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Article Excerpt
SWEENEY AND SWEENEY'S (1977) report on the Great Capitol Hill Baby Sitting Co-op, which has been popularized by Krugman (1999), is without doubt an entertaining anecdote to illustrate the optimum quantity of money. This paper analyzes whether this story is more than a mere anecdote.
The Great Capitol Hill Baby Sitting Co-op was a "cooperative" of about 150 couples, with the goal of sharing baby-sitting fairly among themselves by introducing a coupon system. One coupon entitled each member to receive half an hour's worth of baby-sitting. Initially, one coupon of baby-sitting was issued to each couple. Supposing that coupons circulated, each couple would, over time, do as many units of baby-sitting as they received in return. After a short while, however, the system collapsed, because there was not enough demand for baby-sitting. Krugman (1999) attributes this breakdown to precautionary savings. The Co-op solved this problem simply by issuing more coupons. Having found out that each couple was better off with an increase in the number of coupons available, the Co-op continued to issue more coupons, which eventually resulted in a breakdown of the system. The moral of this anecdote is that a market in which prices are fixed only works efficiently for a specific, "optimal" quantity of money.
The Great Capitol Hill Baby Sitting Co-op is just one example of a trade circle. Trade circles, which have become increasingly common, provide a field for clinical studies on the role of money. Trade circle members can buy or sell services at fixed prices. The supplier of a service receives "artificial" money, or coupons, which he/she can then use to buy services. Prices are fixed by fairness considerations and credit is limited. Money usually has a positive value in exchange for services, and its introduction leads to a Pareto-improvement over the situation without money.
While the importance of the quantity of money has not been reported from other trade circles, the Capitol Hill Baby Sitting Co-op is a beautiful anecdote to illustrate the role of money in simple markets with idiosyncratic uncertainty and fixed prices. It suggests that individual rationality is typically at odds with collective rationality, and that only a specific amount of money helps to overcome this problem if prices are fixed. From a collective point of view, it is preferable that all participants hold more money if there is an excessive amount of it. If money is scarce, then precautionary savings are contrary to the common interest.
The report on the Capitol Hill Baby Sitting Co-op only gives anecdotal evidence for this quite general claim on the existence of an optimum quantity of money. It could still be conjectured that the reasons for these observations are totally different from those put forward above. For example, one might argue that money holdings are determined by myopic expectations on the future resale value, so that the market breaks down because expectations are incorrect in the long term. Whether the Capitol Hill Baby Sitting Co-op is, in fact, more than an anecdote for the optimum quantity of money can only be decided by extracting the underlying fundamental mechanisms and by studying them in a formal model. This approach will provide us with analytical results, and it will make the above reasoning testable under controlled conditions in a laboratory experiment. A sound theory, in combination with additional experimental observations, can provide more solid evidence for the story told by the Capitol Hill Baby Sitting Co-op.
In pursuit of this goal, we develop a formal model of a monetary economy with a perishable good that can be traded in a centralized market. Competitive behavior is ensured by assuming a continuum of agents, each having stochastic preferences. According to this specification, no agent thinks of him/herself to be in a position to change market averages resulting from the actions of all agents. An agent cannot consume his/her own goods, but needs to receive money in order to finance future consumption. The price is fixed, and trade is a one-to-one exchange of money against goods. Market clearing is ensured by rationing. While this model may not be ideal for studying the long-term effects of monetary policy (because of the assumption of fixed prices), it is arguably well suited for studying short-term effects.
The model shares with Levine (1991) and Kehoe, Levine, and Woodford (1992) in assuming stochastic preferences that generate a need for inter-temporal transfers. But in contrast to these papers, we do not pursue a mechanism design approach. There is no possibility of lump sum subsidies, no making or losing money (i.e., no government and no interest involved), and prices are fixed. In Wallace's (2002) view, our model takes the extreme position of idiosyncratic uncertainty across agents and types, anonymity, the absence of any monitoring and the largest possible market. As a result of these features, the optimum outcome cannot be achieved in our model. But by using the total trading volume in the economy as a welfare measure, we can show the existence of an optimum quantity of money. Money is beneficial in our model of a centralized market, in the sense that more allocations are possible with money than without it.
