MATERIALS AND METHODS

Data sources: The study is based on a field survey in rural West Bengal in the year 2006-07. The purpose of the survey was to explore the nature of interlinked transactions in land leasing markets and the role of credit in bringing out allocative efficiency in agriculture in West Bengal. Taking into consideration the extent and the incidence of tenancy practices, out of 18 districts of West Bengal, the district of Burdwan has been selected for the survey⁴. In the second stage, among the 31 blocks under Burdwan district, one block, namely, Raina I has been selected on the consideration of the existence of diversified nature of agricultural practices and the co-existence of varied farms of interlinked transactions. Again, Raina I block has been stratified into two distinct agro climatic zones-one, developed zone with canal irrigation and the other, underdeveloped zone with rain-fed agriculture. From the developed zone, the villages, namely, Saktia and Anguna have been chosen, whereas the villages namely, Dhamash and Boro have been chosen from the underdeveloped zone under the same criteria⁵. Once villages are selected, 203 sampling units, the farm-households, have been chosen using stratified random sampling of farmers with probability being proportional to the farm size so that the sample can represent the actual proportion of all the five strata of the farmers. It is to be noted that 203 households operate over 303 agricultural holdings under alternative mode of cultivation. Our empirical analysis is restricted to 303 holdings. The farm households have been divided into five categories covering landless agricultural labourers, marginal farmers (less than 2.5 acre), small farmers (2.5-5 acre), medium farmers (5-10 acre) and large farmers (above 10 acre).

Data envelopment analysis: In the existing literature, several methodologies were suggested to measure allocative efficiency of farm households. Earlier studies used marginalist principal to measure allocative efficiency (Hopper, 1965; Welsch, 1965; Chennareddy, 1967; Yotopoulos, 1967; Sahota, 1968). These studies estimated a Cobb-Douglas production function to judge efficiency in cross-sectional samples and then tested the equality between the estimated single-valued marginal value products and marginal factor costs of the geometric mean firm with some statistical sampling theory test. In a reappraisal of some of the evidences mentioned by some earlier studies (Hopper, 1965; Chennareddy, 1967; Yotopoulos, 1967). Dillon and Anderson (1971) argued that there were some mixed supports to the hypothesis of profit maximizing behaviour by farmers in traditional agriculture. An alternative hypothesis of utility maximization was suggested in the study to allow subjective risk considerations and to provide a more realistic basis for policies aimed at the modernization of traditional agriculture. In a criticism of marginalist principle, Rudra (1973, 1992), Dey and Rudra (1973) and Hati and Rudra (1973) suggested an alternative test procedure without making any unnecessary assumptions like product and factor prices being the same for all cultivators. In constrained profit maximization, a test is conducted in those studies to examine whether input-output proportions are constant for all the farmers.

However, doubts have been expressed whether neoclassical model of an optimizing competitive firm is valid in traditional agriculture in a less developed country. Junankar (1980a, b, 1982 and 1989) rejected the profit maximizing hypothesis using Indian data and thus, argued against using the profit function. Contrary, the optimization rationale of Indian farmers might be based on cost-minimization principle. Cost minimization is the more appropriate assumption in rural West Bengal as rice is found produced to a large extent for subsistence consumption and so output may be treated as exogenous (Ray and Bhadra, 1993⁶; Varian, 1984).

Following Data Envelopment Analysis (DEA), cost minimization is associated with three types of efficiency measures: cost efficiency, allocative efficiency and technical efficiency. For our purpose, we have used DEA approach to measure allocative efficiency of West Bengal farmers.

The differences in allocative efficiency of farmers can be explained in a two-stage approach, where in the first stage the predicted farm level allocative efficiencies are determined and in the second stage, these predicted allocative efficiencies are related to sources of the efficiency like contract choice⁷ and farmer-specific factors. Allocative efficiency can be measured using the cost minimization DEA model⁸ (Charnes et al., 1978). In present analysis, a Multi input-Multi output Constant Returns to Scale Input Oriented DEA model is used. Following Coelli et al. (2002), let us consider the situation with N Decision Making Units (DMU). Each of the n DMUs produce Q output using V different inputs. A cost minimization linear programming problem is solved for each DMU. The cost minimization problem for the i th DMU is given by:

Where

In the framework of cost minimization, the total Cost Efficiency (CE) or Economic Efficiency (EE) of the i-th firm is measured by the ratio of minimum cost to observed cost as:

A firm is said to have realized allocative efficiency if it is operating with the optimal combination of inputs, given their respective prices. The allocative efficiency is calculated residually by using the following relationship between Cost Efficiency (CE) and Technical Efficiency (TE) as:

We define the following ranges of allocative efficiency as:

In the second stage, the following model is used to determine the various socio-economic determinants of farm specific allocative efficiency. Censored maximum likelihood estimator is used to determine the value of the coefficients. The specification of the empirical model is given by:

Where, γ_i (i = 1, 2,....., 10) are coefficients

Statistical analysis: In this study, the statistical analysis has been made by using two sophisticated statistical packages: DEAP¹¹ Version 2.1 and E-Views. In the first stage to measure allocative efficiency under DEA framework, DEAP statistical package is extensively used. In the second stage, we have used E-Views statistical package to examine the determinants of allocative efficiency.

