Comment on the Aruoba - Wright paper

Despite efforts by some of the best minds in our profession, monetary theory at the start of the 21st Century remains flawed by the same fundamental shortcoming that Clower (1967) pointed out in the 1960s, namely the absence of any useful model of money in which widespread monetary exchange the use of a common money in almost all transactions can be shown to arise endogenously. The models of money that have proven most useful for empirical work are almost all based, to the extent that they have any conceptual basis at all, on the money-in-the-utility-function (MIU) approach developed by Patinkin (1965). But as many writers have observed, MIU starts from the presumption of widespread monetary exchange, a presumption that seems at odds with other aspects of the approach. Although search theory has provided models in which widespread monetary exchange can be shown to exist as an equilibrium phenomenon, a large gap still separates these models from those that have proven useful. The paper by Aruoba and Wright (AW) narrows the gap a little, although not by as much as it claims. Ironically, it narrows the gap not just by making search theory more realistic but also by providing a better foundation to the MIU approach, the approach that search theory was originally intended to supplant. That is, the model AW present is actually a special case of MIU, a case in which the indirect utility of money is rationalized by search theory rather than by Patinkin’s “stochastic payments process.” Monetary exchange in this special case, instead of being widespread, is limited to a shadow economy involving only a subset of all transactions. The paper strengthens search theory by dropping some of its most egregiously counterfactual assumptions, namely the indivisibility of money and the absence of organized exchange. Divisibility has been recognized since Jevons as one of money’s most important attributes, but it has proven remarkably difficult to incorporate into search theory. Technically the problem is that the randomness of the matching process gives rise to a distribution of money holdings across people, and this distribution influences the prices that result from bilateral bargains. Keeping track of the distribution is relatively easy if people can only hold one unit of money or none. But keeping track