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Page 1: Entry and Shakeout in Dynamic Oligopoly - uni-mannheim.deschmidt-dengler.vwl.uni-mannheim.de/fileadmin/user_upload/schmid… · Entry and Shakeout in Dynamic Oligopoly ... shakeout

Entry and Shakeout in Dynamic Oligopoly∗

Paul Hünermund† Philipp Schmidt-Dengler ‡

Yuya Takahashi §

January 16, 2014

In many industries, the number of �rms evolves non-monotonically overtime. A phase of rapid entry is followed by an industry shakeout, where alarge number of producers disappears in a short period of time. We present asimple timing game of entry and exit with an exogenous technological processgoverning �rm e�ciency. We take our model to the data and calibrate it tothe post World War II penicillin industry. The equilibrium dynamics of thecalibrated model closely match the patterns observed in many industries.In particular, our model generates richer and more realistic dynamics thancompetitive models previously analyzed. The entry phase is characterizedby preemption motives while the shakeout phase mimics a war of attrition.Key Words: Life Cycle, Dynamic Oligopoly, Preemption, War of Attrition,PenicillinJEL Classi�cation: L11, O

1 Introduction

New industries often �rst experience substantial growth in the number of �rms, which,

in many cases, is later followed by a rapid decline of �rms active in the industry. Sub-

sequently the number of �rms settles at a level substantially below the observed peak.

Utterback and Suarez (1993) and Suarez and Utterback (1995) document this pattern

∗We thank participants in the session on �Empirical Timing Games� at ESEM 2013 in Gothenburg, inparticular Je� Campbell, as well as seminar participants in Salzburg for helpful comments. Schmidt-Dengler and Takahashi gratefully acknowledge �nancial support from the German Science Founda-tion through SFB TR 15.

†Centre for European Economic Research (ZEW), email: [email protected]‡University of Mannheim, also a�liated with CEPR, CES-Ifo, and ZEW, email: [email protected]

§Johns Hopkins University, email: [email protected]

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for several industries ranging from the typewriter industry which originated in the late

19th century, via automobiles in the early 20th century to television sets in the sec-

ond half of the 20th century (Figure 1). The frequency with which this pattern could

be observed across di�erent industries and over time led Gort and Klepper (1982) to

characterize ��ve stages of industry evolution�: (1) small entrepreneurial �rms enter at

the dawn of an industry, followed by (2) a sharp increase in the number of �rms, (3) a

period of zero net entry, (4) a sharp decline in the number of �rms, and (5) the industry

settling at a stable stage with zero net entry.

The literature has provided several explanations for non-monotone industry evolu-

tions. Shapiro and Dixit (1986) and Cabral (1993) show that such patterns can be

the result of coordination failures arising in a mixed strategy equilibrium of a dynamic

entry and exit game. This type of model can explain why some industries experience

`overshooting' while others do not. Horvath, Schivardi, and Woywode (2001) look at a

strategic model with uncertainty regarding the industry's pro�tability. Firms di�er in

their variable costs. Resolution of this uncertainty �rst drives entry and later exit.

The life cycle pattern of growth in the number �rms followed by a shakeout is often

coupled with increasing output and declining prices over the entire life cycle. This is

hard to reconcile with a declining number of �rms during the shakeout. The most promi-

nent explanations have been provided by Klepper (1996) and Jovanovic and MacDonald

(1994). They study competitive dynamic models with technological change. In Klepper

(1996) �rms make entry and exit as well as R&D investment decisions taking only short

run pro�ts into account. The speci�c dynamics are generated by ex-ante heterogeneity

in �rms' innovative ability and �rms speci�c demand inertia. In contrast, in Jovanovic

and MacDonald (1994)'s model �rms make dynamic entry and exit decisions taking into

account future payo�s. The industry is created by a major innovation triggering the

�rst wave of entry. A subsequent major innovation that increases the e�cient scale is

challenging to develop or adopt. This triggers additional entry. However, only success-

ful innovators increase their scale of production and unsuccessful innovators exit which

eventually causes the shakeout.

Competitive models have been successful at generating general life-cycle patterns of

prices and quantities, but less successful at mimicking actual evolutions of producers in

an industry. The competitive nature of the model by Jovanovic and MacDonald (1994)

with a continuum of �rms generates a rectangular shape for the number of �rms, as

entry and shakeout waves both occur within one period. The model in Klepper (1996)

is able to generate a gradual change in market structure, but �rms' decisions are static

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Figure 1: Examples of shakeouts in di�erent industries

1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 19900

10

20

30

40

50

60

70

80

90

Year

TypewriterTelevisionAutomobilesPenicillin

Notes: Number of active �rms within the industries according to Utterback and

Suarez (1993) and Klepper and Simons (2005, for penicillin).

and the model does not allow for strategic interaction.

This paper studies a dynamic oligopoly model that is close in spirit to Jovanovic and

MacDonald (1994) in the sense that it allows for a simple innovative process. Our ap-

proach complements the existing literature along three dimensions. First, the model has

a stronger empirical nature as it generates aggregate uncertainty in market structure.

This is in contrast to Jovanovic and MacDonald (1994), where changes in market struc-

ture take place in an instant. Entry and shakeout occur within one period due to the

competitive nature of the model with atomistic �rms. In principle our model could be

estimated based on observations of entry and exit in the industry.

Second, in contrast to Jovanovic and MacDonald (1994) and Klepper (1996) our model

involves strategic interaction. Firms in our model are forward looking. In particular, it

allows for the identi�cation of preemption motives in the entry phase and war of attrition

motives in the shakeout phase.

Third, we take our model to the data by calibrating it to the post World War II

penicillin industry. To do so, we estimate demand for penicillin employing a novel

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instrument for price. We argue that the exogenous innovation process, the productivity

enhancement caused by innovation, as well as sunk entry costs and scrap exit values can

be identi�ed by matching key features of the penicillin industry life cycle. Finally we

show that strategic interaction and forward looking behavior are important factors in

determining the life cycle of an industry, by quantifying strategic motives in the entry

and exit decisions.

