In developing countries, informal and formal credit sectors coexist
in spite of large interest rate differentials. This coexistence is
troubling given the recent wave of financial liberalization aimed at
broadening and deepening formal credit markets. Two main explanations
are offered in the literature. First, the informal sector may be the
recipient of "spillover" demand from the formal sector (Bell,
Srinivasan, and Udry 1997; Conning 1996; Hoff and Stiglitz 1990). In
this view, formal lenders have limited local information and must rely
on collateral to solve the moral hazard and adverse selection problems
inherent in credit transactions. Informal lenders' ability to
substitute information-intensive screening and monitoring for collateral
allows them to offer contracts to individuals that are excluded from the
cheaper formal sector.
An alternative explanation is that lower transaction costs allow
informal lenders to offer loans with lower effective cost (Chung 1995;
Kochar 1997; Mushinski 1999). In this view, the informal sector need not
be the sector of last resort but instead may be the preferred sector.
This latter explanation is important because it emphasizes that multiple
dimensions of loan contracts must be considered when analyzing sectoral
choice.
In this article, we expand upon this view and argue that an
additional, crucial dimension of loan cost, namely, risk, has been
neglected. If borrowers are risk averse and insurance markets are
underdeveloped, the relevant cost differential across sectors should be
thought of in terms of expected utility instead of expected income. We
argue that the lower collateral requirements of informal loans imply
greater consumption smoothing for borrowers compared to the formal
sector alternative. (1) If the cost of this implicit insurance, in terms
of lower expected consumption, is not too high, then some borrowers may
undertake expected income enhancing investments that they would forego
if they only had access to a more risky formal loan. The informal
sector, by permitting a reduction in collateral, may thus relax both
quantity rationing and another form of nonprice rationing termed
"risk rationing" by Boucher, Carter, and Guirkinger (2005).
We draw on several strands of the theoretical literature on credit
rationing to formalize these two potential roles of the informal sector.
As in Bester (1987) and Schmidt-Mohr (1997), we acknowledge the use of
collateral as a means used by lenders to address asymmetric information.
The effectiveness of collateral in averting non-price rationing is
limited, however, in rural areas of developing countries, where
collateral assets are scarce and insurance markets are weak. The premise
of our analysis is that informal lenders' better access to local
information allows them to offer contracts with lower collateral. As a
result, an informal loan may be demanded both by those who cannot post
the collateral required by the formal sector and by those who can but
are unwilling to do so because of the associated risk. As in Conning
(1996), we portray the informal lender's information advantage as
the ability to monitor borrowers and impose a penalty for shirking. The
ensuing collateral reduction, however, comes at a cost as informal
lenders expend resources on monitoring that must be recovered via a
higher interest rate. We extend Conning's model, which assumes
borrower risk neutrality, to allow for the more realistic assumption of
risk aversion. By doing so, our analysis shows that the informal sector
not only absorbs the spillover demand of the poorest agents who are
excluded from the formal sector, but also may be preferred by a class of
agents who could obtain a formal loan.
While it is easy to show that spillover demand derives from the
poor, characterizing the location within the wealth distribution of the
second group is complicated because of counter-veiling impacts of wealth
under risk aversion. We derive sufficient conditions regarding agent
preferences to determine the impact of agent wealth on sectoral choice.
The structure of the article is as follows. The next section
motivates the ensuing theoretical analysis by using descriptive evidence
from several recent household surveys to document the multiple roles
played by the informal loan sector. We then lay out a model in which
agents choose both activity and loan sector. We next take up the impact
of agent wealth on activity and sectoral choice. When farm size if
fixed, we show that a fairly strong condition on borrower preferences is
required to deliver the intuitive result that the informal sector
relaxes formal sector risk rationing for agents that are relatively poor
in terms of liquid wealth. The penultimate section extends the model to
allow for heterogeneity in farm size. We show that weaker conditions on
agent preferences are required for the informal sector to relax formal
sector risk rationing for agents that are relatively poor in terms of
land wealth. The final section concludes.
Descriptive Evidence on the Roles of the Informal Sector
In this section, we use data from three recent farm-household
surveys in Latin America to provide descriptive evidence on the
relationship between formal and informal loan sectors and the multiple
reasons that farm households seek informal loans. (2) We define three
loan sectors. The formal sector consists of regulated financial
institutions and includes commercial banks, state development banks,
credit unions and, in the case of Peru, rural and municipal banks. The
informal sector includes moneylenders, input supply dealers, traders,
and agro-processing firms. Finally, the semiformal sector includes
unregulated lending institutions such as NGO's and government loan
programs.
