6 A FEW ADDITIONAL DIFFICULTIES WHEN EXPANSION IS INITIATED SIMULTANEOUSLY BY ALL BANKS

In light of the fact that in this context we are forced to offer a simplified view of the processes of credit expansion, it is now necessary to make a few supplementary points and clarifications. To begin with, the expansion process we have described originates entirely from an increase in money deposited at the original bank (in our example, d represents 1,000,000 m.u. deposited in Bank A). Nevertheless, both historically, as banking developed, and currently, all processes of credit expansion have been characterized by the fact that the new money reaches the banking system not through one single bank, but through many (if not, to a larger or smaller extent, through all the banks in the system). As Richard G. Lipsey reveals,³² credit expansion such as we have described, which takes place ex nihilo and is backed by the creation of the necessary bank deposits, will recur as often as 1,000,000 m.u. are deposited in any of the different banks. Therefore, the widespread expansion process is, in practice, much more substantial and qualitatively more complicated, since it originates simultaneously at many banks and from many deposits. In our example alone, which involved a reserve ratio of 10 percent, loans for the sum of 9,000,000 m.u. were ultimately created, an amount nine times larger than the original deposit, and as a result the total money supply was multiplied by ten. The main conclusion to be drawn is that if all banks simultaneously receive new deposits of money, they will be able to expand credit without having to decrease their cash reserves, because although they grant loans which could lead to a withdrawal of cash (as we have supposed up until now in the accounting entries), they simultaneously receive the deposit of a portion of the money loaned by other banks. Hence in practice, significant decreases in each bank's reserves will not necessarily occur, and each bank, while maintaining its reserves practically intact, will be able to make loans and therefore create deposits without serious risk.

This theoretical argument has prompted various authors, among them Murray N. Rothbard,³³ to write about the process of credit expansion in the banking system from the viewpoint that an isolated bank does not lose reserves when it grants new loans. Instead, while maintaining the volume of its reserves intact, it makes every attempt to make new loans for a multiple determined by the inverse of the reserve ratio. The argument for explaining the bank multiplier in this way, even in the case of an isolated bank, is that the bank will attempt to avoid reducing its reserves in the process of granting loans (i.e., the banker will not wish to keep 100,000 m.u. and loan 900,000). Instead, it is much more advantageous for the bank to maintain its reserve ratio by loaning a much larger amount of money and keeping the initial cash reserves unaltered (that is, by holding 1,000,000 m.u. in cash and creating ex nihilo 9,000,000 m.u. in new loans). In practice, the level of cash reserves can be ensured if the credit expansion process takes place simultaneously at all banks. This is because the decrease in cash a bank experiences upon granting loans will tend to be compensated for by the reception of new deposits originating in loans made by other banks.

When the expansion process is presented in this way, it is not often easily understood by nonspecialists, nor even by professionals in the banking sector, who are accustomed to considering their “business” mere intermediation between depositors and borrowers. However, clear evidence that the approach of Rothbard and others is totally correct lies in the fact that for our purposes it makes no difference whether we study the case examined up to this point (an original deposit, extended throughout the banking system, of 1,000,000 m.u. in Bank A), or we consider a banking system comprised of ten banks, each of which simultaneously receives a deposit of 100,000 m.u. (i.e., a total of 1,000,000 m.u. divided among ten banks). In the latter case, each bank will keep unaltered 100,000 m.u. in cash, making it possible for the banks to expand their loans and create ex nihilo new fiduciary media for the sum of 900,000 m.u. Each bank will be able to maintain stable cash reserves of 100,000 m.u. if possible reductions in these reserves as the result of loans granted are offset by new deposits originating from loans made by other banks. Therefore if all of the banks bring about expansion simultaneously, each one is able to maintain its cash reserves unaltered, and with a reserve ratio of 0.1, create from nothing, in the form of loans backed by new fiduciary media, up to nine times its initial deposits. Let us examine this process of simultaneous expansion in terms of accounting entries.

