NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Insurance and Taxation over the Life Cycle

Emmanuel Farhi, Iván Werning

NBER Working Paper No. 16749
Issued in January 2011
NBER Program(s):   EFG   PE

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.

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Document Object Identifier (DOI): 10.3386/w16749

Published: Emmanuel Farhi, 2013. "Insurance and Taxation over the Life Cycle," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 596-635. citation courtesy of

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