RESULTS AND DISCUSSION

Measurement of allocative efficiency
DEA approach: Allocative efficiencies are estimated by using a Multi input-Multi output Constant Returns to Scale Input Oriented DEA model. The model is comprised of data on output quantities, input quantities and prices of inputs. Output is measured by three variants: output of a particularly paddy variety like amanswarna¹², output of all paddy varieties taken together and output of all crops measured as a equivalent of amanswarna¹³. Three important input variables are chosen, viz., total operated area, total labour (both family and hired) used and total amount of fertilizer used in production. For simplicity, we assume all firms face the same input prices. Table 1 presents the summary statistics of allocative efficiency estimates at three different levels of cultivation. The average allocative efficiency for the sample of all crops is 84%, with a minimum of 11.6%. The corresponding figures for the sample of paddy cultivation is 86% with a minimum of 30.7% while in amanswarna cultivation the estimated average efficiency is 74% with a minimum of 41.1%. This analysis clearly indicates that in most of the holdings inputs have been allocated moderately efficient manner as specified in the ranges of allocative efficiency. In other words, there is a further scope of increasing production of all crops, paddy and amanswarna cultivation by 16, 14 and 26%, respectively. This can be achieved by suitably reallocating production inputs as used by the best practice farms.

Table 1:	Summary statistics of the estimates of allocative efficiency (in percentage) under alternative modes of cultivation
Source: Field Survey 2006-07

Determinants of allocative efficiency: The second stage of the analysis in the section is devoted to identify the sources of allocative efficiency by investigating the relationship between farm specific characteristics and the computed allocative efficiency indices. Censored maximum likelihood estimator is used to estimate the γ coefficients in equation specified in the methodological section. The results under alternative crop cultivations are summarized in Table 2.

The results reveal that the choice of tenurial contract does have a role to play influencing the input allocation decision in production¹⁴. Coefficients of the contract dummy variables defining fixed rent, pure sharecropping and cost sharecropping¹⁵ are all positive. But, all contracts are not equally efficient in allocating resources optimally. Only the coefficients of fixed rent tenancy (i.e, 0.049676 in paddy and 0.035394 in amanswarna cultivations) and cost sharecropping tenancy (i.e., 0.077376, 0.065694 and 0.029185 in three cultivations, respectively) are statistically significant and different from zero.

However, resource allocations are not uniformly efficient in nature across all contracts. To test the empirical relevance of the hypothesis, the study conducted Wald test on the equality of coefficients of alternative tenancy arrangements. Test results are presented in the Table 3. It can be seen that the hypothesis of equality of the coefficients of fixed rent and pure sharecropping (H₀: γ₁ = γ₂) is accepted, while the equality of the coefficients of pure sharecropping and cost sharecropping (H₀: γ₂ = γ₃) and the equality of the coefficients of fixed rent and cost sharecropping (H₀: γ₁ = γ₃) are rejected.

Table 2:	Determinants of allocative efficiency under alternative crop cultivations
Source: Field Survey (2006-07), ***Significant at 1% level, **Significant at 10% level, *Significant at 15% level

Table 3:	Wald test on the equality of coefficients under alternative tenurial contracts
Source: Field Survey 2006-07

This indicates that the difference in allocative efficiencies associated with fixed rent and pure sharecropping is not statistically significant, while allocative efficiency associated with pure sharecropping and cost sharecropping and that of fixed rent and cost sharecropping differ significantly.

In addition to land tenure contracts, several other socio-economic and demographic factors have an influence on the allocative efficiency. The positive and significant coefficient of the years of schooling and experience of the head of the household¹⁶ justify the argument that schooling and experience influence positively the level of allocative efficiency in agriculture. The coefficient of the operated land variable is estimated to be positive and significant in all three regressions. The evidence indicates that larger farmers tend to be more efficient in allocating inputs than small farmers. The result is further supported by the fact that the extent of allocative efficiency is observed to be inversely related to the fragmentation of landholdings. The negative coefficient of BARGA is contrary to our expectation. But it is not significantly different from zero in all crop and paddy regressions. The positive and significant coefficient of interlinkage (INTER) in all three regressions established that interlinked transactions lead to improve the allocative efficiency. The impact of availability of credit (whether formal or informal) on the allocative efficiency of farmers is captured by a LOAN dummy variable. The positive and significant coefficients of the dummy variable justify the catalytic role of credit in improving allocative efficiency of farmers.

