Compound Risk and the Welfare Consequences of Insurance

A focus on consumer welfare of financial decisions implies that we cannot rely on direct revealed preference, or purchase of financial products as a metric. It also implies that we need to evaluate financial decisions in terms of the heterogenous preferences and beliefs of consumers. We assess the welfare implications of decisions of individuals to purchase or not purchase index insurance by eliciting individual preferences that are relevant to financial decisions with compound risk: risk preferences over simple and compound risk, probability weighting, and violation of the Reduction of Compound Lotteries (ROCL) axiom. We find that individuals realize, on average, only 48% of the potential welfare improvements that they could have achieved by making decisions more in line with their preferences, and we show that this is strongly driven by excess purchase. A decomposition of the sources of welfare gains and losses shows that subjects who consistently violate ROCL experience larger welfare losses. A between-subject treatment where we vary the choice architecture by presenting the compound risk in a simple and reduced form, suggests that this negative effect of ROCL violations on the welfare of financial decisions can be mitigated.