Banks as accelerators of the circulation of money

Laurent LE MAUX*

February 2015

The money multiplier approach asserts that banks are unique in that they implement a creation of money, while the finance approach regards banking institutions as financial intermediaries among others. In retrospect, Cantillon's Essai stands between these two extreme approaches. It both challenges the money multiplier approach and grants to banks a significant monetary role. The aim of the paper is to clarify Cantillon's theoretical propositions on bank issuing of debts convertible on demand into money at face value and to explore further the proposition according to which banks contribute to accelerating the circulation of money.

During the last century, the quantity theory, Old view, and monetarism developed the money multiplier approach and maintained that commercial banks are unique among financial institutions in that they increase the quantity of money at will, and, all things considered, act as creators of money [START_REF] Fisher | The Purchasing Power of Money[END_REF][START_REF] Friedman | A Program for Monetary Stability[END_REF][START_REF] Pesek | The Foundations of Money and Banking[END_REF]. Since the New view and the integration of banking in the theory of finance, the pendulum has swung to the opposite extreme [START_REF] Gurley | Money in a Theory of Finance[END_REF][START_REF] Tobin | Commercial Banks as Creators of 'Money[END_REF][START_REF] Fama | Banking in the Theory of Finance[END_REF]. Banks are henceforth considered by contemporary banking theory as financial intermediaries among others and their monetary role has been denied.

An alternative approach standing between these two extreme views was suggested almost 300 years ago. Retrospectively, in his Essai sur la Nature du Commerce en Général, Richard Cantillon at one and the same time challenges the money multiplier approach and grants to banks a significant monetary role. 1 The Essai propounds a twofold theoretical proposition on bank issuing of debts convertible into money, at face value, to the bearer, and on demand. The first proposition is the law of reflux in the form of convertibility, which means that banks cannot issue more than demand debts that the public wants to hold. The first proposition was restated by classical monetary theorists in the late eighteenth and nineteenth centuries, and has been documented by the secondary literature [START_REF] Skaggs | John Fullarton's Law of Reflux and Central Bank Policy[END_REF][START_REF] Glasner | The Real-Bills Doctrine in the Light of the Law of Reflux[END_REF][START_REF] Maux | The Banking School and the Law of Reflux in General[END_REF]. The second proposition, connected to the first, states that banks contribute to accelerating the circulation of money through the issue of demand debts and then considers banks as accelerators of the circulation of money. The second proposition is a very particular contribution from Cantillon to monetary and banking theory. I shall refer to it as the "banking approach of circulation" (regarding banks as accelerators of the circulation of money) in opposition with the "quantity approach of banking" or "money multiplier approach" (viewing banks as creators of money). 2 Cantillon's banking approach of circulation has been largely overshadowed by the Old and New views and is rarely mentioned in literature. Without any explicit reference to the Essai, [START_REF] Wicksell | Interest and Prices[END_REF][START_REF] Wicksell | Lectures on Political Economy-Money[END_REF] expounds a similar proposition when he deals with the "virtual" acceleration of money. Nevertheless, as will be seen, Wicksell's analysis is too broadly formulated, encompassing all manner of credit and not specifically bank credit. However, the term "virtual" is the most appropriate and I shall adopt it to designate the accelerated circulation of money brought about by banks. Later, Holtrop (1929, pp. 506-7) and Rist (1938, pp. 38-9, pp. 69-71) point out the importance of Cantillon's banking approach of circulation and link it with the idea of the virtual velocity of circulation formulated by Wicksell. In subscribing to the money multiplier approach, Schumpeter (1954, pp. 319-21) is maybe the sole who explicitly endeavors to refute Cantillon's proposition. Within the quantity theory, Allais (1987, pp. 533-4) criticizes Rist's-in fact Cantillon's-view, which considers "that the credit mechanism does not lead to the money creation, and that its only effect is to increase the velocity of circulation of basic money. [...] Mathematically, the two formulations are equivalent, but only the [quantity] interpretation is of real significance in terms of economic understanding." This Allais's statement is precisely open to discussion.

Before beginning the substantive discussion, two definitions-explicitly or implicitly given in the Essai-need to be emphasized. First, by money, Cantillon means the silver or gold specie coined at an official price at the Mint. Nowadays, the ultimate money is not specie but the inconvertible liabilities issued by the central bank-the fiat money. Cantillon did not refer to the fiat money standard when expounding the banking approach of circulation, but let us keep in mind that his proposition is independent on whether money is metallic or fiat. As a second definition, a bank is a fractional reserve institution holding money in reserve and, thus, an institution issuing demand debts such as banknotes or demand deposits convertible at face value into money and partially backed by it. Theoretically, Cantillon argues that the form of demand debt is irrelevant and it is only a practical matter (Essai, p. 305) and, most importantly, he draws a clear-cut distinction between money and demand debts. These definitions have been rediscovered by [START_REF] Rolnick | Money, Inflation, and Output under Fiat and Commodity Standards[END_REF]Weber (1997, p. 1311) and imply "that money should be divided into two mutually exclusive categories: objects that represent a convertibility promise by, or claim on, the issuer and objects that represent no convertibility promise or claim. For convenience, we refer to the nonconvertible, unclaimed objects as primary money, and the convertible, claimable objects as secondary money" (original italics). Respectively, I refer to money and demand debts.

In order to discuss the monetary role of banking, the present paper briefly comes back to the law of reflux first held by Cantillon and contrasts it with the quantity approach of banking. Then, it specifies two kinds of circulation drawn by Cantillon termed here the "monetary approach of circulation," which is related to the physical circulation of money, and the "banking approach of circulation," which is related to the virtual circulation of money. Furthermore, two channels of virtual circulation of money provided by banks are considered, namely "externalization" and "internalization," and their characteristics concerning the liquidity risk borne by banks. Finally, the paper provides an analysis of comments on Cantillon's banking approach of circulation.

I. CONSTRAINT OF CONVERTIBILITY AND LIQUIDITY

The Essai describes the banking activities and their implications. On the one side, bankers credit accounts or put notes "payable on demand" into circulation for economic agents who deposit specie with them "to avoid the trouble of keeping this money in their houses and the thefts which be made of it" (Essai, p. 299). On the other side, bankers go beyond the simple service of keeping specie in their vaults: they lend money, or extend credit by issuing demand debts. This credit-granting activity is connected with the law of reflux or the adverse clearing mechanism. Cantillon essentially mentions reflux in the form of demand for convertibility of banknotes into specie and shows how competing issuing banks are compelled to reimburse every note in excess. The convertibility constraint makes over-issuing ruinous for any expansionist bank, because over-issues involve marginal costs that exceed gains, indicating to the bank that the issues exceed the demand for them. In Cantillon's words, bankers "will be ruined in credit if they fail for one instant to pay their notes on their first presentation, and when they are short of cash in hand they will give anything to have money at once, that is to say a much higher interest than they receive on the sums they have lent" (Essai, p. 303).

It is not just the public who ask for notes they do not wish to hold to be redeemed. Rival banks and the banking community as a whole also impose discipline in the matter of bank issues. In effect, if notes issued by a banker "fall into the hands of persons who are not accustomed to deal with him," they stay in circulation for longer and this "delays his payments a few days or weeks"; by contrast, if "his notes come into the hands of those of his own business," these rival bankers "will have nothing more pressing than to withdraw the money from him" (Essai, p. 303). The reflux is fast enough taking only a few "weeks" at most for convertible banknotes (more generally, for demand debts) not to become overabundant, and not to have any inflationary effect. Accordingly nowhere does the Essai state that demand debts could affect prices. In addition, the above-quoted passages introduce two important and interlinked theoretical features of banking: first, the adverse clearing mechanism which involves the collection of rival banknotes, the gross (or possibly net) clearings, and then the demand for settlements; second, an explanation of the velocity of the reflux of demand debts that is clearly distinct from the velocity of the circulation of money as a stock. In sum, the problem is not one of the quantity of money or any monetary aggregate potentially in excess, but fundamentally one of liquidity-and as the ultimate liquidity, money alone is the "true sinews of circulation" (Essai, p. 319).

Hence, Cantillon's analysis is inconsistent with the quantity approach of banking, which rests on (i) the aggregate of "base money" (whether metallic or fiat) and "bank money," (ii) the money multiplier linking the two, and (iii) the twofold postulate of proportionality and causality applied to this aggregate. It is different from the Old view, which considers that commercial banks are "unique" among financial institutions because they are able to "produce money" through the multiplier approach just like a miner "produces some ounces of gold" (Pesek and Saving, 1968, pp. 144, 150). It may be added that Cantillon's view also differs from the New view, which argues that banks are pure intermediaries and their function as such is to satisfy the portfolio preferences, and that the differences between banks and other financial intermediaries "are of degree, not of kind" (Tobin, 1963, p. 418). In attempting to reconcile Old and New views, Selgin (1989, p. 84) points out that exponents of the New view do not state their theory in a manner consistent with the view that "banks face a liquidity constraint and that they will expand their liabilities until this constraint becomes binding." Actually, this liquidity constraint view begins with the Essai.

As I shall detail, according to Cantillon, banks are intermediaries (they issue debts that agents want to hold to some extent and, against these, they grant loans or purchase assets) but of a special kind: their debts are so particular (they are redeemable on demand and at face value in money) that they have a derived and a specific monetary function (banks accelerate or decelerate the circulation of money) that entails a specific risk (that is, the liquidity risk occurring at any time, and not only the transformation occurring at maturity).

