Policy Research Working Paper WPS 5183
Dysfunctional Finance
Positive Shocks and Negative Outcomes
Karla Hoff
The World Bank
Development Research Group
Macroeconomics and Growth Team
January 2010
Policy Research Working Paper 5183
Abstract
This paper shows how badly a market economy an industry in which there are good projects that are
may respond to a positive productivity shock in an productive. The problem is that they are contaminated in
environment with asymmetric information about project the capital market by bad projects because of the banks'
quality: some, all, or even more than all the benefits inability to distinguish good projects from bad.
from the increase in productivity may be dissipated. One possible explanation for the lack of development
In the model, based on Bernanke and Gertler (1990), in some countries, is that screening institutions are
entrepreneurs with a low default probability are charged sufficiently weak that impersonal financial markets
the same interest rate as entrepreneurs with a high default cannot function. If industrialization entails learning
probability. The implicit subsidy from good types to bad spillovers concentrated within national boundaries, and if
means that the marginal entrant will have a negative initially informational asymmetries are sufficiently great
value project. An example is presented in which, after that the capital market does not emerge, then neither
a positive productivity shock, the presence of enough industrialization nor the learning that it would foster will
bad types forces the interest rate so high that it drives occur.
all entrepreneurs out of the market. This happens in
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Dysfunctional Finance:
Positive Shocks and Negative Outcomes
Karla Hoff*
*I thank an extremely generous referee, whose comments directed me to new insights. I also thank Richard
Arnott, Andrew Lyon, and Joe Stiglitz for comments.
The problem of financial fragility has received a great deal of attention. It is well
understood that a negative shock to wealth, prices, or beliefs can lead to the collapse of a
financial market.1 It is less well understood that markets can also become unstable after a
positive shock. Here I show that a positive productivity shock can increase the extent of
asymmetric information in the market as it draws in lowquality borrowers. It can even happen
that a positive shock leads to a complete collapse of investment.
These points are made by analysis of the process of investment finance in Bernanke and
Gertler (1990). They showed that their model has a fragile equilibrium in the sense that it can
be greatly disturbed by a negative wealth shock. What I show here is that under some conditions,
a positive productivity shock can also cause negative movements in the equilibrium, and possibly
large movements. In the model, entrepreneurs who want to undertake investment projects know
their probability of success, but financial intermediaries know only the average success
probability of entrants, and the marginal entrant has the highest risk of failure. In this setting, the
marginal entrant will have a negativevalue project. The highquality borrowers subsidize the
lowquality borrowers. A positive shock that increases the success return to projects will attract a
new set of highrisk, negativevalue projects. This adverse selection process will erode the
ability rents of the inframarginal borrowers. I present an example in which it destroys the
market.
The results of this paper suggest a new reason why institutional change in the financial
sector has often followed technological progress. The usual explanation is that an explosion of
demand for funds can be met only by a widening of the financial market across group boundaries
and geographic distance, which decreases trust and increases the extent of asymmetric
information (e.g., Zucker 1986 and Baskin 1988). The additional explanation suggested in this
paper is that a productivity improvement in an industry can widen the divergence of interests
between entrepreneurs and banks, which provides potentially large returns to improvements in
institutions for economic governance. The returns can be as much as the entire value produced
in the industry, which is at risk of dissipation from financing of negativevalue projects.
1
See, for example, Bernanke and Gertler (1990), Greenwald and Stiglitz (1993), and Morris and Shin (2008).
2
For instance, the first century of investment in railroads in the United States has been
described as a long story of defaults, reorganizations, frauds, and other pitfalls and mishaps
[that] may give the impression that it was at best a question of avoiding losses instead of making
profits" (Veenendaal, 1996, p. 175). The New York Stock Exchange (NYSE) emerged as the
central market for railroad securities and devised a set of screening policies that became
progressively more stringent after 1860. Market screening undertaken by the New York Stock
Exchange allowed certain firms to invest in costly signals to separate their securities from those
of competing ventures....A NYSE listing itself became a signal to American investors of the
quality` of an investment opportunity (Davis and Cull, 1994, pp. 7475). The literature on
financial market development explains this change by the geographical expansion of the market.
However, another factor that may have contributed to the recurrent need for improvements in
screening was that technological progress widened the divergence of interests between
entrepreneurs and banks, as entrepreneurs faced higher incentives to take longshot gambles with
other people`s money.
