I'm so old I can remember 4 (or more, depending how you count them) *different* stories about why the Central Bank raising interest rates would cause inflation to *rise*.

Have I thought about this possibility? Oh yes.

Let's go through them. 1/n

1. "Cost of Production" story.
This one was very popular back in the 1970's.
Basic idea: "Interest is a cost of production, so if the CB raises r, that raises costs, and so raises prices." 2/n

Historically, empirically, that story failed miserably in the 1980's. Which is probably why I haven't heard it since.
(Though @beckyquick83 reminds me of the mortgage interest in CPI story, which is a variant.)

But why, theoretically, did it fail? 3/n

Simplest version of the story I can think of:
Firms borrow to hire labour to produce goods (wine?) that gets sold 1 year later.
So P = (1+r)W in 0 profit equilibrium.
So if r up, P up, right? 4/n

No, wrong.
You could also use that exact same equation to argue r up, so W down.
Or that firms make losses.
Inflation is a *general* not partial (dis)equilibrium question. You need more equations. Think of the economy as a whole. Your ceteris might not be paribus. 5/n

And, *even if* we accept the "cost of production" premise, that gives us only a *one-time rise in the price level*, not an *ongoing higher inflation rate*.

If higher r causes lower Aggregate Demand, it puts *permanent downward pressure* on P & W, until the CB cuts r again. 6/n

2. "Neo-Fisherian" story.
"Given Long Run monetary superneutrality, the Fisher equation tells us nominal r and inflation move together as we change monetary policy. Therefore, if the CB uses a nominal r instrument, r up causes (LR) inflation up." 7/n

A much more recent story (2010ish?).
Put forward by much better (though still totally wrong) economists.
I've already done far too many blog posts on this.
So I'm just gonna do the TLDR (after I get coffee): 8/n

In this story, the equilibrium condition is (approx) correct (IMO).
But do we have a mechanism to get us there/is it stable?
*Generally*, no.
To see why, ask yourself an apparently unrelated question: 9/n

Suppose a CB creates Money by lending it at rate r. If it wants to increase money creation, should it raise or lower r?
The standard answer: it should lower r. Then raise r later, when money growth, inflation, and expected inflation, all rise, to stop them spiralling higher. 10/n

If we assume hyperinflationary/deflationary spirals can't happen [they can], the only possible equilibrium is the LR NeoFisherian one.
But this requires that everyone interprets the higher r as the CB's signal of a higher inflation target, plus 100% CB credibility. Nope. 11/n

3. A "Monetarist" story.
(That surprised you, didn't it?)
You maybe haven't heard this one.
But I'm including it because:
1. It helps us understand the other stories;
2. It's right (under some circumstances) 12/n

To keep it simple:
1. Ignore currency (so CB money is bank reserves, that pay interest r).
2. Assume CB profits/"seigniorage" =0 (or just hold it constant).

Then, CB interest on reserves is financed by creating new reserves.
So r = money growth rate -> inflation rate. 13/n

4. The "Fiscalist" story (or stories).
This one comes in many different versions.
From lots of different parts of the Macroeconomic theory spectrum (horseshoe theory?).
But they all have one thing in common:
A link between monetary & fiscal policy. 14/n

Central Banks are (usually) owned by govt.
(How independent can CBs ultimately be?)
And (usually) give all their profits to govt.
(So fiscal budget linked to CB actions.)
And inflation may depend on both fiscal & monetary policy. And on expected future fiscal & monetary. 15/n

You can see where this is going:
Give any group of economists enough possible interactions between M & F & P, tell them to get creative, and you get lots of different answers for the effect of M on F on P. 16/n

And my "Monetarist" story above is just a very simple version of a "Fiscalist" story:
The govt tells the CB it must make a certain level of annual profit (0 simplest, but whatever), so if the CB pays higher r on reserves, it must print more money, right now.

So how can we resolve this, and figure out which of those theoretical possibilities is right?
1. Empirically. But CB actions don't give us a nice RCT. "Friedman's Thermostat" says targeting inflation is like the *worst possible* experimental design. 18/n https://worthwhile.typepad.com/worthwhile_canadian_initi/2009/01/why-theres-so-little-good-evidence-that-fiscal-or-monetary-policy-works.html

But we can look at (rarer) "regime changes", where the (implicit) inflation target changes.
Old (Canadian) me can remember one big regime change 70s->80s. Where the "cost of production" story failed, and disappeared. Them other stories would have failed too. 19/n

Or we can say "it depends". Because *maybe*, the answer really does differ across countries & times.
And then go back to first principles and try to say what (ideally *minimum* number of *ultimate* things) it depends on. 20/n

So here are *my* ultimate things:
1. "Never reason from an interest rate change". NeoFisherians illustrate one example of how this can go badly wrong. Nominal (even real) interest rates are a bad measure of the tightness/looseness of monetary policy. 21/n

2. We measure inflation against the Unit of Account. And CB money is (currently) that UoA.
Govt bonds are not UoA; they have a price of their own.
So it's Demand & Supply of CB money that ultimately determines the equilibrium price level, not D & S of govt bonds. 22/n

3. Bonds are promises to pay fixed amounts of (CB) money. Money is not a promise to pay fixed amounts of bonds.
It's like an asymmetric pegged exchange rate regime: if USD pegs to CAD, BoC controls US inflation.
B pegs to M, M does not peg to B, so M leads, B follows. 23/n

4. Given the CB's instrument (whatever that is), there are 1001 different things that could affect inflation. Fiscal policy is just 1 of those 1001.
But: an *independent* CB can and will *offset* those 1001 things if it wants to keep inflation on target. 24/n

So ultimately, it comes down to CB independence.
If the CB tightens, this may worsen the govt budget through *multiple* channels.
Will the Big Guy with the AK47 (eventually) respond and tell the CB to loosen even more?
Canada? No (so far). But YMMV. 25/n

But don't say "govts never default on their own-currency obligations" as if that resolves the Chicken endgame.
Can someone please reply/link that old BoE(?) working paper which lists counterexamples? Thanks.

Gotta get dressed. Thanks for reading. 26/end