Chapter I. Introduction
Chapter 4. A Theoretical Inquiry into Top- runner systemrunner system
A s w e m entioned in the introduction, Top-runner system is a regulatory schem e, based on relative perform ance evaluation, w hich induces com petition for energy efficiency im provem ent betw een sim ilar products. In particular, as Top-runner system sets the m ost efficient product as a standard for energy efficiency and enforces other products to satisfy this standard, it has a characteristic of yard-stick com petition in w hich the com panies are regulated based on their relative perform ances.
Y ard-stick com petition is a regulatory m echanism w hich w as proposed for the first tim e by Shleifer(1985) to regulate regionally based natural m onopolies. Shleifer(1985) argues that w hen a regulator w ith asym m etric inform ation about the cost structure of a natural m onopolistic com pany m akes up for its costs, it w ill be social optim um for the regulator to do it based on the sim ilar com panies' perform ances rather than the com pany's ow n perform ance. This is an regulatory structure to lead to a social optim um level of effort for cost reduction through com petition am ong the regional m onopolies supplying the sam e goods or services. In order that the yard-stick com petition m ay be effective, som e econom ic environm ent variables should have
the sam e effect on the perform ance of the regional m onopolies and the natural m onopolistic com panies should em ploy sim ilar production techniques. O nly in such a situation, the yard-stick com petition can induce a social optim um investm ent level for the regional m onopolies' cost reduction, revealing the net perform ance due to each com pany's effort by filtering out the effect of environm ent variables w hich equally affect the regional m onopolies' perform ances.
N evertheless, the yard-stick com petition has som e problem s in a few aspects. Firstly, it gives the regulated com panies an incentive to collude w ith one another. The regulated com panies colluding w ith one another, the yard-stick m echanism w on't w ork out effectively. Shleifer(1985) w ho had proposed for the first tim e a yardstick com petition type of regulation, has pointed out such a w eak point in the regulation. Laffont and M arim ort(2000) have also discussed such possibilities in the view of a generalized relative perform ance evaluation system . In addition, through an experim ental research, Potters et al(2003) has proved that collusion could occur practically under the yardstick com petition.
In this chapter, w e w ill try to review som e problem s inherent in the yardstick com petition type of regulation, w ith exam ining a few theoretical argum ents on the yardstick com petition. W e think such a review w ill provide useful policy im plications for designing an appropriate Top-runner system in K orea.
W hat investm ent incentives do the regulated com panies have under the yardstick com petition regulatory m echanism ? Long ago, W illiam son (1975) insisted that there should be "hold-up"
problem that regulated com panies w ill avoid present investm ent if regulator does not m ake a reliable com m itm ent that he w ill not exploit econom ic rents the regulated com panies w ill achieve in the future through the productivity im provem ent brought by their investm ent. Sobel(1998) and D alen(1998) have related the argum ents of W illiam son(1975) to Y ard-stick com petition.
Sobel(1998) show s that the investm ent incentives of each individual com pany can be m ore distorted under the yardstick com petition than the individual regulation. G enerally, investm ent incentives depend on the am ount of econom ic rents the com panies w ill achieve through their investm ent in the future.
H ow ever, yardstick com petition m echanism can reveal m ore detailed inform ation about the productivity of regulated com panies than individual regulation does, because yardstick com petition can rem ove perform ance variation under the uncertainty applied equally to all the com panies. Then, under dynam ic regulatory setting, regulator can exploit the future's rents w hich are expected to belong to the regulated com panies, utilizing the inform ation acquired through the yardstick
com petition regulation. Therefore, if the investm ent is irreversible and the regulator cannot prom ise not to change current rules in the future, then there w ill be a "hold-up" problem that the investing com panies cannot realize their ow n expected gain. So, the com panies expecting such a situation have an incentive to reduce their investm ent below social optim um level.
