reward the company for waiting longer before filing rate requests by acting quickly on the company's request when it is filed. We therefore expect a negative relationship between this variable and LAG.

APPOINT. We include APPOINT to examine whether the elected-versus-appointed status of commissioners significantly affects LAG, due presumably to different degrees of political responsiveness. Previous work by Nelson |13~ and Hagerman and Ratchford |10~, examining the decisions of state regulatory agencies, did not find this variable to be significant, although Nowell and Tschirhart |15~ presented conflicting evidence. If the capture theory of regulation were an accurate description of regulatory behavior, we would expect to find that elected commissioners are more responsive to the needs of the regulated company and APPOINT should have a negative effect on LAG. If the public interest theory of regulatory behavior were accurate, however, we would expect this variable to have a positive impact. Overall, our prior expectations about signs are weak. TERM. This variable also measures the importance of political pressure on commission decisions. We have weak expectations regarding its effect.

REQREV and RATEBASE. The size of the revenue request and the utility's rate base should increase LAG only to the extent that the commission staff is overburdened. Our expectations are weak regarding the effects of these two variables.

The variables RATEBASE, INTERIM, INFL, AROR, PREFILE, and REQREV should have a positive impact on AUTREV due to rate base regulation. Joskow |11~ found that the requested rate increase is positively related to authorized revenue. BUDGET will have a negative impact on AUTREV if the commission takes an adversarial position. We have no strong prior expectations for the remaining variables, TERM and APPOINT.

IV. Results

Estimated coefficients and asymptotic standard errors as well as estimated values for the likelihood functions for the model explaining LAG are reported in Table III. Estimated coefficients (reported as |Mathematical Expression Omitted~ for the Weibull and |Mathematical Expression Omitted~ for the polynomial hazard models) allow direct analysis of the impact of each variable on LAG. The estimated shape parameter for the Weibull (not reported) indicates a strongly and significantly increasing hazard. The polynomial hazard model with unobserved heterogeneity is somewhat preferable to the Weibull model based on |Mathematical Expression Omitted~. An asymptotic chi-square test that |Beta~ = 0 (global ||Chi~.sup.2~) is strongly rejected for both models. A number of important differences in estimated coefficients are observed between the two models.

The estimated coefficient for BUDGET is positive and significant in both models indicating that larger budgets are associated with longer LAG. Experimentation with budget per case yielded no significant differences. As expected, the coefficient on PREFILE was negative and significant in both models. The implication is that, all else equal, commissioners reward companies which have waited longer periods of time between rate hearings by shortening LAG. Estimated coefficients on the variables AROR and APPOINT were negative in both cases, TABULAR DATA OMITTED but only significantly so in the polynomial hazard model. Thus, some evidence exists that shorter periods of lag are associated with larger increases in allowed rates of return. Although few commissioners are elected, the positive sign associated with the variable APPOINT is consistent with appointed status significantly reducing LAG. As anticipated, the coefficient on INTERIM is positive, although only significantly so in the Weibull model, which indicates that commissions may indeed place less emphasis on shortening LAG when interim rate relief has been granted.

Two variables, the size of the utility and political affiliation of the commissioners', were initially included but subsequently dropped from all equations, since they were found to be highly insignificant. In addition, the covariates REQREV and RATEBASE were highly insignificant in the LAG equation and subsequently dropped.

The contribution of individual regressors to the log hazard is measured using "beta coefficients," defined as the estimated coefficient times the ratio of the sample standard deviations of the kth explanatory variable to that of the log hazard. Examining variables with significant coefficients from the polynomial hazard regression model we obtain ratios of 4.78 for BUDGET, 2.15 for PREFILE, and 1.83 for APPOINT relative to AROR. This indicates that BUDGET contributes the greatest amount of explanatory power and AROR the least amount. Finally, we regress AUTREV on the same set of explanatory variables reported for the LAG equation plus REQREV and RATEBASE. Our results for the AUTREV ordinary least squares regression are given in Table IV.

Estimated coefficients for REQREV and RATEBASE are significant with the expected signs. The coefficient on the political variable APPOINT is also positive and significant, indicating that appointed commissioners, all else equal, are more likely to authorize larger rate increases than their elected counterparts.

Jointly interpreting the results of the equations explaining AUTREV and LAG yields some interesting insights. First, while BUDGET does not seem to impact AUTREV, it does seem to have a positive effect on LAG. Second, higher AROR and PREFILE shorten LAG but have no significant impact on AUTREV. Third, when the firms' REQREV is large, regulatory commissions apparently do not hasten their decisions on the belief that the opportunity cost of waiting is high. Rather, LAG is likely to remain constant and the commission will reward the firm through a larger increase in rates. Since LAG and AUTREV are influenced by different economic factors; the regulatory commission appears to employ LAG and AUTREV as substitute policy tools.

