On the desirability of an efficiency defense in [614875]

On the desirability of an efficiency defense in
merger control
Johan N.M. Lagerlo ¨fa,b,*, Paul Heidhuesb,c
aEconomics Department, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom
bCEPR
cUniversity of Bonn, Lehrstuhl fu ¨r Wirtschaftstheorie II, Adenauerallee 24–42, D-53113 Bonn, Germany
Available online 14 November 2004
Abstract
We develop a model in which two firms that have proposed to merge are privately informed about
merger-specific efficiencies. This enables the firms to influence the merger control procedure bystrategically revealing their information to an antitrust authority. Although the information improves upon
the quality of the authority’s decision, the influence activities may be detrimental to welfare if information
processing/gathering is excessively costly. Whether this is the case depends on the merger controlinstitution and, in particular, whether it involves an efficiency defense. We derive the optimal institution and
provide conditions under which an efficiency defense is desirable. We also discuss the implications for
antitrust policy and outline a three-step procedure that takes the influence activities into consideration.D2005 Elsevier B.V . All rights reserved.
JEL classification: D72; D82; K21; L40
Keywords: Lobbying; Rent seeking; Asymmetric information; Disclosure; Efficiency gains; Antitrust
1. Introduction
b[A] policy of approving anticompetitive mergers for efficiency reasons is likely to
promote a dissipation of resources into rent seeking. Q
Franklin M. Fisher (1987, p. 39)
0167-7187/$ – see front matter D2005 Elsevier B.V . All rights reserved.
doi:10.1016/j.ijindorg.2005.08.005* Corresponding author. Economics Department, Royal Holloway, University of London, Egham, Surrey, TW20 0EX,
United Kingdom.
E-mail addresses: [anonimizat] (J.N.M. Lagerlo ¨f), [anonimizat] (P. Heidhues).
URLs: http://www.JohanLagerlof.org (J.N.M. Lagerlo ¨f), http://www.wiwi.uni-bonn.de/heidhues/ (P. Heidhues).International Journal of Industrial Organization
23 (2005) 803– 827
www.elsevier.com/locate/econbase

The appropriate regulation of mergers is an important policy issue in the U.S. as well as
in Europe, and the question whether efficiency gains (either proven or only claimed) shouldconstitute a reason not to challenge an otherwise anticompetitive merger is much debated.
1
Williamson (1968) was the first to stress that the decision whether to permit a merger
potentially involves a welfare tradeoff: whereas permitting the merger is likely to increasethe merged unit’s market power, as doing this reduces the number of rivals competing in
the market, it may also allow the newly created firm to realize efficiency gains. One strand
of the theoretical literature on mergers has investigated this trade off in various oligopolymodels; see, for example, Williamson (1968) ,Deneckere and Davidson (1985) ,Farrell and
Shapiro (1990) ,a n d Spector (2003) .
While these contributions can inform an antitrust authority’s decision whether to permit
a proposed merger and, for example, provide reasons to be very skeptical, they do notexplain why an antitrust authority as a matter of principle should rule out the possibility
that an anticompetitive merger may be permitted for efficiency reasons: rules and guidelines
that do exactly this (like the previous ones used in the U.S. and the E.U.) cannot be
justified by the literature cited above. However, one conceivable benefit with making anirreversible commitment not to permit mergers for efficiency reasons is that this maydiscourage rent seeking or other forms of influence activities. This point has indeed oftenbeen made in the literature; see, for example, the above quotation by Fisher.
2Yet it is
not clear whether all kinds of influence activities should count as a social cost of allowingfor an efficiency defense. For if the activities take the form of outright monetary bribes,then they merely represent a transfer of wealth between different economic agents.
Similarly, one often-mentioned reason why allowing for an efficiency defense may make
the merger control procedure easier to influence is that the merging firms (hereafter calledtheinsiders ) typically have superior access to information about any efficiencies;
3hence,
by strategically transmitting such information to the antitrust authority, the insiders maybe able to achieve a favorable decision. The welfare effects of such influence activities
1Currently, the American policy allows for an explicit efficiency defense. Until fairly recently, however, the U.S.
policy, as expressed by the Horizontal Merger Guidelines issued by the Department of Justice and the FederalTrade Commission, placed much less weight on the efficiency criterion; for a discussion and evaluation of thesechanges of the Guidelines, in particular with respect to the treatment of efficiencies, see for example Farrell and
Shapiro (2001) and several of the contributions in the Spring 1999 issue of the George Mason Law Review. The
European Commission has also just recently made a move toward taking possible efficiencies into account whenassessing proposed mergers; for discussions, see Ro¨ller et al. (2001) ,Ilzkovitz and Meiklejohn (2001) , and
European Commission (2001) . One reason why the European Commission decided to make this move was that the
increased frequency of cross-border mergers raised the question whether American and European rules should be
harmonized.
2The argument can be found also in Neven et al. (1993, p. 213, footnote 41) and in Ro¨ller et al. (2001, p. 117–118) .
3The Horizontal Merger Guidelines ( U.S. Department of Justice and U.S. Federal Trade Commission, 1997 ,
Section 4) state explicitly that b[…] much of the information relating to efficiencies is uniquely in the possession
of the merging firms. QYao and Dahdouh (1993) discuss the problem of informational asymmetries in merger
control at length and argue that asymmetries in the access to information are particularly important for
efficiencies.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 804

could be either positive or negative, depending on whether the cost of gathering,
processing, and transmitting the information is offset by its social benefits.4,5
Thus, in order to better understand under what circumstances influence activities may serve
as a reason not to allow for an efficiency defense, it is important to model the reason why theymay be influential and then, in an equilibrium analysis, investigate the welfare effects ofdifferent merger control institutions, with and without an efficiency defense. To the best of our
knowledge, there is no attempt in the literature to do this. The present paper tries to fill this
gap.
Although the model we develop is relatively simple, it captures three important aspects of a
merger control procedure: Williamson’s tradeoff between increased market power and possibleefficiency gains, the insiders’ having superior access to information about any efficiencies, andthese firms’ vested interest in having the merger permitted.
In particular, we model the merger control procedure as an interaction between two economic
agents: the insiders (acting as one unit) and society. The efficiency gains due to the merger may
beblowQorbhigh.QWhereas the insiders want to merge regardless of the size of the efficiencies,
society wants the merger to take place only if they are high. Initially, the insiders know onlywhether the efficiencies are high or low. This information, however, is soft (i.e., non-verifiable),which means that in order to be able to credibly transmit it to society, the insiders must firstinvest resources in evidence production. If they do this and if they are successful, they find hard(i.e., verifiable) information about the size of the efficiency gains, which they (if this is in theirinterest) can disclose to society.
6The role of society is to choose a merger control institution, by
which we mean a rule whether to permit the proposed merger conditional on whether the insiders
have submitted a report and whether this report showed that the efficiencies are high or low. We
assume that society commits to such a rule at an ex ante stage. A merger control institution thatballows for an efficiency defense Qis understood as a rule where the fact that the insiders have
provided hard information about the size of the efficiencies (instead of not having done this)affects the probability that the merger is permitted.
5Recently, the consulting firm PricewaterhouseCoopers (2003) conducted a survey that estimates the costs to business of
multi-jurisdictional merger reviews. It shows that, in cases that led to an in-depth review, an acquiring company’s externalcosts (e.g., hiring consultants) amounted to on average 5.4 million euros, and the average internal costs (use of own personnel),measured in person weeks, were 120. For some companies in the sample the numbers are much higher: the corresponding
averages for the top quartile are 15 million euros and 389 person weeks (or around 8 person years). There are also quite large
differences across jurisdictions, with filings in the U.S. leading to significantly higher costs than filings in the E.U.Even though the survey suffers from a low response rate (14%), which might have led to a selection bias, we take thesenumbers as an indication that costs of merger enquiries can be quite substantial. We also want to emphasize, however, that
some of our arguments do not rely on merger reviews being excessively costly. In our model, an efficiency defense can be
suboptimal with a large margin and at the same time induce very low costs. When this happens, the reason why an efficiencydefense is bad is that it makes it too difficult, also from society’s point of view, for the firms to merge (see the example in theend of Section 4).
6Hence, we assume that the insiders incur costs because they must process their information (i.e., transform it from soft
to hard) before being able to communicate it. We would get almost the same results if we instead assumed that theinsiders’ costs concerned the acquisition of information; see our discussion in the concluding section. One may argue
about which assumption is the most plausible; perhaps it is something in between those two polar cases.4An early paper that explicitly interprets rent-seeking expenditures as costs of information gathering is Tullock (1975) .
Later work that has provided informational foundations to the rent-seeking theory, by showing that there may be
overinvestment in information acquisition from a social welfare point of view, includes Shavell (1994) andLagerlo ¨f
(1997) . More generally, lobbying as a form of strategic information transmission has been modeled in, for example,
Austen-Smith and Wright (1992) andGrossman and Helpman (2001) .J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 805