During the entry phase, �rms have an incentive to enter the market early to increase

their chance of becoming innovative and reduce competitors' incentives to enter. In the

shakeout phase however, �rms want to outlast their competitors to secure pro�ts. The

dynamic game thus turns from a preemption race early on into a war of attrition when

the number of �rms has reached its peak.

The remainder is organized as follows. Section 2 presents the dynamic model, char-

acterizes the equilibrium, and illustrates how the model can generate a typical industry

life cycle with entry and shakeout stages. Section 3 gives an overview of the penicillin

industry and the data. It then presents the demand estimates and calibration results,

and illustrates the dynamics of the strategic e�ects. Section 4 concludes.

2 A dynamic model of entry and exit with process

innovation

2.1 Setup

This section describes the elements of the model. We consider a dynamic game of entry

and exit with process innovation in discrete time, t = 1, 2, . . . ,∞. The industry consists

of up to N �rms. The set of players is denoted by N = {1, ..., N} and a typical player

is denoted by i ∈ N . Every period in time, �rms choose whether to be active or not.

In the following, we describe the sequencing of events, the period game, the transition

function, the payo�s, the strategies, and the equilibrium concept.

Publicly observable state vector. Each �rm is endowed with a �rm-speci�c state vari-

able sti ∈ Si = (ω0, ω1, ..., ωK) . sti = ω0 denotes a potential entrant, i.e., a �rm not

being active in the market; sti = ωk for k = 1, ..., K denotes an active �rm that

has achieved e�ciency level k. The vector of all players' public state variables is de-

noted by st = (st1, ..., stN) ∈ S = ×N

i=1Si. Sometimes we use the notation st−i =(st1, ..., s

ti−1, s

ti+1, ..., s

tN

)∈ S−i to denote the vector of states by �rms other than �rm i.

The cardinality of the state space S equals ms = (K + 1)N .

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Symmetric observable state space. We mostly restrict attention to situations in which

the identity of other �rms does not a�ect �rm i's payo�s and decisions. We introduce the

counting measure δ(st−i

)which equals the K-dimensional vector, where each element

contains the number of other �rms in state ωk for k = 1, ..., K. The number of rival

potential entrants (the number of rival �rms in state ω0) is given by N minus the

sum of the elements of δ(st−i

). A typical element of the �symmetric� state space is a

(K + 1)-dimensional vector (sti, δ), which consists of �rm i's state, and the number of

rival �rms in each state, δ(st−i

). The cardinality of the symmetric state space equals(

N+K−1K

)· (K + 1).1

Privately observed payo� shocks. Each �rm i privately observes a two-dimensional

payo� shock εti = (εti0, εti1) ∈ R2 that is drawn independently from a strictly monotone

and continuous distribution function F . Independence of εti from the state variables is an

important assumption, since it allows us to adopt the Markov dynamic decision frame-

work.2 To ensure that the expected period return exists, we assume that E [εtik|εtik ≥ ε]

exists for all ε and k = 0, 1.

Actions. After observing the public state st and the private state variable εti, each

�rm decides whether to be active or not. We let ati ∈ A = {0, 1}, where ati = 0 stands for

a �rm choosing to be inactive and ati = 1 stands for a �rm choosing to be active. All N

�rms make their decisions simultaneously. An action pro�le at denotes the vector of joint

actions in period t, at = (at1, . . . , atN) ∈ A = ×N

j=1Aj. The cardinality of the action space

A is given by 2N . We sometimes use the notation at−i =

(at1, ..., a

ti−1, a

ti+1, ..., a

tN

)∈ A−i

to denote the vector of actions undertaken by �rms other than �rm i.

Process innovation. There is an exogenous process that enhances active �rm's capa-

bilities. In particular, active �rms in state sti = ωk with k > 0 who choose to be active

innovate with probability λk ∈ (0, 1).

State transitions. The state transition is described by a probability density function

g : A × S × S −→ [0, 1], where a typical element g (at, st, st+1) equals the probability

that state st+1 is reached when the current action pro�le and state are given by (at, st).

We require∑

s′∈S g (a, s, s′) = 1 for all (a, s) ∈ A × S. In our application, a �rm's

state st+1i depends on its current state sti and action ati, as well as the outcome of

the stochastic innovation process. The innovation process is governed by a vector of

exogenous parameters Λ = (λ1, . . . , λK−1) where each element of Λ lies on the unit

interval. In particular, if a �rm is a potential entrant, i.e., sti = ω0 we have

1See Gowrisankaran (1999), also for an e�cient representation of the state space in this case.2For a discussion of the independence assumption in Markovian decision problems see Rust (1994).

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st+1i =

ω0 w.p. 1 if ati = 0

ω1 w.p. 1 if ati = 1.

For an incumbent, in state ωk for k = 1, . . . , K − 1 we have

st+1i =

ω0 w.p. 1 if ati = 0

ωk w.p. 1− λk if ati = 1

ωk+1 w.p. λk if ati = 1.

Finally, for an incumbent, who has reached the maximum level of sophistication, i.e.,

sti = ωK we have

st+1i =

ω0 w.p. 1 if ati = 0

ωK w.p. 1 if ati = 1.

Note that a �rm's state transition is governed by the endogenous entry and exit

decisions, ati, as well as the exogenous innovation process described by the probability

of innovation λk.

Period payo�. Payo� of �rm i is collected at the end of the period after all actions

are observed. It consists of the action and state-dependent deterministic payo� and the

private pro�tability shock. We can write period payo�s as a real-valued function de�ned

on S×A× R and given by

πi(ati, a

t−i, s

ti, s

t−i

)+

∑k=0,1

1{ati=k}εtik.

The deterministic pro�t π(·) depends on four elements: (1) the choice of being active

or not undertaken by the �rm, ati, (2) the �rm's own state sti (whether it has already

been active and whether it has successfully innovated), (3) rival �rms' decisions to be

active or not, at−i, and (4) their states at the beginning of the period summarized by st−i.

