Productive efficiency of rice farming under rainfed conditions in Gampaha and Kalutara districts of Sri Lanka

: This study was conducted to evaluate technical and allocative efficiencies of rice farming in the low country rainfed water regime of the Gampaha and Kalutara districts of Sri Lanka. Data of 2009 Yala season, and 2009/2010 Maha season were collected from 49 rainfed farms per season of the Gampaha district and 50 rainfed farms per season of the Kalutara district. Stochastic frontier production functions of Cobb-Douglas form with an intercept dummy variable representing the Kalutara district were estimated for each season. Values of γ above 0.78 in the Yala season and above 0.9 in the Maha season indicated that inefficiencies explain a major portion of the total product variation. The average technical efficiencies were 0.67 in Gampaha and 0.73 in Kalutara districts in the Yala season, and 0.76 in Gampaha and 0.78 in Kalutara in the Maha season. The average allocative efficiencies were 0.59 in Gampaha and 0.46 in Kalutara in the Yala season, and 0.63 in Gampaha and 0.53 in Kalutara in the Maha season. Increase of technical efficiency has resulted in potential cost savings of approximately 33 % in Gampaha and 27 % in Kalutara district in the Yala season, and 24 % in Gampaha and 22 % for Kalutara in the Maha season. About 40 % of the cost of resources in the Kalutara district and 0.27 of that in the Gampaha district in the Yala season, and 37 % of the resource cost in the Kalutara district and 29 % of that in the Gampaha district could be saved by raising allocative efficiency. The average cost savings indicated by raising both forms of efficiencies were Rs.29,375 per farm (Rs 79,325/ha) in the Kalutara district and Rs 27,645 per farm (Rs 85,870/ha) in the Gampaha district during the Yala season while it was Rs. 29,190 per farm (Rs 89,260/ha) in the Kalutara district and Rs. 22,325 per farm (Rs 81,230/ha) in the Gampaha district in the Maha season. Costs of allocative inefficiencies were more prominent in both seasons in the Kalutara district and in the Maha season in Gampaha district, whereas costs of technical inefficiencies were more important in the Gampaha during Yala season


Introduction
Rainfed area constitutes about 24 % of the national rice cultivated extent, and contributes to around 19 % of the annual national rice production in Sri Lanka. Districts in the low country wet zone contribute to 36 % of rainfed rice would cause lesser sunshine days for Kalutara district than the Gampaha district. High rainfall and low lying nature of lands have resulted in Kalutara district having more boggy lands with problems of acidity and iron toxicity.
The new improved varieties in the Bw, Ld and At series are grown in areas with boggy lands in the Kalutara district whereas Bg varieties that have higher yield potential are entirely grown in the Gampaha district. With the same level of use of conventional inputs, Gampaha district is expected to give higher productivity that that in the Kalutara district due to better agro-climatic conditions for rice cultivation in the former. This study was thus, conducted with the objectives (a) to measure technical, allocative, and economic efficiencies of rice farming in the Maha and Yala seasons in rainfed water regimes of Kalutara and Gampaha districts, and (b) to measure the costs of these inefficiencies and the influence of raising efficiency levels on farm profitability. Farrell (1957) introduced two indices of technical efficiency i.e. one in input-output (output-oriented technical efficiency or TE [o] ) space and the other in the inputinput space (input oriented technical efficiency or TE [i] ). Generally, the outputoriented index is used in the measurement of technical efficiency in most of the studies. The technical efficiency index (TE [i] ), allocative efficiency index (AE), and associated economic efficiency (EE) index in the input-input space introduced and elaborated by Farrell (1957) were used in this study to measure the efficiency of production.

