Risk Aversion and the Propensities for Self-Insurance and Self-Protection

Abstract

For a risk-averse individual, methods for reducing expected financial impact of a loss include reducing severity of any loss that occurs (self-insurance) and reducing probability of occurrence of a loss (self-protection).' The literature on this topic has pointed to several anomalies, whereby use of self-protection and self-insurance yield quite unsimilar results. For example, Ehrlich and Becker [5] show that self-insurance is always a substitute for market insurance (an insurance company's indemnifying a loss) whereas self-protection and market insurance might be complements. Dionne and Eeckhoudt [4] show that a more risk-averse consumer would always invest more in self-insurance activities, but not necessarily more in self-protection They argue [4, 42] that this result is counterintuitive and provides an exception to the widely accepted result that increased risk aversion reduces risky activities. Ehrlich and Becker [5, 639] argue that the incentive to self-protect... is not so dependent on attitude towards risk. Both of above papers seem to take for granted that self-protection activities reduce of final wealth distribution. However, as we argue below, this is not case if riskiness is defined as in Rothschild and Stiglitz [14]. Even if we use variance as our risk measure, we do not always reduce risk via self-protection. Dionne and Eeckhoudt suggest that these results might not be robust enough to extend to models that incorporate random initial wealth risk and state-dependent preferences. We show that model seems to be very robust. We also explain why self-protection is not at all an exception to long-standing result of Arrow [1], whereby more risk-averse individuals undertake a lower