Life-Cycle Labor Supply: Models and ‘Metrics
I. Theory
- Life-cycle labor supply models adapt the LCH/PIH to the allocation of time over the life-cycle.
- Key assumptions in the traditional setup: perfect capital markets, parametric wages and prices, intertemporally additive preferences, perfect certainty or expected utility maximization under uncertainty.
- Key theoretical implications: labor supply (and consumption) can be written as a function of contemporaneous wages and prices plus the time-invariant marginal utility of wealth under certainty or expected MU(wealth) plus unpredictable wealth shocks (with uncertainty).
- Key concept: the intertemporal substitution elasticity (ISE) measures the response of hours worked to a change in wages holding MU(wealth) fixed. A little loosely, I think of this as “holding wealth fixed” (e.g., Card 1994 discusses “wealth shocks” not MU shocks.) The slippage here comes from the fact that in some models, we can reallocate earnings over time and change MU(wealth), even with lifetime wealth (a PDV quantity) held fixed.
- The ISE is the largest theoretical labor supply elasticity known to man, an upper bound for LS optimists. The ISE captures the response to anticipated life-cycle wage changes, like higher pay with more experience.
- The ISE approximates the response to wage shocks that are too small to have significant wealth effects.
- Scholars contrast the target earning hypothesis with the ISH. Target earning can be generated by large within-period income/wealth effects, too large to be compatible with the LCH/PIH framework.
II. 'Metrics
- ANCOVA (fixed effects or deviations-from-means) kills the unobserved but fixed MU(wealth) term in a Heckman-MaCurdy LCLS model under certainty. ‘Metrics problems in this framework abound: MU(wealth) may not be fixed; wages are poorly measured and differencing/devs-from-means aggravates bias from measurement error; wages are often measured as average hourly earnings, a quantity that’s almost surely negatively correlated with hours worked if hours are mismeasured (this problem is called division bias).
- The simple LCLS model implies that average hours and average wages are points on an aggregate labor supply curve. In the absence of aggregate wealth shocks or other aggregate supply shifts, the correlation between average hours and average wages can be interpreted as an (economy-wide average) ISE. This has an IV interpretation: the instruments for wages in an individual supply function are time dummies.
- Grouped-data (IV) estimation of the ISE may also solve the measurement error problem.
III. Evidence, Debates
- Random-sample microeconometric ISE estimates for prime-age males are usually small, though positive (e.g., MaCurdy 1981, <.3). These models are probably poorly identified.
- Estimates for specific occupations with flexible hours are usually larger (stadium vendors, bicycle messengers, cab drivers, fisherman). Identification here is usually more credible.
- Angrist (1990, 1991) argues that the simple LCLS models fits average hours and wages surprisingly well. Card (1994) wonders whether the ISE is relevant for cyclical fluctuations in hours: can we really ignore wealth effects?
- Modern labor-supply research looks for natural and laboratory experiments that can be used to measure elasticities, seeking to distinguish intertemporal substitution from target earning, and trying to understand why workers seem to have a strong preference for immediate payouts.