Methodology
There are two alternative approaches that have evolved in the measurement of efficiency of production, i.e. (a) data envelopment analysis (DEA) approach that uses programming methods to derive efficiency frontier, and (b) stochastic frontier production function (SF) approach that uses econometric methods to estimate frontier production function. The coefficients estimated through the SF approach have statistical properties whereas the general DEA estimates do not have statistical properties. Further, SF approach has not been previously used in analysis of allocative efficiency in rainfed rice farming in Sri Lanka. Therefore, the SF approach and efficiency measurement in input-input space (Kopp, 1981;Russel and Young, 1983;Dawson 1985;Karagiannis et al., 2003) was used in this study to measure efficiency of production.
The TE index of a firm is the ratio of the cost of a hypothetical firm operating on the production frontier with the firm's input ratios and output level to the actual cost of the firm. The AE index of the firm is the ratio of the cost of a cost minimizing hypothetical firm operating on the frontier (a technically and allocatively efficient firm) with the firm's output level to the cost at technically efficient input level of the firm. The EE index is the ratio of the cost of a cost minimizing firm operating on the frontier with the firm's output level to the cost of the firm. Accordingly, EE is the product of TE and AE.
The method of measuring AE and TE in input-input space is depicted in Figure 1 for a two-factor case of production. The AB-efficient unit Isoquant represents the various combinations of the two factors, X 1 and X 2 used by technically, perfectly efficient firms of an industry to produce an output, P. Any firm producing an output P cannot be positioned in between AB and the origin O. The Q and S respectively are two technically efficient and inefficient firms that produce an output P. These two firms lie on a "Fixed Inputs Use Proportion Ray" (OT) where inputs X 1 and X 2 are used in the same ratio. The Q' is a technically and allocatively efficient firm that lies on AB-efficient unit isoquant on the point, which touches the price line DD' The input based technical efficiency (hereafter TE [1] ) of the firm S is given as, TE s [i] = C'/C s , where, C s , and C', respectively, are the cost of firm S and the cost of firm Q which is a technically efficient firm that produces, output P using inputs in the same proportion as firm S. As same input proportions are used by the efficient firm (Q) and inefficient firm (j), input based technical efficiency (TE j [i] ) is given also by the vector norm formula OQ/OS. Allocative Efficiency of the firm S has been defined as AEs [i] = C"/C' where, C" is the cost of firm Q (a technically and allocatively efficient firm with the same output level as of firm S) and C' is as given above. Since measurements are made along the fixed input use proportion ray, OT, AE j [i] is represented also by the vector norm formula OR/OQ. The EE index indicates the possibility of cost reduction feasible by eliminating both technical and allocative inefficiencies. The EE of a firm is given by E s where, C" and C j are as given above. By definition, EE is equal to the product of TE [i] and AE [i] and, and given also by the vector norm formula OR/OS.

Specification of the analytical model
The SF function model proposed by Aigner et al. (1977) and Meeusen and van den Borek (1977), and further developed by Coelli (1996) was used in the study. The SF is specified in the log-log linear (Cobb-Douglas) form as shown in Equation 1; where y j is the output of j th farmer, D k ={0,1}, D k is a dummy variable that takes value of 1 for Kalutara district and 0 for Gampaha district, Land j is the land extent used by j th farmer, Labour j is the amount of labour used for production operations excepting labour used for water management and transport operations, material j is the operating expenditure incurred on all inputs, and machine j is the cost of machinery services incurred on land preparation, harvesting, and threshing, ε j is a composite error tem where, ε j = ν j -υ j : ν j is an error term assumed to be distributed identically and independently as N(0,σ ν 2 ) that reckons random variation of output, and u j is one sided (u j ≥0) error term that reckons variation of output due to inefficiency. In this paper u j was assumed to follow a half normal distribution (u. N(0, σ u 2 ). The efficiency parameter γ = (σ υ 2 / σ υ 2 + σ ν 2 ) lies between 0 and 1, and if γ = 0, the difference between farmer's production and production estimated by the frontier function is entirely due to statistical noise. Conversely, γ=1 indicates that the difference of actual and estimated production is entirely due to less than efficient use of technology.

Estimation of technical and allocative efficiency indices
Frontier 4.1 (Coelli, 1996) was used to estimate the model. Then the output oriented technical efficiency index [TE j [o] ] is given by the software. The input oriented technical efficiency for a double log frontier production function is given as TE j [i] = [TE j (2) The cost minimizing point subject to output constraint requires that the inverse price ratios of inputs should be equal to ratios of marginal products (MP 1 / MP 2 = r 1 / r 2 ). The relationship of inputs at cost minimization subject to output constraint of a Cobb-Douglas production function is given as (Henderson and Quandt, 1980).
where, r i and r k are prices of k th and i th inputs gives the equations 4, 5 and 6.
(∑∝ ) Any X ij could be found by substiting a value at X kj in the Equation 3, and the cost of cost-minimising input combination could be found by multiplying the input values by prices faced by farmer. Then, the AE is estimated as given in equation 7.
Estimates of potential cost savings Cost savings feasible for each farm firm by raising technical efficiencies to unity are estimated as ∆S TEj = C j (1 -TE j ) where, C j is the total cost of production of farmer j and ∆S TEj is the potential cost savings for farmer j with raising his technical efficiency to unity. Cost savings feasible for each farm firm by raising allocative efficiencies to unity are estimated as equation 8.
where, ∆S AEj is the potential cost savings for farmer j by eliminating his allocative inefficiency. Accordingly, the term (TE j -EE j ) gives the proportionate cost savings feasible by eliminating allocative inefficiency. Then sample sums of cost savings are divided by aggregate extent to find per acre cost savings.

