Thin Air Fallacy

There is a theory that fractional reserve banking inherently gives banks the ability to create money at no material cost. The theory does not depend on the state privilege of seigniorage. It is considered a consequence of the accounting practices of free banking. This is sometimes referred to as creating money ex nihilo or "out of thin air".

Adherents describe two competing views on money creation:

Naive View

Money is created by miners at a material cost, potentially sold to people, and eventually lent to people. This theory holds that the lender is lending only money he owns. As such the lender is operating at full reserve and cannot engage in the practice of fractional reserve, which is considered fraudulent. As an honest lender he is only able to issue claims (money substitutes) against money in his possession, preventing credit expansion and therefore general price inflation.

Practical View

Money substitutes are created by banks, at no material cost, as a consequence of fractional reserve lending. The supply of these substitutes expands with every loan, contracting only as loans are settled. Given the implied lack of constraint on credit expansion, overall debt grows without bound, creating general price inflation.

In a free market people can perform the same operations as banks, without necessarily calling themselves banks. Therefore the distinction between these two possibilities must be based on obscuration of the supposed fraud. The theory holds that this obscuration is accomplished using an accounting trick that is not widely understood. So let us investigate the difference. Any money will suffice in this investigation of the money substitutes created in either case, including Gold, Bitcoin or monopoly money.

In the naive view, the potential lender has saved both the liquidity required for personal consumption (hoard) and the amount intended for earning interest (investment). All lending in this scenario originates from savings. Savings includes the sum of the hoard (money) and the amount that asset exceeds liability: [savings = money + (asset - liability)]. Money is gold and assets are money substitutes:

	savings	money	asset	liability
Person	100oz	100oz

In this view of personal lending, Person hands over 80oz of gold to Borrower. Borrower accepts an obligation to repay Person with interest at loan maturity. To simplify the accounting we will assume zero interest and no accounting for repayment risk:

	savings	money	asset	liability
Person	100oz	20oz	80oz
Borrower		80oz		80oz

Notice that Person has actually lent to his own enterprise (i.e. lending business) a fraction of his savings for the purpose of earning interest, which is accounted for below. Let us consider that Person hoards 10% of his savings for the liquidity required for near-term consumption and Business hoards at 10% for the same reason:

	savings	money	asset	liability
Person	100oz	10oz	90oz
Business	90oz	9oz	81oz
Borrower		81oz		81oz

Notice that Person's business is operating with no reserve. All of his deposited money is at risk of default. Projecting this into the naive view of banking, we need only rename "Lender" to "Depositor" and "Business" to "Bank". There is no need to assume that these are distinct individuals:

	savings	money	asset	liability
Depositor	100oz	10oz	90oz
Bank	90oz	9oz	81oz
Borrower		81oz		81oz

Then let us assume Borrower deposits his borrowed money with Bank.

	savings	money	asset	liability
Depositor	100oz	10oz	90oz
Bank	90oz	90oz
Borrower			81oz	81oz

Notice that by properly accounting for the Person as putting money at risk (i.e. a depositor) we can see that all lending is fractionally reserved. There are two loans in this scenario, both reserved at 10%, resulting in monetary substitutes of 171% of money. Given the assumption of uniform time preference, Borrower will lend 90% of his savings, as will all subsequent borrowers. Assuming a minimum money divisibility of 1oz, credit expansion terminates at 8.903 times the amount of money, after 43 loans:

Loan	Hoarded	Loaned	Credit
1	10.00	90.00	90.00
2	19.00	81.00	171.00
3	27.10	72.90	243.90
4	34.39	65.61	309.51
5	40.95	59.05	368.56
6	46.86	53.14	421.70
7	52.17	47.83	469.53
8	56.95	43.05	512.58
9	61.26	38.74	551.32
10	65.13	34.87	586.19
11	68.62	31.38	617.57
12	71.76	28.24	645.81
13	74.58	25.42	671.23
14	77.12	22.88	694.11
15	79.41	20.59	714.70
16	81.47	18.53	733.23
17	83.32	16.68	749.91
18	84.99	15.01	764.91
19	86.49	13.51	778.42
20	87.84	12.16	790.58
21	89.06	10.94	801.52
22	90.15	9.85	811.37
23	91.14	8.86	820.23
24	92.02	7.98	828.21
25	92.82	7.18	835.39
26	93.54	6.46	841.85
27	94.19	5.81	847.67
28	94.77	5.23	852.90
29	95.29	4.71	857.61
30	95.76	4.24	861.85
31	96.18	3.82	865.66
32	96.57	3.43	869.10
33	96.91	3.09	872.19
34	97.22	2.78	874.97
35	97.50	2.50	877.47
36	97.75	2.25	879.72
37	97.97	2.03	881.75
38	98.18	1.82	883.58
39	98.36	1.64	885.22
40	98.52	1.48	886.70
41	98.67	1.33	888.03
42	98.80	1.20	889.22
43	98.92	1.08	890.30

