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 [email protected]
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/Working_paper/WorkingPaper/Adhn/ad hn.pdf
1 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 [email protected] ISBN 978-88-96189-28-3
2 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
3 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
4 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:
5 5 5
Ln yi=+ lnXki + ½ j lnXki Xji + (1) k1 k1 k1
;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.
.X4= Average number of man-days of labor used
.X5 = Average number of irrigations applied per feddan per season
= Vi-ui = Composite error term ;Where
Vi =Random variable assumed to be independently and identically
distributed N (0; _²v) and independent of ui.
5 ui =Random variable that accounts for technical inefficiency and assumed to be independently distributed as truncation of the normal distribution with mean μ and
2 2 variance ² = u (|N (μ, ²u)|) . The inefficiency model is estimated from the equation given below;
n ui= m Zi (2) mi :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 = (² /²v); variance of the models (Sigma ), variance of the stochastic
models (²v) and variance of the inefficiency models (²). 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,LR = 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
2 hypothesis, respectively. The null hypothesis is rejected when LR >XC . 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
6 inefficiency effects are zero. This is rejected in favor of the presence of inefficiency effects.
3. H0; =0= 2=…P =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*+½*²) { u*** u**3 Where, u*= (1-) zit-it
*² = (1-)²s
= ² ,²s=² +²v
²s
= Vi-uiand 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
7 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
8 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
9 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
10 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 and are large in all localities and significantly different from zero, indicating a good fit and correctness of the specified distribution assumption. is the ratio of variance of u
() over variance of v (v) 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
2 localities. Gamma) = / (v + ), 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, 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
11 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
12 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 s improved varieties, using tractor in land preparation and other׳sowing, using wheat s pests and diseases, have better accesses׳operations, use chemicals in combating wheat 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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13 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 Stochastic Frontier Production Function for Panel Data. Empirical Economics 20:325-332. Elamin, M.A. (2002).Analysis of Policies Related to Wheat Production in Sudan, Sudan Journal of Agric.Res.ARC.p 81-82. Elamin, M.A and Ishatiag, A.F (2003). Monitoring and Evaluation of Farmer's knowledge, Attitudes and Practices on the Production of Wheat in the Northern Sudan, Gezira Research Station, Socioeconomic Research Program, Anuual Report, ARC and MOST. Elfeil, M.A. (1993). Economic Constrains of Agriculture Production in the Northern Province of Sudan. An Econometric Approach. Ph.D. (Agric.).thesis. University of Khartoum, Sudan. Huffman, W.E. (1980). Farm and Off-Farm Decisions: The Role Human Capital. Review of Economics and Statistics, 62: 14-23. Liu, Z. and Zhuang, J. (2000). Determinants of Technical Efficiency in Post- Collective Chinese Agriculture: Evidence from Farm- Level Data. Journal of Comparative Economics, 28: 545- 564. Mager, W.Y; Paai, K.D, Osman, A. (1969).Cotton Environment in Asymposim to Mark The Fifth Anniversary of The Gezira Research Station, Wad Medani, Sudan. Meeusen, W. and Van den Broeck, J. (1977). Efficiency Estimation from Cobb- Douglas Production Functions with composed Error. International Economics Rev., 18:435-444. Ministry of Agriculture and Forests MOAF, (2003). The Second Agricultural Development Strategy, SADS (2003-2007), Khartoum, Sudan. Ministry of Finance and National Economy (MOFNE). (2000). Microeconomic Performance Reform, Khartoum, Sudan. Mohamed, A.S. (1995). Economics of Crop Production in Dongola Province. M.Sc (Agric) thesis. University of Khartoum, Sudan. Osman, A. H. (2004). The Sudanese Agricultural Development Strategy (SADS) 2003-2007. A critical Review, M.Sc.thesis. University of Reading, U.K.
14 Upton, M (1979) Farm Management in Africa. The English Language Book. Oxford University Press, Oxford, U.K. Wilson, P.; David, H. and Carol, A. (2001). The Influence of Characteristics on the Technical Efficiency of Wheat Farmers in Eastern England. Agricultural Economics 24: 329- 338.