II. MONETARY AND BANKING APPROACHES OF CIRCULATION

Cantillon expounds two distinct approaches, which pertain to the circulation of money. The first-called here the "monetary approach of circulation"-is familiar enough and taken up by the Fisherian analysis. It postulates that "an acceleration or greater rapidity in circulation of money in exchange, is equivalent to an increase of actual money up to a point" (Essai, p. 161). Just like an increase in the quantity of money, an increase in the velocity of money helps to realize new transactions. It is a monetary concept insofar as it can be suggested without any reference to banks' issuing activity, but to money alone. It contributes to speeding up the physical circulation of money. No bank need necessarily intervene. Several factors may speed or slow the physical circulation of money: economic and geographical spheres of exchange, hoarding, precautionary motives for holding money (Essai, pp. 142-7), and a credit instrument: drawing of bills.

The drawing and clearing of bills of exchange contributes to economizing circulation and corresponds to a physical acceleration of money. Indeed, Cantillon (Essai,p. 141) states that offsetting between merchants-which he calls "exchanges by valuation"-seem "to economise much cash in circulation, or at least to accelerate its movement, by making it unnecessary in several hands through which it would need to pass without this confidence and this method of exchange by valuation." For a given volume of transactions, merchants need less money. Cantillon (Essai, p. 177) returns a contrario to the effects of clearing: when purchases are no longer "made by valuation" (by clearing) and are instead "made for cash" (by physical circulation), there is a need for "greater rapidity in the circulation of money" from place to place. As a result, the physical acceleration of money compensates for the discontinuance of the practice of clearing. In dealing further with the issuing and clearing of bills, Cantillon (Essai, repeats that "by exchange or set-off [...] the trouble of sending money from one city to the other" will be saved, the "double transaction or transport may be avoided."

The technique of demand-debt issues by banks is different from those of the drawing and clearing of bills of exchange. It "also" (Essai, p. 141) contributes to speeding up the circulation of money, not by avoiding physical circulation, but by carrying out virtual acceleration. This brings us to the second approach of circulation-called here the "banking approach of circulation." It is essentially a banking feature and pertains to banks in that they are exclusively concerned. It states that banks accelerate the circulation of money through the issuing demand debts. In Cantillon's words: "The bankers and goldsmiths contribute to accelerating the circulation of money. They lend it out at interest at their own risk and peril, and yet they are or ought to be always ready to cash their notes when desired on demand" (Essai, p. 301, italics added; see also, pp. 141-3). The distinction between money (here, specie) and demand debts (here, banknotes) stands for a precise articulation between them inasmuch as demand debts accelerate the circulation of money. The outcome that derives from the acceleration of the velocity of money by banks is that they bear both a credit risk (banks lend "at interest at their own risk and peril") and a liquidity risk (they have to reimburse their issues "when desired on demand"). Finally, the banking approach of circulation (regarding banks as accelerators of the circulation of money) is related with the law of reflux (regarding banks as a fractional reserve institution bearing convertibility constraint).

By the monetary approach of circulation, the circulation of money is external in that the fraction of money held by the public physically circulates outside the bank. In contrast, by the banking approach of circulation, the circulation of money is internal in that the other fraction of money not circulating among the public remains inside the vaults of the banking system; the circulation is also virtual in the sense that the fraction of money held by banks does not circulate physically. And yet, through the banking approach of circulation, money circulates as if monetary approach of circulation were operative: money is not actually circulating among the public, but new transactions may be made just the same. In sum, the virtual acceleration (deceleration) of velocity of money is effective when the banks put into (withdraw from) circulation demand debts in supplying (in asking for reimbursement of) bank credit.

One consideration must be stressed at this stage. The virtual aspect of the banking approach of circulation makes sense only under the fractional reserve banking system. It is fundamentally linked with the fact that several agents who routinely use demand debts as means of payment in place of money consider the same amount of money held by the issuing bank in reserve as immediately available. This characteristic is effective in the case of demand debt issuance, but not in the case of issuance of time obligations such as commercial papers, bills, securities, or even time deposits. In the latter cases, only the creditor (and not several) considers that money is available only at maturity (and not at demand). This fundamental point helps to differentiate clearly drawing of bills from demand-debt issue. Nonetheless, such a distinction is not clear or apparent in Wicksell's writings on circulation. Wicksell (1906, p. 67) lays down the idea of "virtual" circulation of money as opposed to a purely "physical" one, but he applies the virtual character of accelerated circulation to all forms of debts, whereas Cantillon restricts it to demand-debt issuing by banks.

Indeed, Wicksell (1906, p. 67) contends that the "influence of credit" on money may "under all circumstances" be regarded as virtually accelerating the circulation of money (italics original). In such a perspective, the time obligations issued by non-bank agents or financial intermediaries is placed on the same footing as demand debts issued by banks. In the case of pure intermediation, for instance, Wicksell (1898, pp. 62-3, 66) supposes that "the use of bills of exchange" and "centralization of lending in the banks (or on the bourse)" are equivalent as regards their effects on circulation. In the case of ordinary trade bills not discounted at a bank, circulating as a means of payment among merchants, and possibly being set off, Wicksell (1906, p. 70) concludes that "[h]ere also it may be said that the velocity of circulation has been virtually accelerated."

The main criticism that may be made on these Wicksell's contentions is that not all forms of credit bring about a virtual acceleration of money. Let us detail the different cases. In the case of commercial or financial clearing, and as seen previously, the economizing of circulation through clearing corresponds to a physical and not a virtual acceleration of money. In the case of discount or simple credit, one agent (the creditor) considers an amount of money available only at maturity (the debtor considers as available until maturity the same amount that he does not have to lay out immediately) and this entails no virtual character of circulation. In the case of pure intermediation, the financial institution does not keep any money in reserve and only transforms the maturity of time deposits or savings that the public entrusts to it. By contrast, in the case of bank issuing activity, several agents at the same time consider as immediately available the same amount of money as the bank keeps in its vault.

Finally, in the case of demand debts (banknotes as well as deposits convertible at demand at face value into money), and only in this case, Wicksell (1906, p. 68) perfectly echoes Cantillon's banking approach of circulation: "The [physical] circulation of the notes outside the bank may thus be regarded as a virtual [...] circulation of coins lying in the bank's keeping" (italics original).

III. THE VIRTUAL CIRCULATION OF MONEY

Once the Cantillon's banking approach of circulation has been scrutinized, it is possible to detail two different channels cut by the fractional reserve system and by which money can circulate virtually. The first channel, termed here "externalization" of circulation, consists of credit granted by banks in putting into circulation money previously held by the bank. There is a cash withdrawal up to the amount of credit, a transfer of money from the bank to the public that involves a transformation of bank asset maturity. The bank, to the detriment of its own reserve holding, increases the amount of money held by the public, which can therefore make new transactions. Externalization is such that "the banker will often be able to lend 90,000 ounces [of silver] of the 100,000 he owes throughout the year and will only need to keep in hand 10,000 ounces to meet all the withdrawals. [...] As fast as one thousand ounces are demanded of him in one direction, a thousand are brought to him from another. It is enough as a rule for him to keep in hand the tenth part of his deposits" (Essai, pp. 299-301). It can be noted here the idea that the fractional reserve system is sustainable since the efflux and the reflux of liquidity inside the bank are equivalent over a given period of time. This theoretical outcome explains bank debt sustainability-a contrario bank liquidity crises-and also holds for the second channel.

The second channel of the banking approach of circulation, termed here "internalization," consists of a credit granted through the issuing of demand debt up to the amount of credit, and it also entails a disequilibrium between asset and liability maturity. The bank varies its reserve ratio, not by decreasing its reserve, but by increasing the amount of its demand obligations. In other words, internalization is based on (i) the bank credit through the issuing of demand debts and (ii) the circulation of such debts instead of money-so long as they are convertible. "The goldsmiths and public bankers, whose notes pass current in payment like ready money, contribute also to the speed of circulation, which would be retarded if money were needed in all payments for which these notes suffice" (Essai, pp. 141-3, italics added; see also p. 305, about public banks). In this significant passage, the distinction between money and banknotes is not only descriptive but also analytical: demand debts accelerate the circulation of money, which would be delayed if they were not issued.

One or the other channel of virtual circulation of money is, for a supplementary level of transactions, more or less efficient depending on whether it makes the bank more or less vulnerable to liquidity risk. Three modes of circulation may be identified in order to understand their consequence on bank liquidity risk. First, as seen above, "externalization" consists of bank credit such as the amount of money held by the bank decreases with nominal transactions and that held by public increases in consequence. Second, "partial internalization" is similar to externalization insofar as a substantial proportion of money continues to circulate among the public; but it differs from externalization insofar as the bank supplies credit by issuing demand debts and not by withdrawing money. Third, "complete internalization" relies on a more sophisticated payment system than in partial internalization inasmuch as money is very largely (almost completely) centralized in the bank vaults; bank reserves are practically equivalent to the total stock of money and very little (if any) money circulates outside. Thus, the virtual circulation allowed by each mode generates a different liquidity risk for a supplementary level of transactions and for given credit and asset risks. Because of an absence of demand debts issue (that is, because of a money withdrawal, which de facto involves lesser centralization), the liquidity risk is higher with externalization mode than with partial internalization mode. And because of a less centralization of money at the bank, the liquidity risk is higher with partial internalization mode than with complete internalization mode.

Such a categorization brings about that institutional characteristics of the payment system, including (i) demand-debt issuing by banks, (ii) broad acceptability of this demand debt among the public, and (iii) extensive or complete centralization of money at the banks or at the central bank, are crucial. They have direct consequences for liquidity-risk management and reinforce public confidence in the payment system. And it is in this way that we might understand Cantillon (Essai, p. 305) when he writes that: "A general national bank has this advantage over the bank of a single goldsmith that there is always more confidence in it. The largest deposits are willingly brought to it." Demand-debt issuance associated with extensive centralization of money leads to a more efficient payment system: the circulation of money and its acceleration are thus mainly internalized by banks, and the liquidity risk is lower for a given level of transactions; in other words, for a given liquidity risk, a bank can make possible a higher level of transactions.