In an equilibrium of this model, the insiders will never invest in evidence production when
having soft information that the efficiencies are low. When they have soft information that theefficiencies are high, whether and to what extent they invest depend on what institution societyhas chosen. An institution that does not allow for an efficiency defense will not induce anyevidence production at all. Two examples of such institutions that are important in our analysisare what we call the laissez-faire regime (LF) and the strict regime (SR): under LF, a merger is
always permitted while under SR it never is.
7By committing to an institution that to some
extent indeed allows for an efficiency defense, society can induce a positive amount of evidenceproduction. One such institution is the one where a merger is notpermitted if society receives a
report saying that the efficiencies are low or if it does not receive any report at all, and the mergeris permitted with a probability cif society receives a report saying that the efficiencies are high.
Here, the larger cis the more the insiders will invest. In the extreme, when the probability c
equals unity, we obtain the hard evidence regime (HE): a merger is permitted if and only if
society receives a report saying that the efficiencies are high.
Hence, in our model, a possible cost of allowing for an efficiency defense is that this encourages
the insiders to spend resources in order to influence the decision whether to allow the merger. Theresource costs enter the social welfare function and may thus, in principle, be wasted. On the otherhand, the information that the insiders report might be useful for society, in which case there alsoare benefits with an efficiency defense. Society thus faces a tradeoff. It turns out that even thoughsociety has an opportunity to fine tune the insiders’ incentives for evidence production by choosingan institution that gives rise to a positive amount of evidence production but still less than underHE, this is never optimal. That is, the institution that maximizes expected social welfare is either
SR, LF, or HE. One reason for this result is that society can choose the insiders’ amount of evidence
production only indirectly, through its choice of the merger control institution. Thus, society’sability to choose investment incentives is limited by the insiders’ optimal response. In addition,institutions whose outcomes differ from the outcomes of SR, LF, and HE require society to committo an ex post merger decision that uses the available information suboptimally.
Finding the socially optimal institution thus amounts to comparing LF, SR, and HE, of which
only HE involves an efficiency defense. We show that, depending on the parameters of ourmodel, any one of these three institutions can be optimal. By inspecting the conditions needed
for a particular institution to be the best one, we arrive at some non-trivial and sometimes rather
subtle conclusions about the desirability of an efficiency defense and the optimal design of amerger control procedure. First, as the arguments above suggest, an efficiency defense is indeedsometimes desirable. When this is the case, however, the merger should be allowed if and only ifhigh-efficiency evidence is provided. Second, an efficiency defense is more likely to be optimal(from a total surplus point of view) when bhighQefficiencies are so high that they would give rise
to a lower market price. This is because then the insiders’ incentives to invest are such thatsociety should encourage evidence production as much as it can. Third, there is an important
asymmetry between situations with a low respectively high prior probability that a merger would
increase total surplus: when the prior is relatively low, the problem of the insiders’ dissemblingcan be dealt with very easily and at no real cost, whereas this is not true for the case when theprior is relatively high. As a consequence, an efficiency defense is more desirable when themerger is unlikely to be welfare enhancing.
7The important feature of these institutions is that the decision whether to permit the merger is not made contingent on
the insiders’ reports about efficiencies. The decision could, however, very well be contingent on other circumstances, as
long as these are publicly known. See our discussion in Section 5.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 806

Although this paper is, to the best of our knowledge, the first one to investigate the
desirability of an efficiency defense using an equilibrium analysis, there are some other papersthat also study institutional design in the context of merger control. Besanko and Spulber (1993)
andNeven and Ro ¨ller (2000) , for example, study the relative merits of a welfare standard and a
consumer standard. Similarly, Lewis and Poitevin (1997) investigate the desirability of
mandatory disclosure rules in regulatory proceedings. Laffont and Tirole (1993, ch. 15) develop
a model of regulatory capture and institutional design, although not in the context of merger
control. Our paper is also related to a literature that models evidence production in trials orregulatory proceedings; see, for example, Legros and Newman (1999) andSanchirico (2001) .
Similarly, information acquisition and institutional design has also been studied by, for example,Aghion and Tirole (1997) andDewatripont and Tirole (1999) .
8
The remainder of the paper is organized as follows. Next, in Section 2, we present the model.
In Section 3 we begin the analysis and show that the optimal merger control institution is either
LF, SR, or HE. Then, in Section 4 , we compare these three institutions and find the optimal one.
InSection 5 we discuss the implications of our results for antitrust policy. In particular we sketch
a three-step merger control procedure that takes the influence activities into consideration.Section 6 concludes by briefly discussing some possible extensions and variations of our model.
An Appendix contains mathematical derivations relating to one of these extensions.
2. A model of merger control and influence activities
Consider the following simple model of a merger control process. There are two economic
agents: on the one hand society and on the other two firms that have proposed to merge (acting
as one unit). The two firms, which are hereafter called the insiders , should be thought of as
producing and selling a good on an oligopolistic market, although the market interaction will notbe explicitly modeled here. The other firms in that market (the outsiders ), as well as the
consumers, are passive in that they do not attempt to influence the merger control process.
9
The efficiency of the new firm that is created if the merger takes place, denoted e, is either blowQ
(e=eL)o rbhighQ(e=eH). Initially, eis private information to the insiders: society places the prior
probability pon the event that the post-merger efficiency is high, where pa(0,1). Although the
insiders know the true post-merger efficiency from the outset, the information they have is
assumed to be soft (i.e., non-verifiable). This means that, given the preferences that we will specifyshortly, the insiders will not be able to credibly transmit their information to society—for that theywill first have to invest resources in evidence production (more on this later).
We assume that regardless of whether the post-merger efficiency is low or high, it is profitable
for the insiders to merge; that is,
p
HNpLNpN; ð1Ț
where pH(respectively, pL) is the insiders’ profit if the merger is permitted and the post-merger
efficiency turns out to be high (respectively, low), and pNis the insiders’ (joint) profit if the
8Other related papers include Corcho ´n and Faulı ´-Oller (2003) ,Daughety and Reinganum (2000) ,Froeb and Kobayashi
(2001) , and Shin (1998) .
9In the concluding section we briefly discuss how our analysis would be affected if the outsiders or a consumer group
were also taking part in the influence activities.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 807

merger is blocked. Moreover, permitting the merger increases social welfare if and only if the
post-merger efficiency turns out to be high; that is,
WHNWNNWL; ð2Ț
where WH(respectively, WL) is the unweighted sum of consumer surplus and industry profits if
the merger is permitted and the post-merger efficiency turns out to be high (respectively, low),andW
Nis the unweighted sum of consumer surplus and industry profits if the merger is blocked.
Let us for notational ease write Dpiupi/C0pNandDWiuWi/C0WN(fori=L,H). In terms of this
notation, (1) and (2) amount to saying that DpH,DpL, andDWHare all positive, whereas DWLis
negative. Borrowing terminology from Farrell and Shapiro (1990) , we will refer to the case where
DWHbDpHas a situation with negative externalities ,a n dt h ec a s ew h e r e DWHNDpHas a situation
with positive externalities . All our analysis will cover both these cases. The distinction between
positive and negative externalities will be helpful in understanding the results to be derived.
Although our proofs do not rely on it, we use the following assumption to interpret our
results:
DWHNDpHZDCSHN0;
where DCSHis the gain in consumer surplus if the merger is permitted instead of blocked, given
that the post-merger efficiency is high. That is, the assumption states that if there are positiveexternalities, then also the consumers (not only society at large) gain from a high-efficiency
merger. Notice that as long as consumer surplus is affected by the merger only through its effect
on market price and as long as consumer surplus is decreasing in market price, a statement thatDCS
His positive is tantamount to saying that bhighQefficiencies are so high that they induce a
lower post-merger than pre-merger market price.
Fig. 1 shows how, for different values of the efficiency parameter e, the gains and losses that
accrue to the various parties if a merger takes place typically relate to each other.10The figure is
derived from a homogenous-good Cournot model with at least three symmetric firms prior to the0 e∆W
∆CS∆πI
e°ee"'
∆πo
Fig. 1. Gains and losses for different parties due to the merger.
10Fig. 1 is inspired by a similar figure in Neven and Ro ¨ller (2000) .J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 808

