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Insurance and Taxation over the Life Cycle

Author

Listed:
  • Ivan Werning

    (MIT)

  • Emmanuel Farhi

    (Harvard)

Abstract

We consider a dynamic Mirrlees economy in a life cycle context and study the optimal 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 productivity 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 property 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 40% over 40 years, while the average tax on savings falls from 20% to 0% at retirement. We compare 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

  • Ivan Werning & Emmanuel Farhi, 2010. "Insurance and Taxation over the Life Cycle," 2010 Meeting Papers 909, Society for Economic Dynamics.
  • Handle: RePEc:red:sed010:909
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    JEL classification:

    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation

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