In the end, the argum ents of Sobel(1998) show that the
"hold-up" problem can becom e m ore severe under the yardstick com petition m echanism . To reduce such inefficiency, it is im portant for regulators to m ake an reliable com m itm ent that they w ill allow the regulated com panies to carry aw ay a part of the econom ic rents based on the asym m etric inform ation. The Sobel's study w ill be very inform ative for our designing Top-runner system , insisting that such a reliable com m itm ent can be m ade in the form of long-term contract,
O n the other hand, D alen(1998) argues that the yardstick com petition should be likely to reduce such investm ent that the entire industry is affected by. D alen(1988) divided investm ent pattern into investm ent affecting the productivity of individual com pany and investm ent affecting the entire industry. The reason that the investm ent affecting the entire industry decreases under yardstick com petition is as follow s. The investm ent affecting the entire industry have an effect on the productivity of non-investing com panies as w ell as that of investing com panies.
In other w ords, this pattern of investm ent brings about positive externality. The yardstick com petition, how ever, evaluates the perform ance of a specific com pany, com paring it to the perform ance of other com panies. Therefore, the investm ent pattern affecting the productivity of other com panies w on't have a great influence on the relative status of the investing com pany.
A nd, as the com pany has little additional benefit as a result of its investm ent, it w ill have less incentive to invest.
B ut, as the investm ent pattern affecting only the productivity of individual com pany can enhance its relative perform ance, com pared to that of other com panies, the expected gain from the investm ent w ill be relatively high. In other w ords, the investm ent affecting individual productivity can help the investing com pany to be able to appropriate all of the expected gain from the investm ent. So, under the yardstick com petition m echanism , com panies m ay have a tendency to increase their idiosyncratic investm ent.
D alen(1998)'s argum ents like this provide a basis for m aking a judgem ent about w hich groups of products are appropriate to be applied Top-runner system in inducing com pany's investm ent for energy efficiency im provem ent. W e w ill describe in m ore detail Sobel(1998) and D alen(1998)'s policy im plications for designing Top-runner system in the next section.
There have been a num ber of studies on yardstick com petition and collusive incentives since Shleifer(1985) pointed out for the first tim e the possibility of collusion under yardstick com petition m echanism . G enerally, there are tw o types of collusion, explicit collusion and tacit collusion. Explicit collusion is a situation in w hich econom ic agents cooperate legally or secretly w ith one another through explicit com m unication. Tacit collusion is a cooperation w ithout any explicit com m unication.
The debates so far on yardstick com petition and collusive incentives have focused m ostly on explicit collusion. Laffont and M arim ort (2000) show s that if there is stochastically a positive correlation betw een perform ances of regulated com panies. their inform ation superiority over regulator can be easily revealed through relative evaluation system w ithout cost, and therefore the regulated com panies have an incentive to restrict such exposure through their collusive behavior. Tangerås(2002) suggests also a theoretical m odel to analyse explicit collusion am ong regulated com panies under yardstick com petition.
Pointing out the possibility of collusion under yardstick com petition, he show ed that if com panies can prom ise one
another to m ake an explicit collusion contract before the ex post realization of private and correlated inform ation, social w elfare loss due to the collusion is inevitable.
H ow ever, the collusion am ong com panies can be also m ade im plicitly, not explicitly. G enerally, the explicit collusion is strictly regulated by the governm ent. Therefore, it w ill be a m eaningful w ork to show that tacit collusion to avoid the strict governm ent regulation on explicit collusion can also bring about inefficiency. W e w ill introduce below a recent study of C hong and H uet(2009) dealing w ith the possibility of tacit collusion under yardstick com petition. In this study, they m ade an theoretical inquiry into the problem of tacit collusion under yardstick com petition and proposed som e policy alternatives to reduce the possibility of tacit collusion. So, their study can also give us various im plications for the introduction of Top-runner system .
Let's consider tw o sym m etric com panies, A and B, w hich are all regulated by the governm ent. W e assum e also that the tw o com panies are each responsible for half of total consum er surplus and produce an am ount of goods so that they can alw ays achieve such consum er surplus level10). A nd the cost of the tw o com panies is as follow s
(IV -1)
The cost of the com pany ∈ is com posed of an exogeneous cost param eter and a cost reduction w hich can be achieved by an effort of the com pany . In other w ords, the com pany can reduce its cost by w ith an additional effort.
