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Journal of Financial Economics
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Strategic IPOs and product market competition$
Jiri Chod a,1, Evgeny Lyandres b,
a
b
Carroll School of Management, Boston College, Chestnut Hill, MA 02467, United States
School of Management, Boston University, Boston, MA 02215, United States
a r t i c l e in f o
abstract
Article history:
Received 23 June 2009
Received in revised form
12 April 2010
Accepted 28 April 2010
We examine firms’ incentives to go public in the presence of product market competition.
As a result of their greater ability to diversify idiosyncratic risk in the capital market,
public firms’ owners tolerate higher profit variability than owners of private firms.
Consequently, public firms adopt riskier and more aggressive output market strategies
than private firms, which improves the competitive position of the former vis-a-vis
the
latter. This strategic benefit of being public, and thus, the proportion of public firms in an
industry, is shown to be positively related to the degree of competitive interaction among
firms in the output market, to demand uncertainty, and to the idiosyncratic portion of this
uncertainty. Additional empirical predictions concern the effect of a firm’s initial public
offering on its market share and on its rivals’ valuations. We test the model’s predictions
and find empirical support for most of them.
& 2010 Elsevier B.V. All rights reserved.
JEL classification:
G32
L22
Keywords:
IPO
Risk aversion
Product market competition
Demand uncertainty
1. Introduction
In this paper we analyze firms’ decisions to go public in
the presence of product market competition. In particular,
we are interested in the effects of product market competition and demand uncertainty in an industry on the
$
We are grateful to Rui Albuquerque, Gennaro Bernile, Tom Chemmanur, Sudipto Dasgupta, Hamed Ghoddusi, Bruce Grundy, Ulrich Hege,
Ambrus Kecskés, Dino Palazzo, Marcel Rindisbacher, Jacob Sagi, Metin
Sengul, Dino Silveri, Neil Stoughton, Heather Tookes, Masa Watanabe,
Tieying Yu, an anonymous referee, and seminar participants at Boston
College, Research Institute for Industrial Economics, Singapore Management University, Stockholm School of Economics, University of Connecticut, University of Miami, University of New South Wales, Virginia Tech,
2008 Summer Camp of Australian National University, 2008 INFORMS
annual meeting, 2009 Western Finance Association annual meeting, 2009
Indian School of Business Summer Conference, 2009 European Finance
Association annual meeting, and 2010 European Winter Finance Conference for helpful comments and suggestions.
Corresponding author. Tel.: + 1 617 358 2279.
E-mail addresses: [email protected] (J. Chod),
[email protected] (E. Lyandres).
1
Tel.: + 1 617 552 0474.
equilibrium proportion of public firms in this industry,
as well as the effects of a firm’s initial public offering (IPO)
on its industry rivals’ product market strategies, market
shares, and valuations.
Issuing public equity has numerous benefits. In addition
to facilitating the financing of new investments, an IPO
subjects a firm to outside monitoring (e.g., Holmström and
Tirole, 1993); improves its liquidity (e.g., Amihud and
Mendelson, 1986); reduces valuation uncertainty (e.g.,
Benveniste and Spindt, 1989; and Dow and Gorton,
1997), which in turn lowers the costs of subsequent
seasoned equity offerings (SEOs) (e.g., Derrien and
Kecskés, 2007), allows consumers to infer the firm’s
product quality from its stock price (e.g., Stoughton,
Wong, and Zechner, 2001), and improves the firm’s mergers and acquisitions policy (e.g., Lyandres, Zhdanov, and
Hsieh, 2010); increases the firm’s likelihood to become an
acquisition target (e.g., Zingales, 1995); increases the
dispersion of its ownership (e.g., Chemmanur and
Fulghieri, 1999); and loosens financial constraints and
provides financial intermediary certification and knowledge capital (e.g., Hsu, Reed, and Rocholl, 2010). In addition,
0304-405X/$ - see front matter & 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.jfineco.2010.10.010
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
2
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
an underdiversified risk-averse entrepreneur could benefit
from an IPO because diversified investors assign higher
valuations to a risky asset (firm equity) than the entrepreneur herself (e.g., Bodnaruk, Kandel, Massa, and Simonov,
2008). Furthermore, transferring firm ownership from a
risk-averse entrepreneur to diversified investors could
improve profitability because risk considerations generally
prevent profit maximization (e.g., Rothschild and Stiglitz,
1971).
All of the aforementioned studies examining various
reasons for going public abstract from the competitive
interaction among firms in output markets. Our model
shows that product market competition is an important
factor in the decision to go public. The intuition is as
follows. Owners of public firms tend to hold more diversified portfolios than owners of private firms. For instance,
Moskowitz and Vissing-Jørgensen (2002) find that about
three-fourths of all private equity is owned by individuals
for whom such investment constitutes at least half of their
total net worth. Bodnaruk, Kandel, Massa, and Simonov
(2008) show that an IPO substantially increases the degree
of diversification of private firms’ controlling shareholders.
As a result, public firms tend to be less concerned with
idiosyncratic profit variability (e.g., Shah and Thakor, 1988)
and, hence, tend to pursue more aggressive product market
strategies than otherwise similar private firms.
When firms compete in quantities (a la Cournot), a
public firm’s commitment to a more aggressive product
market strategy has an important strategic benefit: It
reduces the equilibrium aggressiveness of the firm’s rivals.
Specifically, a public firm’s commitment to larger output
results in lower equilibrium output levels of the firm’s
competitors and, thus, in higher residual demand for the
firm’s own product. Because the strategic benefit of IPO
increases in the degree of competitive interaction among
product market rivals and in idiosyncratic demand uncertainty, the benefit of going public is more likely to outweigh
the cost of doing so in industries characterized by more
intense competitive interaction and larger idiosyncratic
demand uncertainty.2 This leads to a positive relation
between the equilibrium number and proportion of public
firms in an industry, on the one hand, and the degree of
competitive interaction and idiosyncratic demand uncertainty in this industry, on the other hand. Other implications of the greater product market aggressiveness of
public firms are the adverse effects that an IPO has on
the market shares and valuations of the newly public firm’s
product market rivals.
While our model is not specific to any particular
industry, an interesting illustration of the possible link
between a firm’s decision to go public and the competitive
structure of its industry is provided by the evolution of the
US investment banking industry in the mid-eighties. During this period, the fraction of firms switching underwriters
between their IPOs and SEOs increased considerably
(e.g., Burch, Nanda, and Warther, 2005). The transaction
2
In addition to the underwriting fee (e.g., Chen and Ritter, 2000), the
cost of going public includes underpricing (Loughran and Ritter, 2004) as
well as the loss of private benefits of control (e.g., Benninga, Helmantel,
and Sarig, 2005).
cost economics literature (e.g., Williamson, 1979) suggests
that decreased brand loyalty is associated with an increase
in the competitive intensity in the investment banking
industry. According to Eccles and Crane (1988), the US
investment banking industry was also exposed to
increased competition from US commercial banks and
foreign banks during the same period. This period of
intensifying competition coincided with a wave of investment bank IPOs: Twenty-seven investment banks went
public between 1983 and 1987, compared with just one
bank that was taken public in the preceding ten years (e.g.,
Muscarella and Vetsuypens, 1989). It is difficult to fully
explain such a dramatic increase in the number of IPOs in
the investment banking industry by the generally hot IPO
market in the mid-eighties. While the coincidence of
increased competition and an IPO wave in the same
industry does not establish a causal link, it motivates us
to explore a possible rationale for the existence of such
a link.
The strategic benefit of IPO is similar to the strategic
benefit of debt (e.g., Titman, 1984; Brander and Lewis,
1986; Maksimovic, 1988; Glazer, 1994; and Zhdanov,
2007). Because of limited liability, increasing leverage
raises a firm’s incentive to pursue a more aggressive output
market strategy. Like issuing debt, performing an IPO
allows a firm to commit to a product market strategy
that reduces the equilibrium aggressiveness of its industry
rivals. Thus, one of our key results—the positive relation
between the degree of competitive interaction and
firms’ equilibrium propensity to go public—is parallel to
the positive relation between the degree of competitive
interaction and optimal financial leverage (e.g., Lyandres,
2006).
While our paper focuses on Cournot competition, a
different kind of strategic benefit of going public exists
under Bertrand competition. When firms are price-setters,
profit variability decreases with product market aggressiveness.3 As a result, a price-setting public firm pursues
less aggressive product market strategy than a similar
private firm. However, because under Bertrand-type competition firms’ competitive actions are strategic complements, the less aggressive strategy of a public firm reduces
the aggressiveness of its competitors, which increases the
residual demand for the firm’s product. In other words,
going public has a strategic benefit under both Cournot and
Bertrand competition, although the driving forces behind
this benefit are different in the two scenarios.
Our model of the strategic benefit of going public that
stems from lower risk aversion and resulting greater
aggressiveness of public firms in the product market
complements the literature that highlights the strategic
cost of going public. For example, Maksimovic and Pichler
(2001) and Spiegel and Tookes (2009) consider the release
of valuable information to product market rivals at the time
of IPO and examine the trade-off between this strategic
cost of going public and the lower required returns on
public issues relative to private ones.
3
Under price-setting, profit variance is increasing in price and
decreasing in output.
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
We test the empirical implications of our model using a
sample of IPOs by firms competing in strategic substitutes.
Our empirical analysis confirms that the proportion of
public firms in an industry is positively related to the
degree of competitive interaction in that industry and to
demand uncertainty, and it is negatively related to the
systematic component of demand uncertainty. Our tests
also support the predictions regarding the effects of an IPO
on market shares and valuations of the newly public firm’s
product market rivals, as well as regarding the determinants of these effects.
To sum up, our paper contributes to the literature as
follows. Ours is the first paper to identify a strategic benefit
of going public that stems from the different levels of risk
aversion and resulting product market aggressiveness of
public and private firms. It complements the existing
literature on IPOs and product market competition that
highlights the strategic cost of going public. Furthermore,
we develop and test a series of predictions regarding the
relation between the strategic benefit of going public, on
the one hand, and the degree of competitive interaction,
demand uncertainty, and its systematic and idiosyncratic
components, on the other. In addition to showing that the
strategic benefit of going public is economically and
statistically significant, the empirical analysis allows us
to distinguish the strategic benefit of IPO from the other
benefits of going public described in the literature.
The remainder of the paper is organized as follows. In
the next section, we develop our model. In Section 3, we
present our analytical results and formulate their empirical
implications. Section 4 presents empirical tests of the
model’s predictions. We conclude in Section 5. In
Appendix A, we calibrate our model and illustrate numerically the effect of various model parameters on the
equilibrium. Appendix B summarizes the notation used
throughout the paper and the comparative statics results.
All proofs are provided in Appendix C.
2. Model
In this section, we develop a static model of product market
competition among public and private firms in the presence of
demand uncertainty. We first derive the values of public firms
to diversified investors and the values of private firms to
underdiversified entrepreneurs. We then examine how the
different valuations of public and private firms by their owners
affect the firms’ optimal product market strategies.
To derive the values of publicly traded firms, we follow
the standard assumptions of the Sharpe-Lintner capital
asset pricing model (CAPM). All investors are price takers in
the capital market and maximize the expected utility of
their terminal wealth. The utility of investor i, as a function
of her terminal wealth w, is given by
00
distributed, investor i’s expected utility simplifies into
the mean-variance criterion, i.e.,
a
2
Eui ðwÞ ¼ Ew i VarðwÞ:
ð2Þ
Finally, shares of all publicly traded firms are infinitely
divisible, and all investors are able to borrow and lend at
the risk-free rate, rf. Under these assumptions, each investor maximizes expected utility by holding a certain combination of the risk-free asset and the market portfolio, and
the expected return of firm i is given by
r m rf
p V
p Vi
E i i ¼ rf þ
cov i
,rm ,
ð3Þ
2
Vi
Vi
sm
where pi is the firm’s (normally distributed) profit; Vi is the
value of a public firm, i.e., the cash equivalent of the claim
to the firm’s uncertain profit, pi , to diversified shareholders; and rm is the market portfolio return with mean
r m and standard deviation sm . Solving Eq. (3) for Vi gives the
public firm value
r m r
1
Epi 2 f covðpi ,rm Þ :
ð4Þ
Vi ¼
1þ rf
sm
We now turn to private firms. Reflecting the empirical
observation that owners of private firms hold considerably
less diversified portfolios than owners of public firms (e.g.,
Hansen and Lott, 1996; Moskowitz and Vissing-Jørgensen,
2002; and Bodnaruk, Kandel, Massa, and Simonov, 2008),
we assume that unlike public firms, which are owned by
fully diversified investors, each private firm is owned by a
single entrepreneur.4 Similar to diversified investors,
entrepreneurs maximize the expected utility given in
Eq. (1) and are able to borrow and lend at the risk-free
rate. We also assume that each entrepreneur holds, in
addition to her private firm, the optimal combination of the
market portfolio and the risk-free asset.5
Suppose that firm i is held privately by a single
entrepreneur i. Let w0 be the entrepreneur’s initial endowment outside the firm, and let x be the amount of money
that the entrepreneur invests in the market portfolio.6
Finally, let Vi be the value of private firm i, i.e., the cash
equivalent of the claim to the firm’s uncertain profit, pi , to
the entrepreneur. The private firm value must satisfy the
following equality:
maxEui ððw0 xÞð1 þ rf Þ þxð1 þ rm Þ þ pi Þ
x
¼ maxEui ððw0 þ Vi xÞð1 þrf Þ þ xð1þ rm ÞÞ,
x
ð5Þ
where the left-hand side of Eq. (5) is the firm owner’s
expected utility when she keeps her firm private, and the
2.1. Public and private firm valuations
1
ui ðwÞ ¼ a1
i ai expðai wÞ,
3
ð1Þ
where ai ¼ ui =ui u is the investor’s Arrow-Pratt coefficient
of absolute risk aversion, which measures her attitude
toward risk. Assuming that returns are normally
4
This is a common assumption in the literature that examines
interactions between entrepreneurs and diversified investors (e.g.,
Gomes, 2000; and Bitler, Moskowitz, and Vissing-Jørgensen, 2005).