merger, where demand and cost functions are linear, and where the efficiency parameter eis
subtracted from the marginal cost of the insiders. Although this is only a very simple example,we expect the qualitative features of the figure to hold true for a much larger family of oligopolymodels.
11From the figure we see that the insiders would themselves lose by merging if edid not
exceed a threshold e8. Moreover, for the effect on welfare to be positive, emust exceed a
threshold eV, where eVNe8. Thus, in terms of these threshold values of e, (1) and (2) amount to
assuming that eLa(e8,eV)a n d eHNeV. We also see from the figure that the outsiders’ gain in
profits and the change in consumer surplus always have opposite signs, and these signs changeat a threshold eU, where eUNeV; this is the level of eabove which market price becomes lower
thanks to the merger. At the same threshold level of e, society’s gain from having the merger
starts to exceed the insiders’ gain. Thus, there are negative externalities if e
Ha(eV,eU), whereas
there are positive externalities if eHNeU.
The timing of events is as follows. (i) Society commits to a merger control institution,
z=(zL,zH,zN)a[0,1]3. We will shortly explain exactly what it means to choose a particular z.
(ii) The insiders observe zand then binvest in evidence production; Qthat is, conditional on
knowing that the true state is ia{L,H}, they choose a probability sia[0,1], thereby incurring a
cost C(si). By picking a particular si, the insiders will with that probability find hard (i.e.,
verifiable) information that the post-merger efficiency is ei; with the complementary probability,
1/C0si, the insiders do not find any hard information. (iii) If having found hard information, the
insiders choose whether to bsubmit a report, Qthat is, whether to disclose this information to
society. If they do this, also society learns the true state (since the information is verifiable). (iv)Society decides whether to permit or block the merger, following the previously chosen rule
z=(z
L,zH,zN). The component zL(respectively, zH) of this vector is a probability with which
society permits the merger if the insiders have submitted a report saying that the post-mergerefficiency is low (respectively, high), and z
Nis a probability with which society permits the
merger if the insiders have not submitted a report.
Hence, stage (iv) is simply an implementation of the rule that society has committed to at
stage (i).12Notice that the set of instruments that society has access to when it chooses an
institution does not include monetary transfers between society and the insiders.13Otherwise,
however, society has a great deal of freedom in its choice of an institution. For at the stage where
society implements the rule zit will either know the true state ( LorH) or it will not have
received a report ( N), and we assume that society can commit to any probability of allowing the
merger conditional on any one of these three events.
In terms of these merger control institutions, what does it mean to say that society ballows for
an efficiency defense Q? We interpret this as a situation where a report submitted by the insiders
13We find this assumption reasonable in the context of merger control. For a paper that does allow for such transfers and
which models the merger control procedure as an implementation problem, see Corcho ´n and Faulı ´-Oller (2003) .12There may of course be a credibility problem associated with choosing some particular z, perhaps especially for
bmixed Qzs. One way to implement the desired z-institution in practice may be to delegate the job to an antitrust official
who has the right private preferences; cf. the literature on strategic delegation (to an independent central banker, forexample). A mixed z-institution could also correspond to a set of guidelines that to some extent are open to interpretation
and which therefore make it difficult to predict perfectly the decision whether to challenge the merger. Yet another reason
that we are not too worried about the credibility problem is that, as we will see later, it will never be optimal for society to
choose the mixed zs anyway.11For example, we have verified that all the qualitative features of Fig. 1 can be derived also from a differentiated-goods
Bertrand model with three symmetric firms prior to the merger, linear demand and cost functions, and the efficiency
parameter ebeing subtracted from the marginal cost of the insiders. The only thing that changes in such a setting is that
the insiders gain from the merger even if e=0 (which is a well-known result).J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 809

affects the probability with which the merger is permitted. That is, we say that society allows for
an efficiency defense if either zLpzNorzHpzN. Within the set of merger control institutions that
society can choose among there are three ones that will be of particular interest to us. The first isthe institution where a merger is always permitted, z= (1,1,1); we call this the laissez-faire
regime (LF). The second one is the institution where a merger is never permitted, z=(0,0,0),
which we call the strict regime (SR). The third institution of special interest is the one where a
merger is permitted if and only if society receives a report from the insiders showing that the
post-merger efficiency will be high, z=(0,1,0); we dub this the hard evidence regime (HE).
Clearly, neither LF nor SR involves an efficiency defense, whereas HE does.
As for the cost function for evidence production, C, we assume that this is twice
continuously differentiable, increasing, and convex ( CVN0,CUN0), with C(0)=0, CV(0)=0, and
CV(1)NDp
H. Also, the cost elasticity is weakly increasing: gV(si)z0 for all sia[0,1], where
g(si)uCV(si)si/C(si).14
The cost of evidence production incurred by the insiders enters with full weight in society’s
payoff. Hence, given an outcome j(forj=L,H,N) of the merger control procedure and given
that the insiders have soft information that e=ei(fori=L,H), the insiders’ payoff is pj/C0C(si)
and society’s payoff is Wj/C0C(si). We also assume that the insiders as well as society are risk
neutral and thus maximize their expected payoffs given the information they have access to atthe time of their decisions. Society’s expected payoff ( bexpected welfare Q) is also the welfare
standard that we employ for our normative theory.
15
3. Influence activities and institutional choice
We will solve the model using backward induction. Since the last stage is just a mechanical
implementation of the rule society chooses at stage (i), we are left with three stages where actualdecisions are made: the choice-of-institution stage (i), the evidence-production stage (ii), and thereporting stage (iii).
Recall that the insiders want the merger to be permitted regardless of whether the post-merger
efficiency is low or high. Hence, at stage (iii), given that they have found hard information thate=e
i, the insiders will submit a report for sure if ziNzN;i fzi=zNthey are indifferent between
submitting and not submitting; and if zibzNthey will not submit. Similarly, at stage (ii), given
that they have soft information that e=ei, the insiders will invest in evidence production (i.e.,
choose a siN0) if and only if ziNzN. Clearly, however, society will never choose zLNzN. For if
society knows that the post-merger efficiency is low, it is in its interest to block the merger.(Moreover, setting z
LNzNwould encourage costly evidence production under circumstances
where this is not valuable for society.) As a result, if the institution zis optimally chosen, the
insiders will set sL=0.
When having soft information that e=eH, the insiders face the following problem:
max
sHa0;1½/C138sHzHț1/C0sH ðȚ zN ½/C138 pHțsH1/C0zH ðȚ ț 1/C0sH ðȚ 1/C0zN ðȚ ½/C138 pN/C0CsHðȚ ;
the solution of which, s4
H, equals zero if zHVzNand is implicitly defined by
DpHzH/C0zN ðȚ ¼ CVs4
H/C0/C1
ð3Ț
15In the concluding section we will discuss the implications for our results of using a consumer standard instead.14For some results in the end of the paper we will need the stronger assumption that the cost elasticity is constant. We
will make this clear when we get there.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 810

otherwise. The left-hand side of this first-order condition is the insiders’ marginal benefit from
evidence production when knowing that e=eH. The first factor of the marginal benefit, DpH,i s
the insiders’ gain in profits from having the merger permitted instead of blocked given that e=eH.
The second factor, ( zH/C0zN), is the amount with which the probability of having the merger
permitted increases if the insiders provide hard information that the post-merger efficiency is high.The magnitude of this latter factor is determined by society’s choice of institution. In particular,
(z
H/C0zN) will take its largest possible value under the institution HE, since then zH=1 and zN=0.
Hence, the insiders’ incentives for evidence production when knowing that e=eHwill be the
strongest possible under HE.16Similarly, under LF and SR, the insiders will have no incentives at
all to invest in evidence production ( s4
H=0), since then zH=zN.
What is society’s optimal choice of institution at stage (i)? To answer this question, let us first
formulate expressions for expected welfare at stage (i) under LF, SR, and HE, which we denoteby EW
LF,E WSR, and EWHE, respectively. Since under LF and SR the insiders will not invest in
evidence production, we almost trivially have EWLF=pW H+(1/C0p)WLand EWSR=WN.
Denoting the insiders’ choice of sHunder HE by sHE
H,17we can write
EWHE¼psHE
HWHț1/C0psHE
H/C0/C1
WN/C0pCsHE
H/C0/C1
¼psHE
HDWHțEWSR/C0pCsHE
H/C0/C1
:ð4Ț
This equation highlights a basic tradeoff in society’s choice of institution. By choosing an
institution that encourages evidence production, like HE, instead of one that does not, like SR,society will sometimes be able to avoid the mistake of blocking a welfare enhancing merger; thisbenefit with HE is captured by the term ps
HHEDWHin Eq. (4). Society also cares about the
insiders’ expected cost of evidence production, however, which is captured by the term
pC(sHHE). The comparison of HE and SR thus amounts to a comparison of sHHEDWHand
C(sHHE), where sHHEis implicitly defined by DpH=CV(sHHE). Accordingly, which institution
society should choose will depend on, among other things, how aligned society’s and theinsiders’ interests are and on the properties of the cost function C.
In order to solve society’s problem at stage (i) we will also need a more general expression for
expected welfare that holds for any relevant institution z. Recall that choosing z
LNzNwill always
be suboptimal for society. Moreover, setting zNNzHyields the same outcome as setting zN=zH
(since for any zNzzHthe insiders will choose s4
H= 0 and thus not be able to report when knowing
thate=eH). Hence, without excluding any (uniquely) optimal institution we can suppose that
zLVzNVzH:
Under this assumption, we can write expected welfare at stage (i) as
EW¼ps4
HzHț1/C0s4
H/C0/C1
zN/C2/C3
WHț1/C0p ðȚ zNWLțfp½s4
H1/C0zH ðȚ
ț1/C0s4
H/C0/C1
1/C0zN ðȚ /C138 ț 1/C0p ðȚ 1/C0zN ðȚ g WN/C0pCs4
H/C0/C1
¼ps4
HzH/C0zN ðȚ DWHț1/C0zN ðȚ EWSRțzNEWLF/C0pCs4
H/C0/C1
: ð5Ț
16Notice the importance of the qualifier bwhen knowing that e=eH.QThe institution that provides the strongest
incentives for evidence production more generally is z=(1, 1, 0), since this would make also sL*as large as possible. Of
course, however, choosing an institution that induces a sL*N0 will, as we noted above, never be in society’s interest.
17Formally, sHHE=s4
H|(zH,zN) = (1, 0) .J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 811

