S. A. A. Naqvi, M. Ashfaq / Agricultural Sciences 4 (2013) 536-540

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Tabl e 1 . Summary statistics for variables in the stochastic fron-

tier production functions.

Variables Mean Std. Deviation MinimumMaximum

Yield (Kg) 3570 12.79 2600 4800

Farming Experience

(Year) 22.47 14.65 2 50

Irrigation No 14.78 3.72 10 23

Maize Area (Acre) 7.07 6.17 1 30

Chemical Cost (Rs.) 1733.58 235.02 1200 2550

Threshing Cost (Rs.) 5368.26 29282.65 1850 324,780

Land Preparation

Cost (LPC) (Rs.) 10005.42 1285.73 5250 13,550

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.

3.1. Results of Cobb-Douglas Function

The OLS as well as ML estimates of the estimated

Cobb Douglas model are given in Ta bl e 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 vi. This explores that the random com-

ponent 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 fron-

tier model has significant progress over an average (OLS)

production function. Maximum likelihood coefficient of

fertilizer showed a positive value of 0.31, which was sig-

nificant, 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 in-

puts 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 edu-

cation, extension services, maize cropped area, and sow-

ing 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.

3.2. Results of Translog Production

Function

A stochastic translog production frontier is employed

in order to select best functional form. The model encom-

passes the Cobb-Douglas form, so test of first choice for

one form over the other can bed one by analyzing signi-

ficance 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

Table 2. OLS and Maximum likelihood estimates for parame-

ters of the stochastic frontier (Cobb-Douglas) for Hybrid Maize

Producers.

Coefficients t-Ratio

Variables Parameters

OLS MLE OLSMLE

Intercept β0 1.24 0.54 1.68*** 0.68ns

Land Preparation

Cost (LPC) β1 −1.11 −0.09 −2.15** −1.84*

NPK (Kg) β2 0.35 0.31 4.31*3.48*

Total Irrigation Numberβ3 0.23 0.19 4.97*4.14*

Total Chemical Cost β4 0.16 0.19 2.24** 2.87*

Total Threshing Cost β5 0.78 0.71 10.75*10.03*

Inefficiency ParametersParameters Coefficients t-Ratio

Intercept δ0 0.11 1.49ns

Farming Experience (Year)δ1 0.0004 0.44ns

Education (Year) δ2 −0.001 −0.32ns

Credit δ3 0.04 1.07ns

Extension Services δ4 −0.03 −0.82ns

Maize Cropped Area (Acre)δ5 −0.01 −2.68*

Sowing Time δ6 −0.01 −0.32ns

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 Ta b l e 3 , where coeffi-

cient 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 trans-

log 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.

Tab le 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.

4. CONCLUSION

The primary objective of this study was to evaluate te-

chnical efficiency of hybrid maize farmers of District Chi-

niot and to discover their inefficiency factors. Results ob-

tained showed that from the stochastic frontier estimation,

the average technical efficiency given by the Cobb-Douglas

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