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Regulation through comparative performance evaluation
UtilitiesPolicy,Vol. 6, No. 4, pp. 293-301, 1997 Pergamon PIh S0957-1787(97)00009-X
© 1997 ElsevierScience Ltd. All rights reserved Printed in Great Britain 0957-1787/97 $17.00+ 0.00
Regulation through comparative performance evaluation Kirsty Powell* and Stefan Szymanskit Ofwat used comparative performance regulation in the 1994 periodic review of prices. We consider such a regulatory mechanism when there are technological spillovers. The regulator cannot observe firms effort and must design a regulatory contract which induces the socially optimal level of cost reduction. The extent to which cost reducing activities are non-appropriable is shown to affect the optimal choice of regulation. In general, comparative performance regulation is optimal and yardstick competition emerges only as a special case. However, when spillovers are spread evenly across an industry, an optimal comparative regime does not exist. © 1997 Elsevier Science Ltd. All rights reserved Keywords:regulation; spillovers;yardstickcompetition Introduction
Dissatisfaction with the traditional cost of service regulation has generated enormous interest in the design of regulatory mechanisms in recent years, at both a practical and theoretical level. Attention in the literature has focused on theoretically optimal solutions to specific problems, usually involving information constraints. For examples see Baron and Myerson (1982), Demski and Sappington (1984), Laffont and Tirole (1986), Schmalansee (1989), Sibley (1989), Holmstrom and Milgrom (1990), and Lockwood (1995). A variety of practical regulatory mechanisms and their implications for welfare have also been presented. For example, Glaister (1987) illustrates regulation through an output related profit tax, Sappington and Sibley (1988) introduce the notion of an incremental surplus subsidy, Braetigam and Panzar (1993) examine the impact of changing from rate of return to price cap regulation, while analysis of the The authors are with the Management School, Imperial College of
Science, Technologyand Medicine, 53 Prince's Gate, Exhibition Road, London, SW7 2PG, UK. * Tel: 0171 594 9144, Fax: 0171 823 7685, e-mail: [email protected] t Tel: 0171 594 9107, Fax: 0171 823 7685, email: [email protected]
properties of price caps and sliding scale (or profit sharing) regulation has been presented by Burns et al. (1995) and Mayer and Vickers (1995). One of the more important theoretical insights, referred to as yardstick competition, is due to Shleifer (1985) who proposed that regulating a firm's price by setting it equal to some function of the realised cost of similar firms in its industry can produce socially efficient outcomes. This idea was adopted during the privatisation process and in the development of the regulatory regime for the water industry. ~ The Office of Water Services (OFWAT), the economic regulator of the UK water industry, refer to yardstick competition as comparative performance evaluation. A type of comparative performance analysis was used during the price cap setting process at the first full review of prices since privatisation in 1989. 2 Essentially, price caps for individual firms for the next ten years were set on the basis of comparative efficiency analysis in both operating and capital expenditure. This method of setting price determinations largely on the basis of historical costs is different from the theoretical yardstick scheme in that the regulatory contract is based on ex ante cost realisations rather than ex post cost realisations. Nonetheless, the underlying principle of this hybrid price cap and yardstick regime is regulation through comparative performance evaluation. This paper develops a simple model of regulation through comparative performance evaluation. The price function employed allows the regulator to set a firm's price based on a combination of its own efficiency submissions and on a judgement of the relative efficiency of its rival firms, which closely mirrors Ofwat's price setting methodology. The key insight of the paper 3 is that the optimal form of regulation depends on the extent to which the benefits of cost reducing activities, such as R&D, are appropriable by the firm, and the extent to which they 'spillover' to other firms. In general, we show that comparative performance regulation is optimal, while yardstick competition in the sense of Shleifer (1985), emerges as a special case. We also show that where the benefits of cost reducing activities accrue 293
Regulation through comparativeperformance evaluation equally to all members of the industry, an optimal comparative regime does not exist. The paper is set out as follows: Section 2 explains the notions of yardstick competition, and spillovers in the context of the UK water industry. Section 3, presents some evidence on R&D issues in the water industry. In Section 4, following Shleifer, we show that pure yardstick regulation is inefficient in the presence of spillovers. In Section 5, a formula for optimal comparative performance regulation is derived, followed by a discussion in the final section, Section 6, and some concluding remarks.
Yardstick competition and the water industry During the water privatisation process of 1989, the applicability of price cap regulation or more specifically RPI_+K was analysed. This price cap formula limits allowable price increases to the previous year's retail price index, plus or minus a factor ' K ' , which accounts for companies anticipated efficiency savings, and also for predicted changes in levels of investment and operating costs. In his 1986 report on privatisation and regulation of the water industry, Stephen Littlechild recommended that regulation would need to be permanent; covering quality as well as price. Flotation of the ten existing authorities meant that they were to compete as successor companies in the capital market for funds. The operation of a take-over mechanism would therefore force the companies to strive for improved efficiency. Comparisons between companies of quality and price performance would also be facilitated by the regulator. Periodic revisions of the price cap would be necessary to avoid allocative inefficiency caused by the cumulative deviation of price from marginal cost over long periods. It was recommended that the K factor should be revised according to an industry yardstick to avoid any one company exerting an influence over its own price constraint. Yardstick competition is a mechanism for the economic regulation of spatially differentiated monopoly firms operating in the same industry. The price cap set for each firm depends on the costs of the other (identical) firms. Shleifer (1985) provided a model where, in equilibrium, each firm chooses a socially efficient level of cost reduction. This mechanism also generalises to the case of heterogeneous firms with observable differences which characterises the composition of companies within the UK water industry. The correction for heterogeneity amounts to a regression of costs on properties that determine diversity. During the periodic review of prices in 1994, OFWAT sought to make comparisons of companies' operating costs taking into account explanatory factors arising from their individual circumstances, in order to increase the accuracy of identifying relative
294
company efficiency. Econometric models of water costs, sewerage costs and sewage treatment costs were developed by Professor Mark Stewart of the University of Warwick. 4 Results from the Ordinary Least Squares regressions showed wide variations in companies' costs which could be accounted for by the wide variations in their operating conditions. Therefore, the magnitude of the residual or 'unexplained' differences in costs were attributed to a company's efficiency relative to the average. By comparing similar regulated firms with each other, Shleifer demonstrates, that a firm's attainable cost level can be determined. This forces firms serving different markets effectively to compete. For instance, if a firm reduces its costs, and its 'competitors' do not, it profits; if the other firms reduce their costs, and one firm fails to follow suit, then that firm will incur losses. The model assumes that cost reducing effort cannot be observed by the regulator. However, accounting data provides sufficient information to achieve efficiency. Without knowing the cost of cost reduction, the regulator must use the profit motive of the firms' managers to encourage them to reduce costs. The regulator wishes to maximise the sum of consumers' and producers' surplus. Prices and lump-sum transfers are the instruments available to achieve this aim initially. They are set according to a shadow firm with a cost level and cost reduction level defined as the mean of that of all other firms. Shleifer shows that by setting price and the transfer using this shadow firm, a unique Nash equilibrium, is for each firm to pick a socially efficient level of costs. Yardstick competition works by not allowing an inefficient firm to influence the price and transfer that it receives. It will deliver the first best, in Shleifer's model as long as the regulator shows a commitment to allowing an inefficient firm to go bankrupt. 5 The possible effects of 'technological spillovers' on the capacity of yardstick (or comparative) competition to achieve the 'first best' outcome is not mentioned in the Shleifer model and has received little attention in related literature, except for Dalen (1997). 6 Spillovers occur when the benefits of cost reducing (or demand creating) R&D are imperfectly appropriable. We concentrate attention on non-co-operative spillovers, as distinct from the case where the regulator provides incentives for agents to co-operate, or 'help' each other, to increase social welfare (see Itoh (1991)). Several cost reduction models, in particular those by Reinganum (1982), Levin and Reiss (1984) and Spence (1984) have considered how spillovers affect managerial incentives to engage in R&D. Spence, notably, finds that an increase in spillovers (or a decrease in 'appropriability') lessens the incentives of individual firms to invest in process R&D. If this is the case, then the presence of spillovers between companies regulated by yardstick competition is likely to
Regulation through comparativeperformance evaluation have an impact on the performance of such a regulatory scheme in maximising social welfare.
