Thursday, May 12, 2016

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

p_{M} : AD & \rightleftarrows M\\
r_{M} & \rightleftarrows p_{M}

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.



[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.


  1. If I understand you correctly, you're saying pegging interest rates is a precursor to hyperinflation. And one piece of evidence you cite is the pegging of rates during WWII in the US and the subsequent period of high inflation after the peg was removed. Is that correct?

    1. Hyperinflation takes a bit of time to get started -- even low inflation can be the first part of a hyperinflation (I should really just say accelerating inflation).

      The model I am using has a couple different "solutions", one of which is a kind of general equilibrium solution (GES) and the other is an accelerating inflation solution (AIS).

      With regard to the US, no one solution can fit over the period with the WWII/post-WWII interest rate peg. The GES's work well on either side, but the AIS works well in the middle corresponding to the inflation peaks during/after WWII:

      More on that here:

      Another thing the AIS does is change the relative size of NGDP and M0 so that NGDP is much larger compared to M0. When this is true, high inflation becomes a part of the GES -- and we saw that as the burst of higher inflation during the 1970s. When M0 and NGDP are closer to each other (like in Japan) inflation is low.

      Summary: During the peg, AIS started on its way. That set up conditions for high inflation in the GES that followed (a large economy with a small monetary base).

    2. The problem is that you have ignored the price controls brought in by the Roosevelt administration during 1942. The price of goods and services were more or less suppressed until June 1946 when the price controls were removed. From that point on, inflation took a noticeable turn up. It is said (paper by Paul Evans 1982) prices were suppressed by 30% during this time of controls, so it is no wonder prices took off. Also the interest rate peg wasn't removed until a year later. This all goes to say that the interest rate peg had nothing to do with the inflation burst after 1946. So your blunderbuss way of doing economics has failed you. You have to look behind the raw correlations you see and study economic history in detail. It looks like your new monetary policy technique is dead in the water.

    3. Interest rates remained pegged through 1951 which was ended by the Treasury-Fed accord

      more here. You can see it in the data here:

      You say this:

      The price of goods and services were more or less suppressed until June 1946 when the price controls were removed. From that point on, inflation took a noticeable turn up. It is said (paper by Paul Evans 1982) prices were suppressed by 30% during this time of controls, so it is no wonder prices took off.

      What does "more or less" mean? What does "suppressed" mean? What is the counterfactual? What are the dynamics? What does "took off" mean? What are the order of magnitude sizes of the different effects? Does monetary policy have any impact? Does it have zero impact? Why? What are the relative impacts of monetary policy and price controls?

      How does this fit together in a theory that explains more than just a few years between 1942 and 1946? Does this theory predict anything?

      Is there 1942-1946 US economics, 1946-1951 US economics and 1951-1979 US economics, 1987-2008 US economics, 1970-1990 UK economics, and 2000-2008 Nigerian economics? What good is economics then? A special theory for every event? That's not theory -- that's a series of just so stories.

      As I mention in my footnote, I am open to other ideas but not if they're just talky philosophical just-so stories ...

    4. "What does "more or less" mean? "

      The price control process was not 100% successful. It took some time for control of food and farm prices to a degree to be acceptable to the protocol managers.

      "How does this fit together in a theory that explains more than just a few years between 1942 and 1946? Does this theory predict anything?"

      You're the one that is using this period as evidence for your theory that pegged interest rates are a precursor to hyperinflation. You're the one that's proposing a "special theory" based on one "event".

      I am not proposing a theory but merely reporting the facts - facts which you were not aware of I presume and if you were aware of them you ignored them.

      And for your interest's sake, Evans paper also argues that the same suppression of inflation could have been effected by monetary policy without the employment and output side effects.

      The problem with your approach is that you take a price series and an interest series and think you have identified a correlation upon which basis you develop a new monetary policy approach. You have bitten off more theory than the facts allow you to chew.

      As for this chart:


      This chart you have used is for stock exchange loans. Hardly relevant. Take a look at the 3 month treasury rate chart. It was freed in June 1947. This chart conforms with the chart in your piece:

      You seemed to be more than happy to use it in that piece.

    5. It's not a single event (Germany's hyperinflation was accompanied by pegged interest rates). And it wasn't just the short rates that were pegged at 3/8% -- the long rates were capped at 2 1/2%. The Fed wasn't independent of the Treasury until the Treasury-Fed accord of 1951.

      I think this mis-identifies what I am doing:

      The problem with your approach is that you take a price series and an interest series and think you have identified a correlation upon which basis you develop a new monetary policy approach.

      The underlying model is about information theory, and produces essentially supply and demand arguments to rigorously produce models. The "correlations" are actually just comparison of the models to data. If they fail, they're rejected.

      You also said:

      I am not proposing a theory but merely reporting the facts

      Those are not "facts", they are model dependent conclusions. The model Evans uses in 1982 assumes that price controls suppress inflation and then goes on to show by how much. Without that model, we have no idea what the counterfactual is. Therefore we have no idea if the price controls suppressed inflation and no idea that it produced a post-price control inflation.

