Working Paper: NBER ID: w16749
Authors: Emmanuel Farhi; Ivn Werning
Abstract: We consider a dynamic Mirrlees economy in a life cycle context and study the op- timal insurance arrangement. Individual productivity evolves as a Markov process and is private information. We use a first order approach in discrete and continuous time and obtain novel theoretical and numerical results. Our main contribution is a formula describing the dynamics for the labor-income tax rate. When productivity is an AR(1) our formula resembles an AR(1) with a trend where: (i) the auto-regressive coefficient equals that of productivity; (ii) the trend term equals the covariance pro- ductivity with consumption growth divided by the Frisch elasticity of labor; and (iii) the innovations in the tax rate are the negative of consumption growth. The last prop- erty implies a form of short-run regressivity. Our simulations illustrate these results and deliver some novel insights. The average labor tax rises from 0% to 46% over 40 years, while the average tax on savings falls from 17% to 0% at retirement. We com- pare the second best solution to simple history independent tax systems, calibrated to mimic these average tax rates. We find that age dependent taxes capture a sizable fraction of the welfare gains. In this way, our theoretical results provide insights into simple tax systems.
Keywords: Optimal Taxation; Dynamic Mirrlees Model; Labor Income Tax; Insurance Motive; Welfare Gains
JEL Codes: H21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| labor income tax rate (J89) | individual productivity (O49) |
| age (J14) | labor income tax rate (J89) |
| age-dependent taxes (H29) | welfare gains (D69) |
| covariance of productivity with consumption growth (O49) | labor tax rate (J89) |
| productivity shocks (O49) | labor wedge (J39) |
| marginal tax rates (H29) | productivity shocks (O49) |