# Agriculture in Tunisia

### Application of Stochastic Production Frontier in the Estimation of Technical Efficiency of Irrigated Agriculture in Tunisia

Tawfik Ben Amor* and Christophe Muller**

In this paper we estimate agricultural technology for Tunisian peasants, accounting for the crop choice of peasants and distinguishing inputs for individual crops: vegetable farming, cereal and fruit-trees. The study employed the use of cross-section data from distinguishable irrigated crops survey conducted on a sample of 218 farmers frome 11 regions in Tunisia. The data were collected with the aide of structerd questionnaire and were later analysed. The Cobb Douglass production frontier model is employed in order to analyse data collected. Among the irrigated crop farmers, the significant variables were: farmuar manuar fertiliser quantity, labor, mecanic traction and among of irrigated water applied. The estimated sigma square σ² and gamma γ are widly significants for all irrigated crops and revealed that owver than 90 percent of the variation in the tunisian irrigated output among farmers in the study area are due to the differences in their efficiencies. Howerver, we find that predicted technical efficiency widely varies across farms and crops, from an average of 64.7percent for vegetable farming up to 83 percent for fruit-trees. The study also revealed the existing on inefficiency effects among the farmers as education, price of water, techniques of irrigation, lack of education, market prices of output and price of irrigated water.

Key Words: stochastic ,production, frontier efficiency irrigated agriculture, Tunisia.

### 1. Introduction

The crucial role that agriculture should play on economic development has been recognized for years. Tunisian agriculture provides 16 percent to GDP, ensuring the bulk of food supplies of the country and occupying a quarter of the active population. Agricultural exports, mostly citrus fruits, dates and fish, represent 11 percent of total exports.

In Tunisia, although the irrigated domain occupies 7.3 percent of the useful agricultural area in the country, it contributes to the global output of Tunisian agriculture. During the last economic development plan the production share of the irrigated agriculture moved from 29 percent to 50 percent of the total value of agricultural production. Hydraulics accounts for 32 percent of all agricultural investment and for 4.5 percent of total investment in Tunisia. It contributes to improving rural incomes, creating jobs, bringing flexibility to the necessary adaptation of product supply to market fluctuations.

Crop diversification is a central characteristic of the irrigated Tunisian agriculture. Globally, 45 percent of land is occupied by gardening crops, 34 percent by fruit trees, 13 percent by fodder crops and finally 8 percent by cereals.

Water resources in Tunisia come from rain and underground water reserves. Rain is very variable across regions, seasons and years. Neglecting the salinity factor leads to consider that the North of the country possess most water resources (60 percent), while the Centre and the South have respectively 17 and 23 percent of them. From these potential resources, the Ministry of Agriculture assesses that about 88 percent, i.e. 3,995 Mm3, are immediately exploitable. From this volume, 76 percent, amounting to 3,043 Mm3, are already developed.

Water demand in Tunisia has steadily risen during the last 15 years. Although, the irrigated area has more than doubled, the actual use of water much fluctuates across years depending on the agriculture needs. In part because of this uncertainty the present water pricing system is far from reflecting the economic value of irrigation water. The official price of water (between 0.032 TD/m3 and 0.06 TD/m3) corresponds to the average water cost with total coverage of exploitation costs and partial reimbursement of investment. However, the contribution of peasants to the investment cost is rarely perceived. Similarly, the rental charges that are carried forward only cover from 15 percent to 60 percent of the exploitation costs. The deficit is filled with public subsidies. In practice, the geographical variability of the unit cost of water mostly results from the low irrigation intensity in some regions.

Beyond water scarcity, the agricultural sector suffers from several handicaps. The farmers are generally aged and little educated. 53 percent of them have a mean age of 53 years in 2006 and 75 percent are illiterate. Employment is precarious: 60 percent of salaried and family workers are only employed on a temporary basis. The agricultural workers work on average 140 days per year, to compare with 250 days for the permanent workers.

Although agriculture benefits only from 9 percent of the credits in the economy, most of agricultural investment (60 percent) is originated from the State (Minister of agriculture, 2006).

In these conditions, farm productivity and efficiency, and the question of how to measure them is an important concern for irrigated agriculture in Tunisia. In particular, how water input influences them have obvious consequences on water supply policy. The potential importance of efficiency as a means of fostering production have not yielded a substantial number of studies focusing on Tunisian agriculture. As a matter of fact, it is the firs study in this domain.

