metadata: authors: 0: author: Hoff, Karla
count: World
docna: 0: docna: Dysfunctional finance : positive shocks and
            negative outcomes
docty: Policy Research Working Paper
theme: Legal institutions for a market economy,Public expenditure, financial management and procurement
majtheme: Rule of law,Public sector governance
subtopic: Consumption,Fiscal & Monetary Policy,Financial Intermediation,Educational Sciences,Railways Transport,Financial Sector Policy
teratopic: Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: This paper shows how badly a market
            economy may respond to a positive productivity shock in an
            environment with asymmetric information about project
            quality: some, all, or even more than all the benefits from
            the increase in productivity may be dissipated. In the
            model, based on Bernanke and Gertler (1990), entrepreneurs
            with a low default probability are charged the same interest
            rate as entrepreneurs with a high default probability. The
            implicit subsidy from good types to bad means that the
            marginal entrant will have a negative-value project. An
            example is presented in which, after a positive productivity
            shock, the presence of enough bad type's 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. 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 learning
            spillovers concentrated within national boundaries, and if
            initially informational asymmetries are sufficiently great
            that the capital market does not emerge, then neither
            industrialization nor the learning that it would foster will occur.
repnme: repnme: Dysfunctional finance : positive shocks and
            negative outcomes
display_title: Dysfunctional finance : positive
            shocks and negative outcomes
listing_relative_url: /research/2010/01/11742351/dysfunctional-finance-positive-shocks-negative-outcomes
topicv3: Financial Intermediaries m1326973 2196,Education m1327048 470,Macroeconomic and Structural Policies
            m1327380 439,Railways m1327400 166,Financial Sector Development m1327681 1920
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 28
model_extractions: 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 may respond to a positive productivity shock in an environment with asymmetric information about project quality: some, all, or even more than all the benefits from the increase in productivity may be dissipated. In the model, based on Bernanke and Gertler (1990), entrepreneurs with a low default probability are charged the same interest rate as entrepreneurs with a high default probability. The implicit subsidy from good types to bad means that the marginal entrant will have a negativevalue project. An example is presented in which, after a positive productivity shock, the presence 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.

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 learning spillovers concentrated within national boundaries, and if initially informational asymmetries are sufficiently great that the capital market does not emerge, then neither industrialization nor the learning that it would foster will occur.

This paper—a product of the Macroeconomics and Growth Team, Development Research Group—is part of a larger effort in the department to understand problems of financial markets and governance. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at khoff@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# 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.<sup>1</sup> 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 low-quality 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 negative-value project. The high-quality borrowers subsidize the low-quality borrowers. A positive shock that increases the success return to projects will attract a new set of high-risk, negative-value 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 negative-value 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. 74-75). 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 long-shot 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 high-ability 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 Akerlof writes of his model of the used car market, ―The 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.

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# **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 risk-neutral. 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 self-sustaining.

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 self-finance. The proof follows the lines of Bernanke and Gertler (1990, proposition 2( _i_ )). The intuition for maximum self-finance is that the unwillingness of a risk-neutral 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 three-stage 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_ [1- _W_ ]] _≥ rW_ 5
or, equivalently, that projects with success probabilities equal to or above _p_ * are undertaken, where 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: where p 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 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: where π 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.<sup>2</sup> 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*R-r. p*R-r_ is negative since using (1) and (2) and the fact that _p_ * _<_ 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 λ and 1-λ, respectively. I will refer to an entrepreneur with a project success probability _pL_ (respectively, _pH_ ) as the low (high) ability type.<sup>3</sup> Figure 1 depicts the _banks’ break-even 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‘ break-even 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 _Rʹ_ (with _Rʹ > R_ ) and

> 3 The case of two types generalizes fully to an arbitrary number of discrete types.  This can be seen by considering the ‖ average success probability of inframarginal types in equilibrium as the composite type ― _pH_ and by considering the success probability of the next worst type as ― _pL_ .‖

7
the marginal borrower is low ability.

<!-- Start of picture text --> (A) (B)<br>i i<br>RSP<br>RSP r<br>E(p)<br>r r<br>i i<br>pH pH<br>Banks’ break-<br>r even locus r<br>0 pL 1 p* 0 rW pL 1 p*<br>rW<br>R′-r+rW<br>R-r+rW<br><!-- End of picture text --> Equilibrium occurs at the intersection of the two curves. If they intersect along a horizontal segment of the banks‘ break-even locus, a small shock with have no effect on entry. This case occurs if _pL_ < _p_ * (only the high-ability 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‘ break-even locus, where _pL_ = _p_ *. I will call this ―the intermediate 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.<sup>4</sup> Let _q_ ∈[0,1] denote the fraction of low-ability 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

> 4 This is indeed the _general_ case for a continuum of types, presented in the Appendix.

