3.2. Model specification

To examine the factors that influence the decision of a household to purchase a PT and provide tilling services to other farmers in Bangladesh, Equation (1) is developed as follows:

where Y_1i is a dependent variable that assumes the value 1 if a household owned a PT and provided services to others, and 0 otherwise. Among the explanatory variables, HHC_i is a vector of independent variables that includes age and years of schooling of the household head, the major occupation dummy that assumes a value of 1 if a household head is engaged in non-farm activities as a major source of livelihood and 0 otherwise, and the total number of male family members in the household. Remittance_i is a dummy variable (1 if yes, 0 if no) for households which receive remittances from extended family members living in cities and abroad, Credit_i a self-perceived credit constraint dummy which assumes the value 1 if a household head perceived himself as facing credit constraint and 0 otherwise; Borrowed_i is the amount of money that PT owner either actually borrowed or could borrow from formal sources, and Risk_i is the self-assessed score regarding general risks whose value ranges between 0 at the minimum if a household head is entirely risk averse, and 10 at the maximum if a household head is entirely not averse to risk taking. The independent variable also includes 11 dummies for 12 sampled sub-districts (SD_j)to capture the sub-district level of unobserved influences affecting ownership and providing tillage service by owning a PT by the sampled households. In this case, Birol sub-district of Dinajpur District of Rangpur Division was set as a base (assigned the value 0). It is expected that a risk-taking household head, with more years of schooling and endowed with more male family members, is more likely to be a tilling-service provider compared to others.

In the case of Equation (1), the dependent variable is a binary response variable (0, 1), and thus to estimate the probability of PT ownership and providing tillage services by a household, a maximum likelihood estimation procedure applying a probit model estimation method is applied. In estimating the probability of PT ownership and providing tilling services, five models were estimated. Out of 695 sampled households only 71 owned PTs, all of whom provide tilling services to other farmers. The first model includes the full sample. However, the ubiquity of the households with no PT (Y_i = 0) might divert the estimated results toward biasness. To enhance the balance between yes (Y_i = 1) and no (Y_i = 0) and to check the robustness of the major findings, four additional models are specified. First, four groups of data sets are randomly generated with an almost equal number of observations, each of which includes 167–173 non-PT owner observations. Second, the 71 PT owner observations (Yi = 1) are added to each set, and the models are estimated applying a probit model estimation procedure. By doing this, this study checked the sensitivity of the major findings as well as the robustness of the major policy variables.

Under the fee-for-tilling-service system, service providers charge fees to the client farmers for providing PT tilling services. To examine the factors that affect the service charges, Equation (2) is developed as follows:

where Y_2i is a dependent variable that includes the service charge per hectare for one full tillage in BDT. Among the explanatory variables in the Equation (2), HHC_i is a vector of independent variables that includes all the household level variables described in the case of Equation (1). However, HHC_i also includes an experience variable that is the years a household head has been engaged in the tilling-service business. Sifeng_i is a brand dummy that assumes the value 1 if the PT model is Sifeng, or 0 otherwise; Manager_iis a hired manager dummy that assumes the value 1 if a household hires a manager/worker to operate the PT, or 0 otherwise. Similar to Equation (1), the independent variable includes 11 dummies for 12 sampled sub-districts in which Birol sub-district of Dinajpur District of Rangpur Division is set as the base. Equation (2) also includes λi^, a generalised inverse Mills ratio calculated from Equation (1) following the estimation process suggested by Vella (1998), as an independent variable. Both in Equation (1) and (2), α ₀ andθ₀ are the scalar parameters, and ϕ , Φ, α,θ,βandϕare the parameters to be estimated; I stands for household, and εarethe random error terms. Note that as Equation (2) includes λi^ estimated from Equation (1), to correct for the standard error, we applied the bootstrapping method and replicate the regression estimation procedures 1000 times in the case of Equation (2). Finally, three different model versions are estimated, depending on the inclusion of two additional variables: the engine horsepower (HP) of the PT engine and an interaction term between the PT, HP and hired manager.

To estimate Equation (2), the tobit estimation approach is applied censoring at 0 (in the left), as out of 695 sampled farm households, only 71 of the respondents provide tillage services. As only 71 PT owners provide PT services on a fee basis, applying OLS estimation in this case might generate biased results.