Whereas inflation at least basically forces the wealthy to invest in real assets or else slowly transfer the value of the cash towards debtors.
Yes, we agree on that. However, I think we need to also acknowledge that 1) a large proportion of wage earners have very few, or negative net assets, so deflation actually hurts them and 2) even though deflation helps savers, the biggest savers in the economy are actually the rich. Deflation helps savers, but the people with 80%+ of nominal assets are the already-wealthy.
In fact, the most common form of household wealth is a house, where you own a real asset and owe a nominal debt.
Under inflation, your house value grows at inflation while your debt remains constant, so this even benefits the saver. Under deflation the opposite happens.
> Are we going to act on theories that match the data or does not match the data?
You need more data. The developed world has been on the gold standard since the late 19th century through to the 1970s. During that time the US has seen:
- the Robber Baron age and the Long Depression (where the rich got much richer)
- the roaring 20s, when wealth was more distributed
- the subsequent crash and the Great Depression, where the entire world was in misery (but inequality was very high)
- WW2 and the post-war era, which saw large decreases in wealth inequality
Seems a bit silly to say that 'the gold standard was responsible for lowering wealth inequality', given the huge swings back and forth in inequality while we were on the gold standard over 100+ years.