Application of utility-efficient programming to ...

Cınemre & Ceyhan—Application utility-efficient programming New Zealand Journal of Crop and of Horticultural Science, 2006, Vol. 34: 381–391 0014–0671/06/3404–0381 © The Royal Society of New Zealand 2006

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Application of utility-efficient programming to determine economic efficiency of Turkish farmers in the central Anatolian region

Hüseyİn Avnİ Cİnemre Vedat Ceyhan* Department of Agricultural Economics Faculty of Agriculture University of Ondokuz Mayis 55139 Samsun, Turkey email: [email protected] Abstract  This research generated stochastically efficient farm plans in the relevant range of risk aversion and calculated the efficiency measures for the three representative farm sizes in the central Anatolian region of Turkey. Utility-efficient programming was used to determine an efficient set of farm plans. Research results showed that total net farm revenue increases for all farm sizes as risk aversion decreases. An economic efficiency score of 0.54 for both small and medium size farms indicated that there is considerable scope for farmers to increase their total net farm revenue using existing technology without additional inputs. Allocative and technical inefficiencies of sampled farms were 0.22 and 0.24, respectively. Thus, supplying complete technical packages for farms may stimulate the adoption of new technologies. Focusing on production practices and marketing efficiency in farmers’ training and extension programmes may also help to increase economic efficiency in the research area. Keywords  stochastic efficiency; utility-efficient programming; risk aversion; efficiency analysis

*Author

for correspondence. H05088; Online publication date 20 November 2006 Received 30 July 2005; accepted 24 July 2006

INTRODUCTION For several decades, efficiency in farm practices has received particular attention as a means to accelerate agricultural development. There has been much debate on the efficiency of agricultural production especially in developing countries, yet efficiency of resource use is one of the determinants of agricultural development. Profit maximisation and efficiency are interrelated. Baumol (1977) suggested that the theory of production economics is concerned with optimisation, and this implies efficiency. The analysis of efficiency focuses on the possibility of producing the optimal level of output from a given set of resources (Coelli et al. 1998). Policy makers in developing countries therefore focus on improving agricultural productivity and efficiency. Most of the studies on efficiency are based, directly or indirectly, on both the seminal work of Farrell (1957) and the “poor but efficient hypothesis” advanced by Schultz (1964). Much empirical research has been undertaken to test the allocative or price efficiency of farms and the link between farm size and efficiency by using production function, parametric or non-parametric frontier function, and mathematical programming with cross-sectional, panel, or aggregate data (Chennareddy 1967; Sahota 1968; Lau & Yotopaulos 1971; Sidhu 1974; Papadas & Dahl 1991; Laura Gow & Langemeier 1999; Lerman 2001; Tzouvelekas et al. 2001). Although some criticisms have been directed to the applicability of the neoclassical approach to farm production by many authors (Lipton 1968; Dillon & Hardaker 1971; Upton 1979), and efficiency hypothesis as a standard measure of economic performance has been challenged by Pasour (1981), many of the earlier studies on farm economic efficiency models have been mainly based on the assumption that farmers maximise their profits with adequate information. Considering the presence of inadequate information, farmers’ objective functions involve elements rather than profit. Wolgin (1975) stated that traditional tests of economic efficiency in agriculture are generally mis-specified when

382 New Zealand Journal of Crop and Horticultural Science, 2006, Vol. 34 farmers make decisions under risk. Since risk plays an important role both in the use of inputs and production of outputs, some of the previous studies have focused on risk in the production process (Just 1974; Aigner et al. 1977; Just & Pope 1978; Mapp et al. 1979; Persaud & Mapp 1979; Chambers 1983; Kumbhakar 1987; Battese & Coelli 1995; Battese et al. 1997). Thus, this framework extends and includes producers’ risk preferences into empirical analysis by Love & Buccola (1991), Kumbhakar (1993), Saha et al. (1994), Chavas & Holt (1996), Isik & Khanna (2002), Settlage & Preckel (2002), Shaik & Helmers (2003). Currently, the link between efficiency and the producer’s attitude towards risk has become popular for researchers. Kumbhakar (2002) contributed to the literature on production risk by including production risk and risk preferences, technical inefficiency, and producers’ attitudes toward risk. Villano et al. (2005) used Kumbhakar’s multi-step procedure to incorporate technical efficiency with risk preference and production risk in the Philippines. Alternately, some researchers preferred to incorporate farmers’ risk preferences, revenue fluctuations, and resource restrictions by using mathematical programming where risk aversion was included into the decision makers’ objective functions (Kaiser & Appland 1989; Kingwell 1994; Torkamani & Hardaker 1996; Lien & Hardaker 2001, Hardaker et al. 2004). However, at the time of writing, few studies have addressed the issue of efficiency in Turkish agriculture. Some studies have been performed by incorporating risk into efficiency analysis in Turkish smallholder farms (Günden et al. 1998; Zaim & Çakmak 1998; Aktürk 2000; Demirci 2001). The objectives of this study are to: (1) examine the effects of the changes in risk aversion on the optimal cropping pattern for farms in the Central Anatolian region; and (2) determine the relationship between risk aversion and efficiency measures. METHODOLOGY Utility-efficient programming There have been various methods for incorporating risk in mathematical programming models in agriculture. These methods are reviewed in studies by Anderson et al. (1977) and Hardaker et al. (1991, 1997). Quadratic risk programming (Freund 1956) and its linear approximations such as Minimisation of Total Absolute Deviation (MOTAD) (Hazell 1971) are well-known applications of stochastic

