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NAF

International Working Paper Series Year 2015 paper n. 15/02

Technical Efficiency of Wheat Farms in River Nile State, Sudan

Dr. Adil Ahmed Ali Ibrah

Agricultural Research Corporation (ARC), Sudan adilarc2@yahoo.com

Hanan Suliman Mohamed

Agricultural Economics and Policy Research Centre (AEPRC), Shambat, Sudan

The online version of this article can be found at: http://economia.unipv.it/naf/

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Scientific Board

Maria Sassi (Editor) - University of Pavia

Johann Kirsten (Co-editor)- University of Pretoria

Gero Carletto - The World Bank

Piero Conforti - Food and Agriculture Organization of the United Nations

Marco Cavalcante - United Nations World Food Programme

Luc de Haese - Gent University

Stefano Farolfi - Cirad - Joint Research Unit G-Eau University of Pretoria

Ilaria Firmian -IFAD

Mohamed Babekir Elgali – University of Gezira

Luca Mantovan – Dire Dawa University

Firmino G. Mucavele - Universidade Eduardo Mondlane

Michele Nardella - International Cocoa Organization

Nick Vink - University of Stellenbosch

Alessandro Zanotta - Delegation of the European Commission to Zambia

Copyright @ Sassi Maria ed. Pavia -IT naf@eco.unipv.it ISBN 978-88-96189-28-3

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Technical Efficiency of Wheat Farms in River Nile State, Sudan

Dr.Adil Ahmed Ali Ibrahim Agricultural Research Corporation (ARC) Sudan

Hanan Suliman Mohamed

Agricultural Economics and Policy Research Centre (AEPRC), Shambat, Sudan

Abstract

The main objective of this paper was to empirically estimate the technical

efficiency of wheat farms in River Nile State (R.N.S), Sudan, in view to the

government strategy to revitalize this crop in the state. Within the study 120 farmers

in two state localities were interviewed, using multi-stage stratified sampling

technique. A total of 60 respondents were chosen randomly from each of Abu-

Hammed and El-matamma localities in the northern and southern parts of the state,

respectively during the 2004/05 season. Stochastic frontier production function was

used to estimate the technical efficiency of the farms. The results showed that the

socioeconomic and production factors of farmers' age, credit, timely sowing, use of

improved varieties, tractor plowing and chemical application were found to

significantly increase the level of technical efficiency and show positive marginal

effects, while manual weeding and off-farm activities were found to reduce the level

of efficiency. However, the mean technical efficiencies of wheat farms were 0.67 and

0.64 in Abu-Hammed and El-matamma localities, respectively.

Key words: Wheat, Technical Efficiency, River Nile State, Sudan

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INTRODUCTION

In Sudan, wheat is one of the main food security crops since it is the main food for the

majority of population. It is grown in Gezira, New Halfa, White Nile state, River Nile

and Northern states. The government had adopted the policy of rehabilitation of wheat

production through increasing of planted areas and transfer of modern agricultural

technologies particularly in the River Nile, Northern, West and South Darfur states.

During the period 1970-2000, self-sufficiency in wheat has been a target in most

government economic plans. The latest was the crash programme of 1989, which

emphasized area expansion and particularly yield improvements; arriving at self-

sufficiency in 1992 (Elamin, 2002). Yet, such self-sufficiency has not been

sustainable. The central government subsequently embarked on a new strategy,

namely the Second Agriculture Development Strategy (SADS) to be implemented

over a 25-year period, 2003 - 2027 (Osman, 2004). SADS specified sub-objectives for

specific sectors. For instance in the cereal production sector, ambitious objectives

were set for the irrigated sector for expansion of the cereal areas to reach 3.9 million

hectares up from 1.7 million hectares. This, in addition to, increasing and maximizing

productivity of crops in order to increase the efficiency and competitiveness of the

domestic agricultural products in foreign markets (SADS, 2003). In congruence with

government policies to raise farmers’ productivity and efficiency, this study acquires

importance in analyzing the present level of efficiency among wheat farms in R.N.S.

