Money Is Memory

The paper opens from what it calls a paradox: “Fiat money consists of intrinsically useless objects that do not enter utility or production functions. But at the same time, these barren tokens allow societies to achieve allocations that would otherwise not be achievable,” and the paper’s goal is “to uncover what permits these barren tokens to play this role” (Sec. I, pp. 232-233). Kocherlakota’s strategy is to show that any allocation achievable using money alone could instead be achieved by giving agents costless access to a historical record of past actions, which he terms memory, and concludes that “the role of money is to serve as a (typically imperfect) form of memory” (Sec. I, abstract, p. 232).

The paper defines a general class of environments with a finite number of perishable goods per period, agents who may live different lengths of time, a matching process that partitions currently-alive agents into “matches,” and two restrictions on that process: (A1) no feasible reallocation within a match can Pareto-dominate autarky (so money or memory is needed for any gains from trade at all), and (A2) an agent’s current trading partner’s own past trading partners are disjoint from the agent’s own past network with probability one (so information about a partner’s history can come only from money or memory, not direct prior contact) (Sec. II.1, pp. 234-236). Section II.2 shows this class embeds three of the field’s standard setups: a two-period overlapping-generations economy, Townsend’s (1980) turnpike model of movers and stayers at trading posts along a line, and a simplified Trejos-Wright (1995) random-matching economy with three goods and three agent types (Sec. II.2, pp. 236-238).

Money is defined as “another good that is durable [and] does not enter preferences or production,” with a fixed per-capita supply M, individual holdings restricted to a finite set, and newborn agents starting with zero units (Sec. III.1, pp. 238-239). Memory, by contrast, is “a historical record (spreadsheet) that, for each agent, reports [his] past trading partners at each previous date, and the actions of [him] and his partners in those matches,” with access limited so that an agent can see this record only for individuals in his own trading network Q_t, not for his potential future trading partners (Sec. III.1, p. 239). Outcomes in either environment are evaluated using perfect public equilibrium (PPE) – equilibria in strategies that condition only on publicly observable history, not on an agent’s own private information (Sec. III.2, Definition 3, pp. 241-242).

Proposition 1, a version of Myerson’s revelation principle, shows that any PPE allocation achievable by any “no-commitment trading mechanism” – one in which any agent can always walk away and simply consume what he can produce on his own – is also achievable as a PPE of one particular, canonical mechanism: the “direct mechanism,” in which all agents in a match either jointly announce the same feasible allocation (which is then implemented) or, if they disagree, all get autarky (Sec. III.2-3, Definition 5, Proposition 1, pp. 240-244). This result licenses Definition 6’s notion of incentive-feasibility: an allocation is incentive-feasible if it arises from agents playing a PPE of the direct mechanism, which the paper treats as “an exhaustive description of the allocations that the members of a society can achieve in the absence of commitment” (Sec. III.3, p. 244).

Proposition 2 states that “any incentive-feasible allocation in an environment with money is an incentive-feasible allocation… in the same environment with memory” (Sec. IV.1, p. 245). The proof constructs, for the memory environment, a “summary statistic” for each agent that mimics his money holdings, updated after each match exactly as his money balance would update under the money-environment equilibrium, so that “the allocation in the environment with money is the outcome of agents’ playing these strategies in the environment with memory” (Sec. IV.1, pp. 245-246). The paper’s own gloss on the mechanism is a balance-sheet analogy: “in an environment with memory, an imaginary balance sheet is kept for each agent. When an individual gives consumption to someone else, his balance rises… When he gets consumption from someone else, his balance falls… In the monetary environment, money is merely a physical way of maintaining this balance sheet” (Sec. I, p. 233).

Example 1 shows that in the overlapping-generations environment of Sec. II.2.a, the set of incentive-feasible allocations is exactly the same whether the economy has money or memory, so that “an even stronger result than Proposition 2 is true: money is technologically equivalent to memory” (Sec. IV.2, pp. 246-247), and the paper states that “this stronger result is also true in the turnpike environment” of Sec. II.2.b (Sec. IV.2, p. 247).

Example 2 uses the Trejos-Wright random-matching environment to show the inclusion in Proposition 2 can be strict: a “folk theorem” allocation giving type-(i+1) agents’ production of y* units to type-i agents at every match – which delivers the same ex ante continuation utility after every match – is incentive-feasible with memory (for beta large enough) but “cannot be incentive-feasible in the same environment with money,” because agents who actually produce in a given match must receive higher future utility than otherwise-identical agents who did not produce, a distinction money (via differing balances) can support but a history-blind, equal-treatment allocation cannot (Sec. IV.2, pp. 247-248; credited to a remark by Neil Wallace).

The proof needs memory limited to each agent’s own network Q_t(i) – his trading partners’ trading partners’ trading partners, and so on – rather than every agent’s complete history: “if it is to replicate the benefits of money, memory must include the past actions of all agents in Q_t(i), not just in P_t(i)” (one’s immediate partners alone is too little) (Sec. IV.3, p. 248). But the paper also gives a worked counterexample (Example 3, a four-period overlapping-generations economy with a “deviant” cohort) showing that if memory is pushed the other way – made fully public across the whole economy rather than limited to one’s own network – some allocations that are incentive-feasible with money become infeasible with memory, because agents can then detect in advance that a trading partner is predictably going to default, and refuse to produce (Sec. IV.3, pp. 248-250).

The conclusion argues explicitly against the standard trio of justifications for money – “money is a store of value, money is a medium of exchange and/or money is a unit of account” – as technological explanations, on the grounds that “money does not allow society to transfer resources over time,” “does not reduce the cost of transferring resources from one person to another,” and there is “no immediate technological reason why money should be a better numeraire than other goods” (Sec. V, p. 250). Instead, the paper’s claim is that “‘Money is memory’ is a much more revealing and accurate description of money’s effect on economic primitives (preferences, information, and technology)” than those alternatives (Sec. V, p. 250), while explicitly flagging that the paper studies money and memory “in isolation from one another,” leaving their joint, real-world coexistence (addressed in companion work with Neil Wallace) outside its scope (Sec. V, p. 251).