efficiency analysis to whole farm planning. However, direct maximisation of expected utility is superior to MOTAD and quadratic programming techniques owing to the presence of assumptions of either normally distributed net income for risk averse decision makers (Collender & Chalfant 1986) or a quadratic utility function (Hanoch & Levy 1960). The direct maximisation of expected utility techniques can be applied only to risk averse individuals whose utility functions are known. However, there are obvious difficulties in maximisation of utility. Each farmer may have a different utility function requiring a different set of specifications and utility elicitation. When there are many decision makers, it would be desirable to develop an efficient set of farm plans following the stochastic dominance with respect to a function (SDRF). Patten et al (1988) suggested utility-efficient (UE) programming to avoid these difficulties. UE programming integrates the concept of SDRF into whole farm planning and generates a set of solutions that are stochastically efficient for all decision makers whose coefficient of absolute risk aversion is in the relevant range. Ogisi et al. (1994) have demonstrated that the results are identical to those obtained using SDRF. UE programming was selected for this research since it requires limited information about farmers’ risk attitudes. Moreover, the UE programming model can be solved using a non-linear algorithm or by approximating the utility function using linear or quadratic segments (Patten et al. 1988). Since the utility function for the summex is concave, the latter approach was used in this study. The formulation of the model is as follows: E[U ] = k Pk ( gk ′ wk + λhk ′ wk ) Maximise Subject to Ax ≤ d –ck′ x + vk′ wk = 0 i wk ≤ 1 x, wk ≥ 0 k = 1,……,K Where E[U] is the expected utility, g and h are two parts of the utility function, Pk is the vector of probabilities of activity gross income per unit outcomes of state k, wk is a q by 1 vector of weights representing each of the q segments of g and h for each state k, gk and hk are q by 1 vectors of calculated values of g and h, respectively. Corresponding to the values of zk (total net income) in vk, all state for k, λ is a non-negative parameter, A is the matrix of input-output coefficients, x is the vector of activity levels, d is the vector of the resource constraints, ck is the income share of activities for state k, vk is a

∑

Cınemre & Ceyhan—Application of utility-efficient programming q by 1 vector of values of zk for state k chosen as corner values for the linear segmentation of g and h, and i is a q by 1 vector of ones. The risk attitude of a decision maker is commonly derived by the equally likely certainty equivalent (ELCE) method (Hardaker et al. 1997). In this method, too many incorrect answers are received. Recently, researchers often guessed the degree from the plausible range of relative risk aversion, rr, defined as the elasticity of marginal utility of wealth. Arrow (1965) stated that ra = rr /w, where w denotes wealth. Since farmers’ assets and debts were known, coefficients of absolute risk aversion were guessed for a range of rr, 0.5–4, in this research. Thus, the g and h functions used were g = –exp (–0.0002z) and h = –exp(–0.000002z). The programming models developed for the representative farms in the research area included 24 constraints, e.g., land, rotational constraints, seasonal constraints on labour, seasonal working capital, and barn and feed requirements for dairy herds and sheep. Production activities in the models were paddy, soybean, rape seed, maize, wheat, maize for silage, sugar beet, dry bean, lentil, chickpea, dry onion, tomatoes, lettuce, dairy, and sheep fattening. Additional activities included in the models were labour hiring, borrowing working capital, and feed buying. Farm attributes The data for this research originated from the Kızılırmak basin of the central Anatolian region which comprises some 5200 farms. From these farms, a random sample of 216 farms was selected. The sample farms provided data for the year 2001. Time series data covering each of the years 1987 through 2001 on yields and prices of different crops cultivated in the area together with milk and meat prices were obtained from the regional production statistics and research station records for the region. The elements of production costs and their values Table 1 

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were also collected from the local research station records. Since the production structure among sample farms varies considerably, statistical cluster analysis was applied to ensure group homogeneity (Hair et al. 1998). The cluster analysis divided the sample farms into three class sizes. The representative farms of each group were constructed by using the average value of each group. The representative farms were small (1.1 ha), medium (5.063 ha), and large (8 ha). Table 1 compares the three different average farms in the sample by some major characteristics. Small farms account for half of the sample. Large farms represent 14% of the sample. As expected, there is a negative relationship between farm size and net farm return. Net farm revenue per ha is us$690 for the existing cropping plan of small farms whereas that of medium and large farms are us$617 and us$605, respectively. Similarly, increasing farm size resulted in a decrease of land-labour and capital-land ratios in the research area (see Table 1). Based on the results of the interviews, vocational training levels of farm operators were low whereas the farming system and the farmers’ skills were moderate. Access to institutions such as extension services, cooperatives, and credit was very weak. The number of contacts with extension services had a median value of 2 times a year. Furthermore, 64% of the farm operators were members of at least one agricultural cooperative but they contacted the cooperatives only 3 times a year. They do not have much access to external credit. The average external credit used is only us$700 per year. Both farmers’ subjective judgments and historical data on gross margins of each production activity were used as a basis for the probability distributions incorporated in the models. To preserve aspects of the stochastic dependency in the historical data, a procedure suggested by Hardaker et al. (1997) was followed. First, the effects of inflation and time on the historical data were removed. The wholesale price

Summary of statistics for the representative farms.



