SJA_30_4_433-441

Introduction

Wheat is a main cereal crop and is the staple food of many countries including Pakistan. It is grown almost all over the world. Wheat is one of the most abundant sources of energy and protein for the world population. Wheat is adapted to many soil types, has a short growing season, offers good yield, and grows well in fairly dry and mild climates, although the highest yielding crops require more optimal growing conditions. The total area under wheat in world was 223.56 million hectares in 2008, ranging between 207.66 to 226.85 million hectares during 1991- 2008. Out of the total area under wheat crop, 43.60% area under wheat crop was in Asia followed by Europe (27.6%), America (18.5%), Oceania (6.1%) and Africa (4.2%). Production of wheat in world increased from 546.88 MMT in 1991 to 689.95 MMT in 2008. Thus during the stated period total world wheat production increased significantly. The average annual increase was 1.51% with the strongest average annual growth in Oceania (15.29%) followed by Africa (3.86%), Europe (2.24%), Asia (1.89%) and America (1.42%). Out of total wheat production, 40.6% of world wheat is produced in Asia followed by Europe (36.0%), America (17.2%), Oceania (3.2%) and Africa (3.1%) in 2008 (FAO, 2009).

It appears that Germany is the world top wheat yielder, with the yield ranging between 5961 to 8087 kilograms per hectare (kg ha-1), followed by France (6250 to 7606 kg ha-1), China (3100 to 4762 kg ha-1), US (2304 to3018 kg ha-1), Canada (1832 to 2852 kg ha-1), India (2281 to 2802 kg ha-1), Pakistan (1841 to 2716 kg ha-1), Russian Federation (1360 to 2446 kg ha-1), Turkey (1787 to 2359 kg ha-1), Australia (907 to 2167 kg ha-1) during 1991-2008 (FAO, 2009).

Despite of the fact that Pakistan is the 9th largest wheat producing country in the world, it has remained net importer of wheat in the world market. Pakistan imported, on average, 1.453 million tons (239.221million $) of wheat each year during 1991-2007. During the same period in only three years, Pakistan’s export of wheat has exceeded than imports but the amount was very meagre while in the remaining fourteen years exports were greater than imports (FAO, 2009). Wheat has been imported to meet the minimum food need of the country, over greater period of Pakistan’s existence. Wheat imports in some years went over 2 million tons. In the current year, wheat deficit has further widened.

Wheat is a major source for food security in Pakistan. It provides livelihoods and income to millions of farmers in the country. Wheat has a unique position among the cultivated crops. It covers the largest area as compared to other crops in the country. Its value addition in agriculture, on average, is 13.20 % and it contributed 3.03% to Pakistan’s GDP during 2001-2008 (GoP, 2008).

The importance of wheat crop is relatively more in Khyber Pakhtunkhwa compared to other provinces. In Khyber Pakhtunkhwa total wheat requirement was 2686.0 thousand tons, while its production was 1071.8 thousand tons during the year 2007-08. This is due to the fact that the productivity of wheat was very low in even the irrigated area (1968 kilograms per hectare) as compared to the national average yield (2451 kilograms per hectare) during 2007-08 (Govt. of Khyber Pakhtunkhwa, 2008).

The aforementioned discussion unveils that Pakistan is far behind in wheat production due to low productivity. The national strategic importance of food is evident in its consideration as a key variable in matter relating to national security and in planning against food requirements. However, a major indicator of depressed performance of the Pakistan wheat crop is the food crisis experienced in the country in the past years (Byerlee and Siddiq, 1994; Rajaram et al., 1998; Ahmad et al. (2002).

According to Nishimizu and Page (1982) and Srinivasan (2001) growth in productivity can be divided into two components, first one is innovations that create new and/or improved inputs and techniques of production and new uses for existing products, and second is growth in the efficiency of the use of these technologies. The latter requires technological capability like technical, managerial and institutional skills and building such capabilities in harmony with the dynamism of changing technologies (Kalirajan, 1991; Lall, 1993).

