VENTURE CAPITAL AND CAPITAL ALLOCATION∗
Giorgia Piacentino†
Columbia University
August 23, 2017
Abstract
In this paper, I show that venture capitalists’ career concerns can have beneficial effects
in the primary market: they can mitigate information frictions, helping firms go public.
Because uninformed VCs want to appear informed, they are biased against backing
firms—by not backing firms, VCs avoid taking low-value firms to market, which would
ultimately reveal their lack of information. In equilibrium, VCs back only high-value
firms, creating a certification effect that mitigates information frictions, helping firms
go public. However, this benefit comes at the cost that VCs inefficiently do not back
some high-value firms.
∗I am grateful to Ulf Axelson, the late Sudipto Bhattacharya, Sugato Bhattacharya, Philip Bond, Mike
Burkart, Amil Dasgupta, James Dow, Jason Roderick Donaldson, Alex Edmans, Daniel Ferreira, Itay Gold-
stein, Radhakrishnan Gopalan, Denis Gromb, Christian Julliard, Ohad Kadan, Peter Kondor, Todd Mil-
bourn, Daniel Paravisini, Christopher Polk, Uday Rajan, Anjan Thakor, David Thesmar, Dimitri Vayanos,
Michela Verardo, Kathy Yuan, Konstantinos Zachariadis, Hongda Zhong and audiences at Amsterdam Busi-
ness School, Arizona Sate University, Bocconi University, the 2013 EFA meeting, EIEF, Federal Reserve
Board of Governors, the 2013 FIRS conference, HEC Paris, the 2017 Institutional Investors and Corporate
Governance conference at the Swedish House of Finance, UBC, UNC, University of Maryland, University of
Michigan, Stockholm School of Economics, University of Pennsylvania, University of Warwick, and Wash-
ington University in St. Louis.
†Contact: @
This article is forthcoming in the Journal of Finance.
1 Introduction
Delegated investors wish to be perceived as skilled in order to generate “flows,” ., to
attract new investors and retain existing ones. These career concerns can distort their
trades in secondary markets. For example, delegated investors may trade too much
in the attempt to appear informed, even when they are not. This excessive portfolio
churning can, in turn, decrease secondary market efficiency (Dasgupta and Prat (2006,
2008), Dow and Gorton (1997), and Guerrieri and Kondor (2012)). However, delegated
investors do not only play an important role in secondary markets, where their trading
behavior affects market efficiency, but also in primary markets, where their investment
behavior affects real efficiency. In particular, venture capital funds (VCs) decide which
firms to back and thus which projects go ahead. Therefore, I ask: Do VCs’ career
concerns lead to inefficiencies in primary markets? Specifically, do career-concerned
VCs back the wrong firms in the attempt to appear skilled?
In this paper, I develop a model to address these questions. I show that career-
concerned VCs act conservatively. Specifically, uninformed career-concerned VCs pass
up backing new firms even when they believe that doing so would probably be profitable.
Indeed, they do not want to risk taking bad firms to market, as this could reveal their
lack of information. Hence, to appear informed and appeal to investors, uninformed
VCs underinvest, thereby acting against these investors’ interests. However, these indi-
vidually inefficient actions can be socially efficient. The reason is that they can mitigate
information frictions that may exist at the time of IPO. Since career-concerned VCs
are conservative, they back only the best firms, and thus create a “certification effect”
that helps firms IPO. However, this benefit comes at the cost that VCs inefficiently do
not back some high-value firms.
Model preview. A penniless start-up firm requires outside finance for an invest-
ment that may be good or bad. It looks for a VC to back it, ., to provide capital
and expertise. If the firm receives backing, it gives the VC an equity stake and invests.
Later, the firm raises capital from uninformed bidders in an IPO, in which the VC
retains its stake. Finally, the long-run value of the investment is realized.
The VC can be skilled or unskilled. If it is skilled, it can observe whether the
firm (., its investment) is good or bad, but if it is unskilled it observes nothing. I
consider two cases. First, the VC may be profit motivated, ., it wants to back the
firm whenever it expects to make a profit for its current investors. Second, the VC may
be career concerned, ., it wants to maximize the market’s belief that it is skilled, so
as to maximize the capital it can raise from future investors.
Results preview. I first characterize the equilibrium with a profit-motivated VC.
A skilled VC knows the quality of the firm. Thus, it does not back bad firms and
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it backs good firms as long as it anticipates being able to take them IPO. Hence, a
skilled VC “filters out” bad firms. In contrast, an unskilled VC does not know whether
the firm is good or bad. However, it knows that the market believes that VC-backed
firms are better than average, due to the skilled VC’s filtering. Thus, if the unskilled
VC backs the firm, it raises cheap capital at the time of the IPO—it is subsidized by
pooling with the positively informed skilled VC. As a result, the unskilled VC may also
back the firm, despite its lack of information. This maximizes its expected profit, but
may be socially inefficient. Indeed, the unskilled VC over-invests, and may still back
a firm with negative NPV. When the average NPV is low enough, the unskilled VC’s
over-investment can reduce the average quality of VC-backed firms so much that IPO
bidders are unwilling to provide capital. Thus, in anticipation of being unable to IPO,
skilled VCs do not back firms even when they know they are good—., the collapse of
the IPO market causes the VC market to break down.
What changes if the VC is career-concerned? Now, an unskilled VC is averse to
backing a firm that might end up being bad, but less averse to not backing a firm that
might end up being good. Indeed, since the firm’s value is revealed only if the VC
backs it, the market can determine whether the VC wrongly backed a bad firm, but
not whether it wrongly rejected a good firm. To put it another way, the market can
distinguish between false positives and true positives, but cannot distinguish between
false negatives and true negatives. This biases the unskilled VC toward “negatives,”
., toward not backing the firm. In other words, the unskilled VC acts conservatively.
When the unskilled career-concerned VC rejects a firm, it may act against the in-
terests of its investors. Indeed, if it were only to maximize profits for its investors,
it would want to act exactly like the unskilled profit-motivated VC, backing the firm
to take advantage of the IPO subsidy from the skilled VC. However, this underinvest-
ment can enhance aggregate efficiency. It leads to a certification effect of VC backing
that can prevent market breakdowns: since unskilled career-concerned VCs back the
firm relatively rarely, many VC-backed firms are backed by positively informed skilled
VCs; therefore, the market infers that the VC-backed firms are probably good. This
certification effect mitigates information frictions to help firms IPO.
Even absent market breakdowns, VCs’ career concerns can lead to an increase in
aggregate efficiency. Since the unskilled VC has no information, it backs firms of aver-
age value. If this average NPV is negative, aggregate efficiency is higher with career-
concerned VCs, given they back firms less often than profit-motivated VCs. However,
if this average NPV is positive, aggregate efficiency is lower with career-concerned VCs,
since, in this case, the costs of backing fewer good firms outweigh the benefits of backing
fewer bad firms. Below, I place more emphasis on the negative-NPV case, and hence on
the positive effects of career concerns, because I think this case is realistic: VC partners
2
“source a few thousand opportunities, invest in a handful, and get returns from a few”;
in fact “almost 80 percent of all investments fail” (Ramsinghani (2014), p. 69 and p. 6).
Extensions and robustness. I show that the positive side of career concerns is
robust to a number of extensions. If either (i) the firm has assets in place, so that the
market may learn the quality of the firm even if it does not get VC backing, or (ii) there
is a convex flow-performance relationship, so the VC maximizes a convex function of the
market’s beliefs about its skill, then the results are qualitatively similar, but attenuated.
The results are also qualitatively similar, but amplified, if either (iii) the VC sells its
stake at the time of the IPO, so that even a negatively informed VC free rides on
positively informed VCs, or (iv) there is adverse selection among IPO investors, so that
the firm must issue shares at a discount to induce uninformed investors to participate.
Further, I show that my main results are robust to relaxing some of the other simplifying
assumptions I make in the baseline model.
Layout. The paper proceeds as follows. Next, I discuss the model’s empirical
relevance and some related literature. In Section 2, I present the model. In Section
3, I characterize the equilibria, both for profit-motivated and career-concerned VCs.
In Section 4, I compare these equilibria and show that career concerns increase IPO
prices, prevent market breakdowns, and increase aggregate output for some parameters.
In Section 5, I consider extensions and show that the model is robust to a number of
different specifications. I conclude in Section 6. The Appendix contains the proofs and
the equilibrium refinements.
Realism and Empirical Content
Assumptions. My model is based on the assumption that VCs are career concerned,
in the sense that they have incentive to appear skilled in order to attract capital from
new investors. This assumption reflects practice. VCs’ revenues are based largely on the
amount of capital they manage (see Subsection ) and VCs’ investors invest with VCs
based on their past performance (see, for example, Gompers and Lerner (1998, 2001)).
Further, as in my model, the ability to pick good firms is arguably the most important
component of VC skill—VCs “often receive and evaluate thousands of business plans
each year. Therefore, a [VC] firm’s ability to effectively and efficiently identify win-
ning investment proposals is critical to its success” (Nelson, Wainwright, and Blaydon
(2004), p. 1; see also, ., Gompers, Kovner, Lerner, and Scharfstein (2006)).
Proxies. To compare my model with empirical findings, the challenge is to find
proxies for VCs’ career concerns. In the model, VCs’ career concerns reflect three
components: career-concerned VCs value highly (i) the future relative to the present, (ii)
inflows of client capital relative to immediate fund performance, and (iii) the reputation
they have at stake to lose. Each of these components finds natural proxies: (i) career-
3
concerned VCs are younger,1 (ii) career-concerned VCs have higher fixed fees relative
to performance fees (so they need to increase assets under management to increase
revenue),2 (iii) career-concerned VCs are large (manage a lot of capital)3 and have
strong track More generally, the career-concerned VCs in my model could
correspond to real-world venture capital firms and other delegated primary market
investors that compete for flows, whereas the profit-motivated “VCs” in my model could
correspond to angel investors and other non-delegated primary market investors that
do not compete for flows.
Consistent stylized facts. In light of the proxies for career concerns discussed
above, my model is consistent with a number of empirical findings. First, my result that
more career-concerned VCs help to prevent market breakdowns is consistent with the
finding that VCs are more likely to lead their portfolio companies to successful IPOs
(Krishnan, Ivanov, Masulis, and Singh (2011) and Nahata (2008)). Second, my result
that more career-concerned VCs increase the IPO price is consistent with the empirical
findings that (i) VC-backed firms are less likely to be underpriced at IPO (Barry,
Muscarella, Peavy, Megginson and Weiss (1991) and Vetsuypens (1990)) and, further,
(ii) this underpricing is decreasing in the strength of the reputation of the VC backing
the firm (see Gompers (1996)). My results are also broadly consistent with the fact that
VC-backed companies are more likely to go public when backed by a more reputable VC
(Hsu (2004) and Puri and Zarutskie (2012)). Further, my emphasis on how VCs help
overcome information frictions is consistent with practice, since “[v]enture capitalists
concentrate investments in early stage companies and high technology industries where
informational asymmetries are significant” (Gompers (1995), p. 1462).
New predictions. The main new prediction of my model is that more career-
concerned VCs back firms relatively less often, but back higher-quality firms. Thus,
career concerns predict higher IPO prices (less underpricing) and fewer IPOs in nor-
mal times (because career-concerned VCs back fewer firms), but possibly more IPOs
in downturns (because career concerns prevent market breakdowns when firms have
negative average NPV). The proxies described above make these predictions testable.
1Chevalier and Ellison (1999) use age as a proxy for mutual funds’ career concerns. Gompers (1996) and
Lee and Wahal (2004) use age as a proxy for VCs’ career concerns.
2There is significant variation in VC compensation (see Subsection ). VCs with a larger performance
fee relative to the fixed fee are likely to be relatively less career concerned in comparison to VCs with a lower
performance fee relative to the fixed fee (see Dasgupta and Piacentino (2015) for a discussion).
3Gompers (1998) and Gompers and Lerner (1999) use size as a proxy for reputation.
4See, for example, Krishnan, Ivanov, Masulis, and Singh (2011) and Sörensen (2007).
4
Related Literature
My main contribution to the literature is to show that the individually suboptimal
behavior of career-concerned delegated investors can have positive aggregate effects
in some circumstances. This contrasts with the literature in which career-concerned
agents’ “churning” has adverse effects (see Dasgupta and Prat (2006, 2008), Guerrieri
and Kondor (2012), and Scharfstein and Stein (1990)).5 Career concerns can help in
my setup because they distort the actions of the unskilled VC in such a way that the
actions of skilled positively informed VCs become more informative, thereby mitigating
the inefficiencies that result from asymmetric
This paper builds on a large literature on career concerns instigated by Fama (1980).