At this stage, two considerations are in order. The first is that a definition of the virtual acceleration of money through internalization could be given a contrario. If the demand debts (D) correspond to the totality of money that the bank holds in reserve (M b with M b =D), they circulate as if the money held by the bank circulates among the public. Consequently, the velocities of circulation of M b and D (respectively, v b and v d ) are similar (v b -v d =0). No acceleration of money can take place within the banking system. Now, if the bank is a fractional reserve institution (with M b <D), and if its demand debts circulate as money, then the velocity of money exceeds the velocity of demand debts. The ensuing virtual acceleration of money can be measured by the difference between these two velocities (v b -v d >0). The second consideration importantly pertains to the price level. Because of the constraint of the law of reflux, the issue of demand debts cannot be overabundant. Correlatively, the virtual acceleration of money cannot be "in excess" or inflationary. Inasmuch as the demand for demand debts expressed by agents corresponds to a demand for an increase in the velocity of money, the velocity of circulation remains similar to that demanded. In other words, the law of reflux helps to equalize the "supply" of acceleration by banks and the "demand" for acceleration by the public, without entailing inflationary effect.

IV. COMMENTS IN LITERATURE AND DEVELOPMENTS

Cantillon's banking approach of circulation is not plainly appraised in literature. Schumpeter's History of Economic Analysis is an exception and interestingly endeavors to refute it. One argument is based on the example of a "check-room attendant" of a theater who rents out the coats deposited with him-an example, it can be noticed, which only applies to the externalization channel. It is then supposed that this attendant "is a wizard, and performs the feat of making it possible for two people, the owner and the hirer, to wear the same coat at the same time" (Schumpeter, 1954, p. 320). This case is such that, two persons wearing the same coat at the same time, the attendant would duplicate coats just like bank would multiply money. This is precisely the conclusion of the money multiplier or money creation approach. In this respect, it is not surprising, even significant, that Fisher (1935, p. 42) comes to consider a bank as being "able to perform a miracle." Another case must be considered. There is in fact a rental service of coats with a very particular technology namely, fractional backing of the coat deposits. The attendant does not rent a coat that he buys himself and which belongs to him, but he rents a coat, which has been entrusted to him for a time, while its owner is in the auditorium. If he succeeds in anticipating the return of the coat (by the hirer) and the withdrawal of the coat (by its owner or the initial depositor), our attendant brings into effect (by the technique of a fractional reserve system) an acceleration of the velocity of the coat that, instead of being in the cloakroom, is on the back of a hirer-stroller during the time of the concert. No miracle, but a supplementary circulation of the coat through externalization.

A further argument from Schumpeter (1954, p. 320) shows the difficulty in describing virtual circulation in concrete terms and, faced with this stumbling block, he comes to the idea that it might "perhaps, seem more natural to say that bankers increase not the velocity but the quantity of money"-and here Schumpeter seems to turn over a new leaf-"or of those means of payment that, within limits, serve as well as money." But the idea that the banks issue means of payment such as demand debts does not dismiss that the banks increase the velocity of circulation of money: on the contrary, the former generates the latter. However, Schumpeter maintains, in accordance with the money multiplier approach, that banks "create" deposits or banknotes and "appear to manufacture money rather than to increase its velocity." And this petitio principii collapses when Schumpeter asserts that "it is clear and actually beyond dispute that what the banker does with money cannot be done with any other commodity"; and that "there is no other case in which a claim to a thing can, within limits to be sure, serve the same purpose as the thing itself"; and, as an illustration, that "you cannot ride on a claim to a horse" (Schumpeter, 1954, pp. 320-1).

These assertions are open to various-three at least-rebuttals. The first is that the example of the "claim to a horse" is misapplied. In effect, a commodity can be defined as a good not subjected to minting and circulating at a monetary price. It can be used for production purposes or for consumption. Or it can circulate as a mean of payment. Whichever the case, the concept of circulation is effective both for money and for commodities in the productive and commercial process. By contrast, a service cannot circulate because, by definition, it is destroyed since it is used. There is thus an analytical shift in the example presented by Schumpeter that makes it inappropriate: riding a horse corresponds to a service (transportation or leisure) and not to a commodity (a horse). The reasoning must be made with a horse, a bundle of wheat, or a coat as a commodity, and not as a vector of a service.

The second rebuttal reverses Schumpeter's assertion that "what the banker does with money cannot be done with any other commodity." In fact, a bank actually cannot increase the quantity of any other commodity just as it cannot increase the quantity of money. Hence, the idea that a bank cannot increase either the quantity of a commodity or the quantity of money refutes ex abrupto the money multiplier approach or the quantity approach of banking. It even strengthens the consistency of the alternative approach, namely, Cantillon's banking approach of circulation. If a bank does not increase the quantity of what it is held in reserve, money or any good, the alternative hypothesis is to consider that the bank increases the velocity of what it is held in reserve, money or any good. This leads to the third rebuttal: a fractional reserve institution can also increase the velocity of circulation of a commodity and, consequently, a bank as a fractional reserve institution can do with any commodity (banking in good) what it does with money (banking in money).

To resume this third issue, imagine a market where a commodity, say wheat, is negotiated and circulates. Agents put the wheat in an institution, a warehouse, which reduces transportation and transaction costs. The warehouse issues certificates in order to testify to the deposits of wheat, and these certificates circulate between brokers and merchants in place of the bundles of wheat. As the price for immediate delivery is higher than the price for future delivery, especially when storage and insurance costs are taken into account, the issuance of extra warehouse certificates may be profitable and effective. Thus, the warehouse becomes a fractional reserve institution holding one kind of commodity (and not money) in reserve. Historically, the rice warehouses in Japan in the seventeenth century [START_REF] Crawcour | The Development of Credit System in 17 th Century Japan[END_REF] and the warehouses in Chicago on the wheat market in the late nineteenth century [START_REF] Williams | Fractional Reserve Banking in Grain[END_REF] implemented such practice of credit on the basis of commodity deposits. Williams (1984, pp. 491-2) clearly shows how the warehouse could proceed by internalization as by externalization. According to the banking approach of circulation, the warehouse increases the velocity of circulation of rice or wheat and by no means increases their quantity. Therefore, as an institution issuing demand debts, a fractional reserve institution such as a bank can possibly do with any commodity what it already does with money-and a warehouse can possibly do with money what it already does with wheat. It must be emphasized that wheat does not become any kind of money: even though it circulates as a means of payment through certificates issuance, it remains a commodity with a monetary price.

Accelerating the velocity of commodities is more costly for the reason that a separate kind of fractional reserve institution is necessary for each type of commodity, for each market. And, because money is the means of payment unanimously accepted by the community, one can understand how its acceleration by fractional reserve institutions is so useful and helps the community to make new transactions. Demand for the virtual acceleration of money being higher than demand for the virtual acceleration of commodities, one can also apprehend why banks are the most important and largest fractional reserve institutions. In other words, just as money is the unanimously accepted means of payment, the virtual acceleration of money is a service commonly asked for, which explains the massive development of banks compared with other fractional reserve institutions.

V. CONCLUSION

Cantillon's banking approach of circulation according to which banks accelerate the circulation of money and by no means multiply its quantity is not limited to the metallic standard. More generally, it is relevant since there is convertibility of demand debts at face value into money, which may be metallic (specie money coined at the Mint) or fiat (inconvertible money issued by the Treasury or the central bank). Today's fiat money regime is different from that prevailing in Cantillon's time, but the banking approach of circulation can apply to demand deposits issued by commercial banks: through the issuance of demand debts convertible into central bank money, commercial banks help to virtually accelerate its circulation. The banking approach of circulation is no longer operative with regard to central bank money not convertible into outside money: central bank can sovereignly increase the quantity of fiat money. The banking approach of circulation might, however, be helpful in understanding the function of the central bank under a regime of convertibility into metallic money. The case investigated in this paper concerns demand debts issued, and money reserves held by individual banks. Another case may concern high-powered mediums issued by the central bank and specie reserve that it centralizes in its vaults: it therefore imply the action of the central bank as a lender of last resort under the specie regime. Interestingly, the Essai ends with a description of the phenomenon of sauve qui peut 3 during a panic. The English translation I shall use is Higgs' edition published in 1931 (Cantillon, 1755[START_REF] Cantillon | Essai sur la Nature du Commerce en Général[END_REF]). On the Cantillon's monetary theory, readers might like to refer to [START_REF] Holtrop | Theories of the Velocity of Circulation of Money in Earlier Economic Literature[END_REF], [START_REF] Hayek | Richard Cantillon. Introduction of the German translation of the Essai, Jena: Fischer[END_REF], [START_REF] Schumpeter | History of Economic Analysis[END_REF], [START_REF] Bordo | Some Aspects of Monetary Economics of Richard Cantillon[END_REF], [START_REF] Murphy Antoin | Richard Cantillon: Entrepreneur and Economist[END_REF][START_REF] Niehans | Richard Cantillon and sein "Essai[END_REF]. 2. The quantity approach of banking was first held by David [START_REF] Hume | Political Discourses, in Essays, Moral, Political, and Literary[END_REF][START_REF] Hume | Political Discourses, in Essays, Moral, Political, and Literary[END_REF]). For a synthetic view of Hume's monetary thought, see [START_REF] Wennerlind | David Hume's Monetary Theory Revisited: Was He Really a Quantity Theorist and an Inflationnist[END_REF][START_REF] Wennerlind | An Artificial Virtue and the Oil of Commerce: A Synthetic View of Hume's Theory of Money[END_REF], [START_REF] Schabas | Hume on Money, Commerce, and the Science of Economics[END_REF]. For a comparison of the Cantillon's Essai and the Hume's Discourses on money and banking, see Le [START_REF] Maux | Cantillon and Hume on Money and Banking: The Foundations of Two Theoretical Traditions[END_REF]. 3. In the 1755 edition of the Essai (p. 322), one can read the curious expression "on en viendrait à crever la bombe"-translated by "the bomb would burst" in Higgs's edition (p. 323). Mirabeau's manuscript corrects this in using the expression "on en viendrait à sauve qui peut." See INED edition of the Essai (Cantillon, 1755[START_REF] Cantillon | Essai sur la Nature du Commerce en Général[END_REF], note 1, p. 173) and Salleron (1952, p. lxvi). The French expression sauve qui peut means "every man for himself."