Data used
All input use and output data collected by the Socio-Economics and Planning Center, Department of Agriculture, Sri Lanka for cost of cultivation studies of paddy farming during the above two seasons were processed and used. The samples of each season include randomly selected 49 farmers from Gampaha district and 50 farmers from Kalutara district (total sample size for each season was 99 farms). Lands were mostly owned by the farmers and land rents were rarely recorded in the data set used. Therefore, rent value of land was not explicit. The Paddy Lands Act No. 1 of 1958 and subsequent Agrarian Development Act No. 46 of 2000 prescribe a land rent of 25 % of the output. Accordingly, the value of land is decided as 25 % of the value of average yield for the district during the season.
In deciding on the variable labour, eight hours of work by a man was considered as a man day, and a female work day is considered as equal to 0.7 of man days except in operations of manual weeding and transplanting for which one female work day was considered as equal to one man day. Hired labour was considered as equivalent to family/exchange labour. Some farmers had given harvesting operations on contract and had not reported the amount of labor used for the operation. In such cases, the amount of labour used was estimated by dividing the contract value from the average wage rate for the operation. In valuing labour, family labour was valued by the market wage rate faced by the farmer for a particular operation.
The variable 'Material' was formed by aggregating the operating expenditure incurred on material inputs, which generally include cost of seed, cost of fertilizer received at subsidized prices, cost of pesticides, etc. Machine is a variable representing services of machinery, measured as cost of services. Machine includes cost of draft power services on land preparation, and the machinery cost for harvesting and threshing. Machinery costs were charged on the basis of 'per land area' by the machinery service providers, and therefore, machinery service values on per hour basis were not available. The cost components of material inputs and services of own machinery costs were valued at the costs incurred by the farmer. Own seed was valued by the average price paid for the seed of each variety by farmers who have purchased seed. The rental value of own machinery was estimated by the going rental rate of such machinery. The opportunity cost was computed using the cost incurred on material inputs and machinery and was charged with the interest rate of the banks for loans given through pawning of jewelry.

Results and Discussion
The mean input use levels of the two districts were similar. The land sizes were approximately 0.4 ha in each district during both cultivating seasons, and the costs of material inputs and machinery services were marginally above Rs 10,000 in the Kalutara district and marginally below Rs 14,000 in the Gampaha district during each season. The mean labour use in each district during the Yala season was higher than that during the Maha season, which was mainly due to the higher labour requirement for water management during the Yala season (Table 1).