We assume that pro�ts are bounded: |π (.))| <∞. As we will specify later, π(·) has twoadditively-separable components. The payo� of the period game that is a function of s

only and a second component that depends on a. We leave the structure of the period

game unspeci�ed here with the only requirement that there is no dynamic implication

in it (�static dynamic� breakdown). For example, we exclude the possibility of learning-

by-doing in the product market that lowers investment costs.

Game payo�. Firms discount future payo�s with the common discount factor β < 1.

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The game payo� of �rm i equals the sum of discounted period payo�s written as

E

{∞∑t=0

βt

[π(ati, a

t−i, s

t) +∑k=0,1

1{ati=k}εtik

]∣∣∣∣∣ s0, ε0i}, (1)

where the expectation is taken over future realizations of the state and payo� shocks.

Markovian strategies. Following Maskin and Tirole (2001, 1994), we consider pure

Markovian strategies ai (ε; st). A strategy for �rm i is a function of the �rm speci�c

pro�tability shock and the publicly observable state variables. The assumption that

the pro�tability shock is independently distributed allows us to write the probability

of observing action pro�le at as Pr (at|st) = Pr (at1|st) · · ·Pr (atN |st) . The Markovian

assumption then allows us to abstract from calendar time and subsequently we omit the

time superscript.

Let σi be the set of �rm i's belief about the probability distribution of actions and

state transitions. E.g., σi (a|s) denotes �rm i's belief about the probability that action

pro�le a is taken when the current state is s. Similarly, σi (a−i|s) denotes �rm i's belief

about the probability that its opponents take actions a−i given s. Using the beliefs, a

�rm's value function can be written as

Wi (s,εi;σi) = maxai∈Ai

∑a−i∈A−i

σi (a−i|s)

[π(ai, a−i, s) +

∑k=0,1

1{ai=k}εik

+β∑s′∈S

g(s′|s, ai, a−i) EεWi (s′, ε′i)

]}, (2)

where g(s′|s, ai, a−i) denotes the probability that the industry reaches state s′ given

current state pro�le s and actions (ai, a−i). Eε denotes the expectation operator with

respect to the �rm speci�c payo� shock. The �niteness of the action and state space

guarantees the existence of the value function Wi in equation (2).

2.2 Equilibrium

We start by de�ning a Markov Perfect Equilibrium (MPE) in this game. A MPE is

a pair of strategies and beliefs (a, σ) = (a1, a2, ..., aN , σ1, σ2, ..., σN) that satis�es the

following conditions. First, each �rm's strategy ai is Markovian and a best response to

a−i given beliefs σi. Second, each �rm's beliefs σi are consistent with strategies a.

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Ex-ante Value Function. The �rm's ex-ante value function Vi(·) describes its expectedpayo� in a given observable state before the privately observed pro�tability shock is

realized and actions are taken: Vi(s;σi) = EεWi (s, εi). Given beliefs, we can write the

�rm's ex-ante value function as

Vi(s; σi) =∑a∈A

σi(a)

[πi(a, s) +

∑k=0,1

E(εik|ai = k) + β∑s′∈S

g (s′|s, a)Vi (s′;σi)

].

We now further exposit the optimal actions necessary to characterize and compute

the equilibrium of our model. To do so, we de�ne the choice-speci�c value

vi(ai, s;σi) =∑

a−i∈A−i

σi (a−i)

[πi(ai, a−i, s) + β

∑s′∈S

g(s′|s, ai, a−i)Vi(s′;σi)

].

It is then optimal to choose action ai = 1 under beliefs σi if and only if

vi(1, s;σi) + εi1 ≥ vi(0, s;σi) + εi0. (3)

This characterizes the optimal decision rule up to a set of measure zero.

For this zero measure set we adopt, without loss of generality, that whenever equation

(3) holds with equality, the �rm chooses the higher action. The optimal policy ai satis�es

ai(s;σi) = argmaxk∈{0,1}

{vi(k, s; σi) + εik} .

The probability that �rm i chooses action ai = k is thus given by

p (ai(s;σi) = k) = ψi(k, s;σi)

= Pr (vi(k, s;σi) + εik ≥ vi(j, s;σi) + εij,∀j ̸= k) . (4)

This relationship holds for all �rms i ∈ N and states s, and every action k ∈ {0, 1}.Without loss of generality, we set the choice to be inactive (k = 0) to be the reference

action whose probability is given by 1 − p (ai(s; σi) = 1). This results in a system of

N ·ms equations, which we can write compactly in vector notation as

p = ψ (σ) , (5)

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where p denotes the (N ·ms)-dimensional vector of choice probabilities and σ the (N ·ms)-

dimensional vector of beliefs.

In a Markov perfect equilibrium, it must hold that beliefs σ have to correspond to

choice probabilities p so that equation (5) becomes

p = ψ (p) . (6)

It is immediate that any p satisfying (6) constitutes an equilibrium. Observe that this

is a mapping from a (N ·ms)-dimensional unit simplex into itself. Since the function ψ

is continuous in p, Brouwer's �xed point theorem applies and (6) has a solution in p.

Observe that the restriction to symmetric strategies under symmetric payo�s does not

a�ect the argument.

Multiplicity. Multiplicity of equilibria is a well-known feature inherent to games.

For the prevalence of multiple equilibria in the class of Markov games, see Doraszelski

and Satterthwaite (2010) and Besanko, Doraszelski, Kryukov, and Satterthwaite (2010).

Besanko, Doraszelski, Kryukov, and Satterthwaite (2010) provide su�cient conditions

for uniqueness. If players' decisions are stagewise unique and movements in the state

space are unidirectional, an equilibrium of the game is unique. The �rst condition,

stagewise uniqueness, states that reaction functions given value functions cross only once

at every stage of the game. This does not hold under a general continuous distribution

of payo� shocks. The second condition is not satis�ed either, as any current state may

be reached again later in the game with a strictly positive probability.