NOTES 1 .

 1 Richard Cantillon's Essai sur la Nature du Commerce en Général (hereafter, Essai) was written around 1730 but first published in Paris only in 1755.


Laurent Le Maux

CANTILLON AND HUME ON MONEY AND BANKING: THE FOUNDATIONS OF TWO THEORETICAL TRADITIONS

The distinction between the 'classical' monetary theory and 'quantity' theory has been proposed in literature on money and banking. The overall feature of the classical theory of money is that it holds one principle of regulation for each kind of issue (metallic money, bank issues and paper money) whereas the quantity theory applied the causality and proportionality postulates for all kinds of monies. Without claiming to adjudicate the validity of such a distinction, the paper investigates the foundation of each tradition. In this respect, this paper, respectively, examines, and provides a survey of the secondary literature on, Cantillon's Essai and the Hume's Discourses.

Introduction

Richard Cantillon's Essai sur la Nature du Commerce en Général and David Hume's Political Discourses have aroused interests among the monetary economists from the 1930s onwards and they have generated new interpretations and debates during the three last decades. 1 On the one hand, Hayek (1931) thought that the Discourses was so close to the Essai that Hume could have read Cantillon's manuscript, even if there is no evidence that he knew it. On the other hand, Adam Smith referred by name to Cantillon in the Wealth of Nations and proposed a theory of the value of metallic money and the regulation of bank issues that may also be found in the Essai. Furthermore, Smith did not restate Hume's price-specie-flow mechanism and even explicitly rejected Hume's theory of bank notes. If Discourses and Wealth of Nations are both similar to the Essai, how, then, could they be so different? One way of approaching this problem, evoked by Viner (1937), has been to imagine Smith's nonadherence to Hume's analysis as a 'mystery'.

Another way, suggested here, is to investigate whether the Essai is mostly dissimilar with the Discourses and announced the theoretical framework that the Wealth of Nations fell under. Indeed, the Essai and the Discourses differ in important respects in their treatment of the value of metallic money and more obviously as regards the regulation of bank issues. The Essai and the Discourses are not only different, but could have even inaugurated two theoretical traditions, respectively, the 'classical' theory of money later espoused by Smith (1776) and the Banking School [START_REF] Mill | The currency question[END_REF][START_REF] Tooke | An Inquiry into the Currency Principle[END_REF][START_REF] Tooke | A History of Prices and of the State of the Circulation[END_REF][START_REF] Fullarton | On the Regulation of Currencies[END_REF], and the 'quantity' theory of money supported by [START_REF] Ricardo | The high price of bullion, a proof of the depreciation of bank notes[END_REF]Ricardo ( , 1811[START_REF] Ricardo | On the principles of political economy and taxation[END_REF] and the Currency School [START_REF] Joplin | Currency Reform: Improvement not Depreciation[END_REF][START_REF] Loyd | Remarks on the Management of the Circulation and on the Condition and Conduct of the Bank of England[END_REF][START_REF] Loyd | Thought on the Separation of the Departments of the Bank of England[END_REF][START_REF] Torrens | An Inquiry into the Practical Working of the Proposed Arrangements for the Renewal of the Charter of the Bank of England, and the Regulation of the Currency[END_REF][START_REF] Torrens | An Inquiry into the Practical Working of the Proposed Arrangements for the Renewal of the Charter of the Bank of England, and the Regulation of the Currency[END_REF].

The distinction within the Classical Economics between the 'classical' monetary theory and the 'quantity' theory has been drawn by [START_REF] Niehans | The Theory of Money[END_REF][START_REF] Niehans | Classical monetary theory, new and old[END_REF][START_REF] Niehans | A History of Economic Theory: Classic Contribution, 1720-1980[END_REF], [START_REF] Glasner | A reinterpretation of the classical monetary theory[END_REF][START_REF] Glasner | On some classical monetary controversies[END_REF][START_REF] Glasner | Classical monetary theory and the quantity theory[END_REF] and [START_REF] Skaggs | John Fullarton's law of reflux and central bank policy[END_REF][START_REF] Skaggs | The place of J.S. Mill in the development of British monetary orthodoxy[END_REF][START_REF] Skaggs | Henry Thornton and the development of classical monetary economics[END_REF] -the latter reference studying [START_REF] Thornton | An Enquiry into the Nature and Effects of the Paper Credit of Great Britain[END_REF] monetary analysis. The overall feature of the classical monetary theory is that it proposes one principle of regulation for each kind of issue (specie money, bank issues and inconvertible paper money). As this paper will detail, the cost-of-production theory explains how the value of metallic money and the price level are determined by cost conditions. The law of reflux, which ultimately takes the form of convertibility, explains how the value of demand debts equates to the face value of ultimate money. The quantity postulates of causality and proportionality are only called upon by the classical monetary theory in the case of debasement and cautiously in the case of the supply of inconvertible paper money. In contrast, the feature of the quantity theory of money is the reasoning in terms of the aggregation of all kinds of 'monies' (specie money, bank money and inconvertible paper money) and the application of the causality and proportionality postulates in all cases, irrespective of the kind of issue, the monetary aggregate, or the monetary regime. The distinction between the classical monetary theory and the quantity theory has been discussed by [START_REF] Blaug | Why is the quantity theory the oldest surviving theory in economics[END_REF] and [START_REF] O'brien | Long-run equilibrium and cyclical disturbances: the currency and banking controversy and monetary control[END_REF] with a response from [START_REF] Glasner | Classical monetary theory and the quantity theory[END_REF]. Without pretending to adjudicate the validity of such a distinction, I believe that it is worthwhile to investigate the foundation of each tradition.

In this perspective, Section 2 examines Cantillon's Essai and Hume's Discourses on metallic currency and the dynamic of the balance of trade. They present a similarity with respect to the concept of endogenous money through a trade surplus, but diverge since Cantillon proposed the cost-of-production theory of the value of metallic money and never mentioned the case of exogenous money. Section 3 is concerned with the marked difference between Cantillon and Hume on the question of the monetary role of bank issuing. Cantillon developed the law of reflux and the proposition that banks contribute to accelerating the circulation of money (hereafter, the banking approach of circulation), whereas Hume developed the quantity theory applied to bank notes and the proposition that banks multiply the quantity of money (hereafter, quantity approach of banking). The historical context and the practice of the option clause by Scottish banks in the 1760s partly explain Hume's confusion between convertible bank notes and inconvertible paper money -confusion typical of the quantity theory. In conclusion, this paper suggests that, beyond the historical context, the Cantillon-Hume opposition on money and banking inaugurated the controversy between the classical monetary theory and the quantity theory. For an overview of the concepts used in the paper, the reader may refer to the table in the Appendix.

The Metallic Money

Cantillon and Hume are regarded as precursors, either of the price-specie-flow mechanism, or of the monetary approach to the balance of payments. Both approaches deal with international-reserve-flow mechanism. The price-specie-flow mechanism views the movements of precious metals as a consequence of relative price changes between countries. Money is exogenous in the sense that a shock, say a sudden increase, in the domestic money supply is presupposed. Any excess in the quantity of money then initiates a proportional rise in prices (quantity theory) and the ensuing change in relative prices causes a decline of the competitiveness of domestic products (violation of the law of one price). The ensuing outflow of precious metals decreases domestic prices, therefore prompting a return to equilibrium (automatic adjustment). In the secondary literature, Cantillon and Hume are sometimes listed among the proponents of the price-specie-flow mechanism as a self-equilibrating adjustment. 2 The monetary approach to the balance of payments describes the movements of international reserve as adjustments of quantities and not of relative price levels. The balance of payments and the flows of international reserves are governed by monetary forces reflecting domestic disequilibrium between the demand for and the supply of money [START_REF] Johnson | Further Essays in Monetary Economics[END_REF][START_REF] Johnson | The monetary theory of balance-of-payments policies[END_REF][START_REF] Frenkel | The monetary approach to the balance of payments: essential concepts and historical origins[END_REF]. Money is viewed as endogenous in the sense that the amount of money in an economy is automatically adjusted to the demand through surpluses or deficits in the current balance. Any excess supply of money in a country is withdrawn from circulation through the balance of payments without affecting relative price levels of domestic and foreign goods. The law of one price is thus supposed to be effective in that two similar commodities offered for sale in two different places at the same time sell at the same price. In the secondary literature, Cantillon and Hume are sometimes thought to have espoused the law of one price and to have anticipated the monetary approach to the balance of payments. 3 At first, I shall indicate how Cantillon dealt only with endogenous money in the sense that the production of precious metal and the value of metallic money are determined by cost conditions (Section 2.1). Then, I shall restate the analytical distinction emphasised by [START_REF] Niehans | The Theory of Money[END_REF] between exogenous and endogenous money in Hume's writings (Section 2.2). Moreover, [START_REF] Wennerlind | David Hume's monetary theory revisited: was he really a quantity theorist and an inflationist?[END_REF] explains that an exogenous increase generates a proportional rise in prices without any effect on output (neutrality of money) and an endogenous increase in the money supply generates positive effects on output (non-neutrality of money). The distinction between endogenous and exogenous money goes beyond the distinction in the literature on Humean monetary analysis between short-term non-neutrality and long-term neutrality.

