A Stochastic Dominance Comparison of Reduced Tillage Systems in Corn and Soybean Production under Risk: Comment

Abstract

In a recent AJAE article, Klemme examined stochastic dominance of efficient tillage systems for corn and soybeans. The results obtained with second-degree stochastic dominance indicated that risk-averse farmers who place low values on soil losses may select tillage-intensive systems (conventional and chisel tillage) since they are generally stochastically dominant in the second degree (SSD) over no-till in the production of corn and soybeans (p. 555). However, adding $10-$15 per acre to the cost of conventional tillage systems as a proxy for soil loss values eliminates all second-degree stochastic dominance by those systems. This soil loss value can be interpreted as the annualized present value (equivalent level annuity) of a subsidy required or a loss in income from yield reduction over a specified planning horizon. One of Klemme's objectives is to determine the annual percentage yield loss that is required to generate an annualized present value (annuity equivalent to the present value of the cost of yield loss) equivalent to the per acre difference in return from the tillage systems. He does this by assuming an annual percentage yield loss and a real corn price of $3.00 per bushel and calculating a net present value, based on a real discount rate of 3.5%. Klemme then amortizes the present value, using a nominal discount rate of 12%. This approach is useful for determining how much of a yield loss from additional soil erosion in the conventional tillage systems would be required to make the annualized net return difference zero and, therefore, essentially risk-preference indifferent by SSD criteria. However, because the present value estimates are in 1982 constant dollars, it is inappropriate to amortize with a nominal discount rate. The use of an inappropriate nominal amortization rate affects the interpretation of Klemme's results. The actual values, amortized using the real discount rates of 3.5% and 5.0%, and the original estimates represented by Klemme, are presented in table 1. Table 1 is essentially a reproduction of Klemme's table 4 with the corrected estimates inserted. To find his original values, a nominal discount rate of 12% must be assumed for finding an annuity equivalent to the total present cost of yield losses. Amortizing at 12% implies that the price is inflated at an 8.21% annual rate and discounted at a