Estimated production functions
The dummy variable coefficients for the Kalutara district were negative and significant in frontier production functions for both seasons ( Table 2 The difference of suitability of agro-ecology for rice cultivation may have resulted in the differences of the performance of the two districts. The estimated coefficients for land in frontier production functions for both Yala and Maha seasons were larger than the similar coefficients in the average production functions ( Table 2). Expansion of the elasticity of production of land with raising farm technical efficiencies to frontier level agrees with priority expectations. The gross margin, which is the return to land and management, increased with increase in the technical efficiency to the frontier level. The estimated production elasticity of land indicated that increasing the land extent by 1 % would result in an increase of production by 0.68 % in Yala and 0.44 % in Maha. Although the labour coefficients had positive (expected) signs in both the Yala and Maha seasons in both average and frontier production functions, they were small in magnitude, except in the average production function for Yala 2009, and not significant (p>0.1) ( Table 2). Similar results have been observed by Bhavan and Maheshwaranathan (2008). A negative relationship between output and labour has been reported by Hossain et al., (2008). This situation indicated the flexibility of substitution of labour used for land preparation by machinery and chemicals (initial application of herbicides), weed control by herbicides, and threshing by threshing machines. Displacement of labour used for transplanting by that of seed sowing has a less important role in rainfed paddy farming at present.
The coefficients of material cost and machinery cost were significant in both average and frontier production functions. The estimated elasticities in frontier production functions were 0.145 in the Yala season and 0.219 in the Maha season of material inputs, and 0.164 in the Yala season and 0.2576 in the Maha season for machinery services. The terms σ 2 and γ were significant (p<0.01) in both Yala 2009 Maha 2009/2010 seasons. The term γ indicates the ratio of variation related to efficiency to total variation. Values of γ greater than 0.78 (Table 2) in both seasons indicated that the variation due to efficiency differentials explain a major portion of yield variation, while the random effects explain only a minor portion of the total product variation. Similarly, the potential cost savings for the 2009/2010 Maha season were 22 % for the Kalutara district and 24 % for the Gampaha district. The averages of economic efficiency for the Kalutara and Gampaha districts was 0.33 and 0.39, respectively, during Yala. It was 0.41 and 0.47 during Maha, respectively. During 2009 Yala, the average potential cost savings was about 67 % for Kalutara district and 61 % for Gampaha district, while that of 2009/2010 Maha was 59 % and 53 %, respectively (Table 3).
The proportionate cost savings interpretation of the allocative efficiency alleviation could be taken as the difference between TE [i] and EE. Accordingly, approximately 40 % of the resources cost in the Kalutara district and 0.27 of the Gampaha district during the Yala season, and 37 % of Kalutara district and 29 % of Gampaha during the Maha season could be saved by raising allocative efficiency.  Rs. 29,190 in the Kalutara district and Rs. 22,325 in the Gampaha district. These figures indicate the potential for substantial resources savings (income increases). Costs of allocative inefficiencies are more prominent than technical inefficiencies in both seasons in the Kalutara district, and in 2009/10 Maha season in the Gampaha district, whereas costs of technical inefficiencies were more prominent in the Gampaha district during Yala season. When the computations are done on per hectare basis, potentials for enhancing profits were substantial (Table 4). However, the small farm sizes may act as a barrier to raise efficiency.
Rice farming in rainfed areas could be made financially attractive to farmers in both Kalutara and lampaha districts in both seasons by raising technical and allocative efficiencies of farmers that would lead to increase in profit per land area substantially. The percentage increases of profits were more pronounced in Kalutara district though the current recorded profits per ha are low (Table 6).

The distribution of efficiency indices
During Yala 2009, 82 % of farmers in the Kalutara district and 66 % of the Gampaha district had technical efficiency indices above 0.6. However, higher percentages of farmers in the Kalutara district compared to the Gampaha district had higher technical efficiency ranges during the same season. The economic efficiency indices spread from 0-0.19 to 0.9 in the two districts. The percentage of farmers below the 0.5 economic efficiency in Kalutara and Gampaha districts was 86 % and 61 % in 2009/2010 Maha, and 100% and 72% in 2009 Yala, respectively (Table 6). Accordingly substantial cost savings could be expected by raising technical, allocative and economic efficiencies of sizeable percentages of farmers.

Conclusion
The possible effects of districts on productivity differentials were controlled by introducing a district-specific intercept dummy variable in the model. Variations due to technical efficiency differentials explained the major portion of the total product variation in Gampaha and Kalutara districts. Therefore, productivity of technically inefficient farmers, and the average productivity could be improved by raising technical efficiency of production. The potential to save the resources cost incurred is 30 % in 2009 Yala season and 23 % in 2009/2010 Maha season without reducing farm production by raising technical efficiency. The potential cost savings indicated by raising allocative efficiencies are substantial, leading to ample potential savings by raising economic efficiency. The expost analysis was based on the assumption of certain knowledge. Rice production under rainfed is associated with uncertainty, and therefore, results of an exante analysis by the farmer and expost analysis by an analyst would be different. The implicit nature of land prices, and farmer's behavioral goals deviating from profit maximization reduce precision of conclusions based on allocative efficiency estimates based conclusions. A consistent extension programme facilitating inefficient farmers to work in association with efficient farmers and extension workers may reduce efficiency differentials and increase average farm profitability. Such a programme would reduce abandoning of land or increase land extents and reduce off-farm costs. However, further research on farming systems is needed to enhance long term profitability.