Precaution with multiple instruments: The importance of substitution effects

Using a unified approach, we show how precautionary saving, self-protection and self-insurance are jointly determined by risk preferences and the preference over the timing of uncertainty resolution. We provide a general result when decision-makers use a single instrument at a time. When multiple instruments are used simultaneously, substitution effects arise which attenuate precaution. A numerical analysis demonstrates that these substitution effects can dominate the precautionary effect. For plausible risk and time preference parameters and empirically relevant income risk levels, substitution effects can lead to precautionary disinvestment in self-protection and even crowd out the demand for self-protection entirely. In this case, what looks like lack of precautionary behavior at the surface might not be indicative of lack of prudence but simply be the result of omitted-instrument bias.