Friday, September 6, 2013


If you let the unit of account enter into the equations in the information transfer model (i.e. let $\kappa \rightarrow \kappa (NGDP, MB)$), you get the information trap. In that situation, the price level has only a weak response to changes in the monetary base. This allows an excellent fit for the model to the empirical price level (data is in green, model fit is blue):

If we look at a given year (say 1985) and look at the model response to an increase in the monetary base (at fixed $NGDP$) we have a price level that rises for a bit and subsequently falls. In terms of the value of a dollar ($1/P$), we get a picture with a fall in the value of a dollar followed by a flattening out (actually a rise) in the value:

This is the information trap (diminishing marginal utility of increasing the monetary base). The dashed line shows the traditional economic view (a long run quantity theory of money) that $P \sim MB$. In that case, increasing the base decreases the value of a dollar and leads to inflation ... and eventual hyperinflation.

The question I want to explore is How do we get hyperinflation in the information transfer model? Hyperinflation was declared to be a political phenomenon by Matthew Yglesias, and there isn't complete agreement on the mechanisms behind it. The government's use of seigniorage as a source of revenue for a failing economy is a common theme, as well as the so-called inflation tax. This all points to the use of a model.

I will take an agnostic approach and only make the assumption that in the market $P : NGDP \rightarrow MB$, the monetary base represents a constant information destination that isn't determined by signals from the aggregate demand (as opposed to a floating information source, i.e. a market determined one). One way of viewing this is that the government or central bank begins issuing base money without regard to any market mechanism while the aggregate demand ($NGDP$) does respond to the signal from the detector of the information transfer ($P$). Performing the integral here results in the equations:

$$ \text{(1a) }P= \frac{1}{\kappa }\frac{\left\langle Q^d\right\rangle }{Q_0^s}$$
$$ \text{(1b) }\Delta Q^s = \kappa Q_0^s \log \left(\frac{\left\langle Q^d\right\rangle}{Q_{\text{ref}}^d}\right)$$

These equations actually define a supply curve in the information transfer model (as opposed to a demand curve). If we eliminate $\langle Q^d \rangle$ and replace the supply and demand with $MB$ and $NGDP$, respectively, we obtain:

P = \frac{NGDP_{\text{ref}}}{\kappa MB_0} \exp \frac{\Delta MB}{\kappa MB_0}

If we include the function of the monetary base $MB$ as the unit of account, then $\kappa = \kappa (NGDP, MB)$, we arrive at

P = \frac{\log NGDP/c_0}{\log MB/c_0} \frac{NGDP_{\text{ref}}}{MB_0} \exp \left( \frac{\log NGDP/c_0}{\log MB/c_0} \frac{MB-MB_0}{MB_0} \right)

If we add this function starting at the given year (1985, fitting to the price level in 1985 and borrowing $c_0$ from the price level fit at the top of this post), we happily (well, in the academic sense) get a rapidly decreasing value of the dollar (red curve):

The price level associated with this curve if we fit to the rate of growth versus time starting in 1985 is shown in this graph (again, red):

The price level in this case basically assumes that the monetary base increases at a constant rate (specifically, the average rate from 1983-1987). This path of the price level results in accelerating inflation:

This is an interesting result! It says that a constant rate of increase in the monetary base results in accelerating inflation (as opposed to the traditional economic view where a constant rate of increase of the base, ceteris paribus, is supposed to lead to constant inflation).

Ah, but this is just accelerating inflation. I wanted to achieve hyperinflation. We can do that if we increase the rate of increase of the monetary base (say, to 30% per year), which results in a faster increase in the price level:

We achieve hyperinflation (>50% annual inflation rate) in no time:

The key choice appears to be selecting a constant information destination in the market $P : NGDP \rightarrow MB$. This choice represents a scenario where the aggregate demand responds to price signals, but the monetary base is instead set by the monetary authority without regard to price signals. Aggregate demand "floats" inside the market, while the monetary base doesn't float and is set outside the market.

The price level fit and information trap at the top of this post occur for both a floating information source and floating destination. In that case, information transmission and reception occur in a market (floating = market): the aggregate demand shifts to respond to the price level and the central bank adjusts the monetary base through open market operations that take into account the price level (in the US there is a de facto inflation target on the order of 2%).

In my next post, I plan to take these observations further, summarize the past several market constructions (IS-LM and LS-MS) and outline a "theorem" where any use of a market to set monetary policy (including interest rate, inflation or even NGDP growth or level targeting) can result in an information trap.


  1. The wikipedia entry on supply and demand in its description of the supply curve allows an interesting interpretation:

    "... the supply curve is the answer to the question 'If this firm is faced with this potential price, how much output will it be able to and willing to sell?'"

    One should add "to make money" at the end of that statement.

    To translate: if the central bank is faced with this price level, how much base money will it be willing to print (to make money)? Essentially, it will be willing to print a larger quantity of dollars at a high price level (since they are worth less ~ 1/P, you need more of them) than at a low price level.

    1. Note that in the hyperinflation case, the central bank (or government) should be seen as trying to make money -- they are not trying to target inflation or NGDP.

  2. I have collected many explanations for hyperinflation and will add an entry for yours after I have digested it. I thought you might be interested in my work. I also have a simulation of hyperinflation.

    1. I would be honored to make it on your list! That really is a great resource you have created!

    2. Great! Can I get you to write a one paragraph summary with the key ideas? I will link to this page so people can find more.

    3. Sorry for the delay; here is the summary:

      Inflation is always and everywhere an information theory phenomenon. If one looks at money as a means to transfer information from aggregate demand (the information source, measured by NGDP) to aggregate supply (the information destination, measured by the monetary base), then there are three possible scenarios. One is the information source is exogenous, while the destination is endogenous -- i.e. reacting to market forces. This scenario describes the IS-LM model where aggregate demand is not set by the money supply and the central bank is reacting to economic conditions. A second scenario is where both information source and destination are endogenous; this leads to a quantity theory of money. In this scenario the information source is no longer external, rather the source and destination move together reacting to each other. In the third scenario we have an endogenous information source and an exogenous monetary base. Here aggregate demand reacts to monetary policy set for reasons outside the economy (e.g. printing base money to fund government operations, or pegging interest rates as the US did in WWII). This not only leads to inflation, but accelerating inflation that, if continued long enough, leads to hyperinflation. It can be immediately ended by pegging the currency to an endogenously set currency (Brazil set its currency to the US dollar), ending a pegged interest rate (as the US did after WWII), or targeting inflation, NGDP, base growth or any other economic indicator. Note that these three scenarios can drift into each other. Under certain approximations (and time scales) aggregate demand/NGDP can be seen to be an exogenous factor in the short run (because it reacts more slowly than changes in the base) or an endogenