The research was conducted in Enugu State, Nigeria. The dominant criteria for selecting Enugu State were the prevalence of small scale rice farmers and numerous financial institutions in most of the rural areas in the state. Enugu state is also among the highest rice producing states in Nigeria. In addition, rice production is known to be a major staple and livelihood strategy in the state. The state is made up of 14 core rural local government areas, where rice farming is practised. Enugu State is made up of three agricultural zones, 17 local government areas and 39 Development Centres in the state.
A multi-stage sampling technique was used to select the respondents for the study in the following ways. First, the sample frame for this study was all the small scale rice farmers who applied for credit, whether access or not, from financial institutions in the selected areas formed the sample frame. The list were collected from and with the help of Enugu State Agricultural Development Projects (ENADP). Eight were selected at random out of 14 Local Government Areas (LGAs) located in rural areas. A random sampling technique was used to select two communities from each of the selected rural LGAs, which gives 16 communities. A random sampling technique was used to select 10 crop farmers from eight selected communities, which gave 80 respondents. However, after data cleaning and other exercises of data editing, 75 questionnaire were collected and used for the analysis. Finally, all the financial institutions in the selected LGAs formed the sampling frame for financial institutions. In selecting financial institutions, a purposive sampling technique was used to 16 formal financial institutions that had operated for more than ten years in each of the selected local government areas. This gave a total of 16 formal financial institutions. Therefore, 75 farmers and 16 financial institutions were used for the study. Relevant primary data were collected through questionnaire, focus group discussions and lead informant interviews. The secondary information were also collected from publications. The major analytical tools used to achieve the study’s objectives are descriptive statistics and the Poisson regression model.
Model specification
The Poisson model for count data is suitable for estimating the rice farmers’ decisions on managing credit risks. The binomial distribution represents the probability of repaying
k percentage of credit given
n independent trials.
..........(1)
Where
and
p is the probability of repaying a percentage of credit
k.
The statistical theory states that a repetition of a series of binomial choices, from the random utility formulation, asymptotically converges to a Poisson distribution as
n it becomes large and becomes small.
..........(2)
Where
p = µ
/ n and
m is the mean of the distribution, such as the mean percentage of credit repaid by crop farmers per rice farmer. This formulation allows modelling of the probability that a farmer chooses the percentage of credit to be repaid
k given a parameter µ, the sample mean.
The statistical theory outlined above can be modelled into a series of discrete farmer decisions that sums across an aggregation of choices to a Poisson distribution. The Poisson regression model is the development of the Poisson distribution presented in equation (2) to a non-linear regression model of the effect of independent variables x
i on a scalar dependent variable y
i. The density function for the Poisson regression is
..........(3)
where the mean parameter is the function of the regressors x and a parameter vector b is given by:
..........(4)
where
..........(5)
Also note that
..........(6)
That is the coefficients of the marginal effects of the Poisson model can be interpreted as the proportionate change in the conditional mean if the
jth regressor changes by one unit.
Finally the Poisson model sets the variance to equal to the mean. That is:
..........(7)
This restriction of the equality of the mean and variance in the Poisson distribution is often not realistic as it has been found that the conditional variance tends to exceed the mean resulting in over-dispersion problem (Winkelmann, 2000). If the over-dispersion problem exists, the conditional mean estimated with a Poisson model is still consistent though the standard errors are biased downwards (
Grogger and Carson, 1991). A more generalized model to account for the over-dispersion problem is based on the negative binomial probability distribution expressed as:
..........(8)
where
..........(9)
and a ≥ 0 characterizes the degree of over-dispersion, or the degree to which the variance differs from the mean. That is, in the case of the Negative Binomial model employed here:
..........(10)
Once the negative binomial model is estimated, significant over-dispersion is checked using the alpha coefficient. If the estimated alpha coefficient is zero, then the conditional mean is equal to the conditional variance and the negative binomial model reduces to the Poisson model. If the estimated alpha coefficient is significantly greater than zero, then over-dispersion is present and the estimated negative binomial model is preferable to the Poisson model. An excellent facet of the negative binomial model is that the Poisson model is nested within it (
Cameron and Trivedi, 1998).
The independent variables specified as factors influencing farmers’ repayment performance as proxied by the percentage of credit to be repaid defined as follows:
X1= Age of the respondent (years).
X2 = Educational level (year of formal education).
X3= Farming experience (years).
X4 = Extension education (Yes= 1, No= 0).
X5 = own off-farm employment (Yes= 1, No=0).
X6 = Past experience with risk (severe = 1, mild = 0).
X7 = Obtain credit from commercial Bank.
X8 = Obtain credit from microfinance Bank.
X9 = Obtain credit from informal Institutions.
X10 = Amount borrowed (in naira).
X11 = Interest on loan (per cent).
Note: Obtain credit from State bank is a base variable for where respondents obtain credit