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Dynamic contracting, persistent shocks and optimal taxation

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  • Yuzhe Zhang

Abstract

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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  • Yuzhe Zhang, 2005. "Dynamic contracting, persistent shocks and optimal taxation," Working Papers 640, Federal Reserve Bank of Minneapolis.
  • Handle: RePEc:fip:fedmwp:640
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    References listed on IDEAS

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    1. 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.
    2. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 2000. "Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?," Econometrica, Econometric Society, vol. 68(5), pages 1151-1180, September.
    3. Ivan Werning & Emmanuel Farhi, 2005. "Inequality, Social Discounting and Estate Taxation," 2005 Meeting Papers 358, Society for Economic Dynamics.
    4. Narayana R. Kocherlakota, 2005. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Econometrica, Econometric Society, vol. 73(5), pages 1587-1621, September.
    5. 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.
    6. 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.
    7. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    8. Marek Kapicka, 2004. "Optimal taxation with persistent shocks," 2004 Meeting Papers 689, Society for Economic Dynamics.
    9. Mikhail Golosov & Aleh Tsyvinski, 2003. "Designing optimal disability insurance," Working Papers 628, Federal Reserve Bank of Minneapolis.
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    Cited by:

    1. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    2. Narayana R Kocherlakota, 2005. "Advances in Dynamic Optimal Taxation," Levine's Bibliography 784828000000000518, UCLA Department of Economics.

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