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Credit markets in developing countries
Table of Contents
1. Introduction ...................................................................................................................................... 1
2. Adverse selection and default risk ................................................................................................... 2
2.1 Default risk................................................................................................................................. 2
2.2 Default risk and market instability: A simple example ............................................................. 4
2.3 Adverse selection ....................................................................................................................... 8
3 Access to credit ................................................................................................................................. 9
3.1 The paradox of “credit cycles” .................................................................................................. 9
3.2 Collateral and property rights: A natural experiment .............................................................. 10
4 Does microcredit do miracles?........................................................................................................ 11
4.1 Microcredit and social capital .................................................................................................. 12
4.2 Microcredit and women empowerment ................................................................................... 12
5 Well… Does access to credit really help the poor? ........................................................................ 15
Références .......................................................................................................................................... 17
Appendix ............................................................................................................................................ 18
1. Introduction
Well-functioning credit markets are key to growth as they largely determine the ability of firms to
invest. However, they have been often distorted by various interventions, often designed to channel
funding to cronies and politically-connected firms, or to compensate macroeconomic distortions.
Table 1 shows that financial liberalization seems to correlate with growth, although the
identification is marred by many confounding influences.
1
Table 1: Effet de la libéralisation financière sur la croissance
Source : Bekaert, Geert; C. R. Harvey and C. Lundbladd (2004), “Does financial liberalization spur growth?” mimeo.
While credit markets are important, they are vulnerable:
o Banks keep in reserve only a fraction of their liabilities and are vulnerable to bank runs
o Credit markets are vulnerable to adverse selection and moral hazard
In developing countries, they are often a source of instability.
2. Adverse selection and default risk
2.1 Default risk
Here we show how « actuarily fair » (zero-profit) interest rates depend on the general quality of
risks in the population of borrowers and on the proportion of bad loans that can be salvaged, which
typically depends on well-functioning institutions (judiciary etc.)
Notation
2
p
rF
rB
L

Probability of default of a representative borrower
Borrower’s interest rate
Bank’s cost of funds
Loan size
Loan proportion covered by recoverable collateral.
Suppose that the banking sector is competitive, so that equilibrium profit is zero. The bank’s
expected profit is
E  B    1  rB  L  1  p 1  rF  L  p L  0
(1)
which implies
1  p1  rF   p  1  rB 
(2)
or
1  rF 
1  rB  p
1 p
(3)
Thus, the zero-profit interest rate on borrowers, expressed as a function of p,  and rB , is
rF
E  B 0
 r   , p, rB  
1  rB   p 1  p rB  p 1   


1 p
1 p
1 p
(4)
We can now calculate derivatives of rF with respect to these parameters, the key one being with
respect to the default probability p :
drF 1    rB

0
2
dp
1  p 
(5)
d 2 rF 2 1    rB 

0
3
dp 2
1  p 
The interesting thing to note is that both first and second derivatives are positive ; thus, the curve is
convex and high default probabilities send the zero-profit interest rate to the roof. That is, bad
lending environments can be characterized by prohibitively high interest rates; this is an
observation that is potentially relevant for developing countries.
The effect of the recoverability of collateral is also interesting to note; it is negative, suggesting that
environments where collateral is worthless because courts are dysfunctional or corrupt will also be
characterized by very high interest rates (and hence, at the macro level, by little investment):
drF
p

0
d 1 p
(6)
How important are these effects quantitatively ? Table 2 shows a little simulation based on (5) and
(6) that suggests the effect can be massive.
3
Table 2: Zero-profit interest rate as a function of p and 
β
p
0.05
0.1
0.2
0.3
0.5
0.25
0
13.16
16.67
25.00
35.71
14.47
19.44
31.25
46.43
15.79
22.22
37.50
57.14
These issues are important to understand in a developing-country context, because the ability of
institutions to achieve the resolution of insolvency (  ) correlates negatively with income levels
(Figure 1).
100
0
50
Resolving Insolvency
150
200
Figure 1: Resolution of insolvency and GDP per capita
4
6
8
ln GDP per capita
10
12
Note : The vertical axis measures country rank in terms of how easy it is to resolve insolvency cases. A higher number
means a worse ranking.
Source : World Bank, World Development Indicators (income) and Doing Business (resolving insolvency ranking)
2.2 Default risk and market instability: A simple example
So far we haven’t discussed the nature of collateral. Typically one thinks of tangible things like real
estate or capital equipment. But what if creditors could only seize something that’s proportional to
the value of production? Then a worsening of market conditions could affect not only p but also  ,
creating a vicious circle in which an exogenous deterioration in business conditions leads to a
contraction of credit that makes things worse. This is the idea explored by Foellmi et Oechslin
(2011).
Suppose there are two types of borrowers : safe and risky
Probability of loan repayment
Safe type
Risky type
1
1 p
4
1 
Proportion in the population

