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A Theory of Strategic Mergers
AbstractWe examine how the state of industry demand affects firms' strategic incentives to engage in
horizontal mergers. In a real options framework, we show that mergers motivated by the pursuit of
market power are consistent with the abnormally high takeover intensity during periods of
especially high and low demand, documented in past empirical studies. Such pattern is the result of
firms' strategic interaction in output markets and holds in the absence of any technological and
financial benefits from mergers. We extend the base case model by examining how operatingsynergies, merger-related costs, and variations in industry structure affect the likelihood and timing
of horizontal mergers. Using parametric and semi-parametric regression analysis, we estimate the
empirical relation between the state of demand and takeover intensity. The evidence shows that
there is a U-shaped relation between the state of demand, as proxied by industry sales growth, and
the propensity of firms to merge horizontally, controlling for firms' non-strategic incentives to
merge. Furthermore, consistent with the model's predictions, this relation is driven by horizontal
mergers within relatively concentrated industries, whereas no such relation exists in industries in
which strategic considerations are likely to be less important.
JEL classifications: G34.
Keywords: horizontal mergers, competition, strategic interaction, real options.
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1 Introduction and related literature
Recent years have witnessed an explosion of research on mergers, in particular investigations of the
reasons for and timing of mergers and takeovers. We have satisfactory answers for some merger-related
questions, for example regarding the effects of mergers on bidders and targets values. However, as
Andrade, Mitchell, and Stafford (2001) note in their survey paper, on the issue of why mergers occur,research success has been more limited.
There are several reasons why firms may choose to merge. The list includes, but is not limited
to, efficiency-related gains (e.g., Jovanovic and Rousseau (2002), Erard and Schaller (2002), and Lam-
brecht (2004)), disciplining target management (e.g., Jensen and Ruback (1987) and Morck, Shleifer
and Vishny (1989)), responding to economic shocks (e.g., Gort (1969) and Mitchell and Mulherin
(1996)), and pursuit of market power (e.g., Stigler (1950), Perry and Porter (1985) and Deneckere and
Davidson (1985)). In addition to neoclassical motives, recent studies (e.g., Shleifer and Vishny (2003),
Rhodes-Kropf and Viswanathan (2004), and Rhodes-Kropf, Robinson and Viswanathan (2006)) sug-
gest a link between takeover activity and stock market misvaluation.
Although there is an ongoing debate regarding the merits and deficiencies of each of the proposed
explanations of mergers, there is a consensus on some important empirical aspects of merger activity:
mergers occur in waves and, within each wave, they tend to cluster by industry (e.g., Mitchell and
Mulherin (1996), Andrade and Stafford (2004), and Harford (2005)). Nonetheless, what determines
the timing of mergers remains an open question.
Many existing theories of merger timing focus on firms as independent entities and ignore com-
petition in product markets. The empirical evidence, however, suggests that in many cases mergers
significantly affect an industrys competitive structure, as well as firms pricing strategies. Akhavein,
Berger, and Humphrey (1997) and Prager and Hannan (1998), for instance, document that mergers
in the banking industry generally lead to increased market power and, consequently, lower deposit
interest rates. Similar evidence within the airline industry is reported by Borenstein (1990), Kim and
Singal (1993), and Singal (1996). A case study of acquisitions in the microfilm industry by Barton and
Sherman (1984) indicates significant post-merger price increases. Therefore, it seems reasonable that
market power considerations may affect firms incentives to merge and, thus, the dynamics of mergers.
We explore the link between strategic considerations and the dynamics of mergers and extend
the theoretical merger literature by proposing a model that examines the effects of product market
competition and industry structure on firms incentives to merge. Ceteris paribus, a horizontal merger
increases the combined value of the merging firms, due to the post-merger collusion in output markets.
However, the reduced competitiveness of the industry following a merger also increases the value of a
potential entrant to the industry and its incentives to enter.1 Potential entry reduces the value of the
1 The effect of merger on the incentives to enter is not only a clear result of an oligopolistic competition model, but
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incumbents and, thus, reduces their incentives to combine operations.
When an industry is in expansion, the value of the entry option is high regardless of the industry
structure, and the incumbents cannot deter entry by not merging. When an industry is in recession,
entry is unprofitable regardless of the incumbents decision to merge. Thus, in the extreme states
of demand, the incumbents merger decision has limited impact on the entrants decision, and the
effect of higher incumbents profits due to post-merger collusion dominates the merger decision. In
intermediate states, the merger decision affects the likelihood of potential entry, and the incumbents
are better off not merging in order to delay entry.
Several other studies explore the dynamics of mergers. Lambrecht (2004) examines mergers mo-
tivated by operating synergies. In his model, mergers are likely to occur in periods of economic
expansion. Maksimovic and Phillips (2001) show that mergers and asset sales are more likely follow-
ing positive demand shocks, causing pro-cyclical merger and acquisition waves in perfectly competitive
industries. In their setting, higher quality firms buy lower quality ones when the marginal returns
from adding capacity are large enough to outweigh the decreasing returns to managerial skill. In Lam-
brecht and Myers (2007), takeovers serve as a mechanism to force disinvestment in declining industries.
Their arguments lead to takeover transactions occurring mostly in industries that have experienced
negative economic shocks. Mason and Weeds (2006) examine competition for targets, which results
in delayed mergers relative to the efficient merger timing. Gorton, Kahl and Rosen (2005) show that
technological or regulatory shocks that increase the profitability of future acquisitions can induce a
wave of unprofitable, defensive mergers.
One implication of the existing models of merger timing is that firms incentives to merge aredifferent in periods of economic recessions than those in expansions. We show that, within oligopolistic
industries, strategic incentives may prompt horizontal mergers both in periods of rising and declining
demand. Thus, strategic considerations complement other determinants of firms merger decisions.
Firms merge for various reasons, and the pursuit of market power is but one of them. Nonetheless,
to underscore the relation between industry structure and takeover activity, in our base model we
purposely abstract from potential synergies and takeover costs, and focus exclusively on strategic
motives. Our objective is to show that assuming technological synergies (as in Lambrecht (2004)) or
mergers as an efficient disinvestment mechanism (as in Lambrecht and Myers (2007)) is not necessary toexplain the documented relation between industry demand and merger activity. We recognize, however,
that the assumptions of no production synergies, no merger costs. and duopolistic competition are not
realistic. Therefore, in the models extensions we relax these assumptions and extend our theoretical
analysis to incorporate the effects of synergistic gains, merger-related costs, and varying degrees of
has been documented empirically by Berger, Bonime, Goldberg and White (2004), who examine entry into the banking
industry following bank mergers. See the discussion below.
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industry competition on firms strategic incentives to engage in horizontal mergers. We show that
strategic considerations carry greater weight when the costs of merging and technological synergies
are relatively low and when the degree of industry concentration is relatively high.
We contribute to the empirical merger literature by showing, using parametric and semi-parametric
tests, that an important reason for the U-shaped relation between economic shocks and merger
intensity, documented in Mitchell and Mulherin (1996), Andrade and Stafford (2004), and Harford
(2005), is the effect of demand shocks on firms incentives to merge horizontally. Furthermore, our
tests evince that the U-shaped relation between horizontal merger intensity and the state of industry
demand is present in relatively concentrated industries, whereas it is absent in relatively competitive
ones, in which strategic considerations are likely to play a lesser role. This evidence is consistent with
our model, which predicts that, ceteris paribus, horizontal mergers within oligopolistic industries are
more likely to occur in times of high and low demand relative to times of intermediate demand, and
that such pattern disappears within relatively competitive industries.
Our theory is related to recent models that incorporate product market competition into the analy-
sis of the dynamics of mergers. In a duopoly setting, Lambrecht (2004) finds that the pursuit of market
power tends to accelerate the timing of mergers. Hackbarth and Miao (2007) extend the analysis of
Lambrecht to oligopolistic industries and examine stock returns following acquisition announcements.
Yan (2006) analyzes a setting in which firms incentives to merge are affected by mergers among their
product market rivals, leading to merger waves. An important difference between our study and the
aforementioned models is that the threat of potential entry is a crucial determinant of the dynamics
of mergers in our analysis, whereas entry is not allowed in the other models. 2
Other studies examine entry into an industry within a dynamic setting. They do not incorporate
the possibility of a merger initiated by incumbents, however. Dixit (1989) studies optimal entry and
exit strategies of firms in a duopoly setting. Baldursson (1998) and Grenadier (2002) examine the
case of continuous investments in an oligopoly by focusing on symmetric Nash Equilibrium strategies.