Table 1 compares key contract terms across the three sectors. (3)
The general picture that emerges from table 1 is that in each country
the formal sector offers more attractive loans compared to the informal
sector with respect to size, interest rate, and maturity. (4) The most
striking difference is the case of Peru, where informal loans carry an
average annual interest rate of 117%, which is nearly double the
interest rate in the formal sector. The same patterns hold in Honduras
and Nicaragua.
Table 2 compares participation in the various credit market sectors
for households facing positive supply versus no supply from the formal
sector. Households with positive supply either obtained a formal loan in
the previous twelve months or believed they could obtain one. The
dominance of contract terms in the formal sector discussed above
suggests that a household would only seek an informal loan if it were
denied access to the formal sector. (5) Table 2, however, suggests
otherwise. For example in Peru, 17% of households that had access to a
formal loan borrowed only from the informal sector, suggesting that
these households preferred the informal sector despite the apparently
inferior loan terms it offers. In Honduras and Nicaragua, 7% and 6% of
households with positive formal supply chose to borrow exclusively from
the informal sector. While these percentages are lower than in Peru,
overall household participation in any sector of the credit market is
also lower. In Honduras and Nicaragua respectively, informal borrowers
represent 13% and 20% of households that borrowed and had a choice
across sectors.
Why, then, would a borrower prefer the informal sector? A
comparison of collateral requirements across the two sectors suggests an
answer. A glance back at table 1 reveals that, across these three
samples, at least 58% of formal loans required that the borrower post
physical assets, typically agricultural land, as collateral. Informal
loans, in contrast, required collateral much less frequently. Taken
together, the data suggest that borrowers face a choice between lower
cost but higher risk (collateral) contracts available in the formal
sector and the higher cost but lower risk contracts of the informal
sector. (6)
It would seem, then, that the informal sector indeed plays multiple
roles. Important fractions of households that are shut out of the formal
sector resort to informal loans, suggesting that the informal sector
indeed receives spillover demand from the formal sector. Yet the
informal sector also appears to be the sector of choice for other
households and risk considerations appear to at least partially drive
this choice. In Peru, for example, 46% of households that chose the
informal sector gave the risk associated with posting collateral as the
primary reason for forgoing a formal loan.
Finally, table 2 also reports mean wealth levels for households in
each category. Two patterns emerge. First, households shut out of the
formal sector are poorer. Second, of those households with access to the
formal sector, informal borrowers are poorer than formal borrowers. We
now turn to constructing a conceptual framework that can help explain
the patterns suggested by this descriptive analysis.
Model Setup
In this section and the next, we develop a model that examines
optimal loan contracts in each of two sectors and agents' choice
both across sectors and alternative activities. We begin by outlining
the key assumptions about preferences, technology, and information and
then describe the potential choices that agents may face. The model
contains three types of actors: (a) farmers, (b) formal lenders, and (c)
informal lenders. All farmers are endowed with one unit of land and
labor. Heterogeneity across farmers derives from their endowment of
financial wealth, W [member of] [[W.bar], [bar.W]].
We posit a simple technology that allows us to explore the dual
roles of credit as both provider of liquidity and, potentially,
insurance. Farming requires a fixed investment, K > [bar.W]. In order
to produce on their own land, farmers thus require outside finance. We
further assume that if a farmer borrows, the lender funds the full
amount of the investment, K. (7) Farming is risky. Gross farm revenues
are [X.sub.g] if the state of nature is "good" and [X.sub.b]
if the state of nature is "bad," with [X.sub.g] > K >
[X.sub.b]. Finally, the farmer's fallback, or reservation, activity
is to work as a wage laborer and earn a certain wage, [omega].
The farmer potentially has three choices. The first is whether to
farm or work as a wage laborer. If she chooses to farm, she faces two
additional choices: loan sector and effort level, e, which is committed
after receiving the loan. The effort level, which we assume can be
either high, H, or low, L, affects welfare and choice in two ways. (8)
First, high effort increases the probability of the good state and thus
raises the expected farm returns. Letting [p.sup.H] and [p.sup.L] denote
the probabilities of the good state under high and low effort levels,
this implies [p.sup.H] > [p.sub.L]. Let [[bar.X].sup.H] and
[[bar.X].sup.L] represent expected gross revenues under high and low
effort and [r.sup.F] and [r.sup.I] denote the opportunity cost of
capital for formal and informal lenders, with [r.sup.F] < [r.sup.I].
The following inequalities summarize our assumptions regarding the
impact of effort on expected returns:
(1) [[bar.X].sup.H] - [r.sup.I] K > [omega] > 0 >
[[bar.X].sup.L] - [r.sup.F] K.
