(English) a Theory of Strategic Mergers

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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

12


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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


16/61

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

15


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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

16


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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:

18


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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)


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).


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.


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.


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.


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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Documents

(English) a Theory of Strategic Mergers