Notice that in order for any person to spend from his hoard while maintaining his time preference, a loan must be settled in order to offset the spending. The settlement process moves the money from the former borrower to its lender, and cancels the note. The person in receipt of the spent money must lend it in order to satisfy his time preference, and so on.

No further expansion is possible without an increase in the amount of money or an overall reduction in time preferences. An increase in money increases the absolute amount of credit and a reduction in time preference increases the rate of credit expansion in relation to the money. Given that money and credit evolve together, there is never any actual increase in money substitutes apart from these changes.

In the practical view, we work with the same assumptions, however we apply the view of bank accounting to expose any distinction. In the simple model, Bank has received 100oz from Depositor and hands over 80oz to Borrower. This is identical to the naive view:

	savings	money	asset	liability
Depositor	100oz	10oz	90oz
Bank	90oz	9oz	81oz
Borrower		81oz		81oz

In the practical model of bank accounting (i.e. how it typically happens), Bank does not hand over the money. Instead it creates offsetting accounts for its loan asset ("credit") and liability ("debt"). The savings relation is expanded to include these new accounts: [savings = money + (asset - liability) + (credit - debt)]. At the time of loan issuance, the accounts are as follows:

	savings	money	asset	liability	credit	debt
Depositor	100oz	10oz	90oz
Bank	90oz	90oz			81oz	81oz
Borrower			81oz	81oz

This is where explanations of the theory tend to terminate. The offsetting accounts of both Bank and Borrower balance, but Borrower has 81oz of gold to spend and Bank has not had to turn over any gold to Borrower. There is still only 100oz of money, but both Bank and Borrower have 81oz of money substitute. The theory observes that this implies Bank can create any amount of money substitute. Notice that everything will still balance, and all accounts can be settled, seeming validating the theory.

This however demonstrates no actual use of either the loan asset or the bank credit. Let us take this a bit further by assuming Borrower clears his account, settling the Bank's credit and debit accounts.

	savings	money	asset	liability	credit	debt
Depositor	100oz	10oz	90oz
Bank	90oz	9oz
Borrower		81oz		81oz

Then let us assume Borrower deposits his borrowed money with Bank.

	savings	money	asset	liability
Depositor	100oz	10oz	90oz
Bank	90oz	90oz
Borrower			81oz	81oz

Notice that the this is identical to the final outcome of the naive view. There is no distinction between these supposedly-competing views on money creation, invaliding the theory.

Recall that each loan is reserved at 10%, so Bank can lend up 8.903 times the amount of money on reserve, or 890.3oz of money substitute against 100oz money reserved. This is a reserve ratio of 100:890.3 or ~11.2%.

If Bank reserves each loan at 0%, credit expansion would be unlimited. However this implies zero time preference, or the idea that time has no value, implying that all money is lent indefinitely. In the case of Bank, 0% reserve implies no liquidity to satisfy any withdrawal (i.e. immediate failure). This is no different than any individual or business failing to hoard sufficient to maintain necessary liquidity. In other words, insufficiently low time preference.

