Optimal Demand for Insurance with Consumption Commitments

Some consumption goods, such as housing, involve long-term commitments and their levels of consumption can only be altered with substantial transaction costs. Even though the commitment effect on risk preferences, portfolio choice, and asset prices has been studied, little research has been conducted on its effect on insurance demand. In this paper, we propose a two-stage model to investigate the optimal demand for insurance by agents who derive utility from the consumption of two goods, an easily adjustable good (food) and a commitment good (housing). Our numerical analysis supports the prediction by Chetty and Szeidl (2007) that commitments help rationalize the high demand for insurance against moderate losses. Moreover, our model can explain the low insurance demand for catastrophic risks to some extent. We extend our model to include both insurance purchase and investment in a risky asset. Our results indicate that, with commitments, insurance appears to be a normal good within certain wealth regions. We also find that only when the initial wealth and housing are rather inconsistent individuals are likely to purchase insurance and lottery tickets simultaneously.