The paper is organized as follows. A preview of the results, as well as a deeper motivation of the model, is presented in Section 2. The formal description of the environment, with monitored banks and a nonbank public, is described in Section 3.
In Section 4, I present a benchmark version of the model in which the nonbank public uses outside money and there is no intermediation. The set of allocations considered in this version is helpful for showing that in the limit, when there is no trade risk, inside money is unnecessary. In Section 5, I weaken the perfect anonymity of the nonbank public by introducing the concept of credit lines, restricted to binary credit records.
I derive a necessary and sufficient condition under which credit is implementable.
I then find sufficient conditions under which inside-money allocations result in the banking sector intermediating capital. Section 6 concludes. All the proofs appear in the appendix.
of random meetings. I assume that a subset of the population has known histories;
that is, its members, calledbankers, are no longer anonymous. This is essentially the mechanism-design version, proposed by [3] and [4], of the banks in [2]. A novel re- quirement is the assumption that society keeps a record ofdepositsandwithdrawals made by otherwise anonymousnonbankerswhen interacting with bankers. The bank- ing sector can issueinside moneyto (and receive capital from) the nonbankers who will be consumers in the immediate future, increasing the likelihood that meetings between nonbankers as described in (i) will occur.
The main finding is that the banking sector can provide two functions that in- crease welfare – intermediate capital and issue inside money – based on society’s ability to keep a public record of their actions. Giving a nonbanker a unit of capital or a unit of money is a transfer that banks can credibly make so as to avoid the punishment of autarky following a defection. Moreover, this role of intermediation is accomplished without resorting to the assumption that nonbankers can produce directly to bankers. Because bankers can produce to other bankers without the use of money, they can also make a more efficient use of capital than the nonbank public can. As a result, intermediation can be welfare improving, even without an explicit subsidy to the banking sector. By contrast, nonbankers produce directly for bankers in the Cavalcanti-Wallace [4] model.
In order to keep the scope of the paper limited, I do not describe formally some implementable allocations that can be ruled out as suboptimal. One such allocation would prohibit banks from issuing money but would let them buy and sell capital in exchange for outside money. As a matter of fact, this allocation could emerge out of a regulation that attempts to limit the liquidity created by banks, and maybe that is what proponents of strong reserve requirements had in mind. In the resulting outside- money allocation, any transfer of capital between a banker and a nonbanker is also contingent on the holdings of money of the pair, insofar as bankers are prohibited from creating and destroying money. Since this limitation reduces the likelihood of intermediation, it is clearly suboptimal in my model.
The ability to issue and destroy nominal assets increases the turnover of capital and, therefore, the reliability of the services provided by bankers. In other words, inside money is essential not because it is needed to allow some capital interme- diation, but because it does not constrain the public’s ability to make deposits or withdrawals. Inside money is thus more liquid. Relative to the findings of models that ignore the role of money, the notion that inside money can increase the volume of private intermediation is novel. However, the idea that inside money can increase the set of implementable allocations, relative to outside money, has been cleanly presented by [4] as a set-dominance result. I believe that further research is needed to decide whether the introduction of productive assets or the removal of trade of consumption goods between bankers and non bankers allows for a deeper under- standing of the properties of inside money, relative to what the Cavalcanti-Wallace subset result already states.
The model also offers insights into a broader perspective about banking regu- lation. Friedman [6] did not present a model of money with acceptable microfoun- dations. One can, in principle, state his recommendations as an attempt to induce a
perfect match between the maturities of bank assets and liabilities. The model in [5]
is also free of monetary frictions and can be used to assess the welfare impact of reg- ulations that implement that kind of maturity match. In order to be more explicit (as I am able to do in this paper) about the separation of the investment arm of banks from their depository arm, which can create nominal assets, one could pursue a different approach by starting with the environment of [5] and then trying to add money to it.
One difficulty with this strategy is that fiat objects require infinite horizons to become essential in a credible way, and that difficulty seems to require a major change in the finite-horizon, nonstationary model of Diamond and Dybvig [5].4
In order to compare my model with other views of banking, it may be helpful to have in mind three bank functions. First, the storage function allows real assets to be deposited with the bank for future use. The bank can pool deposits and achieve better allocations, say by implementing a subsidy to the impatient depositor who needs resources in the near future. The storage function is thus a commitment de- vice, a pattern of payments that the bank can commit to, but that individuals facing private-information preference shocks cannot. In my model, banks can implement better allocations by intermediating capital, according to the realization of prefer- ence shocks and random meetings, so as to increase the likelihood of the meetings described in (i). Since banks have known histories, they can perform a commitment function similar to that in [5].
Second, the investment function allows pooled resources to receive positive real returns overtime. In my model, this function is not explored explicitly since capital is in fixed supply. That is done for reasons of tractability. However, it is not clear whether the positive aggregate returns featured in [5] add in any deep way to the commitment function already mentioned. Some readers might prefer a specification with growth. Since that is not the case in this paper, capital in my model can be interpreted as a license to production opportunities, which are in fixed supply. This interpretation is a reasonable one, as long as the reader keeps a clear picture of what kind of allocations remain feasible.
The third function is the extra liquidity allowed by the issue of inside money.
This function is not present in the model of Diamond and Dybvig. When the storage and inside-money functions are combined, two features arise: (iii) not all depositors (of capital, in my model, or of investment goods, in [5]) would demand their deposits at the same time, and (iv) inside money can be issued without difficulties, bringing more capital to intermediaries and helping the depositor satisfy his consumption needs at other bankers and nonbankers. It is true that (iv) can be performed to some extent by reserves of outside money held by bankers, but as discussed above, against the background of the Cavalcanti-Wallace result, inside money is less restrictive to intermediation.
After a careful review, [8] identifies three main ingredients of the role of banks in the Diamond and Dybvig model. One is the uncertainty about when individuals want to make expenditures. Another is that the withdrawal demands of different people must be dealt with separately. While this is done through a sequential-service
4See [1] for an attempt to combine money and banking in a finite-horizon model.
constraint in [8], it is done through the pairwise matching structure in this paper.
The third ingredient is the irreversibility of real investment, which is captured in this paper by the scarcity of capital, which, once transferred to a person, cannot be regained for sure in the near future. This list should help the reader establish a natural connection between the two approaches.
Previous literature emphasizes the fact that banking exploits informational fric- tions that the pooling of resources may help overcome. One of the simplifying as- sumptions in my model is that capital remains truly idle in the hands of a consumer, and thus there is apparently zero opportunity cost of transferring this capital to a producer. However, due to the uncertainty underlying random meetings, an individ- ual that transfers capital in my model to a banker or nonbanker is not guaranteed to receive this capital back at some fixed, future date. That is why having inside money ready to be issued improves the attractiveness of the mechanism for intermediating capital. In other words, the relevant opportunity cost of capital to a consumer is not quite zero, but having fast access to money increases the odds that intermediation is welfare-improving.
On another front, the reader may appreciate that in my model banks themselves update public records, and surmise that this is possibly the first paper in which the role of record updater is explicitly assigned to banks. I have made no attempt to cover the vast banking literature in search of alternative references, but I think that it is quite natural to see the Cavalcanti-Wallace banks performing this function as well, especially since their own informational history is common knowledge.