Risk Preferences and Expected Utility: Evidence from Labor Supply Data
Leonard, Megan De Linde, Economic Inquiry
Why do some people enjoy bungee jumping while others do not? Why do some individuals hold extensive insurance portfolios? It is intuitive to attribute these differences between people to their individual preferences for risk, a concept that is appealing but hard to quantify. Arrow (1965) and Pratt's (1964) coefficient of relative risk aversion (RRA) has been the standard risk measure since the mid-1960s. It relies on expected-utility theory (EUT) and the fact that the utility function is concave over wealth. Although EUT is still widely used in economics, theorists are increasingly unsatisfied with its performance. This is true when applied specifically to risk aversion, as well. For example, Rabin (2000) provides a calibration argument that shows that if an expected-utility maximizer is not essentially risk neutral over a modest-stakes gamble, he will be unrealistically risk averse over a large risk gamble. He concludes that
aversion to modest-stakes risk has nothing to do with the diminishing marginal utility of wealth (1282).
A frequent argument for continuing to use EUT despite failures of its axioms is that it adequately explains behavior. An empirical measure of risk aversion that explains behavior is very desirable as risk preference plays an important role in many decisions of interest to economists. Using a labor supply regression and information on each individual's income and hours of work, I compute a measure of risk aversion, [[gamma].sub.LS], that is the curvature of utility over wealth and compare this measure of risk aversion to one based on the individual's willingness to accept gambles over lifetime income, go. Both should measure an individual's preferences for large-scale risk. While it has been well established that an individual's risk preferences with respect to both large and small-scale risk cannot be adequately explained by EUT, comparing [[gamma].sub.G] and [[gamma].sub.LS] affords an opportunity to see how EUT performs over gambles of the same scale. If EUT is a good predictive model for behavior under uncertainty, individuals who have a very concave utility function as measured by [[gamma].sub.LS] should be less willing to gamble with lifetime income than those with smaller values of [[gamma].sub.LS.] I find no correlation between the two measures, implying that EUT does not explain the variation in risk preferences as measured by a hypothetical gambling frame.
Many economists have questioned whether hypothetical choices are a good proxy for actual decisions in the context of risk, and perhaps the discrepancy in the two measures stems from this. From a preliminary look at how these measures vary with actual risky choices, it appears that the measure of the curvature of utility over wealth does a better job of explaining actual risky choices such as smoking and binge drinking, and the hypothetical gambling frame does a better job explaining people's responses to other hypothetical risky situations. This is of interest for theorists who are trying to find the new direction for choices under uncertainty but also for empiricists who wish to use risk preferences to explain decision making and behavior.
II. MEASURING RISK AVERSION WITH LABOR SUPPLY DATA
Aside from concerns as to the validity of EUT, risk aversion can be difficult to measure as it requires specific information on an individual's utility function. Chetty (2006) uses the fact that RRA is directly related to the ratio of the income and compensated wage elasticities of labor supply and presents a formula that allows for the estimation of the coefficient of RRA using labor supply data. Recall that RRA is proportional to [u.sub.cc]/[u.sub.c] where [u.sub.c] is the first partial derivative of the utility function with respect to consumption and [u.sub.cc] is the second derivative. An agent's compensated wage elasticity is directly related to [u.sub.c]; the larger the marginal utility of consumption, the more benefit the agent gets from an additional dollar of income, so the more willing he is to work when his wage increases. …