5
The assumption that agents exposed to undiversifiable (e.g., labor)
income shocks hedge by changing the weights on the market portfolio and
the risk-free asset without altering the composition of the risky portfolio
is common in the portfolio allocation literature (e.g., Heaton and Lucas,
1997; and Viceira, 2001). This assumption guarantees that the CAPM
valuation of public firms given in Eq. (3) remains valid in the presence of
private equity.
6
We consider the entrepreneur’s initial endowment w0 for expositional purposes only as it impacts neither her decisions nor her firm value.
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
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J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
right-hand side of Eq. (5) is her expected utility when her
claims to the firm’s profit are replaced with cash equivalent
Vi. Solving for the optimal x on each side of Eq. (5) and then
solving for Vi gives the private firm’s value
r m r
1
a
Vi ¼
Epi 2 f covðpi ,rm Þ i Varðpi Þð1r2 Þ ,
1 þrf
2
sm
ð6Þ
where r is the correlation between the firm’s profit pi and
the market portfolio return rm.
The intuition for the difference between the value of a
public firm to diversified investors, given in Eq. (4), and the
value of an otherwise equivalent private firm to an underdiversified entrepreneur, given in Eq. (6), is as follows.
Because a public firm is held by fully diversified shareholders, its value is affected only by its systematic risk. The
impact of the systematic risk on the public firm value,
ððr m rf Þ=s2m Þcovðpi ,rm Þ, is the product of the amount of this
risk, covðpi ,rm Þ=sm , and the market price of this risk,
ðr m rf Þ=sm .
In contrast, a private firm’s owner holds her entire firm
and, therefore, her utility is also affected by this firm’s
idiosyncratic risk, Varðpi Þð1r2 Þ. The impact of the idiosyncratic risk on private firm value also depends on the
owner’s coefficient of risk aversion, ai. The impact of
systematic risk on private firm value is the same as its
impact on public firm value. This is because public and
private firm owners face the same trade-off between
systematic risk and return when choosing their holdings
of the risk-free asset and the market portfolio.
In what follows, we simplify the notation by assuming,
without loss of generality, that the risk-free return rf equals
zero. We also assume that no agency conflicts exist
between firms’ managers and shareholders. Equipped
with the valuations of public and private firms, we next
consider their interaction in the product market.
2.2. Product market competition
Consider N firms competing in quantities in a heterogeneous product market. Assuming linear demand curves,
the market-clearing price of firm i’s product is given by
pi ðq, ai Þ ¼ ai bqi g
N
X
qj ,
i ¼ 1, . . . ,N,
ð7Þ
j ¼ 1,jai
where q= (q1,y,qN) is the output vector of the N firms and
ai , b, and g are the demand curve parameters.7
To reflect demand uncertainty, we assume that demand
curves’ intercepts, a1 , . . . , aN , are stochastic and refer to
them as demand shocks. For analytical convenience, we
assume that the vector of demand shocks, a ¼ ða1 , . . . , aN Þ, is
normally distributed with the mean and variance symmetrical across firms, i.e., Eðai Þ m and Varðai Þ s2 for all i.
To account for the systematic component of demand
uncertainty, we allow each demand shock to be correlated
with the return on the market portfolio. We assume that
7
Linear demand follows from the second-order approximation of
consumer utility function that is additively separable, linear in money,
and concave in consumption of all other goods.
the correlation coefficient r between demand shock ai and
the market portfolio return rm is positive and identical for
all i.8 Thus, each demand shock can be decomposed into
idiosyncratic and systematic component as
ai ¼ Xi þ Y,
ð8Þ
where Xi is independent of the return on the market
portfolio and Y is perfectly positively correlated with the
market portfolio return. We refer to Varðai Þ ¼ s2 ,
VarðXi Þ ¼ s2 ð1r2 Þ, and VarðYÞ ¼ s2 r2 as the total risk,
the idiosyncratic risk, and the systematic risk, respectively.
We also refer to r2 as the proportion of systematic risk and
to 1r2 as the proportion of idiosyncratic risk.
The demand curve coefficients b 40 and g Z 0 measure
the sensitivity of the market-clearing price of a firm’s
product to the firm’s own output and to its rivals’ outputs,
respectively. For tractability, these parameters are also
assumed to be symmetrical across firms. Because, in a
heterogeneous product market, the own-price effect
has to be larger than the cross-price effect, we have
b 4 g.9 Parameter g is of particular interest because it
measures product substitutability and, thus, the degree
of competitive interaction among firms. When g ¼ 0, there
are no cross-price effects, i.e., each firm is a monopolist in
its own market. As g increases, competitive interaction
intensifies.
Before the resolution of demand uncertainty, firm i,
i= 1,y,N, produces qi units of output at a constant marginal
cost c. After that, demand shocks are realized and the
product market clears. Thus, firm i realizes profit
pi ðq, ai Þ ¼ pi ðq, ai Þqi cqi ,
ð9Þ
where the market-clearing price pi ðq, ai Þ is given in
Eq. (7).10
Combining Eqs. (9), (4), and (6), we can write the values
of private and public firms as
8
P
2
>
< m qi bqi gqi jai qj cqi
P
Vi ðqÞ ¼
ai 2 2
2
2
>
: m qi bqi gqi jai qj cqi 2 qi s ð1r Þ
if firm i is public,
if firm i is private;
ð10Þ
where m ¼ mðr m rf Þrs=sm .
We assume, without loss of generality, that firms 1,y,n
are public and firms n + 1,y,N are private. Each firm
chooses its output to maximize its value while taking
into account the output decisions of its rivals. Therefore,
the equilibrium output vector q*(N,n) is given by the
8
We show below that firm i’s profit, pi , is linear in the demand shock,
ai , for each i. Thus, the correlation coefficient between ai and rm is the
same as the correlation coefficient between pi and rm.
9
Formally, this inequality follows from the strict concavity of the
consumer utility function.
10
Under extreme demand shock realizations, the linear demand
model can lead to negative prices. As is common in the industrial
organization literature (e.g., Vives, 1984, p. 77), we assume the variance
of demand intercepts to be sufficiently small to make the probability of
negative prices negligible. We also do not allow firms to withhold any
output from the market after observing the demand shock realization. It
can be shown that even if firms were allowed to withhold output from the
market, they would never do so in equilibrium as long as the demand
shock variance is sufficiently small.
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
Proposition 1.
following system of N equations:
qi ðN,nÞ ¼
argmaxVi ðqi ,qi ðN,nÞÞ,
q
i ¼ 1, . . . ,N,
ð11Þ
i
where q i is the output vector of the N 1 firms other than
i. To simplify the notation, we use pi ðN,nÞ ¼ pi ðq ðN,nÞÞ and
Vi ðN,nÞ ¼ Vi ðq ðN,nÞÞ to denote the profit and value of firm i
evaluated at the equilibrium output vector, respectively.
The next result characterizes the equilibrium output
vector and the corresponding firm values for a given
industry structure (N,n). Because the equilibrium outputs,
profit distributions, and values do not differ across public
firms, we replace the public firm’s index i with pub.
Heterogeneity in entrepreneurs’ risk aversions, however,
leads to heterogeneity in private firms’ equilibrium product market strategies and values. Therefore, unless stated
otherwise, any output or firm value indexed by i refers
hereafter to a private firm.
Lemma 1. For any given industry structure (N,n), there
exists a unique equilibrium output vector q*(N,n), which is
given by
qpub ðN,nÞ ¼
m cgQ ðN,nÞ
,
2bg
ð12Þ
and
qi ðN,nÞ ¼
m cgQ ðN,nÞ
,
2bg þ ai s2 ð1r2 Þ
5
i ¼ n þ 1, . . . ,N,
ð13Þ
where
P
N
2
2 1
ðm cÞ
þ 2bng
j ¼ n þ 1 ð2bg þaj s ð1r ÞÞ
P
Q ðN,nÞ ¼
N
2
2 1 þ n
1þg
j ¼ n þ 1 ð2bg þaj s ð1r ÞÞ
2bg
ð14Þ
is the equilibrium total industry output. The resulting equilibrium firm values are
Vpub
ðN,nÞ ¼ bðqpub ðN,nÞÞ2 ,
ð15Þ
and
Vi ðN,nÞ ¼ ðb þ 12ai s2 ð1r2 ÞÞðqi ðN,nÞÞ2 ,
i ¼ n þ 1, . . . ,N:
ð16Þ
In the next section, we examine how the degree of
competitive interaction in an industry and the magnitude
and type of demand uncertainty affect public and private
firms’ product market strategies and values, as well as the
equilibrium industry structure.
3. Results
3.1. Product market strategies
Our first proposition presents the comparative statics of
equilibrium output levels with respect to demand uncertainty and its composition (systematic versus idiosyncratic), entrepreneurs’ risk aversion, and the degree of
competitive interaction in the industry. All of the
comparative statics results presented in this section are
summarized in Table B2 in Appendix B.
(i) The equilibrium output of a public firm is greater than
that of any private firm.
(ii) The equilibrium output of private firm i is decreasing,
while the equilibrium outputs of all other firms are
increasing in this firm owner’s risk aversion ai.
(iii) The equilibrium output of each firm is decreasing, while
the combined market share of public firms is increasing in
the degree of competitive interaction g.
(iv) The combined market share of public firms is increasing in
total demand uncertainty s2 .
(v) The combined market share of public firms is decreasing
in the proportion of systematic risk r2 .
The intuition behind Proposition 1 is as follows. Private
firms choose lower output levels than public firms to
reduce firm-specific risk to which private firms’ owners
are exposed. The reduction in a private firm’s output due to
idiosyncratic risk considerations is positively related to its
owner’s risk aversion and to the idiosyncratic portion of
demand uncertainty. In the absence of competitive interaction in the product market, idiosyncratic risk has no
effect on public firms whose owners are fully diversified. In
the presence of product market competition, however,
idiosyncratic demand uncertainty does affect public firms
indirectly through its effect on their private competitors. In
particular, public firms take advantage of the lower output
of their private rivals by increasing their own output.
The higher the degree of competitive interaction, the
larger the above effect and the larger the difference
between the equilibrium outputs of private and public
firms. The higher the risk aversion of a given entrepreneur,
or the larger the idiosyncratic portion of demand uncertainty, the lower the output of the corresponding private
firm and the larger the output of its public rivals. Finally,
while the total market share of private firms always
decreases in the degree of competitive interaction and in
the idiosyncratic portion of demand uncertainty, the
market share of private firms whose owners exhibit
relatively low risk aversion, and which, therefore, behave
similarly to public firms, could be increasing in competitive
interaction as well as in idiosyncratic demand uncertainty.
Next, we characterize the effect of a firm going public on
its own and its competitors’ equilibrium outputs.
Proposition 2.
(i) When a firm goes public, its equilibrium output increases,
while the equilibrium output of each of its rivals decreases.
(ii) The relative increase in the IPO firm’s market share is
larger the higher the degree of competitive interaction g.
(iii) The relative increase in the IPO firm’s market share is
larger the larger the total demand uncertainty s2 .
(iv) The relative increase in the IPO firm’s market share is
larger the smaller the proportion of systematic risk r2 .
When a firm goes public, it ceases to be concerned with
idiosyncratic risk and becomes more aggressive by increasing its output. Consequently, the equilibrium output of
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
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J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
each of its competitors decreases, and more so when the
degree of competitive interaction among firms is high. As a
result, the higher the degree of competitive interaction, the
larger the relative increase in the newly public firm’s
market share. The larger the demand uncertainty or the
larger its idiosyncratic proportion, the stronger the effect of
going public on the firm’s product market strategy and,
therefore, on its market share.
In the next subsection, we examine the effect of going
public on firm values and show how this effect depends on
competitive interaction and the two components of
demand uncertainty.
3.2. Firm values and the strategic benefit of going public
In Section 3.1, we show that going public reduces the
total output of the newly public firm’s industry rivals. To
isolate this strategic benefit of IPO from the other benefits
of going public, we decompose the increase in the newly
public firm’s value,
Bi ðN,nÞ Vpub
ðN,n þ 1ÞVi ðN,nÞ 4 0,
ð17Þ
into three non-negative components:
Bi ðN,nÞ ¼ Bdiversification þ Bvalue þ Bstrategic
Bdiversification ¼
where
ai
ð1r2 ÞVarpi ðq ðN,nÞÞ,
2
ð18Þ
ð19Þ
Bvalue ¼ maxVpub ðqi ,qi ðN,nÞÞVpub ðqi ðN,nÞ,qi ðN,nÞÞ,
qi
ð20Þ
and
Bstrategic ¼ maxVpub ðqi ,qi ðN,n þ 1ÞÞmaxVpub ðqi ,qi ðN,nÞÞ,
qi
qi
ð21Þ
2
m Þcovð i ðqi ,
where Vpub ðqi ,qi Þ ¼ Epi ðqi ,qi Þððr m rf Þ=s
p
qi Þ,
rm Þ is the value of public firm i as a function of its own output
and of the output vector of all other firms. The first benefit,
Bdiversification, reflects the fact that, unlike an underdiversified
owner of a private firm, a public firm’s shareholders are able to
diversify idiosyncratic risk in the capital market. The second
benefit, Bvalue, reflects the fact that a public firm’s product
market strategy is not distorted by idiosyncratic risk considerations. Finally, the strategic benefit of going public,
Bstrategic, stems from the effect that a firm’s IPO has on the
equilibrium outputs of the firm’s product market rivals.