The first inequality implies that, even evaluated at the informal
lender's higher opportunity cost of capital, farming with high
effort is more profitable than wage labor. The last inequality implies
that any loan contract will require high effort. Since effort is not
contractible, lenders face a moral hazard problem and must provide
incentives to induce the agent to choose high effort.
While high effort increases expected farm returns, it also causes
disutility. We assume the following additively separable utility
function: U(Y, e, m) = u(Y) - d(e, m). The first term is the utility of
income, which we assume is increasing and concave. To ensure that
quantity rationing may occur, we assume that when income is zero,
utility is finite. (9) Income, Y, in turn is composed of initial wealth
plus the net income from the chosen activity. The second term is the
disutility of effort that depends both upon the effort level chosen by
the farmer and m, the level of monitoring chosen by the lender as
follows:
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
with [bar.d] > [d.bar] > 0 and [beta] [greater than or equal
to] 0. Like effort, monitoring is carried out after the loan is granted.
If she exerts high effort, the borrower's disutility is unaffected
by monitoring. In contrast, if she exerts low effort, her disutility is
increasing (at the constant rate [beta]) in the monitoring level.
Whether or not the borrower decides to shirk depends upon the
private benefit of doing so. Let B denote the reduction in the
borrower's disutility resulting from choosing low instead of high
effort. From equation (2), the private benefit of shirking is: B(m) =
[alpha] - [beta]m, where a = [bar.d] - [d.bar] is the agent's
disutility differential under zero monitoring. Monitoring thus addresses
the moral hazard problem by reducing the borrower's private benefit
of shirking. (10) We posit that informal lenders' access to local
information grants them a monitoring advantage vis-a-vis more
centralized and socially distant formal lenders. Informal lenders are
members of the local community and can thus impose a punishment, for
example, damaging the borrower's reputation, that formal lenders
cannot. We operationalize this informational advantage by assuming
[beta] > 0 for informal lenders and [beta] = 0 for formal lenders.
Formal lenders will thus never monitor.
Formal and Informal Credit Contracts
We now turn to the agent's choice of loan sector. We treat the
loan sectors as independent and allow the agent to borrow from at most
one lender. Finally, we assume perfect competition and risk neutrality
of lenders in each sector.
The Potential for Non-price Rationing in the Formal Sector
We begin with the contracting problem in the formal sector. Let
[R.sup.F.sub.j] be the portion of farm returns retained by the borrower
in state j under a formal contract. (11) To find the optimal contract,
we use a modified principal--agent framework in which the agent (farmer)
chooses the feasible contract that maximizes her expected utility. Let
[V.sub.F](W) be the borrower's formal sector value function, or the
expected utility from the optimal formal sector contract. The optimal
formal contract is the solution to:
(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
subject to:
(5) [u(W + [R.sup.F.sub.g]) - u(W + [R.sup.F.sub.b])]([p.sup.H] -
[p.sup.L]) [greater than or equal to] B(O)
(6) [p.sup.H]([X.sub.g] - [R.sup.F.sub.g]) + (1 -
[p.sup.H])([X.sup.b] - [R.sup.F.sub.b]) - [r.sup.F] K [greater than or
equal to] 0
(7) [R.sup.F.sub.j] [greater than or equal to] - W; for j = g, b.
Equation (5) guarantees that the agent's expected utility gain
from choosing high effort outweighs the private benefit of choosing low
effort. Let the incentive compatibility boundary, ICB(m), denote the
locus of contracts such that this constraint binds under monitoring
level m. Equation (6) is the formal sector participation constraint
(FPC) that requires that the formal lender's expected profits are
nonnegative. Finally, equation (7) is the limited liability constraint
(LLC) that states that borrowers cannot be made liable for an amount
greater than their financial wealth.
The primary features of the problem and the implications of
asymmetric information are illustrated in figure 1. The axes represent
the contractual return to the borrower under each state. Note that, even
if [R.sub.b] is negative, consumption in the bad state is positive as
long as [R.sub.b] > - W. The agent's indifference curves are
convex to the origin. The risk-neutral lender's expected profit
contours are straight lines with slope -1 -[p.sup.H]/[p.sup.H]. Along
one of these contours the agent's expected return is also constant;
however, her expected utility is increasing toward the 45[degrees] line.
The shaded area depicts the set of feasible contracts. These contracts
lie below the ICB(0) curve, to the southwest of the formal lender's
zero-profit contour, [[pi].sup.F.sub.0], and above the LLC, which is the
horizontal line at [R.sup.F.sub.b] = -W. Given the shape of the feasible
contract set, the constrained optimal formal contract, if it exists, is
unique and found at point C, the intersection of the ICB(0) and
[[pi].sup.F.sub.0] curves. (12) Of all the available contracts yielding
the highest expected income, it is the one with lowest risk.
