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Dynamic contracting, persistent shocks and optimal taxation

  • Yuzhe Zhang

In this paper I develop continuous-time methods for solving dynamic principal-agent problems in which the agent’s privately observed productivity shocks are persistent over time. I characterize the optimal contract as the solution to a system of ordinary differential equations, and show that, under this contract, the agent’s utility converges to its lower bound—immiseration occurs. I also show that, unlike in environments with i.i.d. shocks, the principal would like to renegotiate with the agent when the agent’s productivity is low—it is not renegotiation-proof. I apply the theoretical methods I have developed and numerically solve this (Mirrleesian) dynamic taxation model. I find that it is optimal to allow a wedge between the marginal rate of transformation and individuals’ marginal rate of substitution between consumption and leisure. This wedge is significantly higher than what is found in the i.i.d. case. Thus, using the i.i.d. assumption is not a good approximation quantitatively when there is persistence in productivity shocks.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Working Papers with number 640.

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Date of creation: 2005
Date of revision:
Handle: RePEc:fip:fedmwp:640
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  1. Emmanuel Farhi & Ivan Werning, 2005. "Inequality, Social Discounting and Estate Taxation," NBER Working Papers 11408, National Bureau of Economic Research, Inc.
  2. Mikhail Golosov & Narayana Kocherlakota & Aleh Tsyvinski, 2003. "Optimal Indirect and Capital Taxation," Review of Economic Studies, Oxford University Press, vol. 70(3), pages 569-587.
  3. Mikhail Golosov & Aleh Tsyvinski, 2003. "Designing Optimal Disability Insurance," Levine's Working Paper Archive 506439000000000217, David K. Levine.
  4. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-63, September.
  5. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 1996. "Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?," NBER Working Papers 5809, National Bureau of Economic Research, Inc.
  6. Battaglini, Marco & Coate, Stephen, 2008. "Pareto efficient income taxation with stochastic abilities," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 844-868, April.
  7. Marek Kapicka, 2005. "Optimal Taxation with Persistent Shocks," 2005 Meeting Papers 204, Society for Economic Dynamics.
  8. Andrew Atkeson & Robert E. Lucas, 1992. "On Efficient Distribution With Private Information," Review of Economic Studies, Oxford University Press, vol. 59(3), pages 427-453.
  9. Narayana R. Kocherlakota, 2003. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Levine's Bibliography 666156000000000426, UCLA Department of Economics.
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