Limited memory and the essentiality of money

This paper investigates the relationship between memory and the essentiality of money. We consider a random matching economy with a large finite population in which commitment is not possible and memory is limited in the sense that only a fraction m E(0; 1) of the population has publicly observable histories. We show that no matter how limited memory is, there exists a social norm that achieves the first best regardless of the population size. In other words, money can fail to be essential irrespective of the amount of memory in the economy. This suggests that the emphasis on limited memory as a fundamental friction for money to be essential deserves a deeper examination.

Money versus memory

A well–established fact in monetary theory is that a key ingredient for the essentiality of money is its role as a form of memory. In this paper we study a notion of memory that includes information about an agent’s past actions and trading opportunities but, in contrast to Kocherlakota (1998), does not include information about the past actions and trading opportunities of an agent’s past partners. We first show that the first–best can be achieved with memory even if it only includes information about an agent’s very recent past. Thus, money can fail to be essential even if memory is minimal. We then establish, more interestingly, that if information about trading opportunities is not part of an agent’s record, then money can be better than memory. This shows that the societal benefit of money lies not only on being a record of past actions, but also on being a record of past trading opportunities, a fact that has been overlooked by the monetary literature.

The private memory of aggregate shocks

We study constrained efficient aggregate risk sharing and its consequence for the behavior of macro-aggregates in a dynamic Mirrlees’s (1971) setting. Privately observed idiosyncratic productivity shocks are assumed to be independent of i.i.d. publicly observed aggregate shocks. Yet, private allocations display memory with respect to past aggregate shocks, when idosyncratic shocks are also i.i.d.. Under a mild restriction on the nature of optimal allocations the result extends to more persistent idiosyncratic shocks, for all but the limit at which idiosyncratic risk disappears, and the model collapses to a pure heterogeneity repeated Mirrlees economy identical to Werning [2007]. When preferences are iso-elastic we show that an allocation is memoryless only 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 with log preferences. With less than full persistence and risk aversion different from unity both memory and non-separability characterize optimal allocations. Exploiting the fact that non-separability is associated with state-varying labor wedges, we apply a business cycle accounting procedure (e.g. Chari et al. [2007]) to the aggregate data generated by the model. We show that, whenever risk aversion is great than one our model produces efficient counter-cyclical labor wedges.