Capital Assembly

34 Pages·2017·0.46 MB·English

Capital Assembly
Robert Akerlof and Richard Holden∗
February 10, 2018
Abstract
This paper explores the problem of assembling capital for projects. It can
be difficult to assemble capital, when it is disaggregated, for a project that
exhibits increasing returns. Small investors may be reluctant to participate,
as they may question the ability of the project owner to raise the additional
capital he requires. This suggests the possibility that agents with blocks of
capital (capital that is already aggregated) might earn rents. Similarly, agents
with “network capital” — that is, an ability to aggregate the capital of others
— may earn rents. In this paper, we develop a simple theory of the rents
attachedtocapitalassembly,anddiscusstheimplicationsforarangeofissues
frominvestment,togrowth,toinequality.
∗Akerlof: University of Warwick. email: [email protected]. Holden: UNSW Australia
Business School. email: [email protected]. We are grateful to George Akerlof, Pol
Antras, Rosalind Dixon, Drew Fudenberg, Bob Gibbons, Ben Golub, Sanjeev Goyal, Hongyi Li,
JeremyStein,andLuigiZingalesforhelpfuldiscussions,andseminarparticipantsatBrown,Cam-
bridge,LBS,Harvard,MIT,UWA,Warwick,theJapan-HongKong-TaiwanContractTheoryWork-
shop,andthe10thAustralasianOrganizationalEconomicsWorkshop. Akerlofacknowledgessup-
port from the Institute for New Economic Thinking (INET). Holden acknowledges support from
theAustralianResearchCouncil(ARC)FutureFellowshipFT130101159.
1 Introduction
Thispaperexplorestheproblemofassemblingcapitalforprojects. Undertheusual
economic assumption of decreasing-returns-to-investment, this problem does not
arise; but when there are increasing returns over some range, investors may only
be willing to invest in projects when they believe others are willing to do so. In
such instances, assembling capital (or coordinating investors) is a relevant — and
often critical — consideration. This paper addresses the issue by viewing the pro-
cess of assembling capital as part of the equilibrium, and it explores the conse-
quences of capital assembly for a range of features of investment. One striking
implication is that certain agents who possess a privileged network position can
usetheir“networkcapital”toimproveoverallinvestmentandtheyreceiveoutsize
returns for doing so. Our theory also predicts that investors with blocks of capi-
tal will serve as anchor investors for projects and earn higher rates of return than
smallinvestors.
Ourtheoryspeakstoafundamentalaspectoftheinvestmentprocessthatexist-
ing models fail to address. In contrast to existing theories, which assume surplus
maximization, we emphasize the importance of scarce resources — network cap-
ital and block capital — for the execution of valuable projects. This implies that
these resources earn rents — potentially large ones — in market equilibrium. It
also implies that institutions may be important, as they may affect the supply of
these scarce resources, and hence the extent to which valuable projects are imple-
mented.
We analyze a model in which a project owner tries to raise capital for a project
that exhibits increasing returns over some range. We first show that by making an
anchor investment in the project, a large investor with a block of capital can move
theprojectfroma“bad”equilibriumwithlowinvestmenttoa“good”equilibrium
with high investment. Since a large investor spurs others to invest by making an
anchor investment, he need not finance the entire shift to the good equilibrium
himself. Wecharacterizetheminimumcapitalblock-sizeneededtoeffectashiftto
thegoodequilibrium—aswellastherateofreturnearnedonsuchaninvestment.
Interestingly, by holding a subordinated claim rather than a senior claim (equity
orjuniordebt),alargeinvestorcanmovetheprojecttothegoodequilibriumwith
1
asmallerblockofcapital.1
Wethenconsiderthepossibilityofacentralnetworkactorgeneratingarentby
coordinating small investors on a high level of investment; and we discuss how
thismightbemicro-founded.
Akeygoalofthepaperistodevelopasimpleapproachtotheproblemofcapital
assembly and increasing returns that can be applied in a variety of settings. The
details of our analysis, while subtle, can largely be ignored once they have been
considered. Ourformalmodelisgame-theoretic;butitboilsdowntoamodelthat
is essentially price-theoretic.2 We present this simpler, price-theoretic treatment in
Section2andourformalmodelinSection3.
