Comment on “the Distribution of Money Balances and the Non-neutrality of Money,” by Aleksander

Berentsen, Camera, and Waller (henceforth BCW) have written a nice piece that illustrates the effects of monetary policy when the distribution of money balances is non-degenerate across the population at the time of a policy action. The model is very helpful in addressing the issues at hand, and I felt that the article is, in general, quite instructive. Perhaps the closest relative of this article is Lucas (1980). Of course, that is quite appropriate, as Lucas’s article was a key contribution to the first “Models of Monetary Economies” conference. Lucas constructed an environment in which there are heterogeneous infinite-lived agents. In each period, each one of these agents receives a fixed endowment and is subjected to an idiosyncratic preference shock. There is no aggregate risk. The only asset is money and all contingent claims markets are assumed to be shut down. Thus, money is held for insurance purposes (as in a Bewley-type model), and it is also assumed to be held by each agent to satisfy a cash-in-advance constraint. In his analysis, Lucas goes some way toward characterizing a steady-state distribution of money balances across agents. With hindsight, some of Lucas’s comments in his article are intriguing, as he appears to anticipate why later developments in dynamic contracting theory (Green, 1987; Atkeson and Lucas, 1992) would be useful for a model like this. Although heterogeneous-agent models of money such as Lucas (1980) or Bewley (1980) are amenable to numerical solution methods, typically they are analytically difficult. Search models of money typically encounter the same type of difficulty. If money is divisible, then tracking individuals’ money balances over time is difficult in monetary search models. However, some recent approaches, such as those in Shi (1997) and Lagos and Wright (2005), make analytical methods relatively straightforward in search models of money. Shi’s approach is to use a representative-household construct, as in Lucas (1990). Lagos and Wright put a