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Endowments and credit market performance: An econometric exploration of
non-price rationing mechanisms in rural credit markets in Peru.*
Steve Boucher**
October 2002
Abstract: This paper provides an empirical examination of the frequency and determinants of two
forms of non-price rationing in rural credit markets in northern Peru. Quantity rationing is the
conventional form of non-price rationing whereby a household with positive demand for credit is
denied access. Risk rationing, in contrast, occurs when a household voluntarily withdraws from
the credit market for fear of losing collateral even though it has an expected income enhancing
investment. A multinomial logit framework is used to systematically explore how farmers’
endowments are related to the observed credit market rationing outcome. Maps of the
probabilities of each rationing regime are developed in endowment space and show that the
structure of the post-liberalization credit market in Peru is significantly biased against low wealth
farm households.
Key Words: rural finance, credit rationing, financial liberalization
__________________
Acknowledgments: Fieldwork and write-up was supported by a Social Science Research Council
Pre-Dissertation Fellowship, a Fulbright-Hayes Doctoral Dissertation Fellowship, and a
University of Wisconsin Dissertator Fellowship.
*
This is a revised version of Chapter 5 of my dissertation.
Assistant Professor of Agricultural and Resource Economics, University of California - Davis
and member of the Giannini Foundation.
**
1. Introduction
In the last decade, there has been a growing body of literature (Kochar 1998, Conning
1996, Mushinski 1996, Hauge 1998) that attempts to measure the extent and analyze the
determinants of non-price rationing in credit markets. Identifying the incidence of non-price
rationing is important for two reasons. First, it provides one indication of the efficiency of the
credit market and, by comparing rationing outcomes across groups of interest, can also provide
insights into the relationship between asset distribution and credit market structure. Second,
more in-depth analysis of the implications of credit market structure on rural development
requires a conceptual and empirical framework that identifies individuals’ or households’ credit
market rationing mechanisms. This is because the logic of investment and resource allocation
decisions of farmers may be fundamentally different for price rationed versus non-price rationed
farmers. In order to effectively implement econometric models regarding farm input demand,
production, or profit generation, the researcher must be aware of how non-price rationing may
affect the optimization decisions of farmers and have some means of accounting for these
impacts in the estimation procedure.
Previous theoretical literature has focused attention on quantity rationing as the main nonprice rationing mechanism. As such, this work centers on whether or not a farmer has access to a
credit contract. Econometric models of farm resource allocation also separate farmers into two
groups: price rationed farmers whose optimal decisions are independent of their endowments of
working capital and quantity rationed farmers whose optimal decisions are not independent of
their endowments.1 Recent work (Boucher and Carter 2002) suggest, however, that this focus on
quantity as the sole non-price rationing mechanism is too narrow. In particular, when farmers are
risk averse and insurance markets are underdeveloped, information asymmetries can manifest
themselves and impact resource allocation not only through the binary outcome of existence vs
non-existence of a contract, but also by influencing the terms of those contracts that do exist.
Relative to a first best (or symmetric information) world, there may exist a class of “risk
1
The fact that a farmer is price rationed in the credit market does not necessarily imply that she demands the
availab le contract. Instead, it imp lies that her resource allo cation is not affected by a lack o f working cap ital.
1
rationed” farmers who voluntarily withdraw from the credit market because the terms of the best
available contract in the second best world imply excessive risk. These farmers, with a relatively
high collateral wealth to liquidity ratio “choose” to undertake low return projects even though
they could achieve higher expected returns if they accepted the available credit contract. Even
though these farmers have access to a contract, their resource allocation decisions are not
independent of their endowments. As such, their behavior is inconsistent with models based only
on quantity rationing.
This paper has two primary objectives. First, it uses survey data from Peru to examine
the frequency of rationing mechanisms, which are expanded to include both price and quantity as
well as risk and transaction costs. Second, it uses a multinomial logit framework to explore the
determinants of these rationing mechanisms. As such, this chapter represents an initial attempt to
explore the empirical relevance of risk as a non-price rationing mechanism. The structure of the
paper is as follows. Section 2 reviews recent econometric approaches to credit market analysis
when the potential for endogenous quantity rationing is acknowledged. Section 3 introduces risk
rationing as an additional non-price rationing mechanism and discusses additional issues that it
raises. It then uses data collected from 550 farm households from northern Peru to provide a
descriptive analysis of the frequency of rationing outcomes. In this chapter I focus exclusively
on the rationing outcomes in the formal, commercial loan sector. In the descriptive analysis I
look at a series of bivariate distributions of rationing mechanisms with several different wealth
variables. Section 4 develops a more systematic analysis by estimating a multinomial logit
model where the dependent variable is the rationing outcome in the formal, commercial loan
sector. This is a reduced form estimation which does not seek to identify structural parameters of
supply and demand, but rather to test for the existence of systematic relationships between
different components of farmers wealth and rationing mechanism. The estimation results are
used to create mappings of regime probabilities in farmer endowment space. Section 5
summarizes and points to future extensions.
2
2. Empirical approaches to quantity rationing
In the absence of asymmetric information (and exogenous policy restrictions), we could
be reasonably assured that the observed loan quantity represents the intersection of supply and
demand. Conventional econometric techniques could then be employed to explore issues such as
how an individual farmer’s characteristics affect his demand for credit. The asymmetric
information problems endemic to credit transactions give rise to the potential for non-price
rationing, which makes empirical analysis of the credit market challenging and conventional
techniques inapplicable to credit markets.
One of the main difficulties is that the researcher may not be able to infer the rationing
mechanism at work just by observing the loan quantity transacted. Theoretical models such as
those by Milde and Riley (1988) and Gale and Helwig (1985) show that quantity rationing may
take the form of lenders offering some applicants a loan amount that is less than that demanded.
In this situation and without additional information, the researcher cannot identify whether the
market has “cleared” for a particular borrower or if instead the supply is strictly less than
demand. If the latter holds, then quantity serves as the rationing mechanism. As noted in the
econometric literature of disequilibrium models, when price cannot freely adjust to clear a
market, the information provided by a transaction is that the quantity transacted is the minimum
of supply and demand.2 Although it may be incomplete, the observation of a positive loan
amount does at least provide some information about both demand and supply conditions of an
individual. Non-borrowers, in contrast, are more problematic. Theoretic models such as those by
Stiglitz and Weiss (1981) and Carter (1988) show that quantity rationing may also take the form
of full rejection so that the available supply for an individual is zero. In this situation,
differentiating quantity rationed borrowers who have a positive demand at the going contract
terms from price rationed individuals - who have zero demand - is impossible without additional
information.
One option utilized in early empirical studies (Iqbal 1986, Binswanger and Rosensweig
1986) is to assume that price rationing is never in effect and instead that all households face a
2
See, for exam ple, M addala (1986 ) for a review of the issues.