Therearemany“real-world”examplesthatillustratethecapital-assemblyprob-
lem. ConsiderthefoundingofFederalExpressbyentrepreneurFredSmith. Itses-
tablishment required significant capital investment upfront. Before the company
could even open its doors, it needed to have in place a fleet of jets, a central hub
with sorting facilities, and pickup and delivery operations in twenty-five cities.
Furthermore, capital was needed to cover the losses the company could expect to
runforthefirstseveralyears(four,asitturnedout)whileitbuiltupdemandforits
service. While the company eventually became a great success, obtaining investor
participation early on was “like herding cats,” according to Charlie Lea, a venture
capitalistwhoworkedwithSmith.3
Smith relied heavily on his social connections to coordinate investors on the
ideaofhiscompany. AgraduateofYale,hehadbeenamemberofSkullandBones,
where he befriended both George W. Bush and John Kerry; and he established
valuable contacts in the airline industry running a business with his stepfather
that bought and sold jets. Smith was also a talented communicator and salesman.
As one early FedEx employee put it: “Fred turned on the charm in a way that few
otherscanmatch.”4
The success of the company also depended heavily upon Smith’s ability to as-
1Asubordinatedclaimfacilitatescoordination;butalargeinvestormaypreferaseniorclaimif
theprojectisrisky. Seetheconclusionforfurtherdiscussion.
2BulowandRoberts(1989)’spaperonoptimalauctionshasasimilaraim. Theydeveloparig-
orousmechanism-designmodelbutshowthattheirresultscanbereinterpretedinthelanguageof
standardmicrotheory.
3Frock(2006),p. 105.
4Frock(2006),p. 62.
2
sembleatop-notchmanagementteam;thistaskinvolvedcoordinationaswell. For
instance, FedEx’s initial COO Roger Frock remarked: “How could I even consider
joiningFredinhiscrazyscheme?...I...knewthatArt’s[headofairoperations]broad
visionandmellowpersonalitywouldbetremendousassetsforFederalExpress.”5
Warren Buffett’s investment in Goldman Sachs provides a good illustration of
the power of blocks of capital. In September of 2008, soon after the collapse of
Lehman Brothers, Buffett agreed to provide Goldman with $5 billion of capital.
His investment, plus the additional $2.5 billion Goldman was able to raise from
small investors on the back of his investment, helped Goldman weather the fi-
nancial crisis. The deal was made on very favorable terms to Buffett. Berkshire
Hathaway (Buffett’s company) received a 10% annual dividend on its “perpetual
preferred”stock,pluswarrantstobuy$5billionofcommonstockat8%percentbe-
lowthepreviousday’sclosingprice.6 Bycomparison,theinvestorswhoprovided
theadditional$2.5billiondollarsdidnotreceivenearlyasfavorableterms.
Thereisempiricalsupportfortheideathatsocialconnectionsyieldsubstantial
returns. Hochberg et al. (2007), for instance, find that socially connected venture
capital firms do especially well. The VC industry, in general, is characterized by
strong network ties among VC firms that typically syndicate their deals with oth-
ers. Hochberg et al. (2007) find that the “centrality”7 of VCs in their network in-
crease their internal rates of return from 15% to 17% for a one-standard deviation
increase in centrality. Similarly, they find that the more central a VC firm, the bet-
ter the performance of its portfolio companies. A one standard deviation change
inVCcentralityincreasestheprobabilitythataportfoliocompanysurvivesitsfirst
funding-round from 66.8% to 72.4%. A possible interpretation of their findings is
that VC firms provide startups with network capital in exchange for a share of
their returns. Indeed, the well-known venture capitalist Marc Andreessen sees his
mainroleasto“giveourfounders...networkingsuperpower.”8
Outside of economics, sociologist Ronald Burt pioneered the idea that social
capital matters for finance and entrepreneurship (see Burt (2004)). More recently,
5Ibid.,p. 95.
6Bary, Andrew, “WarrenBuffettMakesanOfferGoldmanSachsCan’tRefuse,” TheWallStreet
Journal28September2008,Retrievedfromhttp://www.wsj.com.
7Inthesenseof“eigenvectorcentrality”(Bonacich(1972)).
8Tad Friend, “Tomorrow’s Advance Man,” New Yorker, May 18, 2015, retrieved from http:
//www.newyorker.com.
