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.

| |money |asset |liability | |---------|----------|----------|----------|----------| |Person | 100oz| 100oz| | |

In the naive 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

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.