We find that appointed commissioners tend to be associated with both shorter LAG and larger AUTREV, both of which tend to benefit the firm rather than maximizing social welfare. Apparently when commissioners are elected by the public they tend to make decisions on LAG and AUTREV that are more beneficial to society.

V. Conclusion

Regulatory lag has long been identified as a medium through which regulatory commissions may be able to affect the behavior of the firm. We explain the period of regulatory lag using maximum likelihood methods which incorporate a variety of assumptions about the hazard and the presence of unobserved heterogeneity. We find evidence to suggest that commissions do use lag and authorized rate increases as substitute policy tools, which is consistent with economic theory. As the period since the previous filing for review increases and the market dictates a high rate of return, the commission typically shortens regulatory lag rather than providing larger rate increases. Further, elected and appointed commissioners seem to behave differently in their decisions on both regulatory lag and authorized price increases.

Appendix

Defining the pdf and cdf of |t.sub.i~ (LAG) as f(|t.sub.i~) and F(|t.sub.i~), the survivor function is S(|t.sub.i~) = 1 - F(|t.sub.i~). Further, the baseline hazard, which is the instantaneous probability of failure at time t given survival to time t, is defined as ||Lambda~.sub.o~ (|t.sub.i~) = |f.sub.o~ (|t.sub.i~)/|S.sub.o~ (|t.sub.i~) = -d ln |S.sub.o~ (|t.sub.i~)/d|t.sub.i~, where the o-subscript indicates baseline functions, which are independent of covariates. We consider the well-known proportional hazards specification which assumes that the hazard, |Lambda~(|t.sub.i~), at time t for unit i(i = 1,..., n) is |Lambda~(|t.sub.i~, |x.sub.i~, |Beta~) = ||Lambda~.sub.o~(|t.sub.i~)||Mu~.sub.i~, where ||Mu~.sub.i~ = |Phi~(|x.sub.i~, |Beta~) measures observed heterogeneity among units, |x.sub.i~ is a (K X 1) vector of observations on K explanatory variables for unit i, and |Beta~ is a (K X 1) vector of population parameters. Henceforth, we suppress |x.sub.i~ and |Beta~ as arguments of |Lambda~ for simplicity.

Note that ||Mu~.sub.i~ affects the hazard ||Lambda~.sub.i~ proportionally and that the baseline hazard fully describes ||Lambda~.sub.i~ when ||Mu~.sub.i~ = 1. We assume that ||Mu~.sub.i~ = exp(|x|prime~.sub.i~|Beta~) to assure ||Mu~.sub.i~ |is greater than or equal to~ 0. Further, we assume that the regressors |x.sub.i~ are time invariant.

We define the unconditional survivor function as |Mathematical Expression Omitted~. Again suppressing |x.sub.i~ and |Beta~, the unconditional probability of failure at time t for unit i is f(|t.sub.i~) = |Lambda~(|t.sub.i~)S(|t.sub.i~), where no observations are censored. A popular choice of parametric form for ||Lambda~.sub.o~ (|t.sub.i~) has been the Weibull, where |Mathematical Expression Omitted~.

The polynomial hazard model is considerably more flexible than the Weibull model, since it allows for a non-monotonic hazard with |Mathematical Expression Omitted~, where ||Mu~.sub.i~ = exp(-|x|prime~.sub.i~|Beta~).

Due to unobserved heterogeneity, units with identical |x.sub.i~ and |t.sub.i~ will have different hazard rates. The conditional hazard given unobserved heterogeneity is |Lambda~ (|t.sub.i~|where~|Upsilon~~) = ||Lambda~.sub.o(|t.sub.i~)||Mu~.sub.i~|Upsilon~, where for all individuals the random variable |Upsilon~, 0 |is less than~ |Upsilon~ |is less than~ |infinity~, represents unobserved heterogeneity, has c.d.f. F(|Upsilon~), E(|Upsilon~) |is less than~ |infinity~, and variance |Mathematical Expression Omitted~. Following Lancaster |12~ and Atkinson and Tschirhart |2~, we assume that |Upsilon~ follows the gamma distribution. See Atkinson and Nowell |1~ for more details.

References

1. Atkinson, Scott E. and Clifford Nowell. "Flexible Estimation of the Hazard in Failure Time Models: An Explanation of Regulatory Lag." Mimeo, 1992.

2. ----- and John Tschirhart, "Flexible Modelling of Time-to-Failure in Risky Careers." Review of Economics and Statistics, November 1986, 558-66.

3. -----, -----, and Todd Sandler, "Terrorism as Bargaining." Journal of Law and Economics, 1987, 1-21.