R&D spillovers and regulation in the water industry This section briefly considers the likely empirical significance of technological spillovers in the water industry by examining the pattern of R&D expenditure for the ten water and sewerage companies in the UK. Spillovers may also occur in many other ways, for example, the use of management consultants who advise on changing working practices, the implementation of efficient management structures, or on the use of best available technologies are possible vehicles for spillovers in cost reducing effort between water companies. Spillovers are normally considered in the context of R&D, therefore it is useful to begin with a description of some basic facts.
Levels of R&D expenditure Table 1 shows how levels of real expenditure in R&D have changed in the past decade in the ten UK water and sewerage companies (referred to as WaSCs hereafter). 7 It is clear that the amount of R&D has risen significantly over the five years since privatisation--companies spent an average of £1.3 million in real terms in 1989, which
had increased to an average of £2.8 million by 1994. Three companies: North West, Severn Trent and Thames have traditionally been the biggest investors in innovation and are currently spending over £7 million each per annum in today's prices.
Spillovers and patents Patent statistics are widely used as an indicator of the amount of innovative activity occurring in an industry 8. Table 2 shows the number of patent applications that have been made by the WaSCs during the period 1985-19959 . With only one exception, all of these water companies have increased the number of their patent applications in the period post privatisation compared to the pre-privatisation situation.
Evidence from the water industry Since the role of spillovers and regulation in the water industry is hard to detect purely from published statistics, interviews were conducted with R&D managers at leading water companies. The main aim of the interviews was to gauge the importance to companies of protecting their technological know-how from diffusing through the industry, and hence the potential significance of spillovers. The following points emerged from the discussion:
Table 1. Real Expenditure on R&D in theWater Industry1987-94 (£000s)
Anglian Northumbrian NorthWest Severn Trent Southern SouthWest Thames Welsh Wessex Yorkshire Industry
87
88
89
90
91
92
93
94
Total
2453
2526 374 2432 3181 842 374
1693 260 2431 1997 868 347
1507 159 1983 1983 793 238 3251 872 714 1665 13164
2247 1124 2472 3221 2322 225 5243 899 449 1873 20075
2094 1011 4116 4621 4188 722 5054 578 505 3610 26498
1848 1350 3838 5828 4264 853 5046 569 640 3554 27790
2845 2151 5413 5760 2984 1110 5135 694 555 1180 27828
17213 6429 25235 28900 17172 3869 27165 5174 2863 15584 149604
2552 2310 911 3435
1563 1178 12838
1310 11038
1215 10373
Source: UK R&D Scoreboard, Company Reposing Ltd, June 1994 and 1995 Repots. (All figures deflated by Retail Price Index, base 13 January 1987).
Table 2. Number of paten~ lodged by the Water Industry 1985-1995
Anglian South West Wessex Thames Severn Trent Yorkshire North West Northumbrian Welsh Southern Industry
85
86
87
88
89
90
91
92
93
94
95
1985-89
1990-95
Total
1 0 0 1 0 0 1 0 0 0 3
2 0 2 6 0 0 1 0 0 2 13
2 0 1 11 2 0 1 0 0 2 19
1 1 0 11 1 1 7 0 2 1
1 1 0 12 4 2 11 0 4 0
2 0 0 8 4 2 9 0 1 1
4 2 0 8 2 2 10 0 2 2
2 2 0 11 1 2 13 1 1 2
2 1 0 10 2 3 15 1 3 1
3 0 0 8 0 1 14 0 1 1
0 0 0 5 0 1 3 0 0 0
7 2 3 41 7 3 21 0 6 5
13 5 0 50 9 11 64 2 8 7
20 7 3 91 16 14 2 14 12
25
35
27
32
35
38
28
9
95
169
264
85
295
Regulation through comparative performance evaluation
1. Prior to privatisation, R&D was co-ordinated on an industry wide basis, and information on innovation was shared through the industry. 2. Immediately following privatisation, there was a reluctance among managers to continue sharing information or to work collaboratively. Individual companies focused on developing independent R&D programmes and so, for the first few years of regulation there was virtually no collaboration between companies in R&D. 3. There was a universal increase in individual companies' investment programmes and the number of patent applications. Comparative performance regulation did increase effort in cost reduction and companies did initially attempt to block any spillovers of their technological know-how. 4. Three or four years into the regulatory period, companies became aware that many of their in-house research programmes were being duplicated by rival companies. A view was taken, that in many areas which affect the industry collectively, collaborative research would cut costs and liberate funds that could be better spent on company-specific R&D projects. 5. Reverse engineering means that most technologies can be reproduced in the water industry. One manager said that protection [of intellectual property rights] is in place to ensure, at best, that [the company] maintains a six month lead in the marketing of a product or process either domestically or abroad. 6. The focus for R&D divisions appears to be to achieve significant cost savings in both operating expenditure and on capital programmes 'to beat the K contract' (meaning the price limit determined by OFWAT). Achieving this goal, as one manager proposed would boost profits, give a good return on investment and demonstrate that we are a good company, with a good combination of technology and management skills, which enhances our chances of winning contracts abroad. This view was echoed by the other manager, who said that meeting performance targets in the core utility reflected well on the international branch of the business. 7. There is currently an upward trend in the extent of collaboration between companies in the industry. This is confirmed by one company's manager, who divulged that it had recently formed an alliance with a neighbouring water company. This special relationship heralded a situation of near total co-operation in future engineering, billing, resource planning and R&D. This evidence clearly indicates that companies are aware of the presence of technological spillovers in the water industry, for example, reverse engineering enables one company to quickly copy any visibly innovative tech-
296
nique for cost reduction undertaken by another company. A separate, but related issue concerns the evidence of increasing collaboration in the extent of R&D which is likely to affect the structure of the optimal regulatory mechanism. However, for our present purposes, we are concerned with the impact of non-co-operative spillovers on comparative performance regulation. The next section reviews the implications for yardstick competition when spillovers exist.
Yardstick competition with spillovers In this section we consider the welfare implications of yardstick competition when there are spillovers. Following Shleifer, we consider a one period model with identical risk-neutral firms in an environment without uncertainty, but we restrict the analysis to the two firm case (without loss of generality). Each firm faces a downward sloping demand curve q ( p , ) = a - b p i (with a > b , b< 1) in its respective market. Firm i (similarly firm j) has an initial constant marginal cost ci which can be reduced through its own cost reducing effort R(e~)= (e ~/ 2), and through that of the other firm R(ej), where i ~ j . The extent to which the cost reducing effort of one firm spills over to the other firm is captured through the parameter ce, giving the cost function for each firm (equation ( 1a) ): ci= 1 - a ei - (1 - a)ej
(la)
similarly (equation (2a)), cj= 1 - cr ej - (1 - a)e i
(2a)
The parameter a represents the distribution of cost reduction efforts within the industry. The specification implies that a given level of effort achieves a unique degree of (marginal) cost reduction, whatever the value of a. Profits 7r for each firm are given by (equation (3a)) "17"i:(Pi -- ¢i)qi -- R(e,) + Ti
(3a)
Under yardstick competition, pi=cj, and T~=Rj thus demand for firm i is (equation (4a)) qi=a - bpi=a - bcj
(4a)
and firm i maximises (equation (5a)) e~
"Tri-~(C j - -
ci)qi- ~ + Ti
(5a)
Profit maximisation with respect to effort then implies (equation (6a)): 0"17i
Oqi
Oe-~ = - (1 - 2a)q~+ (1 - 2a)(ej - e~) ~e~ - ei=O
(6a)
and, rearranging to obtain an expression for the profit maximising level of effort hi, in terms of a (equation
Regulation through comparative performance evaluation (7a), equation (7a') and equation (7a")):
and equation (17a)
- (1 - 2c0[a - b(1 - ae s - (1 - o0e,)]
OSW
+(1 - 2a)(ej - ei).b(1 - a) - es=0
(7a)
- {a - b[1 - aei - (1 - a)e.i]}.a
Oei
= [1 +2b(1 - a)(1 - 2a)]ei
(7a')
ei = - (1 - 2 a ) [ a - b - (1 - 2a).bes] 1 +2b(1 - cOO - 2 a ) Simplifying equation ( 7 a ) - ( 7 a " ) following expression for Os (equation
(7a")
above gives the (8a)):
~,= 0, + 0zej
(8a)
rearranging, a [ a - b(1 - (1 - a)ej)] +(1 - c0 [a - b( 1 - aej)] = [1 - b(1 - 2a(1 - a))]e,
- (1 - 2 a ) ( a - b) -
a)(1
-
1 +2b(1 - a)(1 - 2ce)
(19a)
Simplifying this expression, we have (equation (20a))
2a)
(1 - 2ce)Z.b and 02=
(18a)
so, the welfare maximising level of effort e~* is given by equation (19a) a - b + 2bee(1 - a)ej ei*= 1 - b(ce2+(1 - o~) 2)
where (equation (9a, 10a),
1 +2b(1
ei
+ {a - b[1 - ae s - (1 - aei]}.(1 - ce)=0 (17a)
- (1 - 2 a ) [ a - b - (1 - 2a).bej]
01 =
-
el* = Yl + yzej (9a, 10a)
By symmetry, (from equation (8a)) 0r= 01 + Ozei, therefore (equation (11 a)) (lla)
ei = 01 + 02(01 + 02el)
(20a)
where, (equation (21a, 22a)), a-b % = 1 - b ( c e z + ( 1 - a) 2) 2bee(1 - ce) and y2 = 1 - b ( a 2 + ( 1 - ce) z)
(21a, 22a)
which gives (equation (12a))
01 Jr 01 02 ~=
1_/92
01
(12a)
- 1_02
By symmetry, (from 20a) e:*= % + y2ei, therefore (equation (23a))
Yl + "Yl'Y2 % - - -
(23a)
Substituting back for 01 and 02 from expressions (9a) and (10a) gives equation (14a):
es* = 1 - Y2
(24a)
( 2 a - 1)(a - b) ei=e~= l + b - 2 a b
Now, substituting back in for values of Yl and Y2 in equation (24a) we find that expressions for ei* and e:* reduce neatly to (equation (25a)):
and, therefore (equation (13a))
ei* = -
0, ~Y- 1
-
02
(13a)
(14a)
N o w we need to compare these expressions for effort with those that would obtain at the social optimum, that is under conditions o f perfect competition. Here prices equal marginal cost P~=G, therefore profits 7r~ are given by -(e/2/2), from equation (5a). Social welfare is represented by the sum of consumers' and producers' surpluses (equation (15a)): S W = C S i + ~ +CSj+ ~
(15a)
where for the linear demand curve CSi is given by (1)/(2b)[a - bpi]2=(1)/(2b)[a - bci] 2. Therefore, the maximisation problem for ei is (equation (16a)) 1
meaX S W = ~-b { a - b [ 1 - o~e;- (1 - o~)ej] } 2,
e~ 2
+2bl {a_b[l_aes_(l_oOei]}2_
2e~ (16a)
and (equation (24a))
a-b el* =ej* = 1 -- b
(25a)
This result means that the presence of spillovers has no effect on the level of effort in cost reducing R & D which obtains under the social optimum where welfare is maximised. That is, effort levels remain constant as a varies between 0 and 1. Intuitively, the cost reduction technology (equation (1 a) and equation (2a)) implies that effort always reduces the marginal cost by the same amount regardless of the value of ce. Therefore, the social planner requires a given level of effort from each firm but is indifferent as to the beneficiary of that effort. Now comparing ei and e~* we offer the following propositions: Proposition 1. Under yardstick competition all values of 0--
~i
for
297
Regulation through comparative performance evaluation Proof 1. e,* is independent of 4, as shown in equation (25a) 2. substituting for 4 = 1 (no spillovers) in equation (14a) and comparing with equation (25a) we obtain 0~=ei* 3. from equation (14a) if we differentiate 0, with respect to 4 we get (equation (26a)) 0~, 34
(a - b)(1 - b + 2 4 b ) > 0 for all values of 0 - < 4 < 1 (1 + b - 24b) 2 (26a)
Corollary. Yardstick competition will not achieve the first best when 0 - < a < 1. The intuition in this statement is straightforward. Yardstick competition rewards the firm for reducing its costs below that of its rival. When there are no spillovers, effort reduces the firms own costs only. However when spillovers exist, effort also reduces the rival firm's costs and therefore reduces the firm's own price. The incentive to invest in cost reduction therefore falls below the socially optimal level.
Each firm faces a downward sloping demand curve in its respective market
qi=a - bp,=a - bitch+ (1 - fl)ci]
(5b)
substituting in for c~ and cj we obtain equation (6b)
q~=a - b[1 - el+ (e~ - e i ) ( 2 4 f l - t -
a)]
(6b)
Firm i will want to maximise profits (equation (7b), equation (7b')) ~-i= (1 - 2a)(1 - fl)(ej - e~)qi- ~
(7b)
0~'i = (1 - 24)(1 - fl)(ej - e~)[(1 - 4 - t + 2aft)b] 0e~
- (1 - 2a)(1 - fl){a - b[1 - ei+(ej
-- ei)(24 t -
f l - 4)]} -- ei=O
(7b')
therefore, ei--
(1 - 24)(1 - fl)[ - a+b+bej - 2 b ( 4 + f l [1 - (1 - 24)(1 - f l ) 2 b ( a + f l -
24fl)ej]
1 - 24/3)1
(8b) As before, we let (equation (9b))
Optimal
comparative
performance
presence
of spillovers
regulation
in the (1 - 2 4 ) ( 1
We now consider a particular class of regulatory rules in which the firm's price is set as a linear combination of its rival's marginal cost and its own marginal cost. We have chosen this functional form to reflect the main element of OFWAT's hybrid price cap and yardstick scheme, namely that as well as the comparative performance evaluation undertaken during the last periodic review, a water c o m p a n y ' s own bid for funds was a large determinant of the final K factor set (see Table 2, p. 6 of
Future
Charges f o r
Water and Sewerage
Services,
OFWAT, 1994a). This therefore represents a departure from the theoretical yardstick in which prices are set exogenously to a firm's own costs, whilst preserving the basic notion of comparative performance regulation.
p,=/3c,+(1 - fl)c,
(lb)
This formulation (equation (lb)) includes yardstick competition (fl=0) and cost pass through regulation (/3=I) as special cases. The main restriction of this function is that prices are fixed only in relation to marginal costs. We continue to assume that T~=Rj. Recalling equation (la), (2a) and (3a), (equation (2b))
ci = 1 - 4e i - (1 - 4)ej
cj= 1 - o% - (1 - 4)e i
(9b)
and (equation (lOb)) A 2---~
(1 - 24)(1 - fl)b(1 - 2 4 - 2 f l + 4 4 f l ) [1 - (1 - 24)(1 - f l ) 2 b ( a + f l -
1 - 24/3)]
(10b)
~i=al+a2ej and by symmetry ~j=Al+A2ei therefore (equation (1 lb)) al ~i=
(llb)
1 -- A2
Substituting back for & and A2 (equation (12b)) ei =
(1 - 2c~)(1 - f l ) ( b - a) 1 +(1 - 24)(1
- fl)b
(12b)
Differentiating this expression with respect to /3 gives equation (13b)
sgn
[ Ooi ] ~ =sgn[(a-b)(1-24)]
(13b)
which means that (equation (14b))
<0,4>
1
OOi { @ =0,4= 1 (3b)
and profits ~ for each firm are given by equation (4b)
= (p~ - c,)q, - R(e,)
1 - 24fl)]
(2b)
similarly (equation (3b)),
298
- fl)(b - a)
al = [1 -- (1 -- 24)(1 -- f l ) 2 b ( a + f l -
(4b)
>O,a<
(14b)
1
Now we want an expression for the socially optimal level
Regulation through comparativeperformance evaluation of effort ~* which obtains under this type of regulatory regime. Social welfare is given by the sum of consumers' and producers' surplus. Recalling equation (6b) and from symmetry we know that (equation (14b))
qi=a
-
-
b[1
-
e,]
(14b')
and consumers' surplus is given by the expression ,)
CS.= q7 ' 2b
(15b)
Therefore total welfare SW is given by (equation (16b))
CSi[-q'l"i-l-CSj'b~l"J=
[a - b(1 - ~)] 2 b
~2
(16b)
Maximising with respect to/3 gives equation (17b)
OSW OF OF 0/3 =2(a - b) ~ +20(b - 1) 0~ =0
(17b)
Let 0* be the socially optimal level of effort, then 00 (a) from (14b), for a ~ , 0~ ~0, therefore
0.=
a-b - 1-b'
(18b)
from (17b) Note that the right-hand side of equation (18b) is the socially optimal level of effort derived in the previous section, which is both independent of a, and independent of /3. From equation (12b) we can write (equation (19b)) (1 - 2o0(1 -/3)(b - a) 1+(1 - 2a)(1 - / 3 ) b
-
a- b 1-b
(19b)
From inspection we can see that this requires (equation (20b)) 1
(1-2a)(1 -/3)=- 1 or/3,=1+ - 1 -2or
(20b)
Optimal regulation in this model always requires the same level of effort (which follows from the specification of the cost reduction technology), and so optimal regulation requires the adjustment of/3 to ensure that the optimal effort level is chosen. , 0F (b) for all ce=~, ~ =0 (from equation (14b)) and ~=0 (from equation (13b)) When a=½, investment in cost reduction by any one firm benefits both firms equally. Thus the notion of using comparative performance evaluation to provide incentives to invest breaks down completely, since no value of /3 can induce any effort in cost reduction. Intuitively, regulation based on comparative performance can only succeed when there is a potential for one firm to gain a relative advantage, m
Proposition 2. Five cases exist which characterise the relationship between the spillover technology ( a) and the optimal regulatory regime (/3*). (Refer to Figure 1): 1. When 02. In this case firm i's effort in cost reduction reduces its rival's marginal cost by more than its own, and so 13" is set so as to penalise firm i if firm j's costs are high. At the same time, firm i is allowed to pass on more than 100% of its own marginal costs. This is because firm i has very little influence over its own marginal costs, as they are largely determined by firmj's actions.