3
economists have begun to explore the role of social capital for finance (see Guiso
et al. (2004); Hong et al. (2004, 2005), and Gompers etal. (2005)). We see our paper
ascontributingprimarilytothis(stillnascent)literature.
The most closely related paper is Akerlof and Holden (2016). In that paper, we
consider a specific setting in which a networked agent — a “mover and shaker”
— can increase aggregate investment and earn a rent. This paper gives a far more
general treatment of the capital-assembly problem; it is also much simpler. We ac-
complishthisbystrippingoutinformationalconsiderationsandfocusingsquarely
on agents’ coordination problem (using risk dominance rather than global games
as a refinement concept). Our methodology does not require us to make any as-
sumptions about the shape of production functions. It reveals the importance of
blockcapitalaswellasnetworkcapitalforcoordinatinginvestors. Importantly,we
are also able to embed our analysis within a market and study the nature of equi-
librium: both how block capital and network capital are deployed and the rents
theycommand.
Murphy et al. (1989) explore the idea that increasing returns can generate mul-
tipleequilibria. Theyproposethisasareasonforpovertytraps.9,10
Thereisalargeliteratureincorporatefinanceonthevalueofcontrollingblocks
and large shareholders (see Grossman and Hart (1980) and Shleifer and Vishny
(1986) for early contributions and Becht et al. (2003) for further discussion and
references). In these models, the value of large stakes comes from control rights;
but there is scant consideration of the coordination problems involved in raising
capital.
Our paper is also related to the literature on contribution games — especially
Andreoni (1998). In a charitable-giving context, he considers the role of a large
contributor or government in achieving successful coordination. Relative to An-
dreoni (1998), the novel features of our analysis are our focus on an investment
9By contrast, Romer (1986) considers increasing returns that come from technological rather
thanpecuniaryexternalities. Relatedly,AghionandHowitt(1992)emphasizethefactthattechno-
logicalinnovationsimprovethequalityofproducts,renderingprevious,inferiorones,obsolete.
10Thepresenceofincreasingreturnsinourmodelalsonaturallybringstomindthetradelitera-
tureonthesubject—especiallyKrugman(1980,1981),Helpman(1981),andHelpmanandKrug-
man(1985). Thesemodelsfocusonadifferentissuefromourpaper. Theyassume,incontrast,that
the efficient scale can easily be achieved. They explore the tradeoff between efficiency (which is
achievedbyindustriesbeinglarge)andvariety(forwhichconsumershaveapreference).
4
context and our examination of the rents associated with playing a pivotal role in
coordination.11
Building on the work of Segal (1999), who initiated a literature on contract-
ingwithexternalities,BernsteinandWinter(2012)andSakovicsandSteiner(2012)
studysettingswherelargeplayerscanearnrentsbecauseofthepositiveexternali-
tiestheyimposeonsmallerplayers. Anexamplewouldbeashoppingmallopera-
torofferingadiscountedrentalratetoanationalbrandstoreduetoitsimportance
indrivingtraffictosmallerstores.12
The remainder of the paper is organized as follows. Section 2 gives the simple
price-theoretic treatment of our model. Section 3 develops the model more for-
mally. We first examine the role a large investor can play in assembling capital for
a project; we then embed our analysis in a market setting (with multiple projects)
and analyze the market equilibrium; finally, we consider the role that networked
agents can play and examine the returns to network capital. Section 4 discusses
a set of issues related to network capital such as: how it is acquired and whether
agents can invest in it. Section 5 considers some issues raised by our theory and
containssomeconcludingremarks.
2 A simple treatment of the capital-assembly problem
Imagine a project owner is trying to assemble capital for a project. When k units
ofcapitalareinvestedintheproject,ityieldsareturnf(k). Ourtheorycanhandle
production functions with any shape; for the purposes of illustration, though, as-
sume f(k) has the shape shown in Figure 1.13 The production function in Figure 1
exhibits increasing returns for intermediate values of k and decreasing returns for
highandlowvaluesofk.
11Thereisalsoaliteratureon“catalyticfinance”which, unlikeus, considerstheroleofalarge,
non-strategicplayer,suchastheIMF,inavoidingcoordinationfailuresinanon-marketsetting(see,
forinstance,Corsettietal.(2006)andMorrisandShin(2006)).