3
binding supply constraint. Under this assumption, the observed loan amount provides full
information about the supply condition and a lower bound for an individual’s (or household’s)
demand. As pointed out by Kochar (1997), this approach is flawed because it overstates the
incidence of quantity rationing and can thus lead to unwarranted policy interventions. In her
exploration of rural credit markets in India, Kochar points to two reasons that farmers may have
no formal demand for credit. First, farmers may simply have such poor endowments that they are
unable to generate rates of return that approach formal sector interest rates. Second, optimizing
households will compare the terms of all available credit. In particular, they compare the cost of
credit in the formal sector against that of the informal sector. In her data set, for example, over
30% of the informal loans carried an explicit interest rate which was lower than the mean formal
sector rate. Whether or not a farmer receives a formal loan thus depends upon not only the
quantity available in the formal sector, but also the farmer’s productivity and the cost of informal
credit relative to formal credit.
Kochar’s approach is to estimate a set of three structural equations: one for household
credit demand, and one each for formal and informal credit supply.3 All three equations depend
both on regional characteristics and on characteristics of the individual household. Kochar
argues that, depending on individual characteristics, either the formal or informal sector may be
the lowest cost sector. Thus a farmer may be observed with an informal loan either if they are
quantity rationed in the formal sector or if they have access to a formal loan but instead prefer the
informal loan because it is available at a lower cost. Similarly, a farmer who is observed with no
loan may either be quantity rationed in the formal sector and finds informal credit too expensive
or have zero demand for credit from both sectors. 4 Once the parameters of the three equations
are identified, the researcher can predict the probability of each rationing outcome. For example,
the probability of quantity rationing would be equal to the probability that formal supply is less
than formal demand and formal demand is less than informal demand. Policy issues can be
3
The demand equation is assumed to be independent of the loan sector. This is equivalent to assuming that
loan contracts have the same structure across sectors. Bell et al (1998) provide an alternative model which
differentiates demand for inter-linked credit from formal and informal non-linke d credit.
4
Kochar makes the intuitively plausible assumption that because of informational advantages of informal
lenders, farmers are never quantity rationed in the informal sector.
4
explored by seeing how marginal changes in the characteristics of interest - for example an
individual’s titled farm area - affect the regime probabilities. An important characteristic of this
type of model - referred to as a model of partial observability or partial sample separation - is that
it does not require the researcher to directly observe the rationing mechanism for all households.
This is important since most survey data do not permit us to distinguish between a non-borrower
who is quantity rationed from one who is price rationed.
Variations of this model are employed by Conning (1996), Hauge (1998), and Bell et al
(1998) - the first two in the context of Chilean and the latter in the case of Indian rural credit
markets.5 The primary difference is that these three econometric models impose the assumption
that informal credit is at least as expensive as formal credit. Conning and Hauge justify this
assumption on the basis that, in their study areas, informal interest rates almost always exceeded
the mean formal rate. Bell et al give less justification, although they do point to the high
frequency of interlinked informal contracts that carry low explicit interest rates but - usually
through product underpricing - carry high implicit interest rates. There are two advantages to this
modified approach. First, as long as the assumption is reasonably accurate, then this approach
incorporates more available information and raises the efficiency of the parameter estimates
(Pudney 1988). Second, it increases the degree of observable sample separation. For example,
according to this assumption, a farmer that is observed with only an informal loan must be
quantity rationed in the formal sector. This advantage is important because, while estimation
with unobserved sample separation is possible, it is computationally demanding and - especially
for small data sets - may not be feasible.
An alternative approach is to design the survey instrument to directly collect information
that permits full sample separation. Initial examples of this approach include Jappelli (1990)
and Feder et al (1990). Other examples include Zeller (1994), Barham et al (1996) and
Mushinski (1996, 1999). In this approach, farmers are asked qualitative questions - similar to
5
The three mod els are not strictly co mpa rable as they have different ob jectives. Bell et al explore the role
of the informal sector as a recipient of “spillover” demand from the formal sector and they take into account the
potential differences between linked and unlinked informal loans. Conning, meanwhile, explores the role of
monitoring in the informal sector as a means of overcoming informational barriers. Hauge, in contrast, is more
concern ed with the determ inants of and imp acts of participation in group cred it programs.
5
those described in Chapter 2 - that are designed to identify both the supply and demand
conditions - and thus the rationing mechanism for each individual. Consider, for example, the
approach of Mushinski (1996, 1999) who was interested in explaining formal credit market
participation in Guatemala. In addition to loan quantities, the survey asked if farmers had
applied and been rejected by a formal lender. Rejection was taken as evidence of positive
demand and zero supply so that rejected farmers were classified as quantity rationed. Mushinski
further notes that in the presence of positive transaction costs, not having been rejected may be
insufficient justification for classifying a farmer as price rationed. For this reason, farmers who
did not apply to a formal lender were also asked why they did not seek a formal loan. A farmer
was also classified as quantity rationed if she stated that the primary reason for not applying was
that she was reasonably sure she would be rejected. Mushinski calls these farmers “preemptively” rationed since the high subjective probability of default accompanied by positive
transaction costs leads them to not apply. While this type of subjective questioning can greatly
increase sample observability and thus the efficiency of estimation, it should also be pointed out
that there are pitfalls as well. Mushinski shows, for example, that estimation of structural
parameters is sensitive to how the subjective responses are grouped. Because collecting this type
of data requires the use of qualitative, and sometimes hypothetical questions, it requires careful
survey design and extensive training of enumerators.
One commonality of these approaches is that the rationing mechanisms they consider
include only price and quantity. This follows from the assumption that farmers are risk neutral.
As such, the derivations of a farmer’s credit demand schedule and endogenous rationing amounts
are based on expected returns. This assumption simplifies the econometric analysis. Under risk
neutrality, a revealed preference argument leads to the conclusion that an unconstrained farmer
will choose the least cost credit contract. Similarly, a non-borrower must either have no
productive investment and is thus price rationed or is quantity rationed and therefore is forced to
forego a productive investment.
The more intuitive assumption of risk aversion implies several important consequences of
when credit markets are characterized by moral hazard. First, for a given cost (expected
contractual payoff), risk averse farmers strictly prefer credit contracts which offer greater implicit
6
insurance - or less income variability across states of nature. Under DARA, the willingness to
pay for full insurance decreases with a farmer’s wealth. An immediate consequence is that when
farmers compare across contracts - for example across formal and informal sectors - they
consider not just the cost associated with each contract but also how the terms of the contract
affect the smoothness of income across states. Second, the way that lenders “solve” the incentive
problem associated with moral hazard depends on the wealth of each borrower. Under DARA,
lenders shift greater contractual risk onto wealthier borrowers than poorer ones. Thus available
contract terms should be a function of farmer endowments.
Risk rationed farmers have a contract available to them and thus would not be classified
as quantity rationed in the frameworks described above. Classifying them as price rationed,
however, is not satisfactory because their resource allocation depends on their liquidity. It is
clear, then, that risk rationed farmers should be treated as a separate class. We now turn to the
Peruvian data to explore the frequencies of an expanded set of rationing mechanisms, which
includes risk rationing.