There are many markets in which the marginal entrant is the lowest quality type. For
example, in markets in which quality is not observable at the time of purchase and firms differ in
the marginal cost of producing quality, the lowest ability firms will choose to produce the lowest
quality goods. In such a setting, Grossman and Horn (1988) show that highability firms will
choose to build a reputation over time for high quality, and the lowest ability firms will choose to
sell shoddy goods (which they can sell at the price of the average quality) and then exit. The
marginal entrant will produce negative social value.
The surprising result that positive shocks may cause negative outcomes cannot, however,
occur in the model in Akerlof`s seminal paper on the market for lemons (Akerlof 1970). As
The
Akerlof writes of his model of the used car market, bad cars tend to drive out the good (p.
489). There is always too little exchange in his model because the marginal seller, having the
highest quality used car in the market, receives less than its true value. In contrast, I am
concerned with the opposite problem, as were also de Meza and Webb (1987) and Grossman and
Horn (1988). If exchange occurs at all, there is always too much of it because the marginal
investor, having the worst project and the greatest risk, borrows at a better than fair interest rate.
The good types draw in the bad. Under some conditions, a positive shock can worsen the
problem of too much entry.
3
1. A model of the financial market in which good types draw in bad
A. The agents and technology
There are two groups of agents: entrepreneurs and financial intermediaries (banks). All
agents are riskneutral. An entrepreneur chooses whether or not to invest an indivisible level of
effort at utility cost e to design a project. Each entrepreneur can design at most one project. A
project is an independent draw from the distribution H(p), where p is the probability that the
project succeeds. A project pays off R if it succeeds and zero otherwise. A byproduct of
designing a project is that the entrepreneur learns the probability of success of the project, which
he then chooses whether or not to undertake. Undertaking it requires an investment of one unit
of wealth. Entrepreneurs have a wealth endowment W that is strictly positive but less than one,
so that they must obtain outside finance to undertake their projects. There are a large number of
financial intermediaries, each with an unlimited supply of funds at gross interest rate r. r reflects
the gross return on resources that are stored, rather than invested.
B. The financial contract
Contracts must be based on observables. The following assumptions restrict the set of
observables in a way that introduces the problem of adverse selection into the financial market
and ensures that no feasible contract can solve it.
Assumption 1. The distribution of p is known to all, but the specific realization of p is each
entrepreneur`s private information.
Assumption 2. The entrepreneur's effort cannot be monitored.
Assumption 3. A bank cannot observe all the financial contracts that an entrepreneur enters into.
Together with limited liability, Assumption 1 creates a potential problem of adverse
selection. Assumption 2 means that the problem cannot be solved by offering a fixed wage
4
contract to entrepreneurs, since under such a contract the entrepreneur would have no incentive
to expend effort. Assumption 3 means that it is not feasible to mitigate the incentive of
entrepreneurs to undertake bad projects by designing a contract in which a payment is made from
the bank to the entrepreneur in the event that he does not undertake a project. To see this, notice
that if an entrepreneur's success probability was so low that he did not wish to undertake his
project, he would have an incentive to enter into such a contract with every intermediary and
accept the grants. If, alternatively, his success probability was high enough that he wished to
undertake his project, then he would have an incentive to sign a simple debt contract. Hence, a
contract that provided for a payment to the entrepreneur when he did not undertake a project
(thereby inducing the entrepreneurs with the worst projects to withdraw from the financial
market) would not be selfsustaining.
Given these assumptions, the contract that maximizes each entrepreneur`s expected
income subject to the constraint that the bank breaks even is a pure debt contract with maximum
selffinance. The proof follows the lines of Bernanke and Gertler (1990, proposition 2(i)). The
intuition for maximum selffinance is that the unwillingness of a riskneutral entrepreneur to
invest in his own project would signal that it was of poor quality.
Under the equilibrium contract, the entrepreneur pays principal and interest if his project
succeeds, and defaults if his project fails. Let i denote 1 + the interest rate. I will generally refer
to i as the
interest rate, for short.
C. Overview of the game and the equilibrium
Competition is modeled as a threestage game:
In Stage 1, an entrepreneur decides whether or not to design a project.
In Stage 2, banks offer contracts to entrepreneurs.
In Stage 3, entrepreneurs decide whether or not to accept the offers.
Proceeding by backward induction, consider in Stage 3 an entrepreneur who has already
designed a project and learned its success probability p. He will wish to undertake his project if
it is at least as profitable as the alternative use of his wealth. This implies p[R i[1W]] rW
5
or, equivalently, that projects with success probabilities equal to or above p* are undertaken,
where
(1) p* =  1
. Entrepreneurs' reservation success probability (RSP)
In Stage 2, there is perfect competition in the lending activity. Financial market
equilibrium occurs at an interest rate at which banks break even in expected value:
(2) = Banks' breakeven locus
where denotes the average success probability of entrepreneurs who borrow. If, for example,
there are a continuum of types and no mass point at p*, then
(3) = E( )
Thus, the contracts offered in Stage 2 depend on the banks` expectation of entrepreneurs`
response in Stage 3.
