Henry James, T.S. Elliot famously remarked, "Had a mind so fine that no idea could violate it." Similarly, more than a few economics papers involve formal models so fine that no facts can violate them.

Two recent examples purport to demonstrate the instability and inefficiency of "private money." One, on "Private Money and Banking Regulation," appeared in the September 2015 Journal of Money, Credit and Banking (JMCB). Its authors are Cyril Monnet, a Professor at the University of Bern, and Daniel Sanches, an economist at the Philadelphia Fed. The other, by Sanches alone, is called "On the Inherent Instability of Private Money," and is about to be published in the Review of Economic Dynamics (RED, for short).

That the models in these papers are indeed "fine," meaning first-rate, from a strictly analytical point of view, can't be gainsaid. They meet all of the exacting requirements of those economists who insist that a model's institutional features should be "essential" in the sense Frank Hahn had in mind when he argued that monetary GE models should provide an essential role for money. The features must, in other words, overcome frictions inherent in the model environment that would otherwise condemn optimizing agents to lower levels of utility. In particular, the models in question supply "essential" roles for indirect exchange, banks, and banknotes. Yet they are tractable enough to allow their authors to draw inferences from them concerning both the stability and the efficiency of private currency. So far as the realm of formal economic modeling is concerned, these are highly impressive achievements.

As the two papers are similar in their arguments and conclusions, I won't bother to distinguish between them except when necessary. The gist of the argument in each case is that, assuming perfect competition, private money (meaning competitively-supplied, redeemable bank notes) won't work, because people will have good reason to distrust the banks that issue it. That's so because the bankers' willingness to redeem their notes depends on how profitable the banking business is. If it is profitable enough, they can be trusted to redeem their notes, because they're better-off staying in business than reneging on their promises. The trouble is that, with perfect competition, the continuation or "franchise" value of staying in the currency business could well end up being so low that banks are tempted to drop out. Consequently, prospective note-holders aren't able to rule out the possibility that private money will become worthless. To put it in Sanches's more technical language, under perfect competition "there exist multiple equilibrium allocations characterized by a self-fulfilling collapse of the value of privately issued liabilities that circulate as a medium of exchange." A competitive, private currency system is, Monnet and Sanches conclude, "inherently unstable."

In fact, the news for fans of private money is even worse, for the conclusion doesn't just apply to the special case of perfect competition. Although allowing for banking industry concentration and associated market power makes for a greater likelihood that bankers will honor their promises, by increasing banker's expected profits, it doesn't necessarily rule out a collapse. And even if returns were high enough to avert a collapse, in the absence of further regulation banks would earn monopoly profits rather than pay a return on currency sufficient to guarantee an "optimum quantity of money" in the sense made famous by Milton Friedman. Private money would, in short, be either unstable or inefficient.

If unregulated private money won't work, what will? The obvious solution is a government currency monopoly, regulated so as to assure a return on currency sufficient to achieve an optimum money stock. But it's also possible, according to Sanches and Monnet, to achieve an optimal and stable outcome by having the government guarantee bankers a minimum after-tax income regardless of the demand for banknotes, using a subsidy financed by a lump-sum tax on currency users. The guaranteed minimum income rules out the panic equilibrium.

So much for a summary. The question is, do these models really make a persuasive case that unregulated private currency won't work, and that governments can do substantially better? Like many economists, I subscribe to the old-fashioned view that a theory, if it's any good, will yield conclusions that are, or at least appear to be, consistent with relevant experience, meaning, in this instance, the empirical evidence, so far as we are aware of it, concerning arrangements — and unregulated or lightly-regulated ones especially — in which currency did in fact consist of redeemable notes, supplied by competing, private banks. Alas, judged against such experience, rather than for their ingenuity, Sanches and Monnet's models must be considered failures, comparable to André Sainte-Laguë's demonstration that bumblebees cannot fly.

One might well wonder how such clever model-building could go so awry. One might suppose that Sanches and Monnet, themselves believing that theories should agree with facts, consulted relevant empirical work in constructing their theories. But that supposition is, to judge by what their papers reveal, not correct. Between them those papers hardly refer to relevant empirical cases at all, or (despite containing sections labeled "Related Literature") to other works addressing those relevant cases.