H ow ever, such an cost reduction effort incurs som e disutility
of the com pany. The disutility function has a characteristic of ≥ ′ ″ . That is, the effort alw ays incurs a positive am ount of disutility and the increasing rate of disutility w ill be greater than that of effort. In the case w here the regulators supervise both A and B , they know s the total cost of the tw o com panies but don't know and , inside inform ation of the producing com panies, due to a situation of asym m etric inform ation. N evertheless, they can have an influence on the
level of and through a proper m echanism design. In the version of Top-runner system , this situation can be interpreted as follow s: The governm ent can find the final energy efficiency level of the products w hich the regulated com pany have produced, but it cannot identify the potentials of the com panies and the degree of their effort for energy efficiency im provem ent.
To sim plify the discussion, it is assum ed hat has a value of w ith a probability of and
w ith a probability of (but,
). In this case,
m eans that the productivity of the regulated com panies is generally high11).
In addition, w e assum e that regulating authorities not only com pensate com pletely the regulated regional m onopolies for their total cost , but also provide a transfer , and that the objective of regulation is to m axim ize total social w elfare.
Then, each com pany w ill get a rent and the total social w elfare w ill be as follow s;
(IV -2)12)
(IV -3)13)
w here : Potential cost of public funds
: N et consum er surplus
: Producer surplus
Though regulating authorities can know any com pany's total cost, they cannot identify its detailed cost structure(i.e. they can't know and ). In such a situation, the regulators can design a m arket structure w hich has a revelation principle to prevent the com panies from m aking a false report on their cost structure, by adjusting the com panies' revenue structure. For convenience's sake14), Let's express the revenue and the cost as
,
w ith the value(∈
, from now on w e w ill call it revelation value) that com pany reports to regulator. Then, the com pany's utility function according to the revelation value is as follow s; (IV -4)
W e assum e that the regulators ignore the problem of asym m etric inform ation and receives the revelation value as it is in the situation of full inform ation. First, let's consider the case that the companies report as
even though the real value of is
. In other words, this is the case that the companies report their productivity is high even though their actual productivity is low.
For reference, in the situation of full inform ation, an optim al effort level is determ ined at ′ and the com panies w ill be rew arded exactly as m uch as they expend effort( m eans an optim al effort level under full inform ation). In other w ords,
15). Therefore, the com panies cannot realize a positive excess profit.
′
′
So, in the case that the com panies report as
,
and
. A nd, as the com panies have to put in an additional effort (but,
) to m easure up to the cost level, the rent of the com pany
w ill be as follow s.
∆
∆
∆
(V -5)
A s , w e can find
. A nd, as
, if actual , there w ill be no incentive for the com panies to report as
, nam ely to m ake a false report.
O n the contrary, if the actual value of is
and the com pany reports as , then the com pany's utility w ill as follow s.
∆
∆
∆
( -6)
A s , w e can find
. If the com pany reports the actual value of
, its utility is 0 and it w ill have an incentive to m ake a false report.
In the view of Top-runner, this m eans that the regulated com panies have an incentive to report their potential for efficiency im provem ent as low er than actual. In other w ords, at the stage of goal setting, the com panies w ill not reveal sufficiently their potential for technical im provem ent.
O n the other hand, the additional revenue obtained through the false report w ill be . If regulatord can give the com pany an incentive greater than the additional revenue, he can induce the com pany to report the actual value. A s one of such m echanism s, Chong and H uet(2009) proposed a Y ard-stick m echanism as follow s.
U nder yardstick com petition, a regulated com pany's revenue is determ ined by the inform ation reported by the other com panies in the sam e industry as w ell as the inform ation reported by the com pany itself. In case that the com pany reports as and the com pany reports as , let's assum e that the subsidy given to the com pany and its production cost are respectively and . A s w e review ed earlier, the com panies have no incentive to report as even though the actual value is
and the regulator recognizes it very w ell. In such a situation. it is assum ed that the regulator w ill introduce a
m echanism as follow s.
If the revealed(reported) values of the tw o com panies equal(i.e. ), w ill be regarded as an actual value. In this case, the subsidy to each com pany and the com pensation for the cost . To m axim ize the total social w elfare, and .
If the revealed values of the tw o com panies do not equal(i.e.
