Consumption Risk and Family Labor Supply

We develop a life cycle framework with two individuals within the family (husband and wife) making decisions about household consumption and their individual labor supply, subject to uncertainty about offered market wages. The response of consumption to permanent wage shocks depends on two “smoothing” channels: smoothing through savings and smoothing through the two earners’ labor supply. We derive an econometric model that shows how the Frisch elasticities of labor supply, the intertemporal elasticity of substitution and a self insurance parameter can be identified and apply it to 1999-2007 PSID waves. Our findings highlight three key features of household insurance and family labor supply. First, The Frisch elasticity of labor supply of the second earner (in our case the wife) is at least twice as large as the Frisch elasticities of labor supply of the household head (in our case the working male). Second, estimates of the self insurance parameter suggest that the household is more insured than the insurance implied by a single riskless asset model. Third, the second earner is much more responsive not only to its own permanent wage shocks, but also to the second earner permanent wage shocks, implying a large average increase in labor supply of the second earner in response to an adverse permanent shock to the first earner’s wages.