Consider finally the entrepreneur`s problem in Stage 1. He will find it worthwhile to
invest effort to design a project if the expected return is positive:
(4) = [  ]  0 ,
where is the probability that an entrepreneur who designs a project will choose in Stage 3 to
undertake it. This inequality implies a lower bound on wealth below which an entrepreneur loses
access to credit.2 I assume initially, by choice of parameters, that (4) is satisfied.
The process of investment finance described by equations (1) to (3) has the consequence
2
The intuition is that the lower the entrepreneur`s wealth, the lower his stake in his project and thus the lower the
probability of success p* at which he is willing to undertake a project. Hence, the lower is W, the lower the average
quality of borrowers and the higher the interest rate. This rate may be so high that (4) is violated. Bernanke and
Gertler (1990) prove the existence of a critical wealth level below which the market collapses. Without loss of
generality, I consider in this paper only one wealth level. With a distribution of wealth levels across entrepreneurs,
one would have a distribution of markets, each with its own interest rate. Point by point, the results in this paper
would hold for each level of wealth.
6
that entrepreneurs are willing to undertake negative social value projects. The social return to
the entrepreneur who is indifferent between undertaking his project, or not, is p*Rr. p*Rr is
negative since
(5) p* = + [1  ] <
using (1) and (2) and the fact that p* < . Thus, the good types draw in the bad to the financial
market.
D. The equilibrium with a discrete distribution of types
In order to better show the intuition behind the results of this paper, in the text I will focus on the
case of a discrete distribution of types. In the appendix, I will present the case of a continuous
distribution of types.
I now assume that the probability of success for projects is either pL or pH , with 0 < pL <
pH < 1, and that the two types exist in proportions and 1, respectively. I will refer to an
entrepreneur with a project success probability pL (respectively, pH) as the low (high) ability
type.3
Figure 1 depicts the banks' breakeven locus (equation (2)). With discrete types, the
locus is a step function. For p* < pL, the interest rate is r/E(p), where E(p) is the unconditional
expectation. For p* > pL, the interest rate declines to r/pH. The banks` breakeven locus shows
how individual behavior aggregates up to the market interest rate.
Figure 1 also depicts the entrepreneurs' reservation success probability (RSP in equation
(1)). The curve is upward sloping because at a higher interest rate, the entrepreneur requires a
higher success probability to be willing to invest in his project.
FIGURE 1. Equilibrium with two types of entrepreneurs. In panel (A), the success return R is low
and the marginal borrower is high ability. In panel (B), the success return is R (with R > R) and
3
The case of two types generalizes fully to an arbitrary number of discrete types. This can be seen by considering the
p
average success probability of inframarginal types in equilibrium as the composite type H and by considering the
p
success probability of the next worst type as L.
7
the marginal borrower is low ability.
(A) (B)
i i
RSP
RSP r
E(p)
r r
pH i pH i
Banks' break
r even locus r
0 pL 1 p* 0 rW pL 1 p*
rW
Rr+rW
Rr+rW
Equilibrium occurs at the intersection of the two curves. If they intersect along a
horizontal segment of the banks` breakeven locus, a small shock with have no effect on entry.
This case occurs if pL < p* (only the highability type undertakes projects), as shown in panel
(A), or if pL > p* (all entrepreneurs undertake their projects, not shown in the figure).
In the alternative case, as shown in panel (B), the two curves will intersect along a
vertical segment of the banks` breakeven locus, where pL = p*. I will call this intermediate
the
case. Given the result in (5), the intermediate case is one in which there are some entrepreneurs
who should undertake their projects and some who should not, and the latter are at the margin of
entry.4 Let q [0,1] denote the fraction of lowability entrepreneurs that undertake their projects.
With a discrete distribution of p, the average success probability of entrepreneurs that
undertake their projects is a step function
+[1]
(3) = +1
if = (the intermediate case)
(3) = if >
(3) = if <
4
This is indeed the general case for a continuum of types, presented in the Appendix.
8
(3) says that a fraction q+1 of all entrepreneurs undertakes projects, and of these q are low
quality and 1 are high quality.