Because firms’ products are substitutes, private as well as
public competitors respond to the greater aggressiveness of
the firm that has gone public by reducing their own outputs,
i.e., qj ðN,n þ 1Þ oqj ðN,nÞ for all jai. As the competitors’
combined output declines, the equilibrium value of the IPO
firm increases, i.e., maxqi Vpub ðqi ,qi ðN,n þ 1ÞÞ 4maxqi Vpub
ðqi ,qi ðN,nÞÞ.
The next proposition characterizes the effects of risk
aversion, competitive interaction, demand uncertainty,
and its systematic and idiosyncratic components on the
equilibrium values of public and private firms.
(ii) The equilibrium value of private firm i is decreasing, while
the equilibrium values of all other firms are increasing in
this firm owner’s risk aversion ai.
(iii) The equilibrium value of each firm is decreasing, while the
relative benefit of being public for any firm i, V*pub(N,n)/
V*i (N,n), is increasing in the degree of competitive interaction g.
(iv) The relative benefit of being public is increasing in the
total demand uncertainty s2 .
(v) The relative benefit of being public is decreasing in the
proportion of systematic risk r2 .
A private firm’s value is lower than that of a public firm
for the three reasons captured in Eqs. (18)–(21). First, going
public enables full diversification of idiosyncratic risk.
Second, public firms are more profitable than private firms
because their product market strategies are not distorted
by idiosyncratic risk considerations. Finally, the greater
product market aggressiveness of a public firm reduces the
equilibrium aggressiveness of its rivals, further benefiting
the public firm.
As the risk aversion of a private firm’s owner increases,
her firm’s output and value decrease. As a result of the
decreasing output of this firm, the values of all other firms
in the industry increase. Stronger competitive interaction
results in lower prices and, therefore, in lower firm values.
However, public firms suffer less as their strategic commitment to larger outputs (strategic benefit of public incorporation) becomes more valuable. Thus, the relative benefit
of being public increases in the degree of competitive
interaction.
Because the benefit of being public stems from the
ability of public firms’ owners to diversify idiosyncratic
risk, the larger this risk, the larger the relative benefit of
being public. Unlike idiosyncratic risk, systematic risk has
an equally adverse effect on all firms and, therefore, does
not impact the relative benefit of being public. As a result,
the relative benefit of being public increases in total
demand uncertainty and decreases in the systematic
proportion of this uncertainty. The next proposition characterizes the effect of a firm’s IPO on the equilibrium values
of the firm and its product market rivals.
Proposition 4.
(i) When a firm goes public, its equilibrium value increases
while the equilibrium value of each of its rivals decreases.
(ii) The relative increase in the IPO firm’s value and the
relative decrease in its rivals’ values are larger the higher
the degree of competitive interaction g.
(iii) The relative increase in the IPO firm’s value and the
relative decrease in its rivals’ values are larger the larger
the total demand uncertainty s2 .
(iv) The relative increase in the IPO firm’s value and the
relative decrease in its rivals’ values are larger the smaller
the proportion of systematic risk r2 .
Proposition 3.
(i) The equilibrium value of a public firm is greater than that
of any private firm.
The IPO firm’s value increases as the firm starts enjoying
the three benefits of being public described above. Its
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
competitors’ values decrease as a result of the IPO firm’s
increased product market aggressiveness. A stronger
degree of competitive interaction increases the strategic
benefit of going public as well as the adverse effect of the
IPO firm’s greater aggressiveness on its industry rivals.
Finally, in our model the overall impact of an IPO stems
from the ability of the newly public firm’s owners to
diversify idiosyncratic risk. Hence, this impact increases
with total demand uncertainty and decreases with the
proportion of this uncertainty that is systematic.
In the next section, we consider the decision to go public
in the context of industry equilibrium. Namely, we characterize the equilibrium number of public firms in an
industry and show how it depends on the degree of
competitive interaction, demand uncertainty, and its systematic and idiosyncratic components.
Because the benefit of going public increases in the
entrepreneur’s risk aversion, in any equilibrium in which
both types of firms exist, the first n entrepreneurs with the
highest risk aversion take their firms public while the
remaining N n entrepreneurs keep their firms private,
with the nth entrepreneur being indifferent between going
public and staying private, i.e.,
ð1fÞVpub
ðN,nÞ ¼ Vn ðN,nÞ:
Proposition 5. Let
ð22Þ
We assume that the risk aversion coefficient of each
entrepreneur is drawn from a continuous distribution and,
without loss of generality, index all entrepreneurs so that
a1 Za2 Z Z aN . Finally, following a large body of
industrial organization literature, we treat the total number of firms N and the number of public firms n as
continuous variables, so that a(i) is a decreasing continuous
function.12
11
ð2bgÞ
4bð1fÞs2 ð1r2 Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð2bgÞ2 þ 8bgð1fÞð2b þ gÞ þ 4bf :
ð24Þ
Consider an industry with N firms, all of which are
initially private. While product demand is uncertain, each
entrepreneur decides whether to sell her shares to investors
through an IPO. Subsequently, public and private firms
engage in product market competition. In deciding whether
to take her firm public, each entrepreneur weighs the benefit
of going public against its cost. A substantial part of the IPO
cost is the spread charged by the underwriter, which tends
to be a relatively stable percentage of the IPO proceeds (e.g.,
Chen and Ritter, 2000; and Hansen, 2001). Reflecting this
empirical regularity, we assume that the cost of going public
is a fixed fraction f of the public firm’s value.11 Therefore,
the amount of cash received by the entrepreneur who sells
her firm to the public through an IPO is ð1fÞVpub
.
When there are N firms in the industry, n of which are
public, the owner of private firm i has incentives to take it
public if, and only if, the proceeds from taking the firm
public exceed her valuation of the private firm, i.e.,
ð1fÞVpub
ðN,n þ 1Þ 4 Vi ðN,nÞ:
ð23Þ
Eq. (23) implies that there exists a threshold level of risk
aversion, a*, such that entrepreneurs whose risk aversion
exceeds this threshold go public, while entrepreneurs with
risk aversion below this threshold remain private. We
formalize this result in the next proposition.
a 3.3. The decision to go public and industry equilibrium
7
In addition to the spread, the cost of going public involves underpricing (e.g., Loughran and Ritter, 2004) and the loss of private benefits of
control, which include ‘‘the private value of control as well as any savings
in the reporting, monitoring, bonding, and agency costs a public firm
incurs due to the separation between ownership and control’’ (Benninga,
Helmantel, and Sarig, 2005, p. 119).
12
See, for example, Ruffin (1971), Okuguchi (1973), Dixit and Stiglitz
(1977), Loury (1979), von Weizsäcker (1980), and Mankiw and Whinston
(1986). See Suzumura and Kiyono (1987) for a discussion of the effect of
departure from a continuous number of firms on equilibrium conditions.
Seade (1980) justifies the practice of treating the number of firms as a
continuous variable by arguing that it is always possible to use continuous
differentiable variables and restrict attention to the integer realizations of
these variables.
There exists a unique equilibrium number of public firms, n*,
which is given as follows.
(i) If að0Þ 4a 4aðNÞ, some firms go public while others
remain private, and a(n*) =a*.
(ii) If að0Þ r a , all firms remain private, i.e., n* = 0.
(iii) If aðNÞ Za , all firms go public, i.e., n* = N.
Case (i) corresponds to the interior equilibrium, in
which entrepreneurs whose risk aversion exceeds the
IPO threshold, a*, take their firms public, while the remaining entrepreneurs keep their firms private. Case (ii) corresponds to the boundary equilibrium in which the risk
aversion of each entrepreneur is below the IPO threshold
and thus no firm goes public. Finally, case (iii) corresponds
to the other boundary equilibrium in which the risk
aversion of each entrepreneur exceeds the IPO threshold,
and, therefore, all firms go public.
The degree of competitive interaction and idiosyncratic
demand uncertainty affect the equilibrium proportion of
public firms in the industry by altering the threshold risk
aversion, a*, which determines the number of firms that
choose to go public. These effects are characterized in the
next proposition.
Proposition 6.
(i) The equilibrium proportion of public firms in the industry
is increasing in the degree of competitive interaction g.
(ii) The equilibrium proportion of public firms in the industry
is increasing in total demand uncertainty s2 .
(iii) The equilibrium proportion of public firms in the industry
is decreasing in the proportion of systematic risk r2 .
As the degree of competitive interaction increases, so
does the strategic benefit of going public, which leads to
more firms going public in equilibrium. As total demand
uncertainty or its idiosyncratic proportion increase, the
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
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benefit of shareholder diversification enabled by going
public increases, and so does the equilibrium number of
public firms. Because the threshold risk aversion, a*, is
independent of the number of firms in the industry N,
Proposition 6 holds when the total number of firms in the
industry is determined endogenously and the distribution
of risk aversion across entrepreneurs is independent of the
industry size.13
In Appendix A, we calibrate our model to US data and
show that an interior equilibrium, in which both public and
private firms exist, is likely to arise. In this Appendix, we
also numerically illustrate the comparative statics of the
equilibrium with respect to various model parameters to
show their economic significance. In the next subsection
we outline the main empirical predictions following from
the model.
3.4. Empirical implications
Proposition 2, which characterizes the effects of an IPO
on firms’ equilibrium market shares, leads to the following
empirical prediction.
Empirical prediction 1. Under competition in strategic
substitutes (e.g., quantities),
(i) going public increases the firm’s market share;
(ii) the relative increase in the IPO firm’s market share is
positively related to the degree of competitive interaction
in its industry;
(iii) the relative increase in the IPO firm’s market share is
positively related to demand uncertainty in its industry;
and
(iv) the relative increase in the IPO firm’s market share is
negatively related to the proportion of demand uncertainty that is systematic.
The empirical evidence in recent papers by Chemmanur
and He (2008) and Hsu, Reed, and Rocholl (2010) is
consistent with Empirical prediction 1(i).14 There are
reasons that an IPO is likely to have a positive impact on
the firm’s market share other than the one captured by our
model. In particular, a firm could be able to use the capital
raised through its IPO to expand its production capacity.15
Thus, to test our explanation of the increase in the IPO
firm’s market share, it would be useful to test parts (ii)–(iv)
of the prediction, i.e., the relations between the effect of an
IPO on the firm’s market share, on the one hand, and
13
Models in which industry size does not affect the distribution of
firms’ characteristics are common in the industrial organization literature
(e.g., Melitz, 2003; and Ghironi and Melitz, 2005).
14
There also exists some anecdotal evidence supporting Empirical
prediction 1(i). Killian, Smith, and Smith (2001) cite a number of examples
in which firms that went public ahead of their competitors gained a
considerable market share (e.g., Handspring, Affymetrix, Petsmart).
15
In addition, Chemmanur and He (2008) argue that going public
could increase the firm’s market share because of the enhanced credibility
of a public firm with customers, its greater ability to acquire other firms, or
its ability to hire quality employees and motivate them using stock
options.
competitive interaction, demand uncertainty, and the
systematic portion of this uncertainty, on the other hand.
Proposition 4, which characterizes the effects of an IPO
on the values of the firm’s product market rivals, leads to
our second empirical prediction.
Empirical prediction 2. Under competition in strategic
substitutes (e.g., quantities),
(i) going public has an adverse effect on the values of the IPO
firm’s product market rivals;
(ii) the magnitude of this effect is positively related to the
degree of competitive interaction in the industry;
(iii) the magnitude of this effect is positively related to
demand uncertainty in the industry; and
(iv) the magnitude of this effect is negatively related to the
proportion of demand uncertainty that is systematic.
The first part of Prediction 2 is consistent with Slovin,
Sushka, and Ferraro (1995) and Hsu, Reed, and Rocholl
(2010), who report that a firm’s IPO results in abnormally
negative returns to the firm’s competitors, and with Slovin,
Sushka, and Bendeck (1991), who find positive valuation
effects on the industry rivals of firms going private.
However, none of these papers tests whether our explanation, i.e., the change in the IPO firm’s product market
aggressiveness due to shareholder diversification, contributes to this effect. Testing parts (ii)–(iv) of Prediction 2
allows us to empirically distinguish our explanation
from other potential theories such as the deep pockets
argument.
Proposition 6, characterizing the equilibrium structure
of an industry, leads to the following empirical prediction.
Empirical prediction 3. (i) The proportion of public firms in
an industry is positively related to the degree of competitive
interaction in this industry;
(ii) the proportion of public firms in an industry is positively
related to demand uncertainty in this industry; and
(iii) the proportion of public firms in an industry is
negatively related to the proportion of demand uncertainty
that is systematic.
Empirical prediction 3 is a key implication of our model,
which reflects the strategic benefit of diversification associated with going public in the presence of product market
competition. Examining empirically the relation between
the proportion of public firms in an industry and the degree
of competitive interaction in it is of particular interest
because an argument opposite to Prediction 3(i) can be
made based on the information disclosure theory. Namely,
because more intense competitive interaction exacerbates
the cost of releasing valuable information at the time of IPO,
it could lead to fewer public firms in the industry. As we
show in Section 4, the data support Prediction 3, suggesting
that the strategic benefit of going public dominates the cost
of disclosure associated with the release of public incorporation to product market competitors.
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
4. Empirical evidence
In this section we empirically test our predictions
regarding the effects of competitive interaction, demand
uncertainty, and its systematic component on the post-IPO
change in the newly public firm’s market share (Empirical
prediction 1), on the values of the newly public firm’s
product market competitors (Empirical prediction 2), and
on the proportion of public and private firms in an industry
(Empirical prediction 3).