12Oursettingdifferssinceallplayersimposeexternalitiesonallothers(thoseexternalitiesbeing
proportional to players’ size). Bernstein and Winter (2012)’s and Sakovics and Steiner (2012)’s
argumentwhythelargeplayerearnsrentsdoesnotapplyinoursetting.Inourtheorylargeplayers
earnrentsforadifferentreason: theirparticularabilitytoplayacoordinatingrole.
13Foradiscussionofhowourtheorygeneralizestof(k)ofanyshape,seeSection3.4.
5
f(k)

Δ
2
Line 1

Line 2

slope = 1 + r
mkt
Δ
1
k
k k k1 k2 k3 k
L M M M H
Figure1–Anexample
Case1: Smallinvestorsonly
Suppose there are many risk averse investors, each with only a small amount
ofcapital. Theycaninvestintheprojectorearnamarketrateofinterest,r .
mkt
Wewillshowinthenextsectionthattherearetwoequilibria,onegoodandone
bad; however, the bad equilibrium is likely to prevail. In the bad equilibrium, the
project owner obtains k units of capital at the market interest rate and receives
L
a payoff of ∆ . In the good equilibrium, the project owner receives the surplus-
1
maximizingamountofcapital,k ,atthemarketinterestrateandreceivesapayoff
H
of∆ > ∆ .
2 1
Why is the bad equilibrium likely to prevail? Observe that there is a region
in which the project is in the “red,” yielding an insufficient return to pay off in-
vestors (f(k) < (1+r )k). In Figure 1, this is the region between k1 and k3 , in
mkt M M
which f(k) dips below Line 1. Investors take a risk when they try to coordinate
on lending k rather than k , since the project may end up in the region in which
H L
it is undercapitalized and in the “red.” In game-theoretic terms, the bad equilib-
rium “risk dominates” the good one. There is a large literature showing that risk
dominantequilibriatendtobefocal.14
14FornotableearlycontributionsseeCooperetal.(1990)andHuycketal.(1990).
6
Tosummarize,wefindthatabadequilibrium,withak -levelofinvestment,is
L
likely to prevail when capital is disaggregated (i.e., investors have only negligible
amountsofit).
Case2: Onelargeinvestor
Let us assume now that, in addition to small investors, there is a large investor
withablockofcapitalofsizek .
block
Alargeinvestorwithablockofcapitalcanpotentiallyensuretheoptimallevel
of investment (k ). It is obvious that he can do so if k ≥ k ; but he may be
H block H
abletobringabouttheoptimallevelofinvestmentevenifheisunabletofundthe
entireproject. Forinstance,ablockofsizek3 −k1 isadequate. Smallinvestorsare
M M
happy to lend when the project is in the “black”; there is only reluctance to lend
between k1 and k3 , when the project is in the “red.” A block of size k3 − k1 is
M M M M
enoughtobridgethisgap.
Infact,itturnsoutthatthelargeinvestorcanbringaboutthegoodequilibrium
with less capital still. It is sufficient to have a block of size k (k is graphically
represented in Figure 1). Suppose the large investor loans k for the project and,
additionally, enables the project owner to pay off small investors first. (This could
be achieved either by taking junior debt or equity in the project.) Small investors
are paid off in this scenario so long as f(k) does not dip below Line 2. f(k) is
tangent to Line 2 at k2 but never dips below; hence, small investors are certain to
M
bepaidoff. Sincesmallinvestorsneednotworryaboutbeingpaidoff,theywillbe
willing to provide the project owner with the additional capital he needs to reach
thegoodequilibrium.
Therefore,alargeinvestorwithablockofsizek ≥ k cangenerateasurplus
block
ofsize∆ −∆ .