Small

Medium

Large

Farm size (number) Net farm returns (us$ ha) Land/labour (ha/person) Operational capital /land (US$/ha) Vocational training (level)*

110 690 0.18 5187 1

76 617 0.79 4065 1

30 605 1.13 3562 1.5

*1, on job training; 2, apprenticeship; 3, vocational school; 4, high school or university.

384 New Zealand Journal of Crop and Horticultural Science, 2006, Vol. 34 index was used to adjust the individual activities to a common base (2001 prices). Gross margins were then adjusted for time trend using regression. To reflect the chance that similar conditions to those in each of the data years prevailed in the planning period, equal probabilities to the historical years or “states of nature”, from 1987 to 2001 were assigned. The triangular distribution method was used to obtain the subjective marginal distributions of gross margins of each production activity for the sample farms. Judgments of the lowest, highest, and most likely values of gross margin of individual activities for farms in the research area were obtained from an expert group of agricultural researchers. Next, means and standard deviations of activity incomes were calculated assuming that the individual subjective gross margins were approximately triangularly distributed (See Appendix 1). The historical gross margin series was reconstructed, using the formula (Hardaker et al. 1997): σ( s ) j x (n)ij = E x (s) j +  x (h)ij − E x (h) j    σ( h ) j

(

)

(

)

where x(n)ij is the synthesised gross margin for activity j in state i, E(x(s)j) is the subjective mean of the gross margin of activity j, x(h)ij is the corrected historical gross margin of activity j in state i, E(x(h)j) is the mean gross margin from the corrected historical data for activity j, σ(s)j is the subjective standard deviation of the gross margin for activity j, and σ(h)j is the standard deviation of the gross margin for activity j from the corrected historical data. Means and standard deviations for the reconstructed series have been computed while preserving the cross-sectional stochastic dependencies embodied in the historical data. The “state of nature” matrix in Appendix 1 is the discrete distribution of expected activity gross margins for the first year in the model.

Efficiency analysis Economic efficiency (EE) is the degree of ability of a farmer to produce a given level of output at least cost or obtain a maximum level output from a given combination of inputs. EE may be divided into allocative (price) and technical efficiencies (Farrell 1957). Allocative or price efficiency (AE) refers only to the adjustment of inputs and outputs to reflect relative prices. A farm is allocatively efficient when production inputs are allocated according to their relative price. Alternately, technical efficiency refers to the relationship between inputs and outputs independently of all prices. A farm is technically

efficient (TE) when it produces the maximum obtainable level of output from a given amount of inputs, i.e., it must operate at the production possibility frontier. There have been some doubts in using the classical interpretation of allocative and technical efficiencies in a risky world. Torkamani & Hardaker (1996) suggested that in a world where risk and risk aversion behaviour is acknowledged, the usual interpretation of allocative and technical efficiency concepts requires some revision. Since this analysis embodies risk and risk aversion behaviour, the usual interpretation of efficiency concepts was revised by adding certainty equivalents and expected values as alternative performance measures. The procedure suggested by Torkamani & Hardaker (1996) was used in measuring the level of allocative and technical efficiencies. First, the expected total net farm revenue, E[TFNRei], for the existing resource allocations were estimated for three representative farms. Second, allocatively efficient level of total net revenues (E[TFNRpi]) were estimated for three representative farms by using UE programming under present technology, the existing level of resources, and a specified degree of risk aversion. Third, technically efficient level of net revenues (E[TFNRti]) was identified based on the farms with the most efficient input-output coefficients for each crop across all groups. These farms were selected by calculating an index of expected net revenue per ha of each crop for all farms in that group relative to the expected net revenues per ha of that crop for the group’s representative farms. These indices were ranked in ascending order and values at the 95 percentile for each crop were selected. This procedure revealed the most efficient level of expected net revenue per ha for each crop and each group of farm. Next, E[TFNRti] values were estimated through the UE programming method for each representative farm with the same resource endowments as in the other models discussed above but using the TE activity returns. The level of allocative and technical efficiencies for each representative farm and degree of risk aversion were defined as: AEi = E[TFNRei]/E[TFNRpi] TEi = E[TFNRpi]/E[TFNRti] After the estimation of AEi and TEi , the overall efficiency index for the representative farm i (EEi) was calculated from their product (Farrell 1957), which is expressed as: EEi = E[TFNRei]/E[TFNRti]