Graph of BETA for ALPHA between -1 and 2 30,
Figure
1. Graph of BETA for ALPHA between - 1 and 2.
299
Regulation through comparative performance evaluation 1
2. When ~ 1, 0
~
Ti,=\~-2b] +(a-b~ 1-a a-b
b-q*(p*,ei*,ej*), then, the first order condition for 1 the firm implies that the first best effort level is selected for any value of o~.1~This is a more complex scheme than the conventional comparative performance model being investigated here, and whilst theoretically attractive, is much less likely to be implemented in practice.
spread evenly across the industry. In drawing specific conclusions from our analysis for the current regulatory environment of the UK water industry, we must bear in mind that our simple model cannot capture some important aspects. The nature of the regulatory review, for example, means that prices are not reset immediately to take account of any achieved cost reductions but instead are readjusted some considerable time after the effect. Obviously, there are distinct benefits to firms which implement innovatory cost reducing measures, particularly when made early in the review period: firstly, due to the current five year regulatory lag, and secondly, because of the temporal effect in the diffusion and implementation of innovation between the companies. However, we have investigated a regulatory scheme, which although simplistic, does embody the main characteristics of the price capping formula currently employed by Ofwat. Therefore, the presence of spillovers along with the current climate of take-overs and mergers, and evidence of the trend towards increased collaboration between the water companies all have implications for the optimal comparative performance regime. We have concluded that when spillovers exist a pure yardstick scheme is inefficient, while in contrast, a pure price cap regime will achieve optimality. But this begs the question of how a pure price cap can be set in practice without some form of comparative performance evaluation. Future work will consider the issues for optimal comparative performance regulation with cost uncertainty, and co-operation in cost reducing effort between firms.
Discussion and conclusions
This paper has examined the notion of yardstick competition when cost reducing activity of firms takes the form of partially non-appropriable R&D. Proposition 2 shows that it is possible to design an optimal regulatory contract based on comparative performance evaluation. However, yardstick regulation (which is a special case of comparative performance regulation) is only optimal when there are no spillovers, while (marginal) cost pass through is only (asymptotically) optimal when the parameter a approaches infinity (a wildly implausible case). The most interesting cases are 1.-3., where 0_
300
We would like to thank Peter Boulding, Philip Burns, Nick Curtis, Bill Emery, Stewart Goodwin, Pat Green, Mark Hull, David Kennedy, Ben Lockwood, John Vickers and Tom Weyman-Jones for their comments on an earlier draft. tThe 1986 White Paper on Privatisation of the Water Authorities in England and Wales states [T]he regulatory system will enable the comparison of performance to be made between the WSPLCs, and this will both act as an impetus to improvement and - by providing a yardstick to investors to make judgements - facilitate competition between the WSPLCs on the capital market. Section 4 Section 4, para. 56. 2The Periodic Review process began in July 1991, and culminated in the final determination of price limits announced in July 1994. 3Due to Ciaran Driver. 4published as Research Papers 2, 3, and 4 by Ofwat (1994). 5Unless the regulator can credibly threaten to make inefficient firms lose money (or, alternatively, can prove in court that firms chose to be inefficient and that their practices were imprudent), cost reduction cannot be enforced. Shleifer (1985) 6A recent working paper by Dalen (1997), analyses how firms investment incentives are affected by yardstick competition in a dynamic setting. Spillovers are mentioned in two senses. Firstly, for investment made in network industries that is industry-specific, spillovers are regarded as complete; secondly, for investment which is firm-specific it is assumed that no spillovers exist.
Regulation through comparative performance evaluation 7Source: UK R&D Scoreboard, Company Reporting Ltd, June 1995 and 1994 reports. These figures should be treated with care however, since there is not necessarily a consistent reporting base across the industry. 8Foran analysisof patent statistics as economicindicatorssee Griliches (1990). 9The data for 1995 is incomplete. t°Even though in the symmetric equilibrium both firms achieve the same profits. ~We are grateful to Ben Lockwood for this comment.
References Baron, D. P. and Myerson, R. (1982) Regulating a Monopolist with Unknown Costs. Econometrica 50, 911-930. Braetigam, R. and Panzar, J. (1993) Diversification Incentives under "Price-based' and 'Cost-based' Regulation. Rand Journal of Economics 20(3), 373-391. Bums, P., Turvey, R. and Weyman-Jones, T. (1995) General Properties of Sliding Scale Regulation. CRI Technical Paper 3. Dalen, D. (1997) Yardstick Competition and Investment Incentives. Working Paper. Department of Economics University of Oslo. Demski, J. and Sappington, D. (1984) Optimal Incentive Contracts with Multiple Agents. Journal of Economic Theory 33, 152-171. Department, of the Environment (1986) Privatisation of the Water Authorities in England and Wales. HMSO London Cmnd 9734. Glaister, S. (1987) Regulation Through Output Related Profit Tax. The Journal of Industrial Economics 35(3), 281-296. Griliches, Z. (1990) Patent Statistics as Economic Indicators: A Survey. Journal of Economic Literature 28(December), 1661-1707. Holmstrom, B. and Milgrom, P. (1990) Regulating Trade Among Agents. Journal of Institutional and Theoretical Economics 146, 85-105. Itoh, H. (1990) Incentives to Help in Multi-Agent Situations. Econometrica 59, 611-636. Laffont, J.-J. and Tirole, J. (1986) Using Cost Observations to Regulate Firms. Journal of Political Economy 94, 614-641. Levin, R. and Reiss, P. (1989) Cost Reducing and Demand
Creating R&D with Spillovers. Rand Journal Of Economics 19(4), 538-556. Littlechild, S. (1986) Economic Regulation of Privatised Water Authorities.. A report submitted to the Department of the Environment. HMSO London. Lockwood, B. (1995) Multifirm Regulation Without LumpSum Transfers. Journal of Public Economics 56, 31-53. Mayer, C. and Vickers, J. (1995) Price Caps and Profit Sharing: a Review of the Options for Regulated Industries. Brunel University Mimeo. Meyer, M. and Vickers, J. (1994) Performance Comparisons and Dynamic Incentives. Discussion Paper No. 96. Nuffield College Oxford. Powell, K. (1995) The Role of 'Yardstick Competition' in Ofwat's Periodic Review of Price Caps Working paper, Imperial College Management School, London. Reinganum, J. (1982) A Dynamic Game of R&D, Patent Protection and Competitive Behaviour. Econometrica 50(3), 671-688. Sappington, D. and Sibley, D. (1988) Regulating without Cost Information: The Incremental Surplus Subsidy Scheme. International Economic Review 29(2), 297-306. Schmalensee, R. (1989) Good Regulatory Regimes. Rand Journal of Economics 20(3), 417-436. Shleifer, A. (1985) A Theory of Yardstick Competition. Rand Journal of Economics 16, 316-327. Sibley, D. (1989) Asymmetric Information, Incentives and Price Cap Regulation. Rand Journal of Economics 20(3), 392-404. Spence, M. (1984) Cost Reduction, Competition and Industry Performance. Econometrica 52(January), 101-121. Stewart, M (1994) Office of Water Services Research Paper Number 2: Modelling Water Costs 1992-1993, prepared for Ofwat by Professor Mark Stewart. University of Warwick Warwick. Stewart, M (1994) Office of Water Services Research Paper Number 4: Modelling Sewage Treatment Costs 1992-1993, prepared for Ofwat by Professor Mark Stewart. University of Warwick Warwick. Stewart, M (1994) Office of Water Services - Future Charges for Water and Sewerage Services: The Outcome of the Periodic Review. OFWAT Birmingham.
