I'm not sure we understand inflation

Does anyone remember when there was an argument on the internet as to whether an airplane on a treadmill could take off? This is what I feel like whenever I hear any discussion of inflation and hyperinflation.

To some degree it makes sense if you print a lot of money, inflation should result. It also makes sense that if you print a lot of money and people expect it to be taken out of circulation soon, inflation won't result. And I guess you can find a way to rationalize that if you print money to buy up debt, you won't get inflation because money is a government liability just like debt.

This really hinges on two questions that economics has not solved: What is money? and What is inflation? ... and there's a third that economics never asks: What does the data say?

Generally, we get what inflation is. When a pint of blueberries is €4 one day and is €4.20 a year later, you've experienced 5% annual inflation. But what about an iPhone? They've not changed much in price, but they've gotten more capable. There's a quality adjustment. Because of improvements in various parts of the supply chain, blueberries are in better shape at the store and therefore more delicious (to those that like them) -- and so might get a hedonic adjustment.

You also get inflation (in modern macro) if everyone thinks the price of blueberries and iPhones will go up because everyone expects inflation. You don't even have to "print money" for this to happen. As for what "money" is, well, that's a completely different -- and not understood -- story.

This came up because I saw a Bloomberg piece by Noah Smith and a response by Cullen Roche. It feels like the airplane on the treadmill. Noah first:

Many economists believe that if you print a lot of money, inflation will go way up. That makes sense, since usually if you increase the supply of something its value falls -- inflation is just a decrease in the value of a currency in terms of real goods and services. ... But many people now believe that the danger of hyperinflation isn’t as big as economists believed in the past. The Fed doesn’t actually control the money supply -- it’s controlled by banks. If Fed money creation is balanced out by private banks withdrawing money from the economy, then money-printing almost certainly won’t cause hyperinflation. This is exactly what has been happening in the past few years. As the Fed has created unprecedented amounts of money through asset purchases under its quantitative easing program and swelling the monetary base, the money supply has increased at a modest and steady pace ... And even if the money supply does increase, inflation still might not result -- people might spend their money less frequently, leading to muted pressure on prices. ... Hyperinflation, like a stock-market crash or a bank run, is a phenomenon that depends crucially on people’s expectations of what other people will do. If everyone thinks that no one else will spend their dollars, inflation stays low. But if some people start to believe that other folks are about to go out and spend their stockpiles of cash, they will respond by doing the same, so they can buy things before prices start to rise. That will turn inflation into a self-fulfilling prophecy. And just as with bank runs and stock market crashes, we know that expectations can shift very quickly and catastrophically. Hyperinflation is like a bank run on a national currency.

Note that Noah Smith invokes both the supply and demand argument as well as the expectations argument. Increasing money supply causes the value to fall, but if money supply is expected to increase (even without a supply increase) you can still get inflation! In a sense, inflation is over-determined. He also refers to both the monetary base and M2, even though neither is really correlated with inflation directly.

Cullen tells us that [high] inflation due to monetary policy is unpossible [in our current situation under current law -- Ed. see comment below]:

If you worked through the accounting and the scenario analysis of the flow of funds, high inflation just didn’t add up. ... QE is just an asset swap. ... Now, the US Treasury could print up its own notes (as it has done at times and assuming law changes) and retire the national debt. But this is just an accounting gimmick which changes one government liability (a bond note) for another (a cash note). The quantity of government liabilities doesn’t change, they simply get relabeled. ... [certain fiscal policy] would result in a larger deficit. Which is exactly what the economy needs today! We’re living in a time of extraordinarily low inflation, a shortage of safe financial assets, weak household balance sheets and a period where monetary policy is obviously weak. We need an increase in fiscal policy ... We’ve been running about a -2.5% deficit the last few years with disinflationary trends so I suspect that we could easily run a larger deficit without causing very high inflation.

Much like the airplane on the treadmill, there are completely different implicit models at work here. For Noah, inflation is related to monetary policy. For Cullen, it is related to fiscal policy.

One thing to note is that the idea that the money supply is correlated with the price level is well founded for high inflation, for an example see here. Interestingly, this is exactly the regime where the evidence that increasing government debt is correlated with inflation comes from. That is to say our evidence that fiscal or monetary policy can lead to inflation comes from the same high inflation regimes. At low inflation, changes in the monetary base (QE in US and Japan), M2 (generally rejected), or government debt (again, see the US and Japan) are not correlated with inflation. The scientific thing to do would be to assume scope conditions: the fiscal and monetary theories of inflation apply only at high inflation. It would then be irresponsible to extrapolate the impact of fiscal or monetary policy on a low inflation economy.