The analysis of efficiency dates back to Knight (1933), Debreu (1951) and Koopmans (1951). Koopmans (1951) provided a definition of technical efficiency while Debreu (1951) introduced its first measure of the ‘coefficient or resource utilization’. Following Debrew in a seminal paper Farrell (1957) provided a definition of frontier production functions, which embodied the idea of maximization (Shuwu, 2006).

The term ‘technical efficiency’ was first introduced by Farrell (1957). According to Farrell, technical efficiency (TE) is associated with the ability of a firm to produce on the isoquant frontier. Technical efficiency can be measured in a relative sense. It is the departure of a firm from the best performance in a representative peer group.

Results of this study are expected to be helpful for those are engaged in decision making process at farm level and at national level as well. Reliable estimates of technical efficiency level and inefficiency factors are of great importance. Results of this study would provide information to wheat growers regarding better farm management practices. Planners and policy makers would also take help from the findings of this study in formulating appropriate measures to increase wheat production in Khyber Pakhtunkhwa in particular and in Pakistan in general. The objectives of present study are, therefore, to estimate technical efficiency in production across wheat growers and to identify technical inefficiency factors, if any, in wheat production.

Data and Methodology

This study was carried out in Khyber Pakhtunkhwa Province [(formerly known as North West Frontier Province (NWFP)] of Pakistan. The population for this study consisted of total number of wheat growers in Khyber Paktunkhwa Province. Multistage sampling technique was used for selection of the sample. In the first stage district Peshawar was purposively selected, since this is one of the major wheat producing and highly irrigated districts of Khyber Pakhtunkhwa Province (Government of Khyber Paktunkhwa, 2008). District Peshawar has 92% irrigated area under wheat during 2008-09 (Govt. of Khyber Pakhtunkhwa, 2010). In the stage second, one tehsil was randomly selected. In stage third from the selected tehsil two union councils were selected randomly. In stage four from each selected union council one village was randomly selected. 100 respondents were selected through proportional allocation sampling technique as follows (Cochran, 1977):

ni= n/N x Ni----------------------- (1)

Where;

ni = Number of sample respondents in ith village

n = Total sample size

Ni = Total number of wheat growers in ith village

N = Total number of wheat growers

Primary data for the current study were collected through well-structured questionnaire during 2009-10, while secondary data were collected from various published and unpublished sources. An interview schedule was prepared in the light of study objectives. The primary data regarding wheat yield, inputs used in the production process and other factors involved in the production process were collected from 100 wheat growers.

Analytical framework

Review of literature shows that estimation of technical efficiency has been performed by two approaches namely parametric and non-parametric. Parametric approach makes use of econometric method whereas non-parametric approach is based on mathematical method (Data Envelopment Analysis). Battese (1992), Bravo-Ureta and Pinheiro (1997) and Coelli and Perelman (1999) have discussed advantages and disadvantages over each other.

The econometric method is stochastic and it separates the effect of random error (noise) from the effect of inefficiency. The non-parametric method is nonstochastic and lumps noise and inefficiency and is referred to as combination inefficiency.
The econometric method is parametric and restricts the effects of misspecification of functional form (of both inefficiency and technology) with inefficiency. The non-parametric method is non-parametric and less susceptible to this specification error.

However literature review reveals that econometric method is widely used to estimate technical efficiency of firms (Bravo-Ureta and Reiger, 1991; Kalirajin, 1991; Battese and Hassan, 1999; Hassan and Ahmad, 2005; Idiong, 2007; Feng, 2008; Kamruzzaman and Islam, 2008; Tchale, 2009; Theophilus, 2011). According to econometric method stochastic frontier analysis (SFA) was carried out.