3. The frequency of different rationing mechanisms in Piura, Peru
3.1 Definition of rationing categories
In terms of the preceding discussion, I use a “direct” approach to examining the incidence
of non-price rationing with respect to the formal commercial loan sectors for the farmers in the
Peruvian data set. The survey design permits classification of the sample farmers into an
expanded group of rationing categories. The rationing mechanisms are summarized in Table 1.
7
Table 1. Description of Rationing Mechanisms
Rationing Category
Description of Mechanism
1. Price rationed with loan
Applied for loan. Received full amount of application.
2. Partially Quantity
Rationed
Applied for loan. Received less than full amount of application.
3. Fully Quantity Rationed
Applied for loan and was rejected or:
Did not apply because subjective probability of rejection was too
high.
4. Price rationed no loan
Did not apply for loan because interest rate was too high.
5. Risk Rationed
Did not apply for loan for fear of losing collateral.
6. Transaction Cost Rationed
Did not apply for loan because transaction costs were too high.
Based on observed outcomes and responses to qualitative questions, farmers were
grouped into six categories. Farmers that applied to a formal, commercial lender were grouped
into three separate categories. Those that received the full amount of their application were
classified as price rationed with loan. If their loan was approved, but for an amount less than the
desired amount they were classified as partially quantity rationed. If their application was
rejected they were classified as fully quantity rationed. The questionnaire was designed to permit
classification of non-applicants into one of the final four rationing categories in Table 1.
Farmers that did not apply were asked the following hypothetical question: “If you applied to a
commercial lender, would the lender approve the application?” Farmers that answered yes were
then asked why they did not apply. Their open ended responses were classified into three general
reasons - price, risk, and transaction costs. For example, a non-applicant who did not apply
because commercial interest rates were too high would be placed in category 4 - price rationedno loan. If instead the farmer responded that he did not apply for fear of losing his land he would
be placed in category 5 - risk rationed. Finally, if the farmer claimed that he did not apply
because the costs of the ‘tramites’ or the time and expenses implied in the application process
were too high he was placed in category 6 - transaction cost rationed.
Farmers that felt that a commercial lender would not approve their loan were asked the
8
following hypothetical question: “If a commercial lender offered you a loan at the going contract
terms, would you accept?”. Farmers that answered yes were placed in category 3 - quantity
rationed. Farmers that answered no were asked the reason why. They were also grouped into
categories 4-6 based on their open ended responses.
Eliciting subjective responses is, admittedly, not a simple task and several issues merit
discussion. First, these questions had to be asked with respect to a reference lender. Instead of
specifying a specific institution, the survey asked the questions relative to commercial banks and
the Cajas Municipales.6 For example, non-applicants were asked “If you applied to a bank or a
CMAC, would your application be approved?” For example, there may be differences in the
lending policies followed by different formal institutions. For example, the CMAC of Sullana is
more likely to offer non-collateral backed loans than the commercial banks or the CMAC of
Piura. Farmers base their responses to these questions on their perceptions of the loan policies of
a specific institution. As such, there is a possibility that two farmers who are identical in terms
of credit access - say both would get a contract from the CMAC of Sullana and neither would get
one from the Banco de Crédito - would respond and thus be classified differently if they base
their answers on different reference institutions.7
A second issue is that the qualitative responses with respect to formal commercial lenders
do not explicitly control for access to credit in either the formal non-commercial or informal
sectors. Consider two farmers who are identical in that the formal contract implies too much risk
relative to their autarky option so that, if they had no alternatives, they would both self-finance.
Now assume that the first farmer has access to an interest free loan from his sister while the
second farmer has no informal loan available. Instead of stating a fearing of losing his collateral,
the first farmer may instead focus on the cost comparison and claim he did not seek a bank loan
because it was too expensive. The point is that a farmer’s response to subjective and
hypothetical questions will reflect their best alternatives, which vary across farmers.
6
Cajas Municipales de Ahorro y Credito (CM AC) are municipal banks. In the Department of Piura, three
different municipalities operate a CMAC - Piura, Sullana, and Paita.
7
One alternative which I did not use would be to ask with re ference to a sp ecific co ntract and institution.
This, however, would be problematic if all farmers are not familiar with the institution.
9
3.2 Initial evidence on wealth and credit market rationing outcomes
The interaction of asymmetric information and risk raises the potential for credit market
outcomes which are differentiated by household wealth - particularly collateralizable wealth and
liquidity. The following relationships are hypothesized to hold. First, the likelihood of quantity
rationing decreases in collateral wealth. As collateral wealth decreases, it becomes less likely
that farmers can meet the lender’s minimum collateral requirement and they would thus be
denied access to a loan. In contrast, for sufficiently high collateral wealth levels, the probability
of a farmer being price rationed with no loan is increasing in a farmer’s liquidity. Predictions
with respect to risk rationing are more complex. Risk rationed farmers have positive formal
supply, thus they need to have a minimum level of collateral wealth. Farmers with very low
liquidity levels are unlikely to be risk rationed because the expected return differential between
debt finance and self finance would be sufficiently large to justify accepting the risk implied by
the credit contract. On the other hand, farmers with high liquidity would be unlikely to report
themselves as risk rationed since, as mentioned above, they generate sufficiently high returns
under self finance. If incentive problems stemming from asymmetric information are not too
‘severe’, risk rationing may not even occur. Finally, the fixed transaction costs associated with
the application process and posting collateral are likely to lead to average cost of credit which is
decreasing in productive wealth.
Before examining the frequency of the rationing mechanisms by different wealth
components, we first examine the nature of rural wealth in Piura. Table 2 gives a detailed
breakdown of wealth of the farmers in the sample. The average wealth of sample households is
just under $24,000. The distribution of total wealth is fairly compact within the first 4 quintiles
and then becomes more skewed at the top. At about $16,313, the average total wealth of the
farmers in the 4'th quintile is about four times that of the farmers in the first quintile. The jump
in average wealth from the fourth to the fifth quintile, however, is much greater. The top 20% of
households have an average of just over $77,000, which is more than four times as much as the
average of the farmers in the fourth quintile. The majority of household wealth is held in the
form of agricultural land. The average value of agricultural land for sample households is just
10
under $15,000, which represents 63% of mean household wealth. Table 2 also shows that only
those farmers in the top of the total wealth distribution have any business or residential properties
of significant value.
Table 2. The composition of total wealth for sample households
Total Wealth Quintile*
Asset Type
1
2
2,928.6
2,799.8
0.0
128.8
5,686.5
5,465.1
1.7
219.7
Durable Goods
Agricultural machinery
Commercial machinery
Consumer durables
561.8
308.2
53.2
200.3
817.8
372.0
70.3
375.6
Liquidity
Grain/input stocks
Animal stocks
Financial stocks
Profits
Salary/wage income
642.8
42.6
337.0
25.2
87.3
133.2
4,133.2
Land/Structures
Agricultural
Commercial
Residential
Total Wealth
3
8,765.2
8,232.9
0.0
532.3
4
5
Sample
12,260.6
11,633.5
3.4
623.6
59,934.3
45,528.0
1,526.6
12,879.7
17,981.5
14,782.5
308.0
2,891.0
917.0
471.2
107.2
338.7
1,671.9
645.0
219.2
807.7
12,234.2
2,445.0
5,588.3
4,200.9
3,254.1
850.8
1,213.8
1,189.5
1,163.5
57.7
470.6
89.7
180.2
334.3
1,381.6
73.5
508.1
101.1
308.1
365.9
2,381.3
109.1
579.5
280.3
834.7
544.3
5,120.7
469.8
1,694.7
1,069.9
884.4
940.3
2,143.9
151.1
719.5
314.6
460.4
464.6
7,667.8
11,063.8
16,313.8
77,289.2
23,379.5
*
Figures are in $US.
