Many advocates of free banking favor a return to a gold standard. While such proposals often include an option clause for banks to temporarily suspend redemptions of deposits and currency, the option traditionally involved paying bonus interest during any period of suspension. The effect would be a dampening of the increase in nominal interest rates that would otherwise be caused by a credit crunch as depositors and banks scramble to accumulate gold coin and reserves. Negative nominal interest rates are unlikely to develop during such a suspension.
If the fundamental nominal value of the economy with free banking is instead a 3 percent growth path for total cash expenditures, then negative nominal interest rates on some financial instruments might not only be possible, but necessary. With free banking, no one is obligated to issue zero-nominal-interest hand-t0-hand currency. If it becomes unprofitable to issue it, no one will. The only remaining money would be transactions accounts. There is no reason why the nominal interest rates on deposits cannot be negative. If the natural interest rate, the real interest rate where saving equals investment, is negative, then keeping total cash expenditures growing on target might require negative nominal interest rates.
Of course, there is nothing to prevent people from responding to negative nominal interest rates (or negative real interest rates,) by purchasing commodities such as gold. Outside of a gold standard, the impact of a greater demand for gold is an increase in the money price and relative price of gold.
In the most plausible scenario, where the natural interest rate is only temporarily negative, and will return to its normal positive value in the future, this run up in the money and relative price of gold would be temporary. At some future time, when real and nominal interest rates are again positive, this source of added demand for gold would disappear, and the money and relative prices of gold would fall again.
Expectations of this process suggest a simple equilibrium condition. The money price of gold would rise to a point where its expected rate of decrease is equal to the negative nominal interest rate. Nothing in that process puts a floor under the nominal interest rate.
Of course, since negative nominal interest rates in this scenario apply only in the near future, so that only short term assets have negative nominal yields, gold would be very unlikely to have a negative yield. Like long term bonds or equities, the process would simply lower its expected positive yield until markets clear. Further, negative nominal yields most plausibly apply to low risk assets. Since commodities speculation is very risky, any flight to gold created by negative nominal yields on short and low risk assets would simply result in a slightly lower expected yield on gold.
There is a second effect of increased gold demand that does tend to put a floor under the nominal interest rate. Gold is an outside asset. It represents wealth to those holding it, but it is not a liability of anyone. If the money price and relative price of gold rises, those who are holding gold earn capital gains. They are wealthier. No one is poorer.
This added wealth makes increased present and future consumption possible for those individuals earning the capital gains. Assuming that some of those wealth holders face binding budget constraints, then they will consume more now. This is a decrease in current saving. A decrease in the supply of saving raises the natural interest rate. If the natural interest were negative, this makes it less negative. If the effect is strong enough, the natural interest rate will rise above zero. (This is the same thing as the "Pigou effect" in the context of a gold standard.)
Of course, a better way to understand this process is that there is a wealth effect that makes saving more interest elastic. As the natural interest rate falls, capital gains on gold results in more current consumption and a smaller quantity of saving supplied. And there is nothing special about gold. Land is probably the most important outside asset, but silver, jewels, and artwork should have similar effects. The notion that nominal (or real) interest rates might be permanently negative with certainty is very implausible because of this effect. (Though if that is the effect keeping real yields positive in the long run, it would be enough to make make one into a Georgist.)
It is conceivable that increases in the money and relative price of gold could have disruptive as well as equilibrating effects. The process by which the expected nominal yield on gold falls (perhaps turning negative,) involves an initial increase in its price. If there are foolish investors who project past price increases in to the future, and then invest in gold on that basis, an unsustainable bubble might develop. Such a bubble would be exacerbated if investors who understand the fundamentals adopt a "greater fool" strategy aiming at separating the foolish investors from their wealth. Perhaps even more troubling is the prospect of many "greater fool" investors playing poker with one another, speculating on when the bubble will burst. Since such a bubble appears as an investment opportunity, it could even raise investment demand and the natural interest rate!
With a gold standard, changes in the supply or demand for gold still impact its relative price, but the "money price" of gold is fixed by definition. The price level changes with the supply and demand for gold.
For example, if low nominal interest rates on short and safe assets result in an increase in the demand for gold, the equilibrium relative price of gold rises, and the equilibrium price level falls. If prices, including the prices of resources like labor, are perfectly flexible, the actual price level falls with the equilibrium price level. Where does it stop?
If the natural interest rate is negative over a short time horizon--i.e. the real interest rate needed to keep saving and investment equal over a short time horizon is negative--then the relative price of gold rises to a point where its expected future rate of decrease is equal to the negative real interest rate. With a gold standard, the price level falls to a point where the expected rate of inflation is equal to the absolute value of the negative natural interest rate. The nominal interest rate is approximately zero, and the real interest rate is sufficiently negative to keep saving and investment equal in the short run.
In a world with perfectly flexible prices, holding gold is no more risk free than it is in a world where the money price of gold is free to adjust with supply and demand. However, with an effective gold standard, all debt contracts are tied to gold. If the relative price of gold falls and the price level rises, not only gold, but all debt contracts denominated in gold take the same real loss. It is not so much that using gold as a standard makes it a safe investment absolutely, it is rather than it exports any unexpected real loss from gold to otherwise short and safe financial instruments.
The second effect is that the lower price level increases the real value of existing stocks of gold. With a gold standard, some of the gold may be held as currency--full bodied gold coin. Some may be held by banks as reserves. The increase in the real value of gold, monetary or otherwise, increases wealth. This allows for increased consumption both now and in the future. The increase in current consumption is a decrease in the supply of saving. The natural interest rate rises. If it were negative, it becomes less negative.
Therefore, the equilibrating process occurs through two channels. The price level falls to a point where its expected future rise makes the real interest rate on short term and safe financial instruments negative, and the increase in real balances reduces the supply of saving so that interest rates don't need to be as negative as otherwise. Saving equals investment, and real expenditures equals the productive capacity of the economy.
As before, along with these equilibrating effects there could be disruptive consequences. If people project current deflation into the future, and so assume that prices will be still lower, the demand for gold might rise further, generating an unsustainable speculative bubble in gold. The relative price of gold rises to unsustainable levels, which is the same thing as the money prices of other goods fall too low. To the degree there are "greater fool" speculators, trying to separate the fools from their wealth, gold hoarding might be exacerbated. Worse, these "greater fool" investors might play poker with one another, gambling about when the bottom will hit and real assets can be purchased cheap--leaving others with the gold that will soon be losing value.
Leaving aside such catastrophic scenarios, sticky prices and wages and added default risk on what would otherwise be low risk debt instruments due to deflation, add complications to the simple parallel with the impact of a negative natural interest rate on the gold market when the nominal price of gold is free to vary. However, I hope this argument shows that a gold standard in no way guarantees savers a low risk, short term, positive real rate of return. And rather than a correction process that first involves recession and deflation, and then inflation, negative nominal interest rates on safe, short term financial assets is the least bad option. That a gold standard puts a floor on nominal interest rates is a weakness, not a strength.