So we have three questions:

1. What is inflation?
2. What is money?
3. What is empirically valid for low inflation?

I don't necessarily have a definitive answer for all of these questions, but I'd like to outline how one would go about tackling them in the information equilibrium framework.

What is inflation?

So what is the price (detector) that represents inflation? Is it the price of all goods in the economy? Generically, we'd tackle that with an AD/AS model $P : AD \rightleftarrows AS$, but let's rewrite it as a two step process -- demand, money, supply -- $P_{1} : AD \rightleftarrows M$ and $P_{2} : M \rightleftarrows AS$

We have:

$$
P_{1} \; P_{2} = \frac{dAD}{dM} \; \frac{dM}{dAS} = k_{1} \; k_{2} \; \frac{AD}{M} \; \frac{M}{AS}
$$

equivalent to our original market $P : AD \rightleftarrows AS$

$$
P_{1} \; P_{2} = \frac{dAD}{dAS}  = k_{1} \; k_{2} \; \frac{AD}{AS}
$$

i.e. $P = P_{1} P_{2}$ and $k = k_{1} k_{2}$

In the first market, increasing $M$ causes $P_{1}$ to go down, holding $AD$ constant; in the second market increasing $M$ causes $P_{2}$ to go up, holding $AS$ constant. These would offset each other leading to no change -- because you'd be holding both $AD$ and $AS$ constant.

But can you hold $AD$ constant while changing $M$? Yes, but only if inflation is low. Actually, if inflation is low, you recover the IS-LM model. If inflation is high, an increase in $M$ causes an increase in $AD$.

I realize that someone might want to jump in here and say: If $M$ increases, then inflation is going to be high so the low inflation limit never happens. The problem is that statement assumes the model it purports to prove (increases in $M$ causes inflation), so we need to check that empirically.

What is money?

So what is that $M$ in the previous model? That's another question that should be left to empirical analysis. The best answer I've found is "M0", i.e. the monetary base (MB) minus reserves. This is roughly equivalent to printed currency and minted coins [1]. After I did that comparison, it became more clear that the monetary base reserves are not "money" (at least when considering inflation) using data from several countries.

It turns out that M2 may only be good for exchange rates -- which aren't necessarily related to inflation (rather M2 is related to inflation when inflation is high, so again Noah is using the M2 indicator out of scope).

However, the monetary base (including reserves) is "money" if you look at short term interest rates. That brings us to the third question ...

What is empirically valid for low inflation?

The only empirical result that seems to be valid across different monetary policy regimes (that even include possible WWII hyperinflation) and many years are for interest rates. See here for the Great Depression (the last "zero bound"/"liquidity trap" era), and here for the model covering the 1920s through today. That is to say the scope of the interest rate model covers from low to high inflation.

The model itself is relatively simple

$$
\begin{align}
p_{M} : AD & \rightleftarrows M\\
r_{M} & \rightleftarrows p_{M}
\end{align}
$$

This model basically says the interest rate is in information equilibrium with the price of money. Contrary to what happens in economics typically, the model doesn't say the rate is the the price of money. If $M = M0$, then $r_{M0} = r_{long}$ is the long term interest rate (e.g. 10-year). If $M = MB$, then $r_{MB} = r_{short}$ is the short term interest rate (e.g. 3-month). However $M = MZM$ also works for the long term interest rate.

Here is what it looks like:

And here is another view (NGDP = AD) that I used to show more often:

You can see that M0 follows MB for most of the available history -- which means there isn't much to distinguish them. However as QE was put in place, interest rates fell and we got a strong separation.

If the Fed uses short term interest rates to target inflation, the MB line (light blue) can be used to push the M0 line (darker blue) around a bit. But it appears if it gets too far away (to the right, or below, depending on which graph you're looking at), M0 will only grow so fast. Since M0 is related to inflation, if MB is too large, short term interest rates have no effect on inflation.

One thing that has come out of looking at these models is that hyperinflation (or really high inflation) appears to be associated with pegged interest rates (see here, here or here). Under hyperinflation, the information equilibrium model looks a bit like a chaotic dynamical system with exponential separation of elements of phase space (the equations are roughly the same).

It's the pegged interest rates (or exchange rates) that appear to be key to hyperinflation, not monetary base (MB) growth, printing money (M0) or deficits themselves. The latter seem to happen in conjunction with high inflation, but aren't necessarily the cause -- nor should you extrapolate those models outside of their scope. When you peg an interest rate or an exchange rate, you are breaking an information transfer channel by fixing a price.

...

Footnotes:

[1] If you'd like to mention vault cash or that printing bank notes doesn't cause inflation, but happens in reponse to it, I will listen to you if you show me a series of quantitative empirical success that rival the ones on this page.