To be precise, the papers' only references to historical evidence consists of tangential ones, in the JMCB paper, to studies of antebellum U.S. experience. Yet even the evidence to which these few studies point isn't generally consistent with Sanches and Monnet's theory. Instead of illustrating the instability of private money, or of the tendency of the value of private notes to collapse, the Suffolk System, which is referred to by one of the cited papers (albeit one that merely comments on another theoretical work), was famous for keeping the notes of all New England banks circulating at par, that is, at their full specie values, throughout the region. The Suffolk did this, moreover, for more than three decades. During that time only one temporary system-wide suspension of New England bank notes took place, following the Panic of 1837; and even then New England notes continued to be received at par at the Suffolk Bank. (During the 1857 panic, the banks of Maine alone suspended payments temporarily.) In short, banking historian and former Comptroller of the Currency John Jay Knox appears to have been fully justified in regarding the Suffolk episode as proof "that private enterprise could be entrusted with the work of redeeming the circulating notes of the banks, and it could thus be done as safely and much more economically than the same service can be performed by the Government." To say that this conclusion appears inconsistent with one of the main implications of Sanches and Monnet's models is putting things mildly.

As for antebellum "free banking" episodes, to which the other cited works refer, although it's true that large numbers of banks failed in several (but by no means all) U.S. "free banking" systems, these failures were mainly due, not to the public's sudden loss of confidence in their notes, or to the bankers' decision to voluntarily close-up shop because their business no longer seemed profitable enough, but to the depreciation of securities they were compelled by law to purchase as a condition for issuing notes. And, although some fly-by-night or "wildcat" banking also took place, here, too, the trouble was usually traceable to ill-designed bond-deposit requirements that allowed banks to operate with little if any capital, while simultaneously assuring people that those banks' notes were entirely secure and backed by the state. Because Michigan's first, disastrous free banking experiment occurred during the post-1837 suspension of specie payments, the problem of wildcatting was compounded by the fact that Michigan's free bankers could, as Hugh Rockoff notes in one of the cited papers, "issue bank notes with practically no cost to themselves and unchecked by the need to redeem the notes in specie."

Though it was exceptional, the Michigan episode is nevertheless significant, for if the inferences that Sanches and Monnet draw from their private money model can be said to fit any actual private money episode, Michigan's first "free banking" episode is it. And no wonder, because on close inspection, the "banks" and "banknotes" in the Sanches and Monnet models, and in Sanches' RED model especially, involve features of that unique episode that were absent from other past private money systems.

Although Sanches and Monnet refer to the "private money" in their models as "bank notes" and "privately issued liabilities," and also to bankers' willingness (or lack thereof) to "keep their promises" by "redeeming" their notes, such language masks the fact that the "bank notes" in their models differ from most of their historical counterparts in not being fixed-value claims to any definite quantity of real goods, let alone instantly redeemable ones. This is particularly evident in the RED paper, which states that "A banker who issues a note at date t is expected to retire it at date t + 1 at the current market value" (my emphasis), and that the note in question "is equivalent to a debt instrument with a market-determined real return of Φ t+1 /Φ t ," where Φ t+1 /Φ t is the ratio of the note's redemption value to its initial value. The same paper then goes on to observe that, although "it is possible to construct an equilibrium with the property that the value of privately issued notes is stable over time…it is also possible to construct other equilibrium in which the exchange value of notes is not constant over time." Specifically, an equilibrium path exists along which notes' purchasing power declines monotonically. Because a bank's franchise value depends on the purchasing power of its notes, this equilibrium path must eventually result in notes ceasing to be convertible. The only sustainable equilibrium is therefore the stationary one. It is, nevertheless, not the case that that the notes in question have a contractually-fixed redemption value. The model is therefore, strictly speaking, not a model of "redeemable" bank notes in the generally-understood sense of the term, but of something much more like irredeemable private fiat money: like the notes in the RED model, actual fiat monies may be "redeemable" in the sense that they have some positive but variable exchange value, but they are certainly not redeemable according to the conventionally-understood meaning of that term.*