4. Averch, Harvey and Leland L. Johnson, "Behavior of the Firm Under Regulatory Constraint." American Economic Review, December 1962, 1052-69.

5. Bailey, Elizabeth E., "Innovation and Regulation." Journal of Public Economics, August 1974, 285-95.

6. ----- and Roger D. Coleman, "The Effect of Lagged Regulation in an Averch-Johnson Model." Bell Journal of Economics, Spring 1971, 278-92.

7. Bawa, Vijay S. and David S. Sibley, "Dynamic Behavior of a Firm Subject to Stochastic Regulatory Review." International Economic Review, October 1980, 627-42.

8. Bloom, David E. and Mark R. Killingsworth, "Correcting for Truncation Bias Caused by a Latent Truncation Variable," Journal of Econometrics, January 1985, 131-35.

9. Costello, Kenneth W., "Electing Regulators: The Case of Public Utility Commissioners." Yale Journal on Regulation, January 1984, 83-105.

10. Hagerman, Robert L. and Brian T. Ratchford, "Some Determinants of Allowed Rates of Return on Equity to Electric Utilities." Bell Journal of Economics, Spring 1978, 48-65.

11. Joskow, Paul L., "The Determination of the Allowed Rate of Return in a Formal Regulatory Hearing." Bell Journal of Economics, Autumn 1972, 632-44.

12. Lancaster, Tony, "Econometric Methods for the Duration of Unemployment." Econometrica, July 1979, 939-56.

13. Nelson, Randy A., "An Empirical Test of the Ramsey Theory and Stigler-Peltzman Theory of Public Utility Pricing." Economic Inquiry, April 1982, 277-90.

14. National Association of Regulatory Utility Commissioners. Annual Report of Utility and Carrier Regulation. Washington, D.C. 1978-1984.

15. Nowell, Clifford and John Tschirhart, "The Public Utility Regulatory Act and Regulatory Behavior." Journal of Regulatory Economics, March 1990, 21-36.

16. Primeaux, Walter J., Jr. and Patrick C. Mann, "Regulator Selection Methods and Electricity Prices." Land Economics, February 1986, 1-13.

17. Roberts, R. Blaine, G. S. Maddala, and Gregory Enholm, "Determinants of the Requested Rate of Return and the Rate of Return Granted in a Formal Regulatory Process." Bell Journal of Economics, Autumn 1978, 611-21.

18. Sappington, David, "Strategic Firm Behavior Under a Dynamic Regulatory Adjustment Process." Bell Journal of Economics, Spring 1980, 360-72.

19. Sweeney, George, "Adoption and Cost-Saving Innovations by a Regulated Firm." American Economic Review, June 1981, 437-47.

20. Wendel, James, "Firm-Regulator Interaction with Respect to Firm Cost Reduction Activities." Bell Journal of Economics, Autumn 1976, 631-40.

A number of theoretical studies have examined regulated output price and regulatory lag as policy tools of regulatory commissions. Bailey and Coleman |6~ argue that regulatory lag mitigates the Averch-Johnson effect |4~. Wendel |20~ uses a game-theoretic model to show that regulators' and firms' strategies determine R and D expenditures and regulatory lag. Bailey |5~ argues that firms engage in R and D to earn excess profits because of regulatory lag, which is set by regulators. Assuming cost plus regulation, Sweeney |19~ argues that increased regulatory lag can retard adoption of new technologies; Sappington |18~ presents a similar argument--increasing lag induces waste. Bawa and Sibley |7~ assume that regulators directly adjust price to affect rates of return and that regulatory lag is endogenously determined as a function of the difference between the actual and fair rate of return. While we are aware of no econometric studies which explain the length of regulatory lag, a number of authors have attempted to explain the rate of return requested by the firm and that allowed by the commission. Using a recursive econometric model, Joskow |11~ finds a positive correlation between these two variables. This study was criticized by Roberts, Maddala, and Enholm |17~ for not addressing the sample selectivity bias and simultaneity issues. Hagerman and Ratchford |10~ find that both economic and political variables are significant in explaining the allowed rate of return, although the elected-versus-appointed status of the commissioners is not important. Costello |9~ obtains similar results regarding electric rates, although Primeaux and Mann |6~ find weakly conflicting evidence.

While theoretical justification exists for the use of regulatory lag as a policy tool, we believe this is the first attempt to formally model and test this aspect of regulatory commission behavior. The remainder of the paper is organized as follows. Section II presents a theoretical model of a welfare-maximizing regulator who can choose both price and the period of regulatory lag in order to meet a revenue requirement. The implication of the model is that both the optimal price and lag are dependent on a set of exogenous variables, and that lag and price changes may be used as substitutes in order to meet the firms revenue requirement. Section III presents the econometric models used to test the theory. The data and results are reported in section IV. Finally, conclusions are presented in section V.