Now, rewriting the first-order condition that defines s4
H[see Eq. (3)] yields
DpHzH/C0zN ðȚ ¼ CVs4
H/C0/C1
¼gs4
H/C0/C1
s4
HCs4
H/C0/C1
Zs4
HzH/C0zN ðȚ ¼gs4
H/C0/C1
DpHCs4
H/C0/C1
: ð6Ț
Substituting Eq. (6) in Eq. (5) and re-arranging, one has
EW¼pCs4
H/C0/C1DWH
DpHgs4
H/C0/C1
/C0DpH
DWH/C21
ț1/C0zN ðȚ EWSRțzNEWLF;/C20
ð7Ț
which implies that, for gs*
H/C16/C17
bDpH
DWH, society is strictly better off by choosing either LF or SR
rather than an institution that induces investment in evidence production ( s4
HN0). Moreover, if z
is an optimal institution and if it gives rise to gs*
H/C16/C17
¼DpH
DWH, then either LF or SR is (also) an
optimal institution.
Next, suppose gs*
H/C16/C17
NDpH
DWH. We then obtain the following result.
Lemma 1. Let z LVzNVzHand (z H/C0zN)a(0, 1), and suppose that gs*
H/C16/C17
NDpH
DWH.Then
EWb(1/C0zN)E WHE+zNEWLF.
Proof. We can write
EW¼zH/C0zN ðȚps4
HDWH
gs4
HðȚgs4
H/C0/C1
/C0DpH
DWH/C20/C21
ț1/C0zN ðȚ EWSR
țzNEWLFb1/C0zN ðȚpsHE
HDWH
gsHE
HðȚgsHE
H/C0/C1
/C0DpH
DWH/C20/C21
țEWSR/C26/C27
țzNEWLF
¼1/C0zN ðȚ psHE
HDWH/C0psHE
HDpH
gsHE
HðȚțEWSR/C20/C21
țzNEWLF:
Here the first equality follows from Eqs. (6) and (7); the inequality follows from s*
HbsHE
H,zHV1,
andgVz0;18and the last equality is just a re-arrangement of terms. Making use of Eqs. (4) and
(6) evaluated at s*
H¼sHE
H,zN=0, and zH= 1, we have the inequality in the lemma. 5
The following proposition follows immediately from Lemma 1 and the preceding analysis.19
Proposition 1. No institution yields a higher expected welfare than the best one of SR, LF, and
HE. Moreover, an institution where z LNzNis never optimal, and an institution where
(zH/C0zN)a(0, 1)is never optimal if gs/C3
H/C0/C1
pDpH
DWH.
In other words, when society chooses an institution at stage (i), it will optimally select one
that either induces no evidence production at all or one where the insiders’ incentives for
evidence production when knowing that e=eHare as strong as possible—in that sense
society’s problem always has a corner solution. What is the reason for this? One economic
19Note that, even though it involves the endogenous variable s4
H, the case we exclude from consideration in the last
statement of the proposition is indeed non-generic. This is true because the definition of s4
Hdoes not contain DWH, which
means that DWHappears only on the right-hand side of gs*
H/C16/C17
¼DpH
DWH; hence, this equality holds for one unique value of
DWH.18Note in particular that gVz0 implies that the expression on the first line is increasing in s4
H.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 812

force that works in favor of a corner solution is that choosing a bmixed Qz-institution involves
throwing away costly but socially valuable information: by selecting such an institution societywill sometimes learn that the true post-merger efficiency is high, but still it does not permit themerger with probability one. The institutions SR, LF and HE, in contrast, do not involve suchwaste. For under LF and SR there is no investment at all in evidence production. And underHE there is, but then the information is always made use of in the sense that society permits
the merger with probability one when having learned that the efficiencies are high.
More generally, important for the corner-solution result is the fact that society cannot choose
s
LandsHdirectly, only indirectly through its choice of a z-institution. This means that
society’s optimal choice of an institution will depend on the insiders’ response. As aconsequence, society’s objective function is not necessarily a quasi-concave function of thechoice variables. Moreover, even when this objective function happens to be quasi-concave,society’s limited set of instruments will make an institution where the insiders choose aninterior s
Hundesirable.
4. The optimal merger control institution
It remains to answer the question how the three institutions LF, SR, and HE perform in terms
of expected welfare relative to each other. In doing this we will impose a stronger assumption onthe cost function Cthan before. Instead of just assuming that the cost elasticity is everywhere
weakly increasing, we will from now on say that the cost elasticity is constant; that is, C(s
i)=ksig
fori=L,H, where kN0 and gN1.20In order to make the comparisons it will be useful to
distinguish between two parameter regimes: pbp¯(bRegime I Q), and pNp¯(bRegime II Q), where
p¯u(WN/C0WL)/(WH/C0WL).21Regime I should thus be thought of as a situation where society is
relatively skeptical about the possibility of large efficiency gains, whereas in Regime II society isrelatively optimistic about this possibility.
First, it is easy to see that SR dominates LF in Regime I, and vice versa in Regime II. Second,
it turns out that SR strictly dominates HE if and only if gbDp
H/DWH. To see this, simply plug
zN=0 ,s4
H=sHHE, andg(s4
H)=ginto Eq. (7), which yields
EWHE¼pCsHE
H/C0/C1 DWH
DpHg/C0DpH
DWH/C19
țEWSR:/C18
It remains to compare HE and LF. From the above expression for EWHEwe see that
EWHENEWLFis equivalent to
pCsHE
H/C0/C1 DWH
DpHg/C0DpH
DWH/C19
NEWLF/C0EWSR¼pDWHț1/C0p ðȚ DWL;/C18
ð8Ț
the right-hand side of which is negative in Regime I and positive in Regime II. First suppose we
are in Regime I. Then, if gzDpH/DWH, we clearly have EWHENEWLF. In case gbDpH/DWH
21We will ignore the knife-edge case p=p¯.20This stronger assumption will actually only be needed for the comparison of LF and HE. The comparison of LF and
SR will of course not depend on the cost function, and our comparison of SR and HE below easily extends to any
arbitrary elasticity g(si). Still, to simplify the exposition, we make the stronger assumption already from the outset of this
section.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 813

there exists a level of k, call it kˆ, such that EWHENEWLFif and only if kNkˆ. Using Eq. (8), the
fact that
CsHE
H/C0/C1
¼k/C01
g/C01DpH
g/C18/C19 g
g/C01
;
and carrying out some straightforward algebra, we obtain
ˆkkuDpH
g/C18/C19g pDWH
DpHg/C0DpH
DWH/C16/C17
pDWHț1/C0p ðȚ DWL0
@1
Ag/C01
:
Next suppose we are in Regime II. Then for gVDpH/DWHwe always have EWHEbEWLF.I n
casegNDpH/DWH, we can, similarly to above, verify that EWHENEWLFif and only if kbkˆ.
Let us summarize the above results in the following proposition.
Proposition 2. Society ranks the three institutions LF, SR, and HE as follows :
!SRdLF in Regime I, and LF dSR in Regime II .
!HEdSR if and only if gNDpH/DWH.
!In Regime I, HE dLF if and only if either (i) gzDpH/DWHor (ii) gbDpH/DWHand
kNkˆ. In Regime II, LF dHE if and only if either (i) gVDpH/DWHor (ii) gNDpH/DWHand
kNkˆ.
By using Proposition 2 we can easily construct an overall ranking of the three institutions.
Fig. 2 indicates for what parameter values we obtain particular rankings; Panel A of the figure
covers Regime I whereas Panel B covers Regime II. Each panel depicts a diagram with kon the
vertical and gon the horizontal axis, and in each diagram the graphs of two functions are drawn:
kˆdefined above and k8uDpH/g. The latter function gives us a threshold of kabove which this
parameter must be for the insiders’ evidence-production decision under HE to have an interiorsolution (i.e., for s
HHEb1).
Before we proceed to discuss the intuition as to why we obtain the various rankings in
different parts of the parameter space, let us make the observation that the institution HE, whichis the only one of the three institutions that involves an efficiency defense, is indeed sometimesthe best one. Hence, Propositions 1 and 2 tell us that an efficiency defense is sometimesdesirable. When this is the case, however, the merger should be allowed if and only if high-
efficiency evidence is provided —in a sense, the burden of proof should be placed fully on the
insiders.
22The logic behind this conclusion is that an institution where the burden of proof is
placed fully on the insiders will give them strong incentives for evidence production [cf. Eq. (3)and the discussion following that equation]. Moreover, encouraging evidence production willunder certain circumstances be socially desirable.
22We use the expression bburden of proof Qwith some caution: in our model, the insiders are the only ones who have the
opportunity to provide any evidence, so we cannot say anything about whether society should require the insiders in
contrast to, say, the outsiders to provide evidence in favor of their case. The sense in which the burden of proof should beplaced fully on the insiders is that society should take a skeptical stance and make a decision in favor of the insiders only
when they have provided evidence in favor of their case.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 814