We will assume that each of ten banks receives 1,000,000 m.u. in new, original deposits of money. The ten banks are all of the same size, and each has a reserve ratio, c, of 10 percent, and (to keep it simple) a k equal to zero. Let us also suppose that each bank has a market share of 10 percent. In other words, each bank receives the business of 10 percent of all the customers in the market in which it operates. Moreover, these customers are randomly distributed. If these banks simultaneously begin to expand credit according to the process described in entries (42) and following, it is obvious that any one of them, for example Bank A, will eventually receive deposits coming from loans granted by the other banks, as shown in Table IV-2. If all of the banks expand credit simultaneously, Bank A's journal entries would appear as follows:

This decrease in cash would be counteracted by a demand deposit from a final recipient of a loan granted, for example, by Bank B, resulting in the following entries:

Bank A would eventually recuperate these 810,000 m.u. in the form of a deposit originating from loans granted, for example, by Bank C. The journal entries would look like this:

As this process continues, Bank A would receive deposits from the recipients of loans granted by Banks D, E, F, G, H, I, and J. We have greatly simplified the process in our explanation. In reality, the bank receives, on average, 10 percent of the ten loans of 900,000 m.u. granted in the first stage by each bank in the system. It then receives 10 percent of the ten loans of 810,000 m.u. made by each of the banks in the second phase, 10 percent of the ten loans of 729,000 m.u. made by each in the third phase, etc.

Hence, if we suppose that each of ten banks receives 1,000,000 m.u. in original deposits, and the banks expand credit simultaneously, the balance sheet of any of them, Bank A, for instance, would appear as follows:

Therefore, the balance sheet of each bank would coincide with the one we discovered when we assumed k was equal to one (a monopolistic bank or one whose clients are the ultimate recipients of the loans it grants). This is due to the fact that although in this case there is no monopoly, the loss of cash each bank initially experiences upon expanding credit is eventually offset by deposits originating in loans expanded by the other banks.

We may conclude from balance sheet (53) that each banker need not reduce his cash reserves to expand his bank's credit; instead, if the rest of his colleagues expand their credit at the same time, he can maintain his level of cash reserves unaltered and proceed directly to grant loans for a sum equal to a multiple of his reserves. (In our case, each banker holds 1,000,000 m.u. in cash reserves and creates from nothing 9,000,000 m.u. in loans backed by 9,000,000 m.u. in secondary deposits.) Therefore Rothbard's interpretation of the process is correct even in the case of an isolated bank, when each of the other banks in the system also receive original deposits (that is, a proportional amount of the new money created in the system) and all expand their credit simultaneously. The cash each bank would theoretically lose by granting loans is counteracted by deposits received from recipients of loans expanded by the banker's colleagues. Thus each bank can alone expand its credit for the sum of 9,000,000 m.u. In turn, the system's total expansion would be equal to 90,000,000 m.u., and the amount of total deposits or the money supply would be 100,000,000 m.u.

We can achieve numerical results identical to those in Table IV-2 simply by supposing that an original deposit of 1,000,000 m.u. is made at Bank A and is divided equally among the ten banks in the system, each of which receives 100,000 m.u. Those 100,000 m.u. would remain unaltered in each bank's vault. Each bank could expand its credit by 900,000 m.u., and therefore the entire banking system could generate 9,000,000 m.u. in new loans and a total of 10,000,000 m.u. in primary and secondary deposits.

Obviously this last example, which wraps up our accounting analysis of the expansion of loans and deposits by isolated banks and banking systems, is the most realistic. In the current monetary system, increases in the money supply filter throughout the system and reach practically all banks, permitting them to expand their credit simultaneously according to the processes we have studied. In addition, there are clear historical indications that banks have never emerged alone, but in groups. Even Saravia de la Calle mentions that bankers established themselves in groups, offering “guarantors and acting as guarantors for each other.”³⁴ This means that by the time of the sixteenth-century Castilian markets, bankers were already aware of the intimate relationship and strong community of interests uniting them in terms of the success or failure of their businesses, and they realized they needed to support one another mutually.

With respect to the gold standard and a money supply based on the discovery of new gold mines and on the development of extraction techniques, we can assume that new money originating from substantial, new discoveries would initially reach only a few bankers, and from there it would extend throughout the rest of the banking system. Therefore, it would not set off a process of simultaneous expansion, but a gradual process by which the money would filter throughout the entire system.

We can conclude that if there are many banks and many new deposits, and the banks expand their credit simultaneously following the processes we have studied, even an isolated bank will be able to maintain a stable level of reserves and by itself expand loans and deposits for a multiple of this level, an amount determined by the inverse of the reserve ratio (when k =0).³⁵ Therefore it is obviously only in the account books that deposits back the wealth bankers appropriate upon expanding their credit. From an accounting (but not a legal) standpoint, the formal ownership of these loans corresponds to the deposit-holders, since under normal circumstances they consider their deposits money (perfect money substitutes) they can use in their transactions without ever having to withdraw them in physical monetary units. Nonetheless, it is clear that the assets generated by the banking system do not actually belong to anyone. To a large extent, however, they could be considered the property of banks' shareholders, directors and administrators, the people who actually take advantage of many of the economic benefits of this wealth, with the additional advantage of not appearing as the owners, since the account books indicate that the depositors own the wealth.

