INTRODUCTION
Rice (Oryza sativa) according to Jamala et al.
(2011) is one of the cereals most commonly consumed in the world, especially
in Asia and Africa and specifically in Nigeria. According to Kumar
et al. (2008), rice is the prime source of food for nearly half of
the World`s population and it is one of the most important major food crops.
It was noted that since 1973, West Africa’s demand for rice has grown at
an annual rate of 6% driven by the population growth of 2.9%. Rice farming is
widespread in Nigeria. Recent field survey indicates that overall crop yield
improved in 2001 due largely to increased growers usage of improved varieties.
All the ecologies in Nigeria are suitable for cultivation of rice hence; the
nation has the capacity to be self sufficient in rice production. However, all
ecologies in the country are plagued by low and decreasing yields, partly as
a result of increasing production costs and lack of available inputs mainly
fertilizer. Arising from this, rice that is milled traditionally has low demand
due to its poor quality. The demand for rice is expected to grow substantially
in subSahara Africa as the population is increasing at the rate of 3.4% per
annum and demand for rice is growing faster than other major staple foods (Akinwale
et al., 2011).
Despite Nigeria’s potentials, particularly in terms of land availability,
human and capital resources needed to produce enough food for its inhabitants,
there is still food deficit, because Nigeria depends on the food importation
for the welfare of its people. Consequent upon this, the agricultural sector
has ceased from being a major contributor to the foreign earnings of the country.
The bulk of rice consumed in Nigeria is imported mostly from Asia, Due to the
effect of climate change, most of the world highest producers of rice like Thailand
have decided to put on hold export of the commodity in order to satisfy traditional
needs. Despite several efforts of domestic production of rice, Africa has not
been able to meet traditional market demands, forcing many of the countries
in the continent to rely on import. According to Ajetomobi
et al. (2011), the production of rice in Nigeria is generally affected
not only by availability of land, labor, capital and management of this product
but also by the efficiency of production. If the farmers are efficient in the
allocation of inputs, this will lead to minimization of cost. As a result, they
maximize profit and are encouraged to produce more thus leading to food security
in rice production.
The term efficiency is often used synonymously with productivity, the most
common measures of which relate output to single input (Lund
and Hill, 1979). According to Lovell (1993), the term
efficiency refers to the comparison between the real or observed values of input(s)
and output(s) with the optimal values of input(s) and output(s) used in a particular
production process. Efficiency is achieved either by minimizing the resources
required for producing a given output. Moreover, according to the optimal values,
two types of efficiency can be distinguished, that is technical efficiency and
allocative efficiency. According to Njeru (2004), the
ability of a firm to maximize output given a set resource input is known as
Technical efficiency while allocative efficiency is the ability of a firm to
use inputs optimally given their prices and production technology. On the other
hand, economic efficiency can be described as capacity of the firm to produce
a predetermined quantity of output with minimum cost at a given level of technology
(Farrell, 1957; Kopp and Diewert,
1982). This study therefore seeks to compare the economic efficiency between
tradition and improved rice varieties farmers in Oriade Local Government Area
of Osun state:
• 
Ho1: Rice farmers are economically inefficient 
• 
Ho2: Efficiency indexes of rice farmers is not affected by their socioeconomic
characteristics 
MATERIALS AND METHODS
The area of the study is Oriade local government of area of Osun state. The
headquarters of this local government is situated at ErinOke town. The local
government area has average population size of about 148,617 people (NPC,
2006). The area is located in the south western part of the country; it
is situated on latitude 7°.45E and longitude 4°.45N. Simple random sampling
technique was used to select 120 respondents from the list of registered rice
farmers in the local government area. The data obtained were analyzed using
both descriptive and inferential statistics.
Conceptual framework: Over the last decades, Farrell methodology has
been applied widely, while undergoing many refinements and improvements. The
model that will be used in this paper will be based on an extension advanced
by Kopp and Diewert (1982) and further modified by BravoUreta
and Rieger (1990). To begin with, assume that a deterministic production
frontier function is given by the equation:
where, Yj is the output of the jth farm, X_{ij} is the ith input used by farm j and B is a vector of unknown parameters. To simplify the exposition, the subscript j is dropped in what follows. From Eq. 1, it is possible to derive the technically efficient input quantities (X_{it}) for any given level of output Y, by solving simultaneously the following equations:
where, k_{i} is the ratio of the observed level of inputs X_{1} and X_{i} (i>1) at output Y.
Next, assume that the production frontier Eq. 1 is self dual (e.g. CobbDouglas) and that the corresponding cost frontier can be expressed as:
where, C is the minimum cost of producing output Y, P is a vector of input prices and is a vector of parameters. Applying Shephard’s lemma, the system of minimum cost input demand equations can be obtained by differentiating the cost frontier with respect to each input prices. This demand equation for the ith input X_{di} is equal to:
where, Φ is a vector of parameters. From the input demand equations, the economically efficient input quantities, X_{ie }can be obtained by substituting the firm’s input prices P and output Y in to Eq. 4.
Thus far, the input bundles X_{i}, X_{it} and X_{ie }have solved. It is now possible to calculate the cost of actual or observed (COB) input bundle as σx_{i}P_{i,} while the cost of the technically (CTE) and economically efficient (CEE) input combinations associated with the firm’s observed output is given by ΣX_{it} P_{i} and ΣX_{ie }P_{i}, respectively.
These cost measures are the basis for calculating TE and EE as follows:
As already mentioned in the Farrell (1957) methodology,
EE is equal to the product of TE and AE; hence Eq. 5 and 6
are used to calculate AE as:
The Kopp and Diewert (1982) approach is based on a
deterministic frontier function, which imposes a limiting assumption that the
entire deviation from the frontier is due to inefficiency. Schmidt
(1986), among others, argued that efficiency measures obtained from deterministic
models are affected by statistical noise. For this reason, BravoUreta
and Rieger (1991) used a stochastic production frontier function in order
to remove the random element from the efficiency component before deriving the
various efficiency indices.
The stochastic production frontier function can be written as:
where, Y, X_{i} and β are as defined earlier. The essential idea
behind the stochastic frontier model is that ε is a “composed”
error term (Aigner et al., 1977; Meeusen
and van den Broeck, 1977). This term can be written as:
where, V is a twosided (∞<V<∞) normally distributed random
error (V~N (0, σ^{2}_{v}) that captures the stochastic
effects outside the farmer’s control (e.g., weather, natural disaster and
luck), measurement errors and other statistical noise. The term U is a onesided
(u>O) efficiency component that captures the technical inefficiency of the
farmer. In other words, U measures the shortfall in output Y from its maximum
value given by the stochastic frontier function f (X_{i}; β)+V.
This onesided term can follow such distributions as half normal, exponential
and gamma (Aigner et al., 1977; Greene,
1980; Meeusen and van den Broeck, 1977). In this
study, it was assumed that u follows a halfnormal distribution (U~N (0, σ_{u}^{2})
as typically done in the applied stochastic frontier literature. The two components
V and U are also assumed to be independent of each other thus COV (V, U) = O.
The maximum likelihood estimation of Eq. 8 yields consistent
estimators of β, λ and σ^{2} where β is a vector
of unknown parameters, λ = σ_{u}/σ_{v} and σ^{2}
= σ_{u}^{2}+σ_{v}^{2}. Jondrow
et al. (1982) have shown that inferences about the technical inefficiency
of individual farmers can be made by considering the conditional distribution
of U given the fitted values of and the respective parameters. In other words,
given the distribution assumed for V and U and assuming that these two components
are independent of each other, the conditional mean of u given ε is defined
by:
where, σ_{*}^{2} = σ_{u}^{2}σ_{v}^{2}/σ^{2}, f* is the standard normal density function and F* is the distribution function, both functions being evaluated at ε_{j }λ/δ.
Consequently, by replacing ε, σ_{*} and λ by their estimates
in Eq. 8 and 10, we derive the estimates
of V and U. Subtracting V from both sides of Eq. 8 yields
the stochastic frontier function:
where, Y* is defined as the farm’s observed output adjusted for the statistical
noise contained in V (BravoUreta and Rieger, 1991).
Equation. 11 is used to compute X_{it} as well as to derive the cost
frontier function. The cost frontier function is then used to obtain the minimum
cost factor demand equations, which in turn, become the basis for calculating
the economically efficient input.
Production frontier function: For the purpose of this study, the specific
models estimated as adopted by Coelli (1996) are:
A CobbDouglas production frontier function:
Where:
Y 
= 
Rice output (kg) 
X_{1} 
= 
Farm size (ha) 
X_{2} 
= 
Family labour used in rice production (Man days) 
X_{3} 
= 
Hired labour used in rice production (Man days) 
X_{4} 
= 
Quantity of fertilizer used (kg) 
X_{5} 
= 
Quantity of agrochemicals used (liters) 
X_{6} 
= 
Value of seeds used (kg) 
α and β_{i} 
= 
Parameters to be estimated 
V_{i} 
= 
A two sided normally distributed random error 
U_{i} 
= 
A one sided efficiency component with a half normal distribution 
Where:
Where:
Z_{1} 
= 
Age of the rice farmers (years) 
Z_{2} 
= 
Years of education of the rice farmers 
Z_{3} 
= 
Years of farming experience in rice production 
Z_{4} 
= 
Household size of the rice farmers in an house (No. of people) 
i 
= 
1, 2, ..4 
A CobbDouglas functional form was used to specify the stochastic production
frontier, which is the basis for deriving the cost frontier and the related
efficiency measures. The use of single equation model in Eq.
12 and 14 below is justified by assuming that Nigerian
farmers maximize expected profits (BravoUreta and Rieger,
1990; Caves and Barton, 2004; Kopp
and Smith, 1980), despite its well known limitation, the CobbDouglas production
function is chosen because the methodology employed requires that the production
function be self dual. It is also worth stating that this functional form has
been widely used in farm efficiency analysis for both developing and developed
countries.
A transformed CobbDouglas cost frontier function:
Where:
C 
= 
The cost of rice production per farm (N) 
P_{ 1} 
= 
The average rent per hectare of land (N) 
P_{2} 
= 
The cost of labour used (N) 
P_{3} 
= 
The average price of fertilizer used (N) 
P_{ 4} 
= 
The average price of agrochemicals used (N) 
P_{5} 
= 
The quantity of seed used (N) 
Y 
= 
The total farm output measured in kilograms and adjusted for any statistical
noise as previously specified in Eq. 11 
Statistical analysis: Data collected were statistically analyzed using
FRONTIER 4.1 data processing package (Software) to estimate the efficiency level
of the rice farmers using 1, 5 and 10% level of significance.
RESULTS AND DISCUSSION
Estimated of the stochastic frontier production functions
Estimated production functions: The Maximum Likelihood (ML) estimates
of the production parameters for rice farmers in Oriade Traditional Government
area of Osun state is presented in Table 1. The coefficient
of farm size was found to be positive and significant at the 1% level in both
the improved and traditional rice farmers. This implies that farm size is a
significant factor that influences both rice technology output in the study
area. This finding agrees with the study of Ogundele and
Okoruwa (2006), Shehu and Mshelia (2007) and Idiong
(2007). Family labor has a significant but negative relationship with rice
output in both improved and traditional rice farmers. The coefficient of fertilizer
has a positive and significant relationship (at 10% level of significance) with
rice output in Traditional rice farmers while it has a negative and insignificant
relationship with improved rice farmers. This underscores the low use of fertilizers
by the improved rice farmers. The coefficient of agrochemical was found to be
significant at 10 and 5% significant level in both the improved and traditional
rice farmers, respectively. This implies that agrochemical is a positive factor
that influences improved rice output while it is a negative factor in Traditional
rice output. The coefficient of seed has a significant and positive influence
with only improved rice output in the study area.
Table 1: 
Maximum likelihood estimates of the stochastic frontier production
function 

*,**, ***Estimates significant at 10, 5 and 1% level of significance,
RTS: Return to scale 
This finding is not in consonant with the earlier findings by Shehu
and Mshelia (2007) who reported a negative and significant relationship
between output and seed. However, it is in line with the findings of Idiong
(2007) and Piya et al. (2012).
The estimate of sigma squares (0.356 in improved and 0.247 in Traditional rice
farmers are significantly different from zero at different levels. This indicates
a good fit and the correctness of the specified distributional assumption of
the composite error term. This suggests the conventional production function
is not an adequate representation of the data. Moreover, the estimate of gamma,
which is the ratio of the variance of farmspecific technical efficiency to
the total variance of output, was 0.843 in improved rice farmers and 0.724 in
Traditional rice farmers. This indicates that about 84.3 and 72.4% of the variation
in output among farms is due to the differences in their technical efficiencies
among improved and traditional rice farmers, respectively. This result is consistent
with the findings of Shehu and Mshelia (2007).
The return to scale (RTS) analysis which serves as a measure of total resource
productivity is also given in Table 1. The RTS parameter (0.4999
in improved and 0.267 in Traditional rice farmers) is obtained from the summation
of the coefficients of the estimated inputs elasticities which indicates that
both the improved and Traditional rice production in the study area was in stage
II of the production surface. Stage II is the stage of decreasing positive return
to scale where resources and production was believes to be efficient. Hence,
it is advisable that the production units should maintain the level of input
utilization at this stage as this will ensure maximum output from a given level
of input Ceteris paribus. This result is not consistent with the findings
of Shehu and Mshelia (2007) and Idiong
(2007) who reported more than one RTS.
Estimates of the stochastic cost frontier: The estimates of the stochastic frontier cost function are presented in Table 2. The result revealed that all the independent variables conform to a priori expectation as all the estimated coefficients gave positive coefficients except rent in improved rice variety, meaning as these factors increased, total production cost increased Ceteris paribus. The result of tratio test shows that in improved rice variety, the significant variables are labour, fertilizer, agrochemical and output while the significant variables in the Traditional rice variables are labour, agrochemical, seed and output.
The economic efficiency analysis of both rice farmers revealed that there was
presence of cost inefficiency effects in rice production as confirmed by the
significance gamma value of 0.916 and 0.967 in improved and traditional rice
farmers, respectively.
Table 2: 
Maximum likelihood estimates of stochastic frontier cost
function 

*,**, ***Estimates are significant at 10, 5 and 1% level of
significance 
This implies that about 92 and 97% variation in the total production cost is
due to differences in their cost efficiencies among improved and Traditional
rice farmers, respectively.
Efficiency indexes for rice farmers in the study area
Technical efficiencies (TE) indexes: The result derived from ML estimates
indicate technical efficiency (TE) indices range from 0.0279 to 1 with a mean
value of 0.842 for farmers planting improved variety (Table 3).
This means that for an average efficient farmer to achieve the technical efficiency
level of its most efficient counterpart he could realize about (10.842/1) savings
in cost or increase in production. This gives about 15.8% increase in production
or cost saving. The least efficient farmers can now save a cost or increase
in production of 97.9%. (10.279/1) to achieve the required technical efficiency
of the most efficient farmers in the study area. Also, the technical efficiency
indices range from 0.0237 to 1 with a mean of 0.329 for farmers planting Traditional
varieties. This means that for an average efficient farmers to achieve the technical
efficiency level of its most efficient counterpart, he could realize about 67.1%
increase in production or cost saving. Also, the least efficient farmers can
now save a cost or increase in production of 99.8 % to achieve the required
technical efficiency of the most efficient farmers.
To give a better indication of the distribution of TE, a frequency distribution of the predicted TE is presented in Table 3. The frequencies of occurrence of the predicted TE in decile range indicate that the highest number of farmers have TE between 0.91 to 1.00 in improved rice farmers, representing about 30% of the respondents. While the highest numbers of farmers have TE between 0.11 and 0.20 in Traditional rice farmers representing about 22% of the respondents. Also, 38.3 and 8.4% of the improved and traditional rice farmers, respectively have TE of above 0.70 which is an indication that both improved and traditional rice farmers are inefficient.
Allocative efficiency (AE) indices: The result derived from ML estimates
indicates that allocative efficiency (AL) indices ranged from 0.0622 to 1 with
a mean of 0.931 for farmers planting improved variety (Table 4).
This implies that for an average efficient farmer to achieve allocative efficiency
level its most efficient counterpart, he could realize about (10.931/1) saving
in cost or increase in production. This gives about 6.9% increase in production
or cost saving.
Table 4: 
Decile range of frequency distribution of allocative efficiency
of the farmers 

The least efficient farmer can now save a cost or increase in production of
37.8% (10.622/1) to achieve the required allocative efficiencies of the most
efficient farmers in the study area. Also, the allocative indices range from
0.445 to 1, with a mean of 0.861 for farmers planting Traditional varieties.
This means that for an average efficient farmer to achieve allocative efficiency
level of its most efficient counterpart, he could realize about (10.861/1)
percent increase in production or cost savings. This gives about 13.9% increase
in production or cost savings. Also, the least efficient farmer can now save
a cost or increase in production of 55.5% to achieve the required allocative
efficiency of the most efficient farmers.
To give a better indication of the distribution of the AE, a frequency distribution of the predicted AE is presented in Table 4. The frequency of the occurrence of the predicted AE in decile range indicates that the highest numbers of farmers have AE between 0.931.00 in Traditional rice farmers representing about 42% of the respondents while the highest numbers of farmers in improved rice variety have AE of 0.91 to 1.00, representing about 80% of the respondents. Also, 98.3 and 88.4%s of improved and traditional rice farmers, respectively have AE of above 0.70 which is an indication that both improved and traditional farmers are inefficient.
Economic efficiency (EE) indices: The result derived from ML estimate indicates that economic efficiency (EE) indices range from 0.0283 to 1, with a mean of 0.773 for farmers planting improved varieties (Table 5). This means that for an average efficient farmer to achieve economic efficiency level of its most efficient counterparts, he could realize about (10.773/1) saving in cost or increase in production. This gives about 22.7% increase in production or cost savings. The least efficient farmers can now save a cost or increase in production of 97.1%. (10.0283/1) to achieve economic efficiency of the most efficient farmer in the study area. The EE indices range from 0.0231 to 0.834 with a mean of 0.278 for farmer planting Traditional varieties. This means that for an average efficient farmer to achieve the EE level of its most efficient counterpart, he could realise about (72.2)% increase in production or cost saving. Also the least efficient farmer can now save a cost or increase in production of 16.5% to achieve the required economic efficiency of the most efficient farmers.
Table 5: 
Decile range of frequency distribution of economic efficiency
of the farmers 

Table 6: 
Regression result of relationship between efficiency indices
and some socioeconomic variables 

*^{,}**^{,}***Estimates are significant at
10 and 5% level of significance 
To give a better indication of distribution of the EE, a frequency distribution of the predicted EE is presented in Table 5. The frequencies of occurrence of the predicted EE in deciles range indicate that the highest number of farmers have EE between 0.911.00 in improved rice farmers, representing about 30% of the respondents while the highest number of farmers have EE between 0.110.20 in Traditional rice farmers representing about 32% of the respondents. Also, 36.7 and 6.7% of improved and traditional rice farmers, respectively have EE of above 0.70 which is an indication that both improved and traditional rice farmers are inefficient.
Relationship between efficiency indexes and socio economic variables under improved rice variety: To investigate the relationship between efficiency indexes and socioeconomic variables, regression analysis was carried out.
The results presented in Table 6 revealed a non significant
relationship between age and all efficiency indexes among the improved rice
farmers. Education was found to have a positive relationship with all the efficiency
indexes (TE, AE and EE) but insignificant with AE and EE in improved rice farmers.
This implies that improved rice farmers with greater years of formal education
tend to be more technically efficient. This agrees with the findings of Amaza
and Tashikalma (2003); Amos et al. (2004)
and Shehu and Mshelia (2007).
Table 7: 
Regression result of relationship between efficiency indexes
and some socioeconomic variables 

*^{,}**^{,}***Estimates are significant at
10 and 5% level of significance 
The positive coefficient for experience and efficiency in all the efficiency indexes in improved rice farmers implies that improved rice farmers with more years of experience tend to be more economically, technically and allocatively efficient than farmers with less years of experience. However, a negative and insignificant relationship exists between household size and all the efficiency indexes.
The Fstatistics in improved rice farmers is not statistically significant with TE, hence the second hypothesis which stated that the efficiency indexes of rice farmers is not affected by their socioeconomic characteristics is hereby accepted . However, improved rice farmers are statistically significant with AE and EE hence the stated hypothesis is therefore rejected.
Relationship between efficiency indexes and socio economic variables under traditional rice variety: As revealed in Table 7, a significant and positive relationship exists between age and allocative and economic efficiency in the traditional rice farmers. Education has no significant relationship with all the efficiency indexes. Also, the negative coefficient for experience and efficiency indexes in Traditional rice farmers implies that farmers with more years of experience tends to be less economically, technically and allocatively efficient than farmers with less years of experience. However, experience was found to be insignificant with efficiency in traditional rice farmers. Household size was negative and has insignificant relationship with all the efficiency indexes.
In Traditional rice farmers, the Fstatistics is not statistically significant with all the three efficiencies indexes (TE, AE and EE). Hence, the second hypothesis that efficiency indexes of rice farmers is not affected by their socioeconomic characteristics is hereby accepted and the alternative rejected.
CONCLUSION
Findings from the study reveals that rice farmers for both technology produce at optimum level, however, there is existence of cost inefficiency effect in both improved and traditional rice farms. Also, the technical, allocative and economic efficiency effect reveals that rice produced under both technologies were inefficient. On the other hand, improved rice farmers with more years of formal school tend to be technically efficient, hence, it is recommended that traditional rice farmers should be enlightened more to enhance their production capacity.