Note for avid stackers: This post was written with a more general audience in mind that is less experienced with Bitcoin than the people on SN. If certain parts are over-simplified, that's why.

Bitcoin would create full reserve banks without any need for government assistance.

Introduction

Banking has always been a realm of intense controversy. From ancient assaults on tax collectors to modern contentions over interest rates, the way money is created, stored, and transferred has roiled with seemingly irreconcilable disagreement.
One such dispute is the dichotomy between fractional reserve and full reserve banking. Fractional reserve, where banks do not fully back deposits and instead loan out a portion of funds, has long been the norm and is potentially quite unstable. Unfortunately, the alternative of full reserve banking has consistently depended on a government-enforced mandates to ensure banks fully back deposits, prompting many free marketeers to oppose full reserve standards.
The rise of Bitcoin, a digital currency with limited supply and provable ownership, has introduced dynamics that could shift this dilemma. In this article, we will explore how banks using Bitcoin will be incentivized to shift from fractional reserve to full reserve models, especially in economies where Bitcoin becomes the primary currency.

Why Free Marketeers Have Opposed Full Reserves

Save for a few traditions in both the Austrian and Chicago schools, full reserves have historically been a minority position among free market economists. Free bankers especially have opposed full reserves on the principle that full reserve banking requires more government intervention in the economy than fractional reserve.
As George Selgin, an avid free banker, explains:
Every significant 100‐​percent bank known to history was a government‐​sponsored enterprise that depended for its existence on some combination of direct government subsidies, compulsory patronage, or laws suppressing rival (fractional reserve) institutions. Yet despite the special support they enjoyed, and their solemn commitments to refrain from lending coin deposited with them, they all eventually came a cropper.
Government enforcement of full reserve becomes necessary for two reasons. The first is that banks have to charge depositors higher fees on checking accounts, as it is harder to lend out the money and thus make a yield. The second is that depositors have little to no way of auditing the reserves of a bank and thus can't take their money elsewhere when the institution lends fractionally.
Although it has been argued that fractional reserve banking is inherently fraudulent and therefore not outside the state's purview, it is still the case that government involvement would be necessary to punish such fraud. Fortunately, a more free market purist approach to the issue exists: Bitcoin.

Bitcoin Solves the Problem of Fees

Bitcoin has a limited supply of 21 million coins, which is enforced by the protocol's strict distribution cycle. Because of this, it would generally experience deflation, increasing in value at approximately the same rate as the overall production. Warren E. Weber estimates that in a Bitcoin economy, deflation would average 2-3% per year as productivity increased at that same rate.
Note that this type of deflation would not produce a deflationary spiral, as it would be caused to overall productivity rather than economic shocks. Indeed, economic crises in a Bitcoin economy would likely produce inflation as the productivity of society decreased. I suggest this study by the National Bureau of Economic Research to anyone interested in the benefits of deflation.
Because the value of Bitcoin would increase over time, unlike the dollar, there would be a much higher incentive to secure it and a lower incentive to accumulate yield. Consider a depositor with 100 BTC held in a checking account. If the deflation rate is 3%, then that depositor can reasonably accept any fee up to 3 BTC without experiencing any overall loss to the value of their deposit. Contrast that with the current US economy, where more than 3% in yield would be required just to break even.

Bitcoin Solves the Problem of Auditing

For full reserve banks to fully function in a free market environment, there must be mechanisms available for customers to verify that a bank has 100% reserves. Audits by private or public authorities can certainly be conducted, but such audits are costly, can only be accomplished so often, and altogether are a less than ideal solution.
Fortunately, Bitcoin's digital nature makes it easy to regularly verify whether a bank holds the reserves it claims to. Every bitcoin ever created has an identifiable digital signature. For an entity, such as an individual or bank, to prove ownership of a given bitcoin, they can simply sign a message using that same digital signature. Using this signing method, banks can demonstrate to customers that all deposited funds remain in the bank’s custody and have not been loaned out, a process known as proof-of-reserves. Researchers have already drafted proposals for this kind of public auditing system.
Using proof-of-reserves, consumers could regularly watch whether a bank was participating in fractional reserve and immediately take their business elsewhere if they felt the bank was not properly backing their deposits. This gives a mechanism for consumers, rather than governments, to enforce a full reserve standard in ways that do not require unruly subsidies, mandates, or other forms of intervention.

Conclusion

Full reserve banks offer a promising alternative to the traditional fractional reserve model. Unfortunately, they have historically depended on market intervention to stay afloat, which has caused many free market economists to dismiss their use.
If an economy were to transition to a Bitcoin standard, there would be sufficient changes, both economically and technologically, to incentivize the shift to full reserve banks. Moderate deflation would solve the problem of fees, and proof-of-reserves would reduce the difficulty of audits. Full reserve on Bitcoin might not come tomorrow, but it is an intriguing type of financial arrangement that deserves further inquiry.
Outside of forums like this, in my experience most people have no idea about fractional reserve banking, much less realise that the money in their bank account is not legally theirs anymore, you have lent your money to the bank, and they owe you it as a debt, whilst "your" money is lent out to others. Works great till it doesn't!
So most have no idea what causes banking crashes apart from "greedy bankers"; and whilst there is a lot of that at Board level, it's the local staff get the customer grief, and it completely misses the underlying problem
So it would be great to see full reserve banking. Because tbh, self custody of bitcoin is prob never going to be mass market. But at the moment, it solves a hidden problem that most people are not even aware of!?
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