Equations (2) and (3) describe the Nash equilibrium for the intermediate case. Each
entrepreneur`s action is at least tied for his best response to the interest rate charged by the
banks, and no bank has an incentive to deviate from that interest rate. To see why this is the
Nash equilibrium, note that if more than this value of q entered the industry, the interest rate
would rise. At that higher interest rate, p* > pL, so that all the lowability entrepreneurs would
exit, and banks would earn strictly positive profits. Thus, this cannot be an equilibrium. If less
than this value of q entered, the interest rate would fall. At that lower interest rate, p* < pL. All
the lowability entrepreneurs would enter and so banks would suffer losses. This also cannot be
an equilibrium.
Normalizing the number of entrepreneurs to one, y in (4) defines the social surplus. In
the intermediate case, it is
(4) = = (q + 1 ) (R r) e.
The factor Rr is, of course, the average income of entrepreneurs who undertake their projects.
All entrepreneurs with highquality projects undertake them, but as explained above, only a
fraction q of the entrepreneurs who have lowquality projects do so. The first factor, q + 1 ,
is thus the probability that an entrepreneur who designs a project chooses to undertake it. From
this overall return, the cost of project design, e, must be subtracted.
Evaluated at p*= , (1) and (2) imply that R = + 1  .
Rearranging this equation gives a useful result:

(6) R  =
This means that in the intermediate case, any social surplus that is produced arises because the
inframarginal type (the highability type) is producing enough relative to the marginal type (the
lowability type), and because there are enough of the highability type (i.e., 1 is large
enough) to offset the design costs e. The next section will show that under some conditions, a
9
broadly beneficial productivity shock will erode this social surplus.
2. Technological progress
Technological progress, or a positive shock to productivity, potentially affects aggregate income
in two ways: a direct incomeincreasing effect holding the composition of the industry fixed,
and an indirect effect from the change in the set of entrepreneurs who enter the industry. With a
discrete distribution of types, the second effect from a marginal shock will occur only in the
intermediate case, because it is only in this case that there is a type at the margin of entry.
This section considers three kinds of technological change: (a) an increase in the return
of projects that succeed, (b) an increase in the success probability of each type, and (c) an
increase in the return of projects that fail. Consider first an initial equilibrium in which there is
no type at the margin of entry. Then a marginal increase in R or in both pL and pH will not
change the mix of types who undertake projects or the probability of entry ( in equation (4)).
There is a simple outcome: owners of projects get a higher return. It is trivial to see that an
increase in R or in both pL and pH must increase y. I will now show that in the intermediate case,
i.e, when the lowquality type is at the margin of entry, something very different happens.
A. An increase in the return, R
An increase in the success return lowers p* at a given interest rate, which shifts RSP left in Figure
2. In the intermediate case, the social surplus is invariant with respect to a change in R, as can be
seen by substituting (6) into (4), to obtain an expression for y in which R does not appear:
+ 1
(7)  = =
 + 1  
= [1  ]
 1 
The reason for this invariance result is that when the lowability type is at the margin of
entry, an increase in R is exactly offset by a rise in the interest rate in response to the entry of more
10
lowability types. The new entrants impose a cost on highquality borrowers, which they do not
take into account. As q rises from 0 to 1, the interest rate rises from r/pH to r/E(p). These effects
are similar to externalities that occur when a market is missing.5
FIGURE 2. Comparative statics of an increase in the success return
The invariance of income to a general improvement in productivity is a new application of
an old result, the tragedy of the commons. Gordon (1954) showed that if the supply of potential
entrants to the commons, e.g, an openaccess fisheries, was infinitely elastic, then the value of the
commons would be exactly dissipated. The analogy to the commons in the model presented here are
the ability rents to highquality projects. If banks do not distinguish lowquality from highquality
borrowers, then a part of the ability rents of highquality borrowers becomes, in effect, a common
property resource subject to the tragedy of the commons. Improvements in technology that increase
R and thereby induce a larger fraction of the lowquality type to implement their projects will
dissipate the gains from the improvement in technology.
Gordon also showed that if the supply of potential entrants to the commons was less than
5
Greenwald and Stiglitz (1986) provide a general framework that recasts information inefficiencies in an
externalities framework.
11
infinitely elastic, then the rents attributable to the variable factor, e.g., the fish, would be only partly
dissipated. The Appendix shows that this result also carries over to the investment process analyzed
here.
Figure 3 illustrates the erosion of the potential gains from technological progress when the
lowability type is at the margin of entry. In this example6, r = 1, W = 0.7, e = 0.36, pL = 0.2, pH =
0.8, and = 0.8. The upper panel plots q against R.
