2.1. Theoretical Framework As stated earlier, the main aim of this study is first to identify the factors influencing adoption of improved varieties of pulses, and conditional on that choice, identify the drivers of productivity and efficiency of improved variety pulse producers, which was done jointly in order to circumvent the methodological weaknesses in conducting these two analyses separately. The framework required to conduct this joint exercise is known as the ‘sample-selection stochastic frontier analysis. The conventional approach to correct for sample selection bias was proposed by Heckman which is a popular method but still has a weakness because the framework is appropriate for linear models, i.e., standard regression models, only. The method is inappropriate for non-linear models, such as probit or Tobit models, which are the standard methods used to analyse technology adoption decisions. This is because the impact on the conditional mean of the non-linear model of interest (e.g., the probit model of improved pulse technology adoption) may not take the form of an inverse Mills ratio, which was used to correct for the sample-selection bias in Heckman’s approach by incorporating this ratio along with the other regressors in the pulse production function model conducted at the second stage. Also, the bivariate normality assumption needed to justify the inclusion of the inverse Mills ratio in the second model (e.g., the production function) does not appear anywhere in Heckman’s (1976) method. Further, conditioned on the sample selection (i.e., improved variety adopters), the dependent variable (i.e., pulse production) may not have the distribution described by the model in the absence of selection. Subsequently, Greene proposed an internally consistent method of incorporating ‘sample selection bias in a stochastic frontier framework, which was adopted in our study and is described below.
Farmers are assumed to choose between improved and traditional pulse varieties to maximize returns subject to a set of socio-economic factors. The decision of the ith farmer to choose improved pulses is described by an unobservable selection criterion function, Ii *, which is postulated to be a function of a vector of factors representing farmers’ socio-economic circumstances. The selection criterion function is not observed. Rather, a dummy variable, I, is observed. The variable takes a value of 1 for improved pulse producers and 0 otherwise.
2.2. Study Area and the Data The study uses cross-sectional primary data collected during 2012. A total of five major pulses, namely, lentil, mungbean, blackgram, chickpea and grasspea, was considered for this study. These five pulses covered more than 90% of the total pulse area in Bangladesh in 2011. Based on the area coverage of individual pulses in 2011, three districts consisting of high, medium, and low intensity of area under each type of pulses were purposively selected. This would imply selection of 15 districts but because some district produces more than one type of pulse, only a total 10 different districts were covered. These are: Natore, Rajshahi, Chapainawabganj, Jessore, Jhenaidah, Meherpur, Madaripur, Faridpur, Rajbari, and Patuakhali. Next, based on the intensity of area covered under each pulse, three Upazilas (sub-districts) in each district were selected. The information on the area and production of selected pulse was collected from respective Upazilas and district-level Department of Agricultural Extension (DAE) offices. Next, from each Upazila, one village under one block was selected with the help of knowledgeable persons and DAE personnel i.e. Sub-Assistant Agriculture Officer (SAAO). A complete list of all pulse growers from the selected village was prepared with the help of SAAO. From that list, 180 farmers were selected randomly from each Upazila taking 60 farmers from each village. Data were randomly collected from improved and traditional pulse variety growers. Thus, a total of 2700 (3 districts × 3 Upazilas × 60 farmers × 5 pulse types) pulse growers were selected for the interview. The interview schedule was pre-tested and one of the authors and a trained enumerator collected the data using face-to-face interviews with the growers after briefing them about the objectives of the study.
Two sets of variables are needed for this study: One for the probit variety selection equation model and the other for the stochastic production frontier model, discussed below. The dependent variable in the probit equation is the farmers’ variety selection criterion. This is a binary variable that takes the value of 1 if a plot is planted with improved pulse and 0 otherwise. Farmers were specifically asked about the adoption of an improved variety of each pulse type, the details of which are presented in Appendix A Table A1. Table A1 shows that farmers used 6 types of improved varieties of lentil and mungbean, 8 types of chickpea, 3 types of blackgram and 2 types of grasspea in the study areas. The explanatory variables include pulse yield, farming experience, education, subsistence pressure, information on main occupation, agricultural training, extension contact and land type. All the input and output variables used in the stochastic production frontier were measured on a per farm basis. The eight input variables used in the model include land, labour, chemical fertilizers, pesticide, irrigation, mechanical power services, seed and organic manure and all are expected to have a positive relationship with pulse output. Also, dummy variables were used to account for pulse type, non-use of some inputs, location or growing district, optimum sowing period and use of own sourced seed. The variables used in the probit model and the production function model are based on the literature and justification thereof. Since the variables in the probit variety selection equation and the stochastic production frontier differ, the structural model satisfies the identification criterion.