Perhaps the most related paper in this literature is Chen (2015), which builds on the
model in Hölmstrom (1999) to show that career-concerned agents tend to over-invest
when they know their skill. In contrast, I show that if the agent’s skill reflects his
ability to understand the state of the world as in, ., Gibbons and Murphy (1992),
Hölmstrom and Ricart i Costa (1986), and Scharfstein and Stein (1990), rather than to
generate high output, the agent may underinvest.
Asymmetric learning about the agent’s skill also appears in the career concerns
models of Milbourn, Shockley, and Thakor (2001) and Hirshleifer and Thakor (1994).
Milbourn, Shockley, and Thakor (2001) show that a career-concerned manager over-
invests in information, because this improves the odds of rejecting a bad project. This
makes him allocate capital correctly, but this decreases overall efficiency relative to first
best. In my model, in contrast, the unskilled VC underinvests. The main driver of this
contrasting result is that the agent (VC) knows its type in my model, but not in theirs.
Hirshleifer and Thakor (1994) find that skilled managers are reluctant to undertake
projects that might fail Although I also find that career concerns lead
to underinvestment, I find, in contrast, that this can increase aggregate efficiency. This
is because the VC’s decision feeds back into a real decision, ., the IPO bidders’ choice
to provide capital.
5Dow and Gorton (1997) also show that there may be a positive effect of institutional investors’ “endoge-
nous noise trading,” since it may provide risk-sharing opportunities.
6Other papers, following Hölmstrom (1999), have also found positive effects of reputation concerns. In
these papers, reputation concerns mitigate the incentive problem between an agent and a principal—they
provide implicit incentives that make up for lacking explicit incentives. Moreover, in Booth and Smith
(1986) and Chemmanur and Fulghieri (1994), an underwriter’s reputation concerns can mitigate the incentive
problem between a firm raising capital (the agent) and a capital provider (the principal). In my paper, in
contrast, reputation concerns exacerbate the incentive problem between the VC (the agent) and his client
(the principal), but can still increase aggregate efficiency in equilibrium. Khanna and Matthews (2017) show
another downside of VC reputation: high VC reputation can exacerbate a hold-up problem and lead good
firms to loose VC backing.
7Such excessive “conservatism” is a common feature of career concerns models; see, ., Hölmstrom
(1999), Prendergast and Stole (1996), and Zwiebel (1995).
5
Since the VC’s decision to back the firm affects the firm’s ability to IPO in my
model, it is also related to papers on the feedback effects between financial mar-
kets and investment such as Boot and Thakor (1997), Bond, Goldstein, and Prescott
(2010), Dow and Rahi (2003), Bond and Goldstein (2015), Dow, Goldstein and Guem-
bel (forthcoming), Edmans, Goldstein, and Jiang (2015), Fulghieri and Lukin (2001),
Goldstein and Guembel (2008), Goldstein and Yang (2014), and Subrahmanyam and
Titman (2001).
2 Model
In this section, I present the model. In it, a firm gets initial backing from a VC that
takes an equity stake in the firm. Later, the VC takes the firm public in an IPO. After
the IPO, the value of the firm is realized. Critically, the VC’s incentives reflect profit
motivation and career concerns.
Players
Firms. In my model economy, there is a firm that is of one of two qualities θ ∈ {g, b},
where g stands for “good” and b for “bad.” The firm is good with probability ϕ. The
final value of the firm of type θ is Vθ. For the value to be realized, the firm must first get
initial backing from a VC and later raise capital I in an IPO. I refer to NPV of a firm of
type θ as NPVθ := Vθ−I and to the average NPV as NPV := ϕVg+(1−ϕ)Vb−I. Finally,
if the firm either fails to obtain backing from the VC or does not IPO successfully, it is
worth
VCs. There is a VC that can be one of two types, denoted by s and u, where s
stands for “skilled” and u for “unskilled.” The VC is skilled with probability γ ∈ (0, 1).
The difference between the skilled VC and the unskilled VC is that the skilled VC
knows the quality of the firm whereas the unskilled VC does not. I refer to a skilled VC
that observes θ = g as “positively informed” and to a skilled VC that observes θ = b as
“negatively informed.” I denote the VC’s action as a = 1 if it backs the firm and a = 0
if it does not. I assume, for simplicity, that whenever the VC backs the firm, it owns
all of the shares in the Later, when the firm raises capital at the IPO, the VC
8The assumption that the firm has value zero if it does not get funding is realistic for the kinds of start-up
ventures that VCs specialize in. That said, I explore an extension in which the unfunded firm has “assets in
place” with non-zero value in Subsection . The results are qualitatively the same as in the baseline model.
9None of the results would change if the VC instead received a smaller fixed fraction of the firm; this
would just amount to a linear transformation of its payoff. Even so, note that I assume that the VC either
backs the firm or not, but I do not model the precise terms at which the VC acquires its stake. Hence, the
VC cannot signal its information when it backs the firm, ., by buying at a high price. I abstract from this
signaling problem mainly for simplicity. However, it is realistic that outsiders cannot observe many of the
6
retains its shares (although it is diluted by new shares).10
IPO
If the VC backs the firm, the firm may sell an equity stake α ∈ (0, 1) in an IPO to
raise capital I from competitive These IPO bidders are uninformed; however,
they observe whether the firm receives VC-backing, which allows them to update their
beliefs about its quality. If the IPO bidders provide I they get the stake α in the firm
and the IPO is successful.
I use the variable ι to indicate the success of the IPO: ι = 1 if the IPO is successful
and ι = 0 otherwise, ., ι = 0 if either the VC does not back the firm or it backs the
firm and the IPO fails.
Timeline
The sequence of moves is as follows. First, the VC either backs the firm, a = 1, or
does not, a = 0. Second, if the VC has backed the firm, the firm may go public via an
IPO. If IPO bidders provide I then the IPO is successful, ι = 1. Otherwise, the IPO is
unsuccessful, ι = 0. Finally, if the IPO is successful, the long-run value of the firm Vθ is
realized and publicly observed; otherwise, the value of the firm is zero. This sequence
of moves is illustrated in Figure 1.
terms of these deals, and hence a VC’s ability to signal is limited.
10This is realistic, since VCs usually do not sell shares at the time of the IPO. Rather, they exit after a
“lock-up” period of several months after the IPO. Further, VCs often continue to hold shares long after the
lock-up period (see Gompers and Lerner (1998), p. 2164). Moreover, if I allowed VCs in the model to choose
the size of the stake to keep at IPO, they would behave this way endogenously. (To be specific, there would
be a pooling equilibrium in which all types of VCs retain the largest possible stake. Although this equilibrium
is not unique, it is the best equilibrium for skilled VCs with good firms, who want to retain as much of their
firms as possible to maximize the benefits of their private information; hence, it is “reasonable” in the spirit
of Banks and Sobel’s (1987) D1 criterion.) Nevertheless, in Subsection , I consider the variation of the
model in which the VC exits at the IPO. My main results all go through in that setting.
11Note that I have assumed that the stake α is strictly less than one. This assumption is standard in
IPO models: if there are n initial shares and N new shares sold in the IPO, the largest fraction of the firm
the IPO bidders can get is n/(n + N) < 1. This rules out cases in which the VC sells the entire firm and
gets nothing for it. Without this assumption, such cases could arise in equilibrium. These equilibria are
unrealistic, since they require that a VC goes through the trouble of backing a firm knowing that it will
never profit from it. This is a simple way to rule out these unappealing equilibria, without introducing a
cost of VC backing/monitoring, which introduces more complication/notation.
7
Figure 1: Sequence of Moves
the VC backs the firm a = 1 or does not a = 0
if the firm is backed by the VC, it goes public in an IPO
IPO bidders observe the VC’s action and decide to provide I or not
if the IPO is successful, the long-run value Vθ of the firm is realized
The VC’s Payoff—Profit Motivation and Career Concerns
The VC’s payoff takes different forms in different parts of the paper, reflecting the
different preferences of real-world VCs. Today, VC compensation has two parts: a
fixed fee and a variable fee or “performance fee,” which is typically a fixed fraction of
the VC’s profits. These fees vary from VC to VC. For example, younger VCs charge
a higher fixed fee and a lower performance fee than older and larger VCs. The fixed
portion of compensation is usually between % and 3% of the net asset value and
the variable portion is usually about 20% of profits (see Gompers and Lerner (1999)).
Whereas the ability to make profits is key to obtaining the performance fee, the ability
to build reputation is key to obtaining the fixed fee. In other words, VCs can increase
their compensation by improving their reputation as skilled investors. This allows them
to increase their committed capital by retaining old investors and winning new ones.
To analyze the effects of these two components of VC compensation, I study the two
extreme cases below, in which the VC is (purely) profit motivated or (purely) career
concerned. If the VC is profit motivated, I denote its payoff by ΠPM. This case is
standard; the VC’s payoff is proportional to the value of the VC’s long-term equity
holding, ., to the fraction 1− α of the firm that the VC holds after issuing α shares
in the IPO:
ΠPM =
⎧⎨
⎩(1− α)Vθ if IPO succeeds,0 otherwise. (1)
If the VC is career concerned, I denote its payoff by ΠCC. In this case, its payoff reflects
a VC’s reputation, which is equal to the market’s belief that a VC is skilled, given all
8
available information:12
ΠCC = P
[
skilled
∣∣∣ public information ] = P [s | a, ιVθ] . (2)
This expression says that a VC’s reputation consists of the market’s belief that the
VC is skilled based on all observables: the VC’s action a and potentially the long-run
realized value of the firm Vθ. Note, however, that Vθ is observable only if the firm
receives VC backing and successfully raises I in the IPO, or ι = 1. Hence, the belief
above is conditional on ιVθ (and not Vθ).13
Notation. Below, I sometimes differentiate between the payoffs of the skilled VC
and the unskilled VC with superscripts s and u. Further, I sometimes indicate how the
VC’s payoff depends on its action and the type of the firm in parenthesis. For example,
Πs
PM
(a = 1, θ = g) is the payoff of the skilled profit-motivated VC that backs (a = 1)
a good firm (θ = g).
Equilibrium Definition
The equilibrium concept is Perfect Bayesian Equilibrium. An equilibrium comprises the
action a ∈ {0, 1} for each type of VC as a function of its information and the decision to
provide capital I for the IPO bidders. All players’ actions must be sequentially rational
and beliefs must be updated according to Bayes’s rule on the equilibrium path.
Parameter Restrictions
I make two restrictions on parameters. The first one says that the average long-term
value of the firm is positive. The second one says that the bad firm’s long-term value
is negative.
Parameter Restriction 1.
V := ϕVg + (1− ϕ)Vb > 0. (3)
12Dasgupta and Prat (2006) show how these preferences arise endogenously from delegated investors’ in-
centives to attract flows of capital from investors. ., maximizing these flows is equivalent to maximizing
the market’s belief about skill.
13The assumption that the market conditions its beliefs on both ιVθ and a seems realistic. Anecdotal
evidence from Grant Thornton’s Global Equity Report (2016) suggests that VC investors do not look at only
returns (not at only ιVθ), but also demand “multiple meetings, huge amounts of due diligence questionnaires,”
(p. 10) and ask management to “disclose more information [and] to share details of investment pipelines” (p.
5). That said, this assumption is not necessary for my results, since ιVθ is sufficient to infer a in equilibrium—
ιVθ = 0 if and only if a = 0 (Proposition 1 and Proposition 2). Thus, my results also hold if the action a is
private information and the market conditions its beliefs on returns alone.
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Parameter Restriction 2.
Vb < 0. (4)
Parameter Restriction 2 captures the idea that the VC’s costs of monitoring and in-
vestments outweigh the benefits of investing in a bad firm. For simplicity, I capture
these costs in reduced form, by implicitly folding them into Vθ, ., Vθ represents the
value of the firm net of these In Subsection , I relax the assumption that
Vb < 0 and show that if Vb > 0 my results are amplified. However, restricting attention
to Vb < 0 in the baseline analysis helps me to focus on the new economic mechanism
in my paper.
3 Equilibrium Characterizations
In this section, I solve the model. The main results of the section are (i) a characteriza-
tion of the equilibrium given that the VC is profit motivated and (ii) a characterization
of the equilibrium given that the VC is career concerned. But, first, I solve for the stake
α required by the IPO bidders to provide capital to the VC-backed firm. This depends
on their belief about the proportions of good and bad firms that receive VC backing.
IPO Success
In this subsection, I solve for the stake α required by the IPO bidders to provide capital
to the VC-backed firm. Bidders are competitive, so they break even in equilibrium, .,
if they provide capital then α solves
αE
[
Vθ
∣∣ a = 1] = I. (5)
Since, as discussed in Subsection , it must be that α < 1, the IPO succeeds if and
only if the conditional expected value of the firm is greater than the cost of raising
capital I, as summarized in the next lemma.