FIGURE 3. Effect of an increase in R on entry and the social surplus
Fraction of typeL who borrow (q)
1
q in equilibrium
0.5
q in firstbest economy
0
4 4.5 5
Success return (R)
0.3
Social surplus (y)
0.2 y in firstbest economy
0.1
y in equilibrium
0
0.1
4 4.5 5
Success return (R)
The lower panel plots y against R. The figure shows that in equilibrium, when q is increasing, y is
flat: over this range, all potential gains from the increase in R are eroded.7 These curves can be
contrasted with the dotted curves for a firstbest economy (in which banks can distinguish between
good and bad types).
6
The Matlab programs to produce Figures 3 and 5 are at www.econ.worldbank.org/staff/khoff.
7
The same kind of analysis shows that if the innovation in the success returns of projects R is biased toward type L, then
social surplus may fall as a result of the innovation. There are many instances in which firms at the margin are different
from the best firms, and so a nonuniform technological change is natural. For example, in the trucking business the
marginal firms may be those whose entrepreneurs have the lowest ability to repair trucks. In that case, the marginal
firms will benefit the most from technological change in the form of an improvement in publicly provided roads.
12
B. An increase in the probabilities of success
Next consider a technological innovation in the form of a rightward shift in the distribution from
{pL, pH; , 1} to {pL+, pH+; , 1}. The innovation causes the banks` breakeven curve to
shift down (entrepreneurs are more likely to repay) and right (at any value of p*, the set of types
for which p p* weakly increases). See Figure 4. In the intermediate case, the new equilibrium
entails a higher interest rate, since more lowability types enter the market (just as they did in
response to an increase in R).
FIGURE 4. Comparative statics of an increase in the probabilities of success
To assess the impact on y, it is useful to decompose y into three terms: (a) the income earned
by lowquality borrowers, plus (b) the income earned by highquality borrowers, less (c) the design
cost, as follows:
(8) = + = +  1 
+ 1  +  1  
13
If the lowquality type is on the margin, then R  i[1W] = rW/[pL + ]. This fact implies that the
expression for (a) is equal to zero. A marginal productivity change that increases the success
probability of the lowability type makes this type no better off (although it increases the fraction of
this type who implement their projects as compared to the case in which the lowability type had a
probability of success pL). Using the above fact to rewrite the expression for (b), (8) becomes

(9) = + = 1   .
+
(9) means that the surplus y is strictly decreasing in in the intermediate case. The intuition
is easy to explain. A rise in the interest rate for all borrowers that would hold constant the net
income of the lowquality type, who has only a low probability of actually repaying his loan, would
entail a decline in the net income of the highquality type, who has a high probability of repaying
his loan. Formally, the indifference curves of the low and highquality types satisfy a single
crossing property in the space of i and .
Differentiating (9) with respect to gives

10 =  1  < 0.
= + ( + )2
The absolute value of dy/d is increasing in the level of debt finance (rW), in the fraction of good
projects (1 ), and in the gap in success rates between good and bad types (pHpL). Each of these
factors contributes to the rents that the lowquality types dissipate when they enter the market. The
absolute value in (10) is also larger the lower the success probability of the lowquality type, pL + .
The lower this probability, the greater the externality that the lowquality type imposes on others.
Figure 5 presents an example in which the adverse selection problem leads to a collapse of
investment by reducing below zero the entrepreneur`s expected return y to designing a project. The
values of the fixed parameters, including the initial values of pL= 0.2 and pH = 0.8, are the same as
in Figure 3, and the value of R is now fixed at 3.6. The upper panel plots q against a uniform shift
() in pL and pH . The lower panel plots y against . The figure shows that when q is strictly
increasing, the surplus is strictly decreasing. That is, the entry of the lowquality type erodes more
than 100 percent of the potential gains from the increase in success probabilities. These curves can
14
be contrasted with the dotted curves for the firstbest economy, in which types are observable to
banks. The paths diverge at the point where the lowability type first enters the market. The curves
meet again at the point at which is sufficiently great that the lowability type produces positive
social value (in this example, at 0.08). y dips below zero in the interval (0.04, 0.06). Within
this interval, in a rational expectations equilibrium, entrepreneurs would be unwilling to design
projects that would be financed at an interest rate that banks would be willing to offer. The pres
FIGURE 5. Effect of an increase in the probabilities of success
Fraction of typeL who borrow (q)
1.0
0.5
q in equilibrium
q in firstbest economy
0
0 0.02 0.04 0.06 0.08 0.1
Shift in pL and pH
0.15
Social surplus (y)
0.1
y in firstbest economy
0.05
y in equilibrium
0
0.05
0 0.02 0.04 0.06 0.08 0.1
Shift in pL and pH
15
ence of enough bad types forces the interest rate so high that it drives all entrepreneurs out of the
market. This happens in an industry in which there are good projects that are productive. The
problem is that they are contaminated in the capital market by bad projects because of the banks`
inability to distinguish good projects from bad.