The finding that a system of private fiat money may not succeed in winning the public's confidence, let alone in achieving an "optimum" quantity of money, is neither surprising nor new. A substantial literature now exists on the topic, dating back to Benjamin Klein's pioneering work. (Chapter 12 of Larry White's Theory of Monetary Institutions supplies an excellent review.) And though some contributions to that literature suggest that a competitive fiat money system can work under special conditions, the general consensus — and one to which we free banking theorists have long subscribed — is that such a system is unlikely to command any confidence. Indeed, Larry and I have argued that it is precisely for that reason that private banking systems of the past have had to rely, occasional suspensions aside, on "goods-back guarantees," meaning offers to convert paper money into fixed amounts of real goods, to make private notes acceptable.

Nor do the terms "reneging" and "defaulting" mean the same thing in the Sanches-Monnet models as they do in real-world banking systems. Bankers in these models renege, not because they are unable to meet their obligations, but because, judging it no longer worthwhile to go on being bankers, they decide to quit the banking business. A sort of "liquidation" does occur, but it is one in which the bankers themselves consume the goods they acquired in exchange for their notes. The result is much as if the bankers absconded, wildcat style, taking any assets they'd acquired with them. Noteholders, in any event, have no recourse to retiring bankers' assets, for if they did their notes would not become worthless. The notes, in other words, do not even qualify as meaningful (in the sense of enforceable) claims to some positive but variable quantity of real goods. Banking crises happen, in the Sanches-Monnet model economies, not because note holders believe that their banks are in danger of becoming insolvent, but because they believe them to be in danger of becoming insufficiently profitable. Insolvency doesn't enter into it because, strictly speaking (and unless I'm missing something), it isn't possible for a Sanches-Monnet bank to become insolvent.

This last observation brings me to a second feature of most real-world private financial firms, though not of Michigan's wildcats, that is conspicuously absent from Sanches and Monnet's models, namely, bank capital. When a Sanches-Monnet banker, finding that the franchise value of his business has fallen below a critical level, "makes a decision to renege on his promises as the dissolution of his note-issuing business," he sacrifices nothing apart from that franchise value itself, having no other "skin in the game": no initial investment, and certainly no double or unlimited liability, to which bank owners were subject in many historical private currency arrangements. (See also here.)

Think about this. A "banker" offers you a note, which he promises to "redeem," not whenever you like, but at a future date, and not in a definite quantity of goods, but (in the RED model) in some uncertain amount. If the banker chooses to renege, that is, to offer nothing at all for the notes, he loses nothing save whatever profit he might have earned by staying in business. The banker promises to invest the proceeds obtained in exchange for the note, but you have no idea how. The bank has no capital, so that any adverse change to the value of its assets must affect the value of its liabilities by a like amount. Finally, no court will find the banker obliged to pay you, or other note-holders; and no other government agency even pretends to protect you from any loss you might incur should your bank close-up shop.

Will you trade valuable goods for such a note? Neither would I. Nor, I suppose, would any sane person. (In Michigan in 1837 people did accept similar notes because state government authorities assured them that the notes were fully secured by good collateral, and also because there were no other notes to be had.) That the sort of "private money" we're talking about won't fly seems, in fine, self-evident, once its basic features are set forth in plain language. To go to the length of developing a fully-articulated model economy for the sake of reaching the same conclusion hardly seems necessary.

It's a shame that Sanches and Monnet didn't make more than a cursory effort to familiarize themselves with the actual nature and performance of past private currency arrangements, for had they done so they presumably would have constructed a very different sort of model, and reached very different (and perhaps more interesting) conclusions. Instead of confining themselves to a few desultory references to banking in antebellum U.S., they might have read some portion of the heaps of books and articles concerning those historical banking systems that came closer than any U.S. episode did to representing genuine monetary "laissez faire." They might, for starters, have familiarized themselves with the famously stable pre-1844 Scottish free banking episode. They might also have gotten to know the pre-1935 Canadian system, which was almost as stable. They might even have gleaned a clue or two about unregulated private currency from the less well-known, and less long-lasting, free banking episodes of Australia, Switzerland, Ireland, Colombia, France, or Chile. They would have noticed how bank capital and (in some instances) extended liability served in these arrangements to win prospective note holders' trust. What they certainly could not have done was to write the papers they've written, while still imagining that by so doing they were shedding light on what typically happens when currency provision is left to the private marketplace.