Lemma 1. (IPO Success) The IPO succeeds if and only if
E
[
Vθ
∣∣ a = 1] > I. (6)
Equilibrium Characterization with a Profit-motivated VC
In this subsection, I first characterize the equilibrium in which firms successfully IPO
with a profit-motivated VC. I refer to this as the profit-motivation equilibrium. Then, I
14In Subsection , I model these costs explicitly to show that this reduced-form way of modeling them
does not affect my results.
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describe when the market breaks down, ., when there is no equilibrium in which the
VC backs the firm.
Proposition 1. (Equilibrium Characterization with a Profit-motivated
VC) Suppose the VC is profit motivated. If
ϕγNPVg + (1− γ)NPV > 0, (7)
then there is an equilibrium in which the positively informed VC and the unskilled VC
back the firm and the negatively informed VC does not. This is the unique equilibrium
in which the IPO is successful. Further, equilibria in which the IPO is not successful
are Pareto dominated. They are also not robust to a refinement formalized in the proof
of the proposition.
In the profit-motivation equilibrium above, the positively informed VC backs the firm
but the negatively informed VC does not. This is because the negatively informed
VC knows that the long-term value of the bad firm is negative, Vb < 0 (by Parameter
Restriction 2), so it will always lose if it backs the firm. However, the unskilled VC
knows that the long-term value of the average firm is positive, V > 0 (by Parameter
Restriction 1), so it gains on average if it backs the firm, even if the average net
present value is negative, or NPV < 0. The unskilled VC cares about the PV and
not the NPV because there is a cross-subsidy from the positively informed VC to the
unskilled VC at the time of the IPO. In other words, the unskilled VC has incentive
to over-invest, because it can sell over-priced shares in the IPO. This over-investment
reduces the average quality of VC-backed firms. Indeed, the quality reduction from
over-investment may be so severe that it causes the IPO market to break down entirely,
as I describe in the following corollary.
Corollary 1. (Market Breakdown with a Profit-motivated VC) Suppose
the VC is profit motivated. If
ϕγNPVg + (1− γ)NPV ≤ 0, (8)
then there is no equilibrium in which the VC backs the firm.
Observe that the market breaks down even though the VC may be skilled and may
have good information about the underlying quality of the firm. This is because the
unskilled VC pools with the skilled VC, which prevents the skilled VC’s action from
transmitting information to the IPO bidders. This in turn prevents the bidders from
providing the necessary capital at the time of the IPO.
11
Equilibrium Characterization with a Career-concerned VC
In this subsection, I first characterize the equilibrium in which firms successfully IPO
with a career-concerned VC. I refer to this as the career-concerns equilibrium. Then, I
describe when the market breaks down, ., when there is no equilibrium in which the
IPO is successful.
Proposition 2. (Equilibrium Characterization with a Career-concerned
VC) Suppose the VC is career concerned. If either γ ≥ ϕ/(1 − ϕ+ ϕ2) or
ϕγNPVg +
(
ϕγ(1 − ϕ)− γ + ϕ
)
NPV > 0, (9)
then there is an equilibrium in which the VC behaves as follows. If it is positively
informed it backs the firm, if it is negatively informed it does not back the firm, and if
it is unskilled it backs the firm with probability µ∗, where
µ∗ = max
{
0 ,
ϕγ(1− ϕ)− γ + ϕ
1− γ
}
. (10)
This is the unique equilibrium that satisfies a refinement formalized in the proof of the
proposition.
In the career-concerns equilibrium above, the skilled VC “follows its signal” to show off
its information—it backs the firm when it is positively informed and does not when it is
negatively informed. On the other hand, the unskilled VC has the incentive not to back
the firm, to hide its lack of information. Indeed, if the VC does not back the firm, then
the firm’s type is not revealed and, as a result, the market can never infer that the VC
is in fact unskilled. In other words, when the VC does not back the firm, an inference
channel is shut: the market bases its inference only on the VC’s action a = 0, since it
cannot use the value Vθ of the firm to update its beliefs. Thus, by playing a = 0, the
unskilled VC can always pool with the skilled (negatively informed) VC. If, instead, the
firm’s type were revealed regardless of whether it received backing from the VC, then
the unskilled VC would back the firm more often—playing a = 0 would not allow it to
hide. This is summarized in the next lemma.
Lemma 2. (The Unskilled VC Is Conservative) Consider the benchmark in which
the firm’s type is always revealed, ., the market learns the firm’s type even if ι = 0.
The unskilled VC backs the firm less frequently in the career-concerns equilibrium in
Proposition 2 than in this benchmark.
So far, I have explained why the unskilled VC would choose not to back the firm—it
allows it to pool with the skilled negatively informed VC. But why doesn’t the unskilled
VC always play a = 0? Because if it did, then the market would believe that only the
12
skilled VC was backing firms. So, if the unskilled VC backed a firm that turned out to
be good, the market would believe it was skilled for sure. This high upside payoff from
backing the firm and being right can compensate for the risk of backing it and being
wrong (and hence revealing itself as unskilled). This leads to mixing in equilibrium,
where the mixing probability varies as a function of the proportions of skilled VCs and
good firms, as described in the next lemma.
Lemma 3. (Comparative statics on µ∗) Given the equilibrium in Proposition 2, the
probability µ∗ with which the unskilled career-concerned VC backs the firm is increasing
in the proportion of good firms ϕ and decreasing in the proportion of skilled VCs γ.
Intuitively, the unskilled VC is more likely to back a firm that is likely to be good, since
it is likely to be right. Hence, µ∗ is higher when ϕ is higher. However, the unskilled VC
is less likely to back a firm when other VCs are likely to be skilled, since it can pool
with them by choosing not to back the firm. Hence, µ∗ is lower when γ is higher.
Career concerns induce the unskilled VC not to back the firm; however, there may
still be too much VC backing relative to first best in the career-concerns equilibrium—
the unskilled VC may still back a firm with negative expected NPV. As a result, market
breakdowns can still occur, as I describe in the following corollary.
Corollary 2. (Market Breakdown with a Career-concerned VC) Suppose
the VC is career concerned. If γ < ϕ/(1 − ϕ+ ϕ2) and
ϕγNPVg +
(
ϕγ(1 − ϕ)− γ + ϕ
)
NPV ≤ 0 (11)
then there is no equilibrium in which the VC backs the firm.
4 The Costs and Benefits of Career Concerns
In this section, I compare the profit-motivation equilibrium and the career-concerns
equilibrium. I show that career concerns can be beneficial in the following three senses.
(i) Whenever the IPO is successful, the value of the firm at IPO is higher when the
VC is career concerned than when it is profit motivated.
(ii) Market breakdowns are less likely when the VC is career concerned than when it
is profit motivated.
(iii) As long as the expected NPV is negative, total output or “productive efficiency”
is higher when the VC is career concerned than when it is profit motivated.
13
Career Concerns Prevent Market Breakdowns
In this subsection, I compare the likelihood of a market breakdown in the profit-
motivation equilibrium with the likelihood of a market breakdown in the career-concerns
equilibrium. I find that career concerns make market breakdowns less likely. This fol-
lows from the fact that the unskilled career concerned VC over-invests less than the
unskilled profit-motivated VC, as summarized in the next lemma.
Lemma 4. (Underinvestment) Absent market breakdowns, the career-concerned VC
backs the firm less frequently than the profit-motivated VC.
This leads to the next result, that the value of the firm at the time of the IPO is higher
when the VC is career concerned.
Lemma 5. (IPO Value Is Higher with Career Concerns) The value of the firm
at the time of the IPO is higher when the VC is career concerned than when it is profit
motivated:
E
[
Vθ
∣∣ a = 1]∣∣CC > E [Vθ ∣∣ a = 1]∣∣PM . (12)
The value premium associated with career concerns is the result of the behavior of
the unskilled VC. Because the firms that get backing and IPO are backed either by a
positively informed VC or an unskilled VC, the less frequently the unskilled VC backs
the firm, the more likely it is that a firm going IPO is backed by a positively informed
VC, and therefore is a good firm. Hence, firms backed by career-concerned VCs have
higher expected values than those backed by profit-motivated VCs. These higher firm
values lead to fewer market breakdowns as stated in the next proposition.
Proposition 3. (Career Concerns Prevent Market Breakdowns) Market
breakdowns are less likely with a career-concerned VC, in the sense that there is a
market breakdown with a profit-motivated VC whenever there is a market breakdown
with a career-concerned VC, but not the other way around.
This result underscores an important positive role that career concerns can play: they
alleviate the information frictions that prevent firms from being able to raise capital
and make positive-NPV investments. Since VCs back the firm relatively infrequently
in the career-concerns equilibrium, the firm’s expected value at the time of the IPO is
high, as Lemma 5 underscores. Thus, in the career-concerns equilibrium, VC-backing
has a certification effect. This certification effect induces IPO bidders to provide capital,
preventing market breakdowns.
14
Productive Efficiency
In this subsection, I compare productive efficiency in the profit-motivation equilibrium
with productive efficiency in the career-concerns equilibrium.
First, I give a formal definition of productive efficiency.
Definition 1. Productive efficiency is total output minus total input, or
W := ι
(
Vθ − I
)
. (13)
W measures net output because the NPV Vθ − I is realized only if I is successfully
raised in the IPO, or ι =
Now I can compare W in the profit-motivation equilibrium with W in the career-
concerns equilibrium.
Proposition 4. (Career Concerns Can Increase Efficiency) Productive ef-
ficiency is higher in the career-concerns equilibrium than in the profit-motivation equi-
librium if and only if the expected NPV is negative, NPV < 0.
This result points to another positive side of career concerns: with career concerns,
the VC filters out bad firms, increasing the average quality of firms that get backing.
If the average NPV of the firm is negative, then this increases productive efficiency.
However, if the average NPV of the firm is positive, it decreases productive efficiency.
In this case, it is better just to have average NPV firms backed indiscriminately (as in
the profit-motivation equilibrium), than to undertake only a selection of better firms
(as in the career-concerns equilibrium). Regardless of the sign of the average NPV, this
difference in productive efficiency is driven by the behavior of the unskilled VC. Indeed,
the more unskilled VCs there are, the larger is the absolute difference.
Corollary 3. (Productive Efficiency: Comparative Statics With Respect
to γ) The absolute difference between productive efficiency with a career-concerned VC
and with a profit-motivated VC is decreasing in the proportion of skilled VCs, .,
∂
∂γ
∣∣∣E [WCC]− E [WPM] ∣∣∣ ≤ 0. (14)
Proposition 4 says that career concerns help most when the average NPV is negative.
I now ask, given the average NPV is negative, when do career concerns help the most?
Do they help more when there are a lot of fairly good investment opportunities—high ϕ,
but low Vg—or when there are relatively few very good investment opportunities—low
ϕ, but high Vg?
15I think that W is a natural measure of efficiency—it basically coincides with GDP. However, it is worth
noting that this is not a transferable utility model, and career-concerned VCs have preferences not only over
consumption but also over reputation, so there is no perfect cardinal measure of welfare here.
15
Corollary 4. (Productive Efficiency: Comparative Statics With Respect
to ϕ) Suppose NPV < 0. For a given average NPV, the benefits of career concerns for
productive efficiency are decreasing in the proportion of good firms, ., if NPV < 0,
then
∂
∂ϕ
∣∣∣∣∣
NPV=const.
(
E [WCC]− E [WPM]
)
≤ 0. (15)
This result says that career concerns help the most in the environment in which VCs
operate in practice, ., in which most deals involve losing a little bit, but a few deals
(the Googles and the Facebooks) involve making a lot.
5 Extensions and Robustness
In this subsection, I extend the baseline model in several ways and I check the robustness
of the results above.
(i) I add “assets in place,” so that the market may learn about the firm’s type even
if it does not get VC backing.
(ii) I assume the VC sells its equity stake at the time of the IPO, instead of retaining
it.
(iii) I add asymmetric information among IPO bidders to generate an IPO discount.
(iv) I consider an alternative specification of the career-concerns component of the
VC’s preferences to capture a non-linear flow-performance relationship.
(v) I consider the case in which Vb > 0.
(vi) I consider the case in which the VC pays a cost to back the firm.
Assets in Place
In the baseline model, I assume that if the firm does not receive backing then its value is
zero. This assumption determines the VC’s behavior in the career-concerns equilibrium:
because both the good firm and the bad firm have value zero when the VC does not
back them, the market’s ability to update its beliefs about a VC that does not back
a firm is limited. In this subsection, I extend the model to include “assets in place,”
., the firm value is not necessarily zero if it does not receive backing from the VC.