Fries, Miller and Perraudin (1997), Lambrecht (2001), and Zhdanov (2007) examine the interaction of
the dynamic entry into an industry and firms financing strategies.
Finally, some models examine the link between incumbents incentives to merge and outsiders
incentives to enter the industry. However, they typically do not incorporate the dynamics of industryshocks and their impact on firms strategic incentives to merge. Consequently, they do not generate
implications for how merger activity evolves in rising and declining industries. Examples include
2 Similar to other models of takeover dynamics, our analysis adopts a continuos time real options framework. Morellec
and Zhdanov (2005) develop a real options model that focuses on abnormal returns around merger announcements and
incorporates imperfect information and competition among bidding firms. Leland (2007) examines the role of purely
financial synergies in motivating mergers. Margsiri, Mello and Ruckes (2005) dynamic model accounts for both takeover
transactions and internal growth.
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Cabral (2003), Marino and Zbojnk (2006), Toxvaerd (2007), and Werden and Froeb (1998).3
The remainder of the paper is organized as follows. The next section presents the model illustrating
the strategic motives for merging and discusses the models empirical implications. In Section 3 we
present empirical tests of the U-shaped relation between horizontal merger intensity and the state
of demand, predicted by the model. Section 4 summarizes our theoretical and empirical results and
concludes. All proofs are provided in Appendix 1. Appendix 2 presents an extension of the model
to the case of a different type of product market competition and demonstrates that the results are
robust to the choice of the type of competition.
2 The model
2.1 Setup
Assumption 1
There are two incumbents in the industry. Each incumbent is endowed with capital, K. In addition to
the two incumbents, an entry by one firm is allowed, with an equal amount of capital, K. The firms
production functions are of the Cobb-Douglas specification with two factors and constant returns to
scale:
qi = K1
2L1
2
i , (1)
where qi is the instantaneous quantity produced by firm i, and Li is the amount of labor employed by
firm i.4
The cost of one unit of labor per unit of time is denoted pl. The amount of capital is fixed,
hence labor is the only variable input.5 At any given instant, each firm can costlessly adjust its labor
input to produce any output quantity. Since firms are not able to alter the level of capital, firm is
instantaneous variable cost of producing qidt units is
Ci(qi) =q2iK
pldt. (2)
Assumption 2
The firms are subject to heterogenous-products Bertrand competition.
We depart from the common homogenous-products Cournot competition setting to make the model
more realistic. Competition la Cournot implies that products are perfect substitutes. Thus, if taken
literally, the results of a model with Cournot competition would only apply to industries in which
3 See also Gowrisankaran (1999) for a computational approach to the analysis of mergers, investment, exit, and entry.
4 Thus, the quantity produced during a time interval dt is qidt.
5 This assumption does not drive any of the results. With two adjustable factors all the concluisons of the model are
intact. We discuss the intuition behind this result below (see footnote 7).
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products are perfect substitutes. The heterogenous-products Bertrand competition, on the other
hand, can accommodate different degrees of substitutability among products.6 We emphasize right at
the outset that the logic and the results of the model are robust to the choice of the type of product
market competition. To show that, in Appendix 2 we re-examine the model under the assumption
of Cournot competition with homogenous products and show that the qualitative results and the
empirical predictions remain intact.
There are no technological (production) synergies. Because of the symmetry of the utility function
(see below) and the production functions, the equilibrium production quantities of the two incumbents
are the same, q1 = q2 = q. Under the assumption of the same level of capital of the two merged
firms, the cost of producing q1 and q2 separately,q21
Kpl +
q22
Kpl =
2q2
Kpl, is the same as the cost of
producing the same quantities while joining capital: (q1+q2)2
2K pl =2q2
Kpl.
7 We intentionally abstract
from the production (efficiency)-based reasons for merging and focus exclusively on strategic motives
for merging horizontally. We relax the constant returns to scale assumption and investigate the effect
of production synergies on the dynamics of mergers in Section 2.5.
Assumption 3
The demand-side of the industry is characterized by a representative consumer with quadratic instan-
taneous utility function
U(q) = xni=1
qi 12
ni=1
q2i + 2j=i
qiqj
, (3)where , , and are the parameters of the utility function, qi is (annualized) consumption of good
i, n is the number of active firms in the industry, and, thus, the number of available products, and x is
the stochastic shock to the representative consumers utility. This specification of the utility function is
typical in partial equilibrium analysis, which is commonly used in the industrial organization literature
6 In addition, the homogenous-products competition can sometimes result in unrealistic effects of a horizontal merger
on the merging firms and their product market rivals optimal strategies and equilibrium profits, if the merged firms
production function is assumed to be the same as the one of its stand-alone rivals. In the homogenous-products setting,
a merger can create a competitive disadvantage that results in lower combined profit of the merging firms relative to
the sum of their pre-merger profits in all cases except a merger for monopoly (see, for example, Stigler (1950), Salant,
Switzer and Reynolds (1983), and Farrell and Shapiro (1990)). On the other hand, Perry and Porter (1985) demonstrate
that accounting for the larger combined capital of the merging firms relative to that of its stand-alone rivals (as in
our model) can sometimes be sufficient for a horizontal merger to increase the merging firms combined profits in the
homogenous-products Cournot setting.
7 If two inputs were costlessly adjustable, the cost of producing q1 and q2 separately would be 2 [q1 + q2]
plpk, where
pk denotes the cost of one unit of capital. The cost of producing q1 + q2 while joining operations would be the same.
Moreover, with two adjustable inputs, there would be no technological synergies even if the incumbent firms were not
symmetric.
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(see, for example, Vives (2000)). An implicit assumption in this analysis is that there is a numeraire
good (or money), which represents the rest of the economy, and income is large enough, so that the
income constraint is never binding and all income effects are captured by the consumption of the
numeraire good.8 We further assume that x follows a geometric Brownian motion
dxt = xtdt + xtdWt,
where Wt is a standard Wiener process on a filtered probability space (, F , P ).
The conditions that we impose are > 0 and > > 0. These conditions are standard (see Vives
(2000)). > 0 implies that the goods produced are substitutes, which is a reasonable assumption for
products of firms competing in the same industry. > 0 and > imply that the utility function
is concave in each of its arguments. The assumption of the specific functional form of the relation
between the utility and the state of the stochastic shock, x, is made for analytical convenience. As
shown below,
x in the linear term of the utility function translates into a linear relation between
x
and the intercept of the demand function. (It is common in the industrial organization literature to
assume that shocks to demand manifest themselves as changes in the intercept of the demand function.)
The latter relation, in turn, translates into a linear relation between x and firms instantaneous profits.
Equating the marginal utility that the representative consumer obtains from consuming each prod-
uct to its respective price and solving the resulting system of n equations in n unknowns (quantities),
results in the demand function for each of the products as a function of the products own price and
other products prices:
Di(p ) = xa
bpi + cj=i pj , (4)
where
a =
+ (n 1),
b =+ (n 2)
[+ (n 1)]( ) ,
c =
[+ (n 1)]( ) . (5)
Assumption 4
Incumbent firms are endowed with an option to initiate one merger attempt. 9 Attempting to merge
does not entail out-of-pocket costs.10 Once initiated, the merger attempt results in a successful merger
with probability p.
8 Note also that since the income constraint never binds, the cosnumers optimization problem is completely time-
separable, so in any time interval dt the consumer maximizes her instanteneous utility U(q )dt.9 We do not allow for entry combined with acquisition of one of the incumbents, as in McCardle and Viswanathan
(1994).
10 We examine the case of a costly merger in Section 2.5.
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A merger attempt can be unsuccessful for various reasons, for example the opposition by antitrust
authorities and/or difficulties in the negotiation process. Empirically, far from all merger bids are
successful. For instance, in Eckbos (1983) sample of 191 horizontal mergers that occurred between
1963 and 1978, 65 were challenged by either the Justice Department or the Federal Trade Commission.
Boone and Mulherin (2007) report that only 27% of potential bidders that sign a confidentiality
agreement and only 78% of bidders that submit a private written offer succeed in acquiring their
target. Schwert (2000) reports that about 20% of deals in his sample of 2,346 takeover contests
involved an auction among multiple bidders.11
The assumption that the two incumbents are endowed with an option to initiate only one merger
attempt is made for analytical tractability. Unlike Lambrecht (2004), we assume that merging is
costless in the sense that there is no direct cost associated with the merger. However, as discussed
below, merging firms bear an indirect cost resulting from the change in industry structure. A successful
merger attempt makes entry into the industry more attractive and, thus, may erode the profits of the
incumbents.
