New results on precautionary saving and nonlinear risks

We study precautionary saving in a two-period model that allows for nonlinear risks and nonseparable preferences. Permitting nonlinear risk effects is important because they are common in the developing world or when worldwide shocks hit economies, like the COVID-19 pandemic. Allowing nonseparable preferences is also important because they admit the incorporation of intergenerational transfer, habit persistence and other specific features of intertemporal decision making. We decompose the risk shock using Davis's (Int Econ Rev 30(1):131-136, 1989) compensation method and analyze the income and substitution effect of an increase in risk. We prove that the substitution effect is always negative and, therefore, the income effect must be positive and larger in size to have a precautionary net effect. We then apply the method to various sources of risk, such as income, interest rate and wealth risk. We analyze the magnitude of each effect and find the conditions required to guarantee precautionary saving in each case. Our results are presented as signs of covariances, which provides a new perspective on precautionary saving.