If the firm receives backing from the VC and goes IPO, it undertakes an additional
“expansion” project. The degree of correlation, q, between the assets in place and the
expansion project captures the extent to which the VC can prevent the market from
learning by not backing the firm—if q = 1, the market learns the type perfectly from
the value of the assets in place regardless of whether the VC backs the firm. I show first
16
that the career-concerned VC’s behavior is qualitatively the same as it is in the baseline
model. Further, I argue that increasing q attenuates the benefits of career concerns for
market breakdowns (Proposition 3) and productive efficiency (Proposition 4).
Here I assume that if the firm is backed, Vθ is the overall value of the firm, ., the
sum of the value of the assets in place and the value of the new project. If the firm is
not backed, it keeps its assets in place with probability q. With probability 1− q it is
unable to continue at all and the firm value is zero. Specifically, the firm with quality θ
has value χvθ if it does not receive backing, where vθ << Vθ is the value of the assets in
place if the firm continues and χ is an independent indicator random variable indicating
whether the firm continues,
χ =
⎧⎨
⎩1 with prob. q,0 with prob. 1− q. (16)
The first result of this subsection is a characterization of the equilibrium, which is
analogous to the career-concerns equilibrium in Proposition 2.
Lemma 6. (Equilibrium Characterization with a Career-concerned VC
and Assets in Place) Suppose the VC is career concerned. The unskilled VC backs
the firm with probability µq defined by equation () in the proof. If
ϕγNPVg + (1− γ)µ
q NPV > 0, (17)
then there is an equilibrium in which a VC behaves as follows. If it is positively informed
it backs the firm, if it is negatively informed it does not back the firm, and if it is unskilled
it backs the firm with probability µq.
As in the career-concerns equilibrium, the positively informed VC backs the firm, the
negatively informed VC does not back the firm, and the unskilled VC randomizes
between backing and not backing. q captures the extent to which the market relies on
the VC backing the firm to make an inference about the firm’s type. Indeed, if q = 0,
the value of the assets in place is always zero, so the equilibrium coincides with the
career-concerns equilibrium in Proposition 2. In contrast, if q = 1, the assets in place
are perfectly correlated with the value of the firm, so the model coincides with the
benchmark in Lemma 2 in which the VC’s type is always revealed. Because there is no
asymmetric learning in this case, not backing the firm does not help the unskilled VC
to hide its type. The next lemma says that varying q interpolates between the baseline
model and the benchmark model in Lemma 2.
Lemma 7. (Assets in Place Interpolate Between Equilibria) Consider the
model with assets in place and a career-concerned VC. If q = 0, the equilibrium is
17
the career-concerns equilibrium of the baseline model in Proposition 2. If q = 1, the
equilibrium is the career-concerns equilibrium of the benchmark model in Lemma 2. For
q ∈ (0, 1) the unskilled VC backs the firm with probability µq where µq is a continuous
increasing function of q. ., increasing the correlation between the assets in place and
the expansion project monotonically interpolates between the career-concerns equilibrium
and the benchmark equilibrium.
This result implies that increasing q attenuates the effect of career concerns on market
breakdowns (Proposition 3) and on productive efficiency (Proposition 4).
Proposition 5. (Market Breakdowns and Efficiency with Assets in Place)
If the firm has assets in place, the results in Section 4 on the benefits of career concerns
are attenuated as follows:
• (IPO Value) The higher is q the lower is the value premium associated with career
concerns; ., the difference E
[
Vθ
∣∣ a = 1]∣∣CC − E [Vθ ∣∣ a = 1]∣∣PM is decreasing in
q.
• (Market Breakdowns) The higher is q the less career concerns help in pre-
venting market breakdowns.
• (Productive Efficiency) The higher is q the less career concerns affect pro-
ductive efficiency, ., the absolute difference
∣∣E [WCC] − E [WPM] ∣∣ is decreasing
in q.
VC Sells at the Time of the IPO
In the baseline model, I assume that the VC retains its equity stake until the final value
of the firm is realized. In this subsection, I consider the model in which the VC exits
at the time of the IPO. The main difference from the results in the baseline model is
that, in equilibrium, the negatively informed profit-motivated VC backs the firm. This
amplifies my results on the benefits of career concerns in Section 4 above.
Consider the variation of the model in which the VC exits at the IPO, selling its stake
at the market price. Here, the career-concerns component of the payoff is unaffected,
since it does not depend on profits, but only on the market beliefs. In contrast, the
profit-motivation component of the payoff is changed. It is now given by the market
value of the VC’s equity stake, rather than the private value to the VC. If the IPO
succeeds, the VC’s payoff is equal to the expected value of the long-term assets given
VC-backing, net of the investment cost:
ΠPM =
⎧⎨
⎩E
[
Vθ
∣∣ a = 1]− I if IPO succeeds,
0 otherwise.
(18)
18
Observe that this payoff does not depend on the VC’s type, but depends on only the
value that the market assigns to the firm at the time of the IPO. Thus, the positively
informed VC, the negatively informed VC, and the unskilled VC all make the same
profit. This implies that either no type of VC backs the firm or all do, including even
the negatively informed VC. The next result characterizes the equilibrium.
Lemma 8. (Equilibrium Characterization with a Profit-motivated VC that
Sells at IPO) Suppose the VC is profit motivated. If NPV > 0, then there is an
equilibrium in which the positively informed VC, the negatively informed VC, and the
unskilled VC back the firm.
Since even the negatively informed profit-motivated VC backs the firm in this equi-
librium, the over-investment problem in the profit-motivation equilibrium is especially
severe. As a result, the results on the benefits of career concerns in Section 4 are
amplified.
Proposition 6. (Benefits of Career Concerns when VC Sells at IPO) If
the VC sells at the IPO, it amplifies the results in Section 4 on the benefits of career
concerns as follows:
• (IPO Value) The value of the firm at the time of IPO is higher if the VC retains
its stake than if it exits,
E
[
Vθ
∣∣ a = 1]∣∣PM, retain > E [Vθ ∣∣ a = 1]∣∣PM, exit . (19)
Thus, the difference between the value of the firm with career concerns and the
value of the firm with profit motivation is even higher than in the baseline model
(Lemma 5).
• (Market Breakdowns) Whenever NPV < 0, there is no profit-motivation
equilibrium in which the VC backs the firm and the IPO is successful. Thus,
career concerns help prevent market breakdowns for a larger range of parameters
than in the baseline model (Proposition 3).
• (Productive Efficiency) Whenever
NPV <
ϕγNPVg
1− (1− γ)µ∗
, (20)
productive efficiency is higher in the career-concerns equilibrium than in the profit-
motivation equilibrium. Thus, career concerns increase productive efficiency for a
larger range of parameters than in the baseline model (Proposition 4).
19
IPO Discount
In the baseline model, I assume that all IPO bidders are uninformed. In this subsection,
I extend the model to include informed IPO bidders, following Rock (1986). I show
that the results on the benefits of career concerns in Section 4 are amplified whenever
there is adverse selection at the time of the IPO.
In the Rock (1986) model, bidders are rationed when the IPO is oversubscribed.
Because informed bidders subscribe to the IPO only when the firm is good, uninformed
bidders get the whole stake α when the firm is bad but only the rationed stake (1− δ)α
when the firm is good (δ reflects the proportion of the firm that goes to informed bidders
when the IPO is oversubscribed). Thus, the uninformed bidders’ break-even constraint
in equation (5) above is replaced by a version with rationing:
αE
[(
1− 1{Vθ=Vg}δ
) (
Vθ − I
) ∣∣ a = 1] = 0. (21)
This expression implies that there is a lower weight on the payoff when the firm is
good, Vg − I, relative to the payoff when the firm is bad, Vb − I. As a result, the
IPO price is lower, ., the shares are sold at a “discount” because of adverse selection.
Hence, market breakdowns are more likely. This risk of market breakdowns can make
career concerns even more important, since they help to increase the IPO price and
prevent market breakdowns (Lemma 5 and Proposition 3). Indeed, the larger is the IPO
discount δ, the more likely it is that career concerns enhance efficiency, ., Proposition
4 is extended to some positive NPV firms.
Proposition 7. (Career Concerns Can Increase Efficiency More with an
IPO Discount) Suppose that δ is the proportion of the firm that goes to informed
bidders at the IPO. Productive efficiency is higher in the career-concerns equilibrium
than in the profit-motivation equilibrium whenever
NPV <
(δ − γ)ϕ
1− γ
NPVg. (22)
Non-linear Flow-performance Relationship
In the baseline model, I assume that the career-concerns component of the VC’s payoff
ΠCC is linear in the market’s belief about the VC’s skill. However, empirically there is
a non-linear flow-performance relationship in asset management. Chevalier and Ellison
(1999) find that it is convex for mutual funds, whereas evidence in Crain (2016) and
Kaplan and Scholar (2005) suggests it is concave for venture capital and private equity,
respectively. In this subsection, I show that such a concave flow performance relation-
ship amplifies the results in Section 4 on the benefits of career concerns. However,
20
convexity typically induces risk-taking and, as a result, you might think that a convex
flow-performance relationship would overturn these results, leading career-concerned
VCs to back firms more frequently. I show that the first part of this intuition is right,
but the second is not: indeed, a convex flow-performance relationship induces the VC to
back firms more frequently, but it does not overturn the qualitative comparison between
profit motivation and career concerns.
Consider the variation of the model in which the career-concerns component of the
VC’s payoff is proportional to the market’s posterior belief about its type raised to the
power κ:
ΠCC =
(
P [ skilled | public information ]
)κ
=
(
P [s | a, ιVθ]
)κ
. (23)
This captures the convex flow-performance relationship for κ > 1, since then it is
a convex function of the market’s belief, and, likewise, it captures a concave flow-
performance relationship for κ ∈ (0, 1).
This different specification of ΠCC does not affect the profit-motivation equilibrium,
which depends only on ΠPM. The main result of this section is that it does affect
the career-concerns equilibrium. It induces the unskilled VC to back the firm more
frequently than in the baseline model if and only if the payoff is convex in the posterior
(κ > 1). However, it still backs the firm less frequently than in the profit-motivation
equilibrium for all κ > 0.
Proposition 8. (Equilibrium Characterization with a Career Concerned
VC with General Payoff) Suppose that the VC is career concerned with payoff
given by equation (23). If γ ≥ ϕ
1/κ
1−ϕ+ϕ1+1/κ
or
ϕγNPVg +
ϕ1/κ − γ
(
1− ϕ+ ϕ1+1/κ
)
1− ϕ+ ϕ1+1/κ
NPV > 0 (24)
then there is an equilibrium in which the VC behaves as follows. If it is positively
informed it backs the firm, if it is negatively informed it does not back the firm, and if
it is unskilled it backs the firm with probability
µκ = max
{
0 ,
γϕ
(
1− ϕ1/κ
)
− γ + ϕ1/κ
(1− γ)
(
1− ϕ+ ϕ1/κ
)
}
. (25)
The unskilled VC backs the firm more frequently than in the baseline model if and
only if the flow-performance relationship is convex, ., µκ > µ∗ in equation (10) if and
only if κ > 1.
21
Vb Positive
In the baseline model, I assume the final value of the bad firm is negative, Vb < 0.
This reflects a realistic idea: bad VC investments are likely to fail completely, and have
negative value net of the VC’s costs of monitoring and capital investment. However,
this assumption is not necessary for my results. In this subsection, I consider the model
in which Vb > 0. The VC’s equilibrium strategies in this setup coincide with those in
the extension in which the VC exits at the time of the IPO (Subsection ): the only
difference from the baseline model is that the negatively-informed profit-motivated VC
backs the firm. As I show in Subsection , this amplifies my results on the benefits
of career concerns in Subsection 4 above.
Consider the variation of the model in which Vb > 0. Here, the career-concerns
equilibrium is unaffected, since career-concerned VCs care about the market’s beliefs
alone and not profits. But the profit-motivation equilibrium changes: the VC backs
the firm whenever the expectation of its profit (as defined in equation (1)) is positive.
Since Vb > 0, this is now the case whenever the IPO is successful, or α ∈ (0, 1). As in
Subsection , this implies that either no type of VC backs the firm or all do, including
even the negatively-informed VC.
Lemma 9. (Equilibrium Characterization with a Profit-motivated VC when
Vb > 0) Suppose the VC is profit motivated. If NPV > 0, then there is an equilibrium
in which the positively informed VC, the negatively informed VC, and the unskilled VC
back the firm.
As in Subsection , the over-investment problem in the profit-motivation equilibrium
is even more severe here than in the baseline model, amplifying the baseline results on
the benefits of career concerns. In fact, Proposition 6 holds here.