0.495 0.333 0.336 0.337 0.347 0.352 0.378 0.390 0.412 0.550 0.550

0.334 0.366 0.367 0.367 0.341 0.312 0.158 – – – –

– – – – – – – – – – –

– – – – – – – – – – –

– 0.072 0.061 0.057 0.040 0.033 – – – – –

0.063 0.075 0.061 0.057 0.040 0.033 – 0.005 0.073 0.455 0.550

– 0.038 0.030 0.028 0.047 0.073 0.221 0.390 0.412 0.550 0.550

0.271 0.291 0.306 0.310 0.326 0.330 0.343 0.329 0.276 – –

– – – – – – 0.001 0.092 0.276 – –

0.217 0.241 0.269 0.277 0.315 0.330 0.342 0.228 – – –

– 0.038 0.030 0.028 0.021 0.022 0.036 0.056 0.063 0.095 –

– 3.109 5.127 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582

– – – – – – – – – – –

805.98 820.64 858.62 868.37 918.61 940.47 1057.72 1186.77 1211.55 1280.37 1286.18 0.054 0.050 0.037 0.034 0.011 – – – – – – 0.00020 0.00017 0.00016 0.00014 0.00012 0.00010 0.00009 0.00007 0.00006 0.00004 0.00002

In the research area, there are important yield fluctuations and variations of product and input prices. Research results indicated that maize for silage, wheat, paddy, and soybean have the most yield variations. Their coefficients of variation (CV) were 67%, 29%, 26%, and 22%, respectively. However, price variations in dry onion and paddy are higher, whereas wheat and sugar beet are lower compared with others. There is also a wide range of variation in input prices. Fertiliser was the most discriminative input and its CV was 37% followed by variations of feed and fuel prices with 26% and 25%, respectively. These variations in product and input prices and yield resulted in fluctuation of gross margin of individual activities and affected the farm organisations widely in the research area. Programming results revealed that total net farm revenue increases for all farm size groups while risk aversion decreases. Expected net farm return ranged from us$806 to us$1286 associated with risk aversion in small farms, whereas that of medium farms varied from us$3552 to us$4823. In large farms, decreasing risk aversion led to an increase of net farm return from us$5856 to us$8203 (Tables 2–4). Based on the programming results, it was conclusive that decreasing risk aversion provided more net farm return in small farms compared with others. Similar results were obtained in other studies (Prevatt et al. 1992; Dunn & Williams 2000; Held et al. 2002). Allocatively efficient sets for each representative farm indicated that it was independent of farm size. In small farms, decreasing risk aversion influenced less farmland allocation to lettuce, rape seed, chick pea, and lentil. However, the results were the reverse for maize, maize for silage, sugar beet, wheat, and dry onion. Decreasing risk aversion also resulted in an increase in the number of cows for all relevant ranges of risk aversion (Table 2). In medium size farms, decreasing risk aversion led to more land allocation to risky activities such as paddy, maize for silage, and soybean, but resulted in a dramatic reduction in sugar beet, rape seed, dry

Chick Dry E[TFNR] pea onion Dairy Sheep us$

RESULTS AND DISCUSSION

Table 2  Allocatively efficient set for relevant range of risk aversions (small farms). (E[TFNR], expected total net farm revenue.)

The levels of economic inefficiencies (EI) and also relative contributions of allocative and technical inefficiencies (AI and TI, respectively) of the representative farm i were defined as: EIi = (1 – E[TFNRei]/E[TFNRti]) × 100 AIi = {(E[TFNRpi] – E[TFNRei] )/E[TFNRti]}× 100 TIi = {1– E[TFNRpi]/E[TFNRti]} × 100

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Activity level Maize Lettuce Soy Rape (silage) Sugar Dry rA Wheat (II. crop) bean Paddy seed Maize (II. crop) beet bean Lentil

Cınemre & Ceyhan—Application of utility-efficient programming

– – – 0.443 0.546 0.771 1.013 1.624 2.322 2.585 2.585

0.264 0.186 0.112 – – – – – – – –

0.264 0.186 0.112 – – – – – – – –

0.128 0.209 0.680 0.690 0.696 1.011 0.743 0.785 0.398 0.377 0.377

1.426 1.498 1.516 1.346 1.289 1.156 1.124 0.785 0.398 0.001 –

– – – 0.548 0.552 1.156 1.124 0.785 0.397 0.001 –

1.269 1.442 1.516 0.800 0.738 0.001 – – – – –

0.128 0.099 0.146 0.143 0.146 0.162 0.001 – – – –

2.948 2.824 2.540 2.439 2.306 2.232 1.849 1.695 1.721 1.737 1.736

2.694 2.596 2.365 1.997 1.823 1.727 1.226 1.458 1.493 1.508 1.509

– – 0.031 0.419 0.541 0.651 1.226 1.458 1.493 1.508 1.509

– – 0.092 1.257 1.624 1.953 3.677 4.375 4.480 4.526 4.527

– – 2.356 – – – – – – – –

0.588 0.334 0.236 – – – – – 0.150 0.228 0.228

0.252 0.228 0.411 0.442 0.483 0.506 0.624 0.236 0.228 0.228 0.228

2.106 2.352 2.356 1.866 1.764 1.582 0.624 0.236 0.078 0.001 –

– – 0.001 1.578 1.764 1.582 0.624 0.236 0.078 0.001 –

1.764 2.236 2.355 0.288 – – – – – – –

0.252 0.138 0.153 0.153 0.001 – – – – – –

1.853 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582

– 6.733 8.629 8.629 8.629 8.629 8.629 0.002 – 0.096 0.096

5855.68 6447.44 6560.96 7133.60 7341.60 7472.08 8108.00 8182.96 8196.56 8202.64 8202.72

0.342 0.116 – – – – – – – – –

3552.00 3779.99 4001.85 4203.96 4252.77 4362.23 4488.05 4713.75 4788.84 4822.81 4822.91

0.00020 0.00017 0.00016 0.00014 0.00012 0.00010 0.00009 0.00007 0.00006 0.00004 0.00002

– – 8.598 8.629 8.629 8.629 8.629 8.629 – – –

Chick Dry E[TFNR] pea onion Dairy Sheep us$

3.109 5.127 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582 5.582

Activity level Maize Lettuce Soy Rape (silage) Sugar Dry rA Wheat (II. crop) bean Paddy seed Maize (II. crop) beet bean Lentil

Table 4  Allocatively efficient set for relevant range of risk aversions (large farms). (E[TFNR], expected total net farm revenue.)