Let us now discuss the results in the light of existing literatures. It has been found in our study that increased farming experience coupled with higher level of formal schooling lead to enhance the skill of decision making in the use of inputs. However, the association between schooling and experience on the allocative efficiency in the existing literature is quite mixed. Some studies have found a positive connection between schooling and allocative efficiency (Wadud, 2003) while some studies have reported a negative association between education and allocative efficiency (Nwachukwu and Onyenweaku, 2009; Bravo-Ureta and Pinheiro, 1997)¹⁷. On the other hand, some studies also reported a positive relationship between experience and allocative efficiency (Bravo-Ureta and Pinheiro, 1993; Nwachukwu and Onyenweaku, 2009), The link between allocative efficiency and farm size has been the subject of much discussion in the literature (Berry and Cline, 1979). Present result that larger farmers tend to be more efficient in allocating inputs than small farmers is consistent with the findings of Bravo-Ureta and Pinheiro (1997) of Dominican Republic; Wadud (2003) of Bangladesh while they are contradicted with the findings of Nwachukwu and Onyenweaku (2009) of Nigeria. Fragmentation of landholding has an important bearing on allocative efficiency in agricultural production. Present result that highly fragmented land hinders the use of improved technologies conforms to the results obtained by Wadud (2003). In the study, it is expected that successful implementation of the policy of Operation Barga would enhance farmer’s incentive to invest in yield-increasing inputs and to put land to its most productive use¹⁷. However, in the light of our empirical findings, it is to be noted that the successful implementation of Operation Barga in West Bengal has led to marginalization of operational holding NSSO (1997)¹⁸ which is essentially a stylized feature of West Bengal agriculture. So marginalization of landholdings might act an adverse impact on allocative efficiency. On the issue of interlinkage in factor markets and allocative efficiency, our empirical evidence supports the neoclassical presumption that interlinked transactions resulted in improving the allocative efficiency in agricultural production¹⁹. Regarding the impact of availability of credit (whether formal or informal) on the allocative efficiency of farmers our proposition is that the availability of credit either from formal or informal sectors can act as a catalytic role in channeling desired inputs in the process of production and thus it enhances the allocative efficiency level of the farmers. Contrary to present result, Nwachukwu and Onyenweaku (2009) have observed a significant negative relationship between the access of credit and allocative efficiency. Their argument was that inaccessibility of credit acts as a constraint in timely purchases of inputs and engagement of farm resources and thus puts an obstacle in improving the allocative efficiency in agriculture.

CONCLUSION

It is possible to increase agricultural output by reallocating input mix efficiently without any resort to new technology. Allocative efficiency can be measured in three alternative ways: neo-classical profit maximization method where equality between the marginal value products and marginal factor costs is tested; constrained profit maximization method where a test is conducted to examine whether input-output proportions are constant for all the farmers; and constrained cost minimization method of Data Envelopment Analysis. In our study, we have used cost minimizing behaviour to examine allocative efficiency in the light of several criticisms of profit maximization hypothesis in Indian agriculture. Empirical results based on DEA reveals that farmers are moderately efficient in the choice of inputs of rural West Bengal. It is interesting to note that various attributes of farmer and farm specific characteristics determine the input allocation decision in production. Choice of tenurial contracts has a significant role to play in influencing resource allocation of inputs. All contracts are not found to be equally efficient. Fixed rent tenants are able to allocate resources more efficiently than the sharecroppers. Besides tenurial contracts, other determinants which have significant bearings in allocative efficiency are education level of head of the household, operated land, interlinkage of factor markets and availability of credit to the rural household.

¹See Greene (1997) for a survey of the literature.

²The experience of an increase in land productivity in India is mainly caused by the input intensification in the use of fertilizer, tractor and labour (Piya et al., 2011).

³The study on West Bengal agriculture is crucial in the context of changing dynamics of agrarian productivity over time. West Bengal emerged as one of the progressive agriculturally developed states in India during the period of 1980s. However, with the advent of globalization in the nineties and thereafter, West Bengal agriculture lost its past glory and the state evidenced significant decline in agricultural productivity growth (Ghosh, 2010a, b).