4.1. Empirical proxies
4.1.1. The degree of competitive interaction
In constructing a proxy for the degree of competitive
interaction among firms in an industry, we follow
Sundaram, John, and John (1996), who were the first to
develop an empirical measure of the responsiveness of
firms’ profits to changes in their competitors’ actions.
Assuming that sales proxy for firms’ actions, Sundaram,
John, and John (1996) define the Competitive Strategy
Measure (CSM) as the correlation between the ratio of the
change in a firm’s profit to the change in its sales and the
change in the combined sales of the firm’s product market
rivals. For firm i, it is
Dpi
CSM i ¼ corr
, DSi ,
ð25Þ
DSi
where Dpi is the change in firm i’s profit between two
consecutive periods, DSi is the change in its sales, and DSi
is the change in its product market rivals’ combined sales.
As pointed out by Sundaram, John, and John (1996), this
measure is a direct proxy for the cross-partial derivative of
a firm’s value with respect to its own and its rivals’
competitive actions.
Following the definition of Bulow, Geanakoplos, and
Klemperer (1985), a positive cross-partial derivative of a
firm’s value with respect to its own and its rivals’ competitive actions corresponds to competition in strategic
complements, whereas a negative cross-partial derivative
corresponds to competition in strategic substitutes. Thus,
we classify industries with a positive (negative) mean CSM
as those in which firms compete in strategic complements
(substitutes). Because our model assumes competition in
quantities, which are strategic substitutes, we restrict the
sample used in the empirical analysis to firms belonging to
industries with negative mean CSMs.16
Whereas the sign of mean industry CSM indicates the
type of competitive interaction among firms in the industry, its magnitude measures the intensity of this interaction. Because we restrict our attention to industries with
negative mean CSMs, we use the absolute value of mean
industry CSM as a direct proxy for the degree of competitive
interaction in the industry in the empirical tests below.
Similar to Sundaram, John, and John (1996), we use
quarterly Compustat data and define a firm’s profit as its
quarterly operating profit and rivals’ sales as combined
16
This follows from the fact that the second cross-partial derivative of
firm value given in Eq. (10) with respect to its own and its rivals’ combined
output is negative.
9
quarterly sales of all other firms operating in the same
industry. We first calculate the correlation given in Eq. (25)
for each firm for 20-quarter rolling windows. We then
compute the mean industry CSM using all firms with at
least ten non-missing observations for changes in sales and
profits. We assign the mean industry CSM to all firms
operating in that industry during the quarter following the
estimation period. This procedure reduces the noise
involved in estimating each firm’s CSM and also enables
time-varying CSM for each industry.17
We use the Standard Industrial Classification (SIC)
system as well as the North American Industry Classification System (NAICS), which was introduced in 1999 and
which improves SIC’s outdated categorizations of emerging
industries. A deficiency of the NAICS is that industry
assignments are made on a retroactive basis before 1999.
Using both four-digit SIC and six-digit NAICS industry
classifications to determine newly public firms’ product
market rivals results in a more robust depiction of the
strategic effects of IPOs.
The summary statistics of the CSM are presented in
Panel A of Table 1. Overall, slightly more than half of
industry-years have negative estimates of the CSM, consistent with Sundaram, John, and John (1996) and Lyandres
(2006). Among industries with competition in strategic
substitutes, the mean absolute value of the CSM is 0.061
(0.049) according to the NAICS (SIC) classification, and the
median is 0.037 (0.034). While there is considerable
variation in CSMs across industries as evident from
Table 1, mean industry CSMs are rather stable over
time.18 In addition, while there is sizable within-industry
variation of firm CSMs (the average within-industry standard deviation of firm-specific CSM equals 0.26), 76% of
firms in industries with negative mean CSMs have negative
firm-specific CSMs.
4.1.2. Demand uncertainty and its systematic component
We follow the empirical industrial organization literature and use overall sales by firms belonging to an industry
as a proxy for industry demand (e.g., Ghosal, 1991; and
Guiso and Parigi, 1999). Our measure of demand uncertainty is the standard deviation of seasonally adjusted
quarterly industry sales growth. We employ the following
estimation procedure. For 20-quarter rolling windows we
first regress industry sales growth, computed as the sum of
sales of all firms that report quarterly sales throughout all
20 quarters of the estimation period, on four indicator
variables equaling one if the observation belongs to the
first, second, third, or fourth quarter and equaling zero
otherwise. We refer to the residuals from this regression as
seasonally adjusted sales growth. We compute the standard deviation of seasonally adjusted sales growth for each
industry and assign it to the industry-quarter following the
estimation period. Restricting the estimation sample to
17
This procedure is different from that of Sundaram, John, and John
(1996), who calculate the CSM for only one firm in an industry (in their
case, the firm announcing a change in research and development
expenditures) and assign this CSM to all firms in the industry.
18
If an estimated mean industry CSM is negative in a given quarter, it
is negative in about 86% of the other quarters.
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
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J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
Table 1
Summary statistics.
This table presents the summary statistics of the variables used in the empirical tests. Panel A contains statistics for measures of competitive interaction,
demand uncertainty, and the systematic component of this uncertainty. CSM is a measure of the degree of competitive interaction. Absolute CSM is the
absolute value of the CSM. Standard deviation of sales growth is the measure of demand uncertainty. Systematic proportion of sales growth is the measure of
the systematic proportion of demand uncertainty. The construction of these measures is discussed in Subsection 4.1. Full sample refers to all initial public
offerings (IPOs) with non-missing Compustat variables. Strategic substitutes sample refers to all IPOs in industries with negative estimated CSM. NAICS
classification refers to six-digit North American Industry Classification System. SIC classification refers to four-digit Standard Industrial Classification. Panel
B contains statistics for the dependent variables in the regression analysis. One-year (three-year) market share growth is the logarithm of the ratio of the IPO
firm’s market share one year (three years) after the year of the IPO to its market share in the year of the IPO. Market share is the ratio of a firm’s sales to the
sum of sales of all firms in the industry. Three-day rivals’ raw (abnormal) return is the weighted average return during days [ 1,1], where day 0 is the IPO
filing day, of all firms operating in the IPO firm’s industry. Abnormal returns are based on the market model. Proportion of public firms is the ratio of the
number of public firms in a NAICS industry to the number of all firms in that industry with more than one hundred (five hundred) employees. Panel C
contains statistics for control variables in the regression analysis. Age is the difference between the year of observation and the earlier of the founding year
and incorporation year. Assets is the book value of assets at the end of the year preceding the year of the observation. Market-to-book (M/B) is the ratio of the
sum of market value of equity and book value of debt to book assets at the end of the year preceding the year of the observation. Median age (assets, M/B)
refers to median age (assets, M/B) in the firm’s industry. Issue rate is the ratio of the number of primary shares issued during the IPO to the number of shares
outstanding pre-IPO.
NAICS classification
Mean
Standard
deviation
Median
Panel A: Measures of competitive interaction and demand uncertainty
Full sample
CSM
0.006
0.184
0.005
Strategic substitutes
Absolute CSM
0.061
0.065
0.037
Standard deviation
of sales growth
0.161
0.139
0.128
Systematic proportion
of sales growth
5.13%
4.86%
3.84%
Panel B: Dependent variables
One-year market share growth
Three-year market share growth
Three-day rivals’ raw return
Three-day rivals’ abnormal return
Proportion of public firms
(more than five hundred employees)
Proportion of public firms
(more than one hundred employees)
Panel C: Control variables
Age
Median industry age
Assets
Median industry assets
M/B
Median industry M/B
Issue rate
Market share
SIC classification
Number of
observations
Mean
Standard
deviation
Median
Number of
observations
3,836
0.003
0.141
0.007
3,871
1,985
0.049
0.051
0.034
1,993
1,791
0.150
0.128
0.123
1,822
1,791
5.13%
4.39%
3.97%
1,822
0.158
0.334
0.38%
0.43%
1.825
1.570
7.10%
7.98%
0.137
0.171
0.39%
0.41%
1,799
1,305
1,538
1,538
14.338
17.631
692.34
324.11
3.137
1.922
0.252
3.64%
16.577
16.506
8865
1752
2.518
1.116
0.195
11.11%
9
12.5
67.32
75.62
2.272
1.589
0.207
0.31%
1,993
1,993
1,993
1,993
1,765
1,993
1,765
1,993
0.159
0.491
0.46%
0.52%
1.945
1.623
7.87%
9.14%
0.139
0.199
0.40%
0.49%
1,777
1,270
1,472
1,472
28.09%
23.79%
21.43%
335
12.94%
13.31%
7.92%
335
14.338
17.755
692.34
252.75
3.137
2.070
0.252
5.93%
16.577
15.871
8865
694
2.518
1.312
0.195
16.38%
9
13
67.32
80.64
2.272
1.680
0.207
0.31%
1,993
1,985
1,993
1,985
1,765
1,985
1,765
1,985
firms reporting sales throughout the estimation period
circumvents potential problems related to firm additions
(e.g., due to IPOs) and deletions from the database (e.g., due
to mergers or restructuring).
To measure the systematic component of industry
demand uncertainty we estimate rolling-window regressions of seasonally adjusted quarterly industry sales
growth on seasonally adjusted overall sales growth,
defined as the relative change in sales of all firms available
in quarterly Compustat files throughout the estimation
period. We call the ratio of the variance of the residuals
from this regression to the overall variance of seasonally
adjusted industry sales growth the idiosyncratic component of sales growth, and we refer to the ratio of the
variance of the predicted values of industry sales growth to
the overall variance of industry sales growth as the
systematic component of sales growth.19 As follows from
Panel A of Table 1, for industries with competition in
strategic substitutes, the mean value of our proxy for
demand uncertainty is 0.15–0.16. On average, 5% of
demand uncertainty is systematic.
19
Similarly, in the specification in which we proxy for demand
uncertainty using return volatility, we estimate the proportion of
systematic demand uncertainty by regressing firm daily returns on
value-weighted market returns and computing the mean industry ratio
of the variance of the explained portion of returns to the overall variance
of returns.
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
4.2. Test of empirical prediction 1: changes in IPO firms’
market shares
In this subsection we test Prediction 1 according to
which the post-IPO growth in a newly public firm’s market
share is positively related to the degree of competitive
interaction and to demand uncertainty, and it is negatively
related to the systematic proportion of this uncertainty.
Because full coverage of quarterly Compustat database
begins in 1985 and we require 20 prior quarters of
accounting data to estimate the degree of competitive
interaction and demand uncertainty, our sample of IPOs
starts in 1990. We obtain IPO data from the New Issues
database of Thomson Financial’s Securities Data Company
(SDC). To be included in the IPO sample, a firm must
perform an IPO on one of the three major exchanges and
have IPO filing date available in the SDC database. We
exclude rights issues, unit issues, reverse leveraged buyouts, real estate investment trusts (REITs), closed-end
funds, and American Depositary Receipts (ADRs). In addition, we exclude firms with offer prices below $1. Finally,
we require that IPO firms have accounting data available in
the quarterly and annual Compustat databases. Our sample
contains 3,871 IPOs, out of which 1,993 IPOs are by firms
belonging to industries with competition in strategic
substitutes (negative estimated CSMs).
We follow Chemmanur and He (2008) and measure
changes in IPO firms’ market shares over one-year and
three-year post-IPO periods. A firm’s market share in a
given year is defined as the ratio of the firm’s annual sales to
the overall industry sales. We define one-year (three-year)
post-IPO market share growth as the natural logarithm of
the ratio of a newly public firm’s market share in the first
(third) post-IPO year to its market share in the IPO year.
Panel B of Table 1 shows that the mean (median) growth in
the IPO firm’s market share is 16% (14%) in the first year and
33–49% (17–20%) in the first three post-IPO years depending on industry classification. This increase in market share
is consistent with Prediction 1(i) and with Hsu, Reed, and
Rocholl (2010), who show that firms going public exhibit
sizable post-IPO sales growth.
To distinguish our explanation of the increase in newly
public firms’ market shares from alternative explanations,
we also test parts (ii)–(iv) of Prediction 1.20 Namely, we
estimate pulled regressions of post-IPO market share
growth on proxies for the extent of competitive interaction,
demand uncertainty, and its systematic component:
!
DMSi,j ¼ a þ b1 gj þ b2 sj þ b3 rj þ bu zi þ ei,j ,
ð26Þ
where DMSi,j is the post-IPO market share growth of firm i
operating in industry j; gj is the absolute value of the CSM
proxying for the degree of competitive interaction in
industry j; sj is the estimate of the volatility of seasonally
adjusted industry sales growth proxying for demand
uncertainty; rj is the proportion of systematic variance
!
of sales growth; and zi is the vector of control variables
that are expected to be related to the IPO firm’s market
20
In particular, the inflow of cash generated by the IPO can be used to
increase production and sales of the newly public firm.
11
share growth. Because of industry and time clustering of
IPOs (e.g., Ritter, 1984; Lowry and Schwert, 2002; and
Lowry, 2003), we use standard errors clustered by industry
and month (e.g., Petersen, 2009).
In choosing the control variables, we generally follow
Chemmanur and He (2008) and Hsu, Reed, and Rocholl
(2010). Because younger, smaller firms with relatively
more investment opportunities and higher growth potential are expected to benefit more from going public, our
control variables include the IPO firm’s relative age, size,
and market-to-book ratio. Relative age (size, market-tobook ratio) is defined as the natural logarithm of the ratio of
the firm’s age (book assets, market-to-book ratio) to
median age (book assets, market-to-book ratio) of all public
firms operating in the firm’s industry. We define a firm’s
age as the difference between the current year and the
founding year or incorporation year in that order of
availability.21 Motivated by the cash infusion hypothesis,
our control variables also include the IPO issue rate, defined
as the ratio of the number of newly issued shares to the
number of the firm’s pre-IPO outstanding shares.
