Consumption Insurance against Wage Risk: Family Labor Supply and Optimal Progressive Income Taxation

We show that a calibrated life cycle two-earner household model with endogenous labor supply can rationalize the extent of consumption insurance against shocks to male and female wages, as estimated empirically by Blundell, Pistaferri, and Saporta-Eksten (2016) in US data. In the model, 35 percent of male and 18 percent of female permanent wage shocks pass through to consumption, compared to the empirical estimates of 32 percent and 19 percent. Most of the consumption insurance against permanent male wage shocks is provided through the presence and labor supply response of the female earner. Abstracting from this private intrahousehold income insurance mechanism strongly biases upward the welfare losses from idiosyncratic wage risk as well as the desired extent of public insurance through progressive income taxation. Relative to the standard one-earner life cycle model, the optimal degree of tax progressivity is significantly lower and the welfare gains from implementing the optimal system are cut roughly in half. (JEL D15, H21, H24, J16, J22, J31)

Estimation of Wage–Risk Differentials Without Wages

Utilizing the duality properties of a production/profit function, this article estimates the risk premium received by Pennsylvania bituminous coal miners in 1915, without recourse to any information related to wages. A Cobb-Douglas coal production function is fitted to data for 694 mining establishments. Miners received modest risk compensation, expressed as the value of a statistical life (VSL), of US$6,020 for fatal injuries and US$3,550 for nonfatal accidents. Converted to current price and wage levels, the death risk VSL is roughly US$400,000—far below modern multi-million dollar life values for workplace risk. JEL Classifications: II0, JI7, J28, LII, L72