[FIGURE 1 OMITTED]
Figure 1 also demonstrates the potential for nonprice rationing in
the formal credit market. In general the closer a contract is to the
45[degrees] line, the greater is the borrower's consumption
smoothing across states. Indeed, in a first-best world with costless
enforcement of effort, the optimal contract would be at point A and
fully insure the agent's consumption. Under asymmetric information
the lender faces a trade-off in providing insurance versus providing
incentives for the borrower to work hard. In figure 1, the introduction
of asymmetric information effectively "removes" the contracts
between points A and C from the feasible set. In order to induce the
agent to work hard, the lender must reward her with a high return under
the good state and punish her with a low return under the bad state. If
the latter is negative, the borrower must post collateral.
This asymmetric information induced reduction of the set of
available contracts can result in two types of non-price rationing.
Quantity rationing occurs when an agent has a profitable project but
cannot undertake it because the lender makes no contract available. In
figure 1, the agent would be quantity rationed if the LLC was shifted up
above point C. Risk rationing, in contrast, occurs when an agent has a
profitable investment project but chooses not to undertake it, even
though she has access to a loan that would raise her expected income,
because the contract forces her to bear too much risk. Figure 1
illustrates this risk rationing outcome. Point B represents the
reservation activity, which pays co in both states. Although the
agent's expected return from the contract at point C is greater
than [omega], the contract is sufficiently risky such that its certainty
equivalent, at point D, is less than [omega].
Under both forms of nonprice rationing, the agent ends up in the
low return reservation activity. In the case of quantity rationing, she
has no choice because the feasible contract set is empty. If agents were
risk neutral, a non-empty feasible set would be necessary and sufficient
for the agent to undertake the most profitable activity. If agents are
risk averse, access to a contract is necessary but no longer sufficient
for the most profitable activity to be chosen. Identifying the impacts
of asymmetric information on lenders' willingness to offer
contracts is thus insufficient to understand credit market
participation. A complete understanding also requires attention to the
risk implied by contracts and to borrowers' willingness to accept
that risk. (13)
Characterization of the Optimal Contract in the Informal Sector
As in the case of the formal sector, we assume informal lenders are
risk neutral and competitive. They differ from formal lenders in two
ways. First, [r.sup.I] > [r.sup.F], so that the informal
lender's cost of funds is higher than the formal lender's. As
a result, an informal loan will always be more expensive than a formal
one and will yield a lower expected return to the borrower. Second,
informal lenders can monitor borrowers. Like formal loans, informal loan
contracts must induce high effort.
Let [V.sub.I](W) be the agent's informal sector value
function. In addition to specifying the borrower's return in each
state, the optimal informal contract specifies a level of monitoring, m,
and is the solution to the following problem:
[FIGURE 2 OMITTED]
(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
subject to:
(9) [u(W + [R.sup.I.sub.g]) - u(W + [R.sup.I.sub.g])]([p.sup.H] -
[p.sup.L]) [greater than or equal to] B(m)
(10) [p.sup.H]([X.sub.g] - [R.sup.F.sub.g]) + (1 -
[p.sup.H])([X.sub.b] - [R.sup.I.sub.b]) - [r.sup.I] K [greater than or
equal to] m
(11) [R.sup.I.sub.j] [greater than or equal to] - W; for j = g, b.
Monitoring affects the feasible contract set in several ways. An
increase in m lowers the private benefit of shirking and thus relaxes
the incentive compatibility constraint (equation (9)). Monitoring,
however, comes at a cost. Since the lender must recover resources spent
on monitoring, the lender's participation constraint (equation
(10)) tightens. The left-hand panel of figure 2 depicts the upward shift
of the ICB and the downward shift of the LPC accompanying an increase in
monitoring from 0 to m. The optimal contracts conditional on the lower
and higher levels of monitoring are at points E and F, respectively. In
the right-hand panel, the dashed curve traces out the conditional
contract set (CCS), which is the locus of intersections between the ICB
and the LPC for each level of monitoring. The optimal informal contract,
point G in figure 2, is the point on the CCS that maximizes the
borrower's expected utility.
Rethinking the Role of the Informal Sector
An increase in monitoring makes available some new contracts that
require less collateral and are thus less risky but eliminates those
with highest expected returns. A necessary condition for the informal
sector to relax quantity and risk rationing is that the conditional
contract set includes some contracts that require less collateral than
the optimal formal contract while still offering an expected return
greater than the reservation wage. We assume this holds. (14)
Figure 3 depicts the two roles of the informal sector. In the
left-hand panel the informal sector is the recipient of
"spillover" demand from the formal sector. The agent faces
quantity rationing in the formal sector since the minimum collateral
required for the optimal formal contract at point H exceeds the
agent's wealth. The optimal informal contract at point J is both
feasible and preferred to the reservation activity.