Table 2 presents the results of estimating Eq. (26) using
one-year and three-year growth in the IPO firms’ market
shares in six-digit NAICS and four-digit SIC industries. The
coefficients on the absolute value of CSM are positive for
both measures of market share growth and for both
industry classifications, and they are significant at 10%
level in all four specifications. This is consistent with
Prediction 1(ii) and with the intuition that the increased
aggressiveness of a newly public firm has a larger effect on
market shares in industries with higher degrees of competitive interaction. The economic significance of the effect of
the mean industry CSM on market share growth is substantial. Increasing the absolute value of the CSM by one
standard deviation (0.065 for NAICS-based industries and
0.051 for SIC-based industries; see Panel A of Table 1) is
associated with 10–14 percentage points increase in oneyear market share growth and with 11–22 percentage
points increase in three-year market share growth. For
comparison, the mean (median) IPO firm’s one-year market
share growth is 16% (14%).
The coefficients on the standard deviation of industry
sales growth, proxying for demand uncertainty, are positive and highly significant in three out of the four specifications, supporting Prediction 1(iii) and consistent with the
intuition that the increase in the IPO firm’s aggressiveness
is partially due to reduced risk aversion. In addition,
consistent with Prediction 1(iv), the systematic proportion
of the volatility of sales growth is negatively and significantly related to the post-IPO market share changes. The
economic effects of demand uncertainty and its systematic
component on sales growth are also substantial. An
increase of one standard deviation in the volatility of
industry sales growth (0.139 and 0.128 for NAICS and
SIC classifications, respectively) is associated with an
increase of 11–12 percentage points in one-year post-IPO
market share growth and with a 17–19 percentage points
21
We obtain firms’ founding and incorporation years from Boyan
Jovanovic’s website at http://www.nyu.edu/econ/user/jovanovi/.
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
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12
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
Table 2
Changes in IPO firms’ market shares.
This table presents panel regressions of one-year and three-year changes in the IPO firm’s market share on the measures of competitive interaction,
demand uncertainty, and its systematic component using a sample of 1,993 IPOs in years 1990–2008 in industries with competition in strategic substitutes.
One-year (three-year) market share growth is the logarithm of the ratio of the IPO firm’s market share one year (three years) after the year of the IPO to its
market share in the year of the IPO. Issue rate is the ratio of the number of primary shares issued in the IPO to the number of shares outstanding pre-IPO.
Relative age [size, market-to-book (M/B)] is the logarithm of the ratio of firm’s age (book assets, M/B) to median age (book assets, M/B) in the industry. We use
both the North American Industry Classification System (NAICS) six-digit classification and the Standard Industrial Classification (SIC) four-digit
classification to define industries. Absolute CSM is the measure of the degree of competitive interaction. Standard deviation of sales growth is the measure of
demand uncertainty. Systematic proportion sales growth is the measure of the systematic proportion of demand uncertainty. The construction of these
measures is discussed in Subsection 4.1. The regressions are estimated using ordinary least squares. t-statistics, computed using standard errors clustered by
industry and month, are presented in parentheses.
One-year market share growth
Three-year market share growth
NAICS
SIC
NAICS
SIC
Intercept
0.151
(0.72)
0.102
(0.52)
0.368
(1.67)
0.142
(0.63)
Issue rate
0.071
( 0.20)
0.340
( 1.02)
0.333
( 0.93)
0.238
( 0.66)
Relative age
0.124
( 2.24)
0.037
( 0.68)
0.027
( 0.44)
0.048
( 0.84)
Relative size
0.209
( 3.87)
0.107
( 2.12)
0.268
( 4.76)
0.226
( 4.22)
Relative M/B
0.191
(1.78)
0.357
(2.84)
0.233
(2.21)
0.201
(1.65)
Absolute CSM
2.101
(2.04)
1.973
(1.68)
1.666
(1.66)
4.435
(3.14)
Standard deviation of sales growth
0.772
(1.87)
0.918
(2.43)
1.397
(2.68)
1.315
(2.97)
2.447
( 2.02)
3.092
( 2.39)
2.565
( 1.95)
2.569
( 1.77)
R-squared
4.57%
5.30%
5.06%
6.09%
Number of observations
1,777
1,799
1,270
1,305
Systematic proportion of sales growth
increase in three-year market share growth. Increasing the
systematic proportion of demand uncertainty by one
standard deviation (4.86% and 4.39% for the two classifications) reduces market share growth by 12–14 percentage
points.
In addition, smaller firms and firms with higher marketto-book ratios relative to those of their product market
rivals gain more market share post-IPO than larger firms
and firms with lower market-to-book ratios. The coefficients on relative age are negative in all four specifications,
but age is significant only for one-year growth in NAICSbased market share. Surprisingly, the coefficients on the
issue rate variable in market share growth regressions are
insignificant.22
22
Because of industry and time clustering of IPOs, post-IPO change in
a newly public firm’s market share could be affected by the contemporaneous IPOs of the firm’s product market rivals. To examine the robustness
of the results in Table 2, we reestimate Eq. (26) using a subsample of IPOs
that did not occur in hot IPO markets. We follow Helwege and Liang (2004)
and Pástor and Veronesi (2005) and define hot IPO periods as months in
which three-month moving average volume of IPOs belongs to the top
quartile of IPO volume throughout our sample period. The coefficient
estimates for the subsample of IPOs that occurred outside of hot markets
are similar to those reported, albeit somewhat less statistically significant
due to a smaller sample size.
4.3. Test of empirical prediction 2: product market rivals’
returns on IPO announcements
Next, we examine the effect of IPO announcements on
the values of IPO firms’ product market rivals. According to
Prediction 2, this effect is negative and its magnitude is
positively related to the degree of competitive interaction
and demand uncertainty, and it is negatively related to the
systematic component of this uncertainty.
We obtain firms’ daily returns from the Center for
Research in Security Prices (CRSP). To estimate competitors’ abnormal returns around IPO announcements, we use
their betas from 60-month rolling-window firm-level
market model regressions and subtract the product of
estimated betas and daily market returns from firms’ daily
returns.23 We then calculate cumulative abnormal returns
for the window [ 1, 1], where day 0 is the IPO filing date.24
Finally, we compute the weighted average return of all
public firms in the newly public firm’s industry.25
23
Using the Fama and French (1993) three-factor model in defining
abnormal returns leads to results that are similar to those reported below.
24
Using IPO announcement rivals’ returns over one-day or seven-day
windows produces results similar to those reported below.
25
As is standard in the empirical literature (e.g., Hertzel, 1991; Song
and Walkling, 2000; Fee and Thomas, 2004; and Shahrur, 2005 among
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Economics (2010), doi:10.1016/j.jfineco.2010.10.010
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
13
Table 3
Product market rivals’ returns on IPO announcements.
This table presents panel regressions of raw and abnormal value-weighted three-day returns of firms operating in the IPO firm’s industry on the measures
of competitive interaction, demand uncertainty, and its systematic component using a sample of 1,993 IPOs in years 1990–2008 in industries with
competition in strategic substitutes. Three-day rivals’ raw (abnormal) return is the weighted average return during days [ 1,1], where day 0 is the IPO filing
day, of all firms operating in the IPO firm’s industry. Abnormal returns are based on the market model. Issue rate is the ratio of the number of primary shares
issued during the IPO to the number of shares outstanding pre-IPO. Market share is the ratio of the IPO firm’s sales in the year of the IPO to the sum of sales of
all firms in its industry. We use both the North American Industry Classification System (NAICS) six-digit classification and the Standard Industrial
Classification (SIC) four-digit classification to define industries. Absolute CSM is the measure of the degree of competitive interaction. Standard deviation of
sales growth is the measure of demand uncertainty. Systematic proportion of sales growth is the measure of the systematic proportion of demand
uncertainty. The construction of these measures is discussed in Subsection 4.1. The regressions are estimated using ordinary least squares. t-statistics,
computed using standard errors clustered by industry and month, are presented in parentheses.
Three-day return
Three-day abnormal return
NAICS
SIC
NAICS
SIC
Intercept
0.161
(1.01)
0.298
(2.16)
0.069
( 0.34)
0.075
(0.44)
Issue rate
0.069
(0.23)
0.368
( 1.34)
0.071
(0.18)
0.417
(1.23)
Market share
1.088
( 3.17)
1.176
( 3.22)
0.892
( 2.24)
1.319
( 3.19)
Absolute CSM
0.728
( 0.43)
1.387
( 0.91)
0.265
(0.14)
1.082
(0.59)
Standard deviation of sales growth
1.216
( 2.49)
1.685
( 3.32)
0.966
( 1.48)
2.571
( 4.11)
Systematic proportion of sales growth
0.697
(1.41)
1.376
(1.99)
1.828
(3.65)
1.636
(2.87)
R-squared
1.39%
1.86%
1.45%
2.52%
Number of observations
1,472
1,538
1,472
1,538
Panel B of Table 1 shows that the weighted average raw and
abnormal returns of rival firms during the three-day window
around IPOs are negative and significant, ranging between
0.38% and 0.52%. This result is consistent with Prediction
2(i) as well as with the findings of Slovin, Sushka, and Ferraro
(1995) and Hsu, Reed, and Rocholl (2010), who use smaller
samples of IPOs by larger firms and show rival announcement
returns ranging from 0.42% to 1.19% for various
announcement windows. To distinguish our explanation of
the negative competitors’ reactions to IPO announcements
from alternative explanations, we next examine the effects of
competitive interaction, demand uncertainty, and its systematic component on competitors’ reactions to IPO filings, RETi,j:
!
RET i,j ¼ a þ b1 gj þ b2 sj þ b3 rj þ bu zi þ ei,j :
ð27Þ
!
The vector of control variables zi includes the IPO firm’s
market share in the IPO year (an IPO by a larger firm is likely to
have a larger impact on competitors’ values) and the IPO issue
rate (larger IPO proceeds could have a larger impact on the
newly public firm’s competitors).
(footnote continued)
others), we examine the returns to product market rivals’ equity as
opposed to their asset returns. However, we repeat our analysis for asset
returns, i.e., weighted average return on equity and debt, and obtain
results similar to those reported. (Because of unavailability of bond return
data for the vast majority of sample firms, we compute the abnormal asset
returns under the assumption of risk-free debt, i.e., as abnormal equity
returns multiplied by one minus firms’ market leverage.)
The results of estimating Eq. (27) for raw and abnormal
returns of rivals belonging to the IPO firms’ NAICS-based
and SIC-based industries are presented in Table 3. Consistent with Prediction 2(iii), the coefficients on the measure of demand uncertainty are negative in all four
specifications and are significant at 1% level in three
specifications. An increase of one standard deviation in
the demand uncertainty measure reduces the average
rivals’ announcement return by 13–33 basis points. Consistent with Prediction 2(iv), the coefficients on the systematic proportion of demand uncertainty are positive in
all four specifications and are significant in three of them.
An increase of one standard deviation in the systematic
proportion of demand uncertainty is associated with a 3–9
basis points increase in rivals’ announcement returns.
The data do not provide support for Prediction 2(ii) of a
negative relation between the degree of competitive interaction and rivals’ announcement returns. The coefficients on
the absolute value of the CSM are statistically insignificant in
all four specifications. The IPO firm’s market share is significantly negatively related to rivals’ returns, consistent with
IPOs by larger firms having more pronounced effects on
product market rivals’ values. Finally, issue rates are not
significantly related to rivals’ IPO announcement returns.
4.4. Test of empirical prediction 3: Proportion of public firms
in an industry
To examine how the proportion of public firms in an
industry is related to the degree of competitive interaction,
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
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demand uncertainty, and its systematic component, we use
the data on the number of firms in each six-digit NAICS
industry in year 2006 provided by the US Census Bureau.26
We compute the number of public firms in each NAICS
industry by counting all firms in the daily CRSP file having
at least one non-missing return observation in 2006. As
before, we restrict our attention to industries characterized
by competition in strategic substitutes, i.e., those with a
negative mean CSM.
Measuring the proportion of public firms in each
industry is not straightforward. It follows from annual
Compustat data that the mean (median) number of
employees in a public firm was 1,141 (505) in 2006. At
the same time, it follows from the Census data that the
median number of employees in a private firm ranges
between one and four for the vast majority of NAICS
industries. Going public is a costly endeavor, preventing
smaller firms from doing so. Therefore, in computing the
proportion of public firms in each industry we concentrate
on relatively large firms using two specifications. Namely,
for each industry we compute the proportion of public
firms among all firms with more than five hundred
employees and the proportion of public firms among all
firms with more than one hundred employees. Panel A of
Table 2 shows that in an average (median) industry, public
firms constitute 28% (21%) of all firms with more than five
hundred employees and 13% (8%) of all firms with more
than one hundred employees.
To examine the effects of the degree of competitive
interaction, demand uncertainty, and its systematic component on the proportion of public firms in an industry,
PROP_PUBj, we estimate the regression
!
PROP_PUBj ¼ a þ b1 gj þ b2 sj þ b3 rj þ bu zj þ e,j ,
ð28Þ
using a sample of 335 NAICS industries with negative CSM
estimates. We generally follow Chemmanur, He, and
Nandy (2010) in choosing the control variables in
Eq. (28). Older industries with larger firms are expected to
have higher proportions of public firms, and thus, we control
for median age and median size of the firms in the industry. In
addition, firms are more likely to choose public incorporation
in industries with relatively abundant investment opportunities, particularly in high-tech industries. We proxy for the
availability of investment opportunities by the median
industry market-to-book ratio, and we follow Loughran
and Ritter (2004) and Chemmanur, He, and Nandy (2010)
and define a high-tech industry indicator equaling one for the
following industries: computer hardware, communications
equipment, electronics, navigation equipment, measuring
and control devices, medical instruments, telephone equipment, communications services, and software.