The merger allows the incumbents to coordinate their pricing strategies, thus enhancing their joint
value. This leads to the following intuitive result:
Lemma 1 Regardless of the presence of a third firm (the entrant), the combined instantaneous profit
of the two incumbents is always higher if they merge than if they stay separate, ceteris paribus.
Lemma 1 shows that conditional on the presence/absence of the potential entrant, a merger in-
creases the incumbents combined instantaneous profit. However, the entrants instantaneous profitand, therefore, its decision to enter depends on the incumbents decision to merge:
Lemma 2 The entrants instantaneous profit is higher when the two incumbents operate as one entity
than when they stay separate.
The intuition behind Lemma 2 is simple. When the two incumbents merge, they charge higher
prices because they internalize the effect of raising one products price on the quantity sold of the
other product. This benefits the entrant and increases its instantaneous profit.
While this result clearly follows from the static model of oligopolistic competition, it can be argued
that, in a dynamic setting, a merger may create the opposite effect on the profits of potential entrants.
By merging, the incumbents can more credibly threaten entrants with charging lower prices upon
11 The assumption that a merger attempt fails with a positive probability is essential for our analysis, as becomes clear
below. If the probability of success were 100%, the incumbents would not be able to credibly deter entry into the industry
by not initiating a merger.
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entry to keep them out of the industry.12
The relative magnitude of the two effects determines whether a merger is beneficial or detrimental
for future entrants, and is an empirical question. Empirical evidence seems to suggest that the positive
static effect of mergers on the values of existing and potential competitors dominates the negative
dynamic effect. For example, Berger, Bonime, Goldberg and White (2004) report that mergers and
acquisitions in the banking industry are associated with increases in the probability of future entry.
Eckbo (1983) reports that horizontal rivals of merging firms earn positive abnormal returns around
merger announcements. Akhavein, Berger, and Humphrey (1997) and Prager and Hannan (1998),
among others, provide evidence of increases in output prices associated with mergers. This evidence
points in the direction of mergers being beneficial for potential entrants, as in our model.
Since the incumbents decision to merge affects the outsiders entry decision, we need to determine
whether the incumbents combined profit is higher in the case of merger than in the case of no merger
while taking the entrants optimal response into account:
Lemma 3 The incumbents combined instantaneous profit is higher in the case of no merger and no
entry than in the case of a merger and subsequent entry.
Combining Lemmas 1 and 3 enables us to establish the following relations among the combined
instantaneous profits of the incumbents under the four different scenarios (merger/ no merger combined
with entry/ no entry):
incumbents(no entry, merger) > incumbents(no entry, no merger) >
> incumbents(entry, merger) > incumbents(entry, no merger). (6)
This result is important. The first and third inequalities show that given the presence/absence of
the entrant in the industry, the incumbents are always better off merging (Lemma 1), as they optimally
charge higher prices while internalizing the positive effect that increasing the price of product 1 has
on the demand for product 2, and vice versa. The second inequality is the heart of our analysis. The
incumbents are better off in the case of no merger and no entry than in the case of merger and entry.
The reason is that the entrants profit and, thus, incentives to enter the industry are higher when
the incumbents have merged. Thus, the incumbents may be better off not merging to deter potential
entry.
12 Note, however, that such a threat can never be credible within the framework of our model. Since there are no fixed
costs and output quantities are costlessly adjustable (by changing the amount of labor employed), the incumbents cannot
credibly commit to predating on the third firm, should it decide to enter. Absent fixed costs, the profits of the active
firms are always nonnegative, so exit is never optimal. Once entry occurs, the incumbents have no incentives to deviate
from the equilibrium production/ pricing strategies.
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Note that absent any threat of new entry into the industry, the optimal strategy of the two
incumbents would be to initiate a merger attempt immediately, regardless of the current state of
the stochastic shock. This is because the merger attempt is assumed to be costless and, thus, the
incumbents combined instantaneous profits are higher after merging (see Lemma 1). The threat of
potential entry makes the problem more realistic and interesting. Entry always reduces the profits
of the incumbents. On the other hand, the entrants profit depends on whether the incumbents have
merged.
Assumption 5
Upon successful consummation of the merger, the shareholders of each incumbent receive a 50% stake
in the combined equity of the merged entity.
While we established the relation between incumbents combined instantaneous profits under dif-
ferent scenarios, the decision to merge is affected by the division of the merger surplus between the
incumbents. In order for the two incumbents to be willing to merge at a given state of the stochastic
shock, each of them has to benefit from the merger. Since in the model the two incumbents are iden-
tical in all respects, one way to ensure that is to assume that the value of the merged entity is split
evenly between the shareholders of the two merging firms.
Our model incorporates both cash and stock mergers. In our setting it is not important whether
the medium of exchange is cash or stock, as long as the capital markets are efficient and securities
are correctly priced by investors. We do not analyze the misvaluation-based incentives to merge, as in
Rhodes-Kropf and Viswanathan (2004) or in Shleifer and Vishny (2003). What is important is that
upon the merger consummation the shareholders of both incumbent firms receive the value equivalent
to the value of the right to the perpetual entitlement to the half of the cash flows of the merged entity.
Assumption 6
Entry requires the outsider to incur a fixed irreversible cost, I. This assumption precludes immediate
entry for low realizations of the stochastic shock.
Assumption 7
We normalize the amount of installed capital of each firm, K, the cost of labor, pl, and the coefficienton the quadratic term of the utility function, , to one.
This assumption is made for analytical convenience only. Normalizing to one is innocuous. In
addition, it is straightforward to show that the general version of the model with K and pl that are
different from one produces the same conclusions as the more restrictive model we are examining
here.13 Before proceeding to the formal solution of the model, it is worth discussing the structure of
13 This extension of the model is available upon request.
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the strategic game and providing the basic intuition for the results.
2.2 Basic intuition
There are two optimization problems that must be solved simultaneously. First, the outsider decides
whether to enter by trading off the present value of its expected profits against the cost of entry, I. The
expected profits depend on the strategy of the incumbents (see Lemma 2). In particular, a successful
merger alters the industrys competitive structure, leading to an increase in the instantaneous profits
of the entrant and, thus, making earlier entry optimal.
The second optimization problem is that of the incumbent firms, which decide whether to initiate
a merger attempt by trading off the cost and the benefit of merging. The benefit is the increase in
their instantaneous profits due to greater market power. The cost stems from the increased incentive
of the outsider to enter the industry due to its changed competitive structure. After entry occurs, the
incumbents combined instantaneous profits fall below their pre-merger value (see Lemma 3).The optimal restructuring decision depends, of course, on the current realization of the stochastic
shock, x. If x is relatively high (the industry is in expansion), then entry into the industry becomes
attractive regardless of whether the incumbents have merged. In this case, it is no longer possible
for the incumbents to deter entry by not merging. Therefore, the strategic disincentive to merge
disappears, and we observe a merger attempt. On the other hand, when x is relatively low (the
industry is in recession), the industry profits are low regardless of the incumbents decision to merge,
and entry is always unattractive. In this region, the incumbents find it optimal to attempt a merger
to increase their market power. The outsider would not enter until the state of the industry improves,so there is no substantial strategic disincentive to merge. Finally, when the economy is in transition,
and x is neither too high nor too low, the incumbents may optimally decide to postpone their merger
attempt to delay entry.
2.3 Analysis
We now proceed to the formal analysis of the model. In what follows, we incorporate the derivations
of the firms instantaneous profits under different industry structures, found in the proofs of Lemmas
1 and 2 in Appendix 1, and introduce the following simplifying notation for the firms instantaneousprofits under different scenarios:
ne,nminc =1
2xincumbents(no entry, no merger) =
2
2 2(4 + 2)2 , (7)
ne,minc =1
2xincumbents(no entry, merger) =
2
4(2 + ), (8)
e,minc =1
2xincumbents(entry, merger) =
2(4 + 3 32)2(2 + 22)4(1 + )2(8 + 4 92 + 23)2 , (9)
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e,nminc =1
2xincumbents(entry, no merger) =
2(1 + )(1 + 2)2(2 + 3)2
, (10)
nment =1
xentrant(no merger) =
2(1 + )(1 + 2)2(2 + 3)2
, (11)
ment =1
xentrant(merger) =
22(2 2)2(1 + 2)(1 + )(8 + 4
92 + 23)2
. (12)
We first examine the optimization problem of the entrant. Time does not enter the optimization
problem explicitly, and the optimal entry decision takes the form of an upper threshold, such that it
is optimal to enter at the first passage time of the stochastic shock x to the threshold. There are three
possible states of the industry, leading to three optimal entry thresholds:
1) the incumbents have not yet exercised their merger option (but they can do it in the future);
2) the incumbents have initiated a merger attempt, but it did not succeed (and no future attempts
are possible);
3) the incumbents have successfully merged.