Demand for credit
Suppose for simplicity that firms combine only variable capital (inventories) with a fixed factor
(say, « management ») in production, and that capital is entirely financed by borrowing, so the
amount of capital is equal to the loan L. The fixed factor ensures diminishing returns on borrowed
capital, which is needed for the profit-maximization problem to have a solution. Banks cannot
distinguish between safe and risky firms, sot hey charge the same interest rate rF to all; because the
banking market is competitive, rF is determined by setting bank expected profits equal to zero.
For a safe type of firm (S), the profit function is
 S  f  L  1  rF  L
(7)
where f(.) is the production function (increasing and concave, so f’ > 0 et f’’ < 0). The firm decides
how much to borrow for profit maximization:
max L f  L  1  rF  L
(8)
f '  L  1  rF .
(9)
with first-order condition (FOC)
Taking the total differential of (9) with respect to L and rF gives f '' dL  drF , or
dL / drF  1 / f ''  0 ; thatis, the demand for credit goes down with the interest rate. So far so good.
We are interestsed in the derivative of output, YS , with respect to the interst rate. This is given by
 1 
dYS dYS dL
(10)

 f '
0
drF
dL drF
 f '' 
Thus, equilibrium output goes down with the interest rate. This is a little bit like the IS curve in an
ISLM macro model.
For a risky type (R), suppose that the production function is
 f  L  with probability 1  p
YR  L   
(11)
with probability p
 g  L
suppose also that the functions f and g are as in Figure 2 . That is, if the investment works, it
generates enough to pay back the loan at its optimum size L * (blue curve on top of the figure) ;
however, if it fails, it cannot generate enough to cover the loan at any interest rate (red curve).
L’entreprise est alors en défaut et la banque saisit sa production.
Figure 2: Risky type’s production function
5
Tengent to f(L) with slope (1+rF)
Y
f(L)
(1+rF) L
L (45o line)
g(L)
L (Loan size)
L*
The risky type’s profit function is then
E  R   1  p   f  L   1  rF  L   p  g  L   g  L  
 1  p   f  L   1  rF  L 
.
(12)
Comparing with (7), it is apparent that the FOC will be the same. Thus, the demand for credit will
be the same from both segments of the market (safe and risky). But for the risky type, the key
ingredient here is that, because a rise in the interest rate reduces output, it also reduces the collateral
that the bank can seize in case of default. This creates the vicious circle I want to illustrate.
After linearization, we can express equilibrium output as a function of the interest rate and, because
of the total differential calculation we already did, we know that the relationship is negative. This
relationship is what we call the demand for credit:
YR  0  1rF
(13)
where
1 
f'
0.
f ''
Credit supply
The bank’s zero-profit interest rate is given by


E  B    1  rB  L   1  p   1    1  rF  L   pYR


1  p


  1   p 1  rF   1  rB   L   pYR
0
6
(14)
Again, let us solve this in order to generate an expression relating the interest rate with the output of
risky firms, YR :
r E    0 
rB   p
1  p
  p   YR 
 
