Optimal On-Farm Grain Storage by Risk-Averse Farmers
Lai, Jing-Yi, Myers, Robert J., Hanson, Steven D., Journal of Agricultural and Resource Economics
Most previous research on post-harvest grain storage by farmers has assumed risk-neutral behavior and/or made restrictive assumptions about underlying price probability distributions. In this study, we solve the optimal on-farm storage problem for a risk-averse farmer under more general assumptions about underlying price distributions. The resulting model is applied to Michigan corn farmers and findings show, contrary to the "sell all or nothing" risk-neutral rule, risk-averse farmers will spread sales out over the storage season. As farmers become more risk averse, the optimal strategy is to sell more grain at harvest and spread sales over the storage season, even though this practice reduces expected return. This result is more consistent with observed farmer behavior than the "sell all or nothing" risk-neutral rule.
Key words: grain storage, risk aversion, stochastic dynamic programming
On-farm grain storage can have important effects on farm profitability. Thus, it is not surprising many research and extension programs have investigated the optimal timing of sales from storage (e.g., Fackler and Livingston; Ferris; Lence, Kimle, and Hayenga; Tronstad and Taylor; and Zulauf and Irwin). By storing grain at harvest and waiting for prices to rise over the storage season, farmers can sometimes obtain higher total returns, even after accounting for storage costs. Of course, this strategy is risky because prices sometimes fall over the storage season or do not rise enough to cover storage costs. Furthermore, stocks must be sold at some point in time, and determining the best time to sell can be difficult.
In a recent article, Fackler and Livingston solve the optimal on-farm storage problem using stochastic dynamic programming, and apply their model to on-farm storage of soybeans in Illinois. One of the innovations in their analysis is that they model irreversibility by assuming, once sold, on-farm stocks cannot be replenished until the next harvest. Speculative repurchase of grain is ruled out on grounds that on-farm storage is a business marketing activity, and transaction costs from speculative repurchase will discourage such behavior. This appears to be a significant innovation because irreversibility is shown to have an important impact on optimal grain storage decisions, and certainly, very little speculative repurchase of grain is observed among operational grain farms (Sartwelle et al.). Fackler and Livingston's optimal storage strategy under irreversibility is an "all or nothing" rule-sell everything now if the current price is high enough, otherwise wait and sell nothing. The decision to sell is determined by a "cutoff price" that may change over time in response to changing information about the state of the market (and hence expectations about future price levels).
One concern about Fackler and Livingston's "all or nothing" rule is that it seems at odds with the way operating grain farmers actually behave. For example, on-farm corn stocks in Michigan were estimated at 120 million bushels (mb) on January 1, 2002, after the 2001 corn harvest. But stocks had fallen to 80 mb by March 1, 54 mb by June 1, and 16 mb by September 1, 2002 [U.S. Department of Agriculture (USDA)]. Clearly, sales out of on-farm storage are spread out over the storage season, at least at the aggregate state level. Of course, these aggregate data could be reflecting a large number of different individual farmers each making "all or nothing" sell decisions at different points in time. Nevertheless, both the aggregate data and anecdotal evidence suggest many, if not most, farmers with on-farm storage facilities spread sales out over the storage season, rather than selling everything at one time.
The "all or nothing" nature of Fackler and Livingston's optimal decision rule stems from the linearity of their return function and transition equation. Clearly, any model extension which makes the return function strictly concave will result in optimal sales which are spread out over the storage season, at least to some extent. …