Let us revisit the scenario where Bank creates credit at negative reserve (i.e. out of thin air). For example, on deposits of 0oz Bank issues a loan of 1000oz:

	savings	money	asset	liability	credit	debt
Depositor
Bank					1000oz	1000oz
Borrower			1000oz	1000oz

When Borrower spends just 1oz to Merchant, using the money substitute, Merchant's account is credited and Borrower's account debited by 1oz.

	savings	money	asset	liability	credit	debt
Depositor
Bank					1000oz	1000oz
Borrower			999oz	1000oz
Merchant			1oz

The imbalance between Merchant and Bank accounts must be settled. The money must actually be moved from the control of Bank to Merchant (or typically Merchant's bank). At this point Bank has failed. Bank may create as much money substitute as it wants, but negative reserve is just an empty promises. The failure to recognize these principles likely results from failure to consider the clearing process. This likely stems from the failure to recognize the clear and necessary duality of money and money substitutes. This likely stems from the habit of referring to money (e.g. gold) in the same terms as money substitutes (e.g. accounts for gold).

	savings	money	asset	liability	credit	debt
Depositor
Bank		-1oz			1000oz	1000oz
Borrower			999oz	1000oz
Merchant		-1oz

Implications

It should be evident that:

• Fractional reserve is inherent in lending.
• The economic fraction of reserve is time preference.
• Non-positive reserve is not possible.
• Lower reserve reduces chances of being able to settle accounts.
• No distinction exists between naive and practical money creation.
• Banks have no ability to create money.

When Bank has insufficient reserve to satisfy withdrawals, either due to loans in default or a bank run, it has only two options, default or borrow. To prevent the former, central banking exists to provide the latter. This is the meaning of the term "lender of last resort".

There is nothing inherently special about such a lender in free banking, it is just another lender subject to the constraints demonstrated above. However, in state banking this lender is supported by the taxpayer. The state taxes to provide discount loans to member banks. The loans must be at a discount to market rates as otherwise it doesn't constitute a last resort. Banks always have the option to borrow from other banks and potential depositors. Taxation is necessary to support the discount (i.e. cheap money). So if the economic rate of interest is 10%, the state may lend to member banks at 3% and cover the difference with taxes.

The state has many sources of tax revenue, but typically central banks subsidize discount rates with seigniorage. Central banks are famous for proclaiming that they do not "print money", but this is exactly what they do. The U.S. Federal Reserve ("Fed") has the power to order new money from the U.S. Treasury's Bureau of Engraving and Printing. The Fed pays the printing cost for "paper" money and face value for coinage. The Treasury is just the contractor that performs the work. Typically coinage is produced such that it has higher face value than use value, in order to prevent disappearance of the coins.

This implies that the monetary inflation of state fiat is literally the consequence of printing the "paper" money. This process is obscured somewhat. The Fed does not first print the money, stuff it in a vault, and then lend it out. This is unnecessary. The order is reversed in practice. The Fed issues discounted loans, with the presumption of money in its vault. The settlement process established by the Fed maintains track of how much money is in each member bank's reserve. The bulk of settlements can often be netted, but periodically money must be physically moved. To further reduce transportation costs, a significant portion of member bank reserves are required to be held in the Fed's own vault.

Yet the Fed can pretend it has money in its vault and print it only when it is required for settlement. When a member bank requires money it borrows it from the Fed. When the Fed's reserve of actual money is insufficient, it simply makes a withdrawal from the taxpayer by demanding money from the printer (i.e. inflation tax). Without this ability create new fiat the Fed would be unable to settle accounts, just as would any bank if there was insufficient reserve (including that which could be borrowed) to cover withdrawals and defaults. Until the member bank must settle in fiat, such as in the case of cash withdrawal at ATMs, teller windows or with non-member banks and other institutions, there is no need to move the actual money, or print it. But without the ability to print it, the Fed would be subject to default just as any other bank.

Observation

Given these facts, one would expect the level of money substitutes to be no greater than the product of coinage + fiat (and accounting for fiat not yet printed) in curculation, and the "money multiplier" implied by bank reserve requirements:

In equations, writing M for commercial bank money (loans) [money substitutes], R for reserves (central bank money) [money], and RR for the reserve ratio, the reserve ratio requirement is that R/M >= RR; the fraction of reserves must be at least the reserve ratio. Taking the reciprocal, M/R <= 1/RR, which yields M <= R x (1/RR), meaning that commercial bank money is at most R x 1/RR, the latter being the multiplier ignoring leakages into currency [money held outside of banks].

