With a constrained, private central bank, the creation of money has nothing to do with public finance but rather with the profits earned by the owners of the central bank. Allowing a higher inflation rate allows the owners of the central bank to profit more by increasing the benefit of borrowing by issuing currency at a zero nominal interest rate. In other words, there are more profits from borrowing by issuing currency at a more negative real interest rate.
Suppose instead that ownership of the central bank is tied to operating a commercial bank. The Federal Reserve banks are jointly-owned by the member banks--commercial banks in their district. In the U.S., these banks earn only a token share of the profit generated by the Federal Reserve system. They receive a 6 percent annual dividend on the shares of stock they own. But suppose the Fed paid out all of its profits as dividends to the member banks?
At first pass, the most obvious effect would be to provide a powerful incentive for nonmember banks to join the Federal Reserve system. With the current rules, where stock ownership is 3 percent of capital and shares are issued or retired by the Federal Reserve banks at a price of $100, there would also be an incentive for banks to raise capital. Unfortunately, one can imagine sham banks being formed as a mechanism for capturing a share of the profits of the Fed.
On the other hand, it would seem relatively simple to change the rules so that stock ownership in the Fed was tied to total assets or perhaps something more closely tied to the banking business, such as commercial lending. As a monetary economist, the most obvious candidate for such a rule would be checkable deposits. Banks are special because they borrow by issuing deposits that can be used as money.
At least at first pass, if the profit from borrowing by issuing zero-interest hand-to-hand currency is distributed to banks in proportion to their issue of checkable deposits, then banks will compete away those profits by paying higher interest rates on checkable deposits. Such a rule would lead banks to fund more of their assets using checkable deposit. Further, it would seem to result in more finance passing through the banks--more intermediation--rather than direct finance.
Most interestingly, increasing the interest rate on checkable deposits would lower the currency deposit ratio. The typical household or firm would hold and use less currency for payments and instead use checkable deposits. This shift in the currency deposit ratio would not impact the total earning assets of the banking system--both the central bank and the commercial banks together, but rather only which institution holds the assets. The central bank lends less and the commercial banks lend more.
As before, this is not an unconstrained system. While it would be possible to have the central bank's currency redeemable in gold, silver, or foreign exchange, it would also be possible to require it to limit issue so to keep inflation on target. By increasing that constraint--raising the inflation target-- the central bank would benefit more from issuing currency, adding to its profit, which it would pass on to the member bank owners, and competition among those banks would raise the interest rates on deposits. This would be beyond the increase in the nominal interest rate paid on deposits due to the higher nominal earnings on loans due to the Fisher effect. The real interest rate on checkable deposits would rise as well as the nominal interest rate.
For those holding the liabilities of the banking system as a whole--the central bank and the member bank--a higher inflation rate implies a lower real interest rate on currency and a higher real interest rate on deposits. The total real demand for holding the liabilities of the banking system would be little affected, as would the total amount of assets held by the entire banking system, again, including both the central bank and the member banks. Shifting from a system where the profits of the central bank are paid out to member banks and competed away through higher deposit interest rates as compared to one where the owner of the central bank (perhaps even the government) keeps the profit, would increase total bank assets and liabilities. But the shifts in the constraining inflation rate would have little net effect on the total assets or liabilities of the banking system.
Suppose that the central bank makes an error, and expands the quantity of money more rapidly than is consistent with its target for inflation. The thought experiment is not a change in the target inflation rate as before, but rather a mistaken excess supply of money.
Assuming expectations regarding inflation are unchanged, (as they should be,) and given that all money creation is matched by increased lending by some part of the banking system--either the central bank itself or one of the member banks--the result would be a decrease in both real and nominal interest rates. For the most part, this is not beneficial to the banking system. At least if the banking system is perfectly competitive, the lower interest rates reduces its earnings, but with all banks earning less, they also lower interest rates on deposits. With zero nominal interest currency, there would be no decrease in the interest rate paid, but given the monetary regime where those benefits are transferred to banks in proportion to their deposits, the interest rates on deposits fall enough to reflect all of the reduced earnings.
Not only do bank depositors, as creditors earn less due to the lower interest rates, the resulting shift of bank depositors to investments in other securities would tend to drive down the returns to creditors who had been investing in those securities. With banks charging less on their loans, firms using direct finance, for example, selling commercial paper or corporate bonds to nonbank investors, also receive a benefit of lower rates. The increase in the supply of funds to direct finance and decrease in the demand for funds for direct finance, results in lower nominal and real interest rates.
The "Austrian" theory would be that the lower market interest rates impact the composition of demand. Those goods with demands that are relatively more interest elastic gain relatively more demand than those goods with demands that are relatively less interest elastic.
However, consider a business that finances its activity by selling commercial paper or corporate bonds to nonbank investors. They, like every other debtor, benefit and expand their borrowing. Some of the "old money" is shifted by bank depositors to direct finance, and some of the firms that were funding activities by selling commercial paper or bonds switch to banks. But those who had been involved in direct finance always are impacted in exactly the same way as those receiving "new money" from the banking system.
That this monetary regime implies that an excess supply of money impacts credit markets is important, but trying to identify which money is "new" is pointless. Not only is non bank finance impacted in the exact same manner, there is no point in trying to identify which client of the banking system received the added money. If the central bank purchases a newly issued bond (private or public) with the additional money, the reduction in the interest rate paid is no different than all the other borrowers who also borrow "old money" from the banking system. Similarly, the lower interest return obtained by the investor who would have purchased the bond that the central bank grabbed by spending the "new" money is no different from the lower interest return obtained by all of those holding "old" deposits in the banks or those investors using their "old money" to purchase newly-issued commercial paper or corporate bonds.
Further, the change in the pattern of demands depends on the interest elasticity of demand for various goods. Those who make extensive purchases of some good because of the lower interest rates don't necessarily borrow the "new" money. Those borrowing the "new" money might happen to purchase something whose demand is very interest inelastic. They would have made that purchase even if interest rates had fallen very little. In the limit, they would have made that purchase anyway with no reduction in interest rates or even higher interest rates. It could be some other household or firm, borrowing and spending "old money," or perhaps, not even borrowing at all but instead lending less because of the lower interest rates, that expands expenditure more than others.
Further, the benefit of the lower interest rates received by all borrowers is not due to spending money before prices rise. In this scenario, the central bank must reverse its error. Even if prices never rise, the lower interest rates due to the excess supply of money benefits all debtors and injures all creditors. If the government had a national debt, then it would benefit from the excess supply of money, like all debtors. And that would be true even if the central bank never held any government bonds!
Identifying the "Cantillon" effects of money with public finance depends on realistic institutional assumptions. With privatized arrangements, there is no impact on public finance. Still, focusing on who gets the new money first and emphasizing the notion that those receiving the new money first spend it before prices rise is wrongheaded.