While Fractional Reserve Banking with Bitcoin is possible, there is disagreement over what it would entail. Much discussion occurred on the Myths Talk Page.

Keynesian Viewpoint

Fractional Reserve Banking with Bitcoin is possible and practical. It is already implemented with CoinLenders. There is no fundamental difference between classical currencies and Bitcoin as it applies to banking. Banks will still be free to take in bitcoins and present them to customers as "available for withdrawal" while still lending most of those bitcoins to a different customer for a profit. Some of those bitcoins will be held in reserves in case of a bank run. It will be up to the bank to hold a sufficient supply of reserves in order to prevent insolvency in the event of a bank run. Central banks were established to enforce reserve requirements and so, with Bitcoin lacking a central bank, some banks will almost surely collapse, taking their customers' deposits with them. A large bitcoin exchange could tomorrow lend out 10,000 bitcoins to an individual to start a business. The money supply would thus increase by 10,000 and we would instantly have Fractional Reserve Banking. The same amount of bitcoins would still exist in the Block Chain, but the body of people participating in the Bitcoin economy would have the perception that more bitcoins exist. If the value of a bitcoin is stable for a long period of time, then Fractional Reserve Banking is inevitable.

See Fractional reserve banking.

The Monetary Base of Bitcoin is limited to 21 million. But because Fractional Reserve Banking is possible, the money supply of bitcoins (which includes demand deposits) can exceed 21 million by a factor of x where x is the Money Multiplier.

Austrian Viewpoint

According to the Austrian viewpoint:

Fractional-reserve banking (or FRB) is the widespread banking practice in which only a fraction of a bank's demand deposits are kept in reserve and available for immediate withdrawal (as cash and other highly liquid assets), whilst the remaining cash is lent out to borrowers (and so is never actually available for immediate withdrawal to legitimate deposit-holders).

In order for fractional reserve banking to affect the money supply, the debt instruments issued by the bank (for example, bank notes or demand deposits) must be accepted as if they were money proper, in other words, they must be money-substitutes. This is explained for example by Rothbard in Austrian Definitions of the Supply of Money:

And so long as demand deposits are accepted as equivalent to standard money, they will function as part of the money supply. It is important to recognize that demand deposits are not automatically part of the money supply by virtue of their very existence; they continue as equivalent to money only so long as the subjective estimates of the sellers of goods on the market think that they are so equivalent and accept them as such in exchange.

In the historical cases of money based on gold or government issued fiat, the reason why money-substitutes are accepted as if they were money proper is that the money proper has in some circumstances high transaction costs (for example, gold might be too heavy to carry around, or the buyer and seller are not at the same location and want to perform the exchange electronically), or are not legally permitted (normal people are not allowed to obtain central bank reserves). This creates a demand for forms of money which have lower transaction costs. With gold/fiat, this requires the creation of debt instruments, which then, after being generally accepted in exchange, become money substitutes and a part of the money supply.

The situation with Bitcoin is different, because other forms can be created without debt instruments, for example Casascius physical bitcoins or Bitbills. Bitcoin in its "classical" form is similar in function of a bank account (allowing electronic transfers of balances) even though there is no debt instrument. Any object that can store 64 bytes of data (size of Bitcoin keypair) can, hypothetically, be used as a form of Bitcoin. In some cases, shorter forms than 64 bytes are possible too (for example, mini private key format used by Casascius physical bitcoins). Issuers of Bitcoin-based debt instruments, if they expect these instruments to be accepted in exchange, need to create demand for them as a method of payment outside of the Bitcoin network. This is difficult, because a transaction that occurs outside of the Bitcoin network is incompatible with it, so people equipped with software for handling only pure Bitcoin transactions cannot accept it. Furthermore, they also would need to compete against not only Bitcoin, but against other currencies, payment methods and services.

Currently, Bitcoin based debt instruments are restricted to a narrow field of uses. Exchanges allow these instruments to be traded against other currencies. E-wallets allow inter-wallet transfers. GLBSE allows the floating of shares or other contractual arrangements. However, these debt instruments are, in general, outside of these narrow fields, not accepted for exchange as if they were native Bitcoins. They rarely even circulate outside of the internal transactions of the providers of these services. There are very few exceptions, such as the redeemable Mt. Gox code. If the service provider attempted to conduct FRB by overissuing these instruments, they would be exposed at risk of having them redeemed too quickly. One possible way of mitigating this risk is to institute a suspension of specie payments (for example, Mt. Gox. having a default withdrawal limit).

If in the future, P2P exchanges and distributed wallets are available (both have been suggested already at bitcointalk.org forums), this would decrease the demand for Bitcoin-based debt instruments even further.

Historically, in all known situations where an overissue of Bitcoin-based debt instruments was produced, this resulted either in a voluntary elimination of the excess instruments (Mt. Gox hack from June 2011), bankruptcy (the demise of mybitcoin) or a new investor bailout (the demise of bitomat.pl and subsequent takeover by Mt. Gox). Here we have empirical evidence that FRB with Bitcoin is possible.

Putting all this together, there are several steps that need to be addressed regarding Bitcoin-FRB and money supply:

overissue of debt instruments (this would cause FRB) general acceptance of these instruments as a method of payment (this would mean the instruments need to be included in the money supply) market price of these instruments at a different rate than the reserve ratio of the issuer (this would cause inflation or deflation)

Even if we assume that an overissue is possible in long term, there are significant obstacles in phase 2 and 3, as elaborated above. It is therefore unlikely that even if Bitcoin-FRB became widespread, this would significantly affect the money supply of Bitcoins or inflation/deflation.