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Insurance and Taxation over the Life Cycle

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  • Emmanuel Farhi

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 labour-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 labour; 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 labour tax rises from 0% to 37% over 40 years, whereas the average tax on savings falls from 12% 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. Copyright 2013, Oxford University Press.

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File URL: http://hdl.handle.net/10.1093/restud/rds048
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Bibliographic Info

Article provided by Oxford University Press in its journal Review of Economic Studies.

Volume (Year): 80 (2013)
Issue (Month): 2 ()
Pages: 596-635

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Handle: RePEc:oup:restud:v:80:y:2013:i:2:p:596-635

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Cited by:
  1. Peter A. Diamond & Emmanuel Saez, 2011. "The Case for a Progressive Tax: From Basic Research to Policy Recommendations," CESifo Working Paper Series 3548, CESifo Group Munich.
  2. Jean-Baptiste Michau, 2013. "On the Provision of Insurance Against Search-Induced Wage Fluctuations," Working Papers hal-00850547, HAL.
  3. Abraham, Arpad & Koehne, Sebastian & Pavoni, Nicola, 2012. "Optimal income taxation with asset accumulation," MPRA Paper 38629, University Library of Munich, Germany.
  4. Heathcote, Jonathan & Storesletten, Kjetil & Violante, Giovanni L, 2014. "Optimal Tax Progressivity: An Analytical Framework," CEPR Discussion Papers 9866, C.E.P.R. Discussion Papers.
  5. Berliant, Marcus & Fujishima, Shota, 2012. "Optimal dynamic nonlinear income taxes: facing an uncertain future with a sluggish government," MPRA Paper 41947, University Library of Munich, Germany.
  6. Alexander M. Gelber & Matthew C. Weinzierl, 2012. "Equalizing Outcomes and Equalizing Opportunities: Optimal Taxation when Children's Abilities Depend on Parents' Resources," NBER Working Papers 18332, National Bureau of Economic Research, Inc.
  7. Michau, Jean-Baptiste, 2014. "Optimal redistribution: A life-cycle perspective," Journal of Public Economics, Elsevier, vol. 111(C), pages 1-16.
  8. Marios Karabarbounis, 2013. "Heterogeneity in labor supply elasticity and optimal taxation," Working Paper 13-13, Federal Reserve Bank of Richmond.
  9. Marios Karabarbounis, 2012. "Heterogeneity in Labor Supply Elasticity and Optimal Taxation," 2012 Meeting Papers 655, Society for Economic Dynamics.
  10. Sebastian Koehne & Moritz Kuhn, 2014. "Optimal Taxation in a Habit Formation Economy," CESifo Working Paper Series 4581, CESifo Group Munich.

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