Costs of VC Backing
In the baseline model, I assume that the VC gets profit (1 − α)Vθ if it backs the firm
and zero if it does not back the firm; in so doing, I implicitly assume that the cost of
any capital c that the VC provides upfront is embedded in the final payoff Vθ (see the
discussion in Subsection ). Normalizing c to zero simplifies the analysis, but it is not
immediate that it is without loss of generality. Here, I model this explicitly and show
that it is.
Consider the variation of the model in which the VC pays a cost c to back the firm.
Here, the career-concerns component of the payoff is unaffected, since it depends on the
market beliefs, not the profits. In contrast, the profit-motivation component changes.
22
If the VC backs the firm it gets
ΠPM =
⎧⎨
⎩(1 − α)Vθ − c if IPO succeeds,−c otherwise. (26)
If the VC does not back the firm it gets ΠPM = 0.
I show that the profit-motivation equilibrium (Proposition 1) and the career-concerns
equilibrium (Proposition 2) in the baseline model are the equilibria of the corresponding
extended model in which the VC has fixed cost c of backing the firm, under appropri-
ately modified conditions (in particular, I do not require that Vb < 0, since c > 0
captures the VC’s cost of backing the firm). This is summarized in the proposition
below.
Lemma 10. (Equilibrium Characterization with Upfront Costs) Suppose
ϕγNPVg + (1− γ)NPV
ϕγVg + (1− γ)V
V ≥ c ≥
ϕγNPVg + (1− γ)NPV
ϕγVg + (1− γ)V
Vb. (27)
As long as the IPO succeeds, the profit-motivation equilibrium strategies coincide with
those in Proposition 1 and the career-concerns equilibrium strategies coincide with those
in Proposition 2.
6 Conclusion
This paper examines the effects of the career concerns of delegated primary market
investors, namely venture capitalists. In contrast to the findings of the literature on
delegated investment in the secondary market, I find that career concerns can improve
efficiency. VCs can mitigate asymmetric-information frictions in the IPO market, allow-
ing good firms to raise capital due to a a certification effect of VC-backing. In summary,
this paper uncovers a new positive side of delegated investors’ career concerns that is
at work in the primary market.
23
A Proofs
Proof of Lemma 1
Whenever the IPO is successful,
α =
I
E
[
Vθ
∣∣ a = 1] , ()
by equation (5). Thus, α ∈ (0, 1) if and only if E
[
Vθ
∣∣ a = 1] < I.
Proof of Proposition 1
First, I verify that the outcome described in the proposition is an equilibrium (., that
everyone’s strategy is a best response). Second, I show that it is the unique equilibrium
in which the IPO succeeds. Third, I show it Pareto dominates equilibria in which
the IPO does not succeed. And, finally, I show that it is the unique equilibrium that
survives a refinement akin to the Intuitive Criterion.
Verification of the equilibrium
In this proof, I proceed by the usual conjecture-and-verify method of finding Perfect
Bayesian Equilibria. I conjecture an equilibrium in which (i) the positively informed
VC plays a = 1, (ii) the uniformed VC play a = 1, and (iii) the negatively informed
VC plays a = 0. Thus, the expected value of the firm conditional on a = 1 is
E [Vθ | a = 1] =
ϕγVg + (1− γ)V
ϕγ + 1− γ
. ()
Bidders. By Lemma 1, the IPO succeeds if the conditional expected value of the
firm exceeds I, or
ϕγVg + (1− γ)V
ϕγ + 1− γ
> I. ()
This is equivalent to condition (7) in the proposition.
Skilled VC. If the VC is skilled, then its payoff is (1− α)Vθ. Since 0 < α < 1 and
Vg > 0 > Vb, the negatively informed VC prefers not back the firm and the positively
informed VC prefers to back the firm.
Unskilled VC. If the VC is unskilled, then its payoff is (1−α)V . Since 0 < α < 1
and V > 0, the unskilled VC prefers to back the firm.
24
Uniqueness given IPO success
The VC’s best-responses above imply that whenever the IPO is successful, ., 0 < α <
1, the positively informed VC and the unskilled VC back the firm and the negatively
informed VC does not. Thus, the equilibrium is the unique equilibrium in which the
IPO succeeds.
Pareto dominance if IPO unsuccessful
There are also equilibria in which the IPO is unsuccessful (., if a VC that backs
the firm is believed to be negatively informed, then it is a best-response for no VC to
back the firm). These equilibria are Pareto dominated by the equilibrium stated in the
proposition. This is because in these equilibria all types of the VC get zero, whereas
in the equilibrium above, the positively informed VC and the unskilled VC get positive
expected payoffs and the negatively informed VC gets zero. (Bidders break even in
both types of equilibrium.)
Equilibrium selection in the profit-motivation equilibrium
Here I argue further that the equilibrium in which the positively-informed and the
unskilled VC back the firm is the “right” equilibrium. I show that in addition to being
Pareto-dominated, the equilibria in which the IPO is unsuccessful are not robust to a
belief-based refinement akin to the intuitive criterion.
I impose the following restriction on the bidders’ out-of-equilibrium beliefs: the
bidders believe that the deviations come from the type that has the most to gain, in
line with Banks and Sobel’s (1987) D1 Now consider an equilibrium in
which no type of VC backs the firm. The restriction on beliefs implies bidders believe
deviations come from the positively informed VC, since (1−α)Vg > (1−α)V > (1−α)Vb
whenever α ∈ (0, 1). Thus, the positively informed VC indeed deviates (as does the
unskilled VC), which rules out the equilibrium in which no type of VC backs the firm.
It may be worth pointing out that Cho and Kreps’s (1987) Intuitive Criterion also
rules out these equilibria in which no type of VC backs the firm whenever NPV >
0. This is because the Intuitive Criterion restricts beliefs such that bidders assign
16Specifically, in this model the D1 criterion would say that the bidders should believe that deviations
come from the positively informed VC whenever the following two conditions are satisfied: (i) for any belief
about bidders’ behavior for which the unskilled VC wants to deviate, the positively informed VC wants to
deviate too and (ii) for some beliefs about bidders’ behavior the positively informed VC wants to deviate
but the unskilled VC does not. I cannot apply this criterion directly here, since the beliefs that make the
unskilled VC want to deviate are exactly the same as those that make the positively informed VC want to
deviate, even though the positively informed VC’s payoff from deviating is higher. This is because the cost
of backing a firm is zero. Thus, I define a slightly stronger criterion in the text. Alternatively, I could add a
small cost of VC backing and apply the D1 criterion directly to obtain the same result.
25
zero probability to deviations that come from VC types that would be worse off from
deviating, no matter the bidders’ response. Since Vb < 0, this immediately implies the
bidders assign zero probability to deviations coming from the negatively informed VC.
Thus, bidders believe that the deviating VC is at worst unskilled. For positive average
NPV, bidders still provide capital and the unskilled VC deviates and backs the firm
(as does the positively informed VC). For negative average NPV, however, the bidders
will not provide capital if they believe the deviating VC is unskilled. Thus, I require
the stronger refinement above for some parameters.
Proof of Corollary 1
This result follows immediately from the proof of Proposition 1.
Proof of Proposition 2
First, I verify that the outcome described in the proposition is an equilibrium (.,
everyone’s strategy is a best response). Second, I show that this is the unique reasonable
equilibrium that is not perverse, as defined formally below.
Verification of the Equilibrium
In this proof, I proceed by the usual conjecture-and-verify method of finding Perfect
Bayesian Equilibria. I conjecture an equilibrium in which (i) the positively informed
VC plays a = 1, (ii) the negatively informed VC plays a = 0, and (iii) the unskilled VC
plays a = 1 with probability µ.
Beliefs. The market observes the VC’s action a and, if the IPO succeeds, it also
observes the long-run realized value of the firm Vθ. Given this information it updates
its beliefs about the VC’s type. The application of Bayes’s rule gives the following
posterior beliefs about the VC’s type:
P [s | ιVθ, a] =
⎧⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎩
0 if Vθ = Vb and a = 1,
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1− µ)
if a = 0,
γ
γ + (1− γ)µ
if Vθ = Vg and a = 1.
Unskilled VC. If the unskilled VC backs the firm its payoff is
E [ΠuCC(a = 1)] = ϕ
[
γ
γ + (1− γ)µ
]
. ()
This is because, when the VC backs the firm, the IPO succeeds, and the firm value is
26
realized. The firm can be bad or good. The firm is bad with probability 1−ϕ, in which
case the VC reveals that it is unskilled and earns nothing. With probability ϕ the firm
is good and the unskilled VC pools with the positively informed VC.
If the unskilled VC does not back the firm its payoff is
E [ΠuCC(a = 0)] =
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1− µ)
. ()
This is because, when it does not back the firm, the firm value is not realized, and the
market can only make inferences about the VC’s type by observing the VC’s action.
I now consider three possible cases: (i) the unskilled VC always backs the firm,
µ = 1, (ii) the unskilled VC never backs the firm, µ = 0, and (iii) the unskilled VC
backs the firm with probability µ ∈ (0, 1).
(i) The unskilled VC always backs the firm. µ∗ = 1 is an equilibrium if
E [ΠuCC(a = 1)] ≥ E [Π
u
CC(a = 0)] , ()
when µ∗ = 1. This reduces to
ϕγ ≥ 1, ()
which is never satisfied since γ ∈ (0, 1) and ϕ ∈ [0, 1]. Thus, it must be that
µ∗ < 1.
(ii) The unskilled VC never backs the firm. µ∗ = 0 is an equilibrium if
E [ΠuCC(a = 1)] ≤ E [Π
u
CC(a = 0)] , ()
when µ∗ = 0. This reduces to
γ ≥
ϕ
1− ϕ+ ϕ2
=: γ∗. ()
Thus, µ∗ = 0 is an equilibrium if and only if γ ≥ γ∗.
(iii) The unskilled VC backs the firm with probability µ ∈ (0, 1). µ∗ ∈ (0, 1) is an
equilibrium if
E [ΠuCC(a = 1)] = E [Π
u
CC(a = 0)] ()
or
ϕ
[
γ
γ + (1− γ)µ
]
=
(1− ϕ)γ
(1− ϕ)γ + (1 − γ)(1 − µ)
. ()
This reduces to
µ∗ =
ϕγ(1 − ϕ)− γ + ϕ
1− γ
. ()
This expression is between zero and one as long as the condition in equation
27
() is violated. Thus, we have that there is an interior equilibrium as long as
γ ∈ [0, γ∗), which is satisfied by hypothesis.
Bound for µ∗. Before proceeding with the proof, it is useful to establish a bound
on µ∗.
Lemma 11. If there is an interior µ∗ in equation (), we have that
µ∗ ≤ ϕ ≤
1
2− ϕ
. ()
Proof. The proof is by direct computation. From equation () above, we have that
µ∗ ≤ ϕ whenever
ϕγ(1 − ϕ)− γ + ϕ ≤ ϕ− γϕ ()
or ϕ ≤ 1, which is satisfied by assumption.
For the second inequality in the lemma, observe that ϕ ≤ 1/(2 − ϕ) whenever
(ϕ− 1)2 ≥ 0, which is always satisfied.
Skilled VC. I must show that the positively informed VC does not have a profitable
deviation from backing a good firm and that the negatively informed VC does not have
a profitable deviation from not backing a bad firm. The payoff of a positively informed
VC is
E [ΠsCC(a = 1, θ = g)] =
γ
γ + (1− γ)µ∗
()
if it backs the firm and
E [ΠsCC(a = 0, θ = g)] =
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1 − µ∗)
()
if it does not back the firm. The positively informed VC backs the firm if
E [ΠsCC(a = 1, θ = g)] ≥ E [Π
s
CC(a = 0, θ = g)] . ()
This inequality reduces to µ∗ ≤ 1/(2− ϕ) which is satisfied by Lemma 11 above.
The payoff of a negatively informed VC is
E [ΠsCC(a = 0, θ = b)] =
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1 − µ∗)
()
if it does not back the firm and
E [ΠsCC(a = 1, θ = b)] = 0 ()
if it does back the firm. The negatively informed VC does not back the firm if
28
E [Πs
CC
(a = 0, θ = b)] ≥ E [Πs
CC
(a = 1, θ = b)]. This inequality is always satisfied, since
expression in equation () is always positive.
Bidders. By Lemma 1, the IPO succeeds if the conditional expected value of
the firm exceeds I. Given the equilibrium strategies, the expected value of the firm
conditional on a = 1 is
E [Vθ | a = 1] =
ϕγVg + (1− γ)µ∗V
ϕγ + (1− γ)µ∗
. ()
Thus, the IPO succeeds if
ϕγVg + (1− γ)µ∗V
ϕγ + (1− γ)µ∗
> I, ()
or
ϕγNPVg + (1− γ)µ
∗NPV > 0. ()
There are now two cases to be considered: (i) γ ≥ γ∗, so µ∗ = 0 and (ii) γ < γ∗, so
µ∗ is as defined in equation ().
