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The Private Memory of Aggregate Shocks

  • Economics


We study constrained efficient aggregate risk sharing and its consequence for thebehavior of macro-aggregates in a dynamic Mirrlees’s (1971) setting. Privately observedidiosyncratic productivity shocks are assumed to be independent of i.i.d. publiclyobserved aggregate shocks. Yet, private allocations display memory with respectto past aggregate shocks, when idosyncratic shocks are also i.i.d.. Under a mild restrictionon the nature of optimal allocations the result extends to more persistentidiosyncratic shocks, for all but the limit at which idiosyncratic risk disappears, andthe model collapses to a pure heterogeneity repeated Mirrlees economy identical toWerning [2007]. When preferences are iso-elastic we show that an allocation is memorylessonly if it displays a strong form of separability with respect to aggregate shocks.Separability characterizes the pure heterogeneity limit as well as the general case withlog preferences. With less than full persistence and risk aversion different from unityboth memory and non-separability characterize optimal allocations. Exploiting thefact that non-separability is associated with state-varying labor wedges, we apply abusiness cycle accounting procedure (e.g. Chari et al. [2007]) to the aggregate datagenerated by the model. We show that, whenever risk aversion is great than one ourmodel produces efficient counter-cyclical labor wedges.

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