14
We denote the optimal entry thresholds in these three cases by xu (an upper threshold), xe,nm
(entry, no merger is feasible), and xe,m (entry at a time when the incumbents have already merged),
respectively. (The notation will become clear below.) We start by establishing the optimal thresholds
xe,m and xe,nm, corresponding to the cases in which the incumbents have already attempted a merger,
either successfully or not. These thresholds are determined by the following proposition:
Proposition 1 If the incumbents have already exercised their option to attempt a merger and have
not succeeded, then the optimal entry threshold is given by
xe,nm =1
1 1I(r )
nment, (13)
where 1 is the positive root of the quadratic equation12
2( 1) + r = 0,
1 =1
2
2+
1
2
2
2+
2r
2. (14)
If the incumbents have successfully merged, then the optimal entry threshold is
xe,m =
11 1
I(r
)
ment . (15)
14 We do not allow the incumbent firms to engage in collusion and do not consider any crime-and-punishment strategies.
Similar to the majority of dynamic models (e.g., Doraszelski and Pakes (2006), Hackbarth and Miao (2007), and Spiegel
and Tookes (2007)), we focus on Markov strategies. Introducing the possibility of collusion would make the option to
merge worthless in the base version of the model. (The two firms engage in an irreversible merger in order to be able
to coordinate their pricing). Given the extensive empirical evidence, discussed above, indicating that mergers lead to
higher output prices, this seems a reasonable assumption.
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Note that ment > nment implies that xe,nm > xe,m, and a successful merger speeds up new entry. The
optimal entry threshold, xu, corresponding to the situation in which the option to merge is still open,
must be found by jointly examining the optimization program of the incumbents and that of the new
entrant. Since there is uncertainty with respect to the outcome of potential merger attempt, new entry
into the industry in which the incumbents have not yet merged (even if they have not yet exercised
their merger option) is not as attractive as in the case in which the incumbents have successfully
merged. Therefore, in this case the decision to enter must be supported by higher instantaneous
profits, and the following inequality must hold: xu > xe,m. Similarly, new entry into the industry in
which a merger attempt has not been initialized yet is more attractive than in the case in which an
unsuccessful merger attempt has occurred: xu < xe,nm.
When the current state of the stochastic shock, x, is such that xu > x > xe,m, the incumbents
would never want to attempt a merger. A successful merger attempt in this region would immediately
attract new entry (since x > xe,m) and, therefore, would lead to a decline in the incumbents combined
profits (see Lemma 3). For values of x slightly below xe,m a successful merger would not result in
an immediate entry but would increase its probability in the near future. As x further decreases,
this probability declines. When x is sufficiently lower than xe,m, the expected loss in the value of
the incumbents due to an earlier future potential entry is fully offset by the increase in their value
due to immediate higher instantaneous post-merger profits. At a certain critical lower threshold, xl,
the incumbents become exactly indifferent between attempting a merger or staying separate. For the
values of x below xl, it is always optimal to make a merger attempt.
On the other hand, when x reaches xu, new entry inevitably occurs. The profits in the industry
are so high that the incumbents are not able to keep the potential entrant aside by maintaining the
current industry structure and not attempting to merge. Regardless of the incumbents decision to
initiate a merger attempt, new entry occurs. Note, however, that the sequence of events in which new
entry precedes the merger attempt is never optimal from the perspective of both the incumbents and
the potential entrant. Both parties are better off if the merger attempt is initiated first. The reason
is that by initiating the merger the incumbents provide the potential entrant with the opportunity
to observe its outcome. This opportunity eliminates inefficient entry in the case of an unsuccessful
merger attempt and increases the value of both the incumbents and the potential entrant.
Indeed, if the merger attempt turns out unsuccessful, then it is optimal for the outsider not to enter
immediately, since the current state ofxu is below xe,nm, the optimal entry threshold corresponding to
the case of a failed merger attempt. The outsider would enter later, at a stopping time upon reaching
the corresponding threshold xe,nm. This option to wait increases the value of the new entrant. On
the other hand, the incumbents (should the merger attempt not succeed) would be entitled to higher
instantaneous profits, xne,nminc > xe,nminc , while x stays below xe,nm. Therefore, if xu is a critical value
of x high enough to attract entry even if the incumbents do not attempt to merge (they will do so
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immediately upon outsiders entry), then the optimal policy of the incumbents is to initiate a merger
attempt unilaterally when x first reaches the value ofxu. They cannot keep the outsider from entering
anymore, but they can give it a chance to see the outcome of the merger attempt and to postpone its
entry in the case it is not successful. That way the incumbents increase both their own value and the
value of the outsider.
To summarize, we only observe a merger attempt when x either falls to xl or rises to xu. No merger
attempts are made if xl < x < xu. We prove below that this intuitively appealing sequence of events
is a subgame-perfect equilibrium of the entry-merger game. In order to show that, we first need to
find the values of xl and xu.
As argued above, in order to find xl and xu we need to examine the incumbents and entrants
optimization programs simultaneously. The program of the incumbents that have not attempted a
merger yet can be formalized as follows:
Vinc(x) = supTxl>0
Ex{min(Txl ,Txu )
0ertne,nminc xdt+
+ 1Txu
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xu is determined as the outcome of the optimization program of the potential entrant corresponding to
the case in which new entry would precede the merger attempt. The entrants optimization program
reads:
Vnment (x) = supTxu>0
Ex{1Txu
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Equations (20) and (22) are the value matching conditions, which stipulate that the values of
the entrant at the two optimal merger thresholds are exactly equal to their respective expected post-
merger-attempt values. (These values are the weighted averages of the values conditional on a success-
ful and unsuccessful merger attempts.) Equation (21) is the smooth-pasting condition that ensures
the optimality of the outsiders entry decision.
Proposition 2 provides us with three equations in four unknowns (two constants, A and B, and
the optimal merging thresholds, xu and xl). Thus, we need additional conditions in order to solve for
the optimal merging thresholds. The remaining conditions come from the optimization program of
the incumbents in (16). These conditions are derived in the following proposition:
Proposition 3 Ifx is between the optimal lower merging threshold, xl, and the optimal upper merging
threshold, xu, then the value of each incumbent is given by
Vinc(x) = Cx
1
+ Dx
2
+
ne,nminc x
r , (23)whereC andD are constants to be determined together withA, B, xu, andxl. The following conditions
must hold at the upper and lower merging thresholds, xl and xu:
Cx1u + Dx
2u +
ne,nminc xur =
1
r
pe,minc xu + (1 p)
ne,nminc xu +
xu
xe,nm
1(e,nminc ne,nminc )xe,nm
, (24)
Cx1l + Dx
2l +
ne,nminc xlr =
1
r {p
xlxe,m
1(e,minc ne,nminc )xe,m + ne,minc xl
+
+ (1 p)
xlxe,nm
1(e,nminc ne,nminc )xe,nm + ne,nminc xl
}, (25)
1Cx11l
+ 2Dx21l
+ne,nmincr
=
=1
r {p1x11l
(xe,m)1
(e,minc ne,minc )xe,m + ne,minc
+
+ (1 p)
1x11l
(xe,nm)1
(e,nminc ne,nminc )xe,nm + ne,nminc}. (26)
In (23) the term
ne,nminc x
r refers to the present value of each incumbents perpetual entitlement to
instantaneous profits if no structural changes in the industry occur, i.e. if the incumbents never merge
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and the outsider never enters. The remaining terms, Cx1 + Dx2, account for the change in each
incumbents value due to the option to merge and the threat of new entry.
Equations (24) and (25) are the value-matching conditions for each incumbents optimization
problem, while (26) is the smooth-pasting condition that must obtain at the lower merging threshold.
The first term on the right-hand side in (24) is the post-merger value of an incumbent if the merger
attempt is successful, and the second term is the value of the incumbent in case of an unsuccessful
merger attempt. Note that the expression on the right hand side of (24) (unlike that of (20)) accounts
for the fact that the merger attempt would actually precede entry, so the new entrant is able to
postpone its entry decision if the merger attempt is unsuccessful. On the contrary, (20) does not have
the same term on the right hand side because the upper merger threshold is determined as the one
that makes entry optimal even if the potential entrant is not able to anticipate the result of the merger
attempt.