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© 1997 ElsevierScience Ltd. All rights reserved Printed in Great Britain 0957-1787/97 $17.00+ 0.00
Regulation through comparative performance evaluation Kirsty Powell* and Stefan Szymanskit Ofwat used comparative performance regulation in the 1994 periodic review of prices. We consider such a regulatory mechanism when there are technological spillovers. The regulator cannot observe firms effort and must design a regulatory contract which induces the socially optimal level of cost reduction. The extent to which cost reducing activities are non-appropriable is shown to affect the optimal choice of regulation. In general, comparative performance regulation is optimal and yardstick competition emerges only as a special case. However, when spillovers are spread evenly across an industry, an optimal comparative regime does not exist. © 1997 Elsevier Science Ltd. All rights reserved Keywords:regulation; spillovers;yardstickcompetition Introduction
Dissatisfaction with the traditional cost of service regulation has generated enormous interest in the design of regulatory mechanisms in recent years, at both a practical and theoretical level. Attention in the literature has focused on theoretically optimal solutions to specific problems, usually involving information constraints. For examples see Baron and Myerson (1982), Demski and Sappington (1984), Laffont and Tirole (1986), Schmalansee (1989), Sibley (1989), Holmstrom and Milgrom (1990), and Lockwood (1995). A variety of practical regulatory mechanisms and their implications for welfare have also been presented. For example, Glaister (1987) illustrates regulation through an output related profit tax, Sappington and Sibley (1988) introduce the notion of an incremental surplus subsidy, Braetigam and Panzar (1993) examine the impact of changing from rate of return to price cap regulation, while analysis of the The authors are with the Management School, Imperial College of
Science, Technologyand Medicine, 53 Prince's Gate, Exhibition Road, London, SW7 2PG, UK. * Tel: 0171 594 9144, Fax: 0171 823 7685, e-mail: [email protected] t Tel: 0171 594 9107, Fax: 0171 823 7685, email: [email protected]
properties of price caps and sliding scale (or profit sharing) regulation has been presented by Burns et al. (1995) and Mayer and Vickers (1995). One of the more important theoretical insights, referred to as yardstick competition, is due to Shleifer (1985) who proposed that regulating a firm's price by setting it equal to some function of the realised cost of similar firms in its industry can produce socially efficient outcomes. This idea was adopted during the privatisation process and in the development of the regulatory regime for the water industry. ~ The Office of Water Services (OFWAT), the economic regulator of the UK water industry, refer to yardstick competition as comparative performance evaluation. A type of comparative performance analysis was used during the price cap setting process at the first full review of prices since privatisation in 1989. 2 Essentially, price caps for individual firms for the next ten years were set on the basis of comparative efficiency analysis in both operating and capital expenditure. This method of setting price determinations largely on the basis of historical costs is different from the theoretical yardstick scheme in that the regulatory contract is based on ex ante cost realisations rather than ex post cost realisations. Nonetheless, the underlying principle of this hybrid price cap and yardstick regime is regulation through comparative performance evaluation. This paper develops a simple model of regulation through comparative performance evaluation. The price function employed allows the regulator to set a firm's price based on a combination of its own efficiency submissions and on a judgement of the relative efficiency of its rival firms, which closely mirrors Ofwat's price setting methodology. The key insight of the paper 3 is that the optimal form of regulation depends on the extent to which the benefits of cost reducing activities, such as R&D, are appropriable by the firm, and the extent to which they 'spillover' to other firms. In general, we show that comparative performance regulation is optimal, while yardstick competition in the sense of Shleifer (1985), emerges as a special case. We also show that where the benefits of cost reducing activities accrue 293
Regulation through comparativeperformance evaluation equally to all members of the industry, an optimal comparative regime does not exist. The paper is set out as follows: Section 2 explains the notions of yardstick competition, and spillovers in the context of the UK water industry. Section 3, presents some evidence on R&D issues in the water industry. In Section 4, following Shleifer, we show that pure yardstick regulation is inefficient in the presence of spillovers. In Section 5, a formula for optimal comparative performance regulation is derived, followed by a discussion in the final section, Section 6, and some concluding remarks.
Yardstick competition and the water industry During the water privatisation process of 1989, the applicability of price cap regulation or more specifically RPI_+K was analysed. This price cap formula limits allowable price increases to the previous year's retail price index, plus or minus a factor ' K ' , which accounts for companies anticipated efficiency savings, and also for predicted changes in levels of investment and operating costs. In his 1986 report on privatisation and regulation of the water industry, Stephen Littlechild recommended that regulation would need to be permanent; covering quality as well as price. Flotation of the ten existing authorities meant that they were to compete as successor companies in the capital market for funds. The operation of a take-over mechanism would therefore force the companies to strive for improved efficiency. Comparisons between companies of quality and price performance would also be facilitated by the regulator. Periodic revisions of the price cap would be necessary to avoid allocative inefficiency caused by the cumulative deviation of price from marginal cost over long periods. It was recommended that the K factor should be revised according to an industry yardstick to avoid any one company exerting an influence over its own price constraint. Yardstick competition is a mechanism for the economic regulation of spatially differentiated monopoly firms operating in the same industry. The price cap set for each firm depends on the costs of the other (identical) firms. Shleifer (1985) provided a model where, in equilibrium, each firm chooses a socially efficient level of cost reduction. This mechanism also generalises to the case of heterogeneous firms with observable differences which characterises the composition of companies within the UK water industry. The correction for heterogeneity amounts to a regression of costs on properties that determine diversity. During the periodic review of prices in 1994, OFWAT sought to make comparisons of companies' operating costs taking into account explanatory factors arising from their individual circumstances, in order to increase the accuracy of identifying relative
294
company efficiency. Econometric models of water costs, sewerage costs and sewage treatment costs were developed by Professor Mark Stewart of the University of Warwick. 4 Results from the Ordinary Least Squares regressions showed wide variations in companies' costs which could be accounted for by the wide variations in their operating conditions. Therefore, the magnitude of the residual or 'unexplained' differences in costs were attributed to a company's efficiency relative to the average. By comparing similar regulated firms with each other, Shleifer demonstrates, that a firm's attainable cost level can be determined. This forces firms serving different markets effectively to compete. For instance, if a firm reduces its costs, and its 'competitors' do not, it profits; if the other firms reduce their costs, and one firm fails to follow suit, then that firm will incur losses. The model assumes that cost reducing effort cannot be observed by the regulator. However, accounting data provides sufficient information to achieve efficiency. Without knowing the cost of cost reduction, the regulator must use the profit motive of the firms' managers to encourage them to reduce costs. The regulator wishes to maximise the sum of consumers' and producers' surplus. Prices and lump-sum transfers are the instruments available to achieve this aim initially. They are set according to a shadow firm with a cost level and cost reduction level defined as the mean of that of all other firms. Shleifer shows that by setting price and the transfer using this shadow firm, a unique Nash equilibrium, is for each firm to pick a socially efficient level of costs. Yardstick competition works by not allowing an inefficient firm to influence the price and transfer that it receives. It will deliver the first best, in Shleifer's model as long as the regulator shows a commitment to allowing an inefficient firm to go bankrupt. 5 The possible effects of 'technological spillovers' on the capacity of yardstick (or comparative) competition to achieve the 'first best' outcome is not mentioned in the Shleifer model and has received little attention in related literature, except for Dalen (1997). 6 Spillovers occur when the benefits of cost reducing (or demand creating) R&D are imperfectly appropriable. We concentrate attention on non-co-operative spillovers, as distinct from the case where the regulator provides incentives for agents to co-operate, or 'help' each other, to increase social welfare (see Itoh (1991)). Several cost reduction models, in particular those by Reinganum (1982), Levin and Reiss (1984) and Spence (1984) have considered how spillovers affect managerial incentives to engage in R&D. Spence, notably, finds that an increase in spillovers (or a decrease in 'appropriability') lessens the incentives of individual firms to invest in process R&D. If this is the case, then the presence of spillovers between companies regulated by yardstick competition is likely to
Regulation through comparativeperformance evaluation have an impact on the performance of such a regulatory scheme in maximising social welfare.
