Technical efficiency analysis of hybrid maize production using translog model case study in District Chiniot , Punjab ( Pakistan )

In Pakistan, maize accounts for 5.93 percent of the total cropped area and 4.82 percent of the value of agricultural production. Given high cost of the production, there is a belief that it is difficult to boost profitability without enhancing use of pricey inputs. Maximum likelihood estimates of stochastic frontier model were estimated and determinants of technical efficiency were calculated. Using Cobb Douglas model estimated maximum likelihood coefficients for all inputs were significant and showed signs according to expectations. The evaluation with the different models gives different technical efficiencies, which shows that technical efficiency estimations are extremely sensitive to the functional form specified.


INTRODUCTION
Maize (Zea mays L.) is the third cereal for Pakistan after wheat and rice and it accounts for 5.93 percent of the total cropped area and 4.82 percent of the value of agricultural production.Maize being the highest yielding cereal crop in the world is of significant importance for countries like Pakistan, where rapidly increasing population has already out stripped the available food supplies output.Area under maize occupies the third position after wheat and rice, 98% of which is grown in Punjab and N.W.F.P.It is intensely grown on worldwide bases and often referred as "king of grain crops" [1].It is grown on an area of 1083 thousand hectares with a yearly pro-duction of 4271 thousand tones and it has 3944 kg/hectare yield per hectare [2].
Mostly the farms with the same resources are producing different per acre output, because of management inefficiency.The scanty or no role of extension services, poor right of entry to credit, tenant cultivation, low literacy rate, poor communications facilities, and long distance from markets [3] characterize inefficient farms.At present yield level is still up to some extent lower than the potential of our existing varieties.Main constraints to enhance maize productivity are unfavorable weather conditions, unavailability of input at proper time, suboptimal plant density, late sowing, inadequate fertilizer use, inadequate water supply, weed infestation, insect pest attack and the selection of unsuitable cultivars under a given set of environments.Consequently, a farmer's ability to increase his income and productivity level is constrained by a number of factors of which many fall out of his control.Pakistani maize farmers are constrained with many such factors as acquisition of inputs with limited resources.
Normally, the efficiency levels are low when compared to the international per acre productivity: no doubt, some of the factors contributing towards the low productivity are out of control.This inefficiency is also termed as technical inefficiency and Farrel [4] developed its concept.Broadly speaking, technical inefficiency is the failure to produce maximum output from a given level of inputs.
This efficiency has two components: technical and allocative.Technical efficiency is the ability of a firm to produce a maximal output from a given set of inputs or it is the ability of a firm to use as modest inputs as possible for a given level of output.The former is called input oriented measures and the latter is known as output-oriented measures of technical efficiency.Productivity can be in-creased through more efficient utilization of resources of farmers and inputs with current technology.In this study, efficiency of maize producers of District Chiniot is evaluated.Interrelationship between efficiency level and various firm specific factors provides useful policy related information.Main objective of the study is to calculate the technical efficiency and determinants of inefficiency of maize growers.A particular objective of the study is to identify the factors causing technical inefficiency by examining the relationship between efficiency level and various firm specific factors.

MATERIALS AND METHODS
The primary data was used in this study, which was collected from District Chiniot during the year 2010-11.In order to collect data, random sampling technique was used.The sampling procedure involved the three stages: selection of tehsils, selection of villages, and selection of farmers (respondents).Three tehsils were selected for collecting data and three villages were selected from each selected Tehsil.A sample of 120 farmers was taken as total by dividing equally into three groups (large, medium and small) by farm size.A farm was considered small if farm size is less than or equal to 12.5 acres, medium if farm size was more than 12.5 acres and less than 25 acres, and large if farm size is equal to or greater than 25 acres.Three sampling frames were designed at village level by making strata of small, medium and large farmers.Five farmers were selected from each stratum randomly.

Statistical Analyses
The Cobb-Douglas and Translog production frontier functions defined and the inefficiency model were jointly projected by the maximum-likelihood (ML) method using FRONTIER 4.1 [5].By taking the same indicators for the both models, it is clear from the results that Translogrithmic function has a more robustness over the Cobb-Douglas because the mean technical efficiency from the of prior was up to 94% while for subsequent model it was 81.06%.
At this juncturevariant of the stochastic function approach proposed by Battese and Coelli [6] and continued by Greene [7], Hassan [8] and Dey et al. [9] in which technical inefficiency effects in a stochastic frontier are an explicit function of other farm specific explanatory variables, and all parameters are estimated in a singlestage maximum likelihood (ML) procedure.The stochastic production frontieris, Here, Y i is the yield of maize for the i-th farm, x i is a vector of inputs (or cost of inputs),  is a vector of i-th ; and 0 1 where, Y i is the quantity of output (Kg): X 1 is the land preparation cost (Rs); X 2 is N, P, and K nutrients applied (Kg); X 3 is the total irrigation (number); X 4 is the total chemical cost counting both weeding and insecticide cost (Rs) and X 5 is thetotal threshing cost (Rs).Inefficiency regression equation can be written as, where, Z i are farm-specific variables that may cause inefficiency and δ ο and all δ i are coefficients to be estimated.Z 1 is farming experience (year); Z 2 is the education (year); Z 3 is the credit it is in the form of dummy variable it has value 1 if farmer avails credit otherwise it would be equal to 0; Z 4 is the extension facilities, dummy variable assuming value 1 if farmer avails extension facilities, otherwise 0; Z 5 is the maize cropped area (acre); Z 6 is the dummy variable for sowing time assuming value 1 if farmer sow timely, otherwise 0.

Translogrithmic Model
Inefficiency model and variables were same as the Cobb-Douglasmodel.

RESULTS AND DISCUSSION
The summary statistics related tothe variables used in analysis is given in Table 1.
It is clear from the table the mean yield was 3570 kg, farming experience was 22.7 year, up to 15 irrigations were applied on average, and farm area was 7 acre.While for the case of costs, the average chemical, threshing and LPC were 1734, 5368 and 10,005 rupees respectively.

Results of Cobb-Douglas Function
The OLS as well as ML estimates of the estimated Cobb Douglas model are given in Table 2.The estimate of γ is 0.71, which indicates that the vast mass of error variation is due to the inefficiency error u and not due to the random error v i .This explores that the random component of the inefficiency effects does make a significant contribution in the analysis.The one sided LR test of γ = 0 provides a statistic of 26.26 which exceeds the chi-square five percent critical value.It indicates that stochastic frontier model has significant progress over an average (OLS) production function.Maximum likelihood coefficient of fertilizer showed a positive value of 0.31, which was significant, it means by escalating use of all fertilizers by 1% would increase maize yield by 0.31 percent, decreasing return to scale.The estimated ML coefficients for all inputs were significant at 1 percent and positive except land preparation cost (LPC) which was negative, means it has inverse relation with output.
In case of inefficiency variables coefficients of education, extension services, maize cropped area, and sowing time showed negative values.The negative coefficient for education suggests that the educated farmers are more efficient than others are.Those farmers were found to be more efficient than others who have enjoyed extension services and completed in time sowing of maize.

Results of Translog Production Function
A stochastic translog production frontier is employed in order to select best functional form.The model encompasses the Cobb-Douglas form, so test of first choice for one form over the other can bed one by analyzing significance of cross terms in the translog form [10].To review the economic plausibility of the calculated coefficients of translog form is very difficult job and cumber some due to its multifaceted nature.It is, therefore, more suitable to estimate some more easily interpreted estimates [11], oftenly production elasticities of inputs are used also, but here estimated coefficients of translog form are used for coefficients interpretation as Basnayake and Gunaratne [10].
The ML estimates are given in Table 3, where coefficient of land preparation cost (LPC), NPK, and total threshing showed significant effect on output.However, the coefficient of NPK Sqr and total threshing cost Sqr were negative.
The mean technical efficiency obtained from the translog function was 94.10 percent.No one of the parameters in the inefficiency model showed significant effect on inefficiency.Outcome for inefficiency parameters are also given in Table 3. Technical efficiency estimates by Cobb-Douglas and translog models are at variance immensely.The Translogrithmic function shows more robustness over the Cobb-Douglas because the mean technical efficiency from the Cobb-Douglas model was 81.06 percent while the translog model showed a mean technical efficiency of 94.10 percent.
Table 4 shows distribution of technical efficiencies for various farm groups.Technical efficiency ranges from as low as 0.75 percent to as high as 0.96 percent.

CONCLUSION
The primary objective of this study was to evaluate technical efficiency of hybrid maize farmers of District Chiniot and to discover their inefficiency factors.Results obtained showed that from the stochastic frontier estimation, the average technical efficiency given by the Cobb-Douglas  model is 81.06 percent which shows that 18.94 percent output can be increased without increasing the levels of inputs, and this is due to input oriented technical inefficiency.According to the results, older farmers appeared to be more efficient than younger farmers.This is perhaps due to their good managerial skills, which they have learnt over time.Hence, it is necessary to increase educational facilities in the area.It was also discovered that the te-chnical efficiency estimates are highly responsive to the functional form specified because the Cobb-Douglas and translog models resulted in dissimilar technical efficiencies.Although Cobb-Douglas specification gives constant returns to scale, it is widely accepted in the literature.
an error term.The stochastic frontier is also called composed error model, because it shows that the error term (v i − u i ) is decom-

Table 1 .
Summary statistics for variables in the stochastic frontier production functions.

Table 2 .
OLS and Maximum likelihood estimates for parameters of the stochastic frontier (Cobb-Douglas) for Hybrid Maize Producers.

Table 3 .
Maximum likelihood estimates for parameters of the stochastic frontier (translog) for hybrid maize producers.and ** show significance at 1 and 5 percent. *

Table 4 .
Frequency distribution of technical efficiency range according to small, medium and large farmers.