### 2. Materials and Methods

### 2.1 The production frontier literature

The original frontier function model introduced by Farrell (1957) uses the efficient unit isoquant to measure economic efficiency, and to decompose this measure into technical efficiency and allocative efficiency. In this model, efficiency (TE) is defined as the firm‘s ability to produce maximum output given a set of inputs and technology. Stated differently, technical inefficiency reflects the failure of attaining the highest possible level of output given input and technology.

In contrast, allocative (or price) efficiency (AE) measures the firm's success in choosing the optimal input proportions, i.e., where the ratio of marginal products for each pair of inputs is equal to the ratio of their market prices.

In Farrell's framework, economic efficiency is a measure of overall performance and is equal to TE times AE.

The large number of frontier models that have been developed based on Farrell's work can be classified into two basic types: parametric and non-parametric. Parametric frontiers rely on a specific functional form while non-parametric frontiers do not. Due to our data limitations, we follow the parametric approach. Another important distinction is between deterministic and stochastic frontiers. The deterministic model assumes that any deviation from the frontier is due to inefficiency. The deterministic parametric approach was initiated by Aigner and Chu, who estimated a Cobb-Douglas production frontier through linear and quadratic programming techniques.

On the contrary, the stochastic approach allows for statistical noise, and it is the option that we pursue given all the ignorance existing about actual agricultural technical process. In the stochastic production frontier, technical efficiency is measured by one-sided disturbance term. When explicit assumptions for the distribution of the disturbance term are introduced, the frontier function can be estimated using maximum likelihood method. If no assumption are made concerning the distribution of the error term, the frontier can be estimated by the ‘corrected ordinary least squares method' (COLS) which consists of shifting the intercept term of the frontier function upwards until no positive error term remains.

### 2.2 The stochastic production function Model

Given the inherently stochastic nature of data production, the stochastic frontier production function approach is preferred to assess the technical efficiency of data farmers in the irrigated agriculture.

The stochastic frontier production model incorporates a composed error structure with a two-sided symmetric and a one-sided component The one-sided component reflects inefficiency, while the two-sided error captures the random effects outside the control of the production unit, including measurement errors and other statistical noise typical of empirical relationships. (Aigner Lovell, and Schmidt (1977); and Meeusen and van den Broeck (1977), Battese and Broca (1996) Battese and Coelli (1995) Battese and Coelli (1995)).

The Battese and Coelli (1995) model for the cross-sectional data is defined in two equations as:

(1)

where yi denotes the production of the ith farmer in the sample (i = 1, 2, …, n), Xi is a (1×k) vector of input quantities used by the ith farmer, β is a (k×1) vector of parameters to be estimated, f(Xi;β) is an appropriate parametric form for the underlying technology, and ei is a stochastic error term consisting of two independent components ui and vi:

(2) ei = ui - vi

The symmetric component, vi accounts for random variation in output due to factors outside the farmer's control, such as weather and plant diseases. It is assumed to be independently and identically distributed as, independent of ui. ui are non-negative random variables, associated with technical inefficiency in production, which are assumed to be independently distributed with truncations (at zero) of the normal distribution with mean, μi, and variance, σu² [N(μi, σu²)]. Under these assumptions the mean of technical inefficiency effects, μi, can more formally be expressed as follows:

(3) μi = Ziδ,

where Z is a (1×m) vector of observable farm-specific variables hypothesized to be associated with technical inefficiency, and δ is an (m×1) vector of unknown parameters to be estimated.

The variance of e is, therefore: σ2= σu2 σv2 while the ratio of two standard errors is defined as .

The parameter γ can determine whether a stochastic frontier is warranted as opposed to an average (OLS) function. The rejection of the null hypothesis, H0 : γ = 0, implies the existence of a stochastic production frontier.

Jondrow et al. (1982) have shown how measures of efficiency at the individual farm level can be obtained from the error terms. For each farm, the inefficiency measure is the expected value of u conditional on e, i.e.,

(4)

Where f(.) and F(.) are the standard normal density function and the standard normal distribution function evaluated at (el/s). Estimated values for e, l=(su /sv) and s are used to evaluate the density and distribution functions.