Slochostic frontier analysis

Aigner et al. (1977) and Meeusen and van den broeck (1977) independently developed stochostic frontier analysis (SFA) also called composed error model. Their work was based upon the measure of technical efficiency by Farrell in 1957. Assuming a suitable production function, we define the stochastic production frontier as follows:

Yi= f (Xi βi) (i = 1,2,------n) (2)

Yi = βiXi + εi (i = 1,2,--------n) (3)

Where;

Yi = output obtained by ith farmer

Xi = inputs for ith farmer

βi = parameters

єi = composed random error

єi = νi - µi

Where;

νi is symmetric (- ∞ < νi < ∞) and covers the random (stochastic) effects which are beyond the control of farmers i.e., weather, breakdowns and natural disasters etc. It is assumed that vi is independently and identically distributed as N (0, σ2v) (Gujarati and Porter, 2009).

Farm specific technical inefficiency was depicted by µi. In other words it estimates the shortfall of output (Yi) from its maximum possible output given the stochastic frontier [f (Xij, β) + νi] (Aigner et al. 1977). ui comes from a N ( 0, σ2u ) is half normally distributed below 0. ui and vi are independent of each other (Gujarati and Porter, 2009). The term νi and µi are also assumed to be independent of physical inputs Xi.

In the study at hand the stochastic frontier production function approach was used to study the effect of socioeconomic variables on the technical efficiency/inefficiency.

Model specification

Stochastic frontier production model was employed to estimate the technical efficiency in wheat production. This method separates technical inefficiency effects from effects of those factors, which cannot be controlled by the farmers. The first problem encountered with specification of stochastic frontier production model is the choice of functional form. It is desirable to choose that functional form, which meet the economically reasonable restrictions and does not present unreasonably complex estimation problems (Fuss and Mundlak, 1978). In the present study technical efficiency was estimated within the framework of Cobb-Douglas stochastic frontier production function. Cobb-Douglas production functional form has been utilized because of its ease of interpretation and estimation. Moreover, flexible functional form imposes the problem of multicollinearity. Cobb-Douglas stochastic frontier production function for this study is expressed as follows:

In Yi = Σni=1 β i In x i + εi----------------(4)

Where;

Yi = Output of wheat in kilograms per hectare

X1 = Land under wheat crop in hectares (As most of the area under study is irrigated, therefore, land is assumed to be of homogeneous quality)

X2 = Number of labour days (man days) per hectare

X3 = Chemical fertilizers in kilograms per hectare

X4 = Number of tractor plough hours per hectare

X5= Farm yard manure in kilograms per hectare

єi = Composed error term

ln = Natural log

β0 = Intercept

βi = Parameters to be estimated

Estimation of SFA model

Maximum likelihood estimation (MLE) technique was employed for estimation of SFA (Green, 1980). The basic idea of the ML principle is to choose the parameter estimates (β, σ2ε) to maximize the probability of obtaining the data.

ln L = n/2 In [π/2] – n/2 ln σ2 + ∑ni=1 ln [1– F [ εi √γ / σ √(1–γ) ]] – 1/ 2 σ2 ∑n i-1 є2i ---------- (5)

єi = Yi -Xi β (6)

Where; σ2v and σ2u are variances of v and u respectively,

σ2ε =σ2v + σ2u,

γ = σu/ σv

F = Cumulative density function (cdf), estimated at (λ є / σu,)

The MLE of β, γ and σ2ε at which the value of the likelihood function is the maximum are obtained by setting the first order partial derivatives with respect to β, γ and σ2ε equal to zero and solving these non-linear equations simultaneously. Equation (3.8) can be estimated by using a non-linear optimization algorithm to find the optimal values of the parameters.

Estimation of technical inefficiency

For the estimation of technical efficiency it is assumed that vi is distributed as N (0, σ2v) and ui is half normally distributed as N (0, σ2u).