Table 2 also shows the various forms in which farm households hold liquidity. In Peru,
farm household participation in formal savings markets is limited. Only 12% of sample
households had any type of deposit or checking account. Although real deposit rates are positive
and competition for savings has greatly increased in recent years, a history of persistent
macroeconomic instability accompanied by relatively high travel to urban centers contributes to
the low formal savings rate among rural households. In Table 2, the category of financial stocks
includes both deposit accounts and gold and jewelry. Many rural households hold gold coins and
11
jewelry as heirlooms and for use as collateral in for emergency borrowing needs.8 The two other
main forms of holding liquidity are in animal stocks and grain and input stocks. Animal stocks is
the value of all animals - from courtyard fowl to cattle - held at the beginning of the planting
season. Livestock - especially cattle - serves the dual function of investment and savings. They
are included in liquidity because they can be quickly converted into cash for working capital
during the agricultural campaign. Grain stocks are another common form of holding liquidity.
Holding rice stocks is especially common since it is easily stored and is a basic consumption
item. More sample households had savings in the form of rice - 38% - than had bank deposits.
A farmer’s total wealth impacts his demand for credit through its influence on the
capacity to generate income and willingness to bear risk. Where information asymmetries are
severe and lenders require collateral, the composition of total wealth will also be important in
determining whether or not a farmer has access to credit. The lender faces two problems when
requiring collateral: 1) Moral hazard in the maintenance of the assets; and 2) Costs in
establishing property rights over and reselling the asset in the case of default. Since land is
immovable, can be formally titled and, after the rewriting of the land laws, can be resold, it is the
primary form of collateral accepted by formal lenders. Gold and savings accounts can also be
easily held by and transferred to the lender and thus may be considered as potential collateral.
Table 3 shows the mean holdings of sample households of these two primary forms of
collateral accepted by formal, commercial lenders. The mean holding of collateral wealth in the
sample is just under $13,000. The main thing to note from Table 3 is positive correlation
between total wealth and the percentage of wealth held in collateralizable form. Households in
the first and second quintiles of total wealth hold only 20% and 26% of total wealth in collateral
assets. In contrast, collateral assets account for 60% of total wealth for households in the
wealthiest quintile. One explanation of this is that many of the poorest sample households are
members of Comunidades Campesinas, or Peasant Communities. Agricultural land within the
Comunidades Campesinas is owned by Comunidad. Although land is worked individually, it
cannot be sold or mortgaged. The last row in Table 3 shows that the percentage of households in
8
The Cajas M unicipales of the region all advertise a line of cred it against the specific collateral of go ld.
12
each quintile that are members of a Comunidad Campesina is negatively correlated with wealth.
Table 3. The composition of collateral wealth for sample households
Total Wealth Quintile*
Asset Type
Titled Land/Bldgs. (LT )
Agricultural
Commercial
Residential
1
2
3
4
5
875.4
821.8
0.0
53.6
1,870.6
1,751.1
1.7
117.7
4,835.6
4,470.3
0.0
365.2
6,720.0
6,256.0
3.4
460.6
25.2
89.7
101.1
280.3
900.7
1,960.3
4,936.7
7,000.3
49,514.7
12,918.8
4,133.2
7,667.8
11,063.8
16,313.8
77,289.2
23,379.5
(M+LT )/W
0.20
0.26
0.45
0.42
0.60
0.38
% in Comunidad
68.8
62.4
39.4
30.9
10.9
42.4
Financial Stocks (M)
Collateral Wealth (M+LT )
Total Wealth (W)
*
48,444.9
39,797.0
1,526.6
7,121.3
Sample
1,069.9
12,604.3
10,664.6
308.0
1,631.6
314.6
Figures are in $US.
Over 60% of each of the bottom two total wealth quintiles and only 10.9% of the top quintile are
members. By preventing individual ownership and titling of agricultural parcels, membership in
the Comunidades further reduces the ability of the poorest sample households to post collateral.9
Table 4 shows the frequency of loan receipt from the different types of formal lenders by
total wealth quintile. Formal, commercial lenders are those in the first three columns commercial banks, Cajas Municipales (CMAC) and Cajas Rurales (CRAC). The first thing to
note is the positive correlation between total wealth and receipt of formal, commercial credit.
Less than 1% of the households in the first and second quintiles received bank credit, while just
over 12% of the top quintile received a loan from a bank. The presence of the Cajas Municipales
is clearly important in providing low wealth households access to the formal, commercial sector.
9
Tenure re gime o f agricultural land is, of course, only one aspect of the Comu nidad es. W hile membe rship
in the Comunidad may preclude access to individual, collateral based loans it may provide certain services and
options not available to individual, non-members. For example, the Comunidad the organization and political
leadership of the Comunidades has traditionally served as an important voice and lobby for making known the
concern s and issues facing small farmers.
13
Still, the percentage of households with credit from Cajas increases significantly with total
wealth.
Table 4. Participation in Formal Sector by Total Wealth Quintile
% of Households with a Loan from:
Wealth Quintile
Bank
CMAC
CRAC
NGO
PIMA
No Formal
1
2
3
4
5
0.0
0.9
2.8
3.6
12.7
10.1
15.6
19.3
34.5
38.2
0.0
1.8
0.0
0.9
0.0
13.8
19.3
11.0
7.3
0.9
5.5
3.7
7.3
9.1
5.5
70.6
58.7
59.6
45.5
47.3
Sample
4.0
23.6
0.5
10.4
6.2
56.3
The next step in examining credit market performance is to examine the frequency of
each rationing mechanism for households by different wealth components. The following tables
evidence on the bivariate distributions of the rationing categories defined in Table 1 and different
components of farmer wealth. Table 5 shows the frequency of the rationing categories by total
wealth quintiles. Summing the frequencies in columns (1) and (4), gives percentage of farmers
for whom price serves as a rationing mechanism. Of the total sample, 19.6% and 19.9% were
price rationed with and without a loan respectively. Thus price served as the rationing
mechanism for just under 40% of the sample. Looked at another way, 60% of the sample has a
positive loan demand which is unsatisfied because of the presence of information asymmetries.
Moving down the columns from the first to the fifth quintile, we see that the proportion of
households who are rationed by price tends to increase with wealth. Within the first quintile
29.3% of households were price rationed. This figure rise to 55.4% in the fifth quintile.