II. Regulatory Lag and Regulated Price

Regulatory lag is defined as the time a regulatory commission requires to rule on a utility's request for a rate increase. Within the framework of a two-period model, we assume the utility, with an allowed rate |p.sub.1~, files a request for rate relief at time |t.sub.0~. At time |t.sub.1~ the commission rules on the company's request and institutes the new rate, |p.sub.2~. The first period, |t.sub.1~ - |t.sub.0~, is regulatory lag (LAG). The new set of rates is in effect at time |t.sub.2~ when the utility again files for a rate increase (and remains in effect until the new rate is enacted). Thus, |t.sub.2~ - |t.sub.1~, represents the second period.

Demand for the utility's product is represented by the function |q.sub.1~ = |q.sub.1~(|p.sub.1~, t) during the first period and |q.sub.2~ = |q.sub.2~(|p.sub.2~, t) during the second period. In both expressions, |q.sub.i~ represents the quantity demanded per unit of time and |p.sub.i~ is the price per unit, i = 1, 2. Cross elasticities of demand between the two periods are assumed to be zero.

The discounted present value of consumer surplus during the first period is written as

|Mathematical Expression Omitted~,

where ||Delta~.sub.1~ is the discount rate in the first period.

During this period, the utility's variable costs are assumed to be rising, while capital costs are fixed. The firm's discounted profits are

|Mathematical Expression Omitted~,

where

V|C.sub.1~ = the variable cost function,

|Alpha~ = the rate of increase in variable costs during the first period,

|r.sub.1~ = the price of capital during the first period,

|K.sub.1~ = the quantity of capital used during the first period.

Increases in variable costs reduce profits over time. The longer the lag the greater the erosion of profits. Apparently, this occurred in the late 1970s and early 1980s.

During the second period, discounted consumer surplus is

|Mathematical Expression Omitted~,

and discounted profit is

|Mathematical Expression Omitted~,

where the subscripts on variables used in (1) and (2) have been incremented. For simplicity we assume that variable costs are constant in period 2.

The commission must allow the utility an opportunity to earn a fair rate of return. Financial markets determine a fair rate of return for period 1, |S.sub.1~, and for period 2, |S.sub.2~. The regulator chooses |p.sub.2~ and finally |t.sub.1~ to ensure that at least the fair return is earned for the two periods. The regulatory constraint, which requires that the utility's discounted average earned rate of return on capital over the period (|t.sub.0~ - |t.sub.2~) equals or exceeds its discounted authorized return for this period, is

|Mathematical Expression Omitted~.

We now model the behavior of a regulator who maximizes the welfare of producers and consumers. Defining welfare over the two periods as the sum of the discounted present value of the sum of consumer surplus and profits, we can write the regulator's problem as

|Mathematical Expression Omitted~,

subject to (5) satisfied as an equality.

The welfare function is clearly concave in both of the arguments |t.sub.1~ and |p.sub.2~. Thus, second-order conditions will require that the curvature of the welfare function be greater than the curvature of the fixed rate of return locus assuming that it also is concave. If these conditions are met a unique maximum will be located somewhere along the curve. The first-order conditions can be solved for the optimal values, |t*.sub.1~ and |p*.sub.2~. They will be functions of |Alpha~, |r.sub.1~, |r.sub.2~, |S.sub.1~, |S.sub.2~, |p.sub.1~, |t.sub.2~, |K.sub.1~, |K.sub.2~, ||Delta~.sub.1~, and ||Delta~.sub.2~. Social welfare may not be maximized to the extent that the political motivation of the commissioners or the firm's requested |p.sub.2~ influence |t*.sub.1~ or |p*.sub.2~, ceteris paribus.

The rate of return constraint illustrates the tradeoff between |t.sub.1~ and |p.sub.2~. If the commission waits longer to make a decision in a rate case, a higher price must be granted to offset the reduction of earnings due to increases in variable costs. The curvature of the fixed rate of return locus will depend on the response of quantity demanded to changes in price as well as the time period when the utility files a new rate case in response to changes in price by the commission. An increase in the exogenous variable |S.sub.2~ will shift the iso-rate of return locus upward. In order to meet the new constraint a commission may choose different combinations of |p.sub.2~ and |t.sub.1~. The choice variables |p.sub.2~ and |t.sub.1~ can be used as substitutes by the regulatory commission to ensure the utility earns a specific rate of return. That is, higher required rates of return may be associated with long periods of lag and large rate increases, or smaller periods of lag and smaller rate increases.

