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Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach

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  • Marek Kapicka

Abstract

This article studies efficient allocations in a dynamic private information economy with a continuum of idiosyncratic shocks that are persistent. I develop a first-order approach for this environment and show that the problem has a simple recursive structure that relies on only a small number of state variables, making the problem tractable. I find sufficient conditions that guarantee that the first-order approach is valid. To illustrate the first-order approach I numerically compute the efficient allocations in a Mirrleesean economy with productivity shocks that follow a random walk and verify the validity of the first-order approach. I show that persistent shocks create a new trade-off where the social planner decreases the informational rent of the agent today at the cost of providing higher insurance in the future. Copyright 2013, Oxford University Press.

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  • Marek Kapicka, 2013. "Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach," Review of Economic Studies, Oxford University Press, vol. 80(3), pages 1027-1054.
  • Handle: RePEc:oup:restud:v:80:y:2013:i:3:p:1027-1054
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    File URL: http://hdl.handle.net/10.1093/restud/rds045
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    Cited by:

    1. Prat, Julien & Jovanovic, Boyan, 2014. "Dynamic contracts when agent's quality is unknown," Theoretical Economics, Econometric Society, vol. 9(3), September.
    2. Peter Eso & Balazs Szentes, 2014. "Dynamic Contracting: An Irrelevance Result," 2014 Meeting Papers 605, Society for Economic Dynamics.
    3. Koehne, Sebastian & Kuhn, Moritz, 2015. "Optimal taxation in a habit formation economy," Journal of Public Economics, Elsevier, vol. 122(C), pages 31-39.
    4. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    5. Williams, Noah, 2015. "A solvable continuous time dynamic principal–agent model," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 989-1015.
    6. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    7. Zhang, Yuzhe & Ravikumar, B., 2012. "Optimal auditing and insurance in a dynamic model of tax compliance," Theoretical Economics, Econometric Society, vol. 7(2), May.
    8. Stefanie Stantcheva, 2015. "Learning and (or) Doing: Human Capital Investments and Optimal Taxation," NBER Working Papers 21381, National Bureau of Economic Research, Inc.
    9. Maxim Troshkin & Aleh Tsyvinski & Mikhail Golosov, 2010. "Optimal Dynamic Taxes," 2010 Meeting Papers 320, Society for Economic Dynamics.
    10. Vitor F. Luz & Carlos E. da Costa, 2010. "The Private Memory of Aggregate Shocks," 2010 Meeting Papers 368, Society for Economic Dynamics.
    11. Marina Halac & Pierre Yared, 2014. "Fiscal Rules and Discretion Under Persistent Shocks," Econometrica, Econometric Society, vol. 82, pages 1557-1614, September.
    12. Bierbrauer Felix J., 2016. "Effizienz oder Gerechtigkeit?," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 17(1), pages 2-24, April.
    13. Garrett, Daniel F. & Pavan, Alessandro, 2015. "Dynamic managerial compensation: A variational approach," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 775-818.
    14. Vitor F. Luz & Carlos E. da Costa, 2011. "Separability and Memory: Micro Causes, Macro Consequences," 2011 Meeting Papers 916, Society for Economic Dynamics.
    15. Felix Bierbrauer, 2016. "Effizienz oder Gerechtigkeit? Ungleiche Einkommen, ungleiche Vermögen und die Theorie der optimalen Besteuerung," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2016_03, Max Planck Institute for Research on Collective Goods.
    16. Daniel Garrett & Alessandro Pavan, 2014. "Dynamic Managerial Compensation: On the Optimality of Seniority-based Schemes," Discussion Papers 1579, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. Chen, Yunmin & Chien, YiLi & Yang, C.C., 2015. "Individual and Aggregate Constrained Efficient Intertemporal Wedges in Dynamic Mirrleesian Economies," Working Papers 2015-43, Federal Reserve Bank of St. Louis, revised 01 Apr 2016.

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