      This is not to say what I'm saying above isn't model dependent (it is) -- it's just that there really aren't any model-independent "facts" where counterfactuals are involved.

      Whichever model best fits the data and is the most broadly applicable is the best model.

    6. "The "correlations" are actually just comparison of the models to data. If they fail, they're rejected."

      As I've pointed out, the raw correlations don't tell you everything.

      "Those are not "facts", they are model dependent conclusions."

      I have no model. It is a fact that there were price controls during the war.

      "Whichever model best fits the data and is the most broadly applicable is the best model."

      Thanks for that. Any comment on motherhood?

      And as for the German hyperinflation, you can only understand that by understanding the economic history, not by merely noting its correlation to pegged rates.

      You like skating on wafer thin ice, don't you.


    7. I have no model. It is a fact that there were price controls during the war.

      Inflation involves a model. You have nominal prices that are observed; you need a model to figure out the "real" prices and therefore inflation.

      You also need a model (called a counterfactual) in order to say prices would have been different without the price controls.

      Your model is implicit. Let me just quote Paul Krugman:

      Any time you make any kind of causal statement about economics, you are at least implicitly using a model of how the economy works.

      Price controls caused less inflation is a causal statement.

    8. In many respect you argument about counterfactuals borders on the absurd. I think the fact that the Roosevelt administration felt the need to legislate extensively and set up the Office of Price Administration indicates there was a need for price control and that without it prices would have moved off strongly. The fact that as soon as controls were removed prices took off immediately is a correlation you ignore. Why not accept this correlation. You are quick to accept others quickly, why not accept this one?

      Obviously, the answer is that it is does not conform to your latest pet theory.

    9. "
      Inflation involves a model. You have nominal prices that are observed; you need a model to figure out the "real" prices and therefore inflation."

      I've answered this in my previous post.

      It's like you want to argue that a gorilla imprisoned in a cage happily sits there because it wants to. It's sits there because it can't go any where else. It's pretty obvious.

      There is no implicit model.

    10. There is an implicit model.

      I wrote up a new post about the price controls:

      Maybe this will help you understand how you can't have price controls reducing inflation without knowing what inflation would have been otherwise.

  2. Jason,

    Ignoring Noah's apparent confusion (sometimes his theoretical agnosticism leads him to be logically inconsistent, hence your 'inflation is over-determined' statement), economics provides us with a clear understanding (in my opinion) of how inflation works: inflation is the difference between the growth of the (nominal) money supply and (real) money demand. Since I want to think the central bank controls inflation somewhat directly, in this case 'money supply' means monetary base.

    This leaves the question of what shapes the demand for money, which is where all the confusion comes in. Nevertheless, you and I both agree (regardless of how we get to the conclusion) that real money demand depends negatively on short term nominal interest rates and positively on real GDP (equivalently nominal money demand is a negative function of i and a positive function of NGDP).

    In a static model this prescription makes perfect sense: increasing the money supply leads to some combination of lower nominal interest rates and higher NGDP/inflation (depending on stickiness of prices). Add more time periods and rational expectations and everything is a bit more murky; now there are multiple equlibria associated with a nominal interest rate increase, for example. Regardless, a few things remain clear: inflation should follow money growth almost one for one unless 1) the money growth will be (don't care about expectations because central bank can communicate where the money supply will 100% chance be in the next period if it wants) reversed or 2) the nominal interest rate is already zero (i.e., liquidity trap).

    This view seems to be pretty much empirically accurate to my knowledge: liquidity trap countries (EA, UK, Japan, US, etc.) have increased their monetary bases to no avail in the last 8 years while the developing world is chugging along nicely with IS-LM. Thus, I find "I'm not sure we understand inflation" a bit unfounded -- maybe that can be said for the likes of Scott Sumner and now Noah Smith (whose theory agnosticism makes him seem like he doesn't have a clue about monetary economics, which may or may not be true), but existing mainstream economic theory, if people actually understood and paid attention to it, can in my opinion explain just about everything that has happened in the last 8 years. In short, Krugman is right.

    1. Hi John,

      Insightful as always.

      I don't think I made my main thread as clear as I would have liked. Yes, IS-LM does well with today ... but it is something of a disconnected theory. There is no single theory that connects the basics of supply and demand (more money means inflation), the IS-LM model (low inflation), and the high inflation expectations/hyperinflation worlds. As Noah put it, they are little epsilon-sized balls of knowledge with no indication of how big epsilon is -- and they don't seem to overlap.

      And then we need all that plus empirical accuracy.

      That's why I mentioned the airplane on the treadmill. The different explanations are not mutually consistent (and one is flat out wrong).

      I don't have any problem with Noah's agnosticism; it brings into stark relief the issue of multiple mechanisms that exist in various parts of economics (supply and demand, expectations) and there is no ur-theory to tell us which argument to use when. We have to rely on which one gets it right ex post data -- and deciding on a theory ex post data is problematic.

      I agree that the Krugman view seems to get the basic dynamics right, but it's totally inconsistent with hyperinflation. Some central banks are credible and some are not and some can't credibly promise to be irresponsible and some can't credibly promise to be responsible are several disparate islands of knowledge. How do you transition from being credible to not being credible?