 
1  p  L 
risk-adjusted cost of funds
(15)
risk-adjusted collateral value
  0  1YR
where
1  
p
0
1   p  L
(16)
We call (15) the supply of credit.
Equilibrium stability in our simple demand-supply system (15)-(13) requires
f'
p
 1  
0
(17)
f ''
1   p  L
where reacall that λ is the proportion of bad risks on the market and p their default probability.
1 
Comparative statics: Effect of a negative shock
Let us contrast the effect of a shock in a « healthy market » situation where λp is close to zero vs. in
an unhealthy situation where it is high. In Figure 3, panel (a) shows what happens in good
conditions. When λp i slow, the loan supply curve is relatively flat while panel (b) shows what
happens under good initial conditions. The supply curve’s slope is relatively flat; so the shock on
interest rates is only weakly magnified. By contrast, panel (b) shows when initial conditions are
bad. The credit supply curve’s slope is steeper because  p is higher. As a result, the shock on
interest rates is strongly magnified, which also magnifies the negative shock on firm turnover.
Thus, an unhealthy banking system—one in which banks initially have a substantial proportion of
non-performing or potentially non-performing loans in their portfolios—is also a system that is
vulnerable to shocks. In developing countries, prudential rules are sometimes weakly enforced and
banking supervision is not as strict as it should be, making banking systems potentially unstable.
Figure 3: Effect of a negative shock on the market for credit
(a) Healthy market
(b) Unhealthy market
7
Taux d’intérêt de
marché
Taux d’intérêt de
marché
Demande de fonds
(CPO des entreprises)
Demande de fonds
(CPO des entreprises)
Offre de fonds (zeroprofit des banques)
Offre de fonds (zeroprofit des banques)
Chiffre d’affaire
des entreprises
Chiffre d’affaire
des entreprises
Of course, as the events of 2008-9 illustrated, this does not mean that banking crisis are necessarily
more frequent or severe in developing countries than in industrial ones. Data on banking crises in
Laeven and Valencia (2010) does not suggest a clear relationship between GDP per capita and the
average severity, length, or frequency of banking crises.
2.3 Adverse selection
There is “adverse selection” when:
i.
ii.
One side of the market (say, the sellers) is made of heterogeneous agents (say, sellers of
products of variable quality)
Information is “asymmetric”: one side of the market, the heterogeneous agents, know their
type (say, high or low quality sellers), but the other side does not observe it (say, buyers
cannot assess product quality).
In markets with adverse selection, the price plays two distinct and simultaneous roles:
i.
ii.
It clears the market (i.e. ensures that supply equals demand, its traditional role)
It selects the type of heterogeneous agents who are on the market. To see why, let q be the
monetary value of a product of quality Q. If the market price is $2, all sellers of products of
quality q  2 prefer to stay out of the market, as the price does not reflect the quality of their
product and they have no way of convincing buyers, since quality is unobservable.
Because of these two simultaneous roles played by the market price, the “invisible hand” does not
work anymore; that is, the market does not necessarily reach the equilibrium that maximizes
welfare. Suppose for instance that there is an excess supply. In a traditional market, the price goes
down, inducing seller exit and buyer entry until the market clears. With adverse selection, the price
decrease induces the selective exit of the highest quality sellers; knowing this, buyers find the
market less attractive, and some of them may exit. The process may not converge; in fact, the whole
market may collapse.
A formal example is given in the appendix to show how a higher interest rate reduces the net
profitability of good projects more than that of bad ones. Because of this selection effect, a higher
interest rate which banks could use to protect themselves against risky loans will chase good
projects out of the market, leaving only the bad ones. This is the essence of the principle of adverse
8
selection. When such is the case, the perverse dynamics of a market with adverse selection goes like
this:
1. Some initial proportion of the projects are bad (low b)
2. Because of them, the actuarially fair interest rate is higher than if all borrowers were good, and
it is too high for the best of them, who choose to exit the market.
3. The exit of the best risks raises the actuarially fair interest rate
4. At the new, higher rate, more good risks exit, and so on.
What is particularly relevant for developing countries in this? The best way to think about this is to
think of the institutions that mitigate adverse selection:
o
o
o
o
o
A stable environment conducive to repeated interaction, in which quality becomes known
Accounting transparency
More solid collateral with effective procedures to resolve insolvency
Large participation of all firms in financial markets
Strong banks and effective prudential regulation.
All these ingredients are weaker in developing countries, and fail to work in particular for smaller
borrowers.
3 Access to credit
3.1 The paradox of “credit cycles”
Without access to formal credit, the poor tend to borrow from informal networks. A survey in
Hyderabad, India (Duflo et al.. 2009) suggests that about half the poor borrow from local money
sharks, 13% from family, and 28% from friends and neighbors.
Interest rates are strikingly high. It is common to see interest rates of 5% per day, sometimes up to
10%. At 5%, a Rs 100 ($5.10) loan would become $93 million after a year! (Banerjee Duflo 2011).
Most of these loans seem to be for working capital for street vendors (Ananth, Karlan, Mullainathan
2007) who borrow about $20 in the morning to buy the fruit and vegetable they will sell during the
day and pay back $22 in the evening of the same day, avoiding the compounding of interest rates.
Half the respondents of a survey in Chennai said they had been regularly borrowing during the
previous ten years (66% in the Philippines).
Ananth et al. (2007) argue that this is paradoxical, as a limited reduction of net income during a
limited period of time would enable the borrower to self-finance himself, since all he needs is $20
of savings. For instance, assume that out of the $20 of daily turnover, $2 is the net margin allowing
the street vendor to feed his family. By saving $0.20 every day (10% of his net income), after a