Propositions 2 and 3 provide the necessary set of conditions to determine the optimal merger
thresholds together with the equilibrium values of the incumbents. In particular, equations (20)-(22)
and (24)-(26) present a system of six equations in six unknown variables. The numerical solution to
this system provides the lower and upper merger thresholds, xl and xu. In the next proposition we
show that the incumbents strategy of merging at xl and xu (whichever threshold is reached first),
coupled with the outsiders strategy of entering at xe,m if the incumbents merger attempt at xl was
successful, entering right after the merger attempt at xu if it is successful, and entering at xe,nm if the
merger attempt failed, forms a subgame-perfect equilibrium of the game.
Proposition 4
1) The merger-entry game does not have a subgame-perfect equilibrium in which each subgame has a
Nash equilibrium in pure strategies. There are two subgame-perfect equilibria involving mixed strategies.
2) In the first subgame-perfect equilibrium, the incumbents strategy is to attempt a merger at xl, and
to attempt a merger with a probability PM(x) at each x [xu, xe,nm) if the entrant has not enteredprior to reaching x. If the outsider enters at x [xu, xe,nm), the incumbents strategy is to attempt amerger immediately after entry. The entrants strategy is to enter at xe,m if the incumbents merger
attempt at xl succeeded, enter immediately after a successful merger attempt at x [xu, xe,nm), enterwith probability PE(x) at each x [xu, xe,nm) if the incumbents have not merged prior to reaching x,and enter at xe,nm if the merger attempt failed or if merger has not been attempted prior to xe,nm.
The probabilities PE(x) and PM(x) are derived in Appendix 1.
3) In the second subgame-perfect equilibrium, the incumbents strategy is to attempt a merger at a first
passage time to xl or xu, the entrants strategy is to enter at xe,m if the incumbents merger attempt
at xl succeeded, enter immediately after a successful merger attempt at xu, and enter at xe,nm if the
merger attempt failed. The incumbents and entrant play mixed strategies, as in the first subgame-perfect
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equilibrium, in each subgame starting at x (xu, xe,nm).
The intuition for the lack of a subgame-perfect equilibrium in which each subgame involves pure
strategies is as follows. As shown above, xe,m < xu < xe,nm. Assume that a subgame-perfect equi-
librium involves the incumbents attempting a merger at x [xe,m, xe,nm) In order for this strategyprofile to be a subgame-perfect equilibrium, the entrant has to threaten to enter unilaterally at x + ,
where x , and this threat has to be credible. In other words, the outsiders immediate entry in asubgame starting at x + has to be a Nash equilibrium. However, if the entrants strategy is to enter
at x + , then the incumbents optimal response is to attempt a unilateral merger at x + (see Lemma
1). Given this strategy of the incumbents, the entrants optimal response is to deviate by waiting
until immediately after the incumbents merger attempt at x + in order to observe the realization of
the merger attempt. Thus, the entrants threat to enter unilaterally at x + does not lead to a Nash
equilibrium in the subgame starting at x + , and is not credible. Thus, there is no subgame-perfect
equilibria in pure strategies in which the incumbents try to merge at any x [xe,m, xe,nm).
In the first subgame-perfect equilibrium in Proposition 4, the incumbents and entrant choose their
respective merger/entry probabilities at each x [xe,m, xe,nm) in such a way that they are indifferentbetween acting unilaterally (attempting a merger/entering) or waiting. As shown in Appendix 1, these
indifference conditions can not be satisfied in the region x [xe,m, xu). The reason is that in this regionthe entrant is always better off waiting and would never choose to enter first, prior to observing the
result of the merger attempt. The indifference conditions can be satisfied in the region x [xu, xe,nm).Thus, there is a subgame-perfect equilibrium in mixed strategies in which the incumbents attempt to
merge before observing the entrants move with a certain probability (derived in Appendix 1) at each
x [xu, xe,nm), and the outsider enters unilaterally with a certain probability at each x [xu, xe,nm).
Note that because at each x [xu, xe,nm) both the entrant and the incumbents are indifferentbetween waiting and acting, the incumbents expected combined value from playing the mixed strate-
gies at each x [xu, xe,nm) is equal to their combined value in case they attempt a merger at xu withan entry following immediately thereafter if the merger attempt is successful. Similarly, the entrants
expected value from playing the mixed strategy at each x [xu, xe,nm) equals its value from enteringunilaterally at xu with the incumbents attempting a merger immediately thereafter.
Since the outsider is always better off observing the result of the merger attempt before making
the entry decision than entering unilaterally, it clearly prefers the second equilibrium in Proposition
4, in which the incumbents attempt a merger at xu and the entry follows immediately after a success-
ful merger attempt. The incumbents, on the other hand, are indifferent between the two equilibria
described in Proposition 4. In addition, if the incumbents, for some unmodeled reason, dislike un-
certainty, the second equilibrium, in which the incumbents preempt the entry attempt by trying to
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merge at xu, dominates the first equilibrium, involving mixed strategies. Thus, in what follows we
concentrate on the second equilibrium. As described in Appendix 1, the range [xu, xe,nm), in which
the merger can occur in the mixed-strategies equilibrium, is rather narrow, relative to the difference
between xe,m and xe,nm. Thus, the two subgame-perfect equilibria in Proposition 4 result in very
similar empirical predictions.
Note that while Vinc(x) in (16) is the true value of each incumbent, Vnment (x) in (17) is not the
true value of the potential entrant in the equilibrium in which the incumbents try to merge at xu.
Rather, it provides its hypothetical value that would have been realized if the incumbents did not
preempt new entry, and unilateral entry occurred at xu while the option to merge were still open.
Thus, the final quantity to be found is the true value of the potential entrant, Vent(x), corresponding
to the equilibrium strategy in which the merger attempt occurs first. As discussed above, the following
inequality must hold: Vent(x) > Vnment (x), where Vnment (x) is the pseudo-value of the entrant, obtained
if entry occurred before the merger attempt, given in (17). The true value of the potential entrant isgiven by
Vent(x) = F x1 + Gx2 ,
where the pair of constants (F,G) is given by the (numerical) solution of the following system of
equations:
F x1u + Gx
2u = p
mentxur I
+ (1 p)
xu
xe,nm
1 nmentxe,nmr I
, (27)
F x
1
l + Gx
2
l = p xlxe,m1
mentxe,m
r I+ (1 p) xlxe,nm1
nmentxe,nm
r I . (28)Note that while the value-matching condition at the lower threshold (28) has the same form as the
corresponding condition (22), the value-matching condition at the upper threshold (27) accounts for
the possibility to observe the outcome of the merger attempt prior to making the entry decision, and
is, therefore, different from the corresponding condition (20).
The next subsection presents the solutions for the optimal thresholds and the discussion of the
models implications.
2.4 Results and interpretation
This section presents comparative statics of the solutions to the optimization problems (16) and (17).
Figure 1 presents the optimal merging thresholds as functions of the volatility of the demand process,
, and of its expected growth rate, . Figure 2 provides the merging thresholds as functions of the
entry cost, I. Figure 3 depicts the merging thresholds as functions of the extent of substitutability of
firms products, . The following values of the input parameters were used to produce Figures 1 - 3:
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= 1, = 0.01, r = 0.05, = 0.2, I = 5 and = 0.7. The shapes of Figures 1 - 3 are insensitive to
the choice of parameter values.
Insert Figures 1-3 here
Figure 1a reveals positive relations between the merger thresholds, xu and xl, and the volatility
parameter, . This result follows from the analysis of the problem of the potential entrant. Volatilityis positively related to the value of the outsiders option to wait and is, thus, negatively related to
its incentive to enter the industry. Hence, higher volatility leads to higher entry threshold, which
coincides with the upper restructuring threshold, xu. It also raises the optimal entry thresholds in the
two cases in which the incumbents have already initiated a merger attempt, xe,m and xe,nm. Therefore,
an increase in volatility reduces the strategic disincentive to merge for relatively low states of x. The
higher the volatility, the higher the value of x for which the incumbents can afford to merge, and
the higher the value of x corresponding to the lower merging threshold, xl. Likewise, an increase in
the growth rate, , makes it optimal for the potential entrant to accelerate its entry and, therefore,
reduces the optimal entry thresholds and the merger thresholds associated with them.
