@techreport{NBERw16749,
 title = "Insurance and Taxation over the Life Cycle",
 author = "Emmanuel Farhi and Iván Werning",
 institution = "National Bureau of Economic Research",
 type = "Working Paper",
 series = "Working Paper Series",
 number = "16749",
 year = "2011",
 month = "January",
 URL = "http://www.nber.org/papers/w16749",
 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.},
}