Table 1 shows the maximum likelihood parameter estimates of the stochastic production frontier (Eqn.11) for women food croppers along with some descriptive statistics for the sample. For comparison, OLS estimates of average production functions are also shown. In general, the frontier estimates amount to a neutral upward shift of the average function. With the adjusted R2 value of 0.87, the inputs used in the model were able to explain 87 percent of the variation in food crop production for the state. The coefficients of labour, fertilizer, material inputs and equipments were positive and highly significant but agrochemical was negative and not significant. The insignificance of agrochemical could be due to low use of agrochemical in the study area.
On the other hand, the estimates of the stochastic frontier shows that labour, fertilizer, material inputs and equipment have a positive and significant impact on the value of production while agrochemical have a negative and significant impact on the value of production. However, labour has the largest coefficient. This indicates that the largest impact on output, on average, would be experienced if labour could be made available and affordable to farmers. The estimate of sigma-squared (а,2) is significantly different from zero at the 1 percent level (16.04). This indicates a good fit and correctness of the specified distributional assumption. Similarly, the estimate of y, was 0.84. This would mean that more than 84 percent of the variance in output among the women food croppers is due to differences in technical efficiency. This implies that technical inefficiency are highly significant in the analysis of the data.
Table 1: Average Production Functions and Stochastic Production Frontiers for Women Food Croppers in Nigeria.
Figures in parentheses are t – values * – Significant
The dual cost frontier for food crop derived analytically from the stochastic production frontier is shown below.
LnC = – 14.072 + 0.0016 LnPL + 1.006 Ln PF + 1.000 Ln Pm + 0.928 Ln PE + 0.412Ln PA + 0.000069 LnQ*—(13)
Where C is per farm cost of producing food crops; PL daily wage rate per worker; PF price of fertilizer; Pm price of material inputs, PE price of equipment; PA price of agrochemicals; Q* annual total value of food crops adjusted for any statistical noise as specified in eqn (10) above.
The results derived from the MLE indicate that technical efficiency (TE) indices range from 38.5 to 100 percent for the farms in the sample, with an average of 81 percent (Table 2). This means that if the average farmers in the sample was to achieve the TE level of its most efficient counterpart, then the average farmer could realize a 19 percent cost saving or increase in production (i.e. 1 – (81/100)]. A similar calculation for the most technically inefficient farmer reveals cost savings of 62 percent [i.e. 1-(38.5/100)]. The mean allocative efficiency of the sample is 96.5 percent, with a low of 58.8 and a high of 100. The combined effect of technical and allocative factors shows that the average economic efficiency level for this sample is 78.5 percent, with a low of 35.8 percent and a high of 99 percent. This figure indicate that if the average farmer in the sample were to reach economic efficiency of its most efficient counterpart then the average farmer could experience a cost savings of 20.7 percent (i.e. 1-(78.5/99)]. The same computation for the most inefficient farmers suggests a gain of 64 percent in economic efficiency. [i.e. 1 -(35.8/99)].
The sample frequency distributions indicate a clustering of economic and technical efficiency in the region 85-94 percent efficiency range and allocative efficiency in the region greater than 94 percent but less than 100 percent. The implication of the findings above is that given the production resources at the disposal of the women farmers, who are mainly small-scale and resource poor, the women food croppers in Ogun State of Nigeria are fairly efficient in the use of their resources. This result is in line with the findings of Bravo-Ureta and Rieger (1991).
Table 2:Frequency Distribution of Economic (EE), Technical (TE) and Allocative Efficiency Estimates for Women Food Croppers in Nigeria.
To investigate the relationship between efficiency indexes and socio-economics variables, regression analysis was carried out. The variable of education showed positive relation with predicted efficiency in all the efficiency indexes though not significant in economic efficiency. The positive coefficient of education reveals that high level of education results in increases in technical, allocative and economic efficiencies of women food croppers. The negative coefficient for farming experience in technical and economic efficiencies implies that farmers with more years of experience tend to be less efficient. On the other hand, the positive coefficient for the farming experience in allocative efficiency implies that farmers with more experience tend to be more efficient. Experience in food crop production by women farmers was found to be insignificant in determining the economic efficiency of the farmers in the study area.
There was a positive relation between the number of contact with extension agent and economic efficiency. This implies that extension visit tends to increase the economic efficiency of women food croppers. The negative coefficient for extension visit in technical and allocative efficiencies implies that farmers with more number of contact with extension agent tend to be less technically and allocatively efficient. Extension visit is significant in all the efficiency indexes.
Membership of social organization has a negative coefficient in technical and allocative efficiencies, indicating that members of social organization tend to be less technical and allocative efficient in food crop production. On the other hand, the positive coefficient for membership of social organization in economic efficiency implies that members of social organization tend to be more economically efficient in food crop production in the study area. Membership of social organization is insignificant in determining the technical efficiency of women food croppers in the study area.
The most striking conclusion that can be gleaned from the regression results shown in T able 3 is the lack of association between efficiency and some socioeconomic characteristics of the women food croppers in the study area.
Table 3: Regression Results of Relationship between Efficiency Indexes and some Socioeconomic Variables.
The F-value is significant in all the efficiency indexes. This implies that technical, allocative and economic efficiency level of farmers is affected by their socioeconomic characteristics.
This paper uses a stochastic efficiency decomposition methodology to derive technical, allocative and economic efficiency measures for a sample of women food croppers in Ogun State of Nigeria. This analysis shows an average economic efficiency of 78.5%, which reveals that there is considerable room for improvement in the productivity of the farms in the study area. The results of this study suggest that this sample of women farmers could increase output and, thereby, household income through better use of available resources given the state of technology.
Analysis of the relationship between efficiency and four socioeconomic variables revealed that efficiency levels are markedly affected by education, experience, extension visit and membership of social organization. This is supported by the result of the f-value which indicates that technical, allocative and economic efficiency level are affected by their socioeconomic characteristics.