The effect of a full hiking cycle
Every increase in the policy rate must be followed by a future decrease, or the rate must remain elevated. So if one believes that rate hikes decrease inflation, and rate cuts increase inflation, then you are essentially relying on "sticky deflation" for rate hikes to have a net deflationary effect over the cycle. Most of the literature on interest rate policy refers to "shocks", as in the effect of a change in policy rates on inflation or deflation. I am aware of very little research into the effects of the rate level itself, on inflation or deflation. On this question I am not even clear, whether mainstream economists believe an stable elevated rate is inflationary or deflationary. To believe a stable elevated rate is deflationary, appears to contradict the fisher equation. As for the fisher equation, I believe that it has the flaw, that your measure of inflation is flexible(although not arbitrary), so it becomes impossible to distinguish in the general case