In case (i), inequality () is always satisfied; in fact, the inequality re-writes as
ϕγNPVg > 0, ()
which is always
In case (ii), inequality () is satisfied whenever
ϕγNPVg +
(
ϕγ(1 − ϕ)− γ + ϕ
)
NPV > 0, ()
This is the condition given in the statement of the proposition.
Equilibrium selection in the career-concerns equilibrium
In Proposition 2, I characterized the equilibria in which backing a good firm sends a
positive signal about the VC’s skill. However, there may be other equilibria. In this
subsection I show that they are not robust to a refinement, which I introduce now.
Here I extend the model to include a small number of behavioral types in order to
remove equilibria that are supported by “unreasonable” beliefs off the equilibrium path.
Specifically, suppose that with probability η the skilled VC “follows its signal,” ., it
backs if the firm is good and does not back if the firm is bad. I also assume that if
the VC backs the firm, the true type of the firm is revealed with probability δ.18 I will
focus on the limit in which η and δ go to zero (η = δ = 0 in the baseline model). By
introducing “noise” in this way, I ensure that there is not an action a ∈ {0, 1} that is
17Note that γ > 0 and that ϕ > 0 by Parameter Restriction 1 and Vb < 0.
18Including assets in place as in Subsection provides a micro-foundation for this assumption.
29
always off the equilibrium path. Thus I no longer have to deal with off-the-equilibrium
path beliefs.
I now define a perverse equilibrium.
Definition 2. (Perverse Equilibrium) An equilibrium is perverse if beliefs are such
that backing a good firm is viewed as a negative signal about VC skill and backing a bad
firm is viewed as a positive signal about VC skill, .,
P [s|a = 1, Vb] ≥ P [s|a = 1, Vg] . ()
I restrict attention to non-perverse equilibria, since in perverse equilibria the unskilled
VC would make higher profit than the skilled VC and hence investors would prefer to
invest with the unskilled VC rather than with the skilled VC.
The next result says that the equilibria characterized in Proposition 2 above con-
stitute all reasonable, non-perverse equilibria.
Proposition 9. (All Reasonable Non-perverse Career-concerns Equilib-
ria) For η → 0+ and δ → 0+, the equilibrium in Proposition 2 is the unique equilibrium
that is not perverse.
This result says that as long as investors believe that a VC is more likely to be skilled if
it backs a good firm than if it backs a bad firm, then the positively informed VC backs
the firm and the negatively informed VC does not.
Proof. First observe that there is no equilibrium in which all (strategic) types of VC
play a = 0 or a = 1. This is because there is always a proportion of skilled behavioral
types playing the other action. As a result, in any such pooling equilibrium, the VC
has incentive to deviate to the other action and pool with these behavioral types, since
it will be believed to be skilled.
Now I must show that there can be no non-perverse equilibrium in which the skilled
negatively informed VC backs the firm and the skilled positively informed VC does not
back the I prove that this cannot be the case by contradiction.
Suppose a non-perverse equilibrium in which the skilled negatively informed VC
backs the firm and the skilled positively informed VC does not back the firm. Thus the
following two conditions must be satisfied:
1. The skilled negatively informed VC (weakly) prefers to play a = 1.
2. The skilled positively informed VC (weakly) prefers to play a = 0.
19This includes mixed strategies. Formally: there can be no equilibrium in which both (i) the skilled
negatively informed VC plays a = 1 with positive probability and (ii) the skilled positively informed VC
plays a = 0 with positive probability.
30
Substituting for the career-concerned VC’s payoff, we can express these conditions as
follows:
δP [s | a = 1, Vb] + (1− δ)P [s | a = 1, ιVb] ≥ P [s | a = 0] ()
and
P [s | a = 0] ≥ δP [s | a = 1, Vg] + (1− δ)P [s | a = 1, ιVg] . ()
Combining these inequalities implies that
δP [s | a = 1, Vb] + (1− δ)P [s | a = 1, ιVb] ≥ δP [s | a = 1, Vg] + (1− δ)P [s | a = 1, ιVg] .
()
There are two cases to consider, ι = 0 and ι = 1. If ι = 0, P [s | a = 1, ιVg] =
P [s | a = 1, ιVb] so we have that
P [s | a = 1, Vb] ≥ P [s | a = 1, Vg] , ()
implying that if ι = 0 the equilibrium must be perverse. Thus, it must be that ι = 1.
But in this case the inequality above reads
δP [s | a = 1, Vb] + (1− δ)P [s | a = 1, Vb] ≥ δP [s | a = 1, Vg] + (1− δ)P [s | a = 1, Vg]
()
or
P [s | a = 1, Vb] ≥ P [s | a = 1, Vg] . ()
Again, this implies the equilibrium is perverse. This contradicts the hypothesis. Thus,
in all reasonable non-perverse equilibria the skilled positively informed VC plays a = 1
and the skilled negatively informed VC plays a = 0.
Proof of Lemma 2
I first verify that in equilibrium the positively informed VC backs the firm, the nega-
tively informed VC does not back the firm, and the unskilled VC randomizes, backing
the firm with probability µˆ. The proof is analogous to the proof of Proposition 2 (hence
I keep the derivation brief; see the proof of Proposition 2 for more detailed explanations
of the steps). Next, I compare the behavior of the unskilled VC in this equilibrium with
that in Proposition 2.
Beliefs. The market observes the VC’s action a and the long-run realized value of
31
the firm Vθ. Given this information it updates its beliefs about the VC’s type as:
P [s | ιVθ, a] =
⎧⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎩
γ
γ + (1− γ)(1 − µ)
if Vθ = Vb and a = 0,
0 if Vθ = Vb and a = 1 or Vθ = Vg and a = 0,
γ
γ + (1− γ)µ
if Vθ = Vg and a = 1.
Unskilled VC. If the unskilled VC backs the firm its payoff is
E [ΠuCC(a = 1)] = ϕ
[
γ
γ + (1− γ)µ
]
. ()
If the unskilled VC does not back the firm its payoff is
E [ΠuCC(a = 0)] = (1− ϕ)
[
γ
γ + (1− γ)(1− µ)
]
. ()
I now consider three possible cases.
(i) The unskilled VC always backs the firm. µˆ = 1 is an equilibrium if
E [ΠuCC(a = 1)] ≥ E [Π
u
CC(a = 0)] , ()
when µˆ = 1. This reduces to
ϕγ ≥ 1− ϕ. ()
Thus, µˆ = 1 is an equilibrium if and only if γ ∈
[
1−ϕ
ϕ , 1
]
, where the interval is
non-empty if and only if ϕ ∈
[
1
2 , 1
]
.
(ii) The unskilled VC never backs the firm. µˆ = 0 is an equilibrium if
E [ΠuCC(a = 1)] ≤ E [Π
u
CC(a = 0)] , ()
when µˆ = 0. This reduces to
ϕ ≤ (1− ϕ)γ. ()
Thus, µ∗ = 0 is an equilibrium if and only if γ ∈
[
ϕ
1−ϕ , 1
]
, where the interval is
non-empty if and only if ϕ ∈
[
0, 12
]
.
(iii) The unskilled VC backs the firm with probability µ ∈ (0, 1). µˆ ∈ (0, 1) is an
equilibrium if
E [ΠuCC(a = 1)] = E [Π
u
CC(a = 0)] , ()
or
ϕ
[
γ
γ + (1− γ)µ
]
= (1− ϕ)
[
γ
γ + (1 − γ)(1 − µ)
]
. ()
32
This reduces to
µˆ =
ϕ− γ(1− ϕ)
1− γ
. ()
Skilled VC. The payoff of a positively informed VC is
E [ΠsCC(a = 1, θ = g)] =
γ
γ + (1− γ)µˆ
()
if it backs the firm and
E [ΠsCC(a = 0, θ = g)] = 0 ()
if it does not back the firm. Thus, the positively informed VC always back the firm.
The payoff of a negatively informed VC is
E [ΠsCC(a = 0, θ = b)] =
γ
γ + (1− γ)(1− µˆ)
()
if it does not back the firm and
E [ΠsCC(a = 1, θ = b)] = 0 ()
if it does back the firm. Thus, the negatively informed VC never backs the firm.
Comparison between µˆ and µ∗. In the benchmark here, the unskilled backs the
firm with probability µˆ, where
µˆ =
⎧⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎩
0 if ϕ ∈
[
0,
1
2
]
and γ ∈
[
ϕ
1− ϕ
, 1
]
,
1 if ϕ ∈
[
1
2
, 1
]
and γ ∈
[
1− ϕ
ϕ
, 1
]
,
ϕ− γ(1− ϕ)
1− γ
if otherwise.
()
In Proposition 2, the unskilled backs the firm with probability µ∗, where
µ∗ =
⎧⎪⎪⎨
⎪⎪⎩
0 if γ ∈
[
ϕ
1− ϕ+ ϕ2
, 1
]
,
ϕγ(1 − ϕ)− γ + ϕ
1− γ
if otherwise.
()
Consider three cases: (i) γ ∈
[
ϕ
1−ϕ+ϕ2 , 1
]
, (ii) γ ∈
[
0, ϕ1−ϕ+ϕ2
]
and ϕ ≤ 1/2, and (iii)
γ ∈
[
0, ϕ1−ϕ+ϕ2
]
and ϕ > 1/2. In (i), µ∗ = 0, so µ∗ ≤ µˆ. In (ii), γ < ϕ1−ϕ+ϕ2 implies
that γ < ϕ1−ϕ . In this case,
µˆ =
ϕ− γ(1− ϕ)
1− γ
> max
{
0 ,
ϕγ(1 − ϕ)− γ + ϕ
1− γ
}
= µ∗.
33
In (iii),
µˆ = min
{
1,
ϕ− γ(1 − ϕ)
1− γ
}
≥ µ∗
by the argument in (ii).
Proof of Lemma 3
The result follows from differentiating the expression for µ∗ in equation (10). The result
is immediate if µ∗ = 0, since all derivatives are zero. If µ∗ > 0, we have
∂µ∗
∂ϕ
=
1 + γ(1− 2ϕ)
1− γ
> 0 ()
and
∂µ∗
∂γ
= −
(1− ϕ)2
(1− γ)2
< 0. ()
Proof of Corollary 2
The proof follows immediately from Proposition 2. When inequality () is not
satisfied, there is a market breakdown with a career-concerned VC. That is, there is a
market breakdown if
ϕγNPVg + (1− γ)µ
∗NPV ≤ 0, ()
or, substituting for µ∗ from equation (), if γ < ϕ/(1 − ϕ+ ϕ2) and
ϕγNPVg +
(
ϕγ(1 − ϕ)− γ + ϕ
)
NPV ≤ 0, ()
as stated in the proposition.
Proof of Lemma 4
The result follows immediately from comparing the profit-motivation equilibrium in
Proposition 1 with the career-concerns equilibrium in Proposition 2; in particular, it
follows from µ∗ < 1.
Proof of Lemma 5
Comparing the value of the firm when a profit-motivated VC backs it in equality ()
with the value of the firm when a career-concerned VC backs it in equality (), we
34
find that
E
[
Vθ
∣∣ a = 1]∣∣CC − E [Vθ ∣∣ a = 1]∣∣PM = 0 ()
whenever µ∗ = 1. Since
∂E
[
Vθ
∣∣ a = 1]∣∣CC
∂µ
= −
ϕ(1− ϕ)γ(1 − γ)(Vg − Vb)
(ϕγ + µ(1− γ))2
< 0 ()
and E
[
Vθ
∣∣ a = 1]∣∣PM does not depend on µ, the difference E [Vθ ∣∣ a = 1]∣∣CC−E [Vθ ∣∣ a = 1]∣∣PM
is decreasing in µ. In other words, inequality (12) is hardest to satisfy when µ = 1.
Thus, since it is satisfied when µ = 1, it is always satisfied.
Proof of Proposition 3
If VCs are profit motivated there is a market breakdown whenever inequality (8) is
satisfied, or if
τPM := ϕγNPVg + (1− γ)NPV ≤ 0; ()
if they are career-concerned, there is a market breakdown whenever inequality ()
is satisfied, or if
τCC := ϕγNPVg + (1− γ)µ
∗NPV ≤ 0. ()
Note that there are no breakdowns if NPV ≥ 0, so I focus on the case in which
NPV < 0.