The right-hand panel of figure 3 depicts the case of a farmer who
chooses to borrow from the informal sector even though a lower cost
formal contract is available. The optimal informal contract at M
requires sufficiently lower collateral (offers sufficient insurance)
such that it is strictly preferred to both the formal contract at L and
the reservation activity.
[FIGURE 3 OMITTED]
This farmer would be risk rationed in the formal sector since the
certainty equivalent of the optimal formal contract is less than
[omega].
Wealth and Activity Choice
Now that we have depicted the two potential roles of the informal
sector, we turn to the question: For whom does the informal sector play
these roles? In other words, how do we understand the mapping of agents
of different wealth across formal and informal sectors? We proceed in
three steps. First we focus on supply to see who is quantity rationed in
the formal sector. Second, ignoring quantity rationing, we look at the
unconstrained choice across the agent's three options (wage labor,
farm with formal contract, farm with informal contract). We examine the
three pair-wise comparisons. Finally, we bring supply and demand
together to partition the wealth space according to activity choice and
credit market outcomes.
Wealth and Credit Supply
Intuition suggests that if anyone is quantity rationed in the
formal sector, it will be the relatively poor who have insufficient
wealth to post as collateral. This result has been established in the
theoretical literature by various authors including Stiglitz and Weiss
(1981), Carter (1988), and Bester (1987) and also obtains with our
model. The logic of wealth-biased quantity rationing in our model is as
follows. Let [W.sup.*] denote the wealth level such that all three
constraints simultaneously bind. In figure 1, this would correspond to
the horizontal limited liability constraint passing through point C so
that a single contract ([R.sup.*.sub.g], -[W.sup.*]) requiring her full
wealth as collateral is available. If this agent's wealth is
increased by $1 it is easy to see that she will still have at least one
contract available. In particular, the contract ([R.sup.*.sub.g],
-[W.sup.*] -1) is incentive compatible since it holds constant
consumption in the bad state while raising consumption in the good state
by $1, thereby increasing the borrower's incentive to work hard.
This contract also satisfies the lender's participation constraint
as it yields strictly positive expected profits. Thus any agent with
wealth at least as large as [W.sup.*] will have a contract available. A
symmetric argument shows that agents with wealth less than [W.sup.*]
will have no contracts available so that, if anyone is quantity
rationed, it will be the relatively poor.
As discussed above, monitoring allows informal lenders to offer
loans with lower collateral than the formal sector. Thus agents with
marginally less wealth than [W.sup.*] will have access to an informal
loan. We make the further assumption that an informal contract is
available for all agents. (15)
Wealth and Credit Demand
The discussion above established the choices available to agents.
All agents have the same reservation option. Relatively poor agents (W
< [W.sup.*]) choose between the reservation option and informal
finance, while relatively wealthy agents (W [greater than or equal to]
[W.sup.*]) have the additional option of financing production with a
formal loan. Examining the three pair-wise comparisons between
activities will allow us to map activity choice over the wealth
spectrum. For each comparison, we provide sufficient conditions for
either the relatively wealthy or the relatively poor to prefer the
riskier activity.
Reservation Activity versus Farming with Formal Loan
Who prefers high return but risky farming to the reservation
activity? Assume that agents exhibit decreasing absolute risk aversion
(DARA). Intuition suggests that the wealthy would bear the risk of
farming while the poor would retreat to the certain reservation
activity. This intuition, however, fails to consider that contract terms
change with borrower wealth. In fact, the contracts available to
wealthier agents are more risky than those available to poorer agents.
Concavity of the utility function implies that wealthier agents are less
sensitive to a given difference in consumption, and thus in contractual
returns, across states. To provide sufficient incentives for the
wealthier agent to work hard, the lender must increase contractual risk.
What is the net result of these opposing "risk aversion"
and "incentive" effects of wealth? Ultimately, the relative
size of these effects depends on the nature of the agent's
preferences. Several papers in the literature on wealth effects in
principal-agent models develop sufficient conditions for the dominance
of one effect (Newman 1995; Mookherjee 1997; Thiele and Wambach 1999).
Boucher, Carter, and Guirkinger (2005) analyze this question with a
single loan sector equivalent to our formal sector and develop necessary
and sufficient conditions on preferences to determine the direction of
the wealth bias of risk rationing in the absence of monitoring. These
conditions relate to higher-order curvature of the agent's utility
function. Specifically, if the agent's absolute prudence, P, is at
least three times as large as absolute risk aversion, A, then the
relatively poor will be risk rationed. (16) Conversely, if P < 3A
then the relatively rich will be risk rationed. Without additional
assumptions about u(;), the relationship between P and A depends on the
value of consumption at which these functions are evaluated. A useful
specialization is the class of constant relative risk-averse preferences
(CRRA) because it implies that P/A is constant. In the remainder of the
paper, we will restrict attention to this class of preferences.