little more than three months he would have the $20 allowing him to finance his daily purchases
without borrowing. He would then save $2 per day, i.e. double his income!
Why the street vendors do not do that is the unexplained “credit cycle paradox”. One reason might
be that bypassing the loan shark would alienate him, in which case the street vendor would be
unable to borrow larger amounts if, say, he fell sick. Good relations with the loan shark is
essentially an insurance. However, evidence is that loan sharks abuse their position as credit
provider and insurers to make outrageous claims on the families of the poor. An alternative and
9
simpler explanation is that the loan sharks will simply hire street bums to exert violence on street
vendors trying to escape their grip.
3.2 Collateral and property rights: A natural experiment
One problem largely cited as the root cause for the poor’s lack of access to bank credit is the
absence of collateral, in particular in the form of land or building titles. For instance, Hernando de
Soto has made himself famous by arguing left and right that the universal solution to credit
rationing for the poor is to define and enforce property rights for all.
How real is this claim? Like all “universal fix” solutions, it is likely to be overblown, but it is
difficult to assess a causal relationship from property rights to credit access because both are likely
to correlate with a host of unobserved individual characteristics (our old omitted-variable bias), and
even reverse causation is likely, as access to credit may enable individuals to acquire property that
can be used as collateral for further loans.
Galiani and Schargrodsky (2006) identified an almost perfect natural experiment to test the effect of
property titles on access to credit:
“We exploit a natural experiment in the allocation of land titles to overcome this identification
problem. More than twenty years ago, a group of squatters occupied a piece of land in a poor
suburban area of Buenos Aires. When the Congress passed a law expropriating the land from the
former owners with the purpose of entitling it to the occupants, some of the original owners accepted
the government compensation, while others are still disputing the compensation payment in the slow
Argentine courts. These different decisions by the former owners generated an allocation of property
rights that is exogenous in equations describing the behavior of the squatters.” (p. 1)
Put differently, we can estimate the effect of property titles on access to bank credit by using the
former squatters who obtained property titles as the treatment group and those who did not obtain
property titles because their landlords were still litigating as the control group. Because assignment
to each group depends on the landlords’ decision, it is orthogonal to any of the squatters’ individual
characteristics.
Galiani and Schargrodsky’s estimation equation is
yi  0  1Ti  Xiβ  ui
where Xi is a vector of control variables pertaining to the squatters and
if i has a property title
1
Ti  
0 if i's landlord is till litigating
(18)
(19)
The dependent variable is either of two things. In the key regression (testing for access to credit), it
is a binary variable equal to one if i has a bank loan. In a number of other regressions, Galiani and
Schargrodsky test if land titles affect the behavior of squatters in intuitive ways; for instance, if they
make tangible improvements in their house.
Results are shown in Table 3 for investment in housing quality and in Table 4 for access to credit.
Interestingly, squatters with property titles do invest in housing quality, improving walls and roofs,
enlarging built surface, and improving sidewalks.
10
Table 3: Property titles and investment in housing quality
Source : Galiani et Schargrodsky (2005)
However, access to credit does not react at all. The reason is pretty clear to anyone familiar with the
Argentine court system: With or without property titles, a bank trying to recover bad loans will face
years of litigation. Indeed, that is why landlords who refused to give up their tract of land to
squatters still faced litigation years later! The problem is not just the property titles: it is also the
absence of well-functioning institutions to enforce contracts, like an effective justice system.
Table 4: Property titles and access to credit
Source : Galiani et Schargrodsky (2005)
4 Does microcredit do miracles?
Microcredit concerns about 150 million people, 2/3 of whom women (Duflo et al. 2009). The most
frequent principle is that of group lending under collective responsibility: As long as one member
11
has not paid back the loan, no one else can borrow. Repayment rates are typically high (above 95%)
but interest rates are also high (around 50% per year) although much lower than the rates charged
by loan sharks.
4.1 Microcredit and social capital
It is often argued that microcredit works better when social capital is strong. An experiment
reported in Feigenberg, Field, and Pande (2010) suggests that microcredit also reinforces social
capital. The experiment consisted of imposing weekly meetings as part of the participation
conditions for a microcredit scheme (MCS) for a treatment group but not for a control group where
mandated meetings were only once a month. After five months, various proxies for social
interaction had improved. The probability of mutual visit was 90% higher for the TG, and after ten
months the probability of jointly attending events was 40% higher. This is sort of anecdotal. More
importantly, the probability of entering in an economic transaction with a partner outside the family
circle was 19% higher for the TG, and the probability of asking for help from another group
member was 29% higher. Relatedly or not, the probability of default was four times lower for the
TG. A gift-giving experiment also yielded higher rates for the TG (those who met once a week).
4.2 Microcredit and women empowerment
As already noted, microcredit often (although not always) targets women. The primary reason is
that women tend to use credit better than men (i.e. spend less on “sin goods” like alcohol, tobacco,
games etc.). Because the money goes to women and opens up economic opportunities for them, it
has been often argued that microcredit is potentially a powerful vehicle for the empowerment of
women.
Any attempt to assess the impact of microcredit on women empowerment raises the usual selection
