This gets into monetary supply and other economic considerations.
REDUCING THE SUPPLYThis has a net effect of putting upward pressure on the price of the currency (the purchasing power of the currency).
However, this also has another affect on the economy...
INCREASING THE VELOCITY OF MONEYAs the supply is reduced, with other factors holding constant, the velocity of money increases.
https://www.investopedia.com/terms/v/velocity.aspV = PQ/M
- V = velocity of money
- PQ = Nominal GDP, which measures the goods and services purchased
- M = total, average amount of money in circulation in the economy
It's trivial to see there. As M decreases, V increases.
Velocity of money is a touchy subject sometimes. The article above gives some more info on it.
However, HODLing really is just a temporary removal of coins from M. Regular fiat savings function the same way, but as fiat goes down in purchasing power, it makes no sense to HODL fiat. The best strategy is to spend fiat before it's worth less (not a typo, but could be).
Assume that an arbitrary amount of fiat is saved.
We'll call that X% of M.
X should be relatively stable over time with obvious fluctuations around Christmas, Lunar New Year, etc.
In the Bitcoin world, let's say that Y% is HODLed. As BTC is deflationary, we can assume that Y > X by some factor Z (Y/X).
Z would then represent a sort of value premium (desire to save or desire for higher time preferences) that people have for BTC over fiat.
Further, as Z increases, the effective M decreases, V increases, and the purchasing power of the currency (BTC) increases.
If increases in Z tend to bolster confidence in BTC, Z should increase and create a virtuous circle of savings/HODLing.
At the same time, we know M exactly, but we can't really measure Y or Z very well without looking at Bitcoin days destroyed, which I almost never hear anyone talk about anymore.