This is because the aforementioned agricultural strategy is expected to lead to increase

in the technical capability of the farmers in producing farm output from a given set of

inputs. The measurement of efficiency becomes more crucial, given the fact that it is

directly related to the overall productivity of the agricultural sector. The main

objective of this study is therefore to quantitatively determine the level of technical

efficiency of wheat farms and the associated influencing factors using stochastic

frontier production functions.

METHODS

The study depended mainly on primary data collected using structured questionnaire

to interview farmers in R.N.S who grew wheat during 2004/05. A multi-stage,

stratified random sample of 120 respondents was selected with two strata identified by

geographical difference and comprising Abu-Hammad in the north and El-matamma

in the south. A sample of 60 farmers was taken from each locality following random

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selection of villages and eventually farmers from each. Data on physical quantities of

wheat inputs and output were collected. Inputs were collected on land area allotted to

wheat in feddans (one feddan=0.24 hectare), labour (family and hired) in man-days,

number of irrigations applied per season and quantities of seed and fertilizer in kg/

feddan. Data were also collected on relevant socio-economic variables of the farmers.

Such variables included dummies for off-farm activities, credit, timely sowing, use of

improved varieties, tractor plowing, chemical application for pests and weeds, manual

weeding and the active age of farmer as (1=x≤50, 0=x>50).

The stochastic frontier production function, which was proposed by Aigner, et al.,

(1977), Battese and Corra (1977) and Meeusen and Van den Broeck (1977); has been

given serious consideration in an effort to bridge the gap between theory and

empirical work. The translog Cobb-Douglas production function was chosen due to a

number of advantages such as its flexibility and its non-restrictiveness in the

returns-to-scale parameters. The model is specified as follows:

Ln yi=α0+∑=

5

1kακ ln Xki +

½∑=

5

1k

∑=

5

1k

ακj ln Xki

X ji + ει

(1)

Where;

Ln= Natural logarithm

y1= Output of wheat in Kg/ feddan.

X1= Land in feddans.

X2= Quantity of fertilizer in Kg/ feddan.

X3 = Quantity of wheat seed planted in Kg/ feddan.

days of labor used.-verage number of manA =4X

X5 = Average number of irrigations applied per feddan per season.

ει = V i-ui = Composite error term

Where;

V i =Random variable assumed to be independently and identically

distributed N (0; _ σ²v) and independent of ui.

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ui =Random variable that accounts for technical inefficiency and assumed to be

independently distributed as truncation of the normal distribution with mean µ and

variance σ² =σ u2 (|N (µ, σ²u)|) 2.

The inefficiency model is estimated from the equation given below;

ui= δ0+∑=

n

im δm Zi (2)

Where:

Ui = the second part in composite error as defined in equation (1).

Z1 = farmers' active age (1=Farmer age≤50, 0= Farmer age >50).

Z2=Off-farm activity (1= had off-farm activity, 0=had not).

Z3 = Credit access (1= Accessed, 0=Not Accessed).

Z4 = Use of improved varieties (1= Used, 0 = Not used).

Z5 = Timely sowing (1=early sowing, 0=late).

Z6 = Use of tractor in land preparation (1= Used, 0 = Not used).

Z7 = Applying chemicals for pests and weeds control (1= Applied, 0 = Not Applied).

Z8 = Application of manual weeding (1= Applied, 0 = Not Applied).

The first section is the stochastic frontier production function while the second

part captures the inefficiency variables. The models generate variance parameters, i.e.

Lambda, λ = (συ² / σ²v); variance of the models (Sigma σ), variance of the stochastic

models (σ²v) and variance of the inefficiency models (συ²). The model was analyzed

by frontier 4.1 programme - model 2 under the Battese and Coelli (1995)

specifications. The following hypotheses requires testing with the generalized

likelihood ratio test, λ λ λ λLR = 2[L (H1)-L(H0)], where L(H1) and L(H0) are the

maximum values of the log likelihood functions under the alternative and null

hypothesis, respectively. The null hypothesis is rejected when λλλλLR >XXXXC2. The

following hypotheses will be tested:

1. H0=ßik=0, the null hypothesis that identifies the translog production function. It

specifies that the cross terms are equivalent to zero.

2. H0; u=0, the null hypothesis specifies that each farm is operating on the technically

efficient frontier and that the asymmetric and random technical efficiency in the

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inefficiency effects are zero. This is rejected in favor of the presence of inefficiency

effects.

