Insurance and Taxation Over the Life Cycle

54 Pages Posted: 31 Jan 2011 Last revised: 21 Feb 2011

See all articles by Emmanuel Farhi

Emmanuel Farhi

Harvard University - Department of Economics; National Bureau of Economic Research (NBER)

Iván Werning

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: January 2011

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.

Suggested Citation

Farhi, Emmanuel and Werning, Ivan, Insurance and Taxation Over the Life Cycle (January 2011). NBER Working Paper No. w16749, Available at SSRN: https://ssrn.com/abstract=1751447

Emmanuel Farhi (Contact Author)

Harvard University - Department of Economics ( email )

1875 Cambridge Street
Cambridge, MA 02138
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National Bureau of Economic Research (NBER) ( email )

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Ivan Werning

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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Room E52-251
Cambridge, MA 02142
United States
617-452-3662 (Phone)
617-253-1330 (Fax)

HOME PAGE: http://econ-www.mit.edu/faculty/iwerning

National Bureau of Economic Research (NBER) ( email )

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