So far I've emphasized the matter of stability, concerning which the predictions of the Sanches and Monnet models are most glaringly at odds with experience. While free banking systems were often stable, it doesn't follow that they supplied "optimum" quantities of money in Milton Friedman's sense. To the extent that they didn't, their performance agrees with one of the main conclusions Sanches and Monnet draw from their models. But if free banking systems did not fully meet Friedman's ideal, it's unlikely that they veered very far from it, or that any regulated system could do better.

One obvious respect in which historical private money systems departed from Friedman's ideal was in not paying explicit (that is, nominal) interest on circulating banknotes. In The Theory of Free Banking, I acknowledged that, although competition will tend to drive free banks "to pay competitive rates of interest on…deposits," bank notes might still be held in sub-optimal quantities owing to the difficulty of paying interest on circulating notes. But I also noted that the consequence, instead of consisting of sub-optimal quantity of money, might well consist of a cross-subsidy of deposits such as would enhance the demand for them enough to compensate for the sub-optimal demand for currency. What's more, even the relatively minor inefficiency implicit in such a cross subsidy would be limited to the extent that private currency suppliers engaged in non-price competition.

But to regard the absence of an explicit interest return on circulating private bank notes as "sub-optimal" is to suppose that some alternative arrangement could do better. And for that supposition there is, I believe, no sound basis. The circulating notes of government monetary authorities have also tended to be non-interest bearing, and remain so to this very day, despite many authorities' wish that this weren't necessarily the case. The explanation lies in the practical impossibility of keeping tabs on banknotes' owners when the notes change hands frequently and anonymously, as they must do if they are to be convenient exchange media in transactions for which non-circulating forms of money will not serve. Because government monetary authorities must reckon with the same transactions costs of paying interest on circulating notes as their private counterparts, they cannot come closer to Friedman's ideal by that means. Moreover, because competitive pressures do not prevent them from earning monopoly profits, they are likely to stray even further from that ideal, even taking the rate of inflation, and hence the real return on non-interest-bearing notes, as given.

And what about the interventions that Sanches and Monnet recommend? Might they at least help to nudge things closer to Friedman's ideal? I wouldn't count on it. Their proposal, you may recall, is to have the government tax currency users and use the proceeds to subsidize banks enough to keep their franchise values from falling below some critical level. But Sanches and Monnet also assume — and the assumption is absolutely critical to their model — that "agents" apart from bankers themselves "do not observe the amount of collateral (if any) an individual banker holds in reserve to secure his circulating liabilities." Alternatively, "agents" do not know the value of their banks' assets. A bank's franchise value is, however, strictly a function of the quantity of assets it has on hand. Consequently, in order to implement the policy in question, the government must have access to information unobtainable by anyone else. If this vaguely reminds you of the flaw in Diamond and Dybvig's argument for deposit insurance, give yourself a gold star. And give yourself another if you are wondering, as I am, how the government would manage the subsidies in question in a world in which some bankers are just-plain incompetent.

And that, you may rest assured, is a world that doesn't just exist on paper.

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*Although Sanches recognizes that the indeterminacy of the equilibrium value of "bank notes" in his model resembles that of fiat money in other writings, he does not seem to appreciate how the similarity arises owing in large part to the fact that nothing in his model obliges his bankers contractually to redeem their notes at a definite rate.

The JMCB paper differs from the RED paper in that bankers there offer to redeem notes issued in sub-period 1 for a predetermined amount of a good in sub-period 2; still, the notes' purchasing power when first issued can differ from their eventual redemption value. The "notes" in question are therefore neither fiat money in the usual sense of the term nor ordinary banknotes but zero-coupon bearer bonds that mature after a set period, rather like Continental dollars, according to Farley Grubb's understanding of the latter. In referring to the notes in their model as "debt instruments…redeemable on demand," Sanches and Monnet appear to overlook the distinction between "after one sub-period" and "on demand."