2.3 A Numerical Example

We consider the simplest possible case to illustrate the model's ability to generate a

typical industry life cycle with a shakeout. Assume that there are only three �rm

speci�c states: potential entrant ω0, ine�cient incumbent ω1, and e�cient incumbent

ω2. That is, K = 2 and si ∈ {ω0, ω1, ω2} . If an ine�cient incumbent decides to continue,

it becomes e�cient with probability λ. That is, it stays ine�cient with probability 1−λ.In each period, given the vector of �rms' technological states, �rms compete in the

product market. We consider Cournot competition with constant-elasticity demand and

asymmetric costs3. The inverse demand is given by P (Q) = aQ−b with Q =∑

i qi. Costs

are given by

3We also use Cournot competition with linear demand and analyze industry shakeouts. The detailsof this speci�cation are available upon request.

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Ci(qi) =

c1qi if si = ω1

c2qi if si = ω2.

We assume 0 ≤ c2 < c1 < a. This feature models a setting where incumbents can

reduce their costs and thereby increase their pro�ts by successfully innovating.

Let

n1 (s) =∑i∈N

1 {si = ω1}

n2 (s) =∑i∈N

1 {si = ω2}

denote the number of ine�cient and e�cient �rms, respectively. In a symmetric Nash

equilibrium, �rms of the same type will produce the same quantity and earn the same

pro�t. Let q1 and q2 denote the quantities produced by ine�cient and e�cient �rms,

respectively. Let also π̃1 and π̃2 be the corresponding pro�ts.

For bc1 + n2 (c2 − c1) ≥ 0, the equilibrium quantities of the static game are given by

q∗1 (s) =

[c1n1(s)+c2n2(s)

a(n1(s)+n2(s))−ab

]− 1b

b (c1n1 (s) + c2n2 (s))[bc1 + n2 (s) (c2 − c1)] , (7)

q∗2 (s) =

[c1n1(s)+c2n2(s)

a(n1(s)+n2(s))−ab

]− 1b

b (c1n1 (s) + c2n2 (s))[bc2 + n1 (s) (c1 − c2)] . (8)

Otherwise, they are given by

q∗1 (s) = 0,

q∗2 (s) =1

n2 (s)

[c2n2 (s)

an2 (s)− ab

]− 1b

.

The equilibrium price is calculated as

P (s) =c1n1 (s) + c2n2 (s)

n1 (s) + n2 (s)− b.

The operating pro�ts are

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π̃∗1(s) = [P (s)− c1] q

∗1 (s) , (9)

π̃∗2(s) = [P (s)− c2] q

∗2 (s) . (10)

In addition, we assume active �rms incur �xed costs f . If a �rm is inactive, it earns

zero pro�t. Moreover, if a �rm was inactive in the previous period but chooses to be

active this period, it incurs an entry cost ξ. Finally, if a �rm was active in the previous

period but chooses to be inactive this period, it collects a scrap value ϕ.

Our model is su�ciently general to generate various types of evolution of the number

of �rms endogenously. We aim to generate an industry life cycle with the following three

features: (1) a period of time with persistent entry, (2) a large fraction of �rms exiting

during a relatively short period of time, and (3) a period after the shakeout characterized

by an oligopoly with a small number of incumbents and occasional entry and exits.

To replicate the �rst feature, the probability of successful process innovation should

not be too high. With a low success probability, potential entrants keep entering the

market even if there are already many incumbents. For the second feature, the pro�t of

ine�cient �rms should decrease quickly as the number of e�cient rivals increases in the

market. A large cost di�erential (c1 − c2) can achieve the goal. Finally, demand should

not be too high, so that only a few number of e�cient �rms can pro�tably operate at the

same time. In addition, the entry cost and scrap value should be large enough compared

to the period pro�t, so that there is still entry and exit after the market experienced a

shakeout.

With these taken into consideration, we parameterize the model as follows:

N = 25

λ = 0.008

(f, ξ, ϕ) = (0, 200, 30)

(c1, c2) = (40, 1)

(a, b) = (30,1

2.5).

Finally, we assume ε follows the type-1 extreme value distribution with scaling parameter

equal to 25. Note that the value of b implies that the demand elasticity is 2.5.

In order to numerically solve for equilibria, the backward solution algorithm in Pakes

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Figure 2: Probabibility of being active for potential entrants

05

1015

2025

0

5

10

15

20

250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Efficient firms n2

Inefficent firms n1

and McGuire (1994) is used. For a vector of starting values, value functions and policy

functions are updated in every iteration until the sequence of updated numbers converges

to a previously speci�ed criterion. Under these parameter values, we always �nd the

same equilibrium regardless of where we start the solution algorithm. While this does

not mean that the equilibrium is unique, in what follows we analyze the conditional

choice probabilities and industry evolutions implied by this equilibrium.

Figure 2 plots the equilibrium probability of being active for potential entrants (�entry

probability�) for every pair of the number of e�cient rivals and the number of ine�cient

rivals. It is clear that the entry probability is monotonically decreasing everywhere in

both numbers of e�cient and ine�cient rivals. A noteworthy feature is that entry to the

market almost ceases once the number of e�cient rivals reaches three. On the contrary,

they still continue to enter even if there are many incumbents, as long as most of them

are ine�cient. Figure 3 shows the equilibrium probability of being active for ine�cient

incumbents. They tend to stay active even when the number of e�cient rivals is large.

With the small probability of innovation and the large cost di�erential, the preemption

12

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Figure 3: Probabibility of being active for infe�cient incumbents

05

1015

2025

0

5

10

15

20

250.75

0.8

0.85

0.9

0.95

1

Efficient firms n2

Inefficent firms n1

game is essentially over once two or three �rms have successfully innovated. Note that

ine�cient incumbents do not necessarily leave the market even if the number of e�cient

rivals becomes large; i.e., their probability of being active converges to around 0.77.

This is because they have already incurred entry costs, and therefore have an incentive

to wait for their opponents to exit �rst.