C. An increase in the returns to projects if they fail
Up to now I have assumed that a project either succeeds and pays off R, or fails and pays off
zero. Suppose now that a technological change occurs in the form of an increase in the return
when a project fails. Assume that this return is less than r[1W]. Then if a given project fails, the
bank will receive this return. In contrast to the preceding cases, this technological change
reduces the externality imposed by lowability entrepreneurs on highability entrepreneurs. Thus,
the technological change unambiguously increases the surplus. This can be seen
diagrammatically in Figure 1 (A and B) by noting that this kind of technological change would
shift down the banks` breakeven locus, lowering i. At the lower interest rate, each entrepreneur
who would have undertaken his project absent the innovation is made strictly better off; a new
set of entrepreneurs may undertake their projects and can be no worse off; and the banks break
even.
3. Discussion
The results have been developed in the context of specific model of the investment process.
They can be generalized to a wider set of models. The results depend on three key assumptions.
The first is a specific assumption about asymmetric information: among a class of borrowers
who know their distribution of future returns but who are indistinguishable to banks, borrowers
can be ranked by firstorder stochastic dominance (as in Black and de Meza 1994). The second
is that there is perfect competition among financial intermediaries, with an infinitely elastic
supply of funds. The third is an assumption about technology: there is a fixed cost of designing
a project and evaluating its success probability. The first two assumptions mean that an
entrepreneur would be willing to undertake a negativevalue project, since the downside risk is
borne partly by others whereas he benefits fully from the upside risk; but that borrowers as a
whole will fully bear the costs of the defaults. The last assumption means that if externalities
16
from the bad projects are sufficiently great, there will be no incentive to design and evaluate any
project, and so investment will collapse.
An episode from U.S. history provides an example in which the emergence of new
institutions to reduce the extent of asymmetric information may have been causally related to
major technological changes that widened the gap between the highest and lowest quality types
in the market. The railroad gave rise to a vast increase in the demand for capital that could be
met only in a national or international financial market. The capital used in the U.S. railroad
industry increased from $0.3 billion in 1850 to $9$10 billion in 1890 and to $21.1 billion in
1916 (Mitchie 1987, p. 222). The New York Stock Exchange, a cartel of traders with fixed
commission rates, emerged as the central market for railroad securities by the 1870s. In an effort
to reduce informational asymmetries, the NYSE devised a set of screening policies that became
progressively more stringent after 1860 (Mitchie, p. 198). The most obvious ones were its vetting
procedure, which required potential listings to meet high minimum standards in terms of size of
capital, number of shareholders, and proven track record. Listing on the NYSE was voluntary
and provided a signal to investors of the quality of an investment opportunity, enabling firms to
build a national market for their securities. Despite competition from other market exchanges
with lower standards, the price of a seat on the NYSE rose from about $20,000 to $80,000
between 1880 and 1910 (Davis and Cull, 1994, p. 74). What the NYSE did is to bestow labels.
With technological progress that increased rents to high ability, defining and establishing rights
to those labels became especially valuable.
This idea can be formalized in a simple way. Suppose there exists a screening technology
such that banks can perfectly identify a project`s success probability at a fixed cost c per project
screened. Then an entrepreneur with success probability pj would wish to be screened if
(11) [1W]r + c < [1W]
The lefthand side is the expected cost of principal plus interest if he is screened, plus the cost of
screening. The righthand side is the expected cost of principal plus interest if he is not screened. A
positive technological change that causes the set of entrants to extend deeper into the distribution of
potential entrants reduces , which increases the righthand side of (11) for any given value of pj.
Thus, the change can shift the economy from a noscreening equilibrium to a screening equilibrium,
in the language of Stiglitz (1975).
17
The success of the NYSE rested upon the selfinterest of its members and of the
entrepreneurs who sought capital. By 1912 it is estimated that 45 percent of the $58 billion of
securities in circulation in the U.S. were to be found on the NYSE. The provision of this
secondary market made an enormous difference to the willingness of investors to buy and hold
securities of firms listed on the exchange, facilitated the movement of capital within the U.S. and
internationally, and by reducing asymmetric information about the value of securities, made
possible an enormous expansion of lending based on stocks and bonds as collateral (Mitchie, pp.
