Consumption and labor supply with partial insurance: An analytical framework
BibTeX
@article{heathcote2014consumption,
title={Consumption and labor supply with partial insurance: An analytical framework},
author={Heathcote, Jonathan and Storesletten, Kjetil and Violante, Giovanni L},
journal={American Economic Review},
volume={104},
number={7},
pages={2075--2126},
year={2014}
}
Abstract
We develop a model with partial insurance against idiosyncratic wage shocks to quantify risk sharing. Closed-form solutions are obtained for equilibrium allocations and for moments of the joint distribution of consumption, hours, and wages. We prove identification and demonstrate how labor supply data are informative about risk sharing. The model, estimated with US data over the period 1967–2006, implies that (i) 39 percent of permanent wage shocks pass through to consumption; (ii) the share of wage risk insured increased until the early 1980s; and (iii) preference heterogeneity is important in accounting for observed dispersion in consumption and hours.
Notes and Excerpts
I wanted to snip this bit because it’s a nice concise summary of a certain technique used in modelling.
Demographics.—We adopt the Yaari perpetual youth model: agents are born at age zero and survive from age $a$ to age $a + 1$ with constant probability $δ < 1$. A new generation with mass $(1 − δ)$ enters the economy at each date $t$. Thus, the measure of agents of age a is $(1 − δ)δa$ , and the total population size is unity.
This is a good way to illustrate what elasticity means
To see this, note that $log(\tilde{y} t) = log(λ) + (1 − τ) log(yt)$, and thus $(1 − τ)$ defines the elasticity of after-tax earnings to pretax earnings.