The category with highest sample frequency is fully quantity rationed - with 36.7% of
sample farmers. The frequency of full quantity rationing decreases as total wealth increases,
suggesting the importance of a farmer’s asset base on the lender’s supply decision. Still, one
fifth of the farmers in the highest wealth quintile either were, or felt they would be, rejected by
commercial lenders. Just over 8% of farmers were partially quantity rationed - or received a
14
smaller loan amount than they applied for.
Table 5. Rationing mechanism by total wealth quintile
Total
Wealth
Quintile
% of Households that were:
Price rationed
with loan
(1)
Partial
Q-rationed
(2)
Fully
Q-rationed
(3)
Price rationed
no loan
(4)
Risk
Rationed
(5)
T-cost
Rationed
(6)
1
2
3
4
5
7.3
10.1
19.3
24.5
36.4
2.8
8.3
2.8
14.5
12.7
45.9
42.2
41.3
34.5
20.0
22.0
26.6
15.6
16.4
19.1
11.9
10.1
9.2
5.5
9.1
10.1
2.8
11.9
4.5
2.7
Sample
19.6
8.2
36.7
19.9
9.1
6.4
The last two columns show that 9.1% and 6.4% of farmers were rationed by risk and
transaction costs respectively. If farmers were identical in terms of their technology and faced
identical contract terms, then - assuming farmers are described by decreasing absolute risk
aversion - we would expect risk to be decreasing in importance as wealth increases. Comparing
the incidence of risk rationing across wealth quintiles reveals a slight negative correlation
between risk rationing and total wealth. One factor that could explain this is that farmers may
not face similar contract terms. As suggested in the previous theory chapters, under decreasing
absolute risk aversion, wealthier farmers face higher collateral requirements. It is also possible
that the range of wealth in the sample is not sufficient to capture any wealth effects. A similar
result is anticipated with respect to transaction cost rationing. Farmers who demand relatively
small amounts of credit would be most likely to be dissuaded from applying due to fixed
transaction costs. Again, the trend evident in the last column is that the frequency of transaction
cost rationing decreases in total wealth, however the trend is not strong. Tables 6 and 7 give
bivariate frequency distributions of rationing mechanisms with two different aspects of farmer
wealth - collateral wealth and farm size. In general, the same results discussed above hold.
15
Table 6. Rationing mechanism by collateral wealth quintile
Collateral
Wealth
Quintile
% of Households that were:
Price rationed
with loan
Partial
Q-rationed
Fully
Q-rationed
Price rationed
no loan
Risk
Rationed
T-cost
Rationed
1
2
3
4
5
3.7
8.2
14.7
34.5
36.4
0.9
5.5
6.4
12.7
15.5
47.2
50.9
39.4
27.3
19.1
25.9
20.0
25.7
12.7
15.5
10.2
7.3
10.1
9.1
9.1
12.0
8.2
3.7
3.6
4.5
Sample
19.6
8.2
36.7
19.9
9.1
6.4
Table 7 Rationing mechanism by farm size
% of Households that were:
Farm
Size - L
(in ha.)
Price
rationed
with loan
Partial
Q-rationed
Fully
Q-rationed
Price rationed
no loan
Risk
Rationed
T-cost
Rationed
L#1
1<L#3
3<L#5
5 < L # 10
L > 10
7.3
19.4
12.8
28.8
37.3
2.4
10.1
7.1
4.5
11.8
36.6
36.3
46.1
28.8
23.5
34.1
19.0
17.7
19.7
19.6
14.6
8.1
9.9
9.1
7.8
4.9
7.3
6.4
9.1
0.0
Sample
19.6
8.2
36.7
19.9
9.1
6.4
4. The determinants of rationing mechanisms - A multinomial logit framework
4.1 Model description
A more systematic examination of the relationship between farmer characteristics and
rationing mechanisms requires a multi-variate analysis. The approach taken here is to use a
single equation, multinomial choice model to predict the probability that farmers of different
characteristics are found in the different rationing categories. The multinomial logit model
provides a particularly convenient framework. Let Y be a categorical variable which represents
the observed credit market rationing outcome and which takes values 0, 1, ... J. Define Yij* as the
continuous “score” for the i’th individual in the j’th rationing category. Yij* can be considered
16
the unobservable “propensity” of the individual to be in category j and is modeled as a linear
combination of an individual’s characteristics. The i’th individual’s score for the j’th rationing
category is:
(1)
where xi is a (1 x k) vector of characteristics of the i’th individual; $j is a (k x 1) vector of
population parameters associated with the j’th category to be estimated; and gij is the unobserved
component of the i’th individual’s score from category j. The observed category is the one
which yields the highest score. The probability that the i’th individual is in the j’th category is
then:
(2)
The model is operationalized by making assumptions about the joint distribution of the
unobserved terms in the J+1 equations implied by (1). If the J+1, gij terms are independent and
identically distributed with Weibull distribution then the probability in equation (2) can be
expressed as10:
(3)
Multinomial logit models are typically motivated by a random utility framework in which
the unobserved, or latent, variable represents an individual’s expected utility, and individuals
choose the category which maximizes expected utility. The parameters, $j would thus represent
the impact of individual characteristics on the expected utility of each choice. In the current
context, the random utility framework is not appropriate since farmers do not freely “choose”
across the different rationing categories. Instead, the multinomial logit framework is simply used
to impose a probability structure on the outcomes. The logistic form is especially convenient
because it can capture non-linear relationships between the independent variables and the regime
10
The original formulation of the multinomial logit is in McFadd en (1973). M addala (1983 ) presents the
algebra involved in going from the probability statement in equation 2 to the one in equation 3.
17
probabilities and it keeps the probability within the unit interval (Moffit 1999, p. 1385). As
individual characteristics such as education and wealth impact both supply and demand the
parameter estimates will not have any structural interpretation. This is acceptable, however,
since our primary interest here is to estimate MPr(Yij = 1)/MXk - or the marginal impacts of
individual characteristics such as collateral wealth on the probability that a farmer is in a given
rationing regime.
Since there are k individual characteristics influencing the scores of the J+1 categories,
there are a total of k x J+1 parameters in the model. All (k x J+1) parameters of the model,
however, cannot be identified. The intuition behind this result is that what matters in the
individual’s placement among different categories is not the absolute size of the parameters (or
of the score), but instead the difference in the parameters across the different categories. Thus if
we add a non-zero vector of constants, c, to each of the j parameter vectors - $j - we do not affect
the rankings of the scores across the J+1 categories. From equation 3, it is easy to see that if we
substitute the parameter vectors $j + c for the population parameter vectors, $j, the probability
that an individual falls into each category would be unaffected. In order to achieve identification,
we need to fix the values of the parameters associated with one of the categories. The most
convenient normalization is to set the parameters of a “base” category equal to zero. Following
notational conventions, the base category is associated with j=0 so that $0=0.
With this normalization, the probabilities in equation (3) become:
18
(4)
(5)
To construct the sample likelihood function, define the variable dij = 1 if the i’th individual is
observed in the j’th category and dij = 0 if not. For example, if there are three categories and the
first individual is in category 1 we would have: d10=d12=0 and d11=1. The sample likelihood
function, L, is then:
(6)
and the log of the sample likelihood function is:
(7)
where the probabilities are given by equations 4 and 5.
