| The solution of stochastic optimal control problems, under the assumptions of constant relative and constant absolute risk aversion, yields two sets of optimal paths for the debt-to-asset ratio and consumption over time. Analysis of these optimal paths reveals that important characteristics of individual behavior depend on whether constant relative or constant absolute risk aversion is assumed. For example, under constant relative risk aversion, the optimal leverage position does not depend on the firm's equity holdings, while under constant absolute risk aversion, the optimal leverage position decreases as equity increases. Furthermore, the optimal average propensity to consume (out of disposable income) is also independent of equity value under constant relative risk aversion. Under constant absolute risk aversion, however, as the firm accumulates equity over time, the optimal average propensity to withdraw income from the farm operation decreases.;The second part of the study deals with estimating risk aversion measures and testing the restrictions implied by the optimal path equations under the assumptions of constant absolute and constant relative risk aversion, for the aggregate agricultural sector. Even though the restrictions implied by the assumption of constant absolute risk aversion cannot be rejected using the only (asymptotic) test available, the study concludes that the associated optimal paths do not describe the behavior of the aggregate agricultural sector very well. In addition, since the risk aversion measure cannot be placed within empirically meaningful bounds under constant absolute risk aversion, using the estimated optimal paths in simulation or comparative statics would lack any credibility from a statistical standpoint.;The optimal paths associated with the assumption of constant relative risk aversion, on the other hand, appear to be quite consistent with the aggregate behavior of the agricultural sector. Furthermore, the risk aversion measure can be placed within empirically meaningful bounds in this case. Results from comparative statics analysis investigating the effect of changes in the exogenous paths on the optimal leverage position and consumption prove to be quite reliable, from a statistical perspective. |
