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Enduring Relationships in an Economy with Capital and Private Information


  • Latchezar Popov

    (The University of Virginia)

  • B Ravikumar

    (Federal Reserve Bank of St. Louis)

  • Aubhik Khan

    (Ohio State University)


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.

Suggested Citation

  • Latchezar Popov & B Ravikumar & Aubhik Khan, 2012. "Enduring Relationships in an Economy with Capital and Private Information," 2012 Meeting Papers 1056, Society for Economic Dynamics.
  • Handle: RePEc:red:sed012:1056

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    References listed on IDEAS

    1. Feldstein, Martin & Horioka, Charles, 1980. "Domestic Saving and International Capital Flows," Economic Journal, Royal Economic Society, vol. 90(358), pages 314-329, June.
    2. S. Rao Aiyagari & Stephen D. Williamson, 1999. "Credit in a Random Matching Model with Private Information," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 2(1), pages 36-64, January.
    3. Bohacek Radim, 2005. "Capital Accumulation in Private Information Economies," The B.E. Journal of Macroeconomics, De Gruyter, vol. 5(1), pages 1-24, December.
    4. Bart Taub, 1990. "The Equivalence of Lending Equilibria and Signalling-Based Insurance under Asymmetric Information," RAND Journal of Economics, The RAND Corporation, vol. 21(3), pages 388-408, Autumn.
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