3. H0; λ λ λ λ =δδδδ0= δδδδ2=…δδδδP =0, the null hypothesis specifies that the technical inefficiency

effects are not present in the model at every level, the joint effect of these variables on

technical inefficiency is insignificant.

The estimated parameters on the inefficiency model only indicate the direction

of the effects that the variables have on inefficiency levels (where a negative

parameter estimate shows that the variable reduces technical inefficiency). In their

article, Battese and Coelli (1993) show that for the i-th firm in the t-th time period,

technical efficiency (TE) is predicted using the conditional expectation.

TE=E [exp (-ui)/Ei=ei]

=exp (-u*+½σ*²) {φ[( u*/σ*)−σ*]/ φ ( u*/σ*) } ( ( ( (3))))

Where,

u*= (1- γ) zitδ- γεit

σ*² = γ (1- γ) σ²s

γ= συ² , σ²s=συ² +σ²v

σ²s

ει= Vi-ui and φ represents the distribution of the standard normal random variable.

Quantification of the marginal effects of these variables on technical efficiency is

possible by partial differentiation of the technical efficiency predictor with respect to

each variable in the inefficiency function. Partial differentiation of equation (3) was

estimated with respect to each of the inefficiency variables, evaluated at their mean

values or with a value of one for dummy variables and where the residuals ei are

calculated at the mean values of the dependent and independent variables in the

stochastic frontier function (Wilson, et al.,2001). Details of the partial differentiation

are in the appendix (1).

Empirical Results and Discussions

Summary statistics of output and input variables

The summary of the production functions variables is presented in Table 1. The result

indicates that, the mean of wheat yield was 8.8 and 9.6 sacks/fed in Abu-Hammed and

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El-matamma localities, respectively. The land cultivated by wheat in Abu-Hammed

locality was higher on average than in El-matamma locality. The average amount of

fertilizer applied in Abu-Hammed locality was slightly lower than in El-matamma

locality. Mager et al. (1969) pointed out that "the amount of fertilizer applied is

determined in general by soil fertility, soil type, cropping history, management of the

soil and requirement of the crop". Hudieba Research Station (H.R.S) recommends 80

kg urea for wheat. Elamin and Abdullah (2003) reported that usually farmers who

cultivate wheat in islands do not apply fertilizer. Variable amounts of urea were

applied in the range of 50 to 100 kg per feddan. This is due to the fact most of the

farmers depend mainly on their personal knowledge regarding fertilizer amounts.

Super phosphate at 40 kg/fed and 56-70 sack/fed of manure are recommended to add

in the high terrace soil with the objective of improving the soil physical conditions

and strengthening plant roots. The average amount of seed rate was around 49

kg/feddan in both localities of the state. According to H.R.S., the recommended seed

rate for wheat is 50-55 kg per feddan. Elfeil (1993) stated that the quality of seeds and

the amount of seed applied per unit area depends on the farmer's knowledge and

expertise, which are, of course, a function of farmer's education and age as well as a

function of extension services, which are lacking in the Northern Sudan. The average

time of labor engagement in growing wheat was around 35.6 man-days/fed in both

localities of the state. Farmers depend on family labor especially at the time of peak

agricultural operations demand such as harvest. Yet, family size is of great importance

as an indicator for family labour. Wheat has a recommended irrigation regime of eight

waterings at 10-12 days interval (Al-awad, 1994). As noticed from the table it was

less than that by one in El-matamma locality and more than that by two in Abu-

Hammed locality. According to the table, the majority of farmers adopt the

recommended varieties. Although, they cultivate high yielding verities and sell the

produce in the market, they depend heavily on sorghum for food rather than on wheat.