It is interesting to note that the argument that the burden of proof as to efficiencies should
rest on the insiders has been made before in the literature, although the logic leading up to
this conclusion has been quite different from the one here. For example, Fisher (1987, p. 36)
writes: bThe burden of proof as to cost savings or other offsetting efficiencies [ …] should
rest squarely on the proponents of a merger, and here I would require a very high standard.Such claims are easily made and, I think, often too easily believed. QIt seems clear that in
making this statement Fisher is concerned about the truthfulness of the insiders’ claims, andhe thinks of placing the burden of proof on them as a way of controlling this problem. Avery similar point is made by Neven et al. (1993, p. 206) :bWhen the burden of proof is on
the firm, the knowledge that information that it conceals may count against it in the1k°
∆WH∆πHk
η 0LFHESR
LFSRHE
kˆ
1k
η 0()
pL∆Wp-1–A
B∆πH
()∆WLp–1p-∆πHHESRLF
SRHELF
kˆ
SRLFHE
k°
∆WH∆πH∆πHHELFSR
()
pL∆Wp-1–
()∆WLp–1p-∆πH
Fig. 2. Panel A. Welfare comparison of institutions for Regime I. Panel B. Welfare comparison of institutions for
Regime II.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 815

investigation provides a powerful incentive in favour of revelation. QThis argument goes back
to the so-called unraveling result in the disclosure literature, which is due to Grossman
(1981) andMilgrom (1981) . The argument of the present paper is very different from—and
should be thought of as complementary to—the unraveling result. Indeed, updating of beliefsis not an issue here, because of our commitment assumption. Our analysis instead suggeststhat allowing a merger if and only if the insiders provide high-efficiency evidence may,
besides encouraging information revelation, also serve another important purpose, namely to
provide the insiders with strong incentives for socially valuable evidence production (orinformation acquisition).
23
Next, let us consider the condition HE dSR if and only if gNDpH/DWH, which we derived
above and which plays a particularly important role in Panel A of Fig. 2 . If there are positive
externalities (i.e., if DWHNDpH), then this condition says that we always have HE dSR, since
gN1.24This is intuitive, because if having a high-efficiency merger permitted instead of blocked
is worth more to society than to the insiders then the merging firms will underinvest, so society
should encourage evidence production as much as it can. Recall from Section 2 that having
positive externalities means that a bhighQpost-merger efficiency is so high that it would make
consumer surplus increase. Hence, a sufficient condition for HE to dominate SR (and, in RegimeI, for HE to be the best institution) is that, conditional on the event that the merger makes totalsurplus increase, the efficiency gains are so large that they are passed on to consumers in theform of a lower price. The reason why we obtain this result is notthat we are using a welfare
measure that takes into account only changes in consumer surplus—our welfare measure doesindeed consider total surplus.
25Rather, the reason is that when bhighQefficiencies are so high
that they induce a lower post-merger price, then the relationship between society’s and the
insiders’ interests is such that an efficiency defense will never give rise to overinvestment inevidence production and, hence, investment in evidence production should be fully encouraged.
If there are negative externalities, then HE will dominate SR only if the cost elasticity is large
enough. Why does the cost elasticity play such an important role here? One—perhaps rathermechanical—way of seeing this is by noticing that for large elasticities the cost C(s
H) is low
relative to the amount of information that one gets for these expenditures, sH,26which clearly
23Another interesting question concerns the optimal standard of proof: how convincing should one should require a
given piece of evidence to be and what should be the minimal level of efficiency that must be proven? In our model we
have abstracted from these questions since, by assumption, a piece of information either reveals the true state perfectly or
not at all and our state space is binary. In a richer model, in which one or both of those assumptions were relaxed, wewould be able to derive the optimal standard of proof. If we did that, however, we would not generally expect the highestpossible standard to be optimal. For requiring a very high standard of proof would not necessarily create the strongest
possible incentives for evidence production. To see this, imagine an example were there are more than two states and
where the insiders can get their case through only by finding evidence in favor of the very highest state. This might be sodifficult and costly to do that investing in evidence production would not be as worthwhile as under a less stringent
standard-of-proof requirement.
24Notice that both Panel A and B are drawn for the case where there are negative externalities.
26This is a property of the cost function C(sH)=ksHg. To see this, the reader may find it helpful to sketch the
graph of C(sH) as a function of sHfor different gs. For gs close to unity the graph is almost linear whereas for
larger gs it is more curved, which makes it possible to have relatively large sHs and at the same time low levels
ofC(sH).25Compare the following statement by Fisher (1987, p. 38) , who clearly has a consumer standard in mind: b…I would
hesitate to use such efficiencies as an excuse for permitting a merger if those efficiencies are unlikely to be passed on to
consumers. QJ.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 816

makes HE more attractive. Another way of understanding the role of the cost elasticity, which is
more in terms of economics, is to make the following observation: in equilibrium, the costelasticity equals the insiders’ bsurplus from evidence production; Qthat is, if we let B(s
HE
H) denote
the insiders’ gross benefit from having HE instead of SR conditional on knowing that e=eH,27
then we can write28
g¼BsHE
H/C0/C1
CsHE
HðȚ: ð9Ț
Hence, the larger is g, the more do the insiders’ benefits of having HE rather than SR exceed
their costs. As a result, for large enough gs, HE will be socially desirable also when there are
negative externalities.
Now let us move our attention from Panel A to Panel B. Here, for HE to be the best
institution, it does not suffice that gNDpH/DWH. As the figure indicates, the requirement on gis
stronger than that. Moreover, the other parameter in the cost function, k, must not be too large.
Apparently, there is an asymmetry between a situation where society is skeptical about thepossibility of large efficiency gains (Regime I) and one where it is more optimistic (Regime II):in the latter case HE (and, hence, an efficiency defense) is less likely to be optimal. The basicreason for this asymmetry is that the insiders have a vested interest in having the mergerpermitted, regardless of whether the efficiency gains are small or large. Moreover, in Regime I
this vested interest will be easier to deal with for society than in Regime II. For, in Regime I, if
not having received a report it will be optimal for society to block the merger, whereas inRegime II it may in that case be optimal to permit the merger. This means that in Regime Isociety will need to know about a high state, something it can obtain information about with arelatively large likelihood by choosing the institution HE. In Regime II, however, society wouldlike to know about a lowstate, which they never will get information about from the insiders.
The asymmetry between Regime I and II is neatly illustrated by considering the limits pY0
andpY1. In the former case we still have the condition that HE is best if and only if gN
DpH
DWH,
since that condition is independent of p. In the latter case, however, LF is always the best
institution.
Proposition 3 sums up the results.
Proposition 3. The institution that maximizes expected welfare is:
!In Regime I: SR if gbDpH
DWHand HE if gbDpH
DWH.
!In Regime II: LF if gbDpH
DWH,orgNDpH
DWHand k Nkˆ; and HE if gNDpH
DWHand k bkˆ.
The bottom line message of Proposition 3 and the preceding analysis can be stated as follows.
By allowing for an efficiency defense society also encourages costly evidence production (orinformation acquisition). Doing this may be good or bad, depending on (i) how society’s and theinsiders’ interests relate to each other, (ii) how optimistic or pessimistic society is about thelikelihood that the merger will increase total surplus, and (iii) the technology for evidenceproduction (in particular the cost elasticity). An efficiency defense will indeed be optimal under
28To see this, note that, by definition, g=sHCV(sH)/C(sH). Moreover, from the first order condition that defines sHHE,
we have sHHECV(sHHE)=B(sHHE).27Formally, B(sHHE)uE(pHE|e=eH)/C0EpSR=(sHHEDpH+pN)/C0pN=sHHEDpH.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 817

some circumstances—but, when this is the case, the merger should be allowed if and only if the
insiders provide evidence of high efficiencies. Moreover, an efficiency defense is more likely tobe optimal (from a total surplus point of view) when bhighQefficiencies are so high that they
would give rise to a lower market price. This is because then the insiders’ incentives to invest aresuch that society should encourage evidence production as much as it can. Finally, there is animportant asymmetry between a situation where society is pessimistic and where it is optimistic
about the possibility that total surplus will increase due to the merger: an efficiency defense is
more likely to be harmful in the latter case.
We have seen that an efficiency defense can be undesirable because it leads to excessively
high spending on evidence production. As the following example shows, it can also beundesirable (relative to LF) if a high (marginal) cost of evidence production deters theproduction of evidence, which then leads to the blocking of mergers that society would wantallowed. When this happens, an efficiency defense is undesirable even though the observed costsof evidence production are negligible.
Example. Suppose DW
H=DpH=200 (which means that there are bno externalities Q) and
DWL=/C0100. Moreover, let p=1/2, which means that we are in Regime II (i.e., LF dSR).
Further assume that the cost function is quadratic: g=2. We then have that kˆ=k8=100, so the
assumption that we have an interior solution to the evidence production decision ( kNk8)
amounts to kN100. In terms of Panel B of Fig. 2 , we are now somewhere along the vertical line
that crosses the intersection of the graphs of kˆandk8, but above this intersection. As the figure
tells us, in this part of the parameter space LF dHEdSR; that is, here one should not allow for
an efficiency defense but instead allow all mergers.
The investment costs in this example are C(sHE
H)= 10000/ k, an expression that is decreasing
ink; the reason is that, even though kenters directly in the cost function with a positive sign, the
endogenously chosen sHE
His decreasing in k, and this latter effect dominates the first.29Hence,
for a fixed DWH, we can make C(sHE
H) very small by increasing k. Yet, LF dHE (indeed, the
difference EWLF/C0EWHEis increasing in k).
While the argument that an efficiency defense can be undesirable due to excessively high
costs of evidence production is incomplete, it is not incorrect in general. One can construct a
similar example for the case in which SR dLF (so that Panel A of Fig. 2 is relevant). Here the
excessive-cost intuition as to why an efficiency defense may be bad is indeed correct; the easiestway to see this is from Eq. (4) and the discussion following that equation. In particular, inRegime I both the (expected) investment costs and the benefit with having an efficiency defenseare decreasing in k. Hence, also for a very low level of merger review expenditures, the
expenditures may not be worthwhile for society. In contrast to Regime II, however, when in thiscase an efficiency defense is suboptimal and induces very low costs, it is suboptimal only with asmall margin.
5. Implications for antitrust policy
Our results are, of course, derived from a stylized model, and by studying our particular setup
we have abstracted from many economic phenomena that are important for the choice of amerger control institution but which are not captured here. Still, keeping these limitations in
29Since CsHE
H/C0/C1
¼k/C01
g/C01DpH
g/C16/C17 g
g/C01, the endogenously chosen costs of evidence production are always decreasing in k
and hence this fact does not depend on the chosen numerical example.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 818

