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Separability and Memory: Micro Causes, Macro Consequences

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  • Vitor F. Luz

    (Yale University)

  • Carlos E. da Costa

    (Fundacao Getulio Vargas)

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    Abstract

    In a multi-period Mirrlees (1971) setting individuals face privately observed shocks to their ability. Each individual's productivity is the product of this idiosyncratic ability and an aggregate component which is also stochastic but publicly observed. Using a separable iso-elastic specification for preferences, we investigate optimal risk sharing and its macro consequences in this environment. We show that efficient allocations display memory with respect to past aggregate shocks for all levels of risk aversion different from one. This dependence on past aggregate shocks decreases with the persistence of idiosyncratic shocks. At the limit, when the economy becomes a pure heterogeneity one, the constrained efficient allocation is independent of past aggregate shocks and displays a strong form of separability with respect to aggregate shocks. Indeed, these two properties, separability and lack of memory, are shown to be connected: an allocation is memoryless only if it separable. Non-separability is interesting in itself for it is associated with state-varying labor wedges at the micro level. Using numerical examples we show that this non-separability induces efficient counter-cyclical labor wedges at the macro level as well, when risk aversion is greater than one.

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    Bibliographic Info

    Paper provided by Society for Economic Dynamics in its series 2011 Meeting Papers with number 916.

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    Date of creation: 2011
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    Handle: RePEc:red:sed011:916

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    1. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    2. Narayana R Kocherlakota & Luigi Pistaferri, 2005. "Asset Pricing Implications of Pareto Optimality with Private Information," Levine's Bibliography 784828000000000507, UCLA Department of Economics.
    3. Phelan, Christopher, 1994. "Incentives and Aggregate Shocks," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 681-700, October.
    4. Narayana Kocherlakota, 2004. "Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation," Levine's Bibliography 122247000000000729, UCLA Department of Economics.
    5. 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.
    6. Orazio Attanasio & Nicola Pavoni, 2007. "Risk Sharing in Private Information Models with Asset Accumulation: Explaining the Excess Smoothness of Consumption," NBER Working Papers 12994, National Bureau of Economic Research, Inc.
    7. Ana Fernandes & Christopher Phelan, 1999. "A recursive formulation for repeated agency with history dependence," Staff Report 259, Federal Reserve Bank of Minneapolis.
    8. Jonathan Levin, 2002. "Multilateral Contracting And The Employment Relationship," The Quarterly Journal of Economics, MIT Press, vol. 117(3), pages 1075-1103, August.
    9. Narayana R. Kocherlakota & Luigi Pistaferri, 2006. "Household Heterogeneity and Real Exchange Rates," Levine's Bibliography 122247000000001275, UCLA Department of Economics.
    10. Robert M. Townsend, . "Risk and Insurance in Village India," University of Chicago - Population Research Center 91-3a, Chicago - Population Research Center.
    11. Robert Shimer, 2009. "Convergence in Macroeconomics: The Labor Wedge," American Economic Journal: Macroeconomics, American Economic Association, vol. 1(1), pages 280-97, January.
    12. Narayana Kocherlakota & Luigi Pistaferri, 2008. "Inequality and Real Exchange Rates," Journal of the European Economic Association, MIT Press, vol. 6(2-3), pages 597-608, 04-05.
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