(Elamin and Abdalla, 2003). Moderate percentages of farmers did wheat sowing at the

appropriate time in the two localities. Farmers depended mainly on their personal

knowledge regarding the timing of wheat sowing. They stated many reasons behind

late sowing the most important of which are engagement in the cultivation of other

crops (faba beans, vegetables and spices) during November, high temperatures, risk

reduction of bird attack at the milky stage if they grow wheat early, shortage of

finance, late recession of the flood (delayed land preparation), and electricity and fuel

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shortages. Farmers cited that the recession of the flood and removal of silt from the

pump site also have a tremendous effect on determining sowing time of all cultivated

crops in general (Elamin and Abdalla, 2003). The table illustrates few farmers (less

than 20% on the average) adopted manual weeding in the state. The research

recommends weeding for wheat once every 4 weeks (Al-awad, 1994). Non-adopters

of weed control, which is prominent in R.N.S, indicated that the unavailability and

high cost of hired labor were the main limiting factors. Others claim that weeds have

minor effect on the productivity and productivity gain does not outweigh the cost of

weeding. Chemical use, on average, was 0.12 and 0.16 in Abu-Hammed and El-

matamma localities, respectively. This is consistent with Elamin and Abdullah (2003)

who claimed that aphids and birds were the major wheat pests. Chemical control was

little practiced and farmers’ knowledge about pesticides application in wheat was

negligible. Chemical weed control is also practiced by very few farmers using 2/4/D,

topic, pursuit and stomp. High percentages of farmers use tractors in both localities,

due to its advantage of deep ploughing which enables the soil to absorb more water

and hence long irrigation interval. However, they resort to animal draught due to

financial problems, unavailability of tractors, fragmentation of land, easiness in

implementation when the soil is wet, availability when required, lower cost and less

demand for sowing seed.

Most farmers were in active age range in the two localities. Upton (1979) stated

that "the farmer age has an influence on management performance although the

overall direction of this influence is not clear. On the one hand as man ages, he gains

experience and would expect his decision-making ability to improve". As noticed

from the table, farmers at Abu-Hammed locality were slightly more dependent on off-

farm activities on and on financing their wheat production than their counterparts of

El-matamma locality that depend more on formal credit for the same purpose.

Maximum likelihood estimates of wheat stochastic frontier

Production functions (SFPF)

The SFPF estimates of the sampled wheat producers in the State are presented in

Table 2. The first null hypothesis (H0=ßik=0) is rejected in favor of translog

production function in the models. The second null hypothesis is also rejected in favor

of the presence of efficiency effects. The final null hypothesis is rejected confirming

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that the joint effect of these variables on technical inefficiency is statistically

significant as depicted in table 3 of log likelihood ratio tests. Table 4 shows the

calculations of input elasticity's of wheat based on its translog SFPF. Thus, a one

percent increase in land will increase the wheat yield by 0.12% and 0.13% in Abu-

Hammed and El-matamma localities, respectively. This indicates that wheat is

inelastic with respect to land increase. Concerning fertilizer quantity per feddan a one

percent increase in the level of fertilizer will increase the wheat yield by 0.59% and

0.47% in the two localities, respectively. This indicates that wheat is moderately

inelastic with respect to fertilizer application. Mohammed (1995) realized the same

result, arguing that the actual amount of fertilizer applied is very little (50 kg/feddan)

relative to the recommended rate (100 kg/feddan). In case of seed rate, a one percent

increase in seed will increase wheat yield by 1% and 1.2 %. That indicates that wheat

yield is slightly elastic with respect to seed. A one percent increase in labour will

increase the wheat yield by 0.31% and 0.22 % in Abu-Hammed and El-matamma

localities, respectively. This reveals that labor is inelastic. On the other hand, a one

percent increase in the irrigation number will respectively increase the wheat yield by

0.43% and 0.54% in Abu-Hammed and El-matamma localities, respectively. Along

the same line, Mohammed (1995) concluded that high irrigation elasticity's are

enough to explain how the problems associated with irrigation inputs are constraining

the crop production of “Matarat”. These results indicate that the highest yield

responsiveness is due to seed rate followed by fertilizer, number of irrigations, labor

and land in Abu-Hammed locality. In El-matamma locality, wheat yield has highest

responsiveness to the seed rate followed by the number of irrigations, fertilizer, labor

and land. The sums of the elasticites of the variables are 2.45 and 2.55 in Abu-

Hammed and El-matamma localities, respectively. This reflects increasing returns-to-

scale in both localities.