III. Econometric Models And Data

Specification Issues

Turning now to our econometric model, we explain the allowed change in revenues (AUTREV) instead of |p.sub.2~, and LAG instead of |t.sub.1~. AUTREV is actually approved by the commission, while |p.sub.2~ would have to be constructed as a weighted average based on revenues from each aggregate category, rather than as a marginal price faced by the consumer. LAG is defined simply as |t.sub.1~ - |t.sub.0~.

Three issues of econometric specification must be considered in explaining AUTREV and LAG. The first is whether these variables are jointly dependent and part of a simultaneous equations system. Testing the hypothesis of simultaneity is not feasible, since the theory of regulatory bargaining is inadequate to provide identification of such a system or a set of potential instruments. All explanatory variables affect both dependent variables based on our theory in section II. Thus, we estimate reduced form equations for LAG and AUTREV. The second issue is whether the estimators of the effects of explanatory variables on LAG and AUTREV may be subject to self-selectivity bias. A firm requests review only when the latent variable, U, measuring intensity of desire for review exceeds some threshold. We measure this intensity with the latent variable, U. Since variables describing a firm's financial health are available only in this case, the observed counterpart of U is truncated. Unless U is independent of LAG and AUTREV, we must explicitly model sample selectivity to avoid bias.

We test for sample selectivity by estimating the latent truncated variable model developed by Bloom and Killingsworth |8~. Estimated parameters which measure sample selectivity bias are highly insignificant at the .05 level using a one-tailed test.

Finally, for 78 of the 96 rate cases which comprise the data set, laws limiting the maximum lag were in effect. For these 78 cases the mean allowed lag was 256.67 days with a standard deviation of 156.29. Thus, two issues must be considered. First, LAG may be censored for some observations and hence the likelihoods derived below would have to be appropriately modified. In no case, however, was LAG equal to the statutory limit and in 19 cases LAG exceeded this limit. Conversations with state regulatory agency personnel indicated that these limits could be either exceeded without penalty, because of mutual agreement, or because multiple issues were being decided at one time. Hence, censoring is not relevant. Second, the presence of a limit may reduce LAG even if no observations are censored. To test for this possibility we included a dummy variable for the presence of a limit in estimating LAG. In all cases the coefficient associated with this dummy variable was highly insignificant. Thus, we omit this variable from further discussion.

Econometric Models Explaining LAG

Since we can expect LAG to be non-normally distributed, we examine families of failure time models which incorporate such distributions. Recent failure time studies include those of unemployment duration |11~, career length |2~, and duration of terrorist incidents |3~. The problem of estimating regulatory lag is a natural application of time to failure analysis.

Table I characterizes our failure time data. The first column breaks down the length of regulatory lag into ten equal intervals. Column two shows the number of rate cases decided in each interval. Columns three and four indicate the percent of cases not yet decided and the hazard, respectively. The hazard is the probability that the regulatory commission will end the period of regulatory lag at any time during the interval, conditional upon not having reached a decision at the beginning of the interval. The hazard is generally increasing throughout time, implying that the longer the period of regulatory lag, the more likely a decision will be rendered immediately. Note that only six percent of all decisions are made in less than four months (112.8 days) and only eight percent take longer than 13 months (394.8 days).

Several different densities have been used to describe failure time data. The most common are the Weibull and exponential distributions. The exponential regression model assumes a constant hazard rate, an assumption which is obviously inappropriate based on the empirical hazard. The Weibull model allows for a monotonic hazard, either increasing or decreasing, and seems more appropriate for this application. However, the empirical hazard is clearly non-monotonic. In this paper we reject the exponential model and report the results of two different proportional hazards models, the Weibull model and the polynomial hazard model, which allows for a non-monotonic hazard. We also examine the effects of modelling unobserved heterogeneity. The likelihoods for these models are provided in the Appendix.

Table I. Duration Data Time # Entering # Exiting Pct. Surviving Hazard 0-56.4 96 2 1.0 .0004 56.4-112.8 94 4 .979 .0008 112.8-169.2 90 6 .937 .0012 169.2-225.6 84 25 .875 .0062 225.6-282.0 59 17 .615 .0060 282.0-338.4 42 28 .438 .0177 338.4-394.8 14 7 .146 .0118 394.8-451.2 7 5 .073 .0197 451.2-507.6 2 1 .021 .0118 507.6-564.0 1 1 .014 .0355 Table II. Definitions, Means, and Standard Deviations Standard Variable Definition Mean Deviations LAG The time period (100's of days) between when the firm files a rate request and the commission institutes a new set of rates. 2.61 .92 AROR Rate of return authorized during current rate hearing. 11.56 1.43 BUDGET Annual commission budget ($10 millions) during the year of the rate hearing. .95 .86 INFL Growth in maintenance and operating expenses in the year of rate hearing. .10 .11 INTERIM =1 if the commission gave interim rate relief; =0 otherwise. .21 .41 PREFILE The length of time (in 100's of days) the firm's rates had been in effect prior to the time of filing. 2.41 1.77 APPOINT =1 if the commission is appointed; =0 otherwise. .95 .22 TERM Length of term (years) of commissioners. 5.72 1.51 RATEBASE Rate base ($ billions) currently allowed by the commission. 1.83 1.58 REQREV Change in revenues ($100 millions) requested by the firm. 1.67 2.13 AUTREV Change in revenues ($100 millions) authorized by the commission. .82 1.10