⁴The district of Burdwan comprised of 7.83% of total leased in land (wholly and partly) in the state of West Bengal. Only two hill districts, Darjeeling and Jalpaiguri, comprised of 12.11 and 21.28% of leased in area respectively are above Burdwan district. However, terms of leasing in the hill districts are distinct from other districts of West Bengal (Agricultural Census, 2000-01). Thus the choice of the district of Burdwan as our survey area is purely based on the ground of the dominant practice of land leasing for crop cultivation in the state. Historically, the district of Burdwan is known as rice bowl of West Bengal. Potato, rice, wheat, jute and mustard are the principal crops in the district (Ghosh, 2011).

⁵The selection of district, block and villages are based on a-priori information and hence it is purposive and non-random.

⁶In nonparametric tests of cost minimizing behaviour, Ray and Bhadra modified Weak Axiom of Cost Minimization (WACM, Varian (1984) to derive the Weak Axiom of Variable Cost Minimization (WAVCM). In fact, Varian (1984). proposes WACM as an alternative to Linear Programming procedure to solve cost minimization problem. In this nonparametric test, all inputs are considered variable. But Ray and Bhadra (1993) criticized the assumption of variable inputs in WACM in the context of less developed countries, where markets for capital and land are not well developed. An alternative WAVCM is proposed to allow for quasi-fixity of one or several inputs.

⁷To capture four types of contract choice, viz. fixed rent, pure sharecropping, sharecropping with cost sharing and owner contract, we have used three contract dummy variables in the study.

⁸This approach of non-parametric mathematical programming approach to frontier estimation was first developed by Charnes et al. (1978).

⁹2.5 bigha = 1 acre.

¹⁰The government of West Bengal initiated Operation Barga in 1978 to reform the sharecropping system that was widespread throughout the state. The primary objective of Operation Barga is to restructure the agrarian relations and direct them to an egalitarian society by enlarging the land base of the rural poor. By the end of November, 2005, the total number of bargaders recorded in the Record of Rights was 15.31 lakh. The area under these bargaders amounted to 4.54 lakh hectares (Economic Review of West Bengal, 2005-06). The evidence reflects an unparallel history created in reforming property rights in India. However, in our surveyed villages only 17% of the surveyed tenants have participated in the drive of Operation Barga and registered their leased in land. The policy of the West Bengal government to give sharecroppers the possibility of accessing institutional credit using their land rights (in the form of pattadars and bargadars) as collateral is also not found empirical support in a significant extent in present study area

¹¹See Coelli A guide to DEAP version 2.1: A data envelopment analysis (Computer) program, CEPA working paper 96/08.

¹²Amanswarna is most preferred HYV variety of paddy cultivation in terms of coverage of area in our study villages. In fact, aman paddy accounts for about two-thirds of the net cultivated areas in West Bengal (Chandra, 1974).

¹³To measure a composite index of output of all crops, outputs of individual crops are converted as an equivalent of amanswarna. Prices of all crops are taken into account to make the necessary conversion.

¹⁴Ahmed et al. (2002) argued that tenure status significantly influences technical efficiency. Empirical result suggests that fixed rent, sharecropping and gift plots are less efficient compared to owner cultivated plots.

¹⁵Under fixed rent tenancy, the landlord leases out the land to the tenant and in return asks for a fixed rental payment. The sharecropping is a form of tenurial contact under which tenant leases in land from the landlord and shares the output under predetermined contractual arrangement. The sharecropping is again of two types. The cost sharing sharecropping under which the landlord shares the cost of factor of production usually in the same proportion as the share of output. On the other hand, under the arrangements of the sharecropping without cost sharing tenants bear the full cost of production and the proportion of output share to the landlord is usually smaller than under cost-sharing arrangement. Inclusion of cost sharing arrangement in our analysis is particularly relevant in view of the widespread prevalence of the arrangement as a part of the tenancy contract, which is a striking new phenomenon in Indian agriculture (Bardhan, 1984). Coexistence of all three forms of contracts is prevalent in our surveyed villages.

¹⁶Though the coefficients of education of head of the household are found to be significant in all three regressions, the coefficient of experience of head of the household is significant only in paddy cultivation.

¹⁷Some studies also pointed out the favourable impact of agrarian reform on the allocation of resources (Bravo-Ureta and Pinheiro, 1997; Dewalt, 1979; Meyer, 1989; Seligson, 1982).

¹⁸Nearly 81% of the operational holdings in West Bengal now belong to the marginal category (NSSO, 1997).

¹⁹On the impact of interlinked transactions on allocative efficiency, there are two schools of thought: Neoclassical and the Marxist. Present result is in line with the Neoclassical presumption that the institution of interlinkage is conducive to improve allocative efficiency and thus, in turn, induces for more rapid adoption of innovation (Cheung, 1969; Bardhan, 1984, Braverman and Srinivasan, 1981; Braverman and Srinivasan, 1982; Basu et al., 2000).