Finally, the technical efficiency of the ith sample farm, denoted by TEi, is defined in terms of the ratio of the observed output to the corresponding frontier output, conditional on the levels of inputs used by that farmer. It is given as :

(5) TEi = exp (-ui) = Yi / f (Xi; β) exp (vi),

where f(Xi;β)exp(vi) is the stochastic frontier production. The prediction of technical efficiencies is based on the conditional expectation in expression (4), given the model specifications (Battese and Coelli 1988).

In recent years the Battese and Coelli (1995) model for the technical inefficiency effects has become popular thanks to its computational simplicity as well as its ability to examine the effects of various farm-specific variables on technical efficiency in an econometrically consistent manner, as opposed to a traditional two-step procedure, which is inconsistent with the assumption of independently and identically distributed technical inefficiency effects in the stochastic frontier. The main advantage of this technique over the two-stage technique is that it incorporates farm-specific factors in the estimation of the production frontier because these factors may have a direct impact on efficiency.

On the basis of the generalized likelihood ratio test, given the specification of the translog, the Cobb-Douglas form is found to be an adequate representation of the used data. Although the Cobb-Douglas specification is restrictive, it pro-vides an adequate representation of production, as interest lies on efficiency measurement and not on analysis of production structure. The model estimated for the common sample is specified as:

(6)

where subscript i refers to the ith farmer in the sample, ln represents the natural logarithm, y is the output variable and Xk are input variables. βk are parameters to be estimated, and vi and ui are the random variables.

Following Battese and Coelli (1995) the mean of technical inefficiency effects, μi, is further defined as:

(7) μi = δ0 + Σ δk Zik, (k=1,…,5)

where Z are farm-specific variables and δk are unknown parameters to be estimated. The Zik variables included in the model of technical inefficiency are socioeconomic factors (Yao and Liu (1998)).

The technical inefficiency model can be esti-mated only if the technical inefficiency effects, ui, are stochastic and have particular distributional properties (Battese and Coelli 1995). Therefore, it is of interest to test various null hypotheses such as the following: (i) technical inefficiency effects are not stochastic, H0 : γ = 0; (ii) technical inefficiency effects are absent from the production function model, H0 : γ=δ0=δ1=δ2= …=δ5=0. These and other relevant null hypotheses can be tested using the generalized likelihood ratio statistic, λ, given by

(8) λ = -2{ln (L(H0)) - ln (L(H1))},

where L(H0) and L(H1) denote the values of like-lihood function under the null (H0) and alternative (H1) hypotheses, respectively. If the given null hypothesis is true, λ has approximately chisquare distribution or mixed chisquare distribution when the null hypothesis involves λ = 0 (Coelli 1995).

3. Data and definition

The data are taken from a national survey focusing of irrigated agriculture conducted by the Tunisian Ministry of Agriculture in 2006. The sampling scheme is stratified by zone (11 regions equally distributed on an East-West axis across the three agro-climatic region: North, Centre and South), irrigation source, perimeter size and perimeter age.

250 agricultural producers have been surveyed, leaving 218 observations (Table 1) because of missing or erroneous data. The objective of the survey was to gather basic data about producers, their production unit and the use of water. Since the collection was organized around the different crops, we dispose of input and output information that is specific to three crops: fruit-trees, vegetable farming and cereal.

### Table 1 Interviewed perimeters

region

perimeter surveyed

number. of investigations

Ariana

El Battan, Sidi Naji

24

Bizerte

Mateur, Ghezala

13

Nabeul

Menzel Bouzelfa, Lebna

27

Ben Arous

Mornag

13

Jendouba

S.Esssebt, Bouhertma

19

Zagouane

Zagouane

15

Kairouan

Sidi Saad

11

Hajeb

22

Mahdia

Bir Ben Kamla, Hiboun

14

Sousse

Chott Meriam, Sidi Bouali

20

Gabés

Metouia, Zerig, Ketana

21

Kebeli

Matrouha

19

Total

218

The main variables entering the stochastic frontier function, are as follows (Table 2):

### Table 2. Description of Output, Input, and Farm-Specific Variables

Variable Name

Description

Output (Y)

Output for a particular crop (in tons);

Input variables

Manure (X1)

Farmyard manure fertiliser, tons

Labor (X2)

Labor of farmer/family labor, regular and casual labor (in days);

Mecanization (X3)

Mechanic traction, hours

Animal traction(X4)

Animal traction, days

Irrigated water (X5)

Among of water applied, in m3;

Farm size(X6)

Total farm size, acres

Farm-Specific Variables

Farmer's age (Z1)

