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

doi:10.4236/as.2013.410072

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Vol.4, No.10, 536-540 (2013) Agricultural Sciences

http://dx.doi.org/10.4236/as.2013.410072

Technical efficiency analysis of hybrid maize

production using translog model case study in

District Chiniot, Punjab (Pakistan)

Syed Asif Ali Naqvi*, Muhammad Ashfaq

Institute of Agricultural and Resource Economics, University of Agriculture, Faisalabad, Pakistan;

*Corresponding Author: [email protected]

Received 9 January 2013; revised 10 February 2013; accepted 15 March 2013

Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is

properly cited.

ABSTRACT

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 dif-

ficult to boost profitability without enhancing use

of pricey inputs. Maximum likelihood estimates

of stochastic frontier model were estimated and

determinants of technical efficiency were calcu-

lated. Using Cobb Douglas model estimated ma-

ximum likelihood coefficients for all inputs were

significant and showed signs according to ex-

pectations. The evaluation with the different mo-

dels gives different technical efficiencies, which

shows that technical efficiency estimations are

extremely sensitive to the functional form speci-

fied.

Keywords: Maize; Tran slog Model; Maximum

Likelihood Co ef ficie nts

1. 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 agri-

cultural production. Maize being the highest yielding ce-

real crop in the world is of significant importance for

countries like Pakistan, where rapidly increasing popu-

lation 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/hec-

tare yield per hectare [2].

Mostly the farms with the same resources are produc-

ing different per acre output, because of management in-

efficiency. The scanty or no role of extension services,

poor right of entry to credit, tenant cultivation, low lite-

racy rate, poor communications facilities, and long dis-

tance 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 con-

ditions, unavailability of input at proper time, suboptimal

plant density, late sowing, inadequate fertilizer use, ina-

dequate 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 in-

crease his income and productivity level is constrained

by a number of factors of which many fall out of his con-

trol. Pakistani maize farmers are constrained with many

such factors as acquisition of inputs with limited re-

sources.

Normally, the efficiency levels are low when compar-

ed to the international per acre productivity: no doubt,

some of the factors contributing towards the low produc-

tivity are out of control. This inefficiency is also termed

as technical inefficiency and Farrel [4] developed its con-

cept. Broadly speaking, technical inefficiency is the fail-

ure to produce maximum output from a given level of in-

puts.

This efficiency has two components: technical and al-

locative. 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 ori-

ented measures and the latter is known as output-oriented

measures of technical efficiency. Productivity can be in-

S. A. A. Naqvi, M. Ashfaq / Agricultural Sciences 4 (2013) 536-540 537

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 eva-

luated. Interrelationship between efficiency level and va-

rious 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 exa-

mining the relationship between efficiency level and va-

rious firm specific factors.

2. 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, me-

dium and small) by farm size. A farm was considered

small if farm size is less than or equal to 12.5 acres, me-

dium 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 far-

mers. Five farmers were selected from each stratum ran-

domly.

2.1. Statistical Analyses

The Cobb-Douglas and Translog production frontier

functions defined and the inefficiency model were jointly

projected by the maximum-likelihood (ML) method us-

ing FRONTIER 4.1 [5]. By taking the same indicators

for the both models, it is clear from the results that Trans-

logrithmic 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 ap-

proach proposed by Battese and Coelli [6] and continu-

ed 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 single-

stage maximum likelihood (ML) procedure. The stocha-

stic production frontieris,







ln ln,

ijiji



 

i



Here, Yi is the yield of maize for the i-th farm, xi is a

vector of inputs (or cost of inputs),



is a vector of i-th

unknown parameters, (vi − ui) is an error term. The

stochastic frontier is also called composed error model,

because it shows that the error term (vi − ui) is decom-

posed into two components: a stochastic random error

component (random shocks) vi and a technical ineffici-

ency component ui. Where Vi is a symmetrical two sided

normally distributed random error that contains stocha-

stic effects which are uncontrolled. It is assumed to be

independently and identically distributed



0, v



. The

term



i, is one side (



I > 0) efficiency component. The

two error component (v and



) are also assumed to be in-

dependent of each other. The variance parameters of the

model are parameterized as:

222

; and 01

svu



 





 

2.2. Cobb-Douglas Function











011 2233

4455

lnln lnln

ln ln

YXX

XXVU

 



 



where, Yi is the quantity of output (Kg): X1 is the land

preparation cost (Rs); X2 is N, P, and K nutrients applied

(Kg); X3 is the total irrigation (number); X4 is the total

chemical cost counting both weeding and insecticide cost

(Rs) and X5 is thetotal threshing cost (Rs).