Similar intuition applies to the merger thresholds in Figure 2. Higher entry cost deters new entry
and, therefore, raises the optimal merger thresholds. In Figure 3, the lower the degree of substitutabil-
ity among the three firms products, , the less the entrants decision is affected by the incumbents
strategy, and vice versa. Therefore, because the entrants instantaneous profit is decreasing in ,15 the
upper merging threshold and, consequently, the lower merging threshold increase with the degree of
product substitutability. For the same reason, the distance between the two thresholds widens as the
degree of substitutability increases.
2.5 Extensions
In this subsection we analyze how the models restrictive assumptions influence the dynamics of mergers
described in the previous subsection. To that end, we extend the model in three directions. First, we
assume that mergers are costly. This extension is motivated by Lambrecht (2004), in whose model
fixed merger costs, coupled with pro-cyclical merger benefits lead to mergers only in relatively good
states of the economy. We examine whether and to what extent the assumption of costless mergers
in our base model is responsible for our main result that mergers occur both during periods of risingdemand and periods of declining demand. Second, we incorporate potential merger synergies into our
analysis. While we purposely abstract from production-related merger gains in the base model, it
is interesting to explore whether strategic considerations survive in a more realistic setting in which
mergers bring production synergies. Finally, we analyze the effects of industry structure on the models
15 This can be easily verified by differentiating the entrants instantaneous profit for the cases of merger and no merger
in (45) and (44) in Appendix 1 respectively with respect to . Intuitively, the higher the , the tougher the product
market competition, and the further away firms are from a monopolistic setting.
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results. To that end, we depart from the duopolistic setting adopted in the base version of the model
and examine an oligopoly with an arbitrary number of incumbent firms, two of which are allowed to
merge.
2.5.1 Costly mergers
Most takeover transactions are costly. Merger-related costs include but are not limited to legal and
advisory fees paid to lawyers and investment bankers, as well the cost of consolidating the operations
of the merging companies (e.g., severance payments in case of workforce reduction). To examine the
effect of restructuring costs on the timing of market-power-motivated mergers, we follow Lambrecht
(2004) and assume that a fixed cost, Im, must be incurred in order for the two firms to successfully
merge.16 In general, there are three alternative merger strategies, each of which may be optimal
depending on the value of Im. These three cases are analyzed below.
Case 1
If the cost of merger is relatively low, then the incumbents optimal strategy remains qualitatively
similar to their strategy in the base model. There are still two optimal merger thresholds, and a
merger attempt occurs at the first passage time of the demand shock to either of them. To formally
analyze this case, one needs to replace equations (24) and (25) with the following two boundary
conditions.
Cx1u + Dx
2u +
ne,nminc xur
=
pe,minc xu
r Im2
+ (1 p)ne,nminc xu
r + xu
xe,nm
1 [e,nminc ne,nminc ]xe,nmr
,
Cx1l + Dx
2l +
ne,nminc xlr =
p
xl
xe,m
1 [e,minc ne,nminc ]xe,mr +
ne,minc xlr
Im2
+
+ (1 p)xl
xe,nm
1 [e,nminc ne,nminc ]xe,nmr
+ne,nminc xl
r
.These conditions reflect the fact the joint value of the merged firm is reduced by Im following a
successful merger attempt (and the value of each incumbent is reduced by Im/2, since each incumbent
gets a 50% stake of the joint firm).
16 The conclusions of the extended model remain intact if we assume that the merger cost, Im, is incurred at the time
of a merger attempt, regardless of whether it is successful.
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Case 2
For higher values ofIm, the strategic incentive to merge at the low threshold may no longer outweigh
the merger cost. In this case there will be no lower merger threshold, and a merger attempt will
only be observed when x reaches the upper threshold xu. As before, the incumbents wait as long as
they can deter entry and initiate a merger attempt at the moment when entry deterrence is no longer
feasible. Similar to (13) and (15), it is straightforward to show that in this case the upper merger
threshold is given by
xu =1
1 1I(r )
pment + (1 p)nment, (29)
and the value of each incumbent is equal to:
Vinc(x) =ne,nminc x
r +
x
xu
1{p
e,minc xur
Im2
+
(1 p)ne,nminc xur + xuxe,nm
1
[e,nm
inc ne,nm
inc ]xe,nmr }.
Case 3
Finally, if the cost of merger is extremely high, the optimal entry and merger strategies become
independent, as the incumbents can only afford to merge at the states of x exceeding the optimal
entry threshold. Standard analysis yields that in this case the optimal merger threshold, xm, is given
by
xm =1
1
1
Im(r )2p (e,m
inc e,nm
inc
), (30)
while the optimal entry threshold, xe, is
xe =1
1 1I(r )
nment, (31)
Note that in this case xm must be greater than xe, so the following inequality must hold Im/I >
2nment/p (e,minc e,nminc ) . This inequality implies extremely high values of the restructuring cost relative
to the cost of entry, Im 250I for the parameter values in our base case. (Such a high restructuring
cost exceeds the value of the strategic benefit of merger at xu by a factor of 335). Since such extreme
takeover costs are very unlikely to be observed in practice, we disregard this case in the solution of
the extended model.
For each value of the takeover cost, Im, we compare the combined value of the incumbents condi-
tional on following the restructuring strategy as in Case 1 above to their combined value corresponding
to the merger strategy as in Case 2, and choose the restructuring strategy that maximizes the incum-
bents value.
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The effects of the takeover cost on the merger thresholds are illustrated in Figure 4, which plots
the optimal thresholds as functions of the restructuring cost, Im.
Insert Figure 4 here
Consistent with the intuition above, there are two regimes corresponding to different values of the
restructuring cost:
1) it is optimal to merge at the higher and the lower thresholds,
2) it is optimal to merge only at the higher threshold.
The switch from regime 1 to regime 2 occurs at Im = 0.8 (corresponding to 16% of the cost of entry,
I) for the base set of parameter values. Note that in region 1 the lower threshold decreases with Im
because now in addition to trading off the instantaneous strategic benefit of merger with the effect of
merger on subsequent entry, the incumbents incorporate the cost of merger into their decision. This
cost makes the merger less attractive for a fixed value of x and therefore shifts the optimal threshold
down relative to the case of a costless merger. The upper threshold is almost not affected by changes
in Im, since it is mostly determined as the solution to the entrants optimization problem.
2.5.2 Merger synergies
In the base version of the model we intentionally abstract from potential merger synergies in order to
focus exclusively on the strategic reasons to merge. While there is an ongoing debate in the literature
whether mergers are, in general, associated with operating synergies,17 there is little doubt that at least
some acquisitions result in productivity improvements. To the extent they exist, production synergies
would affect the merger decision jointly with the product-market-competition-driven effects. In this
subsection we examine the combined effect of operating synergies and market power considerations on
the timing of mergers.
In order to model the synergistic effect of a merger we assume that the production function exhibits
increasing returns to scale and has the following specification:
qi = KL
1
2
i ,
where > 1
2
. ( = 1
2
, as in our base case, implies zero synergies. > 1
2
leads to cost savings due to
economies of scale and results in a synergistic effect whose magnitude increases with .18)
17 Andrade, Mitchell, and Stafford (2001) and Healy, Palepu, and Ruback (1990) document post-merger improvement
in merging firms accounting performance. On the other hand, Kaplan and Weisbach (1992) and McGuckin and Nguyen
(1995) report insignificant changes in accounting performance after mergers, while Ravenscraft and Scherer (1987) re-
port deterioration of accounting performance. Maksimovic and Phillips (2001) report that changes in productivity are
insignificantly different from zero following mergers and acquisitions.
18 Indeed, if the two incumbents produced q units each using separate production, the combined production cost would
be 2q2
K2pl, while producing 2q units using combined capital would cost
2q2
K22
22pl
1
2.
