Free banking has both microeconomic and macroeconomic aspects.
"Micro" free banking is only loosely related to whatever fundamental nominal anchor exists for the monetary system and monetary policy. Those are the questions that are central to "macro" free banking.
Reforms related to "micro" free banking include the private issue of hand-to-hand currency and token coins, ending reserve requirements, ending restrictions on branching, ending capital requirements, ending government deposit insurance, privatized interbank clearing operations and perhaps more. "Micro" free banking is about deregulation of the banking system. The key idea is that banks should be subject to the general rules regarding freedom of contract. The only "regulation" appropriate to banking would be closely tied to the general prohibition of fraud.
As a rough rule of thumb, each possible reform stands alone. Banks issuing hand-to-hand currency could be subject to reserve or capital requirements. Reserve requirements could go, while capital requirements and the existing ban on banknotes remain. Deposit insurance could be expanded to apply to bank-issued currency or discontinued from some or all deposits.
Of course, there are interactions among regulations. For example, ending capital requirements while keeping government deposit insurance would be very dangerous--especially to the deposit insurer, and so, the taxpayers.
These "micro" reforms are consistent with bank-issued money, both currency and deposits, being denominated in the official unit of account. In the U.S., that is "the dollar." Further, they are consistent with bank-issued money, again, both currency and deposits, being redeemable in dollar-denominated base money. The monetary authority, perhaps organized as a central bank like the Federal Reserve, could still implement a monetary policy. In particular, the Fed could target the federal funds rate and aim to achieve a 2% inflation rate for the CPI starting from where ever the CPI happens to be.
There are two basic categories of "macro" free banking. The Hayek version was outlined in his "Denationalization of Money." Banks issue monetary instruments, both currency and deposits, denominated in unique units. In other words, various banks simultaneously introduce new units of account and hand-to-hand currency and deposits denominated in those units. Hayek assumed, reasonably enough, that each bank would manipulate its issue of monetary instruments to maintain their purchasing power. Households and firms would then choose between monies and units of account based upon whatever criterion they want, though Hayek assumed that monies of stable purchasing power would dominate. While there is a sort of monetary policy under this scheme, these are really monetary policies developed by a variety of different banks. There is no "central bank" providing overall guidance, and so this is a type of "macro" free banking.
The alternative version of free banking, what I call the "Mises" version, is based upon a common unit of account. Rather than the dollar being defined as a unit of money whose value can be manipulated by the monetary authority, it is defined in some other way. The obvious approach, and the one assumed by Mises, is that the dollar is defined as a fixed weight of some commodity, like gold. The nominal anchor of the monetary system, then, would be the fixed dollar price of gold. The assumption is that the various banks denominate their deposits and currencies in dollars and tie them to gold, or whatever commodity is used, by redemption. While there is a sort of "monetary policy" in the system, it is really just a market process that results from the interactions of the banks as well as the supply and demand for gold. Because there is no central bank providing guidance to the system, the result is "macro" free banking.
George Selgin's Theory of Free Banking described a version of "macro" free banking that is a bit unusual. He described the operation of a free banking system where each bank issues dollar-denominated monetary instruments and all of them are redeemable with government-issued base money. However, the quantity of base money is fixed once and for all. This is "macro" free banking because there is no central bank providing overall guidance to the monetary order. It fits into the "Mises" version because the assumption is that there is a common unit of account and that banks tie their monetary instruments to that unit of account by redeemability.
Greenfield and Yeager's "Black-Fama-Hall" payments system is a version of "macro" free banking that is also of the "Mises" variety. There is a common unit of account, like the dollar, but rather than being defined in terms of a single good, like gold, it is defined in terms of a broad bundle of goods. The sum of the dollar prices of the items in the bundle must equal the defined dollar value of the whole bundle, but the dollar price of each good in the bundle is free to vary with supply and demand. Rather than being tied to the bundle-defined unit of account by redemption in all of the various items in the bundle, the dollar-denominated currency and deposits issued by banks are redeemable in terms of some redemption medium, perhaps gold, equal in current market value to the total value of the bundle. The price of the redemption medium varies with supply and demand. This fits into the "Mises" version of macro free banking because there is a common unit of account and the banks tie their money to it by a type of redeemability. There is no central bank providing overall guidance. Any monetary policy is generated by the interactions of the banks operating under the system.
Because of problems with the operation of the BFH system, which I call "the paradox of indirect convertibility," some of those who found the system appealing, chiefly Kevin Dowd (and me,) began to favor a modified system that I call index futures convertibility. Again, the system assumes a common unit of account, like the dollar, with banks issuing dollar-denominated currency and deposits. There is a system of redeemability with index futures contracts that ties each bank's currency and deposits to the common unit of account. This approach to free banking was developed on the assumption that index futures contacts would be on a price index defined on some bundle of goods. However, the system can be modified to stabilize just about anything, including a growth path for a measure of nominal expenditure. There is a sort of monetary policy, though it really just the outcome of the interaction of the banks and speculators in futures contracts. Because there is no central bank providing overall guidance, it is a version "macro" free banking and of the Mises type.
I think it is important to distinguish between "micro" and "macro" free banking, and among the "macro" free banking systems, between the Hayek and Mises types. Of course, there is a broad variety of "macro" free banking systems of the "Mises" type too. Oddly enough, the Rothbardians associated with the Mises Insitute favor a Mises version of macro "free banking." a gold standard, while simultaneously favoring a draconian "micro" regulation of the banking system, a 100 percent reserve requirement.
What do I think? As for "micro" reforms, I think reserve requirements are at best pointless and often harmful and should be dispensed with immediately. I also favor the immediate repeal of the ban on private banknotes. I favor allowing banks to issue dollar-denominated currency and token coins on the same terms as transactions deposits. We will then see if banks can induce their customers to use them, though I expect there would be little problem. If private banknotes and token coins are successful, I would favor withdrawing all government currency, like Federal Reserve notes and coins from the U.S. Mint, from circulation.
I don't favor abolishing deposit insurance overnight, and capital regulations are the least bad means of controlling the moral hazard created by deposit insurance. Careful and gradual reform aimed at weaning the banking system from government deposit insurance, while freeing banks from capital requirements is an appropriate long term goal.
I think the Hayek type of free banking should be permitted immediately. If some bank wants to offer deposits or currency in its own unique units, then they should be permitted to do so. Similarly, banks should be able to issue deposits or currency denominated in gold or silver. We will then see if they can induce their customers to switch to a new unit of account. I doubt it that much will come of it and that banks will continue to issue dollar-denominated monetary instruments redeemable into base money.
As for "Mises" version of free banking, I am skeptical of a gold or silver standard or a frozen quantity of base money. I don't believe all the bugs have been worked out of index futures redeemability, but I think that is the right approach for "macro" free banking. In the meantime, I favor having the Federal Reserve target a slow and steady growth path for nominal expenditures. Imposing index futures convertibility on the Fed is a possible first step towards "macro" free banking.