I Congresso da SBI-Agro


An application for risk estimation on rural credit markets


Ricardo Chaves Lima
Universidade Federal de Pernambuco
CCSA - Departamento de Economia
Av. dos Economistas s/n, Cidade Universitária
50670-901, Recife-PE
fone/fax: (081) 271-8378

Luiz Carlos Miranda
Universidade Federal de Pernambuco
CCSA - Departamento de Ciências Contábeis.
Av. dos Economistas s/n, Cidade Universitária
50670-901, Recife-PE
fone/fax: (081) 361-5399

Wilson Magela Gonçalves
Universidade Federal de Pernambuco
CCSA - Departamento de Ciências Administrativas.
Av. dos Economistas s/n, Cidade Universitária
50670-901 - Recife-PE
fone/fax: 081-271-8368


A produção agrícola em países menos desenvolvidos tem sido caracterizada como uma atividade econômica bastante arriscada. O conhecimento da distribuição da probabilidade associada ao pagamento do crédito rural diminui a incerteza e aumenta a oferta de crédito disponível aos produtores agrícolas. O presente trabalho usa o modelo logit para associar a capacidade dos produtores em pagar um empréstimo às suas características sócio-econômicas e ao volume de crédito tomado. Os coeficientes estimados são usados para examinar a influência de cada característica do produtor à sua capacidade de pagamento. A função logística cumulativa é usada no MS Excel para calcular a probabilidade do produtor pagar o empréstimo, dado o valor do empréstimo tomado e o conjunto de características sócio-econômicas. O programa foi elaborado com a utilização da linguagem de programação Visual Basic, de forma a permitir entradas relacionadas às características dos produtores. A resposta dada é a probabilidade de pagamento do empréstimo.


Agricultural production in less developed countries has generally been regarded as highly risky. The knowledge of the probability distribution associated with paying a loan on rural credit markets is likely to decrease uncertainty, and to increase the supply of landing money available for agricultural producers. In the present work a logit model associates the ability of producers in paying a loan to their social and economic characteristics, and the amount of money borrowed. The estimated coefficients are used to examine the influence of each characteristic of the producer to its ability to paying a loan. The cumulative logistic function estimates are used in the MS Excel to calculate the probability of a producer paying a loan given a set of social and economic characteristics. The application is organized with the aid of Visual Basic Programming Language in a way of allowing entries related to the characteristics of producers. The program output is the loan payment probability for a set of given characteristics of producers.

Key Words

agricultural credit, risk, logit model, credit scoring model.



The availability of agricultural credit have been considered one of the greatest constraint for the development of the rural economy in developing countries. This problem becomes greater for small farmers. The insufficient supply of rural credit, and the low pay back capacity of producers contributes to elevate the interest rate, making agricultural credit non-accessible to smaller producers. The theory of interest determination on rural credit markets considers that interest rate (r) is given by the sum of the following components (Gatak e Ingersent, 1990):


where alpha represents the administration cost of a loan, gama is the opportunity cost, beta is the risk premium, pi is the profits. Assuming that, in general, alpha and gamma are not very high, it can be concluded that interest rate of agricultural loans depend heavily on beta and pi. That is, the risk premium and the profits are the most important factors on the interest rate determination on rural credit markets.

The small supply of credit on rural areas in developing countries leads to an increase on the profits of money lenders, and the lack of collateral increases the risk associated with the loan and, consequently, the premium becomes larger. This is, in general, the situation of rural credit markets on less developed and developing countries. The interest paid in such areas makes agricultural loans unavailable for small farmers. One way of increasing the supply of credit on agriculture is the participation of public agencies. The solution, in many case, have been to take money from informal credit markets paying very high interest, or working on the sharecropping system.

Another problem which contributes to restrain the supply of agricultural credit is the lack of knowledge of the probability associated with an uncertain payment of a loan. That is, money lenders, in general, have few evidence indicating that a given producer is a "good" borrower. Such evidences would decrease the variance of the expected results associated with lending money and, consequently, decreasing interest. Assuming that producers pay back capacity is a function of the amount of credit taken, as well as the socio-economic characteristics of the family, a function can be built to estimating the risk related to money lending, on a credit score type of model. The methodology of such risk function will be presented on the next section.



