Aggregating Elasticities: Intensive and Extensive Margins of Female Labour Supply

There is a renewed interest in the size of labour supply elasticities and the discrepancy between micro and macro estimates. Recent contributions have stressed the distinction between changes in labour supply at the extensive and the intensive margin. In this paper, we stress the importance of individual heterogeneity and aggregation problems. At the intensive margins, simple specifications that seem to fit the data give rise to non linear expressions that do not aggregate in a simple fashion. At the extensive margin, aggregate changes in participation are likely to depend on the cross sectional distribution of state variables when a shock hits and, therefore, are likely to be history dependent. We tackle these aggregation issues directly by specifying a life cycle model to explain female labour supply in the US and estimate its various components. We estimate the parameters of different component of the model. Our results indicate that (i) at the intensive margin, Marshallian and Hicksian elasticities are very heterogeneous and, on average, relatively large; (ii) Frisch elasticities are, as implied by the theory, even larger; (iii) aggregate labour supply elasticities seem to vary over the business cycle, being larger during recessions.