Inefficiency regression equation can be written as,

iii











where, Zi are farm-speciﬁc variables that may cause in-

efficiency and δο and all δi are coefficients to be estimated.

Z1 is farming experience (year); Z2 is the education (year);

Z3 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; Z4 is the extension facilities, dummy variable as-

suming value 1 if farmer avails extension facilities, other-

wise 0; Z5 is the maize cropped area (acre); Z6 is the dum-

my variable for sowing time assuming value 1 if farmer

sow timely, otherwise 0.

2.3. Translogrithmic Model



ln lnln

1, 2, 3,1, 2, 3

itititjtit it

YXXXV

intn



 



 









Inefficiency model and variables were same as the

Cobb-Douglasmodel.

3. 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

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

538

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

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

539

Table 3. Maximum likelihood estimates for parameters of the stochastic frontier (translog) for hybrid maize producers.

Variables Parameters Coefficients t-Ratio

Stochastic Production Function

Intercept β0 13.03 12.67*

Land Preparation Cost (LPC) β1 7.03 2.78*

NPK (Kg) β2 3.76 3.90*

Total Irrigation Number β3 −1.42 −0.88ns

Total Chemical Cost β4 3.31 1.32ns

Total Threshing Cost β5 5.36 4.53*

LPC Sqr. β6 0.14 1.36ns

NPK Sqr. β7 −1.38 −3.21*

Total Irrigation Number Sqr. β8 0.11 0.11ns

Total Chemical Cost Sqr. β9 0.31 0.94ns

Total Threshing Cost Sqr. β10 −0.32 −0.82ns

LPC * NPK β11 1.71 4.06*

LPC * Total Irrigation Number β12 −0.68 −3.21*

LPC * Total Chemical Cost β13 −0.34 −1.06ns

LPC * Total Threshing Cost β14 −0.02 −0.05ns

NPK * Total Irrigation Number β15 1.23 2.85*

NPK * Total Chemical Cost β16 −1.13 −2.10**

NPK * Total Threshing Cost β17 1.09 1.34ns

Total Irrigation Number * Total Chemical Cost β18 1.28 3.87*

Total Irrigation Number * Total Threshing Cost β19 −1.11 −3.87*

Total Chemical Cost * Total Threshing Cost β20 −0.28 −3.28*

Technical Inefficiency Function

Intercept δ0 0.069 1.28ns

Farming Experience (Year) δ1 0.001 4.93*

Education (Year) δ2 0.006 2.31**

Credit δ3 0.008 0.24ns

Extension Services δ4 0.038 1.11ns

Maize Cropped Area (Acre) δ5 −0.012 −4.68*

Sowing Time δ6 0.030 0.84ns

Variance Parameters

σ2 0.05 7.89

Γ 0.72 2.88

Note: * and ** show significance at 1 and 5 percent.

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

Efficiency Range Small Farmers % age of Farmers Medium Farmers% age of FarmersLarge Farmers % age of Farmers

0.75 - 0.85 5 4.16 2 1.67 1 0.83

0.86 - 0.95 15 12.5 5 4.16 1 0.83

0.96 - 100 20 16.67 33 27.5 38 31.66

Total 40 33.33 40 33.33 40 33.33

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 ineffi-

ciency. 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-

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

540

chnical efficiency estimates are highly responsive to the

functional form specified because the Cobb-Douglas and

translog models resulted in dissimilar technical efficien-

cies. Although Cobb-Douglas specification gives constant

returns to scale, it is widely accepted in the literature.

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