8
(3ʹ) says that a fraction _q_ λ+1-λ of all entrepreneurs undertakes projects, and of these _qλ_ are low quality and 1- λ are high quality.

Equations (2) and (3ʹ) 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 low-ability 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 low-ability 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 The factor p _R-r_ is, of course, the average income of entrepreneurs who undertake their projects. All entrepreneurs with high-quality projects undertake them, but as explained above, only a fraction _q o_ f the entrepreneurs who have low-quality projects do so. The first factor, _q_ λ + 1 – λ, 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.

rW r Evaluated at _p*_ =pL, (1) and (2) imply that _R_ = + 1 −W . pL p Rearranging this equation gives a useful result: This means that in the intermediate case, any social surplus that is produced arises because the inframarginal type (the high-ability type) is producing enough _relative_ to the marginal type (the low-ability type), and because there are enough of the high-ability type ( _i.e.,_ 1 – λ 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_ income-increasing 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 (π 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 low-quality 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 (4ʹ), to obtain an expression for _y_ in which _R_ does not appear: The reason for this invariance result is that when the low-ability type is at the ~~m~~ argin of entry, an increase in _R_ is exactly offset by a rise in the interest rate in response to the entry of more 10
<!-- Start of picture text --> i<br>increase in R<br>r a RSP<br>E(p) a“<br>tI -<br>P| “ i<br>0 Pt 1 ?P*<br><!-- End of picture text -->
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 low-ability type is at the margin of entry. In this example<sup>6</sup> , _r_ = 1, _W_ = 0.7, _e_ = 0.36, _pL_ = 0.2, _pH_ = 0.8, and λ = 0.8. The upper panel plots _q_ against _R_ .

FIGURE 3. Effect of an increase in _R_ on entry and the social surplus <!-- Start of picture text --> 1<br>q in equilibrium<br>0.5<br>q in first-best economy<br>0<br>4 4.5 5<br>Success return ( R )<br>0.3<br>0.2 y in first-best economy<br>0.1<br>y in equilibrium<br>0<br>-0.1<br>4 4.5 5<br>Success return ( R )<br>) q<br>Fraction of type-L who borrow (<br>)<br>y<br>Social surplus (<br><!-- End of picture text --> 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.<sup>7</sup> These curves can be contrasted with the dotted curves for a first-best 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 non-uniform 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;_ λ, 1-λ} to { _pL_ +Δ, _pH_ +Δ; λ, 1-λ}. The innovation causes the banks‘ break-even 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 low-ability 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 low-quality borrowers, plus ( _b_ ) the income earned by high-quality borrowers, less ( _c_ ) the design cost, as follows: 13
If the low-quality type is on the margin, then _R - i_ [1 _-W_ ] _= rW_ /[ _pL_ + Δ]. This fact implies that the expression for ( _a_ ) is equal to zero. A marginal productivity change that increases the success probability of the low-ability 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 low-ability type had a probability of success _pL_ ). Using the above fact to rewrite the expression for ( _b_ ), (8) becomes (9) means that the surplus _y_ is _strictly decreasing_ in Δ 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 low-quality type, who has only a low probability of actually repaying his loan, would entail a decline in the net income of the high-quality type, who has a high probability of repaying his loan. Formally, the indifference curves of the low- and high-quality types satisfy a singlecrossing property in the space of _i_ and Δ.