Reservation Activity versus Farming with an Informal Loan
Next we take up the comparison between farming with an informal
contract and the reservation activity. In the informal sector,
monitoring allows the agent to trade risk against expected income. This
additional contractual flexibility may reduce the incidence of risk
rationing in the informal sector, but it need not eliminate it. We are
then left with the question of who (i.e., the relatively wealthy or
poor) is risk rationed in the informal sector? To answer this question,
we first define the following terms. Let [CE.sup.I](W, m) denote the
certainty equivalent associated with the optimal contract at the level
of monitoring m for an agent with wealth W in the informal sector.
Define [m.sup.*](W) as the optimal level of monitoring in the informal
sector for an agent with wealth W. Let [[??].sub.IR] denote the wealth
level of the agent who is indifferent between financing the risky
investment with her optimal informal contract versus the certain
reservation activity so that: u([[??].sub.IR] +
[CE.sup.I]([[??].sub.IR], [m.sup.*]([[??].sub.IR]))) = u([[??].sub.IR] +
w). The following proposition describes the relationship between agent
wealth and risk rationing in the informal sector.
PROPOSITION 1. (Wealth biased informal risk rationing.) P >
(<) 3A [right arrow] [partial derivative]CE.sup.I]/[partial
derivative]W > (<)0 so that any agent with wealth greater than
(less than) [[??].sub.IR] will strictly prefer the risky investment with
their optimal informal contract while agents with wealth less than
(greater than) [[??].sub.IR] prefer the reservation activity. (17)
Note that the same condition on agent preferences that determines
the direction of the wealth bias of risk rationing in the formal sector
holds in the informal sector. This may appear surprising in light of our
previous discussion about the ability of the informal sector to
alleviate risk rationing. It is true that, for a given wealth level, the
ability to monitor provides greater contractual flexibility and thus
raises the maximum expected utility attainable by the borrower.
Monitoring does not, however, affect whether the maximum attainable
expected utility increases or decreases in agent wealth. This result is
due to the separability of the agent's utility in monitoring and
wealth. The same offsetting "incentive" and "risk
aversion" effects described in the formal sector are at play in the
informal sector and are independent of the level of monitoring.
Until now we have focused on the agent's comparison between a
loan in each sector and the reservation activity. The final piece of the
analysis, which will permit us to map wealth into activity and sectoral
choice, is to compare the relative attractiveness of the optimal formal
versus informal contracts.
Farming with Formal versus Informal Loan
We have seen that if P > 3A, the relatively poor prefer the
certain reservation activity to the risky contracts of either sector.
Intuition would suggest that the relatively poor would then prefer the
less risky informal contract to the more profitable formal contract.
However, as shown by Rothschild and Stiglitz (1971) and Ross (1981), in
the expected utility framework the ranking of preferences over two risky
prospects is nontrivial and intuitions derived from the concept of
absolute risk aversion need not hold. Proposition 2 below shows that
this intuition indeed holds, namely, the relatively poor prefer the less
risky informal contract to the formal contract when P > 3A. Let
[[??].sub.FI] denote the wealth level of the agent who is indifferent
between farming with her optimal informal contract and farming with her
optimal formal contract and let [CE.sup.F] denote the certainty
equivalent of the optimal formal contract so that: u([[??].sub.FI] +
[CE.sup.I] ([[??].sub.FI], m* ([[??].sub.FI]))) = u([[??].sub.FI] +
[CE.sup.F] ([[??].sub.FI])).
PROPOSITION 2. (Sectoral choice.) If p >(<) 3A any agent with
wealth greater than (less than) [[??].sub.FI] will strictly prefer the
formal contract while agents with wealth less than (greater than)
[[??].sub.FI] prefer the informal contract. (18)
We have now described the impact of wealth on each of the three
pair-wise activity rankings. This will enable a complete mapping of
activity choices over the wealth spectrum. That is the task to which we
now turn.