4.2 Definition and discussion variables
We now turn to the definition of the variables used in the estimation. Due to the limited
number of observations in the partially quantity rationed, risk rationed and transaction cost
rationed categories, the 6 rationing categories described in Table 5.3 were reduced to four. First,
all farmers that applied for and received a positive loan amount are classified as price rationed
with a loan. Second, farmers that were classified as either risk rationed or transaction cost
rationed were grouped together in a single category called Risk/TC rationed. Farmers in both of
19
these groups are similar in that they have access to a loan and would have positive demand in a
first-best world, however the presence of asymmetric information causes their effective demand
to be zero. The category of price rationed with a loan is taken as the base category. Table 8
summarizes the modified categories and the sample frequencies.
Table 8. Description of rationing categories, Yj, used in the multinomial logit
Sample Distribution
Category Name
j
Price Rationed
with loan
0
Price Rationed
no loan
Risk/TC Rationed
Quantity Rationed
Description
#
%
Applied for and received some loan
152
27.8
1
Did not apply because interest rate too high
109
19.9
2
Did not apply for fear of losing collateral or
size of transaction costs
85
15.5
3
Applied and rejected or;
Did not apply because subjective prob. of
rejection too high.
201
36.7
The non-random component of the j’th category score, g($j,Xij) is modeled as the
following linear function:
(8)
The independent variables and their means are summarized in Table 9 at the end of this
subsection. As discussed above, the composition of a household’s wealth is likely to be a factor
in determining both its demand for and supply of formal, commercial credit. Three types of
wealth are included. Collateral wealth, C, and liquidity, M, were described in detail in Table 3.
Farm size, T, is the irrigable land area owned plus the net area rented in by the household. As
described above, the probability of being in a given rationing regime is hypothesized to be nonlinear in farmer wealth. For example, the model predicts that risk rationed farmers should be
20
found in the interior of collateral wealth/liquidity space. As such, the probability of risk
rationing first rises then falls with both collateral wealth and liquidity. To capture these potential
non-linearities I use a quadratic specification with respect to the three wealth variables. Only two
of the interaction terms are included because of problems with multicollinearity.
The non wealth variables are included to control for individual characteristics which may
influence supply and demand. Age serves as a proxy for farm management experience.
Education is included for several reasons. First, it proxies for human capital and should be
positively correlated with a farmer’s productivity. Farmers with high education levels may be
able to process loan applications more quickly and be less intimidated by the legal and
documentation requirements of formal loans. In addition, educational attainment is likely to be
positively correlated with social status, which may imply greater access to informal insurance
networks. Finally, more educated farmers may be more capable of managing risk. These
considerations suggest that education should be positively correlated with the probability of a
farmer being a borrower and negatively correlated with the rest of the categories.
The next two variables capture different aspects of prior participation in formal credit
markets. L_HIST is a binary variable which takes value 1 if the farmer had at least one formal,
commercial loan in the five years prior to the survey. This variable is included for two reasons.
First, a farmer’s transaction costs may be significantly lower if he has previously been a
borrower. For example, a borrower may not incur the fixed costs of registering the mortgage if
he continues to borrow with the same institution. Banks also may waive some paperwork
requirements for repeat borrowers. The second reason is that this variable helps capture time
invariant, individual characteristics - such as soil quality and how “well connected” a farmer is that affect both supply and demand but were not measured in the survey. L_HIST should be
positively related to the probability of being price rationed with a loan and negatively correlated
with the probability of the other three categories.
DEFAULT is also a binary variable which takes value 1 if a farmer defaulted on any
formal sector loan in the five years prior to the survey. Formal, commercial defaults are
considered as well as defaults on loans from government loan programs such as PIMA and
FONDEAGRO - the latter of which was dissolved by 1996. Defaults from these government
21
sources are included because information on loan repayment to them was publicly available
during the survey period. Commercial lenders usually consult these loan history records as a part
of their screening process. A past default is hypothesized to positively impact the probability of
quantity rationing but should have no impact on the other regimes.
The irrigation variable is included to control for access to ditch irrigation. Farmers that
do not have ditch irrigation must rely on the more expensive tubewell irrigation or pumping from
rivers. Farmers without ditch irrigation would tend to face higher production costs and greater
uncertainty. Finally, the regional dummy variables are included to capture unobserved regional
variation in demand and especially supply conditions. The Chira valley has several
characteristics which should raise the probability of price rationing relative to the non-price
rationing categories. First, farmers in the Chira valley enjoy the best road and irrigation
infrastructure of the four valleys considered. This should enhance productivity and reduce risk.
Second, the Chira valley is the main area of operation of the CMAC of Sullana. As described in
Chapter 2, the CMAC of Sullana is not as likely to require collateral as the other formal
commercial lenders. Holding other factors constant, this should make the probability of loan
access higher in the Chira relative to the other valleys. Bajo Piura occupies the other end of the
spectrum since it is in the primary area of operation of the CMAC of Piura - which has a much
more stringent collateral requirement policy. The remaining two valleys are recognized as areas
of potential operation for both CMAC’s - although they are farther away from both these
institutions as well as commercial banks so that the transaction costs involved in acquiring
formal loans tend to be higher in these two regions.
22
Table 9. Description of Independent Variables
Variable
Name
Description
Sample Mean
C
Collateral wealth of the household in thousands of dollars.
12.9
C2
Collateral wealth squared
2,946.211
M
Household’s pre-planting liquidity in thousands of dollars.
1.2
M2
Liquidity squared
7.4
T
Household farm size in hecatares.
5.1
T2
Farm size squared.
110.1
CT
C x T.
482.1
TM
T x M.
20.1
AGE
Age of household head.
51.7
EDUC
Years of formal education of household head
4.8
L_HIST
Loan history dummy variable.
.28
DEFAULT
Default dummy variable.
.18
BAJO
1 if household’s primary plot is in Bajo Piura 0, if not.
.26
ALTO
1 if household’s primary plot is in Alto Piura, 0 if not.
.15
SANLOR
1 if household’s primary plot is in San Lorenzo, 0 if not.
.08
IRRIG
1 if any of the household’s parcels is irrigated by “gravedad” ditch irrigation without need of pump.
.95
4.3 Estimation results
The results of the multinomal regression are reported in Appendix A. As described
above, the parameters of the vector $j in the multinomial regression model describe the impact of
individual characteristics on the probability of an individual being observed in category j relative
to the base category. By manipulating equations 4 and 5 we can make this statement more
11
One household has collateral wealth of over $1,000,000. When this household is excluded, the mean of
C_sq falls to 988. The regression results are not sensitive to the inclusion of this household.
23
precise:
(9)
Thus the elements of $j give the marginal impacts of individual characteristics on the log of the
odds ratio - which is just the ratio of two probabilities.
