Two complications arise from the inclusion of contract farmers in the empirical analysis. First, the decision to be a contract farmer may not be independent from production decisions and profit per unit, leading to simultaneity bias if a dummy variable for contract farming is included in the second stage regression explaining why some farms are farther from the frontier than others. Second, contract farmers do not pay for feed or other inputs, so their input prices are zero, and their output prices are typically fees negotiated in advance. Thus, there is a conceptual and data problem in comparing independent and contract farmers in the same regression.
The solution adopted for the price problem posed by contracting is to use actual prices paid for inputs (zero) and received for outputs (fees) for contract farmers. These balance each other in the computation of profit for the dependent variable. On the RHS of the first stage regression, the zero input prices for contract farmers are handled using slope dummy variables for coefficients of the prices of inputs provided free to contract farmers, where the slope dummy applies if and only if the farmer in question is a contract farmer. This allows for the estimation within the same regression of different response coefficients to input prices for contract and independent farmers. Finally, particular attention has to be devoted to fixed resources (land, family labor, sunk capital) provided by both contract and independent farmers. It is these variables that are central in explaining production levels of contract farmers, who are not constrained by price in expanding production.
The solution adopted for the endogeneity problem posed by contracting is either to not have a variable for contracting in the stochastic profit frontier, or to use an instrumented variable. The latter can be obtained by using a probit estimator on a regression of the decision to contract (1 if a contractor, 0 otherwise) on all exogenous household and farm characteristics that might explain why a farmer chooses to be a contractor, including at least one variable relevant to the decision to be a contractor (such non-farm income) that is not part of the determinants of relative profitability. Then the predicted contracting status (contractor or independent) from the regression for each farm is used in lieu of the actual status of the farm.