Age, number of years

Price of water (Z2)

In (10-3)dinars/m3

Farmer's education, dummy (Z3)

Value 1if analphabet farmer and 0 otherwise

Propriety, dummy (Z4)

Value 1if owner farmer and 0 if not

Region, dummy (Z5)

Value 1if north region and 0 otherwise

Technique of irrigation, dummy (Z6)

Value 1 if traditional technique of irrigation and 0 otherwise

Benefit parmameter

Price of output (py)

Market price of output, (10-3)dinars/kg

Cost

Cost of production, dinars

Descriptive statistics for the sample of 218 households by crop are shown in Table 3. Data on each input and output were collected by crop. Inputs include the use of farmyard manuar fertiliser, human labor, mechanic traction, animal traction irrigated water, In each, quantity was recorded.

### Table 3. Summary Statistics of Output, Input, and Farm-Specific Variables

Fruit-tree

vegetable farming

cereal

Mean

Std.Dev

Min

Max

Mean

Std.Dev

Min

Max

Mean

Std.Dev

Min

Max

Output(Y)

11,28

20,37

0,03

120

17

31,92

0,15

300

14,28

19,2

0,9

150

Input variables

Manure (X1)

32,23

56,91

0

401,5

39,7

163,3

0,75

2007

13,54

14,8

0,4

72

Labor (X2)

86,47

154,4

25

980

88,6

129,6

250

1080

46,04

43,6

30

200

Mecanization (X3)

6,383

36,55

0

400

4,97

5,841

0

38

406.9

97.6

328

606

Animal traction(X4)

18,3

39,36

0

360

12,3

26,93

0

200

12,29

16,6

0,5

100

Irrigated water (X5)

4478

9382

200

32930

1815

2298

126

15000

5107

4509

1040

33300

Farm size(X6)

1,682

2,266

0,05

18

1,02

1,282

0,05

10

2,486

2,28

0,03

12

Farm-Specific Variables

Farmer's age (Z1)

54,31

14,26

20

97

54

13,97

22

84

53,9

13,5

29

84

Price of water (Z2)

53,98

9,893

33

70

57,5

9,055

24

70

57,61

7,5

48

70

Farmer's education dummy (Z3)

0,541

0,501

0

1

0,58

0,495

0

1

0,567

0,5

0

1

Propriety, dummy(Z4)

0,892

0,311

0

1

0,71

0,457

0

1

0,881

0,33

0

1

Region,dummy (Z5)

0,546

0,5

0

1

0,57

0,497

0

1

0,866

0,34

0

1

Technique of irrigation, dummy (Z6)

0,515

0,502

0

1

0,37

0,484

0

1

0,134

0,34

0

1

FarmBenefit

5570.823

9552.623

110

47750

3132.635

4847.695

100

39000

1861.888

1429.912

295

6080

Price of output

357,3

88,64

220

450

242

70,14

150

300

333,7

164

200

950

Cost of production

776.6716

915.7247

100

4280

926.605

922.215

100

6000

1322.102

1016.356

150

5000

No.Observation

130

201

67

10

Land is generally scarce, and average holding are very small. This average range from 0.03 hectares per household for cereal to 18 hectares per households for fruit-trees.

The average of farm, family and casual labor range from 25 days (fruit-trees) to 1080 days (vegetable farming). This input is more important than mechanization because of the smallest of the land used.

In general, statistical demand curves for irrigation water estimate quantity demanded as a function of, price, incomes; and rainfall. There is no the case in Tunisia; water irrigation demand is correlated with the importance of crop. Cereal is

the important crop encouraged by the government to ensure the alimentary self satisfaction. This crop consumes an average of 5107 m3 by households.

For irrigation, there was small variation in price of water across farms (an average of 0.055 TND[1]/m3 for such crop) (1$=1.43 TND in 2009).

The official price of water (between 0.024 TND/m3 and 0.07 TND/m3) corresponds to the average cost with integral coverage of exploitation costs and partial reimbursement of investment. However, the contribution of peasants to investment cost is rarely perceived. Similarly, the rental charges that are carried forward only cover from 15 percent to 60 percent of the exploitation costs. The deficit is filled with public subsidies.

The farmers are generally aged (mean age 54 years). The education of the head and member of the household is generally very low. Over 53 percent of them cannot read and write a letter (analphabet)

### 4. Results and discussion

The parameters (βk) (k=1,…,4) for the stochastic Cobb Douglass production frontier model and those for the technical inefficiency model (δk) (k=1,…,5) are estimated simultaneously by the maximum likelihood method using the FRONTIER4.1c program.