R&D spillovers and regulation in the water industry This section briefly considers the likely empirical significance of technological spillovers in the water industry by examining the pattern of R&D expenditure for the ten water and sewerage companies in the UK. Spillovers may also occur in many other ways, for example, the use of management consultants who advise on changing working practices, the implementation of efficient management structures, or on the use of best available technologies are possible vehicles for spillovers in cost reducing effort between water companies. Spillovers are normally considered in the context of R&D, therefore it is useful to begin with a description of some basic facts.
Levels of R&D expenditure Table 1 shows how levels of real expenditure in R&D have changed in the past decade in the ten UK water and sewerage companies (referred to as WaSCs hereafter). 7 It is clear that the amount of R&D has risen significantly over the five years since privatisation--companies spent an average of £1.3 million in real terms in 1989, which
had increased to an average of £2.8 million by 1994. Three companies: North West, Severn Trent and Thames have traditionally been the biggest investors in innovation and are currently spending over £7 million each per annum in today's prices.
Spillovers and patents Patent statistics are widely used as an indicator of the amount of innovative activity occurring in an industry 8. Table 2 shows the number of patent applications that have been made by the WaSCs during the period 1985-19959 . With only one exception, all of these water companies have increased the number of their patent applications in the period post privatisation compared to the pre-privatisation situation.
Evidence from the water industry Since the role of spillovers and regulation in the water industry is hard to detect purely from published statistics, interviews were conducted with R&D managers at leading water companies. The main aim of the interviews was to gauge the importance to companies of protecting their technological know-how from diffusing through the industry, and hence the potential significance of spillovers. The following points emerged from the discussion:
Table 1. Real Expenditure on R&D in theWater Industry1987-94 (£000s)
Anglian Northumbrian NorthWest Severn Trent Southern SouthWest Thames Welsh Wessex Yorkshire Industry
87
88
89
90
91
92
93
94
Total
2453
2526 374 2432 3181 842 374
1693 260 2431 1997 868 347
1507 159 1983 1983 793 238 3251 872 714 1665 13164
2247 1124 2472 3221 2322 225 5243 899 449 1873 20075
2094 1011 4116 4621 4188 722 5054 578 505 3610 26498
1848 1350 3838 5828 4264 853 5046 569 640 3554 27790
2845 2151 5413 5760 2984 1110 5135 694 555 1180 27828
17213 6429 25235 28900 17172 3869 27165 5174 2863 15584 149604
2552 2310 911 3435
1563 1178 12838
1310 11038
1215 10373
Source: UK R&D Scoreboard, Company Reposing Ltd, June 1994 and 1995 Repots. (All figures deflated by Retail Price Index, base 13 January 1987).
Table 2. Number of paten~ lodged by the Water Industry 1985-1995
Anglian South West Wessex Thames Severn Trent Yorkshire North West Northumbrian Welsh Southern Industry
85
86
87
88
89
90
91
92
93
94
95
1985-89
1990-95
Total
1 0 0 1 0 0 1 0 0 0 3
2 0 2 6 0 0 1 0 0 2 13
2 0 1 11 2 0 1 0 0 2 19
1 1 0 11 1 1 7 0 2 1
1 1 0 12 4 2 11 0 4 0
2 0 0 8 4 2 9 0 1 1
4 2 0 8 2 2 10 0 2 2
2 2 0 11 1 2 13 1 1 2
2 1 0 10 2 3 15 1 3 1
3 0 0 8 0 1 14 0 1 1
0 0 0 5 0 1 3 0 0 0
7 2 3 41 7 3 21 0 6 5
13 5 0 50 9 11 64 2 8 7
20 7 3 91 16 14 2 14 12
25
35
27
32
35
38
28
9
95
169
264
85
295
Regulation through comparative performance evaluation
1. Prior to privatisation, R&D was co-ordinated on an industry wide basis, and information on innovation was shared through the industry. 2. Immediately following privatisation, there was a reluctance among managers to continue sharing information or to work collaboratively. Individual companies focused on developing independent R&D programmes and so, for the first few years of regulation there was virtually no collaboration between companies in R&D. 3. There was a universal increase in individual companies' investment programmes and the number of patent applications. Comparative performance regulation did increase effort in cost reduction and companies did initially attempt to block any spillovers of their technological know-how. 4. Three or four years into the regulatory period, companies became aware that many of their in-house research programmes were being duplicated by rival companies. A view was taken, that in many areas which affect the industry collectively, collaborative research would cut costs and liberate funds that could be better spent on company-specific R&D projects. 5. Reverse engineering means that most technologies can be reproduced in the water industry. One manager said that protection [of intellectual property rights] is in place to ensure, at best, that [the company] maintains a six month lead in the marketing of a product or process either domestically or abroad. 6. The focus for R&D divisions appears to be to achieve significant cost savings in both operating expenditure and on capital programmes 'to beat the K contract' (meaning the price limit determined by OFWAT). Achieving this goal, as one manager proposed would boost profits, give a good return on investment and demonstrate that we are a good company, with a good combination of technology and management skills, which enhances our chances of winning contracts abroad. This view was echoed by the other manager, who said that meeting performance targets in the core utility reflected well on the international branch of the business. 7. There is currently an upward trend in the extent of collaboration between companies in the industry. This is confirmed by one company's manager, who divulged that it had recently formed an alliance with a neighbouring water company. This special relationship heralded a situation of near total co-operation in future engineering, billing, resource planning and R&D. This evidence clearly indicates that companies are aware of the presence of technological spillovers in the water industry, for example, reverse engineering enables one company to quickly copy any visibly innovative tech-
296
nique for cost reduction undertaken by another company. A separate, but related issue concerns the evidence of increasing collaboration in the extent of R&D which is likely to affect the structure of the optimal regulatory mechanism. However, for our present purposes, we are concerned with the impact of non-co-operative spillovers on comparative performance regulation. The next section reviews the implications for yardstick competition when spillovers exist.
Yardstick competition with spillovers In this section we consider the welfare implications of yardstick competition when there are spillovers. Following Shleifer, we consider a one period model with identical risk-neutral firms in an environment without uncertainty, but we restrict the analysis to the two firm case (without loss of generality). Each firm faces a downward sloping demand curve q ( p , ) = a - b p i (with a > b , b< 1) in its respective market. Firm i (similarly firm j) has an initial constant marginal cost ci which can be reduced through its own cost reducing effort R(e~)= (e ~/ 2), and through that of the other firm R(ej), where i ~ j . The extent to which the cost reducing effort of one firm spills over to the other firm is captured through the parameter ce, giving the cost function for each firm (equation ( 1a) ): ci= 1 - a ei - (1 - a)ej
(la)
similarly (equation (2a)), cj= 1 - cr ej - (1 - a)e i
(2a)
The parameter a represents the distribution of cost reduction efforts within the industry. The specification implies that a given level of effort achieves a unique degree of (marginal) cost reduction, whatever the value of a. Profits 7r for each firm are given by (equation (3a)) "17"i:(Pi -- ¢i)qi -- R(e,) + Ti
(3a)
Under yardstick competition, pi=cj, and T~=Rj thus demand for firm i is (equation (4a)) qi=a - bpi=a - bcj
(4a)
and firm i maximises (equation (5a)) e~
"Tri-~(C j - -
ci)qi- ~ + Ti
(5a)
Profit maximisation with respect to effort then implies (equation (6a)): 0"17i
Oqi
Oe-~ = - (1 - 2a)q~+ (1 - 2a)(ej - e~) ~e~ - ei=O
(6a)
and, rearranging to obtain an expression for the profit maximising level of effort hi, in terms of a (equation
Regulation through comparative performance evaluation (7a), equation (7a') and equation (7a")):
and equation (17a)
