Labor Supply and Risk Aversion: A Calibration Theorem

This paper shows that existing estimates of labor supply elasticities place a tight upper bound on risk aversion in an expected utility model. I derive a formula that relates the coefficient of relative risk aversion (γ) to the ratio of the income elasticity of labor supply to the wage elasticity, holding fixed the degree of complementarity between consumption and leisure. The degree of complementarity can in turn be inferred from data on consumption choices when agents face unemployment risk. Calibration of the formula reveals that an upward sloping labor supply curve — as found in virtually all studies of labor supply — requires γ < 1.25. The bound on γ rises to at most 1.66 over the range of plausible values for the complementarity parameter. These results generalize to dynamic models with time non-separable or Kreps-Porteus preferences. Hence, conventional expected utility models cannot generate a high degree of risk aversion without sharply contradicting established facts about labor supply behavior. ∗E-mail: [email protected]. I have benefited from comments and suggestions by George Akerlof, John Campbell, David Card, Gary Chamberlain, David Cutler, Martin Feldstein, John Friedman, Ed Glaeser, Caroline Hoxby, Louis Kaplow, Larry Katz, Miles Kimball, Greg Mankiw, and Day Manoli, as well as seminar participants at Berkeley, Chicago, Columbia, Harvard, MIT, Princeton, Stanford, UCSD, and Yale. Financial support from the National Science Foundation, National Bureau of Economic Research, and Harvard University is gratefully acknowledged.