entry and shakeout in dynamic oligopoly -...
Post on 05-Jun-2020
12 Views
Preview:
TRANSCRIPT
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: huenermund@zew.de‡University of Mannheim, also a�liated with CEPR, CES-Ifo, and ZEW, email: p.schmidt-dengler@uni-mannheim.de
§Johns Hopkins University, email: juja.takahashi@gmail.com
1
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
2
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
3
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 .
4
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).
5
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.
6
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.
7
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)
8
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.
9
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
10
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
11
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
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
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
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
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
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
17
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).
18
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.
19
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.
20
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
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
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:
23
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
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
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.
26
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.
References
Backus, M. P., and J. F. Stauffer (1955): �The production and selection of afamily of strains in Penicillium chrysogenum,� Mycologia, 47, 275�428.
Barreiro, C., J. F. Martin, and C. Garcia-Estrada (2012): �Proteomics ShowsNew Faces for the Old Penicillin Producer Penicillium chrosgenum,� Journal of
Biomedicine and Biotechnology, pp. 1�15.
27
Besanko, D., U. Doraszelski, Y. Kryukov, and M. Satterthwaite (2010):�Learning-by-doing, Organizational Forgetting, and Industry Dynamics:,� Economet-rica, 78(2), 453�508.
Cabral, L. (1993): �Experience advantages and entry dynamics,� Journal of EconomicTheory, 59(2), 403�416.
Calam, C. T. (1987): Process Developments in Antibiotic Fermentations. CambridgeUniversity Press, Cambridge.
Doraszelski, U., and M. Satterthwaite (2010): �Computable Markov-perfect in-dustry dynamics,� The RAND Journal of Economics, 41(2), 215�243.
Ericson, R., and A. Pakes (1995): �Markov-Perfect Indutry Dynamics: A Frameworkfor Empirical Work,� The Review of Economic Studies, 62(1), 53�82.
Federal Trade Commission (1958): Economic Report on Antibiotics Manufacture.US Government Printing O�ce.
Gort, M., and S. Klepper (1982): �Time Paths in the Di�usion of Product Innova-tions,� The Economic Journal, 92(367), 630�653.
Gowrisankaran, G. (1999): �E�cient Representation of State Spaces for Some Dy-namic Models,� Journal of Economic Dynamics and Control, 23, 1077�1098.
Horvath, M., F. Schivardi, and M. Woywode (2001): �On industry life-cycles:delay, entry, and shakeout in beer brewing,� International Journal of Industrial Or-ganization, 19, 1023�1052.
Humphrey, J. H., M. V. Mussett, and W. L. M. Perry (1952): �The secondinternational standard for penicillin,� Bulletin of the World Health Organization, 9,15�28.
Jovanovic, B., and G. M. MacDonald (1994): �The Life Cycle of a CompetitiveIndustry,� Journal of Political Economy, 102(2), 322�347.
Klepper, S. (1996): �Entry, Exit, Growth, and Innovation over the Product Life Cycle,�The American Economic Review, 86(3), 562�583.
Klepper, S., and K. L. Simons (1997): �Technological Extinctions of IndustrialFirms: An Inquiry into their Nature and Causes,� Industrial and Corporate Change,6(2), 379�460.
(2005): �Industry shakeouts and technological change,� International Journalof Industrial Organization, 23, 23�43.
Maskin, E., and J. Tirole (1994): �Markov perfect equilibrium,� Discussion Paper -
Harvard Institute of Economic Research.
28
(2001): �Markov Perfect Equilibrium: I. Observable Actions,� Journal of Eco-nomic Theory, 100, 191�219.
Neushul, P. (1993): �Science, Government, and the Mass Production of Penicillin,�Journal of the History of Medicine and Allied Sciences, 48, 371�395.
Pakes, A., and P. McGuire (1994): �Computing Markov-Perfect Nash Equilibria:Numerical Implications of a Dynamic Di�erentiated Product Model,� The RAND
Journal of Economics, 25(4), 555�589.
Raper, K. B. (1946): �The development of improved penicillinproducing molds,� An-nals of the New York Academy of Sciences, 48, 41�56.
Rust, J. P. (1994): �Structural Estimationof Markov Decision Processes,� Handbook ofEconometrics, 4, 3082�3139.
Shapiro, C., and A. Dixit (1986): �Entry Dynamics with Mixed Strategies,� The
Economics of Strategic Planning: Essays in Honor of Joel Dean, Lexington Mass.:
Lexington Books. edited by Lacy Glenn Thomas III.
Suarez, F. F., and J. M. Utterback (1995): �Dominant Designs and the Survivalof Firms,� Strategic Management Journal, 16(6), 415�430.
Tornqvist, E. G. M., andW. H. Peterson (1956): �Penicillin Production by High-Yielding Strains of Penicillium chrysogenum,� Applied Microbiology, 4(5), 277�283.
Utterback, J. M., and F. F. Suarez (1993): �Innovation, competition, and industrystructure,� Research Policy, 22, 1�21.
Wooldridge, J. M. (1995): �Score diagnostics for linear models estimated by twostage least squares,� Advances in Econometrics and Quantitative Economics: Essays
in Honor of Professor C. R. Rao, ed. G. S. Maddala, P. C. B. Phillips, and T. N.
Srinivasan, pp. 66�87.
29
top related