26
The Census data, which are available at http://www2.census.gov/
econ/susb/data/2006/us_6digitnaics_2006.txt, contain six-digits NAICS
industry-specific information on the total number of firms belonging to
various brackets in terms of the number of employees. Annual snapshots
of this kind are available for years 1998–2006. We report results only for
the latest available data (from 2006). The results for all other years are
similar and available upon request. We do not use the whole panel in the
analysis because the total number of firms in an industry and the number
of public firms in it exhibit very high autocorrelations.
The results of estimating Eq. (28) are presented in
Table 4. Consistent with Prediction 3(i), the proportion of
public firms in an industry is positively and very significantly related to the degree of competitive interaction in
that industry, as follows from the coefficients on the
absolute value of CSM in both specifications. The effect
of the extent of competitive interaction on the proportion
of public firms is also economically significant. Increasing
the absolute value of CSM by one standard deviation raises
the proportion of public firms among those with at least
one hundred (five hundred) employees by 4 (2) percentage
points. These numbers are substantial in comparison to the
mean and median proportions of public firms reported in
Panel A of Table 1.
Consistent with Predictions 3(ii) and 3(iii), the
coefficients on the proxy for demand uncertainty are
positive and significant at 10% level in both regression
Table 4
Proportion of public firms in an industry.
This table presents cross-sectional regressions of the proportion of
public firms in 335 North American Industry Classification System
(NAICS) industries with competition in strategic substitutes in 2006.
The proportion of public firms is the ratio of the number of public firms in
an industry to the number of all firms in that industry with more than one
hundred (five hundred) employees. Log median age [assets, market-tobook (M/B)] refers to the natural logarithm of median age (assets, M/B) in
each industry. High-tech indicator equals one for the following industries:
computer hardware, communications equipment, electronics, navigation
equipment, measuring and control devices, medical instruments, telephone equipment, communications services, and software. It equals zero
otherwise. Absolute CSM is the measure of the degree of competitive
interaction. Standard deviation of sales growth is the measure of demand
uncertainty. Systematic proportion of sales growth is the measure of the
systematic proportion of demand uncertainty. The construction of these
measures is discussed in Section 4.1. The regressions are estimated using
ordinary least squares. t-statistics of coefficient estimates are presented in
parentheses.
More than one
hundred employees
More than five
hundred employees
Intercept
8.170
(1.88)
22.032
(2.71)
log (median age)
0.002
(0.07)
0.034
( 0.76)
log (median assets)
1.084
(2.05)
1.888
(2.92)
log (median M/B)
0.256
(1.87)
1.245
(2.43)
High-tech indicator
11.511
(3.47)
19.690
(3.18)
Absolute CSM
31.756
(3.83)
56.280
(3.64)
Standard deviation of
sales growth
7.770
12.171
(1.71)
(1.85)
Systematic proportion
of sales growth
3.838
6.452
( 3.15)
( 2.84)
10.02%
9.04%
335
335
R-squared
Number of
observations
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
specifications, whereas the coefficients on the proportion
of systematic demand uncertainty are negative and highly
significant in both specifications. A one standard deviation
increase in demand uncertainty raises the proportion of
public firms by 1.1–1.7 percentage points. Increasing the
proportion of systematic demand uncertainty by one
standard deviation is associated with a reduction of 0.2–
0.3 percentage points in the proportion of public firms. The
coefficients on control variables, with the exception of
median age, are all significant and consistent with the
underlying intuition. Industries with larger firms are more
likely to have larger proportions of public firms, as do
industries with abundant growth opportunities and, in
particular, high-tech industries.
To sum up, the empirical evidence presented in Tables
2–4 is generally consistent with the implications of our
model and allows us to distinguish it from existing theories
of the going public decision. The degree of competitive
interaction, demand uncertainty, and its systematic component have statistically significant and economically
sizable effects on the evolution of newly public firms’
market shares, on their product market rivals’ reactions to
IPO announcements, and on the proportions of public firms
operating in various industries. The only exception is that
our proxy for the extent of competitive interaction does not
seem to have power in explaining product market rivals’
returns to IPO announcements.
5. Conclusions
This paper presents a model of the decision to go public
in the presence of product market competition. Because
going public facilitates shareholder diversification, public
firms are less concerned with idiosyncratic profit variability than otherwise similar private firms. Under Cournot
competition, this leads to greater product market aggressiveness of public firms, which, in turn, reduces the
equilibrium aggressiveness of their competitors. This strategic benefit of IPO and, thus, firms’ incentives to go public
and the equilibrium proportion of public firms in an
industry increase in the degree of competitive interaction
among firms in the product market.
Our model generates several testable empirical predictions. First, going public is expected to increase an IPO
firm’s market share, and more so within industries characterized by stronger competitive interaction, larger
demand uncertainty, and a smaller proportion of this
uncertainty that is systematic. Second, going public is
expected to adversely affect the values of an IPO firm’s
product market rivals, and more so within industries
characterized by stronger competitive interaction, larger
demand uncertainty, and a smaller systematic proportion
of this uncertainty. Finally, the proportion of public firms is
expected to be higher in industries characterized by
stronger competitive interaction, larger demand uncertainty, and a smaller systematic proportion of this
uncertainty.
Most of these predictions are supported by the data. The
degree of competitive interaction, demand uncertainty,
and its systematic component generally have economically
and statistically significant effects on newly public firms’
15
market shares and their product market rivals’ returns on
IPO announcements, as well as on the proportion of firms
choosing the public mode of incorporation.
Appendix A. Model calibration
In this Appendix, we examine whether an interior
equilibrium, in which both public and private firms exist
in the same industry, is likely to arise under reasonable
parameter values. In principle, one could compute the
threshold absolute risk aversion, a*, for a given combination
of model parameters and examine whether it lies within
the range of coefficients of absolute risk aversion typical of
entrepreneurs. There are two difficulties with this
approach. First, determining the range of typical coefficients of absolute risk aversion requires estimating the
distribution of wealth among entrepreneurs within each
industry.27 Second, the value of a* depends on absolute
(dollar) values of firms’ characteristics (e.g., variance of
sales), which vary considerably across firms, making its
estimation impractical.
We circumvent these difficulties by computing the
coefficient of relative risk aversion R that corresponds to
the threshold coefficient of absolute risk aversion a*, and
we compare R* with the coefficients of relative risk aversion
typical of entrepreneurs. The advantage of this approach is
that there is less ambiguity regarding typical levels of
relative risk aversion.28 In addition, the calibration of R*
requires estimating only ratios, which exhibit considerably
lower variation than do dollar variables.29
Consider entrepreneur n*, whose absolute risk aversion
is a* and who is therefore indifferent between going public
and staying private, i.e., Vpub
ðN ,n Þ ¼ Vn ðN ,n Þ. Let R*
be the coefficient of this entrepreneur’s relative risk
aversion, i.e.,
R ¼ ðVpub
ðN ,n Þ þ w0 Þa ,
ð29Þ
where w0 is the entrepreneur’s wealth outside the firm. To
calibrate R , we rewrite Eq. (29) using parameters that can
be estimated empirically.
Proposition 7. The coefficient of relative risk aversion given
in Eq. (29) can be written as
R ¼
mð2g=bÞP=E
4Zdð1fÞð1r2 ÞCV2sales
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð2g=bÞ2 þ 8ð1fÞg=b2g=b þ 4f ,
ð30Þ
27
Wheareas our stylized model assumes constant absolute risk
aversion, in reality absolute risk aversion depends strongly on the
individual’s wealth level. See Rabin (2000) for a detailed discussion.
28
Friend and Blume (1975) estimate the relative risk aversion of
investors to be between 2.21 and 2.39. The empirical estimates of relative
risk aversion reported in the survey by Meyer and Meyer (2005) range
between 1 and 7.03. Heaton and Lucas (2001) calibrate their model with
the relative risk aversion of entrepreneurs ranging between 0.5 to 5.
29
For example, while the absolute risk aversion a* depends on the
variance of sales, the corresponding relative risk aversion R* depends on
the coefficient of variation of sales, which exhibits smaller variation across
firms.
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J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
where
@q p 1 Eppub
Z ¼ E i i ¼
@pi qi i ¼ pub b qpub
is the expected price elasticity of demand,
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Varðppub qpub Þ
CV sales ¼
Eppub qpub
ð31Þ
ð32Þ
is the coefficient of variation of sales,
m¼
Eppub
Eppub qpub
ð33Þ
is the ratio of expected profit to expected sales,
P=E ¼
Vpub
Eppub
ð34Þ
is the price-to-earnings ratio, and
d¼
Vpub
Vn
¼
Vn þ w0
Vpub þ w0
ð35Þ
is the value of firm n* as a fraction of the total net worth
of entrepreneur n*, where all variables are evaluated at
N*,n* and q*.
When written as in Eq. (30), the relative risk aversion of
the ‘‘threshold entrepreneur’’ can be calibrated using
publicly available data. The base-case values of m, P/E,
CVsales, and r are based on the US economy-wide averages
computed from Compustat data. In particular, mean profit
margin, defined as the ratio of operating profit to sales, is
used as a proxy for m. It equals 0.35 during our sample
period. Mean price-to-earnings ratio, defined as end-ofyear share price divided by annual earnings per share, is
close to 10.30 We compute the coefficient of variation of detrended annual sales for each firm in the sample with at
least ten annual sales observations during our sample
period and average these coefficients of variation across
firms. This results in the average CVsales of 0.45.31 We use
the estimated mean systematic proportion of the variance
of quarterly sales growth of 0.05 as a proxy for r2 , as
discussed in Section 4.
The value of d is based on Moskowitz and VissingJørgensen (2002), who estimate the mean percentage of net
worth invested in private equity for households with
positive private equity and net worth to be 41.1%, out of
which 82% on average is invested in one actively managed
firm. This corresponds to d 0:34. Because the entrepreneur might not own the entire firm, the actual d could be
somewhat higher. The price elasticity of demand Z varies
widely among industries. For example, Taylor and
Weerapana (2009) report that typical values of Z range
from 0.1 for phone services to 2.6 for jewelry. Finally, we set
30
We winsorise outliers, defined as firm-years belonging to the top
and bottom percentiles of profit margins and price-to-earnings ratios
when calibrating these variables.
31
Because P/E is the ratio of firm value and annual earnings, CVsales
needs to be the coefficient of variation of annual sales. However, as long as
earnings are independent over time, the ratio of P/E and CVsales, and, thus,
R*, is independent of the time interval for which these parameters are
estimated.
the cost of going public f at 0.07, reflecting the typical
underwriting spread (e.g., Chen and Ritter, 2000).
In Fig. A1, we plot R* as a function of the degree of
competitive interaction g 2 ð0, bÞ, or equivalently as a
function of g=b 2 ð0,1Þ for the following base-case parameter values: m= 0.35, P/E=10, Z ¼ 1:5, d ¼ 0:5, CVsales =
0.45, r2 ¼ 0:05, and f ¼ 0:07. In each graph, we indicate the
base-case by the thick line and vary the various model
parameters as follows: m 2 ð0:2,0:5Þ, P=E 2 ð7,13Þ, Z 2 ð0:6,
2:4Þ, d 2 ð0:2,0:8Þ, CVsales 2 ð0:3,0:6Þ, and r2 2 ð0,0:5Þ.
For the base-case parameter values, the degree of relative
risk aversion of the entrepreneur who is indifferent between
taking her firm public and keeping it private, R*, varies
between 1.2 and 3.65 as the degree of competitive interaction g varies between 0 and b. While there is no complete
agreement on the degree of risk aversion for the typical
entrepreneur, these values of R* are of the same magnitude
as the empirical estimates of relative risk aversion reported
in the literature (See footnote 27). Therefore, given the
heterogeneity of risk aversion among individuals, there are
likely to be entrepreneurs with relative risk aversions below
as well as above R*, resulting in an interior equilibrium in
which both public and private firms exist.
Appendix B. Summary of notation and comparative statics
Appendix C. Proofs
To simplify notation, we let s2X VarðXi Þ ¼ s2 ð1r2 Þ
and s2Y VarðYÞ ¼ s2 r2 .
Proof of Lemma 1. First we prove, by contradiction, that
among pure-strategy equilibria, only symmetric ones, in
which all public firms produce the same quantity, can exist.
Suppose there are two public firms, i and j, which produce
different equilibrium quantities, qi aqj . Because qi maximizes firm i’s objective function given in Eq. (10), it must
satisfy the first-order condition
X
m 2bqi gqj g
qk c ¼ 0:
ð36Þ
kai,kaj
The fact that qi aqj together with Eq. (36) gives
X
m 2bqj gqi g
qk ca0:
ð37Þ
kai,kaj
Hence, qj does not satisfy the first-order condition for
maximizing firm j’s objective and thus cannot be firm j’s
equilibrium output. Therefore, our premise that qi aqj is
false, and the outputs of all public firms in any equilibrium,
if it exists, must be equal.
The equilibrium output vector q*(N,n) defined in Eq. (11)
is given by the first-order conditions
@Vi ðqÞ
¼0
@qi
3
m 2bqi g
X
qj c ¼ 0
for i ¼ 1, . . . ,n,
ð38Þ
jai
and
@Vi ðqÞ
¼0
@qi
3
X
qj c ¼ 0
m ð2b þai s2X Þqi g
for i ¼ n þ 1, . . . ,N:
jai
ð39Þ
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
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10
10
8
8
6
6
4
4
2
2
0
0
0
1
0
1
γ/β
γ/β
10
10
8
η
6
R*
R*
8
4
2
2
0
0
1
δ
6
4
0
0
1
γ/β
γ/β
10
10
8
8
CVsales
6
R*
R*
17
R*
R*
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
6
4
4
2
2
0
0
1
0
ρ
0
1
γ/β
γ/β
Fig. A1. The threshold relative risk aversion R* as a function of the ratio of the degree of competitive interaction, g, and slope of demand function, b, for
different levels of model parameters. See Table B1 for parameter definitions. The thick lines indicate the base-case.
