My takeaways are that:

a.) Interest rates are going way up from here.

b.) Even if the Fed moves to where the dot-plots are projecting - about 3% in 2024 - it is way too little to contain inflation. I think their assumption is that inflation will come down on its own as supply-chain issues abate, but I don't share that assumption with the Fed.

OP's equation for the Taylor Rule is...unorthodox [1]. For those who don't want to calculate equilibrium real interest rates and take logarithms of linear trends of GDPs, the Fed has a heat map tool [2].

It says 7 to 9%, using defaults. Higher than 3%. But within the model's error bars. (All that said, I have more confidence in inflation being manageable than rates remaining below 3%. Trading on that hunch, however, would require fighting the Fed. You don't fight the Fed.)

[1] https://en.wikipedia.org/wiki/Taylor_rule#As_an_equation

[2] https://www.atlantafed.org/cqer/research/taylor-rule

Side question: how do we calculate that correlation? To clarify, I understand that you can take two sets of observations and calculate rho, etc.

What I'm really curious about is how (or whether) the correlation is adjusted. Suppose there is always some kind of base inflation that doesn't correlate with interest rates; do we have a sense for what the additive effect of changing interest rates does?

Sorry to clarify - you can run any correlation on those two lines (wither lagged or not) and you'll find very little direct relationship, but the more important point is:

By saying interest rates and inflation are not correlated, I meant that both inflation and interest rates were declining to historic lows, which is in direct opposition to the theory that 'raising interest rates reduced inflation.' As you can see on this chart, interest rates aren't even that much lower than they were in the period where we were worried we'd never see inflation ever again.

My main gripe with the current narrative around inflation is 'does it really seem logical that moving from 2.5% to 1.0% 10Y yields is what caused inflation (when going from 7.5% to 2.% had no effect), given all we know about how broken our supply chains have become?'

Edit to change QT to QE

2) My gripe with the stimulus argument is 'why is inflation accelerating 12 months after we stopped'? For example, are used cars (a major contributor to current inflation) really going up in price b/c people can afford to pay higher prices, or is it because we are making way fewer new cars? Same story for houses (given that we've chosen to abandon billions of sqft of office space and replace that with at-home offices).

Sure, loose money support isn't helping inflation, but the idea that the solution to our current inflation problem is to decrease demand seems unthoughtful, given the fact that we know we are producing well below our potential (on a global scale).

I actually don't disagree with you that inflation will go down in the next 12 months, but I think it will primarily be on the supply side. At least I hope so.

Okay, these are all demand issues, and you point to the concomitant supply issues as well. And I agree. The supply issues certainly make it worse.

But here's where we disagree and I encourage you to answer this question:

Are cars/gas/consumer goods/food going up in price because consumers can afford to pay more for them (demand-side) or is it because we are making less of that stuff? I agree it's both, but it appears to be supply WAY more than demand (given how loose monetary policy has been for 20+ years and how unprecedented this supply shock is)