Calibration of Agricultural Risk Programming Models Using Positive Mathematical Programming

Beginning in the 1960s, agricultural economists used mathematical programming methods to examine producers responses to policy changes. Today, positive mathematical programming (PMP) employs observed average costs and crop allocations to calibrate a nonlinear cost function, thereby modifying a linear objective function to a nonlinear one to replicate observed allocations. The standard PMP approach takes into account producers risk aversion, which is not a very satisfying outcome because it intricately entangles the cost parameters and the producer s attitudes biophysical aspects of production and human behavior are intertwined so that one cannot study the impact of policy on one in the absence of the other. Several approaches that calibrate both the risk coefficient and cost function parameters have been proposed. In this paper, we discuss two methods mentioned in literature one based on constant absolute risk aversion (exponential utility function) and the other on decreasing absolute risk aversion (logarithmic utility function). We compare these methods to an approach that employs maximum entropy method. Then we use historical data from a region in Alberta s southern grain belt to compare the different outcomes to which the three approaches lead. We find that the latter approach is robust and easier to employ. Acknowledgement :