For decades now, there has been a debate about the measurement of the labor supply elasticity. Indeed, micro-estimates using household or payroll data indicate that the elasticity is about 0.1: a 10% increase in wages would increase the labor supply by 1%. Using aggregate data, macro-estimates obtain an elasticity around 1, an order of magnitude higher.
Finding the "correct" elasticity is important. Think, for example, about business cycle modeling. How much the labor supply responds to changes in wages is crucial in understanding what is happening on the labor market, and how policy can influence it. Much of business cycle theory nowadays works with micro-founded representative agent models. The representative household is defined by preferences and constraints which need to be measured in some way. The labor supply elasticity tells a lot about preferences about leisure, in particular the relative strengths of substitution and income effects.
For such a representative household, which elasticity should be used? The macro-estimate, because one is interested in the aggregate behavior of the economy? That could be defended if there were some good aggregation theorem that stipulates that this high elasticity at the individual level translates to the same at the aggregate level. Or should one use the micro-estimate because the model is calibrated to household data? But then, model results do not seem in line with aggregate data.
Riccardo Fiorito and Giulio Zanella add another twist to this debate. They use PSID data to estimate both micro and macro elasticities. PSID being a larger panel data set following the same households over extended periods of time, such dual estimation is possible. And they obtain the same, distinct estimates of previous studies, the difference being here that they used the same data for both. Interestingly they argue that the difference does not come from aggregation. It is because of a difference in data definition: individual data pertains to individual hours worked (intensive margin) while aggregate data pertains to total hours worked, which also includes the number of people working (extensive margin). And they find that the extensive margin explains most of the difference.
Does this help us in determining what elasticity to use in a business cycle model? No, but it highlights that a model where both extensive and intensive margins are present is required to explain appropriately what is happening on the labor market, and that in this case the micro estimate could be used.