– – – 0.149 0.183 0.256 0.338 0.542 0.774 0.862 0.861

0.157 0.057 – – – – – – – – –

1.690 1.573 1.093 0.947 0.919 0.857 0.720 0.542 0.774 0.862 0.862

0.00020 0.00017 0.00016 0.00014 0.00012 0.00010 0.00009 0.00007 0.00006 0.00004 0.00002

1.554 1.597 1.662 1.637 1.609 1.561 1.463 1.327 1.172 1.239 1.241

Chick Dry E[TFNR] pea onion Dairy Sheep us$

Activity level Maize Lettuce Soy Rape (silage) Sugar Dry rA Wheat (II. crop) bean Paddy seed Maize (II. crop) beet bean Lentil

Table 3  Allocatively efficient set for relevant range of risk aversions (medium farms). (E[TFNR], expected total net farm revenue.)

386 New Zealand Journal of Crop and Horticultural Science, 2006, Vol. 34

Cınemre & Ceyhan—Application of utility-efficient programming onion, chick pea, and lentil. Sheep are included in farm plans as a revenue stabilising activity (Table 3). Decreasing risk aversion resulted in the allocation of more operated land to paddy and soy bean in large farms. Consequently, the land allocated to other cash crops was reduced. The sheep fattening activity was included in optimum plans with the maximum level of 8.629 when absolute risk aversion, rA, was less than 0.00009. When exceeding this level of risk aversion, dramatic reduction is observed in the number of sheep in farm plans (Table 4). Based on the results of efficiency analysis, it would be possible to increase the existing level of E[TFNR], on the average, c. 46% varying from 38% for small farms to 50% for large farms in the research area (Table 5). Allocative inefficiency ranged from 20% to 23% with an average of 22% associated with farm size. This means that given the relative prices, operators could not allocate inputs in a cost minimising way. However, allocative inefficiency is independent of farm size. Small farms, on average, have the chance of increasing their E[TFNR] by 20% if they adopted allocatively efficient farm plans. This value is, on average, 23% for medium and large farms (Table 5). Technical inefficiency associated with farm size varied from 18% to 27% with an average of 24%. There has been a positive relationship between technical inefficiency and farm size. Technical inefficiencies for small, medium, and large farms were 18%, 26%, and 27%, respectively. A technically inefficient farm cannot produce as much output with the same level of input as a technically efficient farm. Technically inefficient farms in the region, therefore,

387

would have increased their average output by 24% if they had worked more efficiently under present conditions (Table 5). Average allocative and technical inefficiencies were 0.22 and 0.24, respectively, indicating that the major problem of the sample farms appears to be the inability to use the inputs in a technically efficient way rather than the inability to allocate inputs in a cost minimising way. Overall economic inefficiency ranged from 38% to 50%, with an average of 46%. There was a positive relationship between farm size and overall economic inefficiency. The small farms had the smallest overall economic inefficiency (38%) compared with the other size groups (Table 5). Like many earlier studies, research findings confirmed the theory of Schultz’s “poor but efficient” hypothesis (Lau & Yotopoulos 1971; Sidhu 1974; Huang & Bagi 1984; Squires & Tabor 1991). However, some authors obtained different results. For example, Torkamani & Hardaker (1996) and Laura Gow & Langemeier (1999) found that economic inefficiency in terms of technical and allocative inefficiencies was independent of farm size. In all farm sizes, decreasing risk aversion generally caused an increase in inefficiency scores when absolute risk aversion, rA, was higher than 0.00002. CONCLUSIONS Utility-efficient programming was used to derive an allocatively efficient set of farm plans in the Kızılırmak basin of the central Anatolian region of Turkey. Technical and economic efficiencies were

Table 5  Measure of economic inefficiencies for relevant range of risk aversions. (AE, allocative or price efficiency; TE, technical efficiency; EE, economic efficiency.) rA 0.00020 0.00017 0.00016 0.00014 0.00012 0.00010 0.00009 0.00007 0.00006 0.00004 0.00002

Small farms AE TE EE 5.65 7.08 9.88 9.82 13.90 15.55 24.77 32.24 33.41 37.51 32.73

16.32 15.88 20.76 27.04 23.56 22.58 14.44 12.07 11.98 9.18 21.25

21.97 22.96 30.64 36.86 37.46 38.13 39.21 44.31 45.40 46.69 53.98

Medium farms AE TE EE 11.76 15.79 18.10 21.46 21.59 23.33 25.28 28.56 29.10 29.05 28.89