15 Table 1:- Summary statistics of output and input variables in wheat Production in River Nile State, Sudan Abu-Hammed El-matamma Locality Locality Description Units Variable Yield Yield Sacks*/fed. 8.8 9.6 (3.711)** (3.281) Land Land Feddan 4 2.4 (8.914) (1.602) Fertilizer fert Kg/fed. 50.1 68.3 (37.46) (26.78) Seed-rate seed Kg/fed. 48.8 48.1 (13.85) (8.567) Labor labor M-days/fed. 35.3 35.6 (3.21) (2.087) Irrigation No. irrig-no NO. 10 7 (2.17) (2.046) Improve verities impv 1=yes,0=No 0.96 0.88 (0.198) (0.331) M-weed control mwc 1=yes,0=No 0.19 0.06 (0.20) (0.242) Chemical use ch-use 1=yes,0=No 0.12 0.16 (0.328) (0.415) Sowing date sd 1=early,0=late 0.59 0.63 (0.491) (0.459) Tractor use tr-use 1=yes,0=No 0.96 0.94 (0.198) (0.242) Age dummy age 1=x≤50,0=x>50 0.69 0.73 (0.461) (0.452) Off farm-income off-inc 1=yes,0=No 0.37 0.23 (0.482) (3.281) Formal credit f.credit 1=yes,0=No 0.02 0.61 (0.141) (0.496) Source: Calculated, 2005. Sack*=100kg. ** Standard Deviation
16 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 ß0 0.10(0.033)a*** 3.01532 0.749(0.29)*** 2.60976 ln land ß1 0.04(0.013)** 3.18193 0.03(0.017)* 1.73211 ln fert ß2 0.99(0.61149) 1.61924 -1.18(0.36)*** -3.30532 ln seed ß3 0.16(0.075)** 2.12117 1.30(0.437)*** 2.97687 ln labor ß4 0.09(0.021)*** 4.21571 -0.61(0.3216)* -1.89707 ln irrig-no ß5 2.17(0.72)*** 2.99487 1.39(0.346)*** 4.01966 lnland² ß6 0.01(0.002)*** 4.28357 0.09(0.049)* 1.83262 lnfert² ß7 0.83(0.51478) 1.61233 0.74(0.358)** 2.06993 lnseed² ß8 0.63(0.267)** 2.36435 0.12(0.03)*** 3.49375 lnlabor² ß9 1.03(0.63547) 1.62085 0.6(0.16)*** 3.80011 ln irrig-no² ß10 1.24(0.43)*** 2.91643 0.23(0.097)** 2.37652 ln land*ln fert ß11 0.03(0.014)** 2.20978 0.01(0.005)* 1.87231 lnland*ln seed ß12 0.08(0.044)* 1.82963 -0.03(0.014)** -2.09205 lnland*lnlabor ß13 -0.01(0.005)* -1.91729 -0.06(0.032)* -1.84957 lnland* lnirrig-no ß14 -0.04(0.017)** -2.29545 -0.01(0.004)** -2.23214 lnfert* ln seed ß15 0.13(0.0743)* 1.75047 -0.21(0.12915) -1.62602 lnfert* lnlabor ß16 -0.25(0.14377) -1.73891 0.34(0.13)*** 2.70485 lnfert*ln irrig-no ß17 -1.97(1.24578) -1.58133 0.04(0.02546) 1.57109 ln seed* ln labor ß18 -0.25(0.1344)* -1.8607 0.29(0.09)*** 3.10194 ln seed* ln irrig-no ß19 -0.30(0.14)** -2.17636 -0.41(0.12)*** -3.28789 ln labor* ln irrig-no ß20 -1.95(0.87)** -2.22969 -0.94(0.32)*** -2.95764 Inefficiency model Constant lnimpv 0.15(0.05) *** 2.73818 -0.32(0.11)*** -2.84607 lnmwc 1 -0.91(0.425)** -2.14362 -0.006(0.003)* -1.91953 lnch-use 0.18(0.11245) 1.60067 0.001(0.00062) 1.62536 lnsd -0.08(0.02315) -3.45504 -0.002(0.001) *** -3.09741 ln tr-use -0.22(0.09)*** -2.80412 -0.003(0.001) *** -2.67012 4 ln age -0.61(0.23)*** -2.63447 -0.005(0.002) *** -3.04216 5 ln off-inc -0.63(0.272)** -2.32005 -0.003(0.0014) ** -2.07559 lnf.credit 6 0.01(0.0041)** 2.41864 0.009(0.005)* 1.81405 Variance Parameters lambda 7 -0.35(0.164)** -2.1296 -0.002(0.001) *** -2.56921
