Dynamic optimization of consumption smoothing, insurance, and debt under liquidity constraint
MetadataShow full item record
The dynamic optimization process of consumption, insurance, and debt and its relationship with farm precautionary wealth are simulated by a stochastic dynamic model. Both finite and infinite optimization horizon are considered to examine the effect of retirement plans on optimal strategy paths and the resulting net wealth path. A risk averse corn farmer in Mitchell, Georgia, is supposed to maximize the expected utility defined over life-cycle consumption. Irrigation, insurance, and credit are considered explicitly as three strategies to cope with risk associated with income shocks. Three types of insurance products, a traditional farm-yield based Multi-peril Crop Insurance (MPCI), an area-yield based Group Risk Plan (GRP), and a precipitation based Weather Derivative (WD), are compared to investigate the impact of basis risk on the optimization process. Effects of liquidity constraint, premium loading, market risk, risk aversion level, impatience level, and interest rate on the optimal process are examined through sensitivity analysis. The results show that the choice variables and state variable wealth evolve over time to reach a steady-state distribution, which provide insight about the behavior of most farmers in the economy. The result concerning marginal propensity to consume (MPC) seems to support Friedman (1957)'s PIH theory and provides intuition that poor farmers use a larger proportion of transitory income for consumption than rich farmers. The result concerning insurance confirms Gollier (2003)'s conclusion, that wealthier farmers tend to reduce insurance purchase. A variety of sensitivity analysis shows that the general shape of the consumption function c(w) (increasing and concave) is unchanged under alternative scenarios. Under stricter liquidity constraint, MPC is higher, indicating that the farmer's consumption level is more influenced by transitory shock to their income than that in benchmark case. More impatient/poor farmers are shown to have higher intention to invest in insurance for precautionary purposes, even if the insurance is expensive. Changes in interest rate and in farmers' credit limit are shown to have great impact on consumption, insurance, and debt, which would be valuable for government agencies interested in monetary policy transmission. Basis risk leads farmers to accumulate desired precautionary wealth and to reduce desired insurance holdings.