Cantillon's Model of Endogenous Money

By money, Cantillon meant the silver or gold specie coined at an official price at the Mint. Specie is the only form of money (qualified by an adjective such as 'real' or 'actual') and Cantillon disapproved of inconvertible paper money (which he held to be 'fictitious' and 'imaginary'). In his mind, ultimate money could not be paper money but specie alone. Hence, in the context of the specie regime, the Essai upholds the theory whereby the value of money depends on its cost of production, and not on its quantity. In Cantillon's words, the 'real or intrinsic value' of a precious metal, like that of any other commodity, is 'proportionable to the land and labour' that enters into its production (Essai, p. 97). The value in exchange for other merchandise is 'necessarily fixed by that which was put upon it at the new mine' (Essai, p. 101). In modern terms, the exchange is adjusted to the cost of the marginal mining product. Finally, it depends on extraction, production and transportation costs on the one hand, and on the 'humour of men' on the other hand (Essai,pp. 175,273,277).

Importantly, the cost-of-production theory means that metallic money entered endogenously in the market with a value. The causality goes from price to supply of the metallic money and the proportionality postulate of the quantity theory is at best a very particular case and not the general theory of the value of metallic money. Cantillon (Essai,pp. 163,167,181) was aware that an increase in the quantity of money triggered by new mines or trade surplus induces an increase in expenditure and finally in the price level, but he did not go so far as to adhere to the quantity theory and its proportionality postulate. Indeed, the price rise caused by new supply of specie 'does not affect equally all the kinds of products and merchandise, proportionally to the quantity of money'. (Essai,p. 181;pp. 161,177). The modern formulation given by Niehans (1978, p. 147) concludes that the quantity theory of money does not strictly apply under the commodity money regime: 'While gold discoveries will certainly tend to push prices up, it would be a coincidence if the money supply and commodity prices moved up in proportion'. Such a coincidence refers to a unit-elastic non-monetary demand for precious metal. Niehans (1987, p. 413) continues: 'Value theory and monetary theory are fully integrated, and the quantity of money adjusts passively, through production or foreign trade, to whatever is demanded. From this point of view, classical writers like Cantillon and Adam Smith were right in denying any strict proportionality of money and prices'. Finally, Niehans (1987, p. 411) regards Cantillon as the 'founder of classical monetary theory' -to which Smith (1776), [START_REF] Senior | Three Lectures on the Value of Money[END_REF], [START_REF] Tooke | An Inquiry into the Currency Principle[END_REF][START_REF] Tooke | A History of Prices and of the State of the Circulation[END_REF] and Fullarton (1845) contributed afterwards -in opposition to the 'quantity theory of money'. Cantillon (Essai,p. 181) posited the following endogenous channels (listed in order of increasing importance): subsidies paid from foreign countries, extraction from new mines of precious metals in the state, 'but above all', by a regular trade surplus. 'It is by this last means that a state grows most substantially, especially when its trade is accompanied and supported by ample navigation and by considerable raw produce at home'. Thus, above all, the commercial power of the state and improvement in industrial production initiate a trade surplus and cause an endogenous supply of money. This 'increase of money will enrich a great number of merchants and undertakers in the state, and will give employment to numerous [craftsmen] and workmen who furnish the commodities sent to the foreigner from whom the money is drawn. This will increase gradually the consumption of these industrial inhabitants and will raise the price of land and labour' (Essai, p. 167) -and, as noted above, this increase will not be proportional. Then, in the foreign countries, where money is rare, cheapness of commodity and labour cause 'the erection of manufactories and works similar to those of the state, but which will not at first be so perfect nor so highly valued' (Essai, p. 169, added italics); and 'though these new establishments of crafts and manufactures be not at first perfect they slacken and even prevent the exportation of those of the neighbouring state into their own country where they can be got cheaper'. (Essai,p. 183,added italics). So, the technological advance, industrial improvement and commercial reputation of the state endogenously initiate a dynamic adjustment in the balance of trade and flows of precious metals. Then, price-competition from foreign countries whose products, however, are not so perfect, diminishes to some extent the trade surplus of the state, without reversing the balance of trade for a long period of time and therefore without entailing a trade deficit. 'The articles and manufactures of the state having a great reputation, and the facility of navigation affording the means of sending them at little cost into distant countries, the state will for many years keep the upper hand over the new manufactures [of foreign countries] and will still maintain a small balance of trade' (Essai, p. 183, added italics). A trade surplus is not automatically absorbed and is maintained so long as the state enhance its industrial and commercial activity. In this line of interpretation, Gillard (2011, pp. 359-360) also argues that an automatic mechanism is not strictly stipulated in the Essai.

Thus, Cantillon's analysis is significantly different from the price-specie-flow mechanism. Metallic money is supplied endogenously, through the production of mines and by way of a surplus in the balance of trade. Unlike Hume in his Discourses, Cantillon never posited an exogenous change in the quantity of metallic money or in the quantity of bank issues.

Hume's Models of Exogenous and Endogenous Money

Hume proposed two models of specie-flow mechanism, one with an exogenous change and the other with an endogenous change in the quantity of money. The literature has mainly retained the model with exogenous money. At first, I shall present the two models proposed by Hume. Then, I shall review the literature that draws the distinction between exogenous and endogenous money in Hume's writings. Finally, if the model with endogenous money is more appropriate to the specie regime that Hume studied in his time, it may be also pointed out that Hume, unlike Cantillon, did not integrate the cost-of-production theory into his monetary theory.

In the first model, Hume told the famous overnight story in which the quantity of specie suddenly changes 'by miracle' and 'in one night' in a state (Discourses, pp. 299, 311;[START_REF] Hume | Letter to Montesquieu[END_REF]Hume, [1955], pp. 188-189)], pp. 188-189). The exogenous increase in the stock of metallic currency generates a proportionate rise in domestic prices, a stimulus of importations and a fall in exportations until the appearance of a trade deficit and an external drain of precious metals. Oscillatory movements of relative prices and corresponding flows of metallic currency provide an automatic adjustment of the distribution of precious metal among countries and restore the level of money to its original equilibrium. This is the price-specie-flow mechanism. But what should have been taken as a simple supposition nevertheless contributed to obscuring another aspect of Hume's analysis. In the second model, indeed, Hume studied the case of the specie inflows resulting from trade surplus, that is, 'when any quantity of money is imported into a nation', when the increase of money is 'not too sudden' (Discourses, pp. 286-287;[START_REF] Hume | [END_REF]Hume, [1955], pp. 197-198)], pp. 197-198). The endogenous increase in the supply of money induced by a trade surplus depends on the economic growth and productivity, that is, when a nation has got a 'superior industry and skill' (Discourses, p. 283), when an 'encrease of its art and industry' occurs (Discourses, p. 314), since 'every thing must become much cheaper in times of industry and refinement' (Discourses, p. 291). In addition, 'the prices of every thing depend on the proportion between commodities and money' (Discourses, p. 290) and the proportion between money holding and output is at an equilibrium level (Discourses, p. 315n). Finally, Hume's second model with industrial improvement and endogenous money has been encapsulated by Wennerlind (2005, pp. 228-229) in these terms: 'improvements in industry lower domestic prices and […] the adjustment process whereby gold flows in and goods flow out […] continues until the proper proportion between circulating money and marketable commodities is re-established'. (See also, [START_REF] Berdell | The present relevance of Hume's open-economy monetary dynamics[END_REF]Berdell, , pp. 1208Berdell, -1209;;Paganelli, 2006, pp. 538-539.) Some authors thus emphasise that Hume should not be suspected of unconditionally adhering to the price-specie-flow mechanism. Niehans (1987, pp. 413-414) spells out that, in the first model, Hume 'suggested a mental experiment in which gold coins are treated as if they could be miraculously created or annihilated; thus he obtained the proportionality proposition' (original italics). However, in the second model, Hume 'went to great lengths in explaining that, in reality, money is supplied endogenously through gold mining and international specie flows'. Unfortunately, the first model 'became the point of departure for the secondary offshoot of the classical tradition'. Cesarano (1998, pp. 177-179) argues that the overnight story was just a 'thought experiment' motivated by the Humean attitude against mercantilism that aimed 'to prove the stability result' in the case of a change in relative prices; on the other hand, a close formulation of the 'law of one price' is believed to be detected in a passage from Hume (Discourses, on the equal proportionality between money and output from one place to another; thus, it is inferred that Hume's second model appears to have anticipated the monetary approach to the balance of payments. Wennerlind (2005, p. 230) differentiates between exogenous and endogenous money supply and thus two facets of the Hume's quantity theory: exogenous money is regulated by the 'simple quantity theory' used in the price-specie-flow mechanism; the regulation of the endogenous money supply bears 'a greater resemblance to the quantity theory of money used in the monetary approach to the balance of payments'.

It is a controversial question as to whether or not Cantillon and Hume had recognised the law of one price -and hence the monetary approach to the balance of payments -especially concerning Hume [START_REF] Fausten | The Humean origin of the contemporary monetary approach to the balance of payments[END_REF][START_REF] Cesarano | Hume's specie-flow mechanism and classical monetary theory: an alternative interpretation[END_REF][START_REF] Schabas | Temporal dimension in Hume's monetary theory[END_REF]. A few comments seem here necessary. First, Cantillon and Hume were aware of transportation costs: indeed, the domestic price of traded goods can only be raised above the price in other countries 'by the cost and risk of importing' traded goods (Essai, p. 179); and the circumstance that 'can obstruct' the similarity of the price level in every country is 'the expense of transporting the commodities' and 'this expense is sometimes unequal' (Discourses, p. 315n). Secondly, whatever the level of transportation costs, Hume's first model that assumes an exogenous change in the quantity of money does not need the violation of the law of one price to derive the stability result that Hume was aiming to prove [START_REF] Samuelson | A corrected version of Hume's equilibrating mechanism for international trade[END_REF]. Thirdly, Hume's second model that assumes an endogenous change in the quantity of money through a trade surplus does not fail by disregarding the law of one price, but more fundamentally by endorsing the quantity theory in the case of metallic money. The monetary regime that Cantillon and Hume examined at their time, that is, the specie regime, was quite different from the monetary regime that proponents of the monetary approach to the balance of payments attempted to grasp in the 1970s, that is, the regime of inconvertible central bank money (fiat money) with a fixed exchange rate. The quantity theory endorsed by Hume or the proponents of the monetary approach might be called upon in the case of the fiat money regime (with or without fixed exchange rate), but it remains unsuitable in the case of the specie regime. In other words, the confusion between the two kinds of monetary regimes makes sense within the quantity tradition (which amalgamates the specie regime and the fiat money regime), but it makes no sense within the classical monetary tradition (which applied different principles for each kind of monetary regime).