- (1 - 2c0[a - b(1 - ae s - (1 - o0e,)]
OSW
+(1 - 2a)(ej - ei).b(1 - a) - es=0
(7a)
- {a - b[1 - aei - (1 - a)e.i]}.a
Oei
= [1 +2b(1 - a)(1 - 2a)]ei
(7a')
ei = - (1 - 2 a ) [ a - b - (1 - 2a).bes] 1 +2b(1 - cOO - 2 a ) Simplifying equation ( 7 a ) - ( 7 a " ) following expression for Os (equation
(7a")
above gives the (8a)):
~,= 0, + 0zej
(8a)
rearranging, a [ a - b(1 - (1 - a)ej)] +(1 - c0 [a - b( 1 - aej)] = [1 - b(1 - 2a(1 - a))]e,
- (1 - 2 a ) ( a - b) -
a)(1
-
1 +2b(1 - a)(1 - 2ce)
(19a)
Simplifying this expression, we have (equation (20a))
2a)
(1 - 2ce)Z.b and 02=
(18a)
so, the welfare maximising level of effort e~* is given by equation (19a) a - b + 2bee(1 - a)ej ei*= 1 - b(ce2+(1 - o~) 2)
where (equation (9a, 10a),
1 +2b(1
ei
+ {a - b[1 - ae s - (1 - aei]}.(1 - ce)=0 (17a)
- (1 - 2 a ) [ a - b - (1 - 2a).bej]
01 =
-
el* = Yl + yzej (9a, 10a)
By symmetry, (from equation (8a)) 0r= 01 + Ozei, therefore (equation (11 a)) (lla)
ei = 01 + 02(01 + 02el)
(20a)
where, (equation (21a, 22a)), a-b % = 1 - b ( c e z + ( 1 - a) 2) 2bee(1 - ce) and y2 = 1 - b ( a 2 + ( 1 - ce) z)
(21a, 22a)
which gives (equation (12a))
01 Jr 01 02 ~=
1_/92
01
(12a)
- 1_02
By symmetry, (from 20a) e:*= % + y2ei, therefore (equation (23a))
Yl + "Yl'Y2 % - - -
(23a)
Substituting back for 01 and 02 from expressions (9a) and (10a) gives equation (14a):
es* = 1 - Y2
(24a)
( 2 a - 1)(a - b) ei=e~= l + b - 2 a b
Now, substituting back in for values of Yl and Y2 in equation (24a) we find that expressions for ei* and e:* reduce neatly to (equation (25a)):
and, therefore (equation (13a))
ei* = -
0, ~Y- 1
-
02
(13a)
(14a)
N o w we need to compare these expressions for effort with those that would obtain at the social optimum, that is under conditions o f perfect competition. Here prices equal marginal cost P~=G, therefore profits 7r~ are given by -(e/2/2), from equation (5a). Social welfare is represented by the sum of consumers' and producers' surpluses (equation (15a)): S W = C S i + ~ +CSj+ ~
(15a)
where for the linear demand curve CSi is given by (1)/(2b)[a - bpi]2=(1)/(2b)[a - bci] 2. Therefore, the maximisation problem for ei is (equation (16a)) 1
meaX S W = ~-b { a - b [ 1 - o~e;- (1 - o~)ej] } 2,
e~ 2
+2bl {a_b[l_aes_(l_oOei]}2_
2e~ (16a)
and (equation (24a))
a-b el* =ej* = 1 -- b
(25a)
This result means that the presence of spillovers has no effect on the level of effort in cost reducing R & D which obtains under the social optimum where welfare is maximised. That is, effort levels remain constant as a varies between 0 and 1. Intuitively, the cost reduction technology (equation (1 a) and equation (2a)) implies that effort always reduces the marginal cost by the same amount regardless of the value of ce. Therefore, the social planner requires a given level of effort from each firm but is indifferent as to the beneficiary of that effort. Now comparing ei and e~* we offer the following propositions: Proposition 1. Under yardstick competition all values of 0--
~i
for
297
Regulation through comparative performance evaluation Proof 1. e,* is independent of 4, as shown in equation (25a) 2. substituting for 4 = 1 (no spillovers) in equation (14a) and comparing with equation (25a) we obtain 0~=ei* 3. from equation (14a) if we differentiate 0, with respect to 4 we get (equation (26a)) 0~, 34
(a - b)(1 - b + 2 4 b ) > 0 for all values of 0 - < 4 < 1 (1 + b - 24b) 2 (26a)
Corollary. Yardstick competition will not achieve the first best when 0 - < a < 1. The intuition in this statement is straightforward. Yardstick competition rewards the firm for reducing its costs below that of its rival. When there are no spillovers, effort reduces the firms own costs only. However when spillovers exist, effort also reduces the rival firm's costs and therefore reduces the firm's own price. The incentive to invest in cost reduction therefore falls below the socially optimal level.
Each firm faces a downward sloping demand curve in its respective market
qi=a - bp,=a - bitch+ (1 - fl)ci]
(5b)
substituting in for c~ and cj we obtain equation (6b)
q~=a - b[1 - el+ (e~ - e i ) ( 2 4 f l - t -
a)]
(6b)
Firm i will want to maximise profits (equation (7b), equation (7b')) ~-i= (1 - 2a)(1 - fl)(ej - e~)qi- ~
(7b)
0~'i = (1 - 24)(1 - fl)(ej - e~)[(1 - 4 - t + 2aft)b] 0e~
- (1 - 2a)(1 - fl){a - b[1 - ei+(ej
-- ei)(24 t -
f l - 4)]} -- ei=O
(7b')
therefore, ei--
(1 - 24)(1 - fl)[ - a+b+bej - 2 b ( 4 + f l [1 - (1 - 24)(1 - f l ) 2 b ( a + f l -
24fl)ej]
1 - 24/3)1
(8b) As before, we let (equation (9b))
Optimal
comparative
performance
presence
of spillovers
regulation
in the (1 - 2 4 ) ( 1
We now consider a particular class of regulatory rules in which the firm's price is set as a linear combination of its rival's marginal cost and its own marginal cost. We have chosen this functional form to reflect the main element of OFWAT's hybrid price cap and yardstick scheme, namely that as well as the comparative performance evaluation undertaken during the last periodic review, a water c o m p a n y ' s own bid for funds was a large determinant of the final K factor set (see Table 2, p. 6 of
Future
Charges f o r
Water and Sewerage
Services,
OFWAT, 1994a). This therefore represents a departure from the theoretical yardstick in which prices are set exogenously to a firm's own costs, whilst preserving the basic notion of comparative performance regulation.
p,=/3c,+(1 - fl)c,
(lb)
This formulation (equation (lb)) includes yardstick competition (fl=0) and cost pass through regulation (/3=I) as special cases. The main restriction of this function is that prices are fixed only in relation to marginal costs. We continue to assume that T~=Rj. Recalling equation (la), (2a) and (3a), (equation (2b))
ci = 1 - 4e i - (1 - 4)ej
cj= 1 - o% - (1 - 4)e i
(9b)
and (equation (lOb)) A 2---~
(1 - 24)(1 - fl)b(1 - 2 4 - 2 f l + 4 4 f l ) [1 - (1 - 24)(1 - f l ) 2 b ( a + f l -
1 - 24/3)]
(10b)
~i=al+a2ej and by symmetry ~j=Al+A2ei therefore (equation (1 lb)) al ~i=
(llb)
1 -- A2
Substituting back for & and A2 (equation (12b)) ei =
(1 - 2c~)(1 - f l ) ( b - a) 1 +(1 - 24)(1
- fl)b
(12b)
Differentiating this expression with respect to /3 gives equation (13b)
sgn
[ Ooi ] ~ =sgn[(a-b)(1-24)]
(13b)
which means that (equation (14b))
<0,4>
1
OOi { @ =0,4= 1 (3b)
and profits ~ for each firm are given by equation (4b)
= (p~ - c,)q, - R(e,)
1 - 24fl)]
(2b)
similarly (equation (3b)),
298
- fl)(b - a)
al = [1 -- (1 -- 24)(1 -- f l ) 2 b ( a + f l -
(4b)
>O,a<
(14b)
1
Now we want an expression for the socially optimal level
Regulation through comparativeperformance evaluation of effort ~* which obtains under this type of regulatory regime. Social welfare is given by the sum of consumers' and producers' surplus. Recalling equation (6b) and from symmetry we know that (equation (14b))
qi=a
-
-
b[1
-
e,]
(14b')
and consumers' surplus is given by the expression ,)
CS.= q7 ' 2b
(15b)
Therefore total welfare SW is given by (equation (16b))
CSi[-q'l"i-l-CSj'b~l"J=
[a - b(1 - ~)] 2 b
~2
(16b)
Maximising with respect to/3 gives equation (17b)
OSW OF OF 0/3 =2(a - b) ~ +20(b - 1) 0~ =0
(17b)
Let 0* be the socially optimal level of effort, then 00 (a) from (14b), for a ~ , 0~ ~0, therefore
0.=
a-b - 1-b'
(18b)
from (17b) Note that the right-hand side of equation (18b) is the socially optimal level of effort derived in the previous section, which is both independent of a, and independent of /3. From equation (12b) we can write (equation (19b)) (1 - 2o0(1 -/3)(b - a) 1+(1 - 2a)(1 - / 3 ) b
-
a- b 1-b
(19b)
From inspection we can see that this requires (equation (20b)) 1
(1-2a)(1 -/3)=- 1 or/3,=1+ - 1 -2or
(20b)
Optimal regulation in this model always requires the same level of effort (which follows from the specification of the cost reduction technology), and so optimal regulation requires the adjustment of/3 to ensure that the optimal effort level is chosen. , 0F (b) for all ce=~, ~ =0 (from equation (14b)) and ~=0 (from equation (13b)) When a=½, investment in cost reduction by any one firm benefits both firms equally. Thus the notion of using comparative performance evaluation to provide incentives to invest breaks down completely, since no value of /3 can induce any effort in cost reduction. Intuitively, regulation based on comparative performance can only succeed when there is a potential for one firm to gain a relative advantage, m
Proposition 2. Five cases exist which characterise the relationship between the spillover technology ( a) and the optimal regulatory regime (/3*). (Refer to Figure 1): 1. When 0
