The Marginal Worker and the Aggregate Elasticity of Labor Supply

This paper attempts to reconcile the high apparent aggregate elasticity of labor supply with small micro estimates. We elaborate on Rogerson's seminal work (1988) and show that his results rely neither on complete markets nor on lotteries, but rather on the indivisibility and the fact that the workforce is homogeneous at the margin. We derive two robust implications of a setup with indivisible labor but without lotteries, using either a complete markets model or an incomplete markets model (solved numerically). (1) Agents with reservation wages far above or below the market wage are less responsive (in labor supply) to the business cycle than agents whose reservation wage is around the market wage. (2) The aggregate elasticity is given by the marginal homogeneity of the workforce. We test implication (1) using the PSID and find support for it. We build an incomplete markets model and calibrate it to cross-sectional moments of hours worked. We show that it can reproduce the feature (1). This allows us to use the model to evaluate the importance of feature (2), i.e. to estimate the aggregate elasticity of labor supply implied by the marginal homogeneity.