Because each firm’s objective is strictly concave in its
output, the first-order conditions are sufficient, i.e., any q
that satisfies Eqs. (38) and (39) is an equilibrium. Taking
advantage of the equilibrium symmetry, we denote the
equilibrium output of each public firm as q*pub. Because the
equilibrium output of each private firm depends on its
owner’s risk aversion, we continue to denote the equilibrium output of private firm i as q*i . Thus, the equilibrium
conditions given in Eqs. (38) and (39) can be written as
m ð2bgÞqpub gQ c ¼ 0,
ð40Þ
Proof of Proposition 1. (i) The result follows directly from
Lemma 1.
(ii) Differentiating q*i given in Eq. (12) with respect to ai
gives
@qi
¼ ðm cÞ
@ai
PN
n
2 1
g 1 þ g
þ
ð2bg þai s2X Þ
j ¼ n þ 1 ð2bg þ aj sX Þ
2
b
g
s2X o 0:
2
PN
n
2 1 þ
1þg
ð2bg þai s2X Þ3
j ¼ n þ 1 ð2bg þ aj sX Þ
2bg
ð42Þ
and
m ð2bg þai s2X Þqi gQ c ¼ 0 for i ¼ n þ 1, . . . ,N,
PN
ð41Þ
where Q ¼ nqpub þ i ¼ n þ 1 qi is the total industry output. It
is straightforward to show that the system of Eqs. (40)
and (41) has a unique solution, which is given in Eqs. (12)
and (13). Plugging Eqs. (12) and (13) into Eq. (10) produces
Eqs. (15) and (16). &
*
Differentiating Q given in Eq. (14) with respect to ai gives
ðm cÞs2X
@Q ¼ @ai
PN
2 1 þ
1þg
j ¼ n þ 1 ð2bg þaj sX Þ
o 0,
2
n
ð2bg þai s2X Þ2
2b g
ð43Þ
and, therefore,
@qpub =@ai 4 0
and
@qj =@ai 4 0
for any jai.
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(iii) Differentiating q*pub and q*i with respect to g gives
@qpub
@g
P
2b2g
gð2bgÞ
N
j ¼ nþ1
2bg þaj s2X
ð2bg þ aj s2X Þ2
2 o0
PN
n
2 1 þ
ð2bgÞ2 1þ g
j ¼ n þ 1 ð2bg þ aj sX Þ
2bg
1n
¼ ðm cÞ
PN
j ¼ nþ1
and
ð44Þ
Because ð2bgÞ=ð2bg þ aj s2 ð1r2 ÞÞ decreases in g for any
j, the combined market share of public firms given in
Eq. (46) increases in g.
(iv) Because ð2bgÞ=ð2bg þ aj s2 ð1r2 ÞÞ decreases in s2
for any j, the combined market share of public firms given
in Eq. (46) increases in s2 .
(v) Because ð2bgÞ=ð2bg þ aj s2 ð1r2 ÞÞ increases in r2
P
PN
2bg þ a s2
2b2g þ ai s2X
gð2bg þ ai s2X Þ
gnai s2X
1n 2bg i X N
j ¼ n þ 1 2bg þ aj s2 j ¼ n þ 1 ð2bg þ aj s2 Þ2 ð2bgÞ2
@qi
X
X
¼ ðm cÞ
o 0:
P
2
@g
N
2 1 þ n
ð2bg þai s2X Þ2 1 þ g
j ¼ n þ 1 ð2bg þ aj sX Þ
2bg
for any j, the combined market share of public firms given
in Eq. (46) decreases in r2 . &
The combined market share of public firms is
nqpub
Q
¼ PN
j ¼ nþ1
n
2bg
þn
2bg þ aj s2 ð1r2 Þ
:
ð46Þ
Proof of Proposition 2. Suppose, without loss of generality, that it is firm n + 1 that goes public.
(i) To show that when firm n + 1 goes public, its output
increases, we need to show that qpub ðN,n þ 1Þ 4 qn þ 1 ðN,nÞ,
which is the case if, and only if,
Table B1
Definition of notation.
Panel A: Main body notation
ai
Coefficient of absolute risk aversion of entrepreneur i
c
Marginal cost of production
n
Number of public firms in the industry
N
Number of firms in the industry
pi
Market-clearing price for firm i’s product
qi
Output of firm i
Q
Total industry output
rf
Risk-free return
rm ðr m Þ (Expected) Market portfolio return
ui( )
Utility of entrepreneur i
Vi
Value of firm i to its owner
w
Entrepreneur’s terminal wealth
w0
Entrepreneur’s initial wealth (outside the firm)
x
Entrepreneur’s investment in the market portfolio
Xi
Idiosyncratic component of the demand shock for firm i’s
product
Y
Systematic component of the demand shock for firm i’s
product
ai
Firm i’s demand shock
Slope of the demand curve, i.e., j@pi =@qi j
b
g
Degree of competitive interaction, i.e., j@pi =@qi j
m
Expected value of demand shock ai
rs
sm
m
m ¼ mðr m rf Þ
pi
r
Profit of firm i
Correlation coefficient between demand shock ai and market
portfolio return rm
Standard deviation of demand shock ai
Standard deviation of the market portfolio return
Proportional cost of going public
s
sm
f
Panel B: Appendix A notation
CVsales Coefficient of variation of sales of a public firm
m
Expected profit over expected sales of a public firm
P/E
Price-to-earnings ratio of a public firm
R
Coefficient of relative risk aversion
Public firm value as a fraction of the total net worth of
d
entrepreneur n*
Z
Expected price elasticity of demand of a public firm
ð45Þ
ð2bgÞ 1þ g
4
ðm cÞ
PN
j ¼ n þ 2 ð2b
g þ aj s2X Þ1 þ
n þ1
2bg
ðm cÞ
PN
2 1 þ
ð2bg þan þ 1 s2X Þ 1 þ g
j ¼ n þ 1 ð2bg þ aj sX Þ
n
2bg
ð47Þ
3
an þ 1 s2X
g
4
þ
N
X
j ¼ nþ2
N
X
2bg þan þ 1 s2X
2bg þ an þ 1 s2X
þn
2
2bg
2
b
g
þ
a
s
j X
j ¼ nþ2
2bg
þn,
2bg þ aj s2X
ð48Þ
which clearly holds.
To prove that the output of all other firms decreases, we
need to show that qpub ðN,n þ 1Þ o qpub ðN,nÞ and
qi ðN,n þ 1Þ o qi ðN,nÞ for all ian þ1, both of which follow
directly from Lemma 1.
(ii) The market share of the IPO firm before going public is
Mn þ 1 ðN,nÞ ¼
qn þ 1 ðN,nÞ
Q ðN,nÞ
¼
ð2bg þ an þ 1 s2X Þ
1
PN
2 1 þ
j ¼ n þ 1 ð2bg þaj sX Þ
:
n
2bg
ð49Þ
The market share of the IPO firm after going public is
Mpub ðN,n þ1Þ ¼
¼
ð2bgÞ
qpub ðN,n þ 1Þ
Q ðN,n þ 1Þ
P
1
N
j ¼ n þ 2 ð2b
:
g þ aj s2X Þ1 þ 2nbþ1g
ð50Þ
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19
Table B2
Summary of comparative statics.
A plus (minus) sign denotes a positive (negative) effect of the parameter on the variable.
Proposition 1
Output of private firm i
Output of any firm other than i
Total market share of public firms
Proposition 2
Relative increase in the IPO firm’s market share
Proposition 3
Value of private firm i
Value of any firm other than i
Ratio of public firm value to private firm value
ai
g
+
+
s2
r
+
+
+
+
+
+
Proposition 4
Relative increase in the IPO firm value
Relative decrease in the value of the IPO firm’s competitors
+
+
+
+
Proposition 6
Proportion of public firms in industry
+
+
Thus, the relative increase of the IPO firm’s market share
equals
Mpub ðN,n þ 1Þ
Mn þ 1 ðN,nÞ
P
N
2 1
ð2bg þ an þ 1 s2X Þ
þ 2bng
j ¼ n þ 1 ð2bg þaj sX Þ
P
N
2 1 þ n þ 1
ð2bgÞ
j ¼ n þ 2 ð2bg þaj sX Þ
2bg
PN
2bg þ an þ 1 s2X
an þ 1 s2X
j ¼ n þ 2 2bg þ aj s2 þ 1 þ n þ n 2bg
X
:
ð51Þ
¼
PN
2bg
j ¼ n þ 2 2bg þ a s2 þ 1 þn
¼
j
j ¼ nþ2
an þ 1 s2X
þ
nan þ 1 s2X
ð2bg þaj s2X Þ2 ð2bgÞ2
ð2bgÞ
þ1 þn
j ¼ nþ2
ð2bg þ aj s2X Þ
!
PN
aj s2X
an þ 1 s2X
nan þ 1 s2X PN
þ
j ¼ nþ2
j ¼ nþ2
2bg
2bg þ aj s2X
ð2bg þ aj s2X Þ2
þ
40:
!2
PN
ð2bgÞ
þ1 þn
j ¼ nþ2
2
ð2bg þaj sX Þ
@ Mpub ðN,n þ1Þ
¼
@g Mn þ 1 ðN,nÞ
@Vi
q s2 ðm cÞ
¼ i X
2
@ai
P
gn
2 1
ð2b þ g þ ai s2X Þ 1 þ g N
þ
g
j ¼ n þ 1,jai ð2bg þ aj sX Þ
2bg
2 o0:
P
2 1 þ gn
ð2bg þ ai s2X Þ2 1 þ g N
j ¼ n þ 1 ð2bg þ aj sX Þ
2bg
ð55Þ
X
Differentiating Eq. (51) with respect to g gives
PN
Proof of Proposition 3. (i) The result follows directly from
Lemma 1.
(ii) We have
PN
ð52Þ
(iii) Differentiating Eq. (51) with respect to s2 gives
We know from Proposition 1(ii) that the output of any firm
jai increases in ai. Hence, it follows from Eqs. (15) and (16)
that the value of any firm jai increases in ai as well.
(iii) We know from Proposition 1(iii) that the output of
any firm decreases in g. Hence, it follows from Eqs. (15) and
(16) that the value of any firm decreases in g as well. The
relative benefit of being public,
Vpub
¼
Vi
2
2b
ai s2 ð1r2 Þ
1
þ
,
2bg
2b þ ai s2 ð1r2 Þ
clearly increases in g.
PN
2bg
n
þ 2bg
j ¼ n þ 2 ð2bg þ s2 a Þ2
@ Mpub ðN,n þ 1Þ
2
X j
¼
ð1
r
Þa
P
n
þ
1
N
2
b
g
@s2 Mn þ 1 ðN,nÞ
þ1þn
j ¼ n þ 2 2bg þ aj s2
X
P
P
aj s2X ð2bgÞ
N
N
1
n
þ
j ¼ n þ 2 2bg þ aj s2
j ¼ n þ 2 ð2bg þ aj s2 Þ2
2bg
X
X
þ ð1r2 Þan þ 1
40:
P
2
N
2bg
þ
1
þn
j ¼ n þ 2 2bg þ a s2
j
(iv) Differentiating Eq. (51) with respect to r2 gives
@ Mpub ðN,n þ 1Þ
s2
@ Mpub ðN,n þ 1Þ
¼
o 0:
2
2
2
@r Mn þ 1 ðN,nÞ
1r @s Mn þ 1 ðN,nÞ
ð54Þ
ð56Þ
ð53Þ
X
(iv) Differentiating Eq. (56) with respect to s2 gives
@ Vpub
2bai ð1r2 Þð2bg þai s2 ð1r2 ÞÞð2b þai s2 ð1r2 Þ þ gÞ
¼
4 0:
@s2 Vi
ð2bgÞ2 ð2b þ ai s2 ð1r2 ÞÞ2
ð57Þ
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
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(v) Differentiating Eq. (56) with respect to r2 gives
!
@ Vpub
s2
@ Vpub
¼
o0:
@r2 Vi
1r2 @s2 Vi
¼
&
ð58Þ
Proof of Proposition 4. Suppose, without loss of generality, that it is firm n + 1 that goes public.
(i) We first show that the value of the IPO firm increases,
ðN,n þ 1Þ 4 Vn þ 1 ðN,nÞ. Using Lemma 1, this inequali.e., Vpub
ity can be written as
bðm cÞ2
2
P
N
2 1 þ n þ 1
ð2bgÞ2 1 þ g
j ¼ n þ 2 ð2bg þ aj sX Þ
2bg
1
2
b þ an þ 1 sX ðm cÞ2
2
4
PN
2
2
2 1 þ
ð2bg þ an þ 1 sX Þ 1þ g
j ¼ n þ 1 ð2bg þ aj sX Þ
n
2bg
2 ,
@
@g
qpub ðN,n þ 1Þ
!
an þ 1 s2X g
¼
ð2b þ gð2bgÞA þ gnÞ2
gnA
A þ 2bB þ gð2bgÞAB þ ngB þ
2bg
!