2 1
Marketratesofreturn: largeversussmallinvestors
Consider next a market setting, with many projects, in which interest rates are
endogenous. In a competitive capital market, if block capital is scarce, large in-
vestorsearnhigherratesofreturnthansmallinvestors. Largeinvestorsreceive,in
additiontor ,thesurplustheirblockshelpgenerate.
mkt
7
For example, an investor with a block of size k who invests in a project of the
typeshowninFigure1receives(1+r )k+(∆ −∆ ).15 Hethereforeearnsarate
mkt 2 1
ofreturn:
∆ −∆
2 1
r = r + .
mkt
k
The difference between large investors’ and small investors’ rates of return is
potentially quite significant. A numerical example helps to illustrate. Figure 1
corresponds to a particular numerical example in which r = 5% and f(k) =
mkt
2.55k −0.0975k2 +0.0016k3 −0.0000075k4. In the good equilibrium, k = 100 and
H
∆ = 25; in the bad equilibrium, k = 10 and ∆ = 6.775. The block size needed
2 L 1
to reach the good equilibrium is k = 14.881. It follows that r = 127.5%. Therefore,
whileasmallinvestorearnsareturnof5%,aninvestorwithablockofsizek earns
areturnof127.5%.
NetworkCapital
Suppose investors are networked. It might be possible for a central network
actor(C)tousehispositiontocoordinatesmallinvestorsonahighlevelofinvest-
ment. AgentCsubstitutesforablockinvestor;hence,heshouldearnanequivalent
rent in a market equilibrium (i.e., ∆ − ∆ if the block investor for which he sub-
2 1
stitutesreceivesarentof∆ −∆ ).
2 1
We can think of agent C as possessing “network capital” and we can think of
∆ −∆ astherentagentCearnsonhisnetworkcapital.
2 1
3 The formal model
This section develops the model more formally. It is organized along similar lines
toSection2. Sections3.1through3.4considerasettinginwhichaprojectowneris
tryingtoraisecapitalfrominvestors. Weinitiallyassumethatthereareonlysmall
investors; we then show that a large investor can improve the overall level of in-
vestment. Section3.5movestoamarketsetting,withmanyprojects,andexamines
15Theprojectownerreceivesapayoffof∆ . Becauseofcompetitionbetweenprojectownersto
1
obtainblockcapital,theblockinvestorreceivestheentiresurplusfromreachingthegoodequilib-
rium(∆ −∆ ).
2 1
8
the market equilibrium. Interest rates are endogenous (in contrast to Sections 3.1
through 3.4). Finally, Section 3.6 discusses network capital and proposes one pos-
siblemicro-foundation.
3.1 Setup
The owner of a project is trying to raise capital from a set of potential investors
(i ∈ {1,2,...,n}). Eachinvestorpossessesasmallamountofcapital,δ.
At time 1, the project owner decides (i) how much capital he will try to raise
(k ≥ 0) and (ii) the interest rate (r ≥ 0) he will pay to those who invest in the
P P
project. We assume the project owner’s capital target, k , must be a multiple of δ
P
(k ∈ {0,δ,2δ,3δ,...}).
P
At time 2, after observing the project owner’s choices, potential investors si-
multaneously decide under what circumstances they are willing to invest in the
project. Eachinvestorchoosesa (κ) ∈ {0,1}forallvaluesofκ < k thataremulti-
i P
ples of δ. a (κ) = 1 indicates that investor i is willing to invest if the project owner
i
hasraisedκunitsofcapitalatthepointheapproachesi.
At time 3, the project owner approaches investors in a random order. Agent
i becomes an investor in the project if, when approached, he is willing to invest
(a (κ) = 1)andtheprojectownerhasyettomeethiscapitaltargetk (κ < k ). Let
i P P
k denotethetotalamountofcapitalraisedattime3.
At time 4, the project yields a return f(k). The project owner receives f(k) −
(1+r )k whentheprojectisinthe“black”(thatis,whenf(k)−(1+r )k ≥ 0)and
P P
0whentheprojectisinthe“red.” Agentswhoinvestedintheprojectreceivearate
of return r when the project is in the “black”; they receive equal shares of f(k)
P
when the project is in the “red,” with an associated rate of return f(k) −1. Agents
k
whodonotinvestintheprojectreceivethemarketrateofinterest,r .
mkt
Theprojectownerisriskneutral. Investori’sutilityisgivenbyu(w ),wherew
i i
denotes the final wealth of investor i. u is strictly increasing and weakly concave:
u(cid:48) > 0,u(cid:48)(cid:48) ≤ 0. w is equal to δ(1 + r ), where r is investor i’s rate of return. As a
i i i
tie-breaking rule, we assume, for ease of later exposition, that investors prefer all
else equal to choose a(κ) = 1 when there is a possibility of being approached by a
9