The primary motivation of this chapter is to examine the relationship between the
performance of the credit market and different components of farmer wealth. To do this, we
would like to see, for example, how the probability of being quantity rationed or risk rationed
changes with the components of wealth. As such, our interest lies not in the coefficient estimates
themselves, but rather in MPij/MX - the marginal impact of the regressors on each rationing
category, where Pij denotes Pr(Yij = 1). Instead of discussing the regression results, we head
directly to these marginal impacts.
Equation 10 give the expressions for these marginal effects:
(10)
Let $j,k be the k’th element of the parameter vector of the j’th category. The non-random
component of the category score, g($j, xi), is linear in the non wealth variables so that, if xk is a
non wealth variable, Mg($j, xi)/Mxk simplifies to $j,k . The wealth variables, in contrast enter in a
non-linear manner. The quadratic specification implies that for collateral wealth, for example,
we have: Mg($j, xi)/MC = $j2+2$j3+$j8Ti.
In addition, the non-linearity of the probabilities (as opposed to the non-linearity implied
by the quadratic specification) implies that the marginal effect of a regressor on the probability of
being observed in a given category depends on the value of the coefficients in all of the
categories (ie. MP1i/Mxk is a function of $1, $2, ... $J) and does not necessarily have the same sign
24
as the regressor’s coefficient. Also, the marginal effects must be calculated for specific values of
the regressors.
Table 10 gives point estimates for the marginal effects calculated at the sample means of
the regressors. The standard errors of the point estimates can be computed using the delta
method (Maddala 1983) and are reported in parentheses. Consider, for example the the marginal
impact of L_HIST. A farmer who has the sample mean for all other regressors and who had a
previous formal loan is 54% more likely to be price rationed with a loan than a farmer who did
not have a previous formal loan. In contrast, a farmer who had a previous loan would be 19%
and 32% less likely to be risk rationed and quantity rationed respectively than a farmer with no
previous loan. A past default also raises the probability of quantity rationing by 27%. Age and
education do not exert a strong influence on the rationing probabilities except for risk rationing.
An additional year of formal education lowers the “mean” farmer’s probability of risk rationing
by 0.84%.
Table 10. Marginal impact of regressors - MPj/Mx - evaluated at sample means
Price rationedwith loan
(MP0/Mxk)
Price rationed no loan
(MP1/Mxk)
Risk /TC
Rationed
(MP2/Mxk)
Quantity
Rationed
(MP3/Mxk)
0.11
(0.17)
0.15
(0.19)
-0.0083
(0.10)
-0.25
(0.21)
C
0.0086 **
(0.0036)
0.00038
(0.00044)
0.0024
(0.0028)
-0.011 **
(0.0052)
M
-0.043 *
(0.027)
-0.0073
(0.036)
0.030
(0.022)
0.021
(0.055)
T
-0.010
(0.016)
-0.085
(0.016)
0.023
(0.014)
0.016
(0.018)
AGE
-0.0014
(0.0022)
0.0021
(0.0022)
0.0019
(0.0012)
-0.00088
(0.0024)
EDUC
-0.00058
(0.0066)
0.00076
(0.0079)
-0.0084 *
(0.0052)
0.0082
(0.0085)
L_HIST
0.54 **
(0.10)
-0.022
(0.082)
-0.19 **
(0.070)
-0.32 **
(0.098)
DEFAULT
-0.074
(0.063)
-0.17 **
(0.075)
-0.029
(0.039)
0.27**
(0.070)
Individual
Characteristic (xk)
Constant
25
IRRIG
-0.16
(0.10)
-.21 *
(0.12)
-0.032
(0.063)
0.40**
(0.14)
BAJO
-0.365 **
(0.088)
0.10
(0.066)
-0.028
(0.038)
0.24**
(0.073)
ALTO
-0.042
(0.074)
-0.086
(0.084)
0.0028
(0.041)
0.12
(0.081)
SANLOR
-0.040
(0.11)
0.038
(0.13)
-0.069
(0.091)
0.071
(0.14)
As predicted, the regional dummy variables pick up strong differences in the
environments of the Bajo Piura and Chira valleys. Other things constant, the mean farmer in
Bajo Piura would be 36.5% less likely to be price rationed with a loan and 24% more likely to be
quantity rationed than an equivalent farmer in the Chira valley.
The hypothesized impact of the wealth variables depends on both the severity of the
asymmetric information problems and the farmer’s endowment. The strongest predictions relate
to the probability of quantity rationing and price rationing with a loan. Quantity rationed farmers
are expected to have the lowest collateral wealth relative to all other categories. Independent of
the farmer’s liquidity, an increase in collateral wealth should, then, decrease the probability of
quantity rationing. The large and negative marginal impact of collateral wealth in Table 10
supports this hypothesis. If we gave the mean farmer an additional $1,000 of collateral wealth,
his probability of being quantity rationed would fall by 1.1%. Farmers with relatively high
collateral wealth but little liquidity are hypothesized to be the most likely to be borrowers. This
is also supported by the data as an additional $1,000 of collateral wealth makes the mean farmer
8.6% more likely to be price rationed with a loan, while an additional $1,000 of liquidity
decreases the probability of being price rationed with a loan by 4.3%. As these are the strongest
hypotheses of the theoretical model, it is encouraging to note that this point estimate is also
significant at the 5% and, in the case of MP0/MM, at the 10%level.
For the mean farmer, collateral wealth does not have a strong impact on the probability of
either the price rationed no loan nor the risk/TC rationed categories. Liquidity is predicted to
raise the probability of risk rationing by 3%, however the estimate is not significantly different
from zero. The estimated impact of farm size is also not significantly different from zero for any
26
of the rationing categories.
4.4 Rationing regime mappings in endowment space
While the point estimates in Table 10 provide some insight into the relationship between
farmer endowments and rationing mechanisms, it is somewhat limiting because it is restricted to
the “mean” farmer. To more completely examine this relationship, we would instead like to see
how the regime probabilities vary as we simultaneously vary these two variables. This is done in
Figures 1a through 1d. These figures plot contours of Pij(M,C|xiN) - or the probability that a
farmer with non wealth characteristics xiN is in rationing regime j - as a function of liquidity and
collateral wealth. For ease of interpretation, I specify a farmer in the Chira valley (BAJO
=ALTO = SANLOR = 0) with irrigation (IRRIG = 1), while the other non wealth variables are
held at the sample means.12
12
In interp reting these figures, it is important to keep in mind that the sam ple means for collateral wealth
and liquidity are approximately $13,000 and $ 1,200 respectively. The greatest density of sample observations
occurs near the origin, while the density to the northeast of say (30,000 , 5,000) is very low. This implies that we
should have the greatest confidence about the estimated probab ilities for endowments closer to the origin.