Therefore, the monetary regime and the related theoretical framework proposed by Cantillon and Hume appears at first more fundamental than the application (or not) of the law of one price during the process of adjustment. Some commentators pointed out that there might be an inconsistency in Hume's position of not maintaining the cost-of-production theory. For [START_REF] Marx | A Contribution to the Critique of Political Economy[END_REF][START_REF] Marx | A Contribution to the Critique of Political Economy[END_REF], p. 164), Hume considered that 'commodities without price and gold and silver without value enter the process of circulation' and therefore he 'never mention [ed] the value of commodities and the value of gold, but sp[oke] only of their reciprocal quantity'. Niehans (1990, p. 54) shares a similar view in stating that Hume treated commodity money 'as if' it was fiat money (original italics). Hume (1769Hume ( [1955]], p. 214) recognised more than a decade after his Discourses that 'money must always be made of some materials, which have intrinsic value', but he did not correspondingly amend his second model. Thus, despite the fact that Cantillon's model and Hume's second model both made the assumption of endogenous money, a divergence may be underlined: Cantillon integrated into his models that specie enters into circulation with any value, whereas Hume did not. Furthermore, Cantillon's theory and the classical monetary theory may include the transportation costs of the precious metal and that of other goods in their respective value. Finally, the concept of endogenous money developed by the classical monetary theory differs from the monetary approach to the balance of payments: it is based on the cost-of-production theory and the law of reflux. The quantity theory is called upon once gold or silver coins are debased or inconvertible paper circulates within the state.

The theoretical distinction setting the classical monetary theory (the cost-ofproduction of the value of the metallic money) against the quantity theory (the causality and proportionality postulates irrespective of the kind of monies) appears fundamental in the case of the specie regime. Another distinction might complete the overall picture by setting the 'metallism' view (according to which money would originally consist of some commodity) against the 'convention' view (according to which money is above all a convention). Cantillon might be suspected of having adopted the metallism view. [START_REF] Caffentzis | Hume, money and civilization: or, why was Hume a metallist?[END_REF][START_REF] Caffentzis | Fiction or counterfeit? David Hume's interpretations of paper and metallic money[END_REF], [START_REF] Wennerlind | The link between David Hume's Treatise of Human Nature and his fiduciary theory of money[END_REF][START_REF] Wennerlind | An artificial virtue and the oil of commerce: a synthetic view of hume's theory of money[END_REF] and [START_REF] Desmedt | L'Analyse de la monnaie et de la finance par David Hume: conventions, promesses et reégulations[END_REF] have accurately shown that Hume adopted the convention view. It may be added that, once the specie regime is supposed, the introduction of cost-ofproduction theory does not necessarily equate to unconditional support of the metallism view. The authors of the Banking School adopted the convention view in general and the cost-of-production theory under the specie regime in particular, at the same time. In other words, the adoption of the convention view does not absolve Hume from theoretical misconception, such as the adoption of the quantity theory in the case of metallic money -and in the case of convertible bank notes as well.

The Monetary Role of Bank Issuing

In the late 17th and early 18th century, banks in London and Britain began to put deposit certificates, bank notes or demand deposits into circulation, which were all convertible at request at face value into specie but not fully backed by metallic reserve, that is, all of which are means of payment that are defined as demand debts. The question was whether banks had a monetary role and, if so, how that role could be analysed. Cantillon and Hume explored two opposite answers: Cantillon suggested that bank issuing involves an acceleration of the circulation of money (hereafter, the banking approach of circulation) and Hume that it corresponds to a multiplication of the quantity of money (hereafter, the quantity approach of banking).

Before describing these two approaches and because Cantillon's banking approach of circulation is not familiar, clarification is required here. Cantillon held two propositions on the circulation of money. The first and well-known proposition states that a change in the velocity of money among the public is equivalent to a change in its quantity. If Petty (1664Petty ( [1899]], pp. 112-113) and [START_REF] Locke | Some Considerations of the Consequences of Lowering of Interest, and Raising the Value of Money, in a Letter to a Member to Parliament[END_REF]Locke ( [1823, p. 23], p. 23]) touched on the idea of velocity of circulation of money, Cantillon (Essai, p. 161) was the first to postulate that 'an acceleration or greater rapidity in circulation of money in exchange, is equivalent to an increase of actual money up to a point'. It is a monetary concept inasmuch as it may apply to money without needing reference to the issuing activity of banks. Cantillon's banking approach of circulation is the second proposition distinct from the first one. As I shall detail, it is a banking concept inasmuch as it necessarily involves banks as issuers of demand debts. 4 The quantity approach of banking set out by Hume remains far more familiar in the monetary literature and has no doubt overshadowed the banking approach of circulation proposed by Cantillon. It mainly rests on a threefold feature that may be found in the Discourses, including (i) the aggregate of 'base money' and 'bank money', (ii) the money multiplier linking the two and (iii) the application of the quantity theory to the monetary aggregate. 5 After a presentation of Cantillon's theory of bank issuing (Section 3.1), I shall compare the analysis by Hume and Cantillon of bank issue and describe the historical Scottish banking practice known as the option clause in order to better understand Hume's confusion between bank notes and inconvertible paper money (Section 3.2).

Cantillon on Banks as Accelerators of the Circulation of Money

Under the institutional design studied by Cantillon, a bank is fractional-reserve institution holding money, that is, an institution issuing demand debts such as bank notes or demand deposits convertible at face value into and partially backed by specie money. Cantillon (Essai,p. 305) underlined that the form of demand debt is only a practical matter: the advantage of demand deposits is that unlike bank notes, they are not subject to counterfeiting; the drawback is that people in the suburbs and a fortiori people in the country 'at a distance from the bank will rather pay and receive in money than to go thither' and, by contrast, 'if the bank notes are dispersed they can be used far and near'. The form of bank issue is a practical matter, not a theoretical matter.

The Essai states a proposition, termed here the banking approach of circulation, which analyses the effect of bank's issue on the circulation. As long as demand debts issued by banks remain convertible at face value and circulate instead of money, they accelerate circulation of money. In this respect, two excerpts are decisive. The 'bankers, whose notes pass current in payment like ready money, contribute also to the speed of circulation, which would be retarded if money were needed in all payments for which these notes suffice' (Essai, pp. 141-143, added italics). They 'contribute to accelerate [sic] the circulation of money. They lend it out at interest at their own risk and peril, and yet they are or ought to be always ready to cash their notes when desired on demand'. (Essai,p. 301,added italics;p. 305). The distinction between specie money and convertible bank notes stands for a precise articulation between them: demand debts accelerate the circulation of money, which would be delayed if they were not issued. By accelerating the velocity of money, banks bear a credit risk at the same time (banks lend 'at interest at their own risk and peril') and a liquidity risk (they have to reimburse their issues 'when desired on demand'). By analogy, money and bank issue may not be equivalent, just as the sailboat may not be equivalent to the wind that helps it to go faster. Once Cantillon's banking approach of circulation is conveyed, one question is to know how demand debts are regulated and whether the acceleration of money they induce is contained and does not entail inflation. Cantillon (Essai,p. 303) implicitly answered by mentioning the reflux in the form of demand for convertibility of bank notes into specie and the mechanism by which competing issuing banks are compelled to reimburse every note in excess. The constraint of reflux implies that bankers 'will be ruined in credit if they fail for one instant to pay their notes on their first presentation, and when they are short of cash in hand they will give anything to have money at once, that is to say a much higher interest than they receive on the sums they have lent'. In modern terms, the marginal cost of redeeming unwanted bank notes or demand debts exceeds the marginal gains from issuing them so that banks are discouraged to pursue an overissue policy. The speed of the regulation depends on the channel by which bank notes are returned to the issuer. On the one hand, the public returns notes they do not wish to hold by asking them for specie: if notes issued by a banker 'fall into the hands of persons who are not accustomed to deal [sic] with him', they stay in circulation for longer and this delays their payments 'a few days or weeks'. On the other hand, and more drastically, rival banks impose discipline with respect to bank issues and speed up the reflux: if 'his notes come into the hands of those of his own business', these rival bankers 'will have nothing more pressing than to withdraw the money from him' (Essai,p. 303). The law of reflux here formulated explains the endogeneity of the supply of demand debts -which is different from the endogeneity of the supply of money resulting from the state of the balance of trade or the condition of production of the precious metal.