Using these equilibrium probabilities, we simulate the model for a period of 45 years

several times and plot the evolution of the number of ine�cient, e�cient, and total active

�rms for each simulation draw in Figure 4. This shows that the model can generate rich

patterns of industry shakeouts. Overall, a promotion of the ine�cient to e�cient triggers

exits of ine�cient �rms. Under the chosen parameter values, the industry becomes stable

once four �rms become e�cient. Since promotions are stochastic, industry shakeouts

show various patterns depending on when each promotion takes place. In the top panel,

many �rms enter the market early and three incumbents become e�cient by period 8.

Therefore, the shakeout is very severe; afterwards, the industry gradually consolidates

over time. The middle panel shows another extreme example. None of the ine�cient

13

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Figure 4: Numerical example

0 5 10 15 20 25 30 35 40 450

10

20

30

InefficientEfficientTotal

0 5 10 15 20 25 30 35 40 450

10

20

30

0 5 10 15 20 25 30 35 40 450

10

20

30

Period

�rms become e�cient for a long time, and therefore, there is persistent net entry for

more than 20 periods. The bottom panel shows another simulated path where the �rst

two promotions occur substantially earlier than the following two. Each promotion wave

triggers an exit wave. This mimics, e.g., the evolution of the TV industry.

To see the average pattern, the top panel in Figure 5 shows averages (over 200 sim-

ulation draws) of the number of ine�cient �rms, e�cient �rms, and the total number

of active �rms. This con�rms that the three features of industry evolution mentioned

above are replicated. Comparing with Figure 3 in Jovanovic and MacDonald (1994), the

bottom panel in Figure 5 plots averages (over 200 simulation draws) of the equilibrium

price and quantity over time. The model thus successfully replicates the basic pattern

of price and quantity over time.

14

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Figure 5: Simulation averages

0 5 10 15 20 25 30 35 40 450

5

10

15

20

25

InefficientEfficientTotal

0 5 10 15 20 25 30 35 40 450

500

1000

1500

Period

0 5 10 15 20 25 30 35 40 450

20

40

60QuantityPrice

3 Application: Penicillin Industry

3.1 Industry Background

Penicillin, the �rst medically useful antibiotic, was discovered in 1928. However, it took

almost a decade until the whole pharmaceutical potential became apparent. The devel-

opment of production at industrial scale was promoted extensively by the US government

since the early 1940s. After the end of World War II the penicillin industry experienced

large entry rates for several years which were followed by a shakeout beginning in 1952.

Core of the penicillin production process is the fermentation of organic matter. Penicil-

lium chrysogenum, a certain species of mold fungi, is grown in a nutrient medium, which

then produces the desired antibiotic substance. This fermentation process was subject

to a spectacular series of process innovations that transformed a once una�ordable drug

into a mass product.

Industry history. Despite its discovery in Great Britain, development of penicillin

15

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Figure 6: The shakeout in the penicillin industry

1945 1950 1955 1960 1965 1970 1975 1980 1985 19900

5

10

15

20

25

30

Year

FirmsEntryExit

Notes: Data collected from Figure 1 in Klepper and Simons (2005).

took place mainly in the United States since wartime Britain could not provide the

necessary resources for the creation of a new product industry. Research was funded

by the US government at various places such as, among others, the Department of

Agriculture's Northern Regional Research Laboratory (NRRL), Stanford University and,

the University of Wisconsin. Right from the beginning, large pharmaceutical companies

such as P�zer, Sqibb and Merck were involved. The joint e�orts during WWII were

coordinated by the War Production Board (WPB).

The WPB e�ectively regulated entry into the wartime penicillin program. Klepper

and Simons (1997, footnote 43) cite that a large amount of applications by �rms were

denied due to considerations of national security or concerns about harmful competition

within the new industry. Beginning in 1945, restrictions were slowly removed. Because

of their strategic importance and the major public stakeholding, all early advances in

penicillin production were licensed on a royalty-free basis and, in principle, available to

entrants (Federal Trade Commission, 1958, p. 228-229) (FTC).

The number of producers soon increased from 21 up to 30 in 1952. As Figure 6

depicts, at this point exit peaked4 and entry rates declined resulting in a shakeout

4Klepper and Simons (2005) emphasize that mergers played only a minor role in shaping the shakeout.Only 3% of the exits after the peak and 0% before were related to acquisitions. Furthermore,acquisitions by �rms outside of the industry were counted as continuations of the acquired �rm (p.25).

16

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Figure 7: Historical sales and prices for penicillin

1945 1950 1955 1960 1965 1970 1975 1980 1985 0

5000

10000

15000

20000

25000

Year1945 1950 1955 1960 1965 1970 1975 1980 1985

0

0.5

1

1.5

2

2.5

x 106

SalesAverage Unit Value

Notes: Average unit values in 1982 USD. Sales in billion international units. Data

collected from SOC reports, various years.

with the number of �rms active in the market decreasing by 70% until the early 1980s.

Klepper and Simons argue that the maximum number of �rms in the industry might

have been a lot higher, had entry been unregulated prior to 1946. Thus, the shakeout

could have been even more severe. It is important to note that the few remaining �rms

nevertheless increased output constantly (see Figure 7) and were able to penetrate the

market e�ectively.

Although information on the early advances in penicillin production was spread ac-

tively, technology adoption was, in general, not trivial. The FTC report describes that

all manufacturers in the industry had prior experience in the pharmaceutical industry.

They had to invest large amounts in their production plants and rapid technological ad-

vances commonly outmoded existing plants (p. 102-105). Firms surviving the shakeout

were, for the predominant part, the largest and earliest producers in the industry (p.

82). This observation is consistent with our model in which e�cient �rms have higher

production capabilities and earlier producers are more likely to be e�cient.

Until the late 1950s, there was only one major product innovation (Klepper and Si-

mons, 1997). The acid-resistant penicillin V survives in the intestinal tract and can

be given orally compared to the previously used injection of benzylpenicillin (penicillin

G). Despite an additional precursor for fermentation, the production process is similar.

This new form of penicillin was introduced commercially in 1955, and is, thus, unlikely

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to be the cause of a shakeout that had begun three years before. On the contrary, sales

of previous penicillin forms remained high and could even be increased (Klepper and

Simons, 1997, Table 15 and 16).