Data

Definitions, means, and standard deviations of the variables used to explain LAG and AUTREV for our sample of electric utility rate hearings are presented in Table II. For the variables which influence the commission's choice of t and p in (6) we employ a dummy variable indicating that interim rate relief was granted (INTERIM), the length of time between previous rate adjustments (PREFILE), and the utility's requested rate increase (REQREV). As a measure of |S.sub.2~, we employ the authorized rate of return for the upcoming period (AROR). We utilize the rate of growth in variable costs (INFL) to measure |Alpha~, and the utility's ratebase (RATEBASE) to measure |K.sub.1~. As political variables we employ the size of the commission's budget (BUDGET), the commissioner's appointed status (APPOINT), and the length of commissioner's terms (TERM). There is little evidence of serious correlation among the explanatory variables. Most simple correlations coefficients are less than .2 in absolute value. The only exception is that between REQREV and RATEBASE, which is .67.

Our sample consists of 96 rate cases, which comprised all electric utility rate cases from 1980-84, with non-missing data for our selected covariates as reported in the Annual Report of Utility and Carrier Regulation published by the National Association of Regulatory Commissioners (NARUC) |14~. The 1980-84 interval was selected for consistency with our theory, since every rate action reported by the NARUC during this period was a request for higher rates. The data are available from the authors upon request. We first examine the hypothesized relationships between the explanatory variables and LAG.

AROR. The rate of return authorized by the commission for the upcoming period signifies the opportunity cost of increasing the length of regulatory lag. The larger the opportunity cost the shorter the expected LAG.

BUDGET. On the one hand, the larger the annual budget of the commission the better able and more quickly they should be able to perform their rate review. On the other hand, we might expect commissions with larger budgets to be more thorough in their investigation, which would lead to larger periods of regulatory lag. Overall, we have no strong expectations for this variable.

INFL. If LAG is used as a policy tool we would expect that in times of high growth rates in a company's variable costs, LAG should be short. Only in this way will the company have a realistic opportunity to earn their authorized rate of return.

INTERIM. We expect that the granting of interim rate relief will cause the commission to lengthen LAG, since at least partial compensation has been provided.

PREFILE. Joskow |11~ has argued that one of a regulatory commission's objectives is to minimize conflict and criticism. During the rate hearing, the commissioners often receive negative publicity for allowing rate increases. Hence, the commission may reward the company for waiting longer before filing rate requests by acting quickly on the company's request when it is filed. We therefore expect a negative relationship between this variable and LAG.

APPOINT. We include APPOINT to examine whether the elected-versus-appointed status of commissioners significantly affects LAG, due presumably to different degrees of political responsiveness. Previous work by Nelson |13~ and Hagerman and Ratchford |10~, examining the decisions of state regulatory agencies, did not find this variable to be significant, although Nowell and Tschirhart |15~ presented conflicting evidence. If the capture theory of regulation were an accurate description of regulatory behavior, we would expect to find that elected commissioners are more responsive to the needs of the regulated company and APPOINT should have a negative effect on LAG. If the public interest theory of regulatory behavior were accurate, however, we would expect this variable to have a positive impact. Overall, our prior expectations about signs are weak. TERM. This variable also measures the importance of political pressure on commission decisions. We have weak expectations regarding its effect.

REQREV and RATEBASE. The size of the revenue request and the utility's rate base should increase LAG only to the extent that the commission staff is overburdened. Our expectations are weak regarding the effects of these two variables.

The variables RATEBASE, INTERIM, INFL, AROR, PREFILE, and REQREV should have a positive impact on AUTREV due to rate base regulation. Joskow |11~ found that the requested rate increase is positively related to authorized revenue. BUDGET will have a negative impact on AUTREV if the commission takes an adversarial position. We have no strong prior expectations for the remaining variables, TERM and APPOINT.