29.16 27.01 30.33 27.36 28.85 27.30 25.65 23.13 23.71 24.70 25.11

40.92 42.80 48.43 48.82 50.44 50.63 50.93 51.69 52.81 53.75 54.00

Large farms AE TE EE 11.05 16.52 16.88 22.26 23.19 23.57 27.30 27.28 27.39 27.36 27.32

21.17 24.54 27.42 24.34 27.71 27.74 27.96 29.07 28.98 29.14 29.25

32.22 41.06 44.30 46.60 50.90 51.31 55.26 56.35 56.37 56.50 56.57

388 New Zealand Journal of Crop and Horticultural Science, 2006, Vol. 34 calculated. Based on programming results, it can be concluded that total net farm revenue increases for all farm sizes as risk aversion decreases. Moreover, decreasing risk aversion provides more net farm return in small farms compared with medium and large ones. Estimated overall efficiency scores relatively low, indicating that greater improvement is needed. Since access to institutions such as extension services, cooperatives, and credit was very limited in the research area, economic inefficiencies among sample farmers were attributed to purely technical inefficiency and market failures. Government policy to improve the working of markets and disseminating information on production technologies as widely as possible could enable farmers to increase their efficiency, especially price efficiency. Alternately, supplying complete technical packages (feed, credit, etc) for farms may increase technical efficiency. Vocational training provided by extension services may foster efficiency. Demiryürek (2000) suggested that there was a positive correlation between efficiency and total information score that reflects the extent of contact with the sources of information. These services are also low cost methods of achieving increases in productive efficiency (Ellis 1993). Hence, future programmes for farmer’s training and extension should focus on human resource development and lead farmers to adjust their family farms to prevailing market conditions.

ACKNOWLEDGMENTS We thank Tillak Persaud of Puerto Rico University for his detailed reading of the paper. His comments resulted in considerable improvements. REFERENCES Aigner DJ, Lovell CAK, Schmidt P 1977. Formulation and estimation of stochastic production function models. Journal of Econometrics 6: 21–37. Aktürk D 2000. An investigation on measurement of efficiency of cotton in farms of Söke District. Unpublished PhD thesis, University of Ankara, Ankara, Turkey. Anderson JR, Dillon JL 1992. Risk analysis in dry land farming systems. Farm System Management Series 2. Rome, FAO. Anderson JR, Dillon JL, Hardaker JB 1977. Agricultural decision analysis. Ames, Iowa, United States, Iowa State University Press.

Arrow KJ 1965. Aspects of the theory of risk bearing. Helsinki, Yrjo Johnsson Saatio. Battese GE, Coelli TJ 1995. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics 20: 325–332. Battese GE, Rambaldi AN, Wan GH 1997. A stochastic frontier production function with flexible risk properties. Journal of Productivity Analysis 8: 269–280. Baumol WJ 1977. Economic theory and operations analysis. Englewood Cliffs, New Jersey, United States, Prentice-Hall. Chambers RG 1983. Scale and productivity measurement under risk. American Economics Review 73: 802–805. Chavas JP, Holt MT 1996. Economic behavior under uncertainty: a joint analysis of risk preferences and technology. Review of Economics and Statistics 76: 329–335. Chennareddy V 1967. Production efficiency in south Indian agriculture. Journal of Farm Economics 49: 816–820. Coelli T, Rao DSP, Battese GE 1998. An introduction to efficiency and productivity analysis. Massachusetts, United States, Kluwer Academic Publishers. Collender RN, Chalfant JA 1986. An alternative approach to decisions under uncertainty using the empirical moment-generating function. American Journal of Agricultural Economics 68: 727–731. Demirci S 2001. Performance analysis of sugar factories and total factor productivity: an application of Malmquist Index. Project No. 2001-17, Publication no. 66, p. 45. Agriculture Economics Research Institute of Turkey, Ankara, Turkey. Demiryürek K 2000. The analysis of information systems for organic and conventional hazelnut producers in three villages of the Black Sea region. Unpublished PhD thesis, Agricultural Extension and Rural Development Department, The University of Reading, United Kingdom. Dillon JL, Hardaker JR 1971. Allocative efficiency, traditional agriculture and risk. American Journal of Agricultural Economics 53: 26–32. Dunn JW, Williams JR 2000. Farm characteristics that influence net farm income variability and losses. Proceedings of the Annual Meetings of the Western Agricultural Economics Association, June 29–July 1, Vancouver, British Columbia, Canada. Ellis F 1993. Peasant economics: farm household and agrarian development. 2nd ed. Cambridge, United Kingdom, Wye Studies in Agricultural and Rural Development, Cambridge University Press.