mind, it is useful to spell out what our results imply for antitrust policy and the design of merger
control institutions.
Let us first be more specific about how we interpret the institutions LF and SR of our model.
We think of these as representing situations where society (or an antitrust authority) has made acommitment not to take efficiency considerations into account when deciding whether to permit
the merger. Still, these institutions are fully consistent with a merger control procedure in which
this decision is contingent on other circumstances, as long as information about these is publicly
available. Thus, what we believe is special with efficiency gains is that this is something that theinsiders are likely to have (or be able to obtain) private information about.
Another important question is how one should understand the insiders’ binfluence
activities. QOne interpretation, which is the one we emphasize here, is that this term refers to
the insiders’ communication with an antitrust authority in a formal regulatory hearing.Another and broader interpretation would be that the influence activities also take place ininformal (and perhaps secret) interactions between the insiders and officials from the antitrust
authority. As long as we are willing to make the former interpretation, it seems reasonable
that the decision whether to allow for an efficiency defense does not have to be made onceand for all, but could be made contingent on information about a particular merger case. If so,then we can make use of the results and insights from the previous section in order to designa merger control procedure that allows for an efficiency defense only when the circumstancesare right.
Below we sketch such a procedure. This involves three steps,
30and it is constructed by means
of simply inspecting Panel A and B of Fig. 2 : first it is determined which panel is the relevant;
then it is decided where in a particular panel we are likely to be. As one moves from Step 1 to
Step 2 and from Step 2 to Step 3 in the procedure, gradually more information about variousparameters is required; for example, when a decision about the merger can be reached alreadyafter Step 1 or 2, one does not need access to any information about the evidence productiontechnology. Hence, even though the nature of the tradeoff that we study in this paper is such thatthe technology for evidence production is bound to matter in at least some situations, theprocedure illustrates how the insights from the model can guide an antitrust authority also whensuch information is unavaliable. Our procedure presupposes that the region in Panel B where HE
is optimal is irrelevant in practice. This is always true if society, whenever it is boptimistic Qabout
having high efficiency gains, is sufficiently optimistic (i.e., that pis large enough). If one
believes that the HE-region of Panel B is sometimes relevant, then the procedure below will be abit more complex.
Step 1 An antitrust authority that is faced with a proposed merger asks itself the following.
Given the information that we have access to at this stage of the procedure (i.e., prior toany reports from the insiders about the size of the efficiencies), do we think that total
surplus (not including any costs of evidence production) will rise thanks to the merger? If
the answer to this question is yes, then the antitrust authority simply permits the merger.If the answer is no, then the antitrust authority proceeds to Step 2.
Step 2 The antitrust authority asks itself the following. Suppose, hypothetically, that we knew
that the total surplus gains due to the merger (not including any costs of evidence
30The steps should be thought of as bsteps of reasoning. QThere is thus no need to let (a significant amount of) time
elapse between one step and the following.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 819

production) indeed would be positive. Then, conditional on that information, do we think
the efficiencies are so high that they would be passed on to consumers (i.e., induce alower post-merger price)? If the answer to this question is yes, then the antitrust authorityasks the insiders to provide it with evidence about the size of the efficiencies. In case theinsiders do come up with convincing evidence that the efficiencies are large enough toraise total surplus (not including any costs of evidence production), then the antitrust
authority permits the merger; otherwise it does not. If the answer to the question is no,
then the antitrust authority proceeds to Step 3.
Step 3 The antitrust authority asks itself the following. Suppose, hypothetically, that we knew
that the total surplus gains due to the merger (not including any costs of evidenceproduction) indeed would be positive. Then, conditional on that information, do we thinkthat the insiders’ technology for evidence production (or information gathering) is suchthat the cost elasticity is large relative to the rise in market price due to the merger? If theanswer to this question is yes, then the antitrust authority asks the insiders to provide it
with evidence about the size of the efficiencies. In case the insiders do come up with
convincing evidence that the efficiencies are high enough to raise total surplus (notincluding any costs of evidence production), the antitrust authority permits the merger;otherwise it does not. If the answer to the question is no, then the antitrust authorityblocks the merger without asking for evidence.
A couple of remarks about this three-step procedure are in order. First, even though it may
look as if the procedure does not consider other important criteria than the possible existence of
efficiency gains, these are indeed captured by Step 1. For when the antitrust authority makes an
assessment of the likelihood that total surplus will increase thanks to the merger, it effectivelyalso appraises, for example, the merger’s impact on the degree of concentration in the relevantmarket. Second, if the antitrust authority has to proceed to Step 3, then information about thecost elasticity will be needed. The magnitude of this elasticity may of course be hard to observein reality. Still, as our procedure indicates, in several cases it will be possible to tell whether ornot an efficiency defense is desirable without knowing the elasticity. Inevitably, though,sometimes knowledge about the cost elasticity will be needed. Hopefully, in those cases the
interpretation of the elasticity as the bsurplus from evidence production, Qwhich we provided
earlier [see Eq. (9)], will be helpful in making informed guesses about its magnitude (or even,after all, estimate it using some observable data).
6. Possible extensions
In this concluding section we will briefly discuss some possible extensions and variations of
our model.
6.1. Evidence production vs. information gathering
In our model we have assumed that the insiders know from the outset whether the
efficiencies are high or low but must invest resources in order to be able to communicate thisinformation. An alternative assumption would be to say that the insiders at the outset have justas little information about the efficiencies as society, but that they can invest resources in orderto find such (hard) information. Hence, the insiders’ investment decision would then not be
contingent on the true state. We were using this model specification in an earlier version of theJ.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 820

paper, and it yields very similar results. In fact, most of the analysis is identical to the one
here—the only difference is the comparison between HE and LF (in particular, the cut-off valuekˆis slightly differently defined), and even for that comparison the qualitative results remain the
same.
6.2. A consumer standard instead of a welfare standard
Throughout we have assumed that society maximizes total surplus (including any costs of
evidence production). How would the analysis change if we instead assumed a consumerstandard? To see this, first notice that if only consumer welfare counts, the costs of evidenceproduction will not enter the social welfare function. Moreover, Fig. 1 tells us what the benefits
for the consumers of permitting a merger (i.e., DCS in the figure) are. We see that as long as
there are negative externalities, society will always want to block the merger (thus making SRoptimal). If there are positive externalities, then the incentive structure will be similar to what we
have under our welfare standard. Since evidence production is bfor free, Qit is fairly easy to see
that here SR is always inferior to HE. Moreover, a bmixed Qz-institution will never be optimal.
The optimal institution is thus either HE or LF. One can show that there is a cut-off value of p
such that below this HE is optimal and above it LF is optimal.
31
6.3. Other parties’ trying to influence the merger control procedure
We have assumed that only the insiders can provide society with information and thereby try to
influence the decision whether to permit the merger. We think of this as the most natural case, since
the insiders should have better access to information about any efficiencies than, for example, theother firms in the market (i.e., the outsiders). Still, one may wonder how the results would beaffected if also the outsiders or the consumers could produce evidence. Again, Fig. 1 helps us
understand the incentives of these other groups. First suppose we have positive externalities (weassume again, as in our main model, a welfare standard). Then we see from the figure that theoutsiders’ interests are always opposed to society’s; hence, the outsiders would not be able tocredibly transmit any information. We also see that the consumers’ and society’s interests are
identical; thus, any information that the consumers had access to would also be available to society,
which would at least mitigate the informational assymmetries between society and the insiders.
31We can write ECSSR=C S N, ECSLF= pCS H+(1/C0p)CS L, and ECSHE=psHHEDCSH+CS N(where the notation is
self-explanatory). As in the total-welfare-standard model, we can without excluding any optimal institution presume thatz
LVzNVzH. Hence, analogously to Eq. (5), we can write
ECS ¼ps4
HzH/C0zN ðȚ DCSHț1/C0zN ðȚ ECSSRțzNECSLF:
An institution where ( zH/C0zN)a(0, 1) cannot be (uniquely) optimal. To see this, suppose that we do have
(zH/C0zN)a(0,1) in an optimal institution. Then we can write
ECSVpsHE
H1/C0zN ðȚ DCSHț1/C0zN ðȚ ECSSRțzNECSLF¼1/C0zN ðȚ ECSHEțzNECSLF;
where the inequality is strict if zHb1. This contradicts the assumption that the institution is (uniquely) optimal. Hence,
either HE or LF is optimal (notice that this result holds without any particular assumptions about the cost elasticity).Straightforward algebra shows that the cut-off value of pabove which LF is best is given by
p¼/C0DCSL
1/C0sHE
H ðȚ DCSH/C0DCSL:J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 821

