Table 2 presents the results of profitability analysis for rain-fed upland rice farmers in the study areas. Table 2 shows the estimate of the costs, revenues as well as gross margin which was used to determine the profitability of rain-fed upland rice production in the study areas. The gross margin per hectare is defined as the difference between gross revenue per hectare and total variable costs of production per hectare. The table 2 showed that average total variable costs per hectare were N16, 192.77 and N13, 682.35 for paddy farmers in Osun and Oyo states respectively. Cost of labour accounted for 57.86 percent and 71.76 percent of average total variable costs per hectare of paddy farmers in Osun and Oyo States respectively.

Table 2 also shows the percentage of the total cost allocated to fixed and variable inputs. For a potential farmer who wants to invest in rain-fed upland rice production, 50.01 percent and 62.45 percent of the average total cost of production per hectare of paddy rice would be expended on hired labour in Osun and Oyo states respectively, 20.03 percent and 4.31 percent would be spent on seeds in Osun and Oyo states respectively, 5. 40 percent and 11.27 percent would be spent on fertilizer respectively in Osun and Oyo states, while 11.0 percent and 9.0 percent on agrochemicals respectively in Osun and Oyo states. For the fixed input items, 5.65 percent would be expended on land in both Osun and Oyo states respectively while 7.91 percent and 7.32 percent would be expended on tools respectively in Osun and Oyo states. The average total revenue per hectare was about N50, 374.20 and N39, 131.20 for paddy farmers in Osun and Oyo states respectively.

The average gross margin per hectare for farmers in Osun State was N34, 181.38 while it was N25, 448.84 in Oyo State. These results which conformed to the findings of Aderinola (1997); Agbamu and Fabusoro (2001); Odoemenem and Inakwu (2011) suggested that rice production was profitable in the two states. However, it was more profitable to produce rice in Osun state than Oyo state because of the highest level of gross margin per hectare obtained in the state; all other factors remaining unchanged.

The data in table 3 shows the summary of the performance ratios of the rain-fed upland rice farmers in both Osun and Oyo states. The Benefit cost ratio (BCR) of 2.69 and 2.49 obtained for farmers in Osun and Oyo states respectively, showed that rain-fed upland rice production was a worthwhile investment since the ratios obtained were greater than one (Harsh etal, 1981).

The rate of return (ROR) of 168.9% and 148.9% estimated for Osun and Oyo states respectively, indicated that for every N1.00 invested in rain-fed upland rice production, about N1.70 naira and N 1. 50 were gained as revenues in Osun and Oyo state respectively. The gross ratio (GR) of 0.37 and 0.40 obtained for Osun and Oyo states respectively implied that for every N1.00 returns to rain-fed upland rice farming, 37 kobo and 40 kobo are being spent respectively by farmers in Osun and Oyo states.

The expense structure ratio (ESR) of 0.14 and 0.13 estimated for farmers in Osun and Oyo states respectively indicated that 14% and 13% of the total costs rain-fed upland rice production in Osun and Oyo states respectively were made of fixed cost components. The results of the performance ratios reported in table 3 therefore lend credence to both the viability and profitability of the rain-fed upland rice production in both Osun and Oyo states of Nigeria.

Table 2: Average Costs and Returns Per Hectare of Upland Rice Production in Osun and Oyo States, Nigeria.