Cınemre & Ceyhan—Application of utility-efficient programming Farrel MJ 1957. The measurement of productive efficiency. Journal of the Royal Statistical Society Association 120: 253–281. Freund RJ 1956. The introduction of risk into a programming model. Econometrica 24: 253– 261. Günden C, Miran B, Sari MA 1998. The development of productivity and efficiency in Turkish agriculture: an application of data envelopment analysis. National Conference of Agricultural Economics Association, October 7–9, Ankara, Turkey. Hair JF, Anderson RE, Tatham RL, Black WC 1998. Multivariate data analysis. New Jersey, United States, Prentice Hall International Inc. Hanoch G, Levy H 1970. Efficient portfolio selection with quadratic and cubic utility. Journal of Business 43: 181–190. Hardaker JB, Pandey S, Patten LH 1991. Farm planning under uncertainty. Review of Marketing and Agricultural Economics 59: 9–22. Hardaker JB, Huirne RBM, Anderson JR 1997. Coping with risk in agriculture. United Kingdom, CAB International, Biddles Ltd. Hardaker JB, Richardson JW, Lien G, Schuman KD 2004. Stochastic efficiency analysis with risk aversion bounds: a simplified approach. Australian Journal of Agricultural and Resource Economics 48: 253–270. Hazell PBR 1971. A linear alternative to quadratic and semivariance programming farm planning under uncertainty. American Journal of Agricultural Economics 53: 53–62. Held LJ, Haag AA, Krall JM, Delenay RH, Miller SD 2002. Risk return analysis of incorporating annual legumes and lamb grazing with dry land crop rotations. Proceedings of the Annual Meetings of the Western Agricultural Economics Association, July 28–31, Long Beach, California, United States. Huang CJ, Bagi FS 1984. Technical efficiency on individual farms in northwest India. Southern Economic Journal 51: 108–115. Isik M, Khanna M 2002. Stochastic technology, risk preferences and adoption of site specific technologies. Annual Meetings of the American Agricultural Economics Association, 28–31 July, California, United States. Just RE 1974. An investigation of the importance of risk in farmers’ decisions. American Journal of Agricultural Economics 56: 14–25. Just RE, Pope RD 1978. Stochastic specification of production functions and economic implication. Journal of Econometrics 7: 67–86.

389

Kaiser HM, Appland J 1989. DSSP: a model of production and marketing decisions on a midwestern crop farm. North Central Journal of Agricultural Economics 11: 157–170. Kingwell RS 1994. Risk attitude and dryland farm management. Agricultural Systems 45: 191–202. Kumbhakar SC 1987. The specifications of technical and allocative inefficiency in stochastic production and profit function. Journal of Econometrics 34: 335–348. Kumbhakar SC 1993. Production risk, technical inefficiency and panel data. Economics Letters 41: 11–16. Kumbhakar SC 2002. Specification and estimation of production risk, risk preference and technical efficiency. American Journal of Agricultural Economics 84: 8–22. Lau LJ, Yotopoulos PA 1971. A test of relative efficiency and application to Indian agriculture. American Economic Review 61: 94–109 Laura Gow MS, Langemeier M 1999. An efficiency analysis of cattle back grounding in Kansas. Paper presented at Western Agricultural Economics Association Annual Meeting, 11–14 July, Fargo, North Dakota, United States. Lerman Z 2001. Productivity and efficiency of individual farms in Poland: a case for land consolidation. Paper presented at Annual Meeting of the American Agricultural Economics Association, 2–31 July, Long Beach, California, United States. Lien G, Hardaker JB 2001. Whole-farm planning under uncertainty: impacts of subsidy scheme and utility function on portfolio choice in Norwegian agriculture. European Review of Agricultural Economics 28: 17–36. Lipton M 1968. The theory of the optimizing peasant. Journal of Development Studies 4: 327–351. Love HA, Buccola ST 1991. Joint risk preferencetechnology estimation with a primal system. American Journal of Agricultural Economics 73: 764–774. Mapp Jr HP, Hardin ML, Walker OL, Persaud T 1979. Analysis of risk management strategies for agricultural producers. American Journal of Agricultural Economics 61: 1071–1077. Ogisi ME, Hardaker JB, Torkamani J 1994. Utility efficient programming: an evaluation. Paper presented at the 38th Annual conference of the Australian Agricultural Economics Society, Victoria University, 7–11 February, Wellington, New Zealand.

390 New Zealand Journal of Crop and Horticultural Science, 2006, Vol. 34 Papadas CT, Dahl CD 1991. Technical efficiency and farm size: a nonparametric frontier analysis. Staff paper P91-53, University of Minnesota, Department of Agricultural and Applied Economics, St. Paul, Minnesota, United States. Pasour Jr EC 1981. A further note on measurement of efficiency and economics of farm size. Journal of Agricultural Economics 32: 135–146. Patten HL, Hardaker JB, Pannell DJ 1988. Utility efficient programming for whole farm planning. Australian Journal of Agricultural Economics 32: 88–97. Persaud T, Mapp Jr HP 1979. Effects of alternative measures of risk efficient farm plans in a MOTAD framework. A contributed paper for the Annual Meeting at the American Agricultural Economics Association, 29 Jul–1 Aug, Pullman, Washington, United States. Prevatt JW, Bauer LL, Kaiser EH, Rathwell PJ 1992. Measuring the effect of capital structure and seasonality on expected returns and risk: the fresh market vegetable case. Southern Journal of Agricultural Economics 24: 171–178. Saha A, Shumway CR, Talpaz H 1994. Joint estimation of risk preference structure and technology ssing expo-power utility. American Journal of Agricultural Economics 76: 173–184. Sahota GS 1968. Efficiency of resource allocation in Indian agriculture. American Journal of Agricultural Economics 50: 584–605. Schultz TW 1964. Transforming rraditional agriculture. New Haven, Connecticut, United States, Yale University Press. Settlage L, Preckel P 2002. Robustness of non-parametric measurement of efficiency and risk aversion. Annual Meetings of the American Agricultural Economics Association, 28–31 July, California, United States.