Second, suppose we have negative externalities. Then Fig. 1 tells us that the outsiders and the
insiders have identical interests. This means that society can receive information from twoparties instead of only one, which could make it less attractive to encourage maximal evidenceproduction through HE. On the other hand, there should also be a free-riding problem, and theconvex cost functions may make evidence production more worthwhile when it is spread out ontwo parties. It is thus not clear whether this alternative model would make an efficiency defense
more or less desirable and whether, as before, the answer would depend only on the magnitude
of the cost elasticities.
32Finally, with negative externalities the consumers will always be against
the merger. Also here is it rather difficult to know how the results would change: there should bedifferent effects working in opposite directions. We leave this and the other open questions tofuture research.
6.4. The insiders’ being able to fabricate evidence
We have assumed that the insiders can, at a cost, obtain hard evidence that confirms their true
type. Consider the following alternative assumption: the low-efficiency insiders can in additionobtain (false) evidence showing that the efficiencies are large.
33Doing this is costly, and it is
modeled in the same way as in our original model. To see how this will change the analysis andthe results, first note that the antitrust authority very well understands that the evidence may befalse and takes this into account when choosing the optimal institution. Moreover, any evidenceproduction costs incurred by the low-efficiency insiders will always be wasted from society’spoint of view: the costs enter society’s objective function and (as long as z
HNzN) the false
evidence leads to a bad merger being allowed. This social cost, which comes on top of any social
costs in the original model, can be avoided only by choosing an institution that does not allowfor an efficiency defense (i.e., by setting z
H=zN).
In the Appendix we show that, under the assumption that the cost elasticities are constant
and identical across types, the optimal institution in this extension of our model is (again)either SR, LF, or HE. Moreover, the comparison between SR and LF is (trivially) unaffectedby the extension. What can and will change, however, are the comparisons between SR andHE and between LF and HE. In both cases, the conditions for HE to be the best institution are
more stringent relative to those in the original model, because of the additional social cost
associated with any institution that involves an efficiency defense. If, however, HE is strictlyoptimal in our original model, it remains optimal if the (marginal) cost of fabricating evidenceis sufficiently large. Furthermore, even if one adopts the extreme view that it is as costly toproduce (real) evidence as it is to fabricate evidence, HE (and thus an efficiency defense) cannevertheless be desirable. The reason is that even if the cost functions for producing andfabricating evidence are identical, insiders that anticipate high efficiency gains have a strongerincentive to obtain evidence in favor of their case (recall that Dp
HNDpL). Thus, even if the
evidence technology is completely ineffective in distinguishing between high- and low-
efficiency firms, in equilibrium, the evidence presented can nevertheless be helpful in reachinga desirable decision.
33This extension has also been studied by Medvedev (2004) in a related model that builds on a discussion paper version
of our paper.32Such a model would also make the z-institutions more complex, since the decision whether to permit a merger could
be made contingent on, for example, whether only one of the interested parties have submitted a particular report or
whether both have done this.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 822

6.5. The verification of reports being costly for the antitrust authority
We have assumed that the antitrust authority can verify the truthfulness of any claim made
by the insiders at no cost. In practice, it may be that the antitrust authority must devote aconsiderable amount of resources—related to lawyers, economists and other support staff, aswell as hiring of external experts—to assess the truthfulness of such claims. If we
incorporated such costly verification into our model, how would this affect our results? The
answer is likely to depend on exactly how one chose to model the costly verification.Under quite broad circumstances, however, the same basic tradeoff as in our present modelshould matter also in such an extension. In particular, in an environment where the antitrustauthority is forced to (or has an ex post incentive to) incur verification costs each time theinsiders make claims about high efficiencies, this will add to the social cost of anefficiency defense. Moreover, since the insiders would not internalize these costs whenmaking their evidence-production decision, we should expect the costs of having an
efficiency defense to be larger in such an environment than in our original model. To what
extent other insights from our analysis would be altered is more difficult to tell (without amore detailed investigation), and we leave this question to future work.
Acknowledgement
This paper was produced as part of a CEPR research network funded by the European
Commission under the TMR program (contract #ERBFMRXCT980203). For helpful
comments we thank three anonymous referees, the two editors, Thorsten Bayindir-Upmann,
Ramo ´n Faulı ´-Oller, Franklin Fisher, Fabienne Ilzkovitz, Karl Morasch, Rainer Nitsche,
Michael Raith, Johan Stennek, Christian Wey, as well as conference and seminar participantsat ESEM 2001 (Lausanne, Switzerland), EARIE 2001 (Dublin), the Verein fu ¨r Socialpolitik
Meetings 2001 (Magdeburg, Germany), Leuven (Belgium), ECARES (Brussels), the 1stBarcelona Workshop on Economic Design 2001, the 10th WZB Conference on IO 2001(Berlin), the TMR workshop in Lisbon 2001, EEA 2002 (Venice, Italy), Auschuss fu ¨r
Industrieo ¨konomik March 2003 in Munich, International Industrial Organization Conference
2003 (Boston), and the IO lunch at MIT. Part of Lagerlo ¨f’s research was carried out while
he visited ECARES at the Free University of Brussels, whose hospitality he gratefullyacknowledges.
Appendix A
In this appendix we provide calculations that verify the claims made in connection to the
penultimate extension discussed in Section 6.
Assume that the insiders, also when knowing that e=e
L, can produce (fabricate) bevidence Q
that the efficiency gains are large. This evidence production is modeled just as in our originalmodel. The cost function for fabricating evidence is denoted K(s
F), where the argument sFis
the fabricating low-efficiency insiders’ investment level, and the corresponding cost elasticity ofevidence fabrication is denoted g
F(sF). When having soft information that e=eL, the insiders
face the following problem:
max
sFa0;1½/C138sFzHț1/C0sF ðȚ zN ½/C138 pLțsF1/C0zH ðȚ ț 1/C0sF ðȚ 1/C0zN ðȚ ½/C138 pN/C0KsFðȚJ.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 823

(they also choose sL, but this will in equilibrium equal zero, so we can safely ignore that choice).
The solution to this problem, sF*, equals zero if zHVzNand is implicitly defined by
DpLzH/C0zN ðȚ ¼ KVs4
F/C0/C1
ð10Ț
otherwise.
The expression for expected welfare at stage (i) under our alternative assumption can be
written as [cf. Eq. (5)]
EW¼ps4
HzHț1/C0s4
H/C0/C1
zN/C2/C3
WHț1/C0p ðȚ s4
FzHț1/C0s4
F/C0/C1
zN/C2/C3
WLțp½s4
H1/C0zH ðȚ
ț1/C0s4
H/C0/C1
1/C0zN ðȚ /C138 WNț1/C0p ðȚ s4
F1/C0zH ðȚ ț 1/C0s4
F/C0/C1
1/C0zN/C2/C3
WN/C0pCs4
H/C0/C1
/C01/C0p ðȚ Ks4
F/C0/C1
¼ps4
HzH/C0zN ðȚ DWHț1/C0p ðȚ s4
FzH/C0zN ðȚ DWL
ț1/C0zN ðȚ EWSRțzNEWLF/C0pCs4
H/C0/C1
/C01/C0p ðȚ Ks4
F/C0/C1
: ð11Ț
Note that this expression is larger for sF*=0 than it is for any sF*N0: fabrication is always bad for
welfare. Restricting attention to the relevant case in which zHzzN, we rewrote the first-order
condition that defines sH*in Section 3 , obtaining Eq. (6) . Similarly, for sF*we have
s4
FzH/C0zN ðȚ ¼gFs4
F/C0/C1
DpLKs4
F/C0/C1
: ð12Ț
Substituting Eqs. (6) and (12) in Eq. (11) and re-arranging, one has
EW¼pCs4
H/C0/C1DWH
DpHgs4
H/C0/C1
/C0DpH
DWH/C20/C21
ț1/C0zn ðȚ EWSRțzNEWLF
ț1/C0p ðȚ Ks4
F/C0/C1DWL
DpLgFs4
F/C0/C1
/C0DpL
DWL/C20/C21
: ð13Ț
The last term is negative for any sF*N0 (recall that DWLb0 and DpLN0). The first term is non-
positive if gs/C3
H/C0/C1
VDpH
DWH. If the sum of the first and the last term is negative, then society is strictly
better off by choosing either LF or SR rather than an institution that induces investment inevidence production.
Let us now prove a result that corresponds to Lemma 1. From now on, we assume that the
cost functions have constant and identical elasticities, denoted by g. The first line of the proof of
Lemma 1 here becomes
EW¼z
H/C0zN ðȚps4
HDWH
gg/C0DpH
DWH/C20/C21
ț1/C0p ðȚ s4
FDWL
gg/C0DpL
DWL/C20/C21 /C26/C27
ț1/C0zN ðȚ EWSRțzNEWLF: ð14Ț
We can write the expression on the first line as ( zH/C0zN)H(zH), where
Hz HðȚuAs4
HțBs4
F;
AupDWH
gg/C0DpH
DWH/C20/C21
;J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 824