Sigma 8 Sigma-squared (u) Gamma 9 0.32 Ln (likelihood) 0.04(0.0220)* 1.82066 0.54(0.3126)* 1.72761
M.TE ² 0.18(0.095)* 1.88545 0.07(0.0398)* 1.75939
²v 0.0018 0.22 0.99(0.31155) 3.17768 0.84(0.291)*** 2.8892 -2.9 17.07 0.67 0.64
Source: Compiled by the author, 2005. a Figures in parentheses are the standard errors.***. **.* Significance level at 1%, 5% and 10%, respectively. Table 3:- Wheat Likelihood Ratio Tests in River Nile State
17 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;1=…P=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;1=…P=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 0.12 0.13 Fertilizer 0.59 0.47 Seed 1 1.2 Labor 0.31 0.22 Irrigation No. 0.43 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 0.0061 0.61 5.38 0.0038 0.383 3.69 M. weeds 0.0012- 0.12- 1.06- 0.0007- 0.070- 0.677- Chemical use 0.0005 0.05 0.47 0.0013 0.134 1.292 Sowing date 0.0015 0.15 1.30 0.0020 0.204 1.969 Tractor use 0.0040 0.40 3.61 0.0029 0.293 2.831 Age 0.0042 0.42 3.72 0.0020 0.204 1.97 Off-income -0.0007 -0.07 0.59- -0.0004 -0.042 0.23- Credit 0.0023 0.23 2.06 0.0014 0.145 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.
18 Fig (1):- Wheat Farmers technical efficiency percentage distrbution in Abu-Hammed locality in R.N.S. during 2004/05 season 0.6
0.5
l 0.4 e v e L y c 0.3 n e i c i f f E 0.2
0.1
0 0.10-0.30 0.30-0.60 0.60-0.90 90> Technical Efficiency
Fig (2):- Wheat Farmers technical efficiency percentage distrbution in El-matamma locality in R.N.S. during 2004/05 season 0.5
0.4 l e v e 0.3 L y c n e i c i f f 0.2 E
0.1
0 0.10-0.30 0.30-0.60 0.60-0.90 90> Technical Efficiency
19 Appendix (1) For the i-th firm, technical efficiency is predicted using the conditional expectation:
TEi = E [exp (-Ui) | Ei = ei]
{Exp (- *+0.5²*)}{ [( * /* )- *]} /{ ( * /* )} = A (B/C) =AD, Where u*= (1-) zit-it
*² = (1-)²s
A = {Exp (- *+0.5²*)}
B = { [( * /*) - *]}
C= { ( * /*)} and
D= { [( * /*) - *]} / { ( * /*)} 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):
* (1)
ZJ * ZJ Furthermore, we have
*= (1-)j
ZJ
` C=1 ( * /*) = C
*
B= 1( * /*)- *] = B` and D={ [( * /* )- *]}/ { ( * /*)}
* and,
10 From this point forward the firm subscript will be dropped. `
*
Using these results we obtain:
AD`+DA`=A (D`-D)
20 ZJ
` =A {[ C B ` - BC ] –B} C2 C =A (CB`-BC``-CB) C2
Thus, using this result and equation (1) and (2) we obtain
11 A (CB`-BC``-CB) (1-)j.(Tim coelli,2001 )
2 ZJ C
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.
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