The findings from the application of the stochastic frontier production function models present a number of noteworthy features of the performance of the irrigated crop producers in relation to their specific characteristics. The common stochastic production frontier model [(6) and (7)] is estimated under three different crops such as fruit-trees, vegetable farming and cereal.

The maximum likelihood estimates for the common stochastic production frontier models and those for the technical inefficiency model are presented in Table4. The estimate of technical efficiency model is based on the half-normal specification. All slope coefficients of the stochastic frontier represent output elasticties of all inputs. The signs of the parameters are as expected.

### Table 4. Maximum likelihood estimates for the parametres of the stochastic frontier production function and technical inefficiency Model

Parameters

cereal

fruit-trees

vegetable farming

coeff

t.ratio

coeff

t.ratio

coeff

t.ratio

Stochastic Frontier

Constant (β0)

1.612

0,023

5,435

12,752

3,370

4,894

ln (farmyard manure) (β1)

0,273

1,931*

0,334

1,659*

0,315

1,742*

ln (labor) (β2)

0,212

1,936*

0,116

2,356**

0,132

2,392**

ln (Mecanization) (β3)

0,032

1,68*

0,155

1,652*

0,188

3,374**

ln (animal traction) (β4)

0,188

0,912

0,176

0,579

0,155

0,86

ln (irrigated water) (β5)

0,213

3,064**

0,193

4,646**

0,165

1, 835*

Ln(farm size) (β6)

0,199

0,275

0,039

0,815

0,326

6,454

Inefficiency Models

Constant(δ0)

1,766

0,495

0,301

0,173

3,411

5,270

Farmer's age (δ1)

-0,031

-1,801

-0,023

-1,654

-0,002

-1,782

Price of water (δ2)

1,071

1,437

-0,016

-1,169

0,001

-0,001

Education dummy (δ3)

0,406

0,616

0,240

0,755

0,070

0,484

Propriety, dummy (δ4)

-0,203

-1,713

-0,517

-1,941

-0,003

-1,923

region dummy (δ5)

0,060

3,191

0,869

2,237

0,086

3,669

Technique of irrigation (δ6)

-0,051

-0,450

-0,304

-0,778

-0,497

-4,219

Variance parameters

σ²

0,714

3.422

0.327

4.2796

0.409

10.123

γ

0,906

5.281

0.911

3.1229

0.918

16.997

Ln(likelihood)

-42.090

-92.563

-195.197

No.obsrvation

67

130

210

Notes: *=5% significant level; **=10% significant leve

l

10

Among the irrigated crop farmers, the significant variables include: farmuard manuar, labor, mecanic traction and among of irrigated water applied. While the animal traction was not significant. Except for the animal traction output estimates for all inputs are significant at the 10% level. The estimate of output elasticity of irrigated crop with respect to irrigation water is significant and its value range from 0.155 to 0.188. An increase of 10 percent in irrigation water can increase the irrigated crop production by 1.88 percent, 1.76 percent and 1.55 percent respectively for fruit-trees, vegetable farming and cereal.

The labor and mechanization coefficients are statistically significant; however, the animal traction has a positive elasticity but is not significant. In view of surplus labor in agriculture, the significant estimate of output elasticity for labor is expected.

The estimated sigma square (σ²) of the irrigated crop farmers are 0.714, 0.327 and 0.409 respectivly for cereal, fruit trees and vegetable farming (all significant at 1%). This indicate a good fit of the model and the correctness of the specified distributional assumption. The estimate gamma (γ) parameter of the irrigate crop farmers are 0.906, 0.901 and 0.918 respecively for cereal, fruit-trees and vegetable farming and higly significant at 1% level of significance. This mean that owver then 90% of the variation in the irrigated crop output among the farmers in Tunisia are due the differences in their technical efficiencies. This results is consisitent with the finding of Yao and Lu (1998) and Ajibefun and Daramola (1999).

Among the crop irrigated farmers in the study area, the coefficients of age,propriety of land (the owner land farmers) and technique of irrigation (traditionnal technique) are negative. The finding reveled means that the younger the irrigated crop farmers, the less technically inefficient they will be, as such the more technically efficient they will be. The coefficients of education, level firme size and region had positive relation ship with technical inefficiency of irrigated crop fields and this was againt the priori expectation and was well incongruent with the finding of Obwana (2000) and Kalirajan (1981).