issues: because taking a loan is a voluntary decision, it is likely to be related to a host of
unobservable individual characteristics (entrepreneurial drive, character strength, etc.) which may
also relate to any measure of the woman’s power within the household. One approach is to use
regression discontinuity design (RDD) on the eligibility cutoff for microcredit (Pitt et Khandker,
1998); however, whether the point of discontinuity in terms of eligibility is sufficiently well
defined to apply RDD has been debated (see Morduch, 1998, or Banerjee, Duflo, Glennerster,
Kinnan 2009, pp. 1-2 for a discussion). The alternative is randomization, but how to randomize is
not obvious. Randomization at the individual level can be difficult to manage from the point of
view of the MCS’s relations with its customer base, and it can create powerful spillovers which
would pollute the results.
Banerjee et al. (2009) set up an experiment with Spandana, a large Indian NGO, in which 53 slum
districts out of 104 were randomly selected to set up MCSs. A baseline survey and a follow-up one,
18 months later, were carried out on 6,850 households in the treated and control districts. The
experiment was not completely clean as other NGOs independently set up MCSs in the control
districts; nevertheless, the probability of getting a loan, for a given household, was 44% (8.3
percentage points) higher in the treated districts.
Unlike in the Grameen Bank, loans were given without conditions under group responsibility to
groups of 6-8 women formed by themselves, with fairly large amounts ($200 at PPP) with a 5012
month maturity and a 12% non-declining interest rate (equivalent to a 20% rate under conventional
terms). Borrowers were not the poorest, having an average income of $550 at PPP. 69% of them
already had loans, and one third had an individual enterprise. In terms of loan use, one third wanted
to use the loan to create a new company, 22% wanted to raise stocks in their company, 30% wanted
to pay back an existing loan, and 15% wanted to use the loan to “smooth” consumption.
Under the assumption of orthogonality of pre-treatment attributes with treatment status, the
estimation equation is simply
yi  0  1Ti  ui
(20)
1 if i belong to the treatment group
Ti  
otherwise
0
(21)
where, as usual
Results on business performance proxies are given in Table 5 and suggest that there was an effect
on business creation and profitability, but none on input use, revenue or employment.
Table 5: Effect of microcredit on business performance
Source : Banerjee et al. (2009)
Effect on consumption are shown in Table 6. Not much either, except more expenditure on durable
goods (bicycle etc.) and on durables used in business, and—interestingly—less on “temptation
goods”.
Table 6: Effect of microcredit on consumption
13
Source : Banerjee et al. (2009)
Most strikingly, Table 7 shows that there was no impact on conventional proxies for the
empowerment of women in the household, which include spending on health and education,
sending children to school (in particular girls), or self-reported power in spending decisions. These
results have sparked a storm of controversy, but there is so far no “hard” evidence suggesting that
these results were special or wrong.
Table 7: Effect of microcredit on proxies for women empowerment
Source : Banerjee et al. (2009)
14
5 Well… Does access to credit really help the poor?
So far the whole discussion was based on the conventional wisdom according to which access to
credit expands the range of economic opportunities and raises income growth. However, Fulford
(2011) cast a doubt on that. He used the rise in the number of bank branches in India between 1970
and 1990 to estimate the long-term effect of access to credit on poverty, using household surveys
carried out by the Indian National Sample Survey on more than 600'000 people in ‘83, ‘87-88, ‘9394, ‘99-2000 et 2004-5. The rise was particularly marked in rural areas, as shown in Figure 4.
Figure 4 : The rise in access to banking services in rural India
Source : Fulford (2011).
Fulford uses only rural data where the time-wise variation is strongest, and estimates the following
equation:
yit  i   t  k 1t k bi ,t k  uit
15
(22)
where i is a region, t a year, yit the poverty headcount or the level of consumption at the region-year
level, and bi,t-1 is the number of bank branches.
Results are shown in Figure 4. Quite strikingly, they suggest that the impact effect of access to
credit on poverty is negative, but the long-term effect is positive (more access to banking raises
poverty rates). One possible conjecture is that as banks expand branches and hire relatively
inexperienced loan officers, the poor end up over-borrowing or borrowing for consumption instead
of for investment, making themselves poorer in the long run.
Table 8: Long-term effect of access to banking services on poverty
15
Source : Fulford (2011).
16
Références
Ananth, Bindu; D. Karlan, and S. Mullainathan (2007), “Microentrepreneurs and Their Money:
Three Anomalies”; mimeo.
Banerjee, Abhijit; E. Duflo, R. Glennerster, et Cynthia Kinnan (2009), “The miracle of
micro.nance? Evidence from a randomized evaluation”; mimeo, MIT.
Fulford, Scott (2011), “The effects of financial Development in the short and long run”; mimeo,
Boston University.
Galiani, Sebastiano, et E. Schargrodsky (2005), “Property Rights for the Poor: Effects of Land
Titling”; Universidad Torcuato di Tella Documento de Trabajo 06/2005
Laeven, Luc, and F. Valencia (2010), "Resolution of Banking Crises: The Good, the Bad, and the
Ugly", IMF working paper.
17
Appendix
How adverse selection may lead to market collapse
Suppose that an investment project requires a loan of size L and has a random return X from a
uniform distribution on [0,b]. Parameter b is the project’s highest possible return and can be
interpreted as the quality of the project; we assume that b  1  r  L where r is the market interest
rate, otherwise the investor would never borrow.
The interest rate can be interpreted as the “price” of the loan, and we first show that a higher
interest rate reduces the investment’s net profitability more for higher-quality project. This will be
the formal equivalent of our earlier statement that the price selects the type of agents on the market.
Here, a higher interest rate will select the worst projects.
The probability density function of X is
f  x 
for x  0, b .
1
b
(23)
The probability of loan default is
p  Pr  X  1  r  L 