Technical inefficiency model is expressed as follows:

µi = δ0 + δ1 Z1i + δ2 Z2i + δ3 Z3i + δ4 Z4i + ωi-------(7)

Where;

µi = Farm specific technical inefficiency

Z1i = Age of the ith farmer in years

Z2i = Farming experiences of the ith farmer in years

Z3i = Education of the ith farmer in years

Z4i = Land under wheat crop of the ith farmer in hectares

ωi = Random error term normally distributed with 0 mean and constant σ2

δ0 and δi are the parameters to be estimated

Estimation of technical efficiency/inefficiency of individual farms

Table 1. Summary statistics of survey variables in technical efficiency model

Variables	Unit	Mean	Std. Dev.	Minimum	Maximum
Yield	kg	2424.15	321.20	1927.46	3113.59
Land under wheat	ha	1.45	1.06	0.10	5.46
Labor	MD	37.62	2.11	34.35	43.24
Chemical fertilizer	kg	267.19	44.76	185.33	398.12
Tractor plough	Hrs	10.00	1.40	7.41	12.36
FYM	kg	3080.79	1172.96	0.00	4497.40
Farmers’ age	Years	47.89	8.24	24.00	68.00
Farming experience	Years	26.96	9.51	8.00	50.00
Farmers’ education	Years	5.83	5.47	0.00	16.00

Source: Survey Data, 2009-10

For the estimation of technical efficiency of individual wheat farms, the following formula was applied.

TEi = Yi / Yi* ----------- (8)

Where

Yi = Observed output of ith farm

Yi* =frontiers output of ith farm that can be achieved

TEi = Technical efficiency of ith farm that ranges between 0 and 1.

For the estimation of technical inefficiency of individual wheat farms, the following formula was applied.

TIi = 1 - TEi ------------ (9)

TIi = 1 – [Yi / Yi*]

Where

TIi = Technical inefficiency of ith farm that ranges between 0 and 1.

Normality test (Jarque-Bera test of normality)

The Jarque-Bera (JB) test of normality is an asymptotic (large sample) test. It uses the formula as:

JB = n [(S2 / 6) + (K-3)2 / 24]

Where

n is sample size, S is Skewness coefficient and K is kurtosis coefficient. Under the null hypothesis that the residuals are normally distributed, JB statistic follows the chi-square distribution (Gujarati and Porter, 2009).

As the estimated p-value (0.124) is insignificant, suggesting that we cannot reject the hypothesis that data is normally distributed.

Results and Discussion

Summary statistics of survey variables in technical efficiency model

Table 1 indicates summary statistics of survey variables in technical efficiency model for District Peshawar. The average yield of wheat in district Peshawar was 2424.15 kilograms per hectare (kg ha-1) ranging from 1927.46 to 3113.59 kg ha-1 with the standard deviation of 321.20 kg ha-1. Average land under wheat crop was 1.45 ha ranging from 0.10 to 5.46 ha with the standard deviation of 1.06 ha. Average numbers of labour were 37.62 man days ranging from 34.35 to 43.24 man days with the standard deviation of 2.11 man days. Average application of chemical fertilizer was 267.19 kg ha-1 ranging from 185.33 to 398.12 kg ha-1 with the standard deviation of 44.76 kg ha-1. Average tractor plough Hrs ha-1 was 10.00 ranging from 7.41 to 12.36 Hrs ha-1 with the standard deviation of 1.40 Hrs ha-1. Average application of FYM was 3080.79 kg ha-1 ranging from 0 to 4497.40 kg ha-1 with the standard deviation of 1172.96 kg ha-1.

Log Likelihood Ratio test for selection of functional form

The formula for the LR test statistic is as under.

LR statistic = 2 [ ln H0 / ln H1 ]

= - 2 [ ln H0 - ln H1 ] ------ (10)

Where

ln H0 denotes the log likelihood of the model when it is assumed that inefficiency is absent and ln H1 the log likelihood of the model when it is assumed that inefficiency is present. If LR statistic is significant, then we reject the null hypothesis of no technical inefficiency. Our calculated LR statistic (15.59) is greater than the critical value (12.59), so we reject the null hypothesis in favour of presence of inefficiency.