168, 235).
4. Conclusion
In this paper, I showed how badly a market economy may respond to a positive productivity
shock in an environment with asymmetric information about the quality of projects: some, all, or
more than all of the possibilities of an increase in wealth may run to waste, and investment may
even collapse. These results have close parallels to the tragedy of the commons. In a
commons with an infinitely elastic supply of entrants, the rents to the commonproperty resource
are fully dissipated. The saying that everybody`s property is nobody`s property captures the
idea. In the model of this paper, banks cannot distinguish good projects from bad. Thus the
entrepreneur with a good project financed partly by debt cannot fully appropriate the surplus
produced by his ability. The result is a pattern of entry of entrepreneurs in response to positive
productivity shocks that, under some conditions, will dissipate the promised gains from the
technological improvement. This is the tragedy.
The analogy to the tragedy of the commons helps explain why positive productivity
shocks can dramatically increase both the social and private returns to screening. An
entrepreneur whose type is identified would appropriate all the rents to his ability; this would
remove the commons problem. Conventional wisdom has it that the gains to better firms from
screening are largely at the expense of the firms with which they would otherwise be grouped;
and thus the social returns to screening are ambiguous. However, in this model, before actually
developing a project, every entrepreneur has the same potential to develop a good or bad project
and so to be a high or lowquality entrepreneur. There are no ex ante distributional
consequences of screening. What screening does is to discourage entry by entrepreneurs who
18
learn that they have negativevalue projectsand who by implementing them would expect to
receive gains less than the costs (the externalities) that they would impose on other borrowers in
the market. The social returns to screening are thus unambiguously positive.
The creation of screening mechanisms has, however, historically been a slow, difficult
process. There are many possible routes that institutional change can take. They include not
only stock exchanges that serve as screens, but also innovations in guarantees, bankruptcy laws,
and governance structures within firms. For example, Acemoglu (1998) argues that the
separation of ownership from control may have occurred in part as a remedy to the kinds of
distortions in entrepreneurs` incentives that are analyzed here. The dynamics between
technological change and institutional change is a central aspect of economic development.
There is a twoway causal relationship. Good institutions for economic governance enable a
country to deploy its resources in highvalue projects, which can spur technological progress.
Technological progress may exacerbate adverse selection and lead to a crisis (an investment
collapse), which can spur improvements in economic governance.
One possible explanation for the lack of development in some countries is that screening
institutions are sufficiently weak that impersonal financial markets cannot function. If
industrialization entails selfdiscoverythe discovery of opportunities for profitand of
innovation with spillovers concentrated within national boundaries (see e.g., Hoff 1997,
Hausman and Rodrik 2003, and Greenwald and Stiglitz 2006), and if initially informational
asymmetries are sufficiently great that the capital market does not emerge because of the tragedy
of the commons, then neither industrialization nor the learning that it would foster will occur. If
the process of developing better screens also entails knowledge spillovers concentrated within
national boundaries, then an economy may be trapped in an inefficient nonscreening
equilibrium, with no industrialization and no screening.
Appendix: A Continuous Distribution of Types of Entrepreneurs
The text established two surprising results for the special case of a discrete distribution of types
when the lowability type is at the margin of entry: dy/dR = 0 and dy/d < 0. The appendix
shows that these effects are also possible in the case of a continuum of types, but other outcomes
(that are not perverse) are possible, too.
19
Let p be distributed according to the continuously differentiable distribution function
H(p) with density function h(.) > 0 if p [0 , pu], and h(.) = 0 otherwise. Thus pu is the upper
bound.
The model is set out in equations (1)(5) in the text. Given p*, the mean success
probability of borrowers in (3) and the social surplus in (4) are
()
=
1( )
and
y = 1  ( ) (R r) e .
Henceforth, to simplify the notation, let H* denote H(p*) and h* denote h(p*).
Figure 1A illustrates the equilibrium. It differs from Figure 1 in that the banks` break
even curve is not a step function but instead slopes down everywhere. This means that anything
that shifts the RSP curve will change p* and, by implication, and i. These three variables are
jointly determined. There is no possibility of the kind of outcome analyzed in the text in which
p* does not change when the RSP curve shifts.
FIGURE 1A. Equilibrium with a continuous distribution of types
i
r RSP
E(p)
Banks'
breakeven
locus, i
r
p*
0 rW pu
Rr+rW
20
RESULT 1. Let p be distributed according to the continuously differentiable distribution function
H(p). Then dy/dR 0, with strict equality in the limit as h(p*) .