From 1958 on, new semisynthetic forms of penicillin were developed. It became pos-

sible to manipulate the side-chain of the penicillin nucleus, 6-aminopenicillanic acid.

These novel forms opened new sub-markets of antibiotics and did not compete directly

with the previously available forms of penicillin since they addressed di�erent kind of

diseases (Klepper and Simons, 1997). Ampicillin, e.g., developed by the British Beecham

Group proved to be e�ective against Gram-negative bacteria that were resistant to stan-

dard penicillin types. Klepper and Simons (1997, p. 431) hold the rise of entirely

new semisynthetic compounds responsible for the anew increasing number of penicillin

producing �rms in the 1980s.

Process innovations. Although the total chemical synthesis of penicillin eventually

became possible in 1959, it never proved to be economically e�cient (Neushul, 1993, p.

384). This was to a large extent due to the realized advances in the fermentation process

that took three directions.

Firstly, the e�ectiveness of penicillin against bacteria was discovered in a petri dish.

The early laboratory experiments followed this path to grow the penicillium mold as a

surface culture. However, the need for submerged growth in large fermentation vessels for

production on an industrial scale soon became obvious. The �rst patent on submerged

production was �led in 1935 (Neushul, 1993, p. 375). Since then, vessels for submerged

growth were subject to constant improvements to establish perfect control on aeration,

agitation, and temperature.

Secondly, researchers at the NRRL were experimenting with the growth medium. A

major breakthrough was achieved in the early 1940s by replacing a formerly used yeast

extract with a production broth that is based mainly on corn steep liquor, a byproduct of

corn milling. This rich growth medium realized a vast increase in production e�ectiveness

(Neushul, 1993, p. 379) and soon became the industry standard (Tornqvist and Peterson,

1956).

Eventually, the development of high-yielding strains of the Penecillium mold had a

substantial impact and was an ongoing process well beyond the end of WWII (see Figure

8). The originally discovered penicillin strain produced about 2 International Units 5

5The International Unit is a measure for the biological activity of a substance (older publications usethe term Oxford Unit). The IU speci�c to penicillin G exhibits a conversion factor of 1,670 IUper mg (Humphrey, Mussett, and Perry, 1952). For di�erent conversion ratios see (Federal TradeCommission, 1958, p. 355).

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Figure 8: Historical development of penicillin yields

1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990

0.1

1

10

100

Year

X−1612

Wis. Q−176

Wis. 49−2105

NRRL 1951

NRRL 1951−B25

Notes: Various sources as described in the text. Regression line was �tted by a

log-linear regression of yield rates on year for 1950 and later following Figure 10.1.

in Calam (1987, p. 120). Data points for strain NRRL 1951, NRRL 1951-B25,

and X-1612 are not used for demand estimation in Section 3.2 and are reported for

illustration only.

6 (IU) per milliliter (or 1.2 µg/ml) of production broth (Barreiro, Martin, and Garcia-

Estrada, 2012). Raper (1946) describes the e�orts that were made to improve this

proportion. Penicillin strains were often subject to considerable variation in laboratory

cultures and thereby, substrains could be separated that possessed higher productivity.

In addition, with the help of the US army, the NRRL conducted a worldwide search for

highly productive natural variants of penicillin (Neushul, 1993). The fact that the by far

most promising strain, however, Penicillium chrysogenum NRRL 1951 (realizing yields

of 100 IU/ml), was found in 1943 on a moldy cantaloupe at a market in Illinois became

anecdotal. This strain showed a very high variability and, thus, was the parent to many

6Klepper and Simons state that an amount of 500,000 IU per day were necessary to treat a severemedical case.

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superior producing strains (Raper, 1946, Figure 1). One of the earliest descendants,

strain NRRL 1551-B25, was especially suitable for submerged growth (Raper, 1946, p.

43) and reached yields up to 250 IU/ml (Backus and Stau�er, 1955, p. 431).

Another step to improve yields was to induce mutation by ultraviolet and X-ray radi-

ation. In 1944, at the Carnegie Institution's Cold Spring Harbor Laboratory in a joint

e�ort with the NRRL, mutant X-1612 was developed (Raper, 1946). With yields of 500-

600 IU/ml it was referred to as the �rst �super-strain". Another mutant of this strain,

the Wis. Q-176 (900 IU/ml), created 1945 at the University of Wisconsin by ultraviolet

irradiation, started the successful Wisconsin family of superior strains (Barreiro, Martin,

and Garcia-Estrada, 2012).

At that time, the penicillin strains employed in the production process naturally

produced yellow pigments that had to be extracted to obtain the pure pharmaceutical

substance. This procedure was usually accompanied with losses. By the time of 1947

pigmentless strains were encountered at Wisconsin (Backus and Stau�er, 1955). Soon,

the members of the pigmentless family (such as Wis. 49-2105) could outperform previous

strains. Some members accomplished yields up to 3000 IU/ml (Barreiro, Martin, and

Garcia-Estrada, 2012, p. 3). Yield rates continued to increase exponentially far into the

1980s (Calam, 1987).

3.2 Demand Estimation

We obtain yearly data on sales and unit values for 1946 to 19847 from the Synthetic

Organic Chemicals (SOC) reports published by the United States Tari� Commission.

Sales were denoted in billion international units8 and we restrict attention to reported

�gures that exclude semisynthetic types.

We calculate average unit prices from SOC's aggregate �gures and de�ate the series

to 1982 dollars. Figure 7 shows sales and price movements. Prices fell sharply in the

beginning of the industry. In 1946, when penicillin was �rst introduced to the open

market (Barreiro, Martin, and Garcia-Estrada, 2012), price was $22,580 per billion IU

on average, which dropped to $520 in 1956. Sales increased until 1974 from where they

show a volatile downward trend. The corresponding time series for sales of semisynthetic

penicillins exhibits its peak not before the beginning of the 1980s.

7Data for the years 1949, 1950, 1951 and 1980 are missing since the particular reports were notavailable on USTC's website (November 2013). For years later than 1984 separate �gures for non-semisynthetic penicillin are not available.

