In most biological production sectors output risk is an inherent feature. An important
characteristic of production risk is that input levels influence the level of output risk. Some
inputs increase while others reduce the level of output risk. There are compelling reasons
for taking this risk into account in empirical analysis of firm behavior and productivity
change. First, risk averse producers choose input levels which differ from the optimal input
levels of risk neutral producers. Second, risk averse producers will be concerned about
risk properties when they consider adoption of new technologies, and may not necessarily
choose the technology with the highest mean output.
The overwhelming majority of econometric productivity studies in agriculture and other
risky production sectors use a deterministic setting, where the typical approach is estimation
of primal or dual translog production models. Under risk dual models are less tractable for
econometric implementation than in the conventional deterministic setting (Coyle, 1995;
Pope and Chavas, 1994; Pope and Just, 1996). The standard translog production function
approach is also problematic since it restricts output risk to increase in input levels.
The framework for much of the subsequent research on production risk was laid in the
important paper of Just and Pope (1978). They proposed a production function which allows
inputs to influence both the mean and variance of output (see Section 1). Several subsequent
empirical studies of production risk using Just and Pope’s approach have provided evidence
of output risk in biological production sectors.1