To prove the proposition, I must show that τCC ≤ 0 implies τPM ≤ 0. This is the
case since
0 ≥ τCC
= ϕγNPVg + (1− γ)µ
∗NPV
> ϕγNPVg + (1− γ)µ
∗NPV + γµ∗NPV
= τPM.
Proof of Proposition 4
Let us consider the case in which there is an IPO both when a VC is profit motivated and
when it is career concerned (Proposition 1 and Proposition 2). In this case, the expected
productive efficiency (as defined in Definition 1) when the VC is profit motivated is
E [WPM] = ϕγNPVg + (1− γ)NPV; ()
35
and the expected productive efficiency when it is career concerned is
E [WCC] = ϕγNPVg + (1− γ)µ
∗NPV. ()
Productive efficiency is strictly higher when the VC is career concerned if E [WCC] >
E [WPM] , or, if
NPV < 0. ()
Proof of Corollary 3
The proof is by direct computation. Define
∆W := E [WCC]− E [WPM] . ()
So, substituting from equations () and (), we
∆W =
(
ϕγNPVg + (1− γ)µ∗NPV
)
−
(
ϕγNPVg + (1− γ)NPV
)
= −(1− γ)(1− µ∗)NPV.
()
Substituting for µ∗ from equation (10) into the expression for ∆W in equation (),
we have that
∆W =
⎧⎪⎨
⎪⎩
−(1− γ)NPV if µ∗ = 0,
−(1− ϕ)(1− γϕ)NPV otherwise.
()
Now, NPV does not depend on γ, so in both cases ∂∆W∂γ < 0 if and only if NPV < 0.
Now, the result follows from Proposition 4 which says that ∆W > 0 if and only if
NPV < 0.
Proof of Corollary 4
Substituting for µ∗ from equation (10) into the expression for ∆W in equation (),
we have that
∆W =
⎧⎪⎨
⎪⎩
−(1− γ)NPV if µ∗ = 0,
−(1− ϕ)(1− γϕ)NPV otherwise.
()
36
If µ∗ = 0 the result is immediate, since NPV = ϕVg + (1 − ϕ)Vb is increasing in ϕ. If
µ∗ ̸= 0, the result follows from direct computation:
∂∆W
∂ϕ
= (1 − γϕ)NPV + γ(1− ϕ)NPV − (1− ϕ)(1 − γϕ)(Vg − Vb), ()
This is negative since, for NPV < 0, each of the terms above is negative.
Proof of Lemma 6
The proof of this lemma is analogous to that of Proposition 2 of the characterization of
the career-concerns equilibrium. The only substantive difference is that with probably
q the type of the VC is revealed even if the firm does not get VC backing.
Beliefs. The market updates its beliefs given what is publicly observable. If the
firm receives backing from the VC (a = 1), then the market observes Vθ. If the firm
does not receive backing from the VC (a = 0), then the market observes the value of the
assets in place vθ if the firm continues (χ = 1). If the firm does not continue (χ = 0),
the market observes nothing about the quality of the firm. Applying Bayes’s rule gives
the following expression for the market’s beliefs:
P [s | ιVθ, a, (1 − ι)χvθ] =
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
0 if Vθ = Vb and a = 1,
0 if χ = 1, vθ = vg, and a = 0,
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1 − µ)
if χ = 0 and a = 0,
γ
γ + (1− γ)(1 − µ)
if χ = 1, vθ = vb, and a = 0,
γ
γ + (1− γ)µ
if Vθ = Vg and a = 1.
Unskilled VC. If the unskilled VC backs the firm its payoff is
E [ΠuCC(a = 1)] =
ϕγ
γ + (1− γ)µ
. ()
If the unskilled VC does not back the firm its payoff is
E [ΠuCC(a = 0)] =
(1− q)(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1− µ)
+
q(1− ϕ)γ
γ + (1− γ)(1− µ)
. ()
I now consider three possible cases. (i) µq = 1, (ii) µq = 0, and (iii) µq ∈ (0, 1).
(i) The unskilled VC always backs the firm. µq = 1 is an equilibrium if
E [ΠuCC(a = 1)] ≥ E [Π
u
CC(a = 0)] , ()
37
when µ = 1. This reduces to
γϕ ≥ 1− qϕ, ()
or
γ ≥
1− qϕ
ϕ
=: γq1 . ()
So, µq = 1 is an equilibrium if γ ∈ [γq1 , 1]. This interval is non-empty if and only
if γq1 ≤ 1 or both ϕ ∈ [
1
2 , 1] and q ∈ [
1−ϕ
ϕ , 1].
(ii) The unskilled VC never backs the firm. µq = 0 is an equilibrium if
E [ΠuCC(a = 1)] ≤ E [Π
u
CC(a = 0)] , ()
when µ = 0. This reduces to
γ(1− ϕ+ ϕ2)− ϕγ2q(1− ϕ)− ϕ
1− ϕγ
≥ 0. ()
Solving the quadratic equation above for γ, this implies that µq = 0 if and only if
γ ≥
1− ϕ+ ϕ2 +
√
(1− ϕ+ ϕ2)2 + 4ϕ2q(1− ϕ)
2qϕ(1 − ϕ)
=: γq0 . ()
(Note that we can restrict attention to the larger root of the quadratic equation
above, since the smaller root is always negative.) Thus, µq = 0 is an equilibrium
if γ ∈ [γq0 , 1]. This interval is non-empty if and only if γ
q
0 ≤ 1 or either ϕ ∈ [0,
1
2 ]
or both ϕ ∈ [12 , 1] and q ∈ [0,
1−ϕ
ϕ ].
(iii) The unskilled VC backs the firm with probability µq ∈ (0, 1). The VC must be
indifferent between backing the firm and not backing the firm, .
E [ΠuCC(a = 1)] = E [Π
u
CC(a = 0)] , ()
or
ϕγ
γ + (1− γ)µ
=
(1− q)(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1 − µ)
+
(1− ϕ)qγ
γ + (1− γ)(1 − µ)
. ()
This is a quadratic equation in µ. Definemq as its solution. So, there is an interior
equilibrium whenever mq ∈ (0, 1).
38
To sum up the unskilled VC’s equilibrium mixing probability µq is
µq =
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
0 if γ ∈ [γq0 , 1],
1 if γ ∈ [γq1 , 1],
mq otherwise.
()
Note that it is never the case that both γq0 < 1 and γ
q
1 < 1, so µ
q above is
generically unique.
Positively informed VC. The payoff of a positively informed VC is
E [ΠsCC(a = 1, θ = g)] =
γ
γ + (1− γ)µq
()
if it backs the firm and
E [ΠsCC(a = 0, θ = g)] =
(1− q)(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1− µq)
()
if it does not back the firm.
The positively informed VC backs the firm if
E [ΠsCC(a = 1, θ = g)] ≥ E [Π
s
CC(a = 0, θ = g)] .
This is always satisfied. To see this, consider three cases, (i) µq ∈ (0, 1), (ii) µq = 1,
and (iii) µq = 0.
(i) µq ∈ (0, 1). In this case, the unskilled is indifferent between backing the firm and
not backing the firm. Relative to the unskilled VC, the positively informed VC
has a higher expected payoff from backing the firm and a lower expected payoff
from not backing the firm, so it always prefers to back the firm:
E [ΠsCC(a = 1, θ = g)] ≥ E [Π
u
CC(a = 1)] = E [Π
u
CC(a = 0)] ≥ E [Π
s
CC(a = 0, θ = g)]
()
by comparing equation () with equation ().
(ii) µq = 1. In this case, the unskilled always prefers to back the firm than not to
back the firm. By the analogous argument to case (i), the skilled VC also prefers
to back the firm:
E [ΠsCC(a = 1, θ = g)] ≥ E [Π
u
CC(a = 1)] ≥ E [Π
u
CC(a = 0)] ≥ E [Π
s
CC(a = 0, θ = g)] .
()
39
(iii) µq = 0. In this case, the unskilled VC never backs the firm. Thus, the skilled
positive informed VC is never pooled with the unskilled VC if it backs the firm.
Thus, in equilibrium, the positively informed VC gets payoff equal to one, given
it knows the firm is good.
Negatively informed VC. The payoff of a negatively informed VC is
E [ΠsCC(a = 0, θ = b)] =
(1− q)(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1 − µq)
+
qγ
γ + (1− γ)(1 − µq)
()
if it does not back the firm and
E [ΠsCC(a = 1, θ = b)] = 0 ()
if it does back the firm. Thus it does not back the firm.
Bidders. By Lemma 1, the IPO succeeds if the conditional expected value of
the firm exceeds I. Given the equilibrium strategies, the expected value of the firm
conditional on VC backing is
E [Vθ | a = 1] =
ϕγVg + (1− γ)µqV
ϕγ + (1− γ)µq
. ()
Thus, the IPO succeeds if
ϕγVg + (1− γ)µqV
ϕγ + (1− γ)µq
> I. ()
This is the condition in the proposition.
Proof of Lemma 7
To see that µq = µ∗ when q = 0 and µq = µˆ when q = 1 observe that equation ()
that defines µq coincides with equation () that defines µ∗ when q = 0 and coincides
with equation () that defines µˆ when q = 1.
From equation (), µq is the solution of
ϕγ
γ + (1− γ)µ
−
(1− q)(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1− µ)
−
q(1− ϕ)γ
γ + (1− γ)(1 − µ)
= 0. ()
Implicitly differentiating with respect to q gives
∂µq
∂q
=
γ(1 − ϕ)
(1− ϕ)γ + (1− γ)(1− µ)
−
γ(1 − ϕ)
γ + (1− γ)(1− µ)
q(1− γ)γ(1− ϕ)
(γ + (1− γ)(1 − µ))2
+
(1− γ)γϕ
(γ + (1− γ)µ)2
+
(1− q)(1− γ) γ(1− ϕ)
((1− ϕ)γ + (1− γ)(1 − µ))2
≥ 0,
()
40
since both the numerator and denominator are positive. This derivate always exists, so
µq is continuous in q.
Proof of Proposition 5
The results follows directly from differentiation. First, compute the difference in IPO
values as
E
[
Vθ
∣∣ a = 1]∣∣CC − E [Vθ ∣∣ a = 1]∣∣PM = (Vg −NPV)(1 − γ)γϕ(1 − µ
q)
(ϕγ + 1− γ)(ϕγ + (1− γ)µq)
. ()
Note that it is decreasing in q:
∂
∂q
(
E
[
Vθ
∣∣ a = 1]∣∣CC − E [Vθ ∣∣ a = 1]∣∣PM
)
= −
(Vg − NPV)(1 − γ)γϕ
∂µq
∂q
(ϕγ + (1− γ)µq)2
, ()
since ∂µq/∂q ≥ 0 by Lemma 7 and Vg −NPV > 0.
Second, compute the difference in productive efficiency as
∣∣E [WCC]− E [WPM] ∣∣ = ∣∣(1− γ)(1− µq)NPV∣∣. ()
Note that it is decreasing in q:
∂|E [WCC]− E [WPM] |
∂q
= −
∂µq
∂q
|NPV|, ()
since ∂µq/∂q ≥ 0 by Lemma 7.
Proof of Lemma 8
The IPO is successful whenever the condition of Lemma 1 holds, or, given all types of
VC back the firm (so a = 1 is uninformative), if
E [Vθ]− I ≡ NPV > 0, ()
which holds by the hypothesis in the lemma.
Now, each type of VC gets NPV if it backs the firm. Thus, again since NPV > 0,
each type indeed backs the firm.
41
Proof of Proposition 6
IPO value. With exit at the IPO, all types of VC back the firm, so the expected firm
value at IPO is just the unconditional expected firm value
E
[
Vθ
∣∣ a = 1]∣∣PM, exit = ϕVg + (1− ϕ)Vb. ()
This is less than the expression for E
[
Vθ
∣∣ a = 1]∣∣PM, retention in equation ().
Market breakdowns. Market breakdowns occur whenever the expected firm value
conditional on VC backing is below I. The result above on the IPO value implies that
this is more likely in the version with exit at the IPO than in the baseline model.
Productive efficiency. First observe that we can focus on the case in which the
IPO is successful in the career-concerns equilibrium. This is because if the IPO is
unsuccessful in the career-concerns equilibrium, it is also unsuccessful in the profit-
motivation equilibrium (see the market breakdowns part of this proposition, proved
above); thus, productive efficiency is zero in both cases.
Now, if the IPO is successful, the productive efficiency in the profit-motivation
equilibrium with exit at the IPO is at most NPV and, as before, the productive efficiency
in the career-concerns equilibrium is given by equation (),
E [WCC] = ϕγNPVg + (1− γ)µ
∗NPV. ()
Thus, career concerns increase productive efficiency whenever NPV < E [WCC] or
NPV <
ϕγNPVg
1− (1− γ)µ∗
, ()
which is the equation in the proposition.
