Zhang, Yuzhe (2009): Dynamic Contracting with Persistent Shocks. Published in: Journal of Economic Theory , Vol. 144, No. 2 (March 2009): pp. 635-675.
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In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. We 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|immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.
|Item Type:||MPRA Paper|
|Original Title:||Dynamic Contracting with Persistent Shocks|
|Keywords:||Persistent Information, Principal-agent Problem, Private Information, Optimal Taxation|
|Subjects:||D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design
D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General
E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E61 - Policy Objectives ; Policy Designs and Consistency ; Policy Coordination
|Depositing User:||Yuzhe Zhang|
|Date Deposited:||10. Jun 2010 16:37|
|Last Modified:||30. Dec 2015 23:00|
Abreu, D., D. Pearce, and E. Staccheti (1990): Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, 58(5), 1041-1063.
Albanesi, S. (2006): Optimal Taxation of Entrepreneurial Capital with Private Information," Working Paper, Columbia University.
Albanesi, S., and C. Sleet (2006): Dynamic Optimal Taxation with Private Information," Review of Economic Studies, 73, 1-30.
Aliprantis, C., and O. Burkinshaw (1990): Principles of Real Analysis, Second Edition. Academic Press, Inc., San Diego, CA, United States.
Atkeson, A., and R. Lucas (1992): On Efficient Distributions with Private Informaton," Review of Economic Studies, 59(3), 427-453.
Battaglini, M., and S. Coate (2003): Pareto E±cient Income Taxations with Stochastic Abilities," NBER Working Paper 10119.
Chari, V. V., P. J. Kehoe, and E. R. McGrattan (1998): Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?," Staff Report 217, Federal Reserve Bank of Minneapolis.
Cvitanic, J., X. Wan, and J. Zhang (2007): Continuous-Time Principal-Agent Problems with Hidden Action and Lump-Sum Payment," Working Paper, Caltech.
Farhi, E., and I. Werning (2007): Inequality and Social Discounting," Journal of Political Economy, forthcoming.
Fernandes, A., and C. Phelan (2000): A Recursive Formulation for Repeated Agency with History Dependence," Journal of Economic Theory, 91, 223-247.
Fleming, W., and H. Soner (2006): Controlled Markov Processes and Viscosity Solutions, Second Edition. Springer Science+ Business Media, Inc., New York, NY, USA.
Fudenberg, D., B. Holmstrom, and P. Milgrom (1990): Short-term Contracts and Long-term Agency Relationships," Journal of Economic Theory, 51, 1-31.
Golosov, M., N. Kocherlakota, and A. Tsyvinski (2003): Optimal Indirect and Capital Taxation," Review of Economic Studies, 70, 569-587.
Golosov, M., and A. Tsyvinski (2006): Designing Optimal Disability Insurance: A Case for Asset Testing," Journal of Political Economy, 114(2), 257-279.
Golosov, M., and A. Tsyvinski(2007): Optimal Taxation with Endogenous Insurance Markets," Quarterly Journal of Economics, forthcoming.
Holmstrom, B., and P. Milgrom (1987): Aggregation and Linearity in the Provision of Intemporal Incentives," Econometrica, 55, 303-328.
Kapicka, M. (2006): Optimal Income Taxation with Human Capital Accumulation and Limited Recordkeeping," Review of Economic Dynamics, 9(4), 612-639.
Kapicka, M. (2007): Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First Order Approach," Working Paper, University of California, Santa Barbara.
Kocherlakota, N. (2005): Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Econometrica, 73, 1587-1621.
Norris, J. (1997): Markov Chains. Cambridge University Press, Cambridge.
Sannikov, Y. (2007a): A Continuous-Time Version of the Principal-Agent Problem," Working Paper, University of California, Berkeley.
Sannikov, Y. (2007b): Games with Imperfectly Observable Actions in Continuous Time," Econometrica, forthcoming.
Schattler, H., and J. Sung (1993): The First-Order Approach to Continuous-Time Principal-Agent Problem with Exponential Utility," Journal of Economic Theory, 61, 331-371.
Walde, K. (2006): Applied Intertemporal Optimization. Lecture Notes, University of WÄurzburg, Germany.
Westerfield, M. (2006): Optimal Dynamic Contracts with Hidden Actions in Continuous Time," Working Paper, University of Southern California.
Williams, N. (2006): On Dynamic Principal-Agent Problems in Continous Time," Working Paper, Princeton University.
Williams, N.(2008): Persistent Private Information," Working Paper, Princeton University.
Zhang, Y. (2006): Dynamic Contracting, Persistent Shocks and Optimal Taxation," Working Paper, University of Minnesota.