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Potential synergistic gains affect incumbents incentives to merge via two different channels. First,
the availability of synergies increases the post-merger profits of the incumbents, making a merger
more desirable, thus potentially offsetting the strategic disincentive to merge. Second, synergies cause
the merged entity to increase its output and reduce prices in equilibrium, adversely affecting the
instantaneous profits and value of potential entrant. As a result of these two effects, the incumbents
have weaker incentives to operate as stand-alone entities to deter entry. This intuition is illustrated
in Figure 5, which plots the equilibrium instantaneous profits of the incumbents and potential entrant
as functions of the value of the merger synergy. The synergy value is computed as the percentage
increase in the instantaneous profits of the merged entity relative to the zero-synergy case:
synergy() =ne,minc ()
ne,minc ( =12)
1. (32)
Insert Figure 5 here
In the left panel of Figure 5, the dashed line shows the profit of the potential entrant facing two
stand-alone incumbents, while the solid line shows the entrants post-merger profit. In the right panel,
the solid line depicts the profit of each of the incumbents if they merge and entry occurs, e,minc , while
the dashed line shows their profit if they stay separate and there is no entry, ne,nminc . Note that as
long as the synergy value is below 33% (Figure 5, right panel), the central inequality in our analysis
still holds: e,minc < ne,nminc , and the incumbents still have a strategic incentive to stay separate, if by
staying separate they can deter entry. However, such strategy is only feasible if the synergy value
does not exceed 5.8% (corresponding to = 0.617), as is evident from the left panel of Figure 5. For
higher synergy values, the profit of the entrant is actually higher if the incumbents stay separate,
as the reduced production costs following merger lead to a decline in equilibrium prices. Thus, for
sufficiently high synergy parameter, entry deterrence by not merging is no longer possible. On the
contrary, by merging, the incumbents are able to deter entry, as in this case xe,nm < xe,m. Thus, the
optimal strategy for synergy values exceeding 5.8% is to merge immediately, provided that the merger
is costless.
The optimal restructuring thresholds as functions of the merger synergy are presented in Figure 6,
which shows that there are still two optimal merger thresholds for relatively low synergy values (below
5.8% for the base set of input parameters).
Insert Figure 6 here
The distance between the two thresholds decreases with the synergy value. Greater synergy implies
lower equilibrium prices and, therefore, lower entrants profit, ment. This, in turn, raises the optimal
entry threshold, xe,m, and reduces the distance between the two entry thresholds, xe,m and xe,nm. Thus,
the effect of the merger on the timing of entry fades as grows. This reduces the strategic disincentive
to merge on the part of the incumbents, raises the lower merger threshold, xl, and reduces the distance
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between xl and xu. For the synergy value equalling the cut-off level of 5.8%, the entrants instantaneous
profits are independent of whether the incumbents merge or stay separate, so the incumbents are no
longer able to deter entry by not merging. For synergy values greater than 5.8%, the entrant actually is
better off if the incumbents do not merge, so the optimal strategy of the incumbents becomes to merge
immediately if the merger is costless. Adding a fixed cost of merger, as in Section 2.5.1, would result
in Lambrechts (2004) setting, in which a merger occurs at a certain upper restructuring threshold.
2.5.3 Analysis of oligopolistic industries
While the duopoly framework adopted in the base version of the model allows us to illustrate the
mechanism driving firms restructuring decisions in a simple and intuitive way, it is interesting to
examine the effect of industry structure on the dynamics of mergers. For this purpose we abstract
from the duopoly setting and assume that the industry consists of n incumbent firms, two of which
are endowed with an option to merge.19 We examine the effects of industry structure on the timing
of mergers under three scenarios:
1) costless merger, no merger synergies;
2) costly merger, no merger synergies;
3) costless merger, positive synergy.
Costless mergers, no synergies
Increasing the number of incumbent firms produces two effects on firms profits. First, firms equi-
librium profits fall due to increased competition. The effect of a merger on the instantaneous profits
of the merging firms is, therefore, reduced. Second, the effect of potential entry on the profits of the
incumbent firms is also diminished. We solve the model with n incumbents following the same steps
as in the solution of the base model in Section 2.3. 20 The resulting takeover thresholds are presented
in Figure 7. The left panel displays the case of n = 5, while the right panel corresponds to n = 12.
Insert Figure 7 here
As before, the merger thresholds are increasing in the cost of entry. Because the profit of the potential
entrant decreases when the number of incumbent firms increases, its optimal entry thresholds are
increasing in n. Therefore the merger thresholds, which are associated with entry thresholds, are also
increasing in the number of incumbent firms (as is obvious by comparing the two panels of Figure 7
with Figure 2, corresponding to the case of n = 2). Finally, the relative distance between the upper
and the lower merger thresholds decreases as the industry becomes more competitive. The ratio of
19 This setting is similar to Hackbarth and Miao (2007).
20 The detailed solution is available upon request.
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the two thresholds, xu/xl goes down from 1.41 in the duopoly setting to 1.34 if n = 5 and further to
1.25 if n = 12 (for the base set of parameter values).
Positive restructuring cost
As before, a positive cost of merger can eliminate the incentive of the incumbents to merge at a
low threshold, leading to a monotonic relation between the state of the stochastic shock and merger
intensity. In oligopolistic industries, the effect of the restructuring cost on the dynamics of mergers
depends on the degree of industry concentration. In relatively competitive industries, the market-
power-based gain from a merger is low and it can be offset by a relatively low restructuring cost. We
are, therefore, more likely to observe pro-cyclical mergers in more competitive industries. On the other
hand, in more concentrated industries, the strategic benefit of a merger is stronger and may outweigh
the merger cost, leading to a U-shaped relation between state of demand and merger activity. This
intuition is illustrated in Figure 8, which plots the optimal merger thresholds for industries with 3 and
4 incumbent firms.
Insert Figure 8 here
As follows from the comparison of Figures 4 (two incumbent firms), 8a (three firms), and 8b (four
firms), the value of the restructuring cost that triggers the switch from regime 1, in which there are
two merger thresholds, to regime 2, in which there is a single merger threshold, decreases in the
number of incumbent firms. Therefore, for a fixed restructuring cost, we are more likely to observe a
U-shaped relation between the state of demand and merger intensity in more concentrated industries
(lower n) and a monotone relation in more competitive ones (higher n). In our numerical example,
the restructuring cost at which the lower merger threshold disappears is 0.8 in the duopoly case (see
Figure 4), it is 0.36 in the case of three incumbent firms (see Figure 8a), and it is 0.17 in the case of
four incumbents (see Figure 8b).
Positive merger synergy
Merger synergy in the oligopoly setting plays a role similar to that of the restructuring cost. A
given level of synergy is more likely to outweigh the strategic benefit of entry deterrence in relatively
competitive industries (in which profits of all firms are less affected by the merger) than in relatively
concentrated ones. Just like in the case of positive merger cost, a U-shaped relation between the state
of demand and merger intensity is more likely to be observed in more concentrated industries.21
21 For the sake of brevity we do not report the comparative statics of the takeover thresholds for the case of synergistic
mergers in oligopolistic industries. These results are available upon request.
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2.6 Empirical predictions
The results of the base model as well as the models extensions take the form of comparative statics
of the merger thresholds with respect to the models parameters. Restructuring thresholds are usually
unobservable and, thus, the empirical predictions of the model take the form of relations between
merger intensity in various states of demand and proxies for the models parameters. Thus, beforesummarizing the empirical predictions, we show that the intuitive transition from merger thresholds
to merger intensity is plausible (i.e. that there is a correspondence between predictions with respect
to takeover thresholds and predictions with respect to merger intensities).
To illustrate this correspondence, Figure 9 presents the relation between a measure of merger
intensity and the state of the industry demand, x. Since there is only one merger allowed in the
model, merger intensity in a given year equals the probability of a merger during that year, i.e. the
probability of reaching either the higher merger threshold, xu, or the lower threshold, xl, within a year
if the current state of demand is given by x.
Insert Figure 9 here
As implied by Figure 9, the existence of two optimal merger threshold produces a U-shaped relation
between a measure of merger intensity and the state of the industry if the current state of demand, x,
is between xe,m and xu. (Note that if the current state of the industry demand is above xu or below
xl then immediate merger is optimal so the probability of a merger attempt is always equal to one.)
The most important result of the model, demonstrated in Figures 1 - 3, is that there are two
distinct merger thresholds. Firms merge either when the industry is growing (i.e. the state of demand
passes the upper merger threshold from below), or when the industry is shrinking (i.e. the state of
demand passes the lower merger threshold from above). The empirical prediction is, thus:
Prediction 1. We are likely to observe more horizontal mergers in industries subject to extremely
high and low states of demand. Put differently, we expect a U-shaped relation between horizontal
merger intensity and the state of demand.
The comparative statics of the merger thresholds with respect to the models parameters in Figures
1-3 lead to the following additional predictions.
Prediction 2a. The trough of the U-shaped relation between horizontal merger intensity and the
state of demand is expected to be increasing in the volatility of demand.
Prediction 2b. The trough of the U-shaped relation is likely to be decreasing in the expected future
demand growth.
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Prediction 2c. The trough of the U-shaped relation is expected to be increasing in the costs of
entering an industry (barriers to entry).
Prediction 2d. The trough of the U-shaped relation is expected to be increasing in the degree of
similarity (substitutability) among industry participants products.