Table III. Estimated Parameters(a) for Proportional Hazards Models for Lag (asymptotic standard errors in parentheses) Polynomial Independent Variable Weibull Hazard-Heterogeneity Intercept 4.0730(b) 6.6423(b) (.3248) (1.2323) AROR -.0380 -.2774(b) (.08345) (.1391) BUDGET .6910(b) 2.2125(b) (.2599) (.7023) INFL -1.5128 -.6107 (1.3996) (2.3360) INTERIM .8061(b) .7098 (.3091) (.6105) PREFILE .2833(b) -.4876(b) (.09047) (.1896) APPOINT .6999 -3.2788(b) (1.0023) (1.5919) TERM .0920 -.1331 (.1199) (.2002) Global |Mathematical Expression Omitted~ 271.16 255.32 |Mathematical Expression Omitted~ -107.55 -100.60 Notes: a. Estimated parameters for the Weibull model |(based on ln(LAG)~ are multiplied by -1 to allow direct analysis of the effects of each covariate on LAG. b. Significant at .05 level using a two-tailed t-test.

IV. Results

Estimated coefficients and asymptotic standard errors as well as estimated values for the likelihood functions for the model explaining LAG are reported in Table III. Estimated coefficients (reported as |Mathematical Expression Omitted~ for the Weibull and |Mathematical Expression Omitted~ for the polynomial hazard models) allow direct analysis of the impact of each variable on LAG. The estimated shape parameter for the Weibull (not reported) indicates a strongly and significantly increasing hazard. The polynomial hazard model with unobserved heterogeneity is somewhat preferable to the Weibull model based on |Mathematical Expression Omitted~. An asymptotic chi-square test that |Beta~ = 0 (global ||Chi~.sup.2~) is strongly rejected for both models. A number of important differences in estimated coefficients are observed between the two models.

The estimated coefficient for BUDGET is positive and significant in both models indicating that larger budgets are associated with longer LAG. Experimentation with budget per case yielded no significant differences. As expected, the coefficient on PREFILE was negative and significant in both models. The implication is that, all else equal, commissioners reward companies which have waited longer periods of time between rate hearings by shortening LAG. Estimated coefficients on the variables AROR and APPOINT were negative in both cases, TABULAR DATA OMITTED but only significantly so in the polynomial hazard model. Thus, some evidence exists that shorter periods of lag are associated with larger increases in allowed rates of return. Although few commissioners are elected, the positive sign associated with the variable APPOINT is consistent with appointed status significantly reducing LAG. As anticipated, the coefficient on INTERIM is positive, although only significantly so in the Weibull model, which indicates that commissions may indeed place less emphasis on shortening LAG when interim rate relief has been granted.

Two variables, the size of the utility and political affiliation of the commissioners', were initially included but subsequently dropped from all equations, since they were found to be highly insignificant. In addition, the covariates REQREV and RATEBASE were highly insignificant in the LAG equation and subsequently dropped.

The contribution of individual regressors to the log hazard is measured using "beta coefficients," defined as the estimated coefficient times the ratio of the sample standard deviations of the kth explanatory variable to that of the log hazard. Examining variables with significant coefficients from the polynomial hazard regression model we obtain ratios of 4.78 for BUDGET, 2.15 for PREFILE, and 1.83 for APPOINT relative to AROR. This indicates that BUDGET contributes the greatest amount of explanatory power and AROR the least amount. Finally, we regress AUTREV on the same set of explanatory variables reported for the LAG equation plus REQREV and RATEBASE. Our results for the AUTREV ordinary least squares regression are given in Table IV.

Estimated coefficients for REQREV and RATEBASE are significant with the expected signs. The coefficient on the political variable APPOINT is also positive and significant, indicating that appointed commissioners, all else equal, are more likely to authorize larger rate increases than their elected counterparts.

Jointly interpreting the results of the equations explaining AUTREV and LAG yields some interesting insights. First, while BUDGET does not seem to impact AUTREV, it does seem to have a positive effect on LAG. Second, higher AROR and PREFILE shorten LAG but have no significant impact on AUTREV. Third, when the firms' REQREV is large, regulatory commissions apparently do not hasten their decisions on the belief that the opportunity cost of waiting is high. Rather, LAG is likely to remain constant and the commission will reward the firm through a larger increase in rates. Since LAG and AUTREV are influenced by different economic factors; the regulatory commission appears to employ LAG and AUTREV as substitute policy tools.

We find that appointed commissioners tend to be associated with both shorter LAG and larger AUTREV, both of which tend to benefit the firm rather than maximizing social welfare. Apparently when commissioners are elected by the public they tend to make decisions on LAG and AUTREV that are more beneficial to society.

