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Enduring Relationships in an Economy with Capital and Private Information

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  • Latchezar Popov

    (The University of Virginia)

  • B Ravikumar

    (Federal Reserve Bank of St. Louis)

  • Aubhik Khan

    (Ohio State University)

Abstract

We introduce capital accumulation into an economy where individuals have private information with respect to productivity shocks. Efficient, incentive-compatible risk-sharing is achieved by conditioning current and future payoffs on the history of productivity reports. We develop a notion of efficiency, similar to that of Atkeson and Lucas (1992). The capital stock in the economy is endogenous in periods after date zero, so our notion of efficiency is minimizing the initial capital stock that is required to attain an initial distribution of promised utility. Under constant relative risk aversion and linear technology, we find that the planner allocates more capital to agents with a history of high productivity reports relative to agents with a history of low productivity reports. This higher allocation of capital occurs despite the fact that the expected marginal product of capital is the same across all agents. In contrast to the unobservable endowment model, the agent's welfare in the private information economy exceeds the value of autarchy in every period. Hence, the contract exhibits voluntary long-term participation by the agent. Risk-sharing does not require net transfers across different wealth groups, so the efficient allocation exhibits scale invariance. The allocation allows a simple decentralization through a sequence of actuarially fair insurance contracts. An alternative, long-run decentralization has implications for the risk-free interest rate in our economy.

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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2012 Meeting Papers with number 1056.

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Date of creation: 2012
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Handle: RePEc:red:sed012:1056

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  1. Edward J. Green, 1994. "Individual Level Randomness in a Nonatomic Population," GE, Growth, Math methods 9402001, EconWPA.
  2. S. Rao Aiyagari & Stephen D. Williamson, 1997. "Credit in a Random Matching Model With Private Information," Game Theory and Information 9705005, EconWPA.
  3. Aubhik Khan & B. Ravikumar, 1998. "Growth and Risk-Sharing with Private Information," Macroeconomics 9802003, EconWPA.
  4. Phelan Christopher, 1995. "Repeated Moral Hazard and One-Sided Commitment," Journal of Economic Theory, Elsevier, vol. 66(2), pages 488-506, August.
  5. Thomas, Jonathan & Worrall, Tim, 1990. "Income fluctuation and asymmetric information: An example of a repeated principal-agent problem," Journal of Economic Theory, Elsevier, vol. 51(2), pages 367-390, August.
  6. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  7. Atkeson, Andrew, 1991. "International Lending with Moral Hazard and Risk of Repudiation," Econometrica, Econometric Society, vol. 59(4), pages 1069-89, July.
  8. Bohacek Radim, 2005. "Capital Accumulation in Private Information Economies," The B.E. Journal of Macroeconomics, De Gruyter, vol. 5(1), pages 1-24, December.
  9. Townsend, Robert M, 1982. "Optimal Multiperiod Contracts and the Gain from Enduring Relationships under Private Information," Journal of Political Economy, University of Chicago Press, vol. 90(6), pages 1166-86, December.
  10. Spear, Stephen E & Srivastava, Sanjay, 1987. "On Repeated Moral Hazard with Discounting," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 599-617, October.
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