An additional prediction following from the comparative statics with respect to the substitutability
parameter in Figure 3 is:
Prediction 3. We are more likely to observe a U-shaped relation between horizontal merger intensity
and the state of demand the more similar (substitutable) the industry participants products.
The comparative statics of the restructuring thresholds within the extended models in Figures 4
and 6-8 lead to the following predictions.
Prediction 4. We are more likely to observe a U-shaped relation between horizontal merger intensityand the state of demand in industries with relatively low restructuring costs.
Prediction 5. We are more likely to observe a U-shaped relation in industries in which potential
production synergies are smaller.
Prediction 6. We are more likely to observe a U-shaped relation in more concentrated industries.
The last prediction follows from three sources. First, the relative distance between the upper
and lower merger thresholds decreases in the number of incumbents (see Figures 2 and 7). Second,
the highest restructuring cost for which two merger thresholds exist is decreasing in the number of
incumbents (see Figures 4 and 8). Third, the highest synergy value for which two restructuring
thresholds exist is decreasing in the number of firms in the industry.
While a full-fledged empirical study of the relation between the state of demand and merger
activity is beyond the scope of this paper, in the next section we test two of the main predictions of
the model. First, and most importantly, consistent with Prediction 1, we document that horizontal
merger intensity seems to have a U-shaped relation with the state of demand. Second, consistent with
Prediction 6, the U-shaped relation is present in relatively concentrated industries and is absent in
relatively competitive ones.
3 Empirical tests
3.1 Data
We collect our sample of mergers and acquisitions from the Securities Data Companys (SDC) data-
base of public and private U.S. targets. The sample period is 1981 - 2004. To be included in our
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sample, we require that a deal satisfies the following criteria:
1) the acquirer is a U.S.-based public company, traded on one of the three major U.S. exchanges
(NYSE, NASDAQ, or AMEX);
2) the acquiring firm owns less than 50% of the target firms equity on the day of acquisition an-
nouncement;
3) the acquiring firm ultimately acquires a larger than 50% stake of the targets equity;
4) the deal value is available from SDC.
We impose the first restriction to allow the matching of acquiring firms from SDC with the COM-
PUSTAT Annual Industrial Files, which we use to define industries and to obtain industry charac-
teristics. We exclude foreign bidders because their incentives to cross-list may be related to factors
other than their desire to gain access to U.S. product markets. It is not obvious, then, that foreign
cross-listed acquirers actively compete in U.S. product markets and have the same strategic incentives
as U.S. firms.22
The second restriction reflects the fact that control over managerial (output/pricing) decisions
is more relevant for our model and empirical tests than the legal status of the target.23 The third
restriction eliminates unsuccessful bids from the sample. In our model, the probability of an attempted
merger being successful is fixed, and the predictions of the model could, in principle, be tested using
both a sample of attempted mergers and a sample of completed mergers. Empirically, however, it is
often the case that multiple bidders make offers for the same target. To the extent that the degree of
competition among bidders is different across industries, using all attempted mergers might bias the
results.24 We base our measure of merger intensity on deal values, hence the fourth restriction.
We obtain firm-year-level accounting information and SIC codes from COMPUSTAT. As in Harford
(2005), we define industries following Fama and Frenchs (1997) classification, which combines four-
digit SIC codes into 49 broader industries. The sample selection criteria discussed above, together with
the COMPUSTAT matching requirement for acquiring firms result in the sample of 21,245 completed
mergers. Our model predicts a non-monotonic relation between the state of industry demand and
firms incentives to engage in horizontal mergers. We classify a merger as horizontal (non-horizontal)
if the firms in the transaction operate in the same (different) Fama-French industry. 25 Based on this
22 In particular, access to U.S. supply of capital and benefits of complying with U.S. regulation of shareholder protectionare widely cited as potential advantages of cross-listing (e.g., Stulz (1999), Reese and Weisbach (2002), Doidge, Karolyi,
and Stulz (2004), and Lins, Strickland and Zenner (2005)).
23 For robustness, we redo all tests while imposing various restrictions on the threshold determining a corporate control
change (i.e. 40% or 30%). The results based on these samples are qualitatively similar to those reported and are available
upon request.
24 The results obtained using the sample of succesful and withdrawn merger and acquisition bids are similar to those
obtained using the successful mergers sample, and are available upon request.
25 In the case of private targets we obtain the industry classification codes from SDC.
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classification, there are 12,269 horizontal deals in our sample.
3.2 Merger intensities
We measure (horizontal) merger intensity within an industry during year t as the sum of the values
of all (horizontal) deals involving acquirers belonging to the industry in year t scaled by the sum of
end-of-year market values of all firms belonging to the industry in year t 1. A firms market value isdefined as the sum of the market value of its equity, COMPUSTAT data item 24 times item 25, and
the book value of its liabilities, item 181.
Our theoretical analysis focuses on horizontal merges. Nonetheless, we also examine the relation
between overall merger intensity and the state of demand because the definition of a horizontal merger
is not straightforward, both theoretically and empirically. On the theory side, our model allows
for different values of the parameter measuring the substitutability among firms products, thus not
requiring the products to be perfect substitutes. On the empirical side, our definition of industries,
which is based on SIC codes is far from being perfect. 26
Table 1 reports descriptive statistics of the absolute and scaled measures of merger intensity for
the sample of all mergers and for the sample of horizontal mergers.
Insert Table 1 here
Panel A presents the summary statistics for all industries and years. The mean (median) annual
number of mergers within an industry is 17 (7), out of which 10 (3) are horizontal. The mean (median)
merger intensity is 2.45% (1.08%) for all mergers and 1.17% (0.35%) for horizontal mergers. PanelB presents the mean number of mergers and merger intensities for the five most active industries
over the whole sample period: candy and soda, health care, shipbuilding and railroad equipment,
coal, and banking.27 Panel C lists the years with the highest merger intensities. Consistent with a
widely documented trend, the second part of the nineties is associated with an all-time peak in merger
activity.
3.3 The state of demand and control variables
We proxy for the state of industry demand by the median annual sales growth within the industry.Specifically, for each firm-year we calculate annual sales growth, defined as the difference between the
firms annual sales, COMPUSTAT item 12, and its previous years sales, scaled by the previous years
sales and use the median sales growth for each industry-year.
26 See Dunne, Roberts and Samuelson (1984) for a discussion of the deficiencies of SIC industry classification as a
measure of economic markets.
27 Each of these five industries belongs to top-three based on either the mean overall merger intensity or mean horizontal
merger intensity.
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Following recent studies of merger waves and industry-level merger activity (e.g., Mitchell and
Mulherin (1996), Andrade and Stafford (2004), and Harford (2005)), we control for other determinants
of firms incentives to merge. The control variables, measured at a previous year-end, are as follows.
Median market-to-book ratio and its standard deviation. Both the misvaluation-based theory of
mergers (e.g., Rhodes-Kropf and Viswanathan (2004) and Shleifer and Vishny (2003)) and the neo-
classical (shock-based) theory posit that industry-level merger intensity is expected to be positively
related to the industry market-to-book ratio, albeit for different reasons.28 Furthermore, both types
of theories predict a positive relation between merger activity and the dispersion of market-to-book
ratios within the industry (e.g., Jovanovic and Rousseau (2002) and Rhodes-Kropf and Viswanathan
(2004)).29 Therefore, we control for the industry-year median market-to-book ratio and its standard
deviation. Firm-level market-to-book ratio is calculated as the ratio of the market value of the firm,
item 24*item 25+item 181, to the book value of its assets. The book value of assets is the book value
of equity plus liabilities, item 181. The book value of equity equals stockholder equity minus preferred
equity plus investment tax credit, item 35, minus retirement benefit, item 330.30
Median three-year annual return. The misvaluation-based theory argues that past returns are
expected to be positively related to overvaluation and to the resulting incentives to merge. The
three-year annual return is defined as the sum of thirty six monthly returns, obtained from CRSP. 31
Median property, plant, and equipment to assets ratio. Larger fixed assets may result in higher
integration costs. Thus, we control for the proportion of tangible assets using the ratio of gross
industry-year median property, plant, and equipment to book assets,
item 7
item 6 .
Average commercial and industrial loans spread. Harford (2005) argues that mergers are more likely
to occur in periods of high credit availability. We follow Harford and use the spread between the average
commercial and industrial loans (C&I) rate and the Fed rate as an inverse proxy for credit availability.
We obtain the C&I rate spread from http://www.federalreserve.gov/releases/e2/e2chart.htm.
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