Consumption Commitments, Unemployment Durations, and Local Risk Aversion

Studies of risk preference have empirically established two regularities that are inconsistent with the canonical expected utility model: (1) risk aversion over small gambles greatly exceeds risk aversion over larger stakes and (2) insurance buyers play the lottery. This paper characterizes risk preferences both theoretically and empirically in a world with two consumption goods, one of which involves a commitment in that an adjustment cost must be paid when the good is sold. In this model, utility over wealth is more curved locally than globally: individuals are more risk averse with respect to moderate-scale income fluctuations than they are to large income fluctuations. Commitments also create a gambling motive. The empirical importance of commitments is tested using the labor-supply method of estimating risk aversion of Chetty (2003a). Global curvature is imputed using existing labor supply elasticities, and variations in unemployment insurance laws are used to estimate local curvature in a dynamic job search model. Commitments significantly change preferences over wealth: The local coefficient of relative risk aversion is an order of magnitude larger than the global one. Implications for a broad set of questions such as optimal social insurance policies and portfolio choice are discussed. ∗E-mail: [email protected]. I thank Nava Ashraf, Julie Cullen, David Cutler, Amy Finkelstein, Ed Glaeser, Jerry Green, Jon Gruber, Jens Hilscher, Emir Kamenica, David Laibson, Adam Looney, Casey Mulligan, Jonah Rockoff, Emmanuel Saez, Jesse Shapiro, Monica Singhal, Jeremy Tobacman, and especially Martin Feldstein, Gary Chamberlain, Larry Katz, and Caroline Hoxby for helpful discussions and comments. I am also indebted to seminar participants at Berkeley, Chicago, Columbia, Harvard, MIT, Princeton, Stanford, UCSD, and Yale. Philippe Bouzaglou and David Lee provided excellent research assistance. Financial support from the National Science Foundation, Harvard University, NBER, and State Farm is gratefully acknowledged. The United States spent approximately $200 billion on social insurance in 2000.1 The large size and continued growth of social safety nets in the US and other countries pose an interesting puzzle in public finance. Work by Baily (1978) and Gruber (1997) suggests that the optimal benefit level for unemployment insurance is lower than 20% of an individual’s pre-unemployment wage, and perhaps even 0.2 The reason is that empirical estimates of the distortionary costs of unemployment insurance tend to outweigh its consumption-smoothing benefits for reasonable levels of risk aversion. The difference between these theoretical predictions and actual benefit levels, which are around 50% of pre-unemployment wages, is striking. This “social insurance puzzle” can be viewed as one manifestation of the general problem of explaining moderate-stake risk aversion using canonical expected utility theory.3 Rabin (2000) gives a powerful calibration theorem which shows that expected utility with strictly concave utility over wealth cannot explain observed risk preferences over small and large gambles simultaneously. To take one notable example, an expected utility maximizer who rejects a 50-50 bet of losing $1000 and winning $1010 will reject a 50-50 bet of losing $100,000 or winning any amount.4 In other words, the level of risk aversion implied by typical preferences over gambles involving moderate stakes — such as the demand for a substantial amount of unemployment, automobile, and non-catastrophic health insurance — translates 1Here, I define social insurance as programs that insure income fluctuations. Unemployment Insurance costs were $25 billion in 2000 (Source: Ways and Means Green Book 2000); Workers Compensation, $56 billion (National Academy of Social Insurance); and Survivors Benefits and Disability Insurance, $113 billion (Office of Management and Budget). 2This is because the consumption-smoothing benefits of UI are outweighed by its distortionary costs. The zero replacement rate result assumes a coefficient of relative risk aversion less than 2, as estimated e.g. in Chetty (2003a). Higher levels of risk aversion obviously increase the optimal replacement rate. 3An alternative view is that social insurance reflects government inefficiency. Those who take this view may prefer to resolve this puzzle using a political economy model that shows why extensive social safety nets emerge even when they do not improve social welfare. This approach is not considered here. 4This claim requires that agents reject the $1000/$1010 bet at all wealth levels, but similar results are obtained when the range of wealth levels over which risk preferences are observed is restricted.