Table 2. MLE results of the sampled farmers

Variables	Unit	Parameters	Coefficients	Std. errors	t ratio
Constant		β0	3.950	0.333	11.861**
Ln Land under wheat	ha	β1	0.052	0.019	2.736**
Ln Labor	MD	β2	0.566	0.108	5.242**
Ln Chemical fertilizer	kg	β3	0.130	0.055	2.363*
Ln Tractor plough	Hrs	β4	0.438	0.054	8.111**
Ln FYM	kg	β5	-0.0035	0.0016	-2.188*
Technical inefficiency model
Constant		δ0	-55.401	39.053	-1.418
Farmers’ age	Years	δ1	0.921	0.754	1.221
Farming experience	Years	δ2	-0.318	0.291	-1.092
Farmers’ education	Years	δ3	-0.359	0.164	-2.189*
Land under wheat	ha	δ4	3.918	2.800	1.400
Sigma-U		σu	0.049
Sigma-V		σv	0.026
Gamma		.γ	0.780
Mean TE		Xmean	0.620
Minimum TE		Xmin	0.340
Maximum TE		Xmax	0.880

** and * indicates significance at 0.01 and 0.05 probability respectively; Source: Survey Data, 2009-10

Table 3. Distribution of individual farmers according to technical efficiencies

Efficiency level	Number
≤ 0.50	13
0.51-0.60	20
0.61-0.70	42
0.71-0.80	15
0.81-0.90	10
≥ 0.91	00
Mean TE	0.62

Source: Survey Data, 2009-10

MLE results of the sampled farmers

Table 2 represents MLE results of technical efficiency of the sampled farmer in Peshawar district. The analysis depicted that explanatory variables i.e., land under wheat crop, labor, chemical fertilizer and tractor plough had positive relationship with wheat production and are found statistically significant. The estimated elasticity for these variables revealed that one percent increase in land under wheat crop, labour, chemical fertilizer and tractor plough would raise the wheat yield by 0.052, 0.566, 0.130 and 0.438 percent respectively and were found statistically significant. The coefficient of farm yard manure (FYM) was -0.0035 but is not according to our expected positive sign with almost negligible magnitude. This negative coefficient may be due to over use of FYM and farmer is operating in stage III of production in the application of FYM (Debertin, 2012). These findings are in line with the findings of Hassan and Ahmad (2005), Kolawole and Ojo (2007), Singh (2007), Hasan and Islam (2010), Nwaru et al. (2011) and Shaheen et al. (2011).

The estimated value of technical efficiency ranges from 34 to 88 per cent for the farms in the sample, with an average of 62 percent. This means that if the average farmer in the sample was to achieve the technical efficiency level of its most efficient counterpart, then the average farmer could increase wheat yield by 30 per cent [i.e., 1− (62/88) = 0.2955]. Similarly the most technically inefficient farmer could enhance wheat yield by 61 per cent [i.e., 1− (34/88) = 0.6136].

Comparing the mean technical efficiency from this study with other studies revealed that the mean technical efficiency is not far from the findings of Ahmad et al. (2002), Ahmad et al. (2005), Dolisca and Jolly (2008), Ghaderzadeh and Rahimi (2008) and Sadiq et al. (2009) with the mean technical efficiency of 68, 67, 63, 67 and 68% respectively. The average technical efficiency recorded from this study is higher than the one recorded by Ahmad (2003), Gul et al. (2009), Tchale (2009) and Shaheen et al. (2011) with an average technical efficiency of 43, 20, 53 and 51% respectively. Similarly the average technical efficiency recorded from this study is higher than the one recorded by Villano and Fleming (2004), Abedullah et al. (2006), Kolawole and Ojo (2007), Nchare (2007), Hossain et al. (2008), Ogundari (2008) and Hasan and Islam (2010) with an average technical efficiency of 79, 84, 73, 89, 75, 75 and 84%, respectively.