V. Conclusion

Regulatory lag has long been identified as a medium through which regulatory commissions may be able to affect the behavior of the firm. We explain the period of regulatory lag using maximum likelihood methods which incorporate a variety of assumptions about the hazard and the presence of unobserved heterogeneity. We find evidence to suggest that commissions do use lag and authorized rate increases as substitute policy tools, which is consistent with economic theory. As the period since the previous filing for review increases and the market dictates a high rate of return, the commission typically shortens regulatory lag rather than providing larger rate increases. Further, elected and appointed commissioners seem to behave differently in their decisions on both regulatory lag and authorized price increases.

Appendix

Defining the pdf and cdf of |t.sub.i~ (LAG) as f(|t.sub.i~) and F(|t.sub.i~), the survivor function is S(|t.sub.i~) = 1 - F(|t.sub.i~). Further, the baseline hazard, which is the instantaneous probability of failure at time t given survival to time t, is defined as ||Lambda~.sub.o~ (|t.sub.i~) = |f.sub.o~ (|t.sub.i~)/|S.sub.o~ (|t.sub.i~) = -d ln |S.sub.o~ (|t.sub.i~)/d|t.sub.i~, where the o-subscript indicates baseline functions, which are independent of covariates. We consider the well-known proportional hazards specification which assumes that the hazard, |Lambda~(|t.sub.i~), at time t for unit i(i = 1,..., n) is |Lambda~(|t.sub.i~, |x.sub.i~, |Beta~) = ||Lambda~.sub.o~(|t.sub.i~)||Mu~.sub.i~, where ||Mu~.sub.i~ = |Phi~(|x.sub.i~, |Beta~) measures observed heterogeneity among units, |x.sub.i~ is a (K X 1) vector of observations on K explanatory variables for unit i, and |Beta~ is a (K X 1) vector of population parameters. Henceforth, we suppress |x.sub.i~ and |Beta~ as arguments of |Lambda~ for simplicity.

Note that ||Mu~.sub.i~ affects the hazard ||Lambda~.sub.i~ proportionally and that the baseline hazard fully describes ||Lambda~.sub.i~ when ||Mu~.sub.i~ = 1. We assume that ||Mu~.sub.i~ = exp(|x|prime~.sub.i~|Beta~) to assure ||Mu~.sub.i~ |is greater than or equal to~ 0. Further, we assume that the regressors |x.sub.i~ are time invariant.

We define the unconditional survivor function as |Mathematical Expression Omitted~. Again suppressing |x.sub.i~ and |Beta~, the unconditional probability of failure at time t for unit i is f(|t.sub.i~) = |Lambda~(|t.sub.i~)S(|t.sub.i~), where no observations are censored. A popular choice of parametric form for ||Lambda~.sub.o~ (|t.sub.i~) has been the Weibull, where |Mathematical Expression Omitted~.

The polynomial hazard model is considerably more flexible than the Weibull model, since it allows for a non-monotonic hazard with |Mathematical Expression Omitted~, where ||Mu~.sub.i~ = exp(-|x|prime~.sub.i~|Beta~).

Due to unobserved heterogeneity, units with identical |x.sub.i~ and |t.sub.i~ will have different hazard rates. The conditional hazard given unobserved heterogeneity is |Lambda~ (|t.sub.i~|where~|Upsilon~~) = ||Lambda~.sub.o(|t.sub.i~)||Mu~.sub.i~|Upsilon~, where for all individuals the random variable |Upsilon~, 0 |is less than~ |Upsilon~ |is less than~ |infinity~, represents unobserved heterogeneity, has c.d.f. F(|Upsilon~), E(|Upsilon~) |is less than~ |infinity~, and variance |Mathematical Expression Omitted~. Following Lancaster |12~ and Atkinson and Tschirhart |2~, we assume that |Upsilon~ follows the gamma distribution. See Atkinson and Nowell |1~ for more details.

References

1. Atkinson, Scott E. and Clifford Nowell. "Flexible Estimation of the Hazard in Failure Time Models: An Explanation of Regulatory Lag." Mimeo, 1992.

2. ----- and John Tschirhart, "Flexible Modelling of Time-to-Failure in Risky Careers." Review of Economics and Statistics, November 1986, 558-66.

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15. Nowell, Clifford and John Tschirhart, "The Public Utility Regulatory Act and Regulatory Behavior." Journal of Regulatory Economics, March 1990, 21-36.

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17. Roberts, R. Blaine, G. S. Maddala, and Gregory Enholm, "Determinants of the Requested Rate of Return and the Rate of Return Granted in a Formal Regulatory Process." Bell Journal of Economics, Autumn 1978, 611-21.

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20. Wendel, James, "Firm-Regulator Interaction with Respect to Firm Cost Reduction Activities." Bell Journal of Economics, Autumn 1976, 631-40.

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Author: | Nowell, Clifford |
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Publication: | Southern Economic Journal |

Date: | Jan 1, 1994 |

Words: | 4854 |

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