In other words, under normal conditions, deposits come from loans and are merely a secondary result, reflected in the account books, of the wealth banks accumulate and retain indefinitely. We will return to this topic later in the book, in a discussion on banknotes and in the last chapter, where we present our proposal for a process of banking reform.

FILTERING OUT THE MONEY SUPPLY FROM THE BANKING SYSTEM

Another complexity derives from the fact that in reality, each time loans are granted and deposits are created and withdrawn, a certain percentage of the money supply “filters” out of the system and is kept by individuals who do not wish to deposit it in a bank. The larger the percentage which physically “filters” into the pockets of individuals at each stage and remains outside the banking system, the smaller the bank's expansive capacity to generate new loans.

In a system of small banks (in which k = 0) with a reserve requirement of 10 percent (c = 0.1), if f refers to the proportion of the money supply that filters out of the banking system and f = 0.15, then when Bank A loans 900,000 m.u., the amount of money which would return to the banking system would be equal to (1 – f) 900,000 = (1 – 0.15) 900,000 = 0.85 × 900,000 = 765,000 m.u. Therefore if we are dealing with a system of small banks and we assume that k=0, c=0.1 and f=0.15, we can use the following formulas:

If D_N refers to the total net deposits, which are comprised of gross deposits, D_G, minus the total sum of money, F, that filters out of the banking system, then:

[29] D_N = D_G - F

The total sum of money that filters out of the banking system will logically be equal to f times the total sum of gross deposits, D_G, where f is the percentage of money which filters out of the system. That is:

[30] F = fD_G

In turn, the amount of money initially deposited is equal to the sum of net deposits multiplied by the corresponding reserve ratio plus the total sum which has filtered out of the system:

[31] d = D_N · c + F

If we substitute into this equation the value of D_N in formula [29] and the value of F in [30], we obtain:

[32] d = (D_G - F) · c + fD_G

If we replace F in the equation with fD_G, we obtain:

[33] d = (D_G - fD_G)c + fD_G

Then we factor out D_G

[34] d = D_G (c - cf + f)

And therefore:

As D_N = D_G(1-f),

This would be the formula for the net deposits created by the banking system. The credit expansion brought about by a banking system out of which some money filters would be equal to:

If we substitute a value of zero for f in the preceding formulas, we are left with the same equations we have used until now to determine the total volume of deposits and the total credit expansion:

and

Let us see to what value credit expansion is reduced if, as before, d = 1,000,000 m.u. and c = 0.1, while in addition 15 percent of the money supply filters out of the banking system (f = 0.15).

Hence, in a banking system where 15 percent of the money supply filters out of the system, the total sum of deposits would be 3,617,021 m.u., instead of 10,000,000 m.u., as is the case when f = 0.

The net credit expansion would be equal to × = 3,617,021 -1,000,000 = 2,617,021, instead of the 9,000,000 m.u. which are created when no money filters out of the system. Therefore, when the percentage of money which filters out is greater than zero, the capacity of the banking system to create loans and generate deposits ex nihilo decreases noticeably.³⁶

THE MAINTENANCE OF RESERVES EXCEEDING THE MINIMUM REQUIREMENT

Another complication which produces effects similar to those covered in the preceding section takes place when banks hold cash reserves exceeding the minimum requirement. This tends to occur at certain stages in the economic cycle in which banks behave relatively more prudently, or they are obliged to increase their reserves due to difficulties in finding enough creditworthy borrowers willing to request loans, or both. This occurs, for example, in the phases of economic recession that follow credit expansion. At any rate, the maintenance of cash reserves exceeding the necessary level reduces the system's capacity for credit expansion in the same way as f, a percentage of the money supply which filters out of the banking system.³⁷

DIFFERENT RESERVE REQUIREMENTS FOR DIFFERENT TYPES OF DEPOSITS

Finally, another complication we could consider derives from the fact that in many countries the reserve requirement for demand deposits differs from the requirement for time deposits, even though as we know, in practice the latter are often true demand deposits. Although the formulas we have considered up until now could be worked out again for both deposit types, the degree of complexity involved would not be worth the slight additional value the analysis could afford, so we have chosen not to do so here.³⁸