Proof of Proposition 7
First, I present two lemmata describing the profit-motivation equilibrium (Lemma 12)
and the career-concern equilibrium (Lemma 13). Then I prove the proposition, which
implies that the larger is the discount δ, the larger is the range of parameters for which
career concerns improve productive efficiency.
Lemma 12. Suppose the VC is profit motivated. If
(1− δ)ϕNPVg + (1− ϕ)(1− γ)NPVb > 0, ()
then there is an equilibrium in which the positively informed VC and the unskilled VC
back the firm and the negatively informed VC does not. If condition () is violated
42
then the VC does not back the firm.
Proof. The proof of this lemma is identical to the proof of Proposition 1 with the
exception of the behavior of the uninformed bidders. Hence, I omit the majority of the
proof.
Bidders. Since it must be that α < 1, the IPO succeeds if and only if the conditional
expected value of the firm is greater than the cost of raising capital I. From equation
(21), this is
E
[(
1− 1{Vθ=Vg}δ
) (
Vθ − I
) ∣∣ a = 1] > 0 ()
or
(1− δ)ϕ
ϕ+ (1− ϕ)(1 − γ)
(Vg − I) +
(1− ϕ)(1 − γ)
ϕ+ (1− ϕ)(1 − γ)
(Vb − I) > 0 ()
which is the condition in the lemma above.
Lemma 13. Suppose the VC is career concerned. As long as either γ ≥ ϕ/(1 − ϕ+ ϕ2)
or
(1− δ)ϕ2
(
1 + (1− ϕ)γ
)
NPVg + (1− ϕ)
(
ϕγ(1 − ϕ)− γ + ϕ
)
NPVb > 0, ()
then there is an equilibrium in which the positively informed VC backs the firm, the
negatively informed VC does not back the firm, and the unskilled VC backs the firm
with probability µ∗ as defined in equation (). If γ > ϕ/(1 − ϕ+ ϕ2) and condition
() is violated then the VC does not back the firm.
Proof. The proof of this lemma is identical to the proof of Proposition 2 with the
exception of the behavior of the uninformed bidders. Hence, I omit the majority of the
proof.
Bidders. From equation (21), the IPO succeeds if
(1− δ)ϕ
(
γ + (1− γ)µ∗
)
ϕγ + (1− γ)µ∗
(Vg − I) +
(1− ϕ)(1 − γ)µ∗
ϕγ + (1− γ)µ∗
(Vb − I) > 0. ()
Substituting for µ∗ from equation () it yields the condition in the lemma above.
Efficiency. If VCs are profit motivated there is a market breakdown whenever
τPM := (1− δ)ϕNPVg + (1− ϕ)(1 − γ)NPVb < 0. ()
Now observe that the condition in the proposition (equation (22)) is exactly the con-
dition for τPM < 0, so there is always a market breakdown if the VC is profit mo-
tivated. Hence, when this condition is satisfied, productive efficiency is zero in the
profit-motivation equilibrium. This implies immediately that productive efficiency is
43
weakly higher in the career-concerns equilibrium, since productive efficiency is never
negative. I now show that productive efficiency can be strictly higher, since there are
parameters satisfying this condition for which there is not a market breakdown with ca-
reer concerns. In particular, if the VC is career concerned there is a market breakdown
whenever
τCC := (1− δ)ϕ
(
γ + (1− γ)µ∗
)
NPVg + (1− ϕ)(1− γ)µ
∗NPVb < 0. ()
Now the result follows from the fact that τCC > τPM:
τCC − τPM = −(1− δ)ϕNPVg − (1− ϕ)NPVb > 0, ()
whenever inequality (22) is satisfied.
Proof of Proposition 8
The proof of this proposition is analogous to that of Proposition 2 of the characterization
of the career-concerns equilibrium. The only substantive difference is that the career-
concerned VC’s payoff is a non-linear function of its beliefs. I will outline only the
points of departure from that proof.
Beliefs. For a given mixing probability µ of the unskilled VC, the expressions are
the same as those characterized in Proposition 2.
Unskilled VC. I consider three possible cases: (i) the unskilled VC always backs
the firm, µ = 1, (ii) the unskilled VC never backs the firm, µ = 0, and (iii) the unskilled
VC backs the firm with probability µ ∈ (0, 1).
(i) The unskilled VC always backs the firm. µκ = 1 is an equilibrium if
E [ΠuCC(a = 1)] ≥ E [Π
u
CC(a = 0)] , ()
or
ϕ
[
γ
γ + (1− γ)µ
]κ
≥
[
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1 − µ)
]κ
, ()
when µ = 1. This reduces to
ϕ1/κγ ≥ 1, ()
which is never satisfied for κ > 0. Thus, it must be that µκ < 1.
(ii) The unskilled VC never backs a firm. µκ = 0 is an equilibrium if
E [ΠuCC(a = 1)] ≤ E [Π
u
CC(a = 0)] , ()
44
or
ϕ
[
γ
γ + (1− γ)µ
]κ
≤
[
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1 − µ)
]κ
, ()
when µ = 0. This reduces to
γ ≥
ϕ1/κ
1− ϕ+ ϕ1+1/κ
. ()
Thus, µκ = 0 is an equilibrium if and only if γ ≥ ϕ
1/κ
1−ϕ+ϕ1+1/κ
=: γk.
(iii) The unskilled VC backs a firm with probability µ ∈ (0, 1). µκ ∈ (0, 1) is an
equilibrium if
E [ΠuCC(a = 1)] = E [Π
u
CC(a = 0)] ()
or
ϕ
[
γ
γ + (1− γ)µ
]κ
=
[
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1 − µ)
]κ
. ()
This reduces to
µκ =
γϕ
(
1− ϕ1/κ
)
− γ + ϕ1/κ
(1− γ)
(
1− ϕ+ ϕ1/κ
) . ()
This expression is between zero and one as long as the condition in equation
() is violated, or γ ∈
[
0, γk
)
, which is satisfied by hypothesis.
Bound for µκ. Before proceeding with the proof, it is useful to establish a the
following lemma.
Lemma 14. If there is an interior µκ in equation (), we have that
µ∗ < µκ ()
if and only if κ > 1 and
µκ <
1
2− ϕ
, ()
whenver κ > 0.
Proof. The proof is by direct computation. From equations () and () above,
we have that
µ∗ − µκ =
(
1 + γ(1− ϕ)
)
(1− ϕ)
(
ϕ− ϕ1/κ
)
(1− γ)
(
1− ϕ+ ϕ1/κ
) < 0, ()
since 1 − ϕ + ϕ1/κ > 0 for κ > 0 and ϕ < ϕ1/κ if and only if κ > 1. This proves the
inequality in equation ().
From equation () above, we have that
µκ −
1
2− ϕ
= −
(
1 + γ(1− ϕ)
)
(1− ϕ)
(
1− ϕ1/κ
)
(1− γ)(2− ϕ)
(
1− ϕ+ ϕ1/κ
) ≤ 0, ()
45
since 1 ≥ ϕ1/κ and 1− ϕ + ϕ1/κ > 0 for κ > 0. This proves the inequality in equation
().
Skilled VC. The positively informed VC backs the firm if
E [ΠsCC(a = 1, θ = g)] ≥ E [Π
s
CC(a = 0, θ = g)] , ()
or [
γ
γ + (1− γ)µκ
]κ
≥
[
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1− µκ)
]κ
. ()
This inequality reduces to µκ < 1/(2 − ϕ) which is satisfied by Lemma 14 above.
The negatively informed VC does not back the firm if
E [ΠsCC(a = 0, θ = b)] ≥ E [Π
s
CC(a = 1, θ = b)] , ()
or [
(1− ϕ)γ
(1− ϕ)γ + (1− γ)(1− µκ)
]κ
≥ 0 ()
This inequality is always satisfied.
Bidders. Following from Lemma 1, the IPO succeeds if
ϕγVg + (1− γ)µκV
ϕγ + (1− γ)µκ
> I. ()
There are now two cases to be considered: (i) γ ≥ γk, so µκ = 0 and (ii) γ < γk, so
µκ =
γϕ
(
1−ϕ1/κ
)
−γ+ϕ1/κ
(1−γ)(1−ϕ+ϕ1/κ)
.
In case (i), inequality () re-writes as
ϕγNPVg > 0, ()
which is always
In case (ii), inequality () is satisfied whenever
ϕγNPVg +
ϕ1/κ − γ
(
1− ϕ+ ϕ1+1/κ
)
1− ϕ+ ϕ1/κ
NPV > 0. ()
This is the condition given in the statement of the proposition.
Given the equilibrium behavior of the skilled VC and bidders coincides with the
baseline model, Lemma 14 that µ∗ < µκ if and only if κ > 1—., if and only if the
flow-performance relationship is convex—establishes the proposition.
20Note that γ > 0 and that ϕ > 0 by Parameter Restriction 1 and Vb < 0.
46
Proof of Lemma 9
Suppose an equilibrium in which all types of profit-motivated VCs back the firm. Then,
the expected value of the firm conditional on a = 1 is
E [Vθ | a = 1] = V . ()
Bidders. By Lemma 1, the IPO succeeds if the conditional expected value of the
firm exceeds I, or
V > I. ()
This is equivalent to the condition in the proposition.
Skilled VC. If the VC is skilled, then its payoff is (1− α)Vθ. Since 0 < α < 1 and
Vg > Vb > 0 both the positively informed VC and the negatively informed VC back the
firm.
Unskilled VC. If the VC is unskilled, then its payoff is (1−α)V . Since 0 < α < 1
and V > 0, the unskilled VC backs the firm.
Proof of Lemma 10
Profit-Motivation Equilibrium
Suppose an equilibrium in which the VC’s behavior is as described in Proposition 1.
I must verify that it is indeed an equilibrium if Vb > 0 and the profit-motivated VC’s
payoff is as in equation (26).
Bidders. Following Lemma 1, the IPO succeeds if
ϕγVg + (1− γ)V
ϕγ + 1− γ
> I. ()
If this condition is not satisfied, firms’ value is not realized and VCs will not provide
initial capital c to the firms. If this condition is satisfied, the IPO succeeds and I can
solve for α from the bidders’ break-even condition in equation (5) as
α =
(
ϕγ + 1− γ
)
I
ϕγVg + (1− γ)V
()
Unskilled VC. I now verify that the unskilled VC prefers to back the firm rather
than not to back the firm. From equation (26), the unskilled VC’s expected payoff if it
backs the firm is
E [ΠuPM] = (1− α)V − c =
ϕγNPVg + (1− γ)NPV
ϕγVg + (1− γ)V
V − c, ()
47
having substituted for α from equation (). If this is positive, the unskilled VC
backs the firm.
Positively informed VC. The no-deviation condition for the positively informed
VC follows immediately from the no-deviation condition for the unskilled VC. This
is because the positively informed VC’s payoff is always higher, since it knows it will
receive (1− α)Vg − c > (1− α)V − c.
Negatively informed VC. The negatively informed VC must prefer not to back
the firm than to back the firm. Its expected payoff from backing is
E [ΠuPM] =
ϕγNPVg + (1− γ)NPV
ϕγVg + (1− γ)V
Vb − c. ()
If this is negative, it prefers not to back the firm.
Career-concerned Equilibrium
Since the payoff of the career-concerned VC does not depend on profits, it is not affected
by the addition of the upfront cost c. Thus, its behavior is unchanged.
48
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Introduction
Realism and Empirical Content
Related Literature
Model
Players
IPO
Timeline
The VC's Payoff—Profit Motivation and Career Concerns
Equilibrium Definition
Parameter Restrictions
Equilibrium Characterizations
IPO Success
Equilibrium Characterization with a Profit-motivated VC
Equilibrium Characterization with a Career-concerned VC
The Costs and Benefits of Career Concerns
Career Concerns Prevent Market Breakdowns
Productive Efficiency
Extensions and Robustness
Assets in Place
VC Sells at the Time of the IPO
IPO Discount
Non-linear Flow-performance Relationship
Vb Positive
Costs of VC Backing
Conclusion
Proofs
Proof of Lemma 1
Proof of Proposition 1
Proof of Corollary 1
Proof of Proposition 2
Proof of Lemma 2
Proof of Lemma 3
Proof of Corollary 2
Proof of Lemma 4
Proof of Lemma 5
Proof of Proposition 3
Proof of Proposition 4
Proof of Corollary 3
Proof of Corollary 4
Proof of Lemma 6
Proof of Lemma 7
Proof of Lemma 8
Proof of Proposition 6
Proof of Proposition 7
Proof of Lemma 9
Proof of Lemma 10