The estimated coefficients of the explanatory variables for the technical inefficiency function are represented in the lower part of table 2. The relationship between farmers’ age and technical inefficiency was positive but statistically insignificant implied that farmers’ age has no significant effect on technical efficiency in district Peshawar. The coefficient of farming experience was negative and statistically insignificant. The coefficient of farmers’ education was negative and statistically significant. The relationship between technical inefficiency and land under wheat crop was positive but statistically insignificant.

Distribution of individual farmers according to technical efficiencies

Table 3 shows the frequency distribution of individual farmers of District Peshawar. Average technical efficiency of wheat producers were 0.62. The lowest efficiency ratio for Peshawar was 0.34 and highest efficiency ratio was 0.88. Results further revealed that 42 percent of District Peshawar farmers lied between 0.61-0.70 in the efficiency ratio.

Conclusions and Recommendations

Land under wheat crop, labour, chemical fertilizer and tractor plough and FYM were found to be the major determinants of wheat productivity. Results indicated that one percent increase in value of land under wheat crop, labour, chemical fertilizer, tractor plough and FYM would raise the wheat yield by 0.052, 0.566, 0.130, 0.438 and -0.0035 percent respectively and were found statistically significant.

The estimated coefficient of farmers’ age and technical inefficiency was positive and statistically insignificant implied that farmers’ age was not significantly affecting technical efficiency of wheat producers. The coefficient of farming experience was negative but statistically insignificant. The coefficient of farmers’ education was negative and statistically significant which implied that inefficiency decreases with increase in the farmers’ education in the study area. The relationship between technical inefficiency and land under wheat crop was positive but statistically insignificant.

These results suggest that yield of wheat may be achieved from existing resources and techniques of farming. More use of labour in different activities would increase the wheat production. Tractor plough increased wheat production implying that wheat producers should apply more tractor hours to fully prepare the soil for wheat cultivation. This would increase wheat production in the study area. The analysis revealed that the technical efficiency increases with the increase in the level of education. Therefore Government of Pakistan should focus on formal as well as informal education in the country. Government should also need to provide better educational opportunities to the rural population and extension education to wheat producers.