Bank reserve requirements in the U.S. are as follows, implying a minimum reserve ratio of less than than 10%:

A depository institution's reserve requirements vary by the dollar amount of NTAs [Net Transaction Accounts] held by customers of that institution. Effective January 18, 2018, institutions with net transactions accounts:

• Of less than $16 million have no minimum reserve requirement;
• Between $16 million and $122.3 million must have a liquidity ratio of 3% of NTAs;
• Exceeding $122.3 million must have a liquidity ratio of 10% of NTAs.

The total amount of U.S. Dollars in circulation is referred to as M0:

M0: The total of all physical currency including coinage. M0 = Federal Reserve Notes + US Notes + Coins. It is not relevant whether the currency is held inside or outside of the private banking system as reserves.

According to the U.S. Federal Reserve, at the end of January 2019, there was approximately $1,700,000,000,000 of money in circulation:

There was approximately $1.70 trillion in circulation as of January 31, 2019. This figure includes Federal Reserve notes ($1,655.2 billion), U.S. notes ($0.2 billion), currency no longer issued ($0.2 billion), and coins outstanding ($47.2 billion).

However that money accounted for but not yet printed is not included above, so we cannot rely on this number:

In the United States, a bank's reserves consist of U.S. currency held by the bank (also known as "vault cash") plus the bank's balances in Federal Reserve accounts. For this purpose, paper currency on hand and balances in Federal Reserve ("Fed") accounts are interchangeable (both are obligations of the Fed).

The total amount of U.S. Dollars and equivalents in circulation in May 2019 was approximately $3,250,000,000,000.

The sum of all U.S. Dollar money and money substitutes is referred to as M3:

• M1: The total amount of M0 (cash/coin) outside of the private banking system plus the amount of demand deposits, travelers checks and other checkable deposits
• M2: M1 + most savings accounts, money market accounts, retail money market mutual funds, and small denomination time deposits (certificates of deposit of under $100,000).
• M3: M2 + all other CDs (large time deposits, institutional money market mutual fund balances), deposits of eurodollars and repurchase agreements.

According to the Federal Reserve Bank of St. Louis, M3 was $14,613,500,000,000 in May of 2015, the last date provided. According to the OECD, M3 in May 2019 was 121% of M3 in 2015, or $17,682,335,000,000.

The amount of money substitutes is the difference between M3 and M0, or $14,432,335,000,000. The actual reserve ratio is therefore $3,250,000,000,000 divided by $14,432,335,000,000, or 22.52%. Given that the reserve requirement is no more than 10%, the level of monetary expansion is less than half that allowed by law. This implies that time preference, not the regulatory reserve requirement, is currently controlling the rate of credit expansion. The implied an iteration of loans at a reserve rate on each loan of 18.38%.

While these numbers exclude the expansion implied by private U.S. Dollar lending, it seems clear that credit expansion by banks is limited by both money and time preference. However, there is a significant amount of money available should lending increase due to lowering of time preferences. As this money starts competing for goods as opposed to sitting in vaults, a significant increase in price inflation should be expected. This highlights the point that monetary expansion alone does not immediately create price inflation, but instead is its harbinger.

As loans to member banks are settled, the Fed's "vault money" can be destroyed with the opposite effect of its printing. While the Fed has contracted M0 by almost 20% in the four years since its peak in 2015, as negative seigniorage this comes at a cost to tax revenue. The Fed itself operates as a non-profit organization, so net income derived from its loans to member banks is remitted to the U.S. Treasury annually.

The Federal Reserve increased the federal funds rate target seven times since between Dec. 2015 and June 2018. This has implications for the path of the federal deficit and federal debt in two ways:

• Directly through net interest payments
• Indirectly through the yearly remittances from the Fed to the U.S. Treasury Department

The yearly remittances to the Treasury are essentially the leftover Fed revenue after operating expenses. By law, this additional revenue must be turned over to the Treasury.

The revenue sent to the Treasury peaked at $97.7 billion in 2015 and has been steadily falling since. In January, the Fed sent $80.2 billion to the Treasury. In this blog post, I explore why these transfers are likely to continue declining.

Conclusion

Money is not created "out of thin air" by banking accounting. It is literally created out of old blue jeans by the state.