As seen in Section 2.1, Cantillon rejected the proportionality postulate of the quantity theory in the case of metallic money and he did not explicitly mention it in the case of inconvertible paper money. Debasement, that is, an alteration of the monetary convention, and not a change in the quantity of money, is the sole case in which Cantillon (Essai,p. 113) explicitly referred to the proportionality postulate. In addition, Cantillon (Essai,p. 311) treated specie and inconvertible paper money as having an effect on prices: 'abundance of fictitious and imaginary [paper] money' and 'an increase of real [metallic] money in circulation' cause the same effect 'by raising the price of land and labour'. As seen in Section 3.1, the reflux of bank issues is fast enough (taking only a few 'weeks' at most) to avoid overabundance and inflation. Hence, Cantillon's monetary theory treats bank notes very differently from inconvertible paper money, which in contrast produces inflationary effects. By formulating the law of reflux, Cantillon also established the foundation of the classical monetary theory in opposition to the quantity theory. Afterwards, within the classical monetary tradition, Adam Smith and the Banking School challenged the Humean and Currency School's quantity approach to money and banking.

Hume on Banks as Multipliers of the Quantity of Money

As seen in Section 2.2, Hume applied the price-specie-flow mechanism in the case of the overnight story and exogenous supply of money. However, what should have been restricted to a hypothetical experiment, positing a miraculous increase in the quantity of metallic currency, was considered by Hume himself in the end as possible in reality within the banking system. As the Section 3.2 will examine, in contrast to the Cantillon's analysis, Hume was convinced that banks 'multiply' money and could artificially supply any monetary quantity: indeed, he described bank notes as if they were not convertible and concluded that their effects on prices are similar. In addition, Hume seemed to grant analytical importance to the form of bank liabilities: he described the technique of 'bank-credit' that consisted of an advance on current account (Discourses, p. 319) and, without explanation, did not explicitly apply his quantity approach to demand deposits as he did to bank notes.

The Discourses sustain a proposition, termed here the quantity approach of banking, which contains three postulates. First, convertible bank notes are considered equivalent to specie money. Moreover, bank notes such as issued by the Scottish banks during Hume's time are amalgamated with paper money of the kind issued in the colonies -the same term 'paper credit' is systematically employed for the two kinds of issue. This analytical confusion led Hume to believe that both could raise the quantity of money and have a similar effect on prices (Discourses,. Second, banks carry out 'the multiplication of money' and by contrast 'the Bank of Amsterdam did not multiply money' [START_REF] Hume | New Hume letters to Lord Elibank, 1748-1776[END_REF][START_REF] Hume | New Hume letters to Lord Elibank, 1748-1776[END_REF], p. 441) insofar as it was believed that its liabilities were fully backed by reserves. Third, bank notes as well as inconvertible paper money alter prices in proportion to their quantity. Thus, the following passage from 1752 perfectly sums up the three points of the quantity approach of banking in the case of the specie regime: '[banks] render paper equivalent to money, circulate it throughout the whole state, make it supply the place of gold and silver, raise proportionably the price of labour and commodities, and by that means either banish a great part of those precious metals, or prevent their farther encrease'. (Discourses, p. 316). Hume fully adhered to the quantity theory and applied the price-specie-flow mechanism to bank notes, which purge a great part of the precious metals from the state. In the 1752 edition, Hume vehemently argued against bank notes, supposed to create a lot of inconveniences and to set the pricespecie-flow mechanism in motion (Discourses,pp. 284,(317)(318). In the 1764 edition, Hume's opinion on bank notes is less straightforward. In a supplementary passage (Discourses, p. 318), which contains neither theoretical proof, nor normative conclusion, it is 'confessed' that their advantages could be superior to their disadvantages and a 'right use of paper-money' (here, bank notes) is recommended. However, from a theoretical point of view, Hume did not attempt to amend the pricespecie flow mechanism applied to bank notes. He even repeated it in 1764 (Discourses, p. 320) by considering again that 'besides giving too great facility to credit, which is dangerous', bank-issuing inventions 'banish the precious metals'.

These three postulates of the quantity approach of banking may be analysed in the light of the Cantillon's theory of banking. By stating that 'paper' issued by banks is 'equivalent to money', Hume failed to see the analytical distinction held by Cantillon between money and demand debts whatever their form. Since the demand debts accelerate the circulation of money, they may not be considered as equivalent, just as the wind cannot be the equivalent of the sailboat, and any aggregation between money and demand debts makes no sense. Furthermore, by stating that bank notes 'circulate throughout the whole state', Hume failed to perceive that the note exchange and clearing mechanism depicted early on by Cantillon works like a sponge that catches and absorbs all bank notes in excess and annuls their circulation. Finally, Hume disregarded Cantillon's theoretical outcome which implies that banks issue demand debts as long as their marginal cost does not exceed the interest on loans; that the supply of demand debt is endogenously determined by the demand of them and is constrained in the immediate short term by convertibility; and finally that no relation between quantity of demand debts and prices may arise.

In accordance with his own theory of bank note issue, Hume recommended the 100% reserve requirement and believed that this was the case of the Bank of Amsterdam (Discourses,: 'it must be allowed, that no bank could be more advantageous, than such a one as locked up all the money it received, and never augmented the circulation coin, as is usual, by returning part of its treasure into commerce'. Hume was a forerunner of the Currency School with regard to the analysis of the bank issue, for a twofold reason. First, he made the factual claim that bank notes enter into the monetary aggregate, mentioned the money multiplier principle, and applied the quantity theory to bank notes to conclude with the pricespecie-flow mechanism. Second, he advocated the 100% reserve rule, that is, the currency principle.

It is noteworthy that, from a methodological viewpoint, Hume's thought on money and banking is equivocal. In the case of the metallic money (Discourses, p. 311), the overnight story was justified in order to prove the impossibility of disequilibrium of the balance of trade with 'general argument' (the hypothetical experiment) rather than to 'refute by particular detail' (the state of the exports and imports in Britain). In the case of bank issuance (Discourses, p. 320), by contrast, there was a need to find proof of arguments with 'particular detail' (the comparison of the past and present state of Scotland). The reference to empirical or historical proof could reveal some insufficiencies in his theory of bank issue or, at least, could be misleading. Indeed, the Scottish banking system at the time of Hume suffered from issuance of very small denominations and above all from a widespread use of the option clause [START_REF] Checkland | Scottish Banking: A History, 1695-1973[END_REF][START_REF] Munn | The origins of the Scottish note exchange[END_REF][START_REF] Munn | The Scottish Provincial Banking Companies[END_REF][START_REF] Dowd | Option clauses and the stability of a laisser faire monetary system[END_REF]. The option clause gave to an issuing bank the opportunity to transform bank notes that were convertible on demand into short-term bills bearing interest. It was mainly used by Scottish banks in 1750-1760 as an answer to an aggressive strategy, 'note duelling', whereby banks attempted to accumulate rival bank note holdings and to present them en masse so as to siphon off the reserve of the target banks. In order to alleviate a drastic fall of reserve that would have threatened their liquidity, target banks implemented the option clause, which allowed them to defer convertibility on demand, for 6 months, and consequently pay an interest of 5% on the deferred bills. Thus, demand debts became short-time obligations and their value fluctuated just like any other term bills, according to the solvency risk. The use of the option clause signalled the liquidity problem of the target bank publicly. It ensued that the option clause might have given the illusion that bank notes could fall in value due to the quantity in excess. In other words, the same piece of paper transformed into term bills that dropped in value could create confusion among the public and cause the theoretician to conclude that the bank note issued was 'depreciated' in relation to specie; another step could be easily overcome by adding that the 'depreciation' of the bills could be in proportion to the quantity in excess. The illusion created by the option clause possibly explains why Hume confused convertible bank notes, deferred bills and, finally, inconvertible paper money; why he used the similar reasoning when he dealt with notes issued by Scottish bank (under the option clause or not) as well as with inconvertible paper money created in the colonies. It is interesting to note that Robert Peel, in his speech at the British parliament in May 1844 (Peel, 1844), restated the same misapprehension resulting from a confused analysis of the option clause.

In contrast, Adam Smith was plainly aware of the distinct feature of bank notes convertible at face value on demand, short-term bills under the option clause and inconvertible paper money. [START_REF] Smith | Thoughts concerning banks, and the paper-currency of Scotland. The Scots Magazine November 1763[END_REF] had judiciously advocated the prohibition of the option clause so as to avoid mix-ups among an unsatisfied public. The option clause prohibition was voted by the Scottish Parliament in 1765 and then gave a strong incitement to Scottish banks to cooperate, based on a system of mutual acceptance and regular clearing of bank notes. The mutual and regular acceptance of bank notes then substituted for note duelling and it progressively took place in the 1770s through bilateral arrangements that the Bank of Scotland and Royal Bank of Scotland had been experimenting with since the early 1750s, and even through multilateral arrangements that Smith could have begun to observe at the end of the 1770s. Once it had been implemented and generalised within the Scottish banking system, the practice of note acceptance and clearance allowed bank notes and more generally, demand debts, to be routinely exchanged at face value and on demand; and it lessened the raison d'être of the option clause and its corresponding discount on deferred bills. The illusion that convertible bank notes could fall in value disappeared with the option clause, but not the theoretical confusion that had appeared with it.