8Since values were reported in pounds only in later years we used a conversion ratio of 0.7 billion unitsper pound over di�erent product classes, following Klepper and Simons (1997), p. 430.

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We employ a log-linear demand speci�cation with a constant elasticity of demand and

control for income and a linear time trend. As instruments for the endogenous price,

we have three variables at hand. First, we obtain average hourly earnings of production

and nonsupervisory employees in manufacturing from Federal Reserve's Economic Data9.

This serves as a measure for the input price of labor. Unfortunately, the corresponding

time series for the pharmaceutical industry separately was not available.

As previously mentioned, since the basic research conducted by the NRRL during

World War II, corn steep liquor was an important input factor in the penicillin fer-

mentation. From the Feed Grains Database, provided by United States Department of

Agriculture10, we extract data on the weighted-average farm price of corn which serves

as a supply shifter.

Eventually, we make use of the previously outlined history of process innovations in

yields of penicillin per amount of production medium. The growth in yield rates was one

of the most important determinants of a reduction in manufacturer's costs. In general,

investments in research and development (R&D) are not independent of demand shocks.

However, we argue that in the case of penicillin the innovation outcome can be regarded

as exogenous due to the high involvement by the public sector. By the beginning of

the 1940s at the latest, penicillin was of highest priority to military and government.

Also, the groundbreaking potential of the new drug to save millions of lives, if it only

could be obtained in su�cient quantities, was realized very soon. Therefore, the level

of R&D for high-yielding strains and improved rates of yields was oriented towards a

socially optimal level. The type of basic research responsible for the enormous advances

in penicillin yields is, in our view, not a�ected by unobserved demand shocks at the

aggregate level.

Because of the high public and scienti�c interest, innovations in penicillin are well

documented until the 1950s. From the previously cited sources we are able to collect data

for the highest possibly attainable yields in a year produced by the until then developed

strains as a measure of the extensive margin of production in the industry. For the

years 1950 and later we consult Calam (1987). Since this time series is not complete

we apply di�erent methods of imputation. The �rst consists of constant interpolation,

constituting a step-function of yield. Secondly, we interpolate linearly. As a last method

we use log-linear parametric interpolation, following the observation in Calam (1987)

that yield rates have doubled every 6 to 7 years since 1950 (see Figure 8).

9See: http://research.stlouisfed.org/fred2 (November 2013).10See: www.ers.usda.gov/data-products/feed-grains-database (September 2013).

21

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Table 1: Penicillin Demand Estimates

(1) (2) (3) (4) (5)

ln (Price) -1.432*** -1.423*** -1.337*** -1.154*** -1.129***(0.306) (0.298) (0.254) (0.098) (0.059)

ln (GDP) -1.760 -1.715 -1.240 -0.226 -0.092(1.756) (1.723) (1.492) (1.067) 0.993

Year -0.093*** -0.093*** -0.095*** -0.099*** -0.100***(0.034) (0.034) (0.034) (0.034) (0.034)

Constant 217.526*** 217.488*** 217.092*** 216.248*** 216.135***(61.191) (61.146) (60.850) (59.997) (59.905)

N 35 35 35 35 35R2 0.809 0.811 0.830 0.860 0.863

First Stage:

F 8.050 5.470 25.457 12.842 15.087χ2 (p-val.) - 0.244 0.371 0.872 0.845

* (p < 0.1), ** (p < 0.05), *** (p < 0.01)Instruments: (1) hourly wage in manufacturing, (2) hourly wage and average farm-price ofcorn, (3) to (5) wage, corn price and, yield of penicillin per liter of production medium. In(3) years between innovative breakthroughs in yield are approximated by a step function,in (4) we use linear interpolation, and in (5) a log-linear approximation.Heteroskedasticity- and autocorrelation-robust standard errors in parantheses. Estimateswere obtained via 2SLS. The Table reports F-statistics for the joint signi�cance of the ex-ogenous variables in the �rst-stage regression. The χ2 test of the overidentifying restrictionsis based on Wooldridge (1995).

22

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Table 1 reports two-stage least squares estimation results. Column (1) represents

estimation with hourly wage being the sole instrument. Column (2) shows estimation

with wage and corn price employed as instrument. And columns (3) to (5) depict

estimation with the full set of instruments with varying imputation methods for yield in

gram per liter as described above. One can see that results are robust to the choice of

instruments. A test of overidentifying restrictions lends credibility to the exogeneity of

our instruments and �rst-stage F-statistics give further assurance on the validity of our

instruments. The last regression (5) includes a potential collinearity problem given the

parametric interpolation of yield and a log-linear time trend. Observe, however, that

our estimates of the demand elasticity are fairly robust to the choice of instruments.

3.3 Calibration

We calibrate the simpli�ed model that we analyze in Section 2.3. Using the �static-

dynamic" breakdown, we �x the demand parameters and calibrate other parameters by

matching the predictions of the model with their empirical counterparts. We use the

demand elasticity in speci�cation (3) of Table 1. To identify the parameters, we need

the following normalizations.

First, recall that

Q = n1q1 + n2q2

P =c1n1 + c2n2

n1 + n2 − b.

Using the optimal solution in (7) and (8), q1 and q2 are implied by (c1, c2, n1, n2). Know-

ing (n1, n2) , the two equations above pin down c1 and c2. However, only the sum of n1

and n2 is observed in the data. Therefore, we can at most identify c1 relative to c2 (or

vice versa). Second, given that the price is a measure-free index and that pro�ts are not

observed, we can freely choose the demand parameter a. Third, since it is not feasible to

separately identify the entry cost, scrap value, and the �xed cost based solely on entry

and exit data, we normalize f = 0. Finally, we set the potential number of �rms to 30.

To summarize:

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N = 30

f = 0

c2 = 1

(a, b) = (250,1

1.337).