    2. Jason,

      The only reason I see for IS-LM failing to explain hyperinflation is that it assumes constant prices. I don't see how you could ask a model that can't have a hyperinflation to explain dynamics during a hyperinflation.

      This is why using dynamic models is important -- m_t - p_t = y_t - a i_t is literally the LM curve in IS-LM, just allowing for multiple periods. Add sticky (but not permanently stuck) prices and a Fisher relation (i.e., a dynamic IS curve) and you have a model that explains everything at once. Exactly how you get to sticky prices and the kind of expectations you use determine the dynamics of the model -- ad-hoc Phillips curve and adaptive expectations get you neoclassical synthesis and NKPC and rational expectations get you a New Keynesian model -- but the basic story remains clear: mainstream macro is remarkably consistent on inflation, so as long as you ignore MMT and Market Monetarists, you should find something relatively clear (granted a lot of people don't have a clue about how theories fit together and don't realize that, e.g., FTPL is a special case of the same model that they probably use, but what different people say doesn't change the math).

      I think I've linked this to you before, but this textbook chapter from Michael Woodford and Benjamin Friedman explains everything pretty well, especially how FTPL fits in with mainstream theory: link

  3. "Cullen tells us that inflation due to monetary policy is unpossible:"

    I've never said that. I said this specific instance of QE within this specific environment wouldn't cause inflation. In fact, I've repeated (hundreds of times) that QE1 definitely caused inflation. And I've clarified on hundreds of other occasions that there are implementations of monetary policy that would absolutely be inflationary.

    Jason, are you sure you understand the approaches you're regularly criticizing? It looks to me like you don't. Your recent criticisms of SFC and accounting have been way off base and your criticism of me is just flat out wrong....

    I love a good internet back and forth, but when the critic clearly doesn't understand what they're criticizing it doesn't help anyone better understand anything.

    That said, I appreciate what you're doing and find it very interesting!



    1. Cullen,

      Sorry if I misrepresented your view -- I thought discussing everything in the context of today's low inflation environment and quoting the piece about law changes identified it as specific to the US situation; I will add more clarification.

      I do think I grasp your main point. Describing QE as an asset swap a) means high inflation won't happen and b) is a perfectly logical deduction. I am not primarily concerned here with accounting identities or the SFC approach.

      The main reason I borrowed your quote was that a) you think fiscal policy can lead to higher inflation and b) your blog post was in direct response to Noah's. I would have used an older Paul Krugman post on fiscal policy in the absence of your post. I have no specific problem with fiscal policy raising nominal output -- I believe it myself.

      So I'll add a clarification restricting the "unpossibility" of high inflation to our current situation.

      RE: SFC

      I'll admit I must not get what is going on. If you couple a change in stock to a flow, you should get a time scale (time constant). On one side I have a stock/segment of highway (ΔS), on the other I have a flow/speed (v = dx/dt). These are not the same thing, so the only logical way to connect them is with a coefficient ΔS = c dS/dt. It's fine if you want to assume c = 1, but it is an assumption. I am not some kind of slouch when it comes to differential geometry and what we have here is a pretty clear case of a trivial connection.

    2. Hi Jason,

      I think we're really far apart on the way we view things. I'll just say that you still don't have my views on QE in this environment right (and it's more operational and less about the specific environment).

      I've described my views on QE in excruciating detail so if people learn something from them then great. But I am not really into trying to convince people that my view is right or that they should even care about it so I'm gonna go drink some beer instead.

      Have a great weekend. Keep up the good work.


    3. You have a great weekend too.

      I think all I said was that you disagreed with Noah about how QE worked and thought fiscal policy could raise inflation; if that is a mis-characterization then I'm sorry and I've misunderstood.

  4. Japan is pegging interest rates negative all the way out to 10 year bonds. Do you then predict they are headed for hyperinflation?

    1. This does not appear to be true; I see no pegging in the interest rate data ...

      Is there some other source of this information?

    2. So if a country keeps lowering their interest rate peg you would not count it as an interest rate peg? You do realize that these negative interest rates are due to actions by the central banks, right?

    3. What peg? There are fluctuations up and down at each point in the 10 year rate. A peg would appear as a flat spot or a series of steps. Like this:

      An interest rate target (conducting OMOs to maintain a given interest rate) is not an interest rate "peg" (a fixed price for a treasury bill).

  5. Cullen defines money to include government bonds. If you do this then "making money and buying bonds" is "just an asset swap". What Cullen ignores is if you do this then every time the government issues new bonds it is increasing the money supply and inflationary.

    1. I would also argue that counting bonds as the same as money does not fit with the empirical evidence of inflation as well. In practice just issuing bonds and spending is not nearly as inflationary printing money and spending is. You can think of this as bonds not circulating like regular money so lowering the overall velocity of money, and so not causing inflation. But it seems easier to just not to count bonds as money. But there are such long and variable delays in inflation that it is tricky to analyze.

    2. That implies a model where increasing the money supply is always inflationary ... however, I would agree there is no evidence that issuing bonds leads to inflation.


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