Graph of BETA for ALPHA between -1 and 2 30,
Figure
1. Graph of BETA for ALPHA between - 1 and 2.
299
Regulation through comparative performance evaluation 1
2. When ~
~
Ti,=\~-2b] +(a-b~ 1-a a-b
b-q*(p*,ei*,ej*), then, the first order condition for 1 the firm implies that the first best effort level is selected for any value of o~.1~This is a more complex scheme than the conventional comparative performance model being investigated here, and whilst theoretically attractive, is much less likely to be implemented in practice.
spread evenly across the industry. In drawing specific conclusions from our analysis for the current regulatory environment of the UK water industry, we must bear in mind that our simple model cannot capture some important aspects. The nature of the regulatory review, for example, means that prices are not reset immediately to take account of any achieved cost reductions but instead are readjusted some considerable time after the effect. Obviously, there are distinct benefits to firms which implement innovatory cost reducing measures, particularly when made early in the review period: firstly, due to the current five year regulatory lag, and secondly, because of the temporal effect in the diffusion and implementation of innovation between the companies. However, we have investigated a regulatory scheme, which although simplistic, does embody the main characteristics of the price capping formula currently employed by Ofwat. Therefore, the presence of spillovers along with the current climate of take-overs and mergers, and evidence of the trend towards increased collaboration between the water companies all have implications for the optimal comparative performance regime. We have concluded that when spillovers exist a pure yardstick scheme is inefficient, while in contrast, a pure price cap regime will achieve optimality. But this begs the question of how a pure price cap can be set in practice without some form of comparative performance evaluation. Future work will consider the issues for optimal comparative performance regulation with cost uncertainty, and co-operation in cost reducing effort between firms.
Discussion and conclusions
This paper has examined the notion of yardstick competition when cost reducing activity of firms takes the form of partially non-appropriable R&D. Proposition 2 shows that it is possible to design an optimal regulatory contract based on comparative performance evaluation. However, yardstick regulation (which is a special case of comparative performance regulation) is only optimal when there are no spillovers, while (marginal) cost pass through is only (asymptotically) optimal when the parameter a approaches infinity (a wildly implausible case). The most interesting cases are 1.-3., where 0_
300
We would like to thank Peter Boulding, Philip Burns, Nick Curtis, Bill Emery, Stewart Goodwin, Pat Green, Mark Hull, David Kennedy, Ben Lockwood, John Vickers and Tom Weyman-Jones for their comments on an earlier draft. tThe 1986 White Paper on Privatisation of the Water Authorities in England and Wales states [T]he regulatory system will enable the comparison of performance to be made between the WSPLCs, and this will both act as an impetus to improvement and - by providing a yardstick to investors to make judgements - facilitate competition between the WSPLCs on the capital market. Section 4 Section 4, para. 56. 2The Periodic Review process began in July 1991, and culminated in the final determination of price limits announced in July 1994. 3Due to Ciaran Driver. 4published as Research Papers 2, 3, and 4 by Ofwat (1994). 5Unless the regulator can credibly threaten to make inefficient firms lose money (or, alternatively, can prove in court that firms chose to be inefficient and that their practices were imprudent), cost reduction cannot be enforced. Shleifer (1985) 6A recent working paper by Dalen (1997), analyses how firms investment incentives are affected by yardstick competition in a dynamic setting. Spillovers are mentioned in two senses. Firstly, for investment made in network industries that is industry-specific, spillovers are regarded as complete; secondly, for investment which is firm-specific it is assumed that no spillovers exist.
Regulation through comparative performance evaluation 7Source: UK R&D Scoreboard, Company Reporting Ltd, June 1995 and 1994 reports. These figures should be treated with care however, since there is not necessarily a consistent reporting base across the industry. 8Foran analysisof patent statistics as economicindicatorssee Griliches (1990). 9The data for 1995 is incomplete. t°Even though in the symmetric equilibrium both firms achieve the same profits. ~We are grateful to Ben Lockwood for this comment.
References Baron, D. P. and Myerson, R. (1982) Regulating a Monopolist with Unknown Costs. Econometrica 50, 911-930. Braetigam, R. and Panzar, J. (1993) Diversification Incentives under "Price-based' and 'Cost-based' Regulation. Rand Journal of Economics 20(3), 373-391. Bums, P., Turvey, R. and Weyman-Jones, T. (1995) General Properties of Sliding Scale Regulation. CRI Technical Paper 3. Dalen, D. (1997) Yardstick Competition and Investment Incentives. Working Paper. Department of Economics University of Oslo. Demski, J. and Sappington, D. (1984) Optimal Incentive Contracts with Multiple Agents. Journal of Economic Theory 33, 152-171. Department, of the Environment (1986) Privatisation of the Water Authorities in England and Wales. HMSO London Cmnd 9734. Glaister, S. (1987) Regulation Through Output Related Profit Tax. The Journal of Industrial Economics 35(3), 281-296. Griliches, Z. (1990) Patent Statistics as Economic Indicators: A Survey. Journal of Economic Literature 28(December), 1661-1707. Holmstrom, B. and Milgrom, P. (1990) Regulating Trade Among Agents. Journal of Institutional and Theoretical Economics 146, 85-105. Itoh, H. (1990) Incentives to Help in Multi-Agent Situations. Econometrica 59, 611-636. Laffont, J.-J. and Tirole, J. (1986) Using Cost Observations to Regulate Firms. Journal of Political Economy 94, 614-641. Levin, R. and Reiss, P. (1989) Cost Reducing and Demand
Creating R&D with Spillovers. Rand Journal Of Economics 19(4), 538-556. Littlechild, S. (1986) Economic Regulation of Privatised Water Authorities.. A report submitted to the Department of the Environment. HMSO London. Lockwood, B. (1995) Multifirm Regulation Without LumpSum Transfers. Journal of Public Economics 56, 31-53. Mayer, C. and Vickers, J. (1995) Price Caps and Profit Sharing: a Review of the Options for Regulated Industries. Brunel University Mimeo. Meyer, M. and Vickers, J. (1994) Performance Comparisons and Dynamic Incentives. Discussion Paper No. 96. Nuffield College Oxford. Powell, K. (1995) The Role of 'Yardstick Competition' in Ofwat's Periodic Review of Price Caps Working paper, Imperial College Management School, London. Reinganum, J. (1982) A Dynamic Game of R&D, Patent Protection and Competitive Behaviour. Econometrica 50(3), 671-688. Sappington, D. and Sibley, D. (1988) Regulating without Cost Information: The Incremental Surplus Subsidy Scheme. International Economic Review 29(2), 297-306. Schmalensee, R. (1989) Good Regulatory Regimes. Rand Journal of Economics 20(3), 417-436. Shleifer, A. (1985) A Theory of Yardstick Competition. Rand Journal of Economics 16, 316-327. Sibley, D. (1989) Asymmetric Information, Incentives and Price Cap Regulation. Rand Journal of Economics 20(3), 392-404. Spence, M. (1984) Cost Reduction, Competition and Industry Performance. Econometrica 52(January), 101-121. Stewart, M (1994) Office of Water Services Research Paper Number 2: Modelling Water Costs 1992-1993, prepared for Ofwat by Professor Mark Stewart. University of Warwick Warwick. Stewart, M (1994) Office of Water Services Research Paper Number 4: Modelling Sewage Treatment Costs 1992-1993, prepared for Ofwat by Professor Mark Stewart. University of Warwick Warwick. Stewart, M (1994) Office of Water Services - Future Charges for Water and Sewerage Services: The Outcome of the Periodic Review. OFWAT Birmingham.
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