The model also shares some features with the neo-Keynesian models developed by Clower, Barro, and Grossman, Benassy, Malinvaud, and Dreze. (1) In those models, prices are fixed, and demand and supply is coordinated by quantity rationing. However, while the use of money in the standard neo-Keynesian model is justified by a temporary equilibrium approach, the microeconomic foundation of money that our model provides is based on complete rationality under rational expectations.
Last, but not least, our model has some features in common with the recent literature on the micro-foundation of money, originating in the seminal papers of Kiyotaki and Wright (1989, 1991, 1993). In this strand of research, markets are no longer considered to be well organized, but traders meet randomly in pairs (see e.g., Boldrin, Kiyotaki, and Wright 1993, Trejos and Wright 1995). Our paper suggests a microfoundation of money that is complementary to the standard search model. On the one hand, we assume that markets are well-organized, in the sense that each potential supplier and each potential demander of a service can meet traders of the other side of the market in each period. On the other hand, we assume that the market participants have stochastic preferences: one day a trader would prefer to supply a service, while on another day he/she prefers to demand it. In this view, the role of money is to enable the traders to transfer income from supply days to demand days. (2) From a more general perspective, our model is similar to the Kiyotaki-Wright model because, in both approaches, the incentive to hold money arises from the uncertainty of whether one will be a demander or a supplier of a service in the future. This uncertainty arises from the stochastic preferences in our model, and from the possibility of being matched with a trading partner who does not have "coincident wants" in the Kiyotaki-Wright model. Indeed, in the formal analysis of our model (relying on the study of Bellman equations) we reach a similar conclusion to Berentsen 2000, Lemma 1)--using the Kiyotaki-Wright framework. From this viewpoint, the essential difference of our model is the use of rationing to clear the market.
Since our model will be based on a rigorous idealization--the notion of stationary competitive equilibria with rational expectations in a stochastic game--it is important to contrast the theoretical predictions with the actual behavior of only a few, possibly bounded rational participants in a laboratory experiment with a finite horizon. The experimental design benefits from the previous laboratory test of the Kiyotaki-Wright model by Duffy and Ochs and McCabe (1989). Duffy and Ochs conclude that implementing a model with a continuum of players, an infinite time horizon and discounting as a game between finitely many players and a finite time horizon, has only a minor influence on the results. McCabe finds that, even if the number of time periods is fixed and small (six periods in his paper), only experienced participants show behavior inducing a non-monetary equilibrium. Our main interest is in the behavior of experienced participants. All participants therefore play a sequence of increasingly demanding games that constitute a "learning" phase that lasts about 4 hours. Afterward, a strategy game is conducted with the aim of eliciting the strategies from experienced participants. The games comprise individual decision making experiments and market experiments with interaction. This will allow to determine whether a participant's behavior is shaped by individual optimization or market interaction. This design allows for a rather detailed test of the predictions derived from the theory.
The laboratory experiment culminated in games in which groups of six participants formed a market to repeatedly buy and sell services in exchange for money, called coupons. Each participant's potential payoff in a period (representing an instantaneous utility) was drawn randomly across agents and time from a common probability distribution. While this distribution was common knowledge, the realized, individual payoff values were not revealed to other participants. All contract positions (buy, sell, and stay idle) were available to a participant, except for "buy" if he/she had no money.
Even though each group consisted of only six participants, their behavior conformed with the best response to market averages. This observation shows that the participants' behavior coincided exactly with the theoretical results, based on a rational solution concept: agents behave competitively and act according to the optimal solution of the individual maximization problem. We attribute this result to the fact that, as we prove analytically, stationary monetary equilibria can be implemented using three simple heuristics: (i) holding no money implies offering baby-sitting services, (ii) a high payoff-value results in seeking baby-sitting services, provided money holdings are positive, and (iii) a low payoff-value leads to offering baby-sitting services, as long as money holdings are below a certain quantity [bar.m] (specified...
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