≠ ),
w ill be regarded as a actual value. In this case, regulator can m ake all the com panies report the true values through punishing the com pany w hich has falsely reported or rew arding the com pany w hich has correctly reported. That is, regulators can differentiate the subsidy to the falsely reporting com pany from the subsidy to the correctly reporting com pany as follow s; for the falsely reporting com pany
, for the correctly reporting com pany
(but, ≥ ).
Let's express each com pany's utility w ith its ow n revealed value(), the other com pany's revealed value() and its ow n actual value(), as follow s.
(IV -7) In this case, the follow ing conditions should be satisfied in order that to report alw ays the truth m ay be a N ash equilibrium of the tw o com panies.
≥
(IV -8)
≥
(IV -9) These inequalities are the conditions for the com pany not to report falsely its cost structure w hen the com pany reports only the truth. W e can rearrange these expressions as follow s.
≥ ∆ (IV -10)
≥ (IV -11)
A s ∆ , if then the inequalities are alw ays valid. Therefore, in the structure of Chong and H uet(2009) m odel, it is sufficient to punish the com pany w hich reports its cost being higher than actual in order that reporting only the truth m ay be a N ash equilibrium of the tw o com panies.
Eventually, under the m echanism like this, the tw o com panies w ill report only the truth and it w ill be unnecessary for regulators to punish any com pany. So, w e can achieve the sam e efficiency as the full inform ation situation gives us.
Figure IV -1 and Figure IV -2 show each com pany's rent according to its revelation value in case that its actual value is respectively and
.
com pany1
com pany2 revelation value=
revelation value= revelation
value=
∆
∆
∆
∆ revelation
value=
∆
∆
Table IV-1. Payoff matrix in case that the actual value=
com pany1
com pany2 revelation value=
revelation value= revelation
value=
revelation
value=
∆
∆ Table IV-2. Payoff matrix in case that the actual value=
The regulatory authorities can m ake a dom inant strategy equilibrium from com pany's revealing its truth. For this, the inequalities below should be satisfied.
≥
(IV -9)
≥
(IV -10)
≥
(IV -11)
≥
(IV -12)
These expressions can be rearranged as follow s.
≤ ∆ (IV -13)
≤ (IV -14)
≥ (IV -15)
≥ ∆ (IV -16)
So, if the regulators w ant to m ake a dom inant strategy equilibrium from telling the truth, they have only to set the punishm ent level at 0. In case that the tw o com panies' revelation values are different, they aw ard an appropriate com pensation to the com pany reporting low er revelation value(
). In this case, the range of com pensation is as follow s.
∆ ≤ ≤ ∆ (IV -17)
A s w e have discussed hitherto, the regulators m ay overcom e the problem of asym m etric inform ation and m ake it possible the sam e equilibrium as the full inform ation situation brings about, through designing a Y ard-stick com petition schem e w ith proper com pensation and punishm ent system s.
G enerally, the relationship betw een regulators and regulated
com panies are repetitive over m ultiple periods. Chong and H uet(2009) have discussed a case of endless repetitive gam es in w hich can change in each gam e. For the convenience of discussion, w e assum e that, in each gam e, takes a value of or
w ith a probability of or respectively.
A s Figure IV -1 and Figure IV -2 show , w e can easily find that the tw o com panies can achieve extra-profits, m aking false reports through collusion. For instance, if is realized the tw o com panies w ill reveal honestly . B ut, if
is realized the tw o com panies w ill collude w ith each other and report falsely as their cost structure to m ake a unfair profit. If the tw o com panies have continuously collusive incentives to report falsely their cost structure, it m eans that yardstick com petition does not w ork any m ore. So it's very im portant to analyze collusive incentives of the regulated com panies.
Let's analyze the problem of tacit collusion in the gam e of
"grim trigger strategy". In other w ords, it is assum ed that the tw o com panies m aintain their collusion before one of them w ithdraw s from the collusion, but if a com pany w ithdraw s from the collusion to report honestly , all of the tw o com panies report honestly in the follow ing gam es.
W ith discounting factor being , the discounted expected utility of the com pany in the continuing collusion w ill be as follow s.