This work uses logit model to estimate the relationship between producers attributes and the probability of paying a loan. The estimated coefficients are used to build an application on Microsoft Excel/Visual Basic which permits credit analysts to calculate the risk associated to rural credit.

The first phase of building the computer demonstration program is to estimate, using logit maximum likelihood, the coefficients of the following function:

y = f (x1, x2, x3, ..) (2)

where y assume value one for producers who paid their loans and zero otherwise, and x1, x2, x3, ..., represent the attributes of the producers such as farm size, family size, schooling, age, average income, non-farm income, etc., and the amount of credit required. The logit function can be estimate using any statistic package which works with this type of function, such as SHAZAM, SAS, or SPSS. Once the coefficients are estimated, a macro is built on Microsoft Excel with the following formula:

where P is the probability of an agricultural producer paying a loan, exp is the exponent applied to the base e, and B0, B1, B2, ..., are the estimated coefficient of x1, x2, x3, ...,. For further details on the estimation process of logit type of functions see Greene (1993) and Pyndick and Rubinfeld (1981).

The computer program is composed of 3 main parts. The first part presents the cover of the program and some basic information on the methodology used for estimating the coefficients and building the macro on Excel. The second part is a form-type sheet in which information on the amount of credit required and on the attributes of the producer are recorded. This part of the program shows the following outputs:

  • the probability that the producer considered will pay the loan;
  • the maximum amount of loan that the producer should be allowed to take given its attributes for different levels of risk (e.g. 1%, 5%, 10%, etc.).

The third part of the program is used to build up scenarios such as the occurrence of insurance markets (on private of public institutions) and government subsidies. Different scenarios are built based on the agricultural credit market reality on Brazil, but the program can be adapted to other realities.



The results were obtained by simulating a risk function with a vector of explaining variables composed of 3 characteristics of producer (income, age, and education) and the amount of loan taken. The dependent variable was assumed to be dichotomous assuming value 1 if the producer paid the loan and 0 otherwise. Instead of using income and the amount of credit taken separately in the equation it was preferred to use the ration income/loan. Such variable gives a measure of producer's income relatively to the amount of credit taken. The dependent variables in the risk function was defined as follows:

Income/Loan - producer's income (US$) divided by the amount of loan taken (US$);

Age - producer's age;

Education - producer's years of formal education;

The coefficients of the risk function were defined using simulation as follows:

Table 1 show some results of the simulated risk function for 10 producers with different characteristics and amount of loan taken. The Probability of Paying a Loan (PPL) was calculated on a spreadsheet (MS-EXCEL) according the formula on equation (3).

Producer Income Age Education Loan (US$) PPL Risk
1 $ 2,000.00 35 17 $ 4,000.00 75% Medium Risk
2 $ 10,000.00 33 8 $ 6,000.00 82% Medium Risk
3 $ 3,000.00 38 8 $ 1,100.00 93% low Risk
4 $ 2,000.00 56 3 $ 800.00 91% low Risk
5 $ 1,500.00 24 15 $ 10,000.00 62% Medium Risk
6 $ 4,000.00 36 3 $ 11,000.00 51% high Risk
7 $ 4,600.00 57 17 $ 3,000.00 91% low Risk
8 $ 2,000.00 45 3 $ 5,000.00 56% high Risk
9 $ 1,800.00 34 6 $ 4,000.00 57% high Risk
10 $ 5,000.00 45 17 $ 1,000.00 99% low Risk

Table 1: Risk simulation for 10 producers

Credit operations were classified according to the probability of paying a loan in the following way:

High Risk (0 < PPL < 60%);

Medium Risk (60% < PPL < 90%);

Low Risk (90% < PPL < 100%).

