A Two-Shock Model of the Impact of Crop Insurance on Input Use: Analytic and Simulation Results

Abstract

By altering the probability distribution of farm income, crop insurance programs affect farmer's input use decision. Ramaswami's (1993) one-shock model analyzed the effect of the crop insurance on single input use by allowing the randomness of yield while keeping price constant in revenue determination. The total effect of actuarially fair insurance on input use was decomposed into risk reduction effect and moral hazard effect, and the directions of the two effects were examined. He showed that the total impact of actuarially fair crop insurance on input use was a) to reduce it if the input was risk decreasing and b) indeterminate if the input was risk increasing. However, the evidence from previous empirical work has been mixed. Horowitz and Lichtenberg (1993) suggested insured farmers raising corn use more fertilizers and pesticides while Smith and Goodwin (1996) obtained the opposite result for wheat. Smith and Goodwin also used more comprehensive econometric tests and had a higher quality data set. A common belief is that fertilizer is risk increasing and pesticide risk decreasing. Ramaswami's model assumed crop price was constant and yield was the only source of randomness in farmer's revenue. In reality, market price is a random variable and often negatively correlated with the farmer's yield. For example, bad weather conditions tend to reduce yield across farms in a common region, which may cause diminished quantities supplied and higher crop price. Our paper extends Ramaswami's one-shock model to a two-shock model, and generalizes the two propositions in that paper by introducing randomness to price as well as yield. With two random shocks, the total insurance effect on input use is indeterminate for both risk increasing and risk decreasing inputs, which is consistent with the mixed empirical evidence. Our study also provides a numerical method to decompose the total insurance effect into a risk reduction effect and a moral hazard effect using empirical data. The simulation based on 75 percent coverage level suggests the total insurance effect is economically small to the farmer as are the risk reduction effect and moral hazard effect under mild risk aversion. And the moral hazard effect is less significant than the risk reduction effect. However, the moral hazard effect becomes larger if a higher coverage level is used.