Technical Efficiency

Technical efficiency is computed for each farm in each locality according to the early

stated equations. The results for the wheat mean technical efficiency and its variance

parameters at each locality are presented in Table 2. The mean technical efficiencies

of wheat were 0.67 and 0.64 in Abu-Hammed and El-matamma localities,

respectively. This means that, in the short run, there are ranges for increasing wheat

production by 0.33 and 0.36 in the two localities, respectively. That can be attained by

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adopting technologies used by the best practice of wheat farmers. It suggests that, on

average; about 33% and 36% of yields in Abu-Hammed and El-matamma localities,

respectively, are foregone because of inefficiencies. However, farms in the two

localities have different estimated technical efficiencies and their distributions are

illustrated in figures 1 and 2. It is evident from the table that the estimates of λ and σ

are large in all localities and significantly different from zero, indicating a good fit

and correctness of the specified distribution assumption. λ is the ratio of variance of u

(συ) over variance of v (σv) and is an indication that the one-sided error term u

dominates the symmetric error v. Therefore, variation in actual wheat yield comes

from differences in farmer’s practice rather than random variability for the two

localities. Gamma (γ) =σ2υ / (σv

2+σ2υ), is also a measure of the level of the

inefficiency in the variance parameter; it ranges between 0 and 1. In the translog

stochastic models, γ is estimated at 0.99 and 0.84 for Abu-Hammed and El-matamma

localities, respectively. This can be interpreted as follows: 99% and 84 % of random

variation in wheat production in Abu-Hammed and El-matamma localities,

respectively, is explained by inefficiency.

Socio-economic characteristics

The effects of socio-economic characteristics were studied according to their

coefficients signs. Thus, a negative sign means a reduction in technical inefficiency,

which means increase in technical efficiency and a positive sign increase in technical

inefficiency or decrease in technical efficiency as displayed in table 2. Negative signs

on the dummy variables of using improved verities of wheat are statistically

significant at 5% and 10% in Abu-Hammed and El-matamma localities, respectively.

That indicates, using them will decrease technical inefficiency and increase technical

efficiency. The coefficients of dummy variable of manual weed control have positive

signs and insignificant, which indicates manual weed control insignificantly increase

technical inefficiency in these localities. Mohammed (1995) mentioned that in the

study area weeding is more practiced for faba bean, fennel and garlic. It is not

practiced for wheat and the reason reported is that the crop is not planted in ridges.

Another reason is that the crop is too dense to allow considerable weed growth. The

dummy variables of using chemical control have negative signs coefficients and they

are statistically significant at 1%, meaning that they increase efficiency in both

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localities. The interpretation is that, in spite of farmers' little knowledge about

pesticides application and its high prices, they increased technical efficiency. The

coefficients of dummy variable of sowing date have negative signs and they are

statistically significant at 1%. In general that reveals sowing wheat early increase

technical efficiency. The coefficients of dummy variables of tractor-use have negative

signs and they are also significant at 1% in these localities. It concludes that using

tractors in land preparation reduces technical inefficiency. Compared to the use of

manual labor, use of tractors allows deep tillage of the soil that enhances yield. In

addition, tractors use ensures timely land preparation, planting and weeding. This

finding is consistent with findings by Awudu and Eberlin (2001) in Nicaragua. The

dummy variables for age are also negative and the variables are significant at 5% in

the both localities, suggesting that younger farmers, who are less than 50 years, are

more efficient than the older ones. The reason for this is probably that the age variable

picks up the effects of physical strength as well as farming experience of the

household head. Although farmers become more skillful as they grow older, the

learning by doing effect is attenuated as they approach middle age, as their physical

strength starts to decline (Liu and Zhung, 2000). The positive signs of off-farm

activities in both localities indicate that farmers earning off-farm income tend to show

high levels of inefficiency. The positive relationship suggests that involvement in

non-farm work is accompanied by reallocation of time away from farm related

activities, such as adoption of new technologies and gathering of technical

information that is essential for enhancing production efficiency. Other researchers

that made similar finding are: Huffman (1980); Awudu and Eberlin (2001); Liu and

Zhung (2000). Access to formal credit has negative signs. This finding is consistent

with a study by Bravo-Ureta (1994) for the peasant farmers in Eastern Paraguay,

where he found evidence that credit had a positive impact on technical efficiency.

Marginal effects

Marginal effects of the wheat technical efficiency variables were measured by partial

differentiation illustrated in Battese and Coelli (1993) and shown by the equations in

appendix (1). TE will be interpreted oppositely where a positive sign refers its

increase and a negative one points to its decrease. As depicted in table 5, the highest

marginal effects were for farmers who planted improved varieties of wheat by (61%)

and (38%) with margins of 5.4 and 3.7 sacks/fed in Abu-Hammed and El-matamma

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localities, respectively. The lowest were for those who used chemicals (5%) and

(13%), equivalent to 0.47 and 1.3 sacks/fed, respectively.

Conclusions

Wheat farms in Abu-Hammed and El-matamma localities of the River Nile State have

respective mean technical efficiencies of 0.67 and 0.64. The farm-specific factors used

to explain inefficiencies indicate that those farmers who active in their age, timely

sowing, using wheat׳s improved varieties, using tractor in land preparation and other

operations, use chemicals in combating wheat׳s pests and diseases, have better accesses

to credit and those who do less off-farm work and manual weeding of wheat tend to be

more efficient. Calculations of marginal effects have shown that the highest increase in

technical efficiency will be for farmers who used improved varieties and the lowest for

those that used chemicals. The policy implications revealed that applying technical

packages and sowing improved varieties of wheat, have positive role in increase

efficiency of farmers who Sudan depending on to supply food security for the rapid

urban population.

References

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Awudu, A. and Richard, E. (2001). Technical Efficiency during Economic Reform in

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Bravo-Ureta, B.E. and Pinheiro, A.E.. (1997). Technical, Economic and Allocative

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Battese, G.E and Coelli, T.J. (1993). A Stochastic Frontier Production Incorporating a

Model for Technical Inefficiency Effects. Working Papers in Econometrics

and Applied Statistics, No.69, Department of Econometrics, University of

New England, Armidale, pp.22.

Battese, G.E and Coelli, T.J. (1995). A model for Technical Inefficiency Effects in a

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20:325-332.

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Upton, M (1979) Farm Management in Africa. The English Language Book.

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Table 1:- Summary statistics of output and input variables in wheat

Production in River Nile State, Sudan

Variable

Description

Units

Abu-Hammed

Locality

El-matamma

Locality

Yield

Land

Fertilizer

Seed-rate

Labor

Irrigation No.

Improve verities

M-weed control

Chemical use

Sowing date

Tractor use

Age dummy

Off farm-income

Formal credit

Yield

Land

fert

seed

labor

irrig-no

impv

mwc

ch-use

sd

tr-use

age

off-inc

f.credit

Sacks*/fed.

Feddan

Kg/fed.

Kg/fed.

M-days/fed.

NO.

1=yes,0=No

1=yes,0=No

1=yes,0=No

1=early,0=late

1=yes,0=No

1=x≤50,0=x>50

1=yes,0=No

1=yes,0=No

8.8

(3.711)**

4

(8.914)

50.1

(37.46)

48.8

(13.85)

35.3

(3.21)

10

(2.17)

0.96

(0.198)

0.19

(0.20)

0.12

(0.328)

0.59

(0.491)

0.96

(0.198)

0.69

(0.461)

0.37

(0.482)

0.02

(0.141)

9.6

(3.281)

2.4

(1.602)

68.3

(26.78)

48.1

(8.567)

35.6

(2.087)

7

(2.046)

0.88

(0.331)

0.06

(0.242)

0.16

(0.415)

0.63

(0.459)

0.94

(0.242)

0.73

(0.452)

0.23

(3.281)

0.61

(0.496)

Source: Calculated, 2005. Sack*=100kg. ** Standard Deviation

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Table 2:- Wheat's (SFPF) in River Nile State in (2004/05) variables Symbol Abu- Hammed Locality El-matamma Locality

parameters T-Ratio parameters T-Ratio

Stochastic Frontier

Intercept

ln land

ln fert

ln seed

ln labor

ln irrig-no

lnland²

lnfert²

lnseed²

lnlabor²

ln irrig-no²

ln land*ln fert

lnland*ln seed

lnland*lnlabor

lnland* lnirrig-no

lnfert* ln seed

lnfert* lnlabor

lnfert*ln irrig-no

ln seed* ln labor

ln seed* ln irrig-no

ln labor* ln irrig-no

Inefficiency model

Constant

lnimpv

lnmwc

lnch-use

lnsd

ln tr-use

ln age

ln off-inc

lnf.credit

Variance Parameters lambda

Sigma

Sigma-squared (u)

Gamma

Ln (likelihood)

M.TE

ß0

ß1

ß2

ß3

ß4

ß5

ß6

ß7

ß8

ß9

ß10

ß11

ß12

ß13

ß14

ß15

ß16

ß17

ß18

ß19

ß20

δ0

δ1

δ2

δ3

δ4

δ5

δ6

δ7

δ8

λ

σ

συ²

σ²v

γ

0.10(0.033)a***

0.04(0.013)**

0.99(0.61149)

0.16(0.075)**

0.09(0.021)***

2.17(0.72)***

0.01(0.002)***

0.83(0.51478)

0.63(0.267)**

1.03(0.63547)

1.24(0.43)***

0.03(0.014)**

0.08(0.044)*

-0.01(0.005)*

-0.04(0.017)**

0.13(0.0743)*

-0.25(0.14377)

-1.97(1.24578)

-0.25(0.1344)*

-0.30(0.14)**

-1.95(0.87)**

0.15(0.05) ***

-0.91(0.425)**

0.18(0.11245)

-0.08(0.02315)

-0.22(0.09)***

-0.61(0.23)***

-0.63(0.272)**

0.01(0.0041)**

-0.35(0.164)**

9

0.04(0.0220)*

0.18(0.095)*

0.0018

0.99(0.31155)

-2.9

0.67

3.01532

3.18193

1.61924

2.12117

4.21571

2.99487

4.28357

1.61233

2.36435

1.62085

2.91643

2.20978

1.82963

-1.91729

-2.29545

1.75047

-1.73891

-1.58133

-1.8607

-2.17636

-2.22969

2.73818

-2.14362

1.60067

-3.45504

-2.80412

-2.63447

-2.32005

2.41864

-2.1296

1.82066

1.88545

3.17768

0.749(0.29)***

0.03(0.017)*

-1.18(0.36)***

1.30(0.437)***

-0.61(0.3216)*

1.39(0.346)***

0.09(0.049)*

0.74(0.358)**

0.12(0.03)***

0.6(0.16)***

0.23(0.097)**

0.01(0.005)*

-0.03(0.014)**

-0.06(0.032)*

-0.01(0.004)**

-0.21(0.12915)

0.34(0.13)***

0.04(0.02546)

0.29(0.09)***

-0.41(0.12)***

-0.94(0.32)***

-0.32(0.11)***

-0.006(0.003)*

0.001(0.00062)

-0.002(0.001) ***

-0.003(0.001) ***

-0.005(0.002) ***

-0.003(0.0014) **

0.009(0.005)*

-0.002(0.001) ***

0.32

0.54(0.3126)*

0.07(0.0398)*

0.22

0.84(0.291)***

17.07

0.64

2.60976

1.73211

-3.30532

2.97687

-1.89707

4.01966

1.83262

2.06993

3.49375

3.80011

2.37652

1.87231

-2.09205

-1.84957

-2.23214

-1.62602

2.70485

1.57109

3.10194

-3.28789

-2.95764

-2.84607

-1.91953

1.62536

-3.09741

-2.67012

-3.04216

-2.07559

1.81405

-2.56921

1.72761

1.75939

2.8892

Source: Compiled by the author, 2005. a Figures in parentheses are the standard

errors.***. **.* Significance level at 1%, 5% and 10%, respectively.

18

Table 3:- Wheat Likelihood Ratio Tests in River Nile State

Crop Wheat

Locality Null hypothesis C*.Value DF P-Value Decision

Abu- Hammed H0=ßik=0 25.90 14 0.05 Reject H0

H0; u=0 25.90 1 0.05 Reject H0

H0;δ1=…δP=0 25.90 8 0.05 Reject H0

El-matamma H0=ßik=0 27 14 0.05 Reject H0

H0; u=0 27 1 0.05 Reject H0

H0;δ1=…δP=0 27 8 0.05 Reject H0

Source: Compiled by the author, 2005. C*.Value= Calculated value

Table 4:- Wheat inputs elasticities in River Nile State

Input variable Abu- Hammed Locality El-matamma Locality

Land Fertilizer Seed Labor Irrigation No.

0.12 0.59

1 0.31 0.43

0.13 0.47 1.2 0.22 0.54

Source: Calculated by the author, 2005.

Table 5:- Marginal effects of wheat's efficiency measuring variables in River Nile

State

Abu- Hammed Locality El-matamma Locality

∆TE* ∆TE% ∆S/F ∆TE ∆TE% ∆S/F

Improved varieties

M. weeds

Chemical use

Sowing date

Tractor use

Age

Off-income

Credit

0.0061

-0.0012

0.0005

0.0015

0.0040

0.0042

0.0007-

0.0023

0.61

-0.12

0.05

0.15

0.40

0.42

0.07-

0.23

5.38

-1.06

0.47

1.30

3.61

3.72

-0.59

2.06

0.0038

-0.0007

0.0013

0.0020

0.0029

0.0020

0.0004-

0.0014

0.383

-0.070

0.134

0.204

0.293

0.204

0.042-

0.145

3.69

-0.677

1.292

1.969

2.831

1.97

-0.23

1.40

Source: Calculated by the author, 2005. *∆ TE =Change in tech * ∆ TE%=Change in technical efficiency percentage.

*∆ S/F = Change in sacks per feddan.

19

Fig (1):- Wheat Farmers technical efficiency percentage distrbution in Abu-Hammed locality in R.N.S. during 2004/05 season

0

0.1

0.2

0.3

0.4

0.5

0.6

0.10-0.30 0.30-0.60 0.60-0.90 90>

Technical Efficiency

Effi

cien

cy L

evel

Fig (2):- Wheat Farmers technical efficiency percentage distrbution in El-matamma locality in R.N.S. during 2004/05 season

0

0.1

0.2

0.3

0.4

0.5

0.10-0.30 0.30-0.60 0.60-0.90 90>

Technical Efficiency

Effi

cien

cy L

evel

20

Appendix (1)

For the i-th firm, technical efficiency is predicted using the conditional expectation:

TEi = E [exp (-Ui) | Ei = ei]

{Exp (-µ *+0.5σ²*)}{ φ [(µ * /σ* )- σ*]} /{ φ (µ * /σ* )}

= A (B/C) =AD,

Where

u*= (1- γ) zitδ- γεit

σ*² = γ (1- γ) σ²s

A = {Exp (-µ *+0.5σ²*)}

B = { φ [(µ * /σ*) - σ*]}

C= {φ (µ * /σ*)}

and

D= { φ [(µ * /σ*) - σ*]} / { φ (µ * /σ*)}

We wish to obtain the partial derivative of the technical efficiency measure with

respect to the j-th element of the z vector. Now, by the chain rule we have (10):

∂ΤΕ=∂ΤΕ ∂µ * (1)

∂ ZJ ∂µ * ∂ ZJ

Furthermore, we have

∂µ *= (1- γ) δj

∂ ZJ

∂ C=1 φ (µ * /σ*) = C`

∂µ σ*

∂ B= 1φ [(µ * /σ*)- σ*] = B` and D={ φ [(µ * /σ* )- σ*]}/ { φ (µ * /σ*)}

∂µ σ*

and,

10 From this point forward the firm subscript will be dropped.

∂ Α = −Α=Α`

∂µ *

Using these results we obtain:

21

∂ΤΕ=AD`+DA`=A (D`-D)

∂ ZJ

=A {[C B`- BC` ] –B}

C2 C

=A (CB`-BC``-CB)

C2

Thus, using this result and equation (1) and (2) we obtain

∂ΤΕ= A (CB`-BC``-CB) (1- γ) δj.(Tim coelli,200111)

∂ ZJ C2

11 An adjusted version of the cost function case by Scott .W. Frame and Tim.J.Coelli,

.2001. “U.S. Financial Services Consolidation: The Case of Corporate Credit

Unions”, Review of Industrial Organization 18: 229–242, 2001.