Items | Mean Figure | Mean Figure | ||||||

Osun | % of TFC | % of TVC | % of TC | Oyo | % of TFC | % of TVC | % of TC | |

Farm size (ha) | 1.30 | 1.90 | ||||||

Rice output (kg) | 2183.3 | 2200.4 | ||||||

Rice yield(kg/ha) | 1679.48 | 1158.11 | ||||||

Total Revenue (N) | 65486.40 | 74349.26 | ||||||

Total Revenue/ha (N/ha) | 50374.15 | 39131.19 | ||||||

Variable Cost | ||||||||

Cost of seeds (N) | 4879.68 | 23.18 | 20.03 | 1286.32 | 4.95 | 4.31 | ||

Cost of fertilizer (N) | 1315.79 | 6.25 | 5.40 | 3366.79 | 12.95 | 11.27 | ||

Cost of labour (N) | 12179.60 | 57.86 | 50.01 | 18656.09 | 71.76 | 62.45 | ||

Cost of agrochemicals (N) | 2675.53 | 12.71 | 11.0 | 2687.27 | 10.34 | 9.00 | ||

Total Variable Cost (N) | 21050.60 | 100.0 | 25996.47 | 100.0 |

Items | Mean Figure | Mean Figure | ||||||

Osun | % of TFC | % of TVC | % of TC | Oyo | % of TFC | % of TVC | % of TC | |

Total Variable Cost/ha(N/ha) | 16192.77 | 13682.35 | ||||||

Gross Margin (N) | 44435.80 | 48352.79 | ||||||

Gross Margin/ha (N/ha) | 34181.38 | 25448.84 | ||||||

Fixed Cost | ||||||||

Rent on land(N) | 1376.99 | 41.69 | 5.65 | 1689.11 | 43.58 | 5.65 | ||

Depreciation on tools(N) | 1926.07 | 58.31 | 7.91 | 2187.20 | 56.42 | 7.32 | ||

Total Fixed Cost(N) | 3303.06 | 100.0 | 3876.31 | 100.0 | 100.0 | |||

Total Fixed Cost/ha (N/ha) | 2540.82 | 2040.16 | ||||||

Total Cost (N) | 24353.66 | 100.0 | 29872.78 | |||||

Total Cost/ha (N/ha) | 18733.58 | 15722.52 | ||||||

Net Farm Income (N) | 41132.74 | 44476.48 | ||||||

Net Farm Income/ha (N/ha) | 31640.57 | 23408.67 |

(US1 dollar =132 Nigeria naira)

Source: Results obtained from Data Analysis.

Table 3: Performance Measures for the Rain-Fed Upland Rice Farmers in Osun and Oyo States

Measure | Osun | Oyo |

Benefit Cost Ratio | 2.69 | 2.49 |

Rate of Return on Investment | 168.9 | 148.9 |

Gross Ratio | 0.37 | 0.40 |

Expense Structure Ratio | 0.14 | 0.13 |

Source: Results obtained from Data Analysis.

Maximum Likelihood Estimates of Stochastic Frontier Production Functions

The ordinary least squares estimates (OLS) (Model 1) and the maximum likelihood parameter estimates (MLE) (Model 2) of the stochastic frontier production functions for Osun and Oyo States are presented in tables 4 and 5.

The coefficients of the variables are very important in discussing the results of the analysis of data. For Osun state, farm size had the highest coefficient with a value of 0.949 and 0.961 (Table 4) for the two models respectively. Farm size, family labour, quantity of fertilizer and amount spent on agrochemicals carried positive sign for the two models while hired labour, quantity of rice seed planted and expenditure on implements carried negative signs. The variables with positive coefficients implied that any increase in such a variable would lead to an increase in rice paddy output, while an increase in the value of the variable with a negative coefficient would lead to a decrease in output of rice paddy. Negative coefficient on a variable might indicate an excessive utilization of such a variable. In Oyo state, however, all the variables carried positive signs (Table 5) while the coefficients of the farm size and hired labour were significant at 5.0% level of significance across the two states.

The elasticity of rice output with respect to farm size (from model 2) had the highest value across the two states (0.961 for Osun and 0.314 for Oyo). This was an indication of the fact that land was the most important factor in the production of rice; hence, there was the need for the farmers to increase their farm size in order to increase the output of rice. Other variables that were of significant importance in increasing rice output were hired labour, quantity of fertilizer, amount spent on agrochemical and family labour.

