What’s the math on inflation?

I’m not a macro person, I can’t even play one on TV.  That said, from 20,000 feet, with my admittedly blurry glasses on, I really don’t understand why the Fed and other central banks are pushing so hard on the brakes.  What follows are questions, skeptical about rate hikes, but genuinely questions.

What exactly would have happened if the Fed had raised rates more moderately, or even not at all?  Would inflation have spiraled out of control?  It’s hard to see how that would happen; instead, it seems that demand would have come back into balance with supply as pandemic savings get spent and inflation slowly wears away at real wages and supply problems caused by the pandemic and energy problems in Europe from the war in Ukraine ease.  And even if inflation were to become embedded (whatever exactly that means) and overshoot a bit, and maybe lead to a slowdown in a year or two, well, would that be worse than a world wide recession induced by central bankers?

On the other side of the ledger, the risks to the world economy seem pretty high right now, with turmoil in Britain and China, the war in Ukraine, a looming energy crisis in Europe, and rising interest rates putting pressure on countries around the world.  And does it really make sense to encourage large capital flows and cause asset prices to plunge, given the hard to quantify risks that poses to financial stability?  Maybe a modestly overheated economy with a bit of inflation is just what we need to power our way through the current unsettled situation.

I’d like to see someone describe possible outcomes in detail and put probabilities on different outcomes under different interest rate policies.  How likely is it that the price level rises more than 5% in 2023 or by a cumulative 10% through 2024 if the Fed leaves interest rates alone (or rolls back past hikes)?  How bad is this?  How likely are different recession scenarios?  What exactly happens if inflation becomes embedded?  How likely is this despite the lack of cost of living contracts?  Will embedded inflation, if it occurs, lead to a worse recession than sharp rate hikes now?  With what probability?  Would the Fed lose credibility if it fails to take tough action on inflation, even if there is no indication of ongoing monetary or fiscal unsustainability?  What does this look like?  Where do investors park their money if not here?  And how confident are we that a recession right now is better than a recession in a couple of years, given the current state of the world?  What’s the math here? 

To what extent does the optimal response here depend on the extent to which inflation is being driven by supply constraints rather than demand?  What do we really know about adjustment to supply shocks?

Is the case against inflation primarily political (people hate inflation, Fed needs to defend itself, whatever) rather than economic?  Is the fear that politics will force an even more severe rate hike if inflation doesn’t moderate in the next few months?  How likely is this, and how does this scenario get downgraded if gas prices are the main driver of political discontent?  No matter what your political analysis is, how sure are you that the political benefits of inducing a recession at this rather fraught moment justify tightening? Maybe the Fed is right to hit the brakes.  There are smart people I greatly respect who think so, but I haven’t seen anyone work through the different scenarios and assign values and probabilities to different outcomes.  Does the Fed do this internally?  I have no idea; my fear is that people latch on to specific theories and then discount the possibility that those theories are wrong.  Can someone point me to this kind of analysis?  Isn’t this what we should look for?