PROOF OF RESULT 1. Differentiating y with respect to R gives
(1A) = + = [1H*] + h* [p* R r]
Direct effect Effect of entry of
of the bad projects
innovation
where D = R i [1W]  *[1W] > 0.
(1A) expresses dy/dR as the sum of two terms. The first is the gain holding the
composition of the industry fixed. The gain is the probability of undertaking a project multiplied
by the average success rate of projects that are undertaken. The second term is the loss due to
the change in the composition of the industry. This term is proportional to the social loss on the
marginal entrant (p*Rr).
The density of projects h* enters twice into the last term in equation (1A): once through
y/p* =  h*[p*Rr] (as shown), and a second time (not shown explicitly) through dp*/dR = 
p*/D. The greater is h*, the greater the reduction in y due to a marginal change in p*. However,
through its effect on the interest rate, the greater is h*, the less the composition of the industry
will change as a result of an increase in R. This can be seen by writing D explicitly:
(2A) D = {  [1W] + [ ] [1W] }
1
using di/dp* =  and d/dp* = [ ].
1
Substituting (2A) into the righthand side of (1A) and rearranging gives
(3A) = [1  ]  1  + 1 1  1  + .
21
The last term inside the large square brackets is p*. Rewriting that term using (5), it can be
checked that the entire expression inside the large square brackets is zero, so (3A) is equivalent
to
1
= [1H*] [  (1W)] > 0
which also means (since D as h* ) that lim h* dy/dR = 0.
RESULT 2. Let p be distributed according to the continuously differentiable distribution function
H(p) on (0, pu). Then dy/d is ambiguous in sign.
PROOF OF RESULT 2. The result is proved if dy/d is shown to be ambiguous in sign for any
continuously differentiable distribution function of p. I will prove the result for a uniform
distribution of p. Clearly, allowing a nonuniform distribution of types (in which case the
density for the marginal type could be arbitrarily small or large) would greatly expand the
conditions under which dy/d was ambiguous in sign.
But assume here that the density is uniform on [0 , pu]. This means that after a
productivity shock that shifts the success probability of every type by , the density is
1
h(p) =
for p [ , pu+ ]
and h(.) = 0 otherwise. For a given value of p*, it follows that
+ +
=
2
,
2
=
+ +
and
22
+
y =
(  ) e .
Differentiating y with respect to gives, as usual, a positive effect for a fixed
composition of projects and a negative effect from the adverse change in the composition of
projects that are undertaken.
(4A) = +
(5A) = +  (Direct effect of the innovation)
[1]
(6A) + [  ] (Effect of entry of bad projects)
[1] 2
The direct effect in (5A) is determined by differentiating y at a fixed value of p*. The
direct effect is the expected return on the highestquality project multiplied by the density at that
point.
The indirect effect in (6A) can be explained as follows. Moving from right to left, an
increase in lowers the interest rate (by r/22 ), which, in turn, lowers p*. (These effects are
determined, respectively, by differentiating (2) with respect to and differentiating (1) with
respect to i.) The first factor in expression (6A) is obtained by differentiating y with respect to
p*. From (5), p*R r < 0, and so the indirect effect is negative.
I now evaluate the net effect (the sign of (4A)) in two cases. In the first case, W1. It
is easy to see that in this case, (6A) approaches zero and so dy/d > 0.
In the second case, W < 1/3 and R is arbitrarily large. Recall that the constraint that y 0
implicitly defines a minimum lower bound on . This bound approaches zero as R becomes
arbitrarily large (using (4)). Since 0 < p* < , it follows that p* as R becomes arbitrarily
large. Recall from (1) that Ri(1W) = rW/p* . Using this fact, (4A)(6A) imply that
23
<0
=0
if
 1  2
< .
 2
As R becomes arbitrarily large, the lefthand side approaches
(by l`Hôpital`s rule) and the
squared expression on the righthand side approaches one. For W < 1/3, the first factor on the
righthand side is more than one. Thus, the inequality is satisfied by choice of the parameter pu
sufficiently small (so pu/p* < [1W]/2W ). Intuitively, this case corresponds to a scenario in
which the upside risk (R), from which the entrepreneur gains, is extremely large; whereas he
bears little of the downside risk because his stake in his own project, W, is small. In these
circumstances, the ex ante surplus from investment, y, will be near zero and a marginal change in
, by increasing adverse selection, will reduce the surplus further. If the positive productivity
shock reduces y below zero, then, of course, the shock will destroy the market.
24
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