Thus the traditional average (OLS) production function, with no technical inefficiency effects, is not an adequate representation of irrigated crop involved in this study. Generalized likelihood ratio tests of various null hypotheses involving the restrictions on the variance parameter, γ, in the stochastic production frontier and the δ coefficients in the technical inefficiency model are presented in Table 5.

The null hypotesis specifies tha the irrigated crop farmes in Tunisia were technically efficient in their production, the variation in their output was only due to random effects. The hypothésis is defined thus H0: γ=0. The generalised likelihood ratio test was conducted and Chi-square (X2) statistic was computed. Table 5 shows the results of generalised likelihood ratio test for the absence of technical inefficiency effects. The nul hypotesis, γ=0 was rejeced among the crop irrigated agriculture in the study area. This revealed that the technical inefficiency effects existed among faremers and that the variation in their production processus may due to certain inefficiency factors.

### Table 5 Likelihood Ration Test of the one-sided error H0:γ=0

Irrigated Crop

L(H0)

L(Ha)

Critical value ()

No.Observation

Decision

Fruit-trees

-109,332

-92,603

33,458

16,92

130

Reject H0

Cereal

-57,393

-42,06

30,666

16,92

67

Reject H0

Vegetable farming

-230,481

-195,19

70,582

16,92

210

Reject H0

10

Given a particular technology to transform physical input into output, some farmers may be able to achieve maximum efficiency while others are technically inefficient. This discrepancy could be due to lack of adequate technical knowledge. Timmer (1971), Khalirajan and Shand (1989), Coelli, Battese (1996), Battese and Lundvall (1998) and Wilson, Hadley, Ramsden, Kaltsas (1998) have suggested that the technical efficiency of farmer is determined by socio-economic and demographic factors.

As indicated, to determine the impact of some management factors on irrigation allocation, technical efficiency could be used as a measure of management capability, and thus as an index of sustainability. Given that there are differences in efficiency levels among irrigated crop farmers in this study, it is appropriate to question why some farmers can achieve relatively high efficiency while others are technically less efficient. Variations in the technical efficiencies of farmers may arise from farm characteristics that affect the ability of the farmer to use the existing technology adequately.

All the frequency distributions of technical efficiency measures are summarized in Table 6. The mean value of technical efficiency for all farms is estimated to be 0.647, for vegetable farming with a range from 0.285 to 0.98 and 0.743 for cereal with a range from 0.256 to 0.993 and 0.836 for fruit-trees with a range from 0.402 to 0.964.

This result indicate that output can be increased on average by 35.3 percent (vegetable farming), 25.7 percent (cereal) and 16.4 percent (fruit-tree) with the present state of technology and the same amount of inputs as before if the technical inefficiency are removed completely.

Statistics indicate that half of the farmers are fewer than 58.3 percent efficiency for vegetable farming. About 94 percent of the farmers (190) are at an efficiency level of 75 percent or below and only 11 farms above 75 percent. Thus, there is considerable room for improvement in the technical efficiency of this culture in Tunisian agriculture.

However, cereal and fruit-trees have almost disreptive statistic for efficiency level. Owver than 80 percent of the farmers have efficiency level under 75 percent (inefficiency at 25 percent).

In summary, these statistics are quite comparable to those reported by previous frontier studies in agriculture in developing countries. For example, the overall average level of technical efficiency computed from all the studies presented by Thiam, Bravo-Ureta, and Rivas (2001) is 68 percent. The parametric studies relying on the Cobb-Douglas form reported technical efficiency measures ranging from 52 percent to 84 percent, with an average of 71 percent.

### Table 6. Frequency Distributions of Technical Efficiency Estimates

Efficiency Index (%)

vegetable farming

cereal

Fruit-tree

< 25

18(9%)

1(1.5%)

0(00.0%)

25-50

99(49.3%)

17(25.8%)

22(16.9%)

50-75

73(36.3%)

48(57.8%)

83(63.8%)

75-100

11(5.5%)

13(19.4%)

25(19.2)

No.Obs

201

67

130

Mean

0.647

0.743

0.836

Minimum

0.285

0.256

0.402

Maximum

0.98

0.993

0.964

Standard deviation

0.199

0.206

0.128

### 5. Policy Implications

Agricultural policy in Tunisia is largely determined by considerations of food security, self-sufficiency, and import-substitution practices. Apart from tourism, agriculture provides the main source of income for the inhabitants of the Tunisian peasant.

