I have long advocated privatized hand-to-hand currency, and over the last few years, I have emphasized one benefit--to allow for negative nominal interest rates. While this might be necessary to allow for low, but positive, real interest rates in the face of an expected deflation, I have generally been concerned with the situation where negative real interest rates are necessary. By necessary, I mean needed to coordinate saving and investment at levels of real output and income consistent with the productive capacity of the economy.
Similarly, while it might be conceivable that all real interest rates might need to be negative into the indefinite future, I have yet to worry much about such a scenario, being much more concerned by situations where the real yields on short and safe assets need to be negative for a limited period of time. In other words, I am generally concerned with a scenario where market clearing involves positive real yields on risky and long-term to maturity assets (BAA corporate notes or 30 year Treasuries) but negative real yields on six month T-bills or FDIC insured checkable deposits.
Perhaps most advocates of privatized currency favor some version of the gold standard. (Silver or some other precious metal would do as well, of course.) While such a system would provide many of the benefits of privatized hand-to-hand currency, it would not allow for negative nominal interest rates. As nominal interest rates fall, at some point, storing gold (or whatever metal is used) would become less costly than lending. The zero (or near zero) nominal bound would apply.
With a managed fiat currency, one solution to a zero nominal bound is to generate sufficiently high expectations of inflation. At the zero nominal bound, expectations of rising prices reduces the real interest rate consistent with a zero nominal interest rate to whatever level is necessary. If the shortest, safest asset needs a -5% real interest rate, then a zero nominal interest rate and 5% expected inflation will clear markets. The yields on longer and riskier assets can have positive nominal rates consistent with the appropriately higher real rates.
If monetary policy is based upon some kind of inflation target, keeping expected inflation rate at 2%, for example, then this policy is not possible. The zero nominal bound translates into a -2% real bound.
But leave those issues aside. Suppose that privatized hand-to-hand currency breaks the zero nominal bound for interest rates or else, expectations of future inflation can be freely manipulated so that a zero nominal interest rate is consistent with negative real interest rates.
What happens to the gold market when real interest rates on financial assets become more negative?
Certainly, it seems likely that the demand for gold would rise.
Outside of a gold standard, the increase in the demand for gold would result in a higher nominal and real price of gold. Basic supply and demand would suggest that the quantity of gold supplied would rise and the quantity of gold demanded would fall. The market for gold would clear.
Why would the market for gold clear? First, consider a processes narrowly tied to the relative price of gold.
Suppose there is "the" real interest rate and it is negative. The future nominal and relative price of gold is certain. .
If the relative price of gold is expected to be stable or rise, and the real interest rate remains negative, then the demand for gold would rise, raising its current price. If the relative price of gold is expected to fall, but at a rate less than the real interest rate, then the demand for gold must rise, and so the price rises further. If the price of gold is expected to fall faster than the rate of interest, then holding gold is less attractive than holding financial assets, and the demand for and price of gold will fall.
This suggests a simple process leading to equilibrium. The price of gold rapidly to a point sufficiently high that its future rate of price decrease is equal to negative real rate of interest. The price of gold rises to a point where the real rate of return on holding gold is no better or worse than holding financial assets.
In a more realistic scenario, where the real interest rate on short and safe financial assets is negative, and risky financial assets have positive real yields, and further, the nominal and real price of gold is uncertain, then a decrease in real interest rates on short and safe assets should raise the nominal and relative price of gold, but its expected price should be expected to continue to increase at a rate equivalent to financial assets with similar risk characteristics.
More exactly, the assumption would be that a lower (more negative) real rate on short and safe assets causes a substitution into longer and more risky assets, which would include gold. Its price would rise until future expected appreciation matches the return on similar assets.
A second sort of process involves changes in the real interest rate that is needed to clear markets. Again, the lower real interest rates cause some of those who would have held financial assets to instead buy gold, increasing demand, and raising its price. Those who held that gold earn a capital gain and are wealthier. Because of their greater wealth, they increase consumption. In other words, they reduce saving. The decrease in saving raises the natural interest rate.
In other words, this is a process by which a decrease in the real interest rate (perhaps to negative levels) reduces the quantity of saving supplied, and matches it to the quantity of investment demanded. Assuming that some market force or policy rule adjusts the market real rate to the "natural" or market clearing level, this process is one that also reduces the quantity of gold demanded to the quantity supplied as the relative price of gold rises.
Finally, there is the impact on the gold mining industry--the quantity of gold supplied. Thinking in terms of saving supply and investment demand, it is a bit difficult to characterize the impact on the natural interest rate. The gold being mined out today will be available for future industrial purposes. Is it investment? On the other hand, if people had sold off bonds to pay to have their furniture covered with gold leaf, it would look like consumption and reduced saving. Looking at the relationship between the "IS" curve and potential output, this looks to be a rightward shift anyway--added demand for current output.
Of course, the increase in the quantity of gold supplied helps clear the market for gold, but there is also some small effect on the interest rate needed to clear markets. This demand for new gold production is a demand for real output.
And so, looking at the gold market, when nominal and real interest rates fall, the demand for gold may rise. And the result will be a higher nominal and real price of gold. This reduces the expected real yield on gold, but it may also tend to increase the real interest rate that clears markets. It is even conceivable that these effects could keep the real (and ignoring expected deflation,) the nominal interest rate above zero.
One final note--if some investors observe a rising price of gold, and project past price increases into the future, a speculative bubble could develop. Clever investors should sell short into that bubble, and stop it. But, some speculators might buy into the bubble, hoping to sell at the peak, stripping as much wealth as possible from "greater fools."
Even so, the nominal and relative price of gold adjusts to clear the market for gold.
Now, what happens if the nominal price of gold is fixed because gold services as medium of account?