Differentiating (9) with respect to Δ gives The absolute value of _dy_ / _d_ Δ is increasing in the level of debt finance ( _rW_ ), in the fraction of good projects (1- λ), and in the gap in success rates between good and bad types ( _pH_ - _pL_ ). Each of these factors contributes to the rents that the low-quality types dissipate when they enter the market. The absolute value in (10) is also larger the lower the success probability of the low-quality type, _pL_ + Δ. The lower this probability, the greater the externality that the low-quality 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 (Δ) in _pL_ and _pH_ . The lower panel plots _y_ against Δ. The figure shows that when _q_ is strictly increasing, the surplus is strictly decreasing. That is, the entry of the low-quality 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 first-best economy, in which types are observable to banks. The paths diverge at the point where the low-ability type first enters the market. The curves meet again at the point at which Δ is sufficiently great that the low-ability type produces positive social value (in this example, at Δ ≈ 0.08). _y_ dips below zero in the interval Δ ∈ (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 presFIGURE 5. Effect of an increase in the probabilities of success <!-- Start of picture text -->
1.0<br>0.5<br>q  in equilibrium<br>q  in first-best economy<br>0<br>0 0.02 0.04 0.06 0.08 0.1<br>Shift in  pL  and  pH<br>0.15<br>0.1<br>y  in first-best economy<br>0.05<br>y  in equilibrium<br>0<br>-0.05<br>0 0.02 0.04 0.06 0.08 0.1<br>Shift in  pL  and  pH<br>) q<br>Fraction of type-L who borrow  (<br>)<br>y<br>Social surplus  (<br><!-- End of picture text -->

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_ [1- _W_ ]. 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 low-ability entrepreneurs on high-ability 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‘ break-even 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 _first-order 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 negative-value 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 The left-hand side is the expected cost of principal plus interest if he is screened, plus the cost of screening. The right-hand 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 p , which increases the right-hand side of (11) for any given value of _pj_ . Thus, the change can shift the economy from a no-screening equilibrium to a screening equilibrium, in the language of Stiglitz (1975).

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The success of the NYSE rested upon the self-interest 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 common-property 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 low-quality 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 negative-value projects—and 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 two-way causal relationship. Good institutions for economic governance enable a country to deploy its resources in high-value 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 ―self-discovery‖—the discovery of opportunities for profit—and 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 non-screening 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 low-ability type is at the margin of entry: _dy_ / _dR_ = 0 and _dy_ / _d_ Δ < 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.

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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 and Henceforth, to simplify the notation, let _H*_ denote _H_ ( _p_ *) and _h_ * denote _h_ ( _p_ *).

Figure 1-A illustrates the equilibrium. It differs from Figure 1 in that the banks‘ breakeven 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, p 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 1-A. Equilibrium with a continuous distribution of types <!-- Start of picture text --> i<br>r RSP<br>E ( p )<br>Banks’<br>break-even<br>locus, i<br>r<br>p*<br>0 rW pu<br>R-r+rW<br><!-- End of picture text --> 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 (1-A) 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_ * _R-r_ ).

The density of projects _h*_ enters twice into the last term in equation (1-A): once through ∂ _y_ /∂ _p*_ = - _h*_ [ _p*R-r_ ] (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: Substituting (2-A) into the right-hand side of (1-A) and rearranging gives 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 (3-A) is equivalent to 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_ Δ _is ambiguous in sign._ PROOF OF RESULT 2. The result is proved if _dy/d_ Δ 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 non-uniform 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_ Δ 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 Δ, the density is and _h_ (.) = 0 otherwise. For a given value of _p_ *, it follows that and 22
Differentiating _y_ with respect to Δ 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.

The direct effect in (5-A) is determined by differentiating _y_ at a fixed value of _p*._ The direct effect is the expected return on the highest-quality project multiplied by the density at that point.

The indirect effect in (6-A) can be explained as follows. Moving from right to left, an increase in Δ lowers the interest rate (by – _r/_ 2p<sup>2</sup> ), which, in turn, lowers _p*._ (These effects are determined, respectively, by differentiating (2) with respect to Δ and differentiating (1) with respect to _i._ ) The first factor in expression (6-A) 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 (4-A)) in two cases. In the first case, _W→_ 1. It is easy to see that in this case, (6-A) 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 p . This bound approaches zero as _R_ becomes arbitrarily large (using (4)). Since 0 < _p* <_ p _,_ it follows that _p*→_ p as _R_ becomes arbitrarily large. Recall from (1) that _R-i_ (1- _W_ ) = _rW/p*_ . Using this fact, (4-A)-(6-A) imply that 23
if <u>pu</u> As _R_ becomes arbitrarily large, the left-hand side approaches (by l‘Hôpital‘s rule) and the p<sup>∗</sup> squared expression on the right-hand side approaches one. For _W_ < 1/3, the first factor on the right-hand side is more than one. Thus, the inequality is satisfied by choice of the parameter _pu_ sufficiently small (so _pu/p*_ < [1- _W_ ]/2 _W_ ). 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.

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