Following the outcome of the non-normality test and transformation of data sets for the study of profitability of smallholder sugarcane farming systems in Tanzania, the quantitative data was analysed using descriptive statistics such as mean, standard deviation and percentage to investigate the relative importance of major variables hypothesized to influence the profitability of sugarcane farming systems and its correlation to loan repayment rate.
One way ANOVA, and an independent t-Test, at significance level of p = 0.05 have been applied to test the variability of the means of the factors of profitability of the two smallholder sugarcane farming systems. Spearman‟s rank correlation test have been used to assess the association between profitability and land size, sugarcane yield, sucrose content, price of sugarcane per tonne and total cost per hectare . The causal effect of the hypothesized factors on profitability have been analysed by the use of Tobit regression analysis. The correlation between profitability and loan repayment rate have been analysed by the Spearman‟s rank correlation test.
3.9.1 Regression Analysis of the Determinants of Profitability of the Farming Systems.
Two - limit Tobit regression model as explained in detail by Amemiya (1985) and shown in Equations 9 and 10 in Chapter two was applied to examine causal effect of the hypothesized factors of the profitability of the smallholder sugarcane farming systems in Tanzania. The Tobit model was censored between 0 and 0.8 basing on arbitrary assumption that smallholder farmers will spend at least 20% of their revenue to finance both pre- harvest and post-harvest operations per hectare. The lower limit was chosen basing on an arbitrary assumption that the revenue expected equals the total cost spent. The general Tobit model for the regression analysis of the profitability factors is presented in Equation 23:
PROFIT = β0 + β1LAND + β2YIELD + β3SUCROSE + β4PRICE + β5COST + ε………..………. (23)
PROFIT represents profitability which is a ratio found by dividing the operating income to the total revenue achieved by each respondent. LAND represents the size
of land in hectares used for sugarcane farming in a particular year as indicated by each respondent. YIELD is measured in tonnes per hectare and was calculated by dividing the total tonnes supplied by an individual farmer to the total area harvested in a particular year.
SUCROSE measured in percentage is the content of sucrose amount measured from a volume of sugarcane juice. Sucrose content is measured in sugar factories laboratories and is a key determinant of sugarcane price. The model variable PRICE stands for the price of sugarcane per tonne in Tanzania shillings. COST stands for the total cost incurred by the smallholder sugarcane farmers per hectare. Total cost per hectare was calculated by dividing the total cost incurred by each respondent to the size of the farm planted with sugarcane. The cost includes pre-harvest and post-harvest costs. βi are the coefficients of the model.
3.9.2 Interpretation of the Tobit Coefficients as the Effects of the IV on DV
Contrasting ordinary least square regression, Tobit coefficients cannot be interpreted as the effect of the independent variables (IV) on the dependent variable (DV), (Amemiya, 1979). Mc Donald & Moffitt (1980), presented two formulas for predicting the observed dependent variable y, as indicated in Equations 24 and 25 without subscripts:
If , then ………..………….……..………...….(24) If , then ………..………....…………...………..(25) Where Xβ is a vector of the values on X (the independent variables multiplied by the approximate Tobit coefficient β) and e is the normally-distributed error term.
Mc Donald & Moffitt (1980) also presented a formula for finding the expected value of the dependent variable for all cases as shown in Equation 26.
) )……..………...……….…….. (26) Where X and β are defined as in Equation 25, Ey is the expected value of the dependent variable, F(z) is the cumulative normal distribution function associated with the proportion of cases above the limit, f(z) is the unit normal density (value of the derivative of the normal curve at a specific point), z is the z-score for an area under the normal curve, and sigma is the standard deviation of the error term reported by the applicable Tobit model.
First-order partial derivative of Equation 27 as presented by Mc Donald & Moffitt (1980) is used to find the effect of an independent variable on the expected value of the dependent variable Ey, for all cases in a Tobit analysis. The formula for this derivative, δEy/δXi is:
) ) ………..……….. (27) Where F(z) is as defined in Equation 26, Ey* is the expected value of y for the cases above the limit. δEy*/δXi, is the change in the expected value of y for cases above the limit. δF(z)/δXi, the change in the cumulative probability of being above the limit associated with an independent variable.
The two terms in Equation 27 identify the two effects in the Tobit model. Mc Donald
& Moffitt (1980) presented formula for calculating these two terms and Madalla, (1992) gave their derivations. For cases above the limit Equation 28 is applicable:
* ( ) )) ) ) +……….……… (28)
For the case at the limit, Equation 29 is used:
)
) ………..……….…………. (29) Where βi is the Tobit coefficient for a partial independent variable, z is z score associated with the area under the normal curve, and the terms are as defined earlier.
Mc Donald & Moffitt (1980) provided a simple strategy for finding F(z) that provides the key to obtaining z and f(z). They showed that the first-order partial derivative across all cases in Equation 27, δEy/δXi, equals F(z) x βi. They described the first-order partial derivative with respect to a particular independent variable across all cases. Madalla (1992) defined the first-order partial derivative as the effect of an independent variable on the observed dependent variable without information whether any observed value is greater than zero. Because F(z), which corresponds to the proportion of cases above the limit, is always less than 1.0, the influence of any independent variable across all cases is always some proportion of the Tobit coefficient. If F(z) ≥ 0.5, the preferred area is obtained by subtracting 0.5 from the F(z) value. If F(z) ≤ 0.5, the looked-for area is 0.5 – F(z).