Explaining regulatory commission behavior in the electric utility industry.

• Author: Atkinson, Scott E.

1. 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.

2. 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...