The sum of the elasticities (1.40 and 0.83) obtained from model 2 for Osun and Oyo states respectively showed that farms in Osun state had increasing returns to scale and that the rice farmers were operating in the irrational zone of production (Stage I). However, in Oyo state, returns to scale (RTS) parameter had a value between 0 and 1 (0.83), which showed that the rice farmers were operating in the rational zone of production (Stage II) and that the resources were being efficiently used in rice production in Oyo state. The overall economic implication of these results is that farmers in Osun state can improve on their productivity by employing more resources while farmers in Oyo state can only improve their productivity by reducing their current level of resource-use.

The estimated gamma (g) parameter of farms in Osun state was 0.99 and highly significant at 5.0% level of significance (Table 4). This means that 99% of the variation in rice output among the farms in Osun state was due to the differences in their technical efficiencies. In the case of the farms in Oyo state however, it was only about 16% of variation in their rice output that was accounted for by differences in technical efficiency (Table 5). These results confirm the presence of the one sided error component in the model, therefore, making the use of Ordinary Least Squares (OLS) in model 1 inadequate in representing the data. These results are consistent with the findings of Ajibefun et al (2002); 2 Ajibefun and Aderinola (2004); Idiong et al (2006). The estimated sigma square ( 7 ) of each of the farms were 0.008 and 0.018 for farmers in Osun and Oyo States respectively. The values were large and significantly different from zero (Tables 15 and 16). This was an indication of a good fit of the model and the correctness of the specified distributional assumptions.

Table 4: Maximum Likelihood Estimates for the Parameters of the Stochastic Frontier Production Function for Rice Farmers in Osun State.

Variables | Model 1 | Model 2 |

General Model (Production Function) | ||

Constant | 2.703 | 2.943 |

(7.720) | (11.31) | |

Farm Size | ж0.949 | 0.961* |

(18.95) | (22.24) | |

Family Labour | 0.011 | 0.016 |

(0.803) | (1.459) | |

Hired Labour | -0.014 | ж-0.036 |

(-0.435) | (-2.136) | |

Quantity of Fertilizer | 0.240 | 0.534* |

(0.808) | (2.479) | |

Quantity of Rice Seed Planted | 0.024 | -0.063* |

(0.525) | (-2.098) | |

Amount spent on Agrochemicals | ж0.068 | ж0.037 |

(4.354) | (2.788) | |

Expenditure on Implements | 0.020 | ж-0.047 |

(0.067) | (-2.506) | |

Inefficiency Model | ||

Constant | 0 | 0.3947 |

(7.301) | ||

Age of Farmer | 0 | -0.007* |

(-4.139^{)} |
||

Years of Education | 0 | -0.003 |

(-0.869) |

Contact With Extension Agents | 0 | -0.014* |

(-1.993) | ||

Variables | Model 1 | Model 2 |

General Model (Production Function) | ||

Years of Farming Experience | 0 | 0.001 |

(0.935) | ||

Amount of Credit Available to Farme | 0 | 0.007 |

(1.152) | ||

Variance Parameters | ||

Sigma Squared | 0.004 | ж0.008(8.260) |

Gamma | 0 | 0.999* |

(236.2) | ||

Log Likelihood Function | 199.2 | 217.4 |

Notes: * means estimated coefficients which were significant at 5.0% level.

Figures in parentheses are t-ratio values.

Source: Results obtained from Data Analysis.

Table 5: Maximum Likelihood Estimates for the Parameters of the Stochastic Frontier Production Function for Rice Farmers in Oyo State