Shaik S, Helmers GA 2003. Incorporating risk in efficiency analysis. Paper presented at the Southern Agricultural Economics Association Annual Meeting, 1–5 February, Mobile, Alabama, United States. Sidhu SS 1974. Relative efficiency in wheat production in the Indian Punjab. American Economic Review 64: 740–751. Squires D, Tabor S 1991. Technical efficiency and future production gains in Indonesian agriculture. The Developing Economies 29: 258–270. Torkamani J, Hardaker JB 1996. A study of economic efficiency of Iranian farmers in Ramjerd District: an application of stochastic programming. Journal of Agricultural Economics 14: 73–83. Tzouvelekas V, Christos CP, Christos F 2001. Technical efficiency of alternative farming systems: the case of Greek organic and conventional olive-growing farms. Food Policy 26: 549–569. Upton M 1979. The unproductive production function. Journal of Agricultural Economics 30: 179–194. Villano RA, O’Donnell CJ, Battese GE 2005. An investigation of production risk, risk preferences, and technical efficiency: evidence from rain fed lowland rice farms in the Philippines. Working paper 2005-1, University of New England, Graduate School of Agricultural and Resource Economics and School of Economics, Australia. Wolgin JM 1975. Resource allocation and risk: a case study of smallholder agriculture in Kenya. American Journal of Agricultural Economics 57: 622–630. Zaim O, Çakmak E 1998. Efficiency in Turkish agriculture: trends and comparative analysis. Agriculture Structure and Employment in Agriculture. Ankara, State Statistics Institution. Pp. 353–379.

1

2

3

Reconstructed gross activity incomes Probability 0.067 0.067 0.067 Wheat 132.38 132.16 132.01 Soy Bean 382.45 347.35 316.17 Lettuce 436.92 419.18 403.67 Paddy 528.52 495.07 600.85 Rape seed 208.71 206.36 205.00 Maize 413.90 419.31 378.67 Maize for silage 134.27 127.20 121.23 Sugar beet 410.73 423.41 434.41 Dry bean 260.19 305.08 344.35 Lentil 391.35 397.36 402.33 Chick pea 307.30 317.71 327.35 Dry onion 284.45 324.24 357.99 Dairy 109.77 106.61 103.88 Sheep 22.32 22.93 23.53

State



0.067 131.80 289.67 382.61 518.52 205.00 364.40 117.43 444.02 376.48 406.24 336.33 385.84 101.56 24.13

4 0.067 131.56 266.77 378.17 517.16 206.24 352.47 114.73 452.14 402.10 409.20 344.54 407.65 99.66 24.73

5 0.067 131.42 247.96 377.06 478.42 208.59 342.78 113.57 458.68 421.12 411.02 352.09 423.57 98.19 25.34

6 0.067 131.20 233.67 373.74 518.92 212.17 335.46 113.83 463.83 433.45 411.78 358.86 433.44 97.14 25.94

7 0.067 130.98 223.30 373.74 463.14 216.99 333.38 115.50 467.40 439.27 411.49 364.98 422.39 96.29 26.54

8 0.067 130.83 216.95 377.06 525.00 223.04 327.56 118.84 469.48 438.49 410.16 370.32 420.62 95.87 26.54

9 0.067 130.61 214.78 382.61 657.50 230.33 327.08 123.47 469.97 431.02 407.77 375.00 412.66 96.08 27.15

10 0.067 130.39 216.78 391.47 665.61 238.73 328.76 129.64 469.08 417.04 404.05 378.91 398.66 96.50 27.75

11 0.067 130.24 222.80 403.67 541.40 248.37 332.80 137.35 466.60 396.46 399.85 382.17 378.78 97.35 27.75

12 0.067 130.02 233.00 418.07 437.86 259.37 339.17 146.48 462.74 369.27 394.31 384.77 352.83 98.61 28.35

13 0.067 129.87 247.21 435.81 554.36 271.35 347.71 157.15 457.19 335.40 387.72 386.59 321.00 100.08 28.35

14

SD

Mean

16.50 30.74 62.38 83.32 21.36 32.72 13.14 18.22 66.46 10.18 20.26 34.87 1.98 0.36

SD

Subjective Historical Mean

0.067 129.65 131.00 12.17 148.43 265.60 261.67 51.39 289.35 456.87 401.67 26.38 376.62 597.73 540.00 66.67 528.15 284.69 228.33 26.39 235.38 358.60 351.67 26.38 366.31 169.23 129.33 16.89 108.36 450.26 453.33 18.05 473.60 295.02 377.67 57.72 378.77 380.08 401.66 9.72 408.60 387.64 358.33 26.38 370.27 297.86 381.67 51.39 360.07 102.19 100.00 4.17 96.06 28.95 26.00 2.17 27.01

15

Appendix 1  Summary statistics of raw-time series data and distribution of reconstructed gross activity incomes by state of nature (us$ ha).

Cınemre & Ceyhan—Application of utility-efficient programming 391