References

Ahmad, M. 2003. Agricultural productivity, efficiency, and rural poverty in irrigated Pakistan: A stochastic production frontier analysis. The Pakistan Development Review, 42(3): 219–248.
Ahmad, M., G. M. Chaudhry and M. Iqbal. 2002. Wheat productivity, efficiency and sustainability: A stochastic production frontier analysis. The Pakistan Development Review, 41(4) Part II: 643–663.
Ahmed A. E., F. Kuhlmann, M. Mau, H. A. Elobeid and E.M. Elamin. 2005. Analysis of factors affecting sorghum production in the Gezira Scheme, Sudan and implications on the household food security. Paper presented in conference on International Agricultural Research for Development. Stuttgart-Hohenheim, October 11–13.
Aigner, D. J. C., A. K. Lovell and P. Schmidt. 1977. Formulation and estimation of stochastic frontier production function model. J. Econ., 6: 21–37.
Battese, G. E. 1992. Frontier production functions and technical efficiency: A survey of empirical application in agricultural economics. Agric. Econ. 7: 185-208.
Battese, G. E. and S. Hassan. 1999. Technical efficiency of cotton farmers in the Vehari district of Punjab, Pakistan. Pakistan Journal of Applied Economics, 15: 41-53.
Bravo-Ureta, B. E. and L. Rieger. 1991. Dairy farm efficiency measurement using stochastic frontiers and neo classical duality. American Journal of Agricultural Economics, 73(2): 421-428.
Bravo-Ureta, B. E. and A. E. Pinheiro. 1997. Technical, economic, and allocative efficiency in peasant farming: Evidence from The Dominican Republic. The Developing Economies, XXXV-1: 48–67.
Byerlee, D. and A. Siddiq 1994. Has the green revolution been sustained? The quantitative impact of the seed-fertiliser revolution in Pakistan revisited. World Development, 22(9): 1345–1361.
Cochran, W. G. 1977. Sampling Techniques, 3rd Edition. John Wiley and Sons, New York. pp. 37–45.
Coelli, T and S. Perelman. 1999. Comparison of parametric and non-parametric distance functions: With application to european railways. EJOR, 117(2): 326-339
Debertin, D. L. 2012. Agricultural Production Economics, 2nd Edition. Macmillan Publishing Company, New York.
Debreu, E. 1951. The coefficient of resource utilization. Econometrica, (19): 273–292.
Dolisca F, Jolly CM (2008). Technical efficiency of traditional and nontraditional crop production: A case study from Haiti. World. J. Agri. Sci. 4(4): 416-426.
Farrell, M. J. 1957. The measurement of productive efficiency. Journal of the Royal Statistical Society. 120(3): 253–290.
Feng, S. 2008. Land rental, off-farm employment and technical efficiency of farm households in Jiangxi Province, China. China Centre for Land Policy Research, Nanjing Agricultural University, 55(4): 363–378.
Food and Agricultural Organization (FAO). 2009. Year wise world wheat statistics, www.faostat.fao.org.
Fuss, M. and Y. Mundlik. 1978. A survey of functional form in econometrics analysis of production. Poduction Economics: A dual approach to theory and application. North Holand. 234–237.
Ghaderzadeh, H. and M. H. Rahimi. 2008.Estimation of technical efficiency of wheat farms “A case study in Kurdistan Province, Iran. American-Eurasian J. Agric. & Environ. Sci., 4(1): 104-109.
Government of Khyber Pakhtunkhwa. 2005. NWFP development statistics, Planning and development department, Khyber Pakhtunkhwa.
Government of Khyber Pakhtunkhwa. 2008. Bureau of statistics, Crop Reporting Services, Khyber Pakhtunkhwa.
GoP. 2008. Economics Survey of Pakistan, 2007-08. Economic advisory Wing. Finance Division, Islamabad, Pakistan.
GoP. 2009. Agricultural Statistics of Pakistan, 2008-09. Ministry of Food, Agriculture and Livestock, Economic Wing, Islamabad, Pakistan.
Government of Khyber Pakhtunkhwa. 2010. Revenue department, Potwar of district Peshawar, Khyber Pakhtunkhwa.
Gujarati, D. N. and D. C. Porter. 2009. Basic Econometrics, 4th Edition. Mc Graw Hill Inc., New York.
Green, W. H. 1980. Maximum Likelihood Estimation of frontier production function. Journal of Econometrics, 13: 27–56.
Gul, M., B. Koc., E. Dagistan., M. G. Akpinar and O. Parlakay. 2009. Determination of technical efficiency in cotton growing farms in Turkey: A case study of Cukurova region. African Jounal of Agricultural Research, 4(10): 944-949.