The set of calibrated parameters includes the promotion probability λ, the marginal

cost of ine�cient �rms c1, the entry cost ξ, and the scrap value ϕ. To capture important

features of industry shakeouts, we include the following six moments: (1) the average

number of active �rms, (2) the maximum number of �rms, (3) time until the number

of �rms reaches the maximum, (4) the minimum number of active �rms after the peak,

(5) the total number of entry, and (6) the total number of exits. The �rst four moments

jointly pin down the location and shape of the inverse-U path of the number of active

�rms. The �rm turnover, given by the �fth and sixth moments, mainly pins down the

entry cost and scrap value.

We make use of the data from 1946 to 1991 to calculate the empirical moments.

To obtain moments implied by the model, for any parameter values, we compute an

equilibrium and take averages over 200 simulated sample paths over 46 time periods11.

The objective function is de�ned as the sum of the percentage deviation between the

data and model moments. Table 2 reports the calibrated parameters. One striking result

is that the marginal cost of ine�cient �rms is very high compared to the one of e�cient

�rms. Although this appears to be unrealistic from the viewpoint of our application

it may not be surprising since we aim to replicate a complicated industry pattern by a

simple innovation process with only two technology levels. Table 3 shows that the model

is able to match the empirical moments very well.

3.4 Strategic Incentives

Our dynamic oligopoly model departs from the existing literature on the industry life

cycle by explicitly allowing for strategic interaction. In this subsection we illustrate the

role strategic incentives play in �rms' entry and exit decisions. We focus on two types

of incentives. The life cycle pattern of an industry like the penicillin industry suggests

11As before, there may be multiple equilibria. We always start the solution algorithm from Vi(s;σi) =π(s)1−β and p (ai(s;σi) = 1) = 0.1 for all s, and use the equilibrium that we �nd �rst.

24

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Table 2: Calibrated parameters

Parameter Calibrated Value

λ: Promotion probability 0.0045ξ: Entry cost 132.575ϕ: Scrap value 17.463c1: MC of ine�cient �rms 50.423

Table 3: Empirical and calibrated moments

Moment Data Model

Average n 15.98 15.89Maximum n 30.00 27.36

Time until n reaches maximum 6.00 6.04Minimum n after the peak 9.00 7.95

Number of entry 40.00 39.72Number of exit 51.00 51.55

that the game starts in a preemption phase early on and subsequently turns into a war

of attrition phase.

Preemption Incentive. Firms want to enter early, and thereby reduce rival �rms'

incentives to enter. This is o�set by a desire of �rms to wait for a favorable entry

draw. We quantify the preemption incentive by comparing the expected numbers of

competitors an individual �rm faces depending on its own state, e(si, s−i). Since we are

focusing on symmetric strategies, s−i can be summarized by the number of ine�cient

and e�cient incumbents, n1 and n2. We examine how a �rm can a�ect the number of

rival competitors with its entry, comparing the expected number of competitors of a �rm

being inactive (si = 0) with a �rm being an ine�cient incumbent (si = 1),

e(0, n1, n2)− e(1, n1, n2).

To illustrate the e�ect further, we also compute the e�ect of entry on a �rm's ex-ante

value function with reversed signs, V (1, n1, n2)− V (0, n1, n2).

War of Attrition Incentive. Firms want to outlast their rivals, since it increases their

own probability of survival. Once a su�cient number of rival �rms have innovated, the

returns to becoming a successful innovator are small. Firms, thus, have an increasing

incentive to outlast their rivals and obtain one of the remaining �slots� among pro�table

25

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Figure 9: Preemption incentive

0

5

10

0

5

100

0.05

0.1

0.15

0.2

Efficient firms n2

Inefficent firms n1

(a) Expected number of competitors

0

5

10

0

5

1040

60

80

100

120

140

Efficient firms n2

Inefficent firms n1

(b) Ex-ante value function

successful innovators. To quantify this we compute the e�ect of an ine�cient incumbent

outlasting one ine�cient rival on the expected number of rival �rms,

e(1, n1, n2)− e(1, n1 − 1, n2).

Similarly, we document the e�ect by looking at di�erences in ex-ante value functions,

V (1, n1, n2)− V (1, n1 − 1, n2).

Figure 9 depicts the preemption incentive. The left panel for the expected number

of �rms and the right panel for value functions paint a very similar picture: a strong

preemption incentive at the beginning of the game when no or few �rms have entered.

The incentive is largely una�ected by the number of ine�cient rival incumbents, but

declines very quickly as the �rst �rms innovate successfully.

Figure 10 shows the war of attrition incentive. Again, the left panel illustrates the

incentive for the expected number of �rms and the right panel for value functions. A

slightly di�erent picture emerges. The e�ect is barely present when no �rm has yet

successfully innovated and attains its peak when around two �rms have successfully

innovated. This corresponds to the point where the preemption incentive has become

negligible and con�rms our hypothesis about a gradual transition in the relative impor-

tance of the two strategic incentives present in the game.

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Figure 10: War of Attrition Incentive

0

5

10

0

5

100.4

0.5

0.6

0.7

0.8

0.9

Efficient firms n2

Inefficent firms n1

(a) Expected number of competitors

0

5

10

0

5

100

0.5

1

1.5

Efficient firms n2

Inefficent firms n1

(b) Ex-ante value function

4 Conclusion

The paper demonstrates how the frequently observed industry life cycle pattern of a

massive entry wave followed by a shakeout can be rationalized within a parsimonious

dynamic oligopoly similar in spirit to models developed by Ericson and Pakes (1995) and

subsequent authors. Substantial potential gains of operating at the industry's technolog-

ical frontier gives entrepreneurs incentives to enter a new industry as early as possible.

With the �rst adopters of highly innovative technology becoming dominant in the mar-

ket, prospects of unsuccessful �rms diminish quickly, causing them to exit the market

gradually.

The model presented is close to Jovanovic and MacDonald (1994) but allows for strate-

gic interaction. We have shown that substantial strategic e�ects are present by calibrat-

ing the model to the life cycle of the US postwar penicillin industry. In particular, we

showed that prior to successful innovation preemption incentives are present. After only

a few incumbents have successfully innovated, �rms are more concerned with outlasting

their competitor incumbents, which is characteristic of a war of attrition.

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