Mapping Wealth into Activity and Sectoral Choice
In this final step, we bring together the supply-side results that
described which agents have access to contracts in each sector with the
demand-side results that described the impact of wealth on the
preference ranking of available activities. The mapping of agent wealth
into activity and sectoral choice will depend upon two key relationships
derived from the model's underlying parameters. The first is the
direction of the sufficient condition regarding agents'
preferences. As shown above, if P > 3A, the willingness to accept the
(endogenously) greater risk associated with higher expected return
contracts is increasing in agent wealth. The second is the ordering of
the three threshold wealth levels, [[??].sub.FR], [[??].sub.IR], and
[[??].sub.FI], and the minimum collateral requirement in the formal
sector, [W.sup.*]. While it would appear that there is an unwieldy
number of potential orderings to consider, we are able to rule out many
of them. Here we will only consider outcomes under the case P > 3A. A
symmetric analysis obtains when P < 3A.
Propositions 1 and 2 establish the relative magnitudes of the
slopes of the agent's three value functions at wealth levels such
that two value functions cross. In particular, under P > 3A, the
value function of the relatively riskier activity is steeper at a
crossing point. This result, combined with the uniqueness of the three
crossing points implies only two possible orderings of the three
threshold wealth levels: [[??].sub.FI] > [[??].sub.FR] >
[[??].sub.IR] and [[??].sub.IR] > [[??].sub.FR] > [[??].sub.FI].
(19)
Figure 4 depicts the three value functions when the first ordering
holds. (20) Which of the two orderings obtains depends upon the relative
attractiveness of the informal sector. Either an increase in the
opportunity cost of funds in the informal sector or a decrease in the
efficiency of monitoring (i.e., a reduction in 13) would lead to a
downward shift of the informal sector value function while leaving
unchanged the other two value functions. If the downward shift is
sufficiently large the second ordering would obtain.
[FIGURE 4 OMITTED]
Figure 4 shows that if the informal sector did not exist, no agent
poorer than [[??].sub.FR] would farm. Even with the informal sector, the
poorest agents (W < [[??].sub.IR]) do not farm because the available
informal contracts, although raising the agent's expected income,
are too risky. Slightly wealthier agents ([[??].sub.IR] < W <
[W.sup.*]) accept the risk of their informal contract and undertake
farming. For this group, the informal sector plays the role of recipient
of "spillover demand" since these agents are shut out of the
formal sector for lack of collateral wealth. For agents in the next
portion of the wealth spectrum ([W.sup.*] < W < [[??].sub.FR]),
the informal sector relaxes formal sector risk rationing. Although a
more profitable formal contract is available to them, they prefer the
less risky, monitored loan of the informal sector. Agents with wealth
greater than [[??].sub.FR] would farm even if the informal sector did
not exist. The wealthiest agents (W > [[??].sub.FI]) are willing to
bear the risk of the formal sector contract. The slightly less wealthy
([[??].sub.FR] < W < [[??].sub.FI]) instead prefer an informal
loan.
The informal sector thus plays a critical role for agents in the
intermediate range of the wealth spectrum ([[??].sub.IR] < W <
[[??].sub.FR]) as it affects their activity choice and allows them to
undertake the socially desirable activity. For a given ordering of the
threshold wealth levels, the overall impact of the informal sector on
the economy would thus depend on the distribution of wealth.
Extension to Multiple Farm Sizes
In the previous section, we saw that the assumption that P > 3A
results in an intuitive mapping of wealth into activity and sectoral
choice in which the beneficiaries of the insurance provided by the
informal sector are the relatively poor. This assumption, however, is
restrictive. Specifically, under CRRA preferences, P > 3A corresponds
to a coefficient of relative risk aversion, [rho], smaller than 0.5.
Several empirical studies, such as those cited in Gollier (2001) suggest
that plausible ranges of p are between one and four. In this section, we
follow the strategy used by Boucher, Carter, and Guirkinger (2005) in
the context of a single loan sector by allowing heterogeneity not only
in financial wealth but also in the agent's endowment of productive
wealth, i.e., their farm size. This extension yields an intuitive
partitioning of the two-dimensional wealth space when the restrictive
preference assumption (P > 3A) is relaxed.
Why would financial and land wealth have different impacts? The
intuition is as follows. For a given farm size, the difference in
expected consumption under farming with a loan contract versus the
reservation activity is independent of the agent's financial
wealth. Lenders, however, must shift greater contractual risk toward the
borrower in order to induce financially wealthier agents to exert high
effort. Under P < 3A (i.e., preferences consistent with empirical
evidence), above a threshold level of financial wealth, farming becomes
too risky to justify the gain in expected income from farming so that
the financially wealthiest agents withdraw to the reservation activity.
In contrast, as the agent's land wealth increases, the expected
consumption foregone by choosing the reservation activity increases, so
that agents with a greater land endowment are more willing to bear the
risk of the contract and to farm.
