Expected utility is the workhorse framework used to model risk preferences, which play a central role in the analysis of many economic problems. Despite its wide application, this canonical framework raises several puzzles and does not always match empirical evidence on individual behavior. One important assumption in the standard expected utility model is that agents consume a single consumption good, a composite commodity. This project plans to investigate risk preferences when such a composite commodity does not exist, because one of the consumption goods involves a "commitment" in that its consumption can only be adjusted at a cost. The researrch results will be applied to three issues: 1) Optimal portfolio choice; 2) Optimal social insurance; 3) The impact of commitments and background risk on excess returns.
The basic intuition underlying this project can be summarized using the following model. When agents have commitments such as housing, the static budget constraint implies that moderate-scale shocks are fully borne over the subset of discretionary consumption goods like food. Since shocks are concentrated on a subset of goods, the marginal utility of wealth rises quickly. As a result, risk aversion over moderate-stake gambles is high relative to that over larger gambles, when the shock can be spread over the entire budget set. In preliminary work, the investigators have extended this intuition to a dynamic model with a time-dependent adjustment rule where commitments can only be adjusted infrequently. They show that higher commitments amplify risk aversion and lead to fewer risky assets in household portfolios. They test this prediction by using the timing of marital shocks (marriage, divorce) to create exogenous variation in commitments, and find that commitments play an important role in explaining the heterogeneity in portfolios. An important limitation of the previous work is that it does not simultaneously model dynamics and adjustment costs. This project builds a model that incorporates both of these features, as well as borrowing constraints. Two new, opposing factors will affect the impact of commitments on risk preferences: intertemporal substitution and cash commitments like mortgage. Given these forces, the quantitative relevance of commitments for risk preferences becomes an empirical question. This model suggests two strategies to obtain estimates of the importance of commitments in micro data: 1) Compare the elasticity of discretionary consumption to unemployment shocks for households with different commitment levels. 2) Test whether households facing shorter unemployment spells (smaller shocks) reduce discretionary consumption more in the short run. These estimates will be used in two applications. The first is to improve our understanding of social insurance. In contrast with actual government policies, most existing studies about optimal social insurance programs find that insurance should be provided primarily for large-scale shocks. However, this project finds that commitments will generate a countervailing force that makes the optimal insurance level for small, transitory shocks such as unemployment significantly higher. The second application is in asset pricing. The investigators plan to investigate the idea that the presence of uninsurable labor income risk can have a large impact on the equity premium and stock market participation when commitments magnify risk aversion.
The broader impacts of the project include normative results that should be of interest to both policy makers and investors. The project would enable the investigators to compute the magnitude and gauge the importance of the commitments effect on the optimal structure of major government expenditure programs such as unemployment and disability insurance. It also has quantitative lessons for the optimal design of portfolios (e.g., in a privatized social security system), and informs the portfolio choice of investors with substantial spending commitments, such as universities.
