The effect of fertilizer on risk: a heteroscedastic production function with measurable stochastic inputs

Rosegrant, Mark W.; Roumasset, James A. 1985. The effect of fertilizer on risk: a heteroscedastic production function with measurable stochastic inputs. American Journal of Agricultural Economics 29(2): 107-121. https://doi.org/10.1111/J.1467-8489.1985.TB00651.X

The sources of production risk are many and diverse in nature. Estimating risk as a black box, without explicit recognition of its sources, can lead to inferior estimates of optimal inputs under risk aversion. In this paper, a method is presented for estimating production functions with measurable stochastic inputs and for generating the parameters of the probability distributions of yield for various environments and input levels. Based on this method, it appears that moderate risk aversion can account for a 6.7 per cent to 16.7 per cent reduction in nitrogen use (relative to the risk‐neutral solution) for selected rice producing areas of the Philippines. Estimating optimal inputs without environment specific information about the sources of risk leads to large errors. This underscores the value of collecting information about the sources of risk and of exercising caution when such information is not available.