4bn
gnðn1Þ
gn
2
þ
þ
þ
1
þ
g
Aþ
s
C
,
2bg X
ð2bgÞ2 ð2bgÞ2
qn þ 1 ðN,nÞ
ð63Þ
A¼
B¼
N
X
1
,
ð2
b
g
þaj s2X Þ
j ¼ nþ2
N
X
1
2 2
j ¼ n þ 2 ð2bg þ aj sX Þ
ð64Þ
,
ð65Þ
:
ð66Þ
and
ð2b þ an þ 1 s2X Þ
12
N
X
gð2bg þ an þ 1 s2X Þ
gnð2bg þ an þ 1 s2X Þ A
@1 þ
þ
2 Þð2b þ a
2Þ
ð2
ð2
b
g
þ
a
s
s
b þ an þ 1 s2X Þð2bgÞ
n
þ
1
j X
X
j ¼ nþ2
4 2b@1 þ
j ¼ nþ2
we have
which can be further rewritten as
0
PN
where
ð59Þ
0
gð2bg þ an þ 1 s2X Þ an þ 1 s2X ng
þ
þ gn
2bg
ð2bg þ aj s2X Þ
,
P
gð2bgÞ
þ gn
2b þ N
j ¼ nþ2
2
ð2bg þaj sX Þ
ð62Þ
2b þ an þ 1 s2X þ
12
N
X
gnð2b þan þ 1 s2X Þ A
gð2bgÞ
þ
:
2 Þ2b
ð2
ð2
b
g
þ
a
s
b þan þ 1 s2X Þ2b
j
X
j ¼ nþ2
ð60Þ
Because each term on the left-hand side of the above
inequality is positive and greater than the corresponding
term on its right-hand side, the inequality holds.
The fact that the values of public and private rivals of the
ðN,n þ 1Þ o Vpub
ðN,nÞ and
IPO firm decline, i.e., Vpub
Vi ðN,n þ 1Þ o Vi ðN,nÞ, follows from the fact that their outputs decline [Proposition 2(i)] and from Eqs. (15) and (16).
(ii) The relative increase in the IPO firm value equals
Vpub
ðN,n þ 1ÞVn þ 1 ðN,nÞ
Vn þ 1 ðN,nÞ
¼
b
2
b þ 12an þ 1 sX
!2
qpub ðN,n þ 1Þ
qn þ 1 ðN,nÞ
C¼
aj
g þaj s2X Þ2
j ¼ n þ 2 ð2b
Clearly, ð@=@gÞðqpub ðN,n þ1Þ=qn þ 1 ðN,nÞÞ 40, which implies
ðN,n þ1ÞVn þ 1 ðN,nÞ=Vn þ 1 ðN,nÞÞ 40 as well.
that ð@=@gÞðVpub
The relative decrease in the value of a public and a private
rival of the IPO firm is
Vpub
ðN,nÞVpub
ðN,n þ 1Þ
¼ 1
qpub ðN,n þ 1Þ
!2
,
ð67Þ
!2
qpub ðN,n þ1Þ
qi ðN,n þ 1Þ 2
¼ 1
,
¼ 1
qi ðN,nÞ
qpub ðN,nÞ
ð68Þ
ðN,nÞ
Vpub
qpub ðN,nÞ
and
Vi ðN,nÞVi ðN,n þ 1Þ
Vi ðN,nÞ
1:
ð61Þ
N
X
Therefore, to prove that the expression given in Eq. (61)
increases in g, it is enough to show that qpub ðN,n þ 1Þ=
qn þ 1 ðN,nÞ increases in g. Given that
respectively. Thus, to show that the expressions given
in Eqs. (67) and (68) are increasing in g, it is enough to
show that qpub ðN,n þ 1Þ=qpub ðN,nÞ is decreasing in g. Given
that
qpub ðN,n þ1Þ
qpub ðN,n þ 1Þ
qn þ 1 ðN,nÞ
qpub ðN,nÞ
PN
n
2 1
ð2bg þ an þ 1 s2X Þ 1 þ g
þ
j ¼ n þ 1 ð2bg þ aj sX Þ
2bg
¼
PN
2 1 þ n þ1
ð2bgÞ 1þ g
j ¼ n þ 2 ð2bg þaj sX Þ
2bg
@
@g
qpub ðN,n þ 1Þ
qpub ðN,nÞ
!
2
X an þ 1
¼ s
g2
PN
1þ
PN
¼
4bðbgÞ þ 2aj s2X ð2bgÞ þ g2 þ aj an þ 1 s4X
g
j ¼ n þ 2 ð2bg þ aj s2 Þ
X
1þ
PN
þ ð2bg þga
g
j ¼ n þ 2 ð2bg þ aj s2 Þ
X
s2X Þ
1Þ
þ g2ðnbþ
g
n
þ 2bg
g
,
ð69Þ
2
þ 4b þ 2bs2X an þ 1 þ g2 n
,
P
gn þ g 2
1
ð2bgÞ2 ð2bg þan þ 1 s2X Þ2 1þ g N
j ¼ n þ 2 2bg þ a s2 þ 2bg
j ¼ nþ2
nþ1
ð2bg þ aj s2X Þ2
j
ð70Þ
X
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
we have
which is clearly negative.
(iii) Differentiating the relative increase in the IPO firm’s
value given in Eq. (61) with respect to s2 gives
!
@ Vpub ðN,n þ 1ÞVn þ 1 ðN,nÞ
@s2
Vn þ 1 ðN,nÞ
qpub ðN,n þ 1Þ
ð1r2 Þan þ 1 b
¼ 2 q ðN,nÞ
1
2
2 b þ 2an þ 1 sX
nþ1
r2 Þ2b þ ð1
2
a
bþ1
2 n þ 1 sX
!2
!
qpub ðN,n þ 1Þ @ qpub ðN,n þ 1Þ
:
qn þ 1 ðN,nÞ @s2X
qn þ 1 ðN,nÞ
ð71Þ
ðN,n þ 1ÞVn þ 1
Therefore, to prove that ð@=@s2 ÞðVpub
ðN,nÞ=Vn þ 1 ðN,nÞÞ4 0, we need to show that
!
q ðN,n þ 1Þ
an þ 1
@ qpub ðN,n þ1Þ
pub
þ
40:
1
qn þ 1 ðN,nÞ
qn þ 1 ðN,nÞ
@s2X
4 b þ an þ 1 s2X
2
ð72Þ
(iv) The relative increase in the IPO firm value given in Eq.
(61), and the relative decrease in the values of public and
private rivals of the IPO firm given in Eqs. (67) and (68) are
all decreasing in r2 because they are increasing in s2 [as
shown in part (iii)] and because s2X s2 ð1r2 Þ. &
Proof of Proposition 5. We first show, by contradiction,
that in any equilibrium where firm i is public and firm j is
private, we must have i oj. Suppose that firm i is public,
firm j is private, and i4 j. Because i is public, we have
ð1fÞVpub
ZVi . The fact that i 4j implies aðiÞ o aðjÞ, which
in turn implies Vi 4 Vj . Thus, ð1fÞVpub
4 Vj and firm j has
an incentive to go public, which is a contradiction with the
industry being in equilibrium. Therefore, in any equilibrium, firm i is public if i on , and it is private if i 4 n .
Before we address each of the three cases (i)–(iii), it is
useful to establish several facts. We define f ðnÞ ð1fÞ
ðN,nÞVn ðN,nÞ so that the equilibrium condition given
Vpub
in Eq. (23) can be written as f(n)= 0. Because
Using Eq. (62), we have
qpub ðN,n þ 1Þ
@
@s2X
f ðnÞ ¼ !
qn þ 1 ðN,nÞ
an þ 1 þ g
an þ 1 ð2bg þ aj s2X Þð2bg þ an þ 1 s2X Þaj
PN
j ¼ nþ2
¼
2b þ an þ 1 s2X þ
ð2bg þaj s2X Þ2
PN
gð2bgÞ
þ gn
2b þ j ¼ n þ 2
ð2bg þ aj s2X Þ
gð2bg þ an þ 1 s2X Þ ngð2bg þ an þ 1 s2X Þ
þ
j ¼ nþ2
2bg
ð2bg þ aj s2X Þ
PN
þ
2b þ
N
X
j ¼ nþ2
an þ 1
þ ng
2bg
PN
j ¼ nþ2
gð2bgÞ
þ gn
ð2bg þ aj s2X Þ
!2
gð2bgÞaj
:
ð2bg þ aj s2X Þ2
ð73Þ
Using Eqs. (62) and (73), the desired inequality given in
Eq. (72) becomes
an þ 1 ðgð2bgÞA þ gnÞ 2b þ an þ 1 s2X þ ð2b þ an þ 1 s2X þ gÞgA
ngðan þ 1 s2X þ 2b þ gÞ
þ
ð2bgÞ
ngðan þ 1 s2X þ2b þ gÞ
þ 2ban þ 1 2b þ an þ 1 s2X þ
ð2bgÞ
þ 2an þ 1 g2 ð2b þan þ 1 s2X Þð2bgÞB
þ 2an þ 1 bgð2bgÞA þ 2a2n þ 1 s2X ðbgÞgA 4 0,
ð74Þ
ðN,n þ1Þ
which is clearly satisfied. Therefore, ð@=@s2 ÞðVpub
Vn þ 1 ðN,nÞ=Vn þ 1 ðN,nÞÞ 40.
To prove that the relative decreases in the values of a
public and a private rivals of the IPO firm given in Eqs. (67)
and (68) are increasing in s2 , we need to show that
qpub ðN,n þ 1Þ=qpub ðN,nÞ is decreasing in s2 . Differentiating
Eq. (69) with respect to s2 gives
@
qpub ðN,n þ 1Þ
@s2
qpub ðN,nÞ
!
¼ ð1r2 Þgan þ 1
1
2bg þ an þ 1 s2X
1 þ gA þ
gs2X
gn þ g
þ
C
2bg
2bg
2
gðn þ 1Þ
ð2bg þ an þ 1 s2X Þ 1 þ gA þ 2bg
which is clearly negative.
,
ð75Þ
21
ðm cÞ2
1þ
RN
g
n 2bg þ aðxÞs2
X
n
dx þ 2bg
g
2
!
b þ 12aðnÞs2X
,
ð2bgÞ2 ð2bg þaðnÞs2X Þ2
ð1fÞb
ð76Þ
and a(n) is decreasing in n, f(n) is decreasing in n as well.
Furthermore, it is easy to verify that if a(n)=a*, where a* is
given in Eq. (24), then f(n) =0.
Consider case (i) first. Because að0Þ 4 a 4 aðNÞ and a(n) is
continuous and decreasing, there exists a unique n 2 ð0,NÞ
such that a(n*) =a* and, therefore, f(n*)= 0 or, equivalently,
ðN,n Þ ¼ Vn ðN,n Þ. Because V*i (N,n*) is increasing
ð1fÞVpub
ðN,n Þ 4 Vi ðN,n Þ for any i on and
in i, we have ð1fÞVpub
ðN,n Þ oVi ðN,n Þ for any i4 n . Hence, all firms
ð1fÞVpub
that are public (those whose index is less than n*) are better
off being public while all firms that are private (those
whose index is greater than n*) are better off being private,
and n* is therefore the unique equilibrium.
Next, we consider case (ii). The fact that að0Þ r a implies
aðnÞ r a for any n Z0. Thus, for any n Z0, we have f ðnÞ r0,
i.e., ð1fÞVpub
ðN,nÞ rVn ðN,nÞ. Hence, ð1fÞVpub
ðN,0Þ r
V0 ðN,0Þ o Vi ðN,0Þ for any i 4 0. Therefore, when n = 0, no
firm has the incentive to go public and the industry is in
equilibrium. At the same time, for any n 4 0, we have
f ðnÞ o 0, i.e., the nth firm has the incentive to go private and,
thus, n 40 cannot be an equilibrium. In other words, n* = 0
is the unique equilibrium.
Finally, consider case (iii). The fact that aðNÞ Z a implies
aðnÞ Z a for any n r N. Thus, for any n rN, we have f ðnÞ Z0,
ðN,nÞ Z Vn ðN,nÞ. Hence, ð1fÞVpub
ðN,NÞ Z
i.e., ð1fÞVpub
VN ðN,NÞ 4Vi ðN,NÞ for any i oN. Thus, when n = N, no firm
has the incentive to go private and the industry is in
equilibrium. At the same time, for any n o N, we have
f ðnÞ 4 0, i.e., the nth firm has the incentive to go public and
thus, n oN cannot be an equilibrium. In other words, n* =N
is the unique equilibrium. &
Please cite this article as: Chod, J., Lyandres, E., Strategic IPOs and product market competition. Journal of Financial
Economics (2010), doi:10.1016/j.jfineco.2010.10.010
22
J. Chod, E. Lyandres / Journal of Financial Economics ] (]]]]) ]]]–]]]
Proof of Proposition 6. The result follows from the facts
that @a =@g o 0, @a =@s o0, @a =@r 4 0, and n* decreases
in a*. &
Proof of Proposition 7. In what follows, we suppress the
equilibrium notation while recognizing that all variables
are evaluated at N*, n* and q*. Using Eq. (24), the relative risk
aversion of entrepreneur n* given in Eq. (29) can be
written as
R ¼
Vpub bð2g=bÞ
4dð1fÞs2 ð1r2 Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð2g=bÞ2 þ 8ð1fÞg=b2g=b þ 4f ,
ð77Þ
where d is given by Eq. (35). Realizing that q2pub
s2 ¼ Varðqpub ppub Þ, this can be further rewritten as
R ¼
q2pub bVpub ð2g=bÞ
Varðqpub ppub Þð1r2 Þ4dð1fÞ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð2g=bÞ2 þ8ð1fÞg=b2g=b þ 4f
¼
mð2g=bÞP=E
4Zdð1fÞð1r2 ÞCV2sales
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð2g=bÞ2 þ8ð1fÞg=b2g=b þ 4f ,
ð78Þ
where Z is given by Eq. (31), CVsales is given by Eq. (32), m is
given by Eq. (33), and P/E is given by Eq. (34) as stipulated in
Proposition 7. &
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