Conclusion

The 'classical' monetary theory expounds one principle of regulation for each kind of issue: the cost-of-production theory explains the value of metallic money, the law of reflux explains the regulation of issues of demand debts and the quantity theory is only applied in the case of debasement and cautiously in the case of inconvertible paper money. In this respect, after Cantillon, Smith (1776) and the Banking School [START_REF] Mill | The currency question[END_REF][START_REF] Tooke | An Inquiry into the Currency Principle[END_REF][START_REF] Tooke | A History of Prices and of the State of the Circulation[END_REF][START_REF] Fullarton | On the Regulation of Currencies[END_REF] belong to the classical monetary theory. In contrast, the 'quantity' monetary theory reasons in terms of the aggregation of all kinds of monies and then applies the causality and proportionality postulates irrespective of the kind of issue, the monetary aggregate, or the monetary regime. When Hume (Discourses, p. 281) stated that 'prices of commodities are always proportioned to the plenty of money' (added italics), he applied the quantity theory to miraculous supply of metallic currency, the multiplication of bank notes as well as the inconvertible paper money. [START_REF] Ricardo | The high price of bullion, a proof of the depreciation of bank notes[END_REF][START_REF] Ricardo | Proposals for an economical and secure currency[END_REF][START_REF] Ricardo | On the principles of political economy and taxation[END_REF] is often interpreted in literature as a quantity theorist and the Currency School [START_REF] Joplin | Currency Reform: Improvement not Depreciation[END_REF][START_REF] Loyd | Remarks on the Management of the Circulation and on the Condition and Conduct of the Bank of England[END_REF][START_REF] Loyd | Thought on the Separation of the Departments of the Bank of England[END_REF][START_REF] Torrens | An Inquiry into the Practical Working of the Proposed Arrangements for the Renewal of the Charter of the Bank of England, and the Regulation of the Currency[END_REF][START_REF] Torrens | An Inquiry into the Practical Working of the Proposed Arrangements for the Renewal of the Charter of the Bank of England, and the Regulation of the Currency[END_REF] clearly supported the quantity theory and merely posited the case of exogenous money. Therefore, continuities may be found within the two theoretical traditions. Within the classical monetary theory, Smith and the authors of the Banking School held the cost-of-production theory of the value of money and challenged the Humean and Currency School analyses of bank notes by further developing the law of reflux in general. Within the quantity theory, Ricardo and more significantly the Currency School repeated the quantity approach of banking, which finally prevailed in economic analysis with regard to bank notes during the 19th century and bank deposits during the 20th century.

Notes

1. On Cantillon and the Essai sur la Nature du Commerce en Ge ńe ŕal (written around 1730 and first published in 1755, Higgs' edition in 1931 [START_REF] Cantillon | Essai sur la Nature du Commerce en Général[END_REF][START_REF] Cantillon | Essai sur la Nature du Commerce en Général[END_REF]), hereafter Essai), see Jevons (1881), [START_REF] Higgs | Richard Cantillon[END_REF][START_REF] Higgs | Cantillon's place in economy[END_REF], Hayek (1931[START_REF] Hayek | Review: Essai sur la nature du commerce en général by Richard Cantillon[END_REF], Rist (1938Rist ( [1940]]), [START_REF] Salleron | Note Pre ́ liminaire[END_REF], [START_REF] Sauvy | Sur la nature du commerce en général[END_REF], [START_REF] Spengler | Richard Cantillon: first of the modern[END_REF], [START_REF] Bordo | Some aspects of monetary economics of Richard Cantillon[END_REF], [START_REF] Murphy | Richard Cantillon: Entrepreneur and Economist[END_REF][START_REF] Brewer | Cantillon and mercantilism[END_REF][START_REF] Brewer | Richard Cantillon: Pioneer of Economic Theory[END_REF], Thornton (2007aThornton ( , 2007b)), [START_REF] Gillard | Le statut de la monnaie dans le Traité de Montchrestien et dans l'Essai de Cantillon[END_REF], [START_REF] Van Der Berg | Richard Cantillon's early monetary views?[END_REF]. On David Hume as a monetary economist and the Political Discourses (first edition in 1752, Miller's edition in 1985 [START_REF] Hume | Political Discourses, in Essays, Moral, Political, and Literary[END_REF][START_REF] Hume | Political Discourses, in Essays, Moral, Political, and Literary[END_REF]), hereafter Discourses), see [START_REF] Rotwein | Introduction to David Hume: Writings on Economics[END_REF], [START_REF] Duke | David Hume and monetary adjustment[END_REF], [START_REF] Fausten | The Humean origin of the contemporary monetary approach to the balance of payments[END_REF], [START_REF] Mayer | David Hume and monetarism[END_REF], [START_REF] Samuelson | A corrected version of Hume's equilibrating mechanism for international trade[END_REF], [START_REF] Rashid | David Hume and eighteenth-century monetary thought: a critical comment on recent views[END_REF], [START_REF] Perlman | Of a controversial passage in Hume[END_REF], [START_REF] Mcgee | The economic thought of David Hume[END_REF], [START_REF] Berdell | The present relevance of Hume's open-economy monetary dynamics[END_REF], [START_REF] Gatch | To redeem metal with paper: David Hume's philosophy of money[END_REF], [START_REF] Cesarano | Hume's specie-flow mechanism and classical monetary theory: an alternative interpretation[END_REF], [START_REF] Schabas | David Hume on experimental natural philosophy, money, and fluids[END_REF][START_REF] Schabas | Temporal dimension in Hume's monetary theory[END_REF], [START_REF] Wennerlind | The link between David Hume's Treatise of Human Nature and his fiduciary theory of money[END_REF][START_REF] Wennerlind | David Hume's monetary theory revisited: was he really a quantity theorist and an inflationist?[END_REF][START_REF] Wennerlind | An artificial virtue and the oil of commerce: a synthetic view of hume's theory of money[END_REF], [START_REF] Caffentzis | Hume, money and civilization: or, why was Hume a metallist?[END_REF][START_REF] Caffentzis | Fiction or counterfeit? David Hume's interpretations of paper and metallic money[END_REF], [START_REF] Dimand | David Hume on Canadian paper money: an overlooked contribution[END_REF], [START_REF] Paganelli | Hume and endogenous money[END_REF][START_REF] Paganelli | The good policy of the magistrate: deflation as a policy option in David Hume's economic essays[END_REF][START_REF] Paganelli | David Hume on monetary policy: a retrospective approach[END_REF], [START_REF] Desmedt | L'Analyse de la monnaie et de la finance par David Hume: conventions, promesses et reégulations[END_REF], [START_REF] Schabas | Hume on money, commerce, and the science of economics[END_REF].

2. The interpretation considering Cantillon and Hume as proponents of the pricespecie-flow mechanism may be found in the following literature. Regarding Cantillon, see [START_REF] Angell | The Theory of International Prices[END_REF], pp. 213-214), Viner (1937, pp. 86, 292), Wu (1939, pp. 68-69), Schumpeter (1954, p. 223, 316, 331, 365-367), Patinkin (1956, p. 375), [START_REF] Vickers | Studies in the Theory of Money, 1690-1776[END_REF], pp. 210-211), Fetter (1965, p. 4), [START_REF] Petrella | Adam Smith's rejection of Hume's price-specie-flow mechanism: a minor mystery resolved[END_REF], p. 365), O'Brien (1975[2004], p. 171), Brewer (1988, p. 453;[START_REF] Brewer | Richard Cantillon: Pioneer of Economic Theory[END_REF], p. 186), Thornton (2007a, pp. 460-461), pp. 460-461). Laidler (1988, pp. 78, 92) claims that the quantity theory took a 'classical form' with the work of Cantillon, whose treatment of the quantity theory would have anticipated that of David Hume and his price-specie-flow mechanism. Concerning Hume, see Angell (1926, p. 47, 51, 214), Wu (1939, pp. 76-78), Patinkin (1956, p. 375), Vickers (1959, p. 236-237), [START_REF] Sekine | The discovery of international monetary equilibrium by Vanderlint, Cantillon, Gervaise and Hume[END_REF], p. 277), O'Brien (1975[2004] [2004, p. 171]), Fausten (1979, p. 664), Samuelson (1980, pp. 146-147), Murphy (1986, pp. 270-272;2009, pp. 105-106), [START_REF] Berdell | The present relevance of Hume's open-economy monetary dynamics[END_REF], p. 1207), Thornton (2007a, pp. 460-461), Arnon (2011, pp. 17-19).

3. The interpretation considering Cantillon and Hume as proponents of the monetary approach to the balance of payments may be found in the following literature. Regarding Cantillon, see Bordo (1983, pp. 244-246), Murphy (1986, p. 272). Notwithstanding, Murphy (2009, pp. 88-89) adds that a passage of the Essai (pp.

165-167) 'represents a clear statement of the self-adjustment price specie flow mechanism'. Concerning Hume, see Johnson (1972, pp. 229-230;1976, p. 274), Cesarano (1998, pp. 182-184), Wennerlind (2005, p. 230).

4. In the secondary literature, Holtrop (1929, pp. 506-507) followed by Rist (1938Rist ( [1940], pp. 38-39, 69-71) ], pp. 38-39, 69-71) underlined the importance of Cantillon's banking approach of circulation. Monroe (1923, p. 256), Wu (1939, pp. 65-66), Spengler (1954, p. 414), Murphy (1986, pp. 276-277) and Brewer (1992, p. 103) mention it in passing. Schumpeter (1954, pp. 319-321) explicitly attempted to refute it. Vickers (1959, p. 215) claims that Cantillon's conception of the function of banking relies on 'a virtually complete oversight of the importance of the moneycreating function ' and Bordo (1983, pp. 237, 256) that Cantillon 'was unaware of the role of banks as money creators through the bank multiplier process'. In fact, Cantillon provided an alternative theory to the money-multiplier principle. As [START_REF] Gillard | Le statut de la monnaie dans le Traité de Montchrestien et dans l'Essai de Cantillon[END_REF] points out, the approach of bank issuing in the Essai is not consistent with the quantity approach of the money multiplier.

5. In the secondary literature, Hume's quantity approach of banking has been less commented than that of the overnight story. Petrella (1968, pp. 372-373) and Paganelli (2006, pp. 541-542) mention that, for Hume, bank notes are supposed to exert strong inflationary pressures. Caffentzis (2001, pp. 320-322;2008, pp. 147-149) questions Hume's supposed hostility to paper credit without specifying however whether bank notes or inconvertible paper money were concerned. Wennerlind (2005, pp. 234-235) indicates that Hume's analysis of bank issuing fits into the model with an artificial and exogenous expansion of money. Desmedt (2008, pp. 18-19) links Hume's opinion on bank notes with the monetary disorder in Scotland during the 1750s.

Appendix: The 'classical' and 'quantity' traditions