Idiong, I. C. 2007. Estimation of farm level technical efficiency in small scale swamp rice production in Cross River State of Nigeria: A stochastic frontier approach. World Journal of Agricultural Sciences, 3(5): 653–658.
Hassan, S. and B. Ahmad. 2005. Technical efficiency of wheat farmers in mixed farming system of the Punjab, Pakistan. International Journal of Agriculture & Biology, 7(3): 431–435.
Hasan and Islam. 2010. Technical inefficiency of wheat production in some selected areas of Bangladesh. Bangladesh J. Agril. Res., 35(1): 101-112.
Hossain, M. A., M. K. Hasan and Q. Naher. 2008. Assessment of technical efficiency of potato producers in some selected areas of Bangladesh. J. Agric. Rural Dev., 6(1&2): 113-118.
Kalirajan, K. P. 1991. The importance of efficient use in the adoption of technology: A micro panel data analysis. Journal of Productivity Analysis, 2: 113-126.
Kamruzzaman, M. and M. H. Islam. 2008. Technical efficiency of wheat growers in some selected sites of Dinajpur district of Bangladesh. Bangladesh Journal of Agricultural Research, 33(3): 363–373.
Knight, F. 1933. The Economic Organization. Harper and Row: New York.
Kolawole, O. and S. O. Ojo. 2007. Economic efficiency of small scale food crop production in Nigeria: A stochastic frontier approach. J. Soc. Sci., 14(2): 123–130.
Koopsman, T. C. 1951. An analysis of production as an efficient combination of activities, in Koopsman, T. C. (Ed.), activity analysis of production and allocation. Cowles Commission for Research in Economics, Monograph No: 13, Wiley, New York.
Lall, P., D. W. Norman, and M. R. Langemeier. 2001. A comparative analysis of productive efficiency among Kansas crop farms: Small versus large farms. Journal of the ASFMRA. 99-106. www.asfmra.org
Meeusen, W. and Van den Breock. 1977. Efficiency estimation from Cobb-Douglas production functions with composed error. International Economic Review, 18(2): 435–444.
Nchare, N. 2007. Analysis of factors affecting technical efficiency of Arabica coffee in Camroon. African Economic Consortium, Nairobi, AERC Research paper No. 163.
Nishimizu, M and J. M. Page. 1982. Total factor productivity growth, technological progress and technical efficiency change: Dimensions of productivity change in Yugoslavia, 1965-78. Economic Journal, 92: 920-936.
Nwaru, J. C., B. C. Okoye and P. C. Ndukwu. 2011. Measurement and determinants of production efficiency among small holder sweet potato (Ipomoea Batatas) farmers in Imo State, Nigeria. European Journal of Scientific Research, 59(3): 307-317.
Obare, G. A., D. O. Nyagaka, W. Nguyo and S. M. Mwakubo. 2010. Are Keynan small holders allocatively efficient? Evidence from Irish potato producers in Nyandarua north district. Journal of Development and Agricultural Economics, 2(3): 78-84.
Ogandri, K. 2008. Resource productivity, allocative efficiency and determinants of technical efficiency of rainfed rice farmers: A guide for food security policy in Nigeria. Agric. Econ. 54(5): 224-233.
Rajarams, P. R. Hobbs, and P. W. Heisey (1998) Review of Pakistan’s wheat and maize research systems. Report submitted to PARC by a multidisciplinary team of CIMMYT Scientists visited Pakistan.
Sadiq, G., Z. U. Haq, F. Ali, K. Mehmood, M. Shah and I. Khan. 2009. Technical efficiency of maize farmers in various ecological zones of AJK. Sarhad J. Agric. 25(4): 607-610.
Singh, S. 2007. A study on technical efficiency of wheat cultivation wheat cultivation in Haryana. Agricultural Economics Research Review, 20: 127-136.
Shaheen, S., M. H. Sial, G. Sarwar and R. Munir. 2011. Nexus between human capital and technical efficiency of cauliflower growers in soon valley, Punjab: A panel data analysis. International Journal of Humanities and Social Science, 1 (14): 129–135.
Shuwu, H. T. 2006. Profit efficiency among rice producers in eastern and northern Uganda. Unpublished PhD thesis submitted to the school of graduate studies of Makerere University.
Srinivasan, G. 2001. A comment made in business world. Vol. 20, Issue 37, 16-22 January.
Tchale, H. 2009. The efficiency of small-holders agriculture in Malawi. AFJARE, 3(2): 101–121.
Theophilus, G. M. 2011. Economic efficiency of smallholder sweet potato producers in Delta State, Nigeria: A case study of Ughelli South Local Government Area. Research Journal of Agriculture and Biological Sciences, 7(2): 163-168.