Variable | Model 1 | Model 2 |

General Model (Production Function) | ||

Constant | 2.093 | 2.376 |

(9.676) | (9.603) | |

Farm Size | ж0.306 | ж0.314 |

(3.692) | (3.933) | |

Family Labour | 0.162* | 0.142* |

(2.943) | (2.563) | |

Hired Labour | 0.308* | 0.284* |

(3.783) | (3.588) | |

Quantity of Fertilizer | 0.010 | 0.001 |

(0.556) | (0.044) | |

Quantity of Rice Seed Planted | 0.065 | 0.026 |

(0.846) | (0.346) | |

Amount spent on Agrochemicals | 0.007 | 0.010 |

(0.323) | (0.437) | |

Expenditure on Implements | 0.079 | 0.051 |

(1.239) | (0.794) | |

Inefficiency Model | ||

Constant | 0 | 0.061 |

(0.609) | ||

Age of Farmer | 0 | 0.001 |

(0.573) | ||

Years of Education | 0 | 0.008 |

(1.526) | ||

Contact with Extension Agents | 0 | -0.067 |

(-1195) | ||

Years of Farming Experience | 0 | -0.002 |

(-0.491) | ||

Amount of Credit Available to Farmers | 0 | -0.00001 |

(-1.471) | ||

Variance Parameters | ||

Sigma Squared | 0.019 | 0.018*(8.047) |

Gamma | 0 | 0.159 |

(1.613) | ||

Log Likelihood Function | 90.16 | 93.65 |

Notes: * means estimated coefficients which were significant at 5.0% level.

Figures in parentheses are t-ratio values.

Source: Results obtained from Data Analysis.

The distribution of decile range of technical efficiency estimates of the farmers (Table 6) showed that technical efficiency (TE) indices ranged from a minimum of 66.8% to a maximum of 99.8% for the farms in Osun state, with a mean of 90.1% and a standard deviation of 6.6%. Thus, in the short run, there was a scope for increasing rice production of an average farmer by about 10.0% by adopting the technology and techniques used by the best practiced (most efficient) rice farmers. Such farmers could also realize a 9.7% cost savings (i.e., 1-[^{90}^g9 gJ) in order to achieve the TE level of his most efficient counterpart (Bravo-Ureta and Pinheiro, 1997 and Raphael, 2008). For the most technically inefficient farmer, he has to achieve a cost saving of about 33.0% (i.e., 1- [^{66}.8gg $]) to become the most efficient farmer. This could be achieved by addressing the issue of negative elasticities of hired labour, quantity of rice seed planted and expenditure on implement (Table 4). The decile range of the frequency distribution of the TE indicates that about 1.0% of the rice farmers had TE of less than 71.0% while about 99.0% had TE of equal or greater than 71.0% (Table 6).

In Oyo state, the predicted farm specific TE indices ranged from a minimum of 84.4% to a maximum of 99.4% for the farms in the sample, with a mean of about 94.0% and a standard deviation of 4.3%. Thus, in the short run, there is a scope for increasing rice production of an average rice farmer by about 6.0% by adopting the technology and technique used by the best-practiced (most efficient) rice farmer. Such a farmer could also realize a 5.1% cost savings (1194.3/99 4-1) (Bravo-Ureta and Pinheiro, 1997 and Raphael, 2008). A similar calculation for the most technically^99.4^{])}.

This could be achieved by addressing the issue of low elasticities obtained for quantity of fertilizer, amount spent on agrochemicals and expenditure on implements (Table 5). The decile range of the frequency distribution of the TE indicates that about 83.0% of the rice farms had TE of over 90.0% and about 17.0% had TE ranging between 71.0% and 90.0%.

Table 6: Decile Range of Frequency Distribution of Technical Efficiencies of Rain-fed Upland Rice Farmers in Osun and Oyo States

Decile Range of Technical Efficiency (%) | Osun state | Oyo state | ||

No | % | No | % | |

> 90 | 73 | 48.67 | 124 | 82.67 |

81 – 90 | 66 | 44 | 25 | 16.67 |

71 – 80 | 10 | 6.67 | 1 | 0.66 |

61 – 70 | 1 | 0.66 | 0 | 0 |

Total No of Farms | 150 | 100 | 150 | 100 |

Mean % | 90.1 | 94.3 | ||

Minimum % | 66.8 | 84.4 | ||

Maximum % | 99.8 | 99.4 | ||

Standard Deviation | 6.6 | 4.3 |

Source: Results obtained from Data Analysis.