27
28
These figures give a clearer idea of the relationship between the performance of the credit
market and farmers’ endowments. The top two figures give an indication of how the probability
of price rationing varies with endowments. Focusing first on Figure 1a, we see that - for liquidity
less than $5,000 - the probability of being a borrower, as predicted by the model, is strictly
increasing in collateral wealth. At first, Figure 1b is not consistent with the theory, which
suggested that farmers with highest collateral wealth and highest liquidity would be the most
likely to be price rationed with no loan. In Figure 1b, however, the farmers in the extreme
northeast have relatively low probabilities of being price rationed with no loan. A somewhat
more consistent image emerges, however, if we restrict attention to collateral endowments less
than $30,000. In this range, farmers are increasingly likely to have no need for a formal loan as
their liquidity increases.
The bottom two figures show the relationship between the probability of non price
rationing and endowments. Figure 1d is straightforward. It shows a strong negative relationship
between endowments - in particular collateral wealth - and the likelihood of quantity rationing.
Even in the Chira Valley, with its relatively good infrastructure and supply conditions, the model
predicts that farmers near the origin have over a 50% chance of being quantity rationed. It is also
interesting to note that although ownership of collateral apparently does relax quantity constraints
and lower the probability of quantity rationing, the rate at which it does so is not very great. For
example, the probability of quantity rationing for a farmer with collateral wealth of about $5,000
and liquidity of $2,500 is about 55%. If we hold liquidity fixed and move along a horizontal line
in endowment space, the probability of quantity rationing decreases, but is still almost 40% at a
collateral wealth of $2,000 - which is almost double the sample mean. It is not until collateral
wealth rises above $50,000 that the probability of quantity rationing falls below 10%.
Finally, Figure 1c identifies a region in the interior of endowment space where risk/TC
rationing is most likely. This is consistent with the model in that risk rationed farmers have
sufficient collateral that they have access to a contract, but they are not so wealthy that risk
considerations do not enter into their decisions. Similarly, risk rationed farmers are not likely to
have extremely low liquidity levels since that would imply a very low income under autarky - so
that they would instead accept the debt contract. For reasons described above, farmers with
29
relatively high liquidity are also unlikely to self report as risk rationed and would instead self
report as price rationed with a loan. The other thing to note is that while the “location” of risk
rationed farmers in endowment space is consistent with model predictions, the probabilities of
being in this regime are quite low. - at most about 12%.
5. Conclusions
This paper has provided some evidence about the relationship between farmer
endowments and the performance of the formal, commercial credit market in Piura, Peru. In
contrast to previous empirical work which focuses on quantity rationing, this analysis has
identified risk (and transaction costs) as a potential non-price rationing mechanism. Risk
rationed farmers voluntarily withdraw from the credit market even though they have access to a
loan that would permit a higher expected income. They do not accept the loan because the lender
- in response to asymmetric information - requires the farmer to bear too much contractual risk.
Empirical research that seeks to explore the breadth of credit market imperfections or the impact
of credit market structure on the efficiency of resource allocation is likely to understate the role
of asymmetric information if it neglects the potential for risk rationing. This is especially
important where insurance markets are least developed and incentive problems due to
information barriers are greatest.
The empirical analysis showed that the performance of the credit market in Piura is
strongly correlated with farmer endowments. Over half of the sample farmers were non-price
rationed, with quantity rationing being significantly more important than risk rationing. The
econometric exercise controlled for variation in non-wealth characteristics so that the
relationships between endowments and rationing mechanisms could be more rigorously explored.
Particularly strong results emerge regarding quantity rationing. Movements towards low
collateral, low liquidity endowments rapidly raise the probability of quantity rationing. The
overall explanatory power of the multinomial logit model was relatively poor and several of the
estimates of the marginal impact of several wealth variables were not significantly different from
zero for the price rationing with loan and risk rationing categories.
There are several needs that should be addressed in extensions of this work. First, greater
30
attention should be paid to the confidence intervals associated with the probability mappings in
endowment space. One option would be to portray the set of endowments where we expect to
find, with confidence at the 90% level, farmers above a given regime probability. The challenge
would be to portray both the direction of change in the probabilities as well as the confidence
intervals.
A more significant change would be to move away from the reduced form towards a
structural econometric modeling approach. This would potentially allow the incorporatoin of a
greater amount of information into the estimation process. One possible approach would be to
specify four equations: 1) Expected utility conditional on credit receipt; 2) Expected utility
conditional on no credit; 3) Credit supply; and 4) Expected income conditional on no credit.
Regimes which are consistent with the theoretical model can be defined based on the
relationships between these four equations. This approach, while potentially rewarding, is likely
to pose computational challenges since it would involve the evaluation of multiple integrals.
Additional restriction would also have to be considered to deal with ranges in endowment space
where certain regimes are not defined.
31
Appendix A. Results of multinomial regression
Table A1. Multinomial Logit coefficient estimates
Coefficients and standard errors associated with rationing category:
Individual
Characteristic
Price rationed - no loan
($1 )
Risk /TC Rationed
($2 )
Quantity Rationed
($3 )
Constant
-0.11
(1.13)
-0.70
(1.41)
-1.25
(1.31)
C
0.046 *
(0.027)
-0.042
(0.029)
-0.082 **
(0.028)
0.46x10-4
(0.34x10 –3)
-0.13x10 -3
(0.62x10 -3)
0.95x10-4
(0.34x10 -3)
M
0.16
(0.17)
0.45*
(0.24)
0.43*
(0.25)
M_SQ
-0.014
(0.016)
-0.071
(0.38)
-0.041
(0.037)
T
-0.16
(0.12)
0.20
(0.17)
0.11
(0.11)
T_SQ
0.0018
(0.0059)
-0.021
(0.015)
-0.54x10 -3
(0.0058)
C_T
-0.0073
(0.003)
0.0031
(0.0059)
0.41x10-3
(0.0031)
T_M
0.19
(0.013)
0.042
(0.032)
-0.0068
(0.018)
AGE
0.015
(0.017)
0.97
(0.018)
0.0060
(0.017)
EDUC
0.006
(0.052)
-067
(0.060)
0.023
(0.051)
L_HIST
-3.20 **
(0.40)
-4.70 **
(0.66)
-3.90 **
(0.42)
DEFAULT
-0.14
(0.53)
0.19
(0.53)
1.07**
(.047)
IRRIG
0.23
(0.78)
0.67
(0.81)
1.89**
(0.78)
BAJO
2.48 **
(0.60)
2.36**
(0.64)
2.70**
(0.59)
ALTO
-0.51
(0.60)
0.27
(0.60)
0.54
(0.54)
C_SQ
32
SANLOR
0.36
(0.88)
Log Likelihood
Restricted L og-L
Significance level
% p redicted co rrectly
-0.34
(1.05)
*
-653.27
-729.96
1.0x10-7
60%
0.41
(0.85)
indicates significan t at the 10 % level.
indicates significan ce at the 5% level.
**
Table A2. Frequencies of actual and predicted outcomes from Multinomial Logit Model
Predicted Category
Price Rationed
with loan
Price Rationed
no loan
Risk
Rationed
Quantity
Rationed
Total
Price Rationed
with loan
120
7
4
21
152
Price Rationed
no loan
10
14
5
80
109
Risk Rationed
2
4
13
66
85
Quantity Rationed
9
7
5
180
201
141
32
27
347
547
Actual
Category
Total
33
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