A straightforward modification of the model captures this
intuition. An agent is now endowed with financial wealth, W, and land,
T. The agent chooses between farming on her entire land endowment and
renting it out at fixed rental rate [gamma]. The required farm
investment is now TK and gross revenues are [TX.sub.g] and [TX.sub.b] in
the good and bad states. As before, the agent needs outside financing to
farm. The optimal formal sector contract now specifies the
borrower's return per unit land in each state and is the solution
to the following program:
(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
subject to:
(13) [u(W + [TR.sup.F.sub.g]) - u(W + [TR.sup.F.sub.b])]([p.sup.H]
- [p.sup.L]) [greater than or equal to] B(0)
(14) [p.sup.H] ([X.sub.g - [R.sup.F.sub.g]) + (1 -
[p.sup.H])([X.sub.b] - [R.sup.F.sub.b]) - [r.sup.F]K [greater than or
equal to] 0
(15) [TR.sup.F.sub.j] > - Wj = g, b.
The formal lender's participation constraint is unchanged
since returns and investment per unit of land have not changed. The
incentive compatibility and limited liability constraints, however, are
modified to account for T. The optimization program in the informal
sector is modified in a similar fashion.
In this model extension, the role of financial wealth in sectoral
and activity choice is unchanged. Namely, under CRRA, [rho] < 0.5 is
necessary and sufficient such that agents with low financial wealth are
more likely to prefer the relatively safe activity. A change in land
wealth, however, may yield a different outcome. Holding W constant, p
< 0.5 is sufficient but no longer necessary for the land poor to
prefer the relatively safe activity. While an analytic expression for
the maximum value of p such that this intuitive result holds does not
exist, we know that it is larger than 0.5 and is increasing in the
difference between the land rental rate and the expected per-hectare
return from farming. (21)
Figure 5 maps the activity and sectoral choices in (W, T) space
that result from a numerical computation of the model. (22) For the
computation, a CRRA utility function with [rho] = 0.75 was chosen. (23)
Other parameters were chosen so that quantity rationing does not occur.
This allows us to focus on the role of financial wealth and farm size on
the choice between available contracts and activities.
Consider the agent at point N who is indifferent between farming
with a formal and an informal loan. The vertical ray shows the
counter-intuitive role of financial wealth for a farm size of 2.5.
Financially poorer agents than N farm with a formal loan; those with
slightly greater financial wealth farm with an informal loan; while the
financially wealthiest retreat to the reservation activity. Movements
along the horizontal ray show the opposite and more intuitive result.
Holding financial wealth constant at 900, agents with a larger land
endowment than N farm with a formal loan; those with smaller land
endowment prefer an informal loan; while the land-poorest rent their
land out. The indifference frontiers, [[??].sub.IR] (T) and
[[??].sub.FI](T) divide wealth space into activity choice and are upward
sloping. The magnitude of their slopes, in turn, depends on underlying
model parameters. Ultimately, the importance of the informal sector will
depend on both the shape of these frontiers and the empirical
distribution of wealth. If, as we expect, there is a positive
correlation between the two types of wealth so that farmers are grouped
along the diagonal ray in figure 5, then the informal sector would be
chosen by farmers of intermediate wealth while the richest would seek
out the formal sector.
[FIGURE 5 OMITTED]
This analysis shows that heterogeneous asset types have different
impacts on incentives and thus the nature of contracts available.
Therefore both heterogeneity of asset types controlled by an individual
as well as heterogeneity of total wealth across individuals are
important in understanding household participation in credit markets.
Conclusion
In this article, we have developed a model that suggests a
re-evaluation of the role of the informal loan sector in rural areas of
developing countries. The informational advantage of informal lenders is
portrayed as their ability to monitor borrowers. Monitoring, by limiting
the private benefit the borrower perceives by shirking, reduces the
incentive problem and allows for contracts with lower collateral. This
enables informal lenders to serve two types of clients: (a) Those who
cannot post the collateral required by the formal sector; and (b) those
who are able but do not want to post collateral. These borrowers are
willing to accept a lower expected income in exchange for lower
contractual risk. The model is thus consistent with the conventional
view of the informal sector as recipient of spillover demand from the
formal sector. It also suggests an additional role of the informal
sector, namely, as provider of partial insurance. Previous models, by
assuming risk neutrality of borrowers, do not permit this role because
they rule out contractual risk as a determinant of sectoral choice.
Neglecting the impact of risk-sharing rules of credit contracts is
particularly problematic in rural areas of developing countries where
risks are high and insurance markets are thin.
While the informal sector always plays the first role (i.e.,
relaxing quantity rationing in the formal sector) for the relatively
poor, for whom the informal sector relaxes risk rationing in the formal
sector depends upon the nature of agents' preferences. Because of
multiple and offsetting effects of agent wealth, the less risky informal
sector may be chosen by either the relatively wealthy or the relatively
poor. P