1 r  L
0
f  x  dx
1 r  L
1

b0

(24)
1  r  L
b
while the probability of non-default is
b  1  r  L
b
Let C be the loan’s collateral. Expected return on the project, for the investor, is
1 p 
18
(25)


E     pC  1  p  E  X X  1  r  L   1  r  L
 b xf  x  dx

 1 r  L

  pC  1  p  
 1  r  L 
1 p




  pC  
b
1 r  L
xf  x  dx  1  p 1  r  L
x
dx  1  p 1  r  L
1 r  L b
  pC  
b
b
x2
  pC 
 1  p 1  r  L
2b 1 r  L
  pC 
b 2  1  r  L 
2
 1  p 1  r  L
2b
This can be rewritten as
E     pC 
b2  1  r  L 
2
 1  p 1  r  L
2b
b  1  r  L  b  1  r  L  b  1  r  L
  pC  

1  r  L
2b
b
1  r  LC  b  1  r  L  b  1  r  L   2 1  r  L b  1  r  L 

b
2b
2b
1  r  LC  b  1  r  L  2 1  r  L  b  1  r  L 

b
2b
1  r  LC  b  1  r  L  b  1  r  L 

b
2b
1  r  LC  b  1  r  L 

b
(26)
2
2b
Differentiating with respect to the interest rate gives
E   2 b  1  r  L    L  LC


r
2b
b

L 
C  b  1  r  L 

(27)
b 

+


 0.
Thus, a higher interest rate reduces the investment’s net profitability, which is natural. More
interesting is the cross partial derivative with respect to b, the project’s quality.
19
 2 E    L
 L 
  2 C  b  1  r  L   

rb
 b 
b

L  C  b  1  r  L 
 1
b 
b

(28)
L  C  1  r  L 
0
b 
b

Thus, a higher interest rate reduces the net profitability of good projects (high b) more than that of
bad ones (low b), and chases good projects out of the market, leaving the bad ones. This is the
essence of the principle of adverse selection.

20