and
Bu1/C0p ðȚ DWL
gg/C0DpL
DWL/C20/C21
:
In order to get the second line of the lemma, it suffices to show that if H(zH)N0, then
(zH/C0zN)H(zH) is increasing in zH. Differentiating ( zH/C0zN)H(zH) with respect to zHand
requiring the resulting expression to be greater than zero yield
As4
HțBs4
FțzH/C0zN ðȚ ABs4
H
BzHțBBs4
F
BzH/C20/C21
N0ZAs4
H1țzH/C0zN ðȚBs4
H
s4
HBzH/C20/C21
țBs4
F1țzH/C0zN ðȚBs4
F
s4
FBzH/C20/C21
N0: ð15Ț
Recall the first-order conditions that define sH* and sF*:
zH/C0zN ðȚ DpH¼CVs4
H/C0/C1
ð16Ț
and
zH/C0zN ðȚ DpL¼KVs4
F/C0/C1
: ð17Ț
Using these, one can easily check that
Bs4
H
BzH¼DpH
CWs4
HðȚð18Ț
and
Bs4
F
BzH¼DpL
KWs4
FðȚ: ð19Ț
Using Eqs. (16)–(19) in Eq. (15), we have
As4
H1țCVs4
H/C0/C1
DpHDpH
s4
HCWs4
HðȚ/C20/C21
țBs4
F1țKVs4
F/C0/C1
DpLDpL
s4
FKWs4
FðȚ/C20/C21
N0:
Under the constant (and identical) elasticity assumption, this simplifies to
As4
H1ț1
g/C01/C20/C21
țBs4
F1ț1
g/C01/C20/C21
N0
or equivalently AsH*+BsH*N0. Hence, under the assumption that H(zH)N0, the first line of Eq.
(14) is increasing in zH. This means that we have
EWb1/C0zN ðȚpsHE
HDWH
gg/C0DpH
DWH/C20/C21
ț1/C0p ðȚ sHE
FDWL
gg/C0DpL
DWL/C20/C21
țEWSR/C26/C27
țzNEWLF;
which parallels the second line of the proof of Lemma 1. The remaining steps are completely
analogous to the ones in the proof of Lemma 1 and therefore omitted.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 825

Thus, allowing for the fabrication of evidence as modeled above, we obtain the following
variant of Proposition 1:
Proposition A1. No institution yields a higher expected welfare than the best one of SR, LF, and
HE. Moreover, an institution where z LNzNis never optimal, and an institution where
(zH/C0zN)a(0,1) is never optimal except possibly in a knife-edge case .
References
Aghion, Philippe, Tirole, Jean, 1997. Formal and real authority in organizations. Journal of Political Economy 105,
1 –29.
Austen-Smith, David, Wright, John R., 1992. Competitive lobbying for a legislator’s vote. Social Choice and Welfare 9,
229–257.
Besanko, David, Spulber, Daniel F., 1993. Contested mergers and equilibrium antitrust policy. Journal of Law,
Economics, and Organization 9 (1), 1 –29.
Corcho ´n, Luis C., Faulı ´-Oller, Ramo ´n, 2003. bTo merge or not to merge: that is the question Q. Review of Economic
Design 9 (1), 11 –30.
Daughety, Andrew F., Reinganum, Jennifer F., 2000. On the economics of trials: adversarial process, evidence, and
equilibrium bias. Journal of Law, Economics, and Organization 16 (2), 365–394.
Deneckere, Raymond, Davidson, Carl, 1985. Incentives to form coalitions with Bertrand competition. RAND Journal of
Economics 16, 473– 486.
Dewatripont, Mathias, Tirole, Jean, 1999. Advocates. Journal of Political Economy 107, 1 –39.
European Commission, 2001. Green paper on the review of council regulation (EEC) No 4064/89 Available at. http://
europa.eu.int/comm/competition/mergers/review/ .
Farrell, Joseph, Shapiro, Carl, 1990. Horizontal mergers: an equilibrium analysis. American Economic Review 80,
107–126.
Farrell, Joseph, Shapiro, Carl, 2001. Scale economies and synergies in horizontal merger analysis. Antitrust Law Journal
68, 685–710.
Fisher, Franklin M., 1987. Horizontal mergers: triage and treatment. Journal of Economic Perspectives 1, 23– 40.
Froeb, Luke M., Kobayashi, Bruce H., 2001. Evidence production in adversarial vs. inquisitorial regimes. Economics
Letters 70, 267– 272.
Grossman, Sanford J., 1981. The informational role of warranties and private disclosure about product quality. Journal of
Law and Economics 24, 461– 483.
Grossman, Gene M., Helpman, Elhanan, 2001. Special Interest Politics. MIT Press, Cambridge, MA.Ilzkovitz, Fabienne, Meiklejohn, Roderick, 2001. European merger control: do we need an efficiency defence?
European Economy 5, 3 – 30. (Available at: http://www.europa.eu.int/comm/economy _finance/publications/european _
economy/2001/eers0501 _en.pdf ).
Laffont, Jean-Jacques, Tirole, Jean, 1993. A Theory of Incentives in Procurement and Regulation. MIT Press, Cambridge,
MA.
Lagerlo ¨f, Johan, 1997. Lobbying, information, and private and social welfare. European Journal of Political Economy 13,
615–637.
Legros, Patrick, Newman, Andrew, 1999. bInterference: Contracts and Authority with Insecure Communication. QMimeo,
ECARES, ULB. Available at: http://homepages.ulb.ac.be/~plegros/research.htm .
Lewis, Tracy, Poitevin, Michel, 1997. Disclosure of information in regulatory proceedings. Journal of Law, Economics,
and Organization 13 (1), 50– 73.
Medvedev, Andrei, 2004. bEfficiency Defense and Administrative Fuzziness in Merger Regulation. QCERGE-EI Working
Paper 234. Available at: http://www.cerge-ei.cz/pdf/wp/Wp234.pdf .
Milgrom, Paul, 1981. Good news and bad news: representation theorems and applications. Bell Journal of Economics 12,
380–391.
Neven, Damien J., Ro ¨ller, Lars-Hendrik, 2000. Consumer Surplus vs. Welfare Standard in a Political Economy Model of
Merger Control. CEPR Discussion Paper, vol. 2620.
Neven, Damien, Nuttall, Robin, Seabright, Paul, 1993. Merger in Daylight: The Economics and Politics of European
Merger Control. CEPR, London, UK.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 826

PricewaterhouseCoopers, 2003. A tax on mergers? Surveying the time and costs to business of multi-jurisdictional
merger reviews. QA study commissioned by the International Bar Association and the American Bar Association
Available at. http://www.pwcglobal.com/uk/eng/about/svcs/vs/pwc _mergers.pdf .
Ro¨ller, Lars-Hendrik, Stennek, Johan, Verboven, Frank, 2001. Efficiency gains from mergers. European Economy 5,
31–128. (Available at: http://www.europa.eu.int/comm/economy _finance/publications/european _economy/2001/
eers0501 _en.pdf ).
Sanchirico, Chris William, 2001. Relying on the information of interested–and potentially dishonest–parties. American
Law and Economics Review 3, 320– 357.
Shavell, Stephen, 1994. Acquisition and disclosure of information prior to sale. RAND Journal of Economics 25,
20–36.
Shin, Hyun Song, 1998. Adversarial and inquisitorial procedures in arbitration. RAND Journal of Economics 29,
378–405.
Spector, David, 2003. Horizontal mergers, entry, and efficiency defences. International Journal of Industrial Organization
21, 1591– 1600.
Tullock, Gordon, 1975. On the efficient organization of trials. Kyklos 5, 745– 762.U.S. Department of Justice, U.S. Federal Trade Commission, 1997. 1992 Horizontal merger guidelines [with April 8,
1997, revisions to section 4 on efficiencies] Available at. http://www.ftc.gov/bc/docs/horizmer.htm .
Williamson, Oliver E., 1968. Economies as an antitrust defense: the welfare tradeoffs. American Economic Review 58,
18–36.
Yao, Dennis A., Dahdouh, Thomas N., 1993. Information problems in merger decision making and their impact on
development of an efficiencies defense. Antitrust Law Journal 61, 23–45.J.N.M. Lagerlo ¨f, P. Heidhues / Int. J. Ind. Organ. 23 (2005) 803–827 827