Except for the intercept, the coefficients in the risk function are all positive, what indicates that income/loan, age, and education are positively related to the probability of paying a loan. That is, individuals with high income relatively to the amount of loan taken are assumed to be associated to a higher probability of paying the loan. By the same token, older and more educated individuals are also assumed to be more likely to pay their debts. The logit function capture the joint effects of the explaining variables. Producer 1, for instance, took a loan which was twice his income. Although he/she has 17 years of formal education his/her PPL was 75% (medium risk). Producer 3 is almost of the same age as producer 1, and has only 8 years of formal education, but was classified as low risk. The difference is that producer 3 took a loan which is close to one third of his/her income. Producer 6 showed the lowest PPL. The amount of loan taken by this producer was almost three times his income, he/she had only 3 years of formal education and was 34 years old. On the other hand producer 10 showed the highest PPL. This producers took a loan which was one fifth of his income, had 17 years of formal education, and was 45 years old.



The risk function calculates the probability of a producer paying a loan according to his/her socio-economic characteristics, and the amount of credit taken. Many other explaining variables may be introduced in the risk function according to what the credit institution believes influence producer's ability to paying a loan. The advantage of using a logit type of function is that risk can be estimated as a joint function of factors determining producer's pay back capacity. The application built on the spreadsheet, based on the risk function estimated on a statistic package, permits an immediate calculation of the risk associated with credit operations. The knowledge of the probability distribution associated with the risk decreases the variance of expected returns of loans, bringing more money lenders into the credit markets. An increase on the supply of credit money is likely to influence a decrease on the interest rate, what makes credit available to a large portion of agricultural producers.



  • Gatak, S. and Ingersent, K. (1990). Agriculture and Economic Development. Johns Hopkins.
  • Greene, W. H. (1993). Econometric Analysis. New York, Macmillan.
  • Pindyck, R. S. e Rubinfeld, D. L. (1981) Econometric Models and Economic Forecasts. McGraw-Hill, New York.



Ricardo Chaves Lima

Ricardo Chaves Lima é Engenheiro Agrônomo pela UFC, Mestre em Economia Agrícola pela UFC, e Ph.D. (Economia Agrícola) pela Universidade do Tennessee nos Estados Unidos. Suas áreas de interesse incluem Economia Agrícola e Econometria. Foi professor visitante da Universidade Federal do Ceará, onde desenvolveu pesquisas em análise de preços agrícolas e desenvolvimento rural. É professor adjunto do Departamento de Economia e do PIMES, pesquisador do CNPq, e consultor de empresas. Atualmente é responsável pelas disciplinas de desenvolvimento econômico e análise estatística de séries temporais.

Luiz Carlos Miranda

Luiz Carlos Miranda é Bacharel em Economia, Mestre em Contabilidade (Controladoria) pela USP, e Ph.D. (Agribusiness e Contabilidade Gerencial) pela Universidade de Illinois. Suas áreas de interesse incluem Contabilidade Gerencial, Controladoria, Sistemas de Informações Intra e Inter-Empresariais, Desempenho Gerencial, Supply Chain Management, Agribusiness. Trabalhou no Banco Central do Brasil, no Grupo Sanbra/Santista, onde foi responsável pela coordenação do sistema de planejamento (na Holding, em São Paulo, e nasTintas Coral do Nordeste, onde foi controller. É professor adjunto do Departamento de Ciências Contábeis e do Executive MBA em Finanças da UFPE e consultor de empresas. Coordena a pós-graduação em Ciências Contábeis da UFPE. Publicou diversos artigos em revistas e participou como apresentador e coordenador de vários seminários.

Wilson Magela Gonçalves

Wilson Magela Gonçalves é Engenheiro Agrônomo pela ESAL/UFLA e mestre em Administração Rural pela mesma Universidade. Suas áreas de interesse incluem Estratégia Empresarial e Agribusiness. Foi professor do Departamento de Economia e Administração da UFLA e da Faculdade de Administração do Instituto GAMMON. Foi consultor do SEBRAE/MG. É professor assistente do Departamento de Ciências Administrativas da UFPE e consultor de empresas. Atualmente é responsável pelas disciplinas Teoria Geral da Administração e Estágio Supervisionado.