The empirical estimates of technical efficiency in irrigated agriculture have proved to be useful. Naturally, for the water resources manager in the semi-arid and arid zones, it is interesting to know how far agricultural production can be expected to increase its output by simply increasing its productive efficiency, without absorbing further resources, given the level of technology involved. The econometric estimation of the farm-level technical inefficiencies in agricultural production reveals that the farmers produce well below their potential agricultural output. It has been estimated that, for the same amounts of inputs, output could be increased by up to 36 percent for vegetable farming and 26 percent for fruit-tree and only 16 percent for cereal. The results indicate that there is a considerable potential for improving household income by improving productive efficiency. Observeb benefits and benefit at full efficiency levels are presented in Table 6 for the three crop.

### Table 7. Various Benefit Levels wiht and without inefficiency

Crop

π=Observed Benefit Levels[2]

π*=Benefit Levels at Full Efficiency[3]

Mean

Mean

Std Dev

Min

Max

Vegetable farming

3132.635

5540

8534.124

122

72300

Fruit-tree

5570.823

10169.34

17488.19

142.352

87878

Cereal

1861.888

3658.168

2697.519

211.037

11566.56

By reaching full efficiency levels, farmers would be able to increase their actual benefits by 76.8[4] percent; 82.5 percent and 96.5 percent respectivly for vegetable farming, fruit-trees and cereal. Based on these results, farmers are shown to provide increased local economic benefits, which would promote local rural development.

Farm policy that leads to more diversified and smaller scale farming is necessary if irrigated agriculture are to more effectively contribute to long-term rural community development and vitality.

Understanding the differences efficiency level between farmers can help policymakers and advocates define and guide policy in response to societal goals. For example, if rural development is a goal, policies and programs can be targeted to those types of farms that provide the most benefits to the community. Improved performance could be a rationale for rural economic development programs.

There is a vast potential for Tunisia to increase its total grain output by raising yields per hectare. The main challenge of policy makers in these areas is how to attain food self-sufficiency by promoting output growth.

Keeping more money in the community might be desirable as it would have the effect of maintaining or strengthening local economic health and resiliency.

### 6. Conclusion

In this study, we have used survey data on input and output by farms to measure farm-level inefficiency of Tunisian irrigated crop production (cereal fruit-trees and vegetable farming) in Tunisia using stochastic production frontier (SPF) models. The proposed parametric approach framework provides some evidence of substantial inefficiencies. On average, cereal and fruit-trees are found to be slightly more efficient than vegetable farming.

We find that irrigated production crop could be explained mainly by four variables: farmyard manure fertiliser, labor, mechanization and, water quantity. Output elasticities of all inputs are found to be positive and significant except for the animal traction. For the technical inefficiency model, none of the socio-economic variables seem to matter. This result is due to the lack of variability in these variables. The majority of the farmers have the same characteristics.

From a policy standpoint, more accurate technical efficiency estimates are crucial in guiding policy decisions dealing with farm extension and training programs, among others. The results reveal significant technical inefficiencies for the sample irrigated crop producers. On average, vegetable farming farmers are found to be technically a little less efficient than cereal and frit-trees. For example, the mean technical efficiency level for vegetable farming is 0.647 , 0.678 for cereal and fruit-tree.

The efficiency level is negatively correlated with lack of education and with traditional irrigation technic. In contrast, the prices of output and of irrigation water are found to have a positive impact on efficiency.

Improving the irrigation public price system is a way to enhance farm output (McGukin, Gollehon and Ghosh (1992)). However, water resource scarcity continues to characterize water demand and supply environment in Tunisia.

Agriculture, by far the largest user of water, accounts for roughly 80% of water use. In this sector, the application of highly subsidized associated inputs such as water has drained pubic budgets. Then, attention has turned towards better usage of the existing irrigation infrastructure and improving water conservation.

Our estimates are a first step in the direction of better measurement of water specific technical efficiency of Tunisian farmers for irrigated crops which can provide useful insights into enhancing farm output and improving water resource use

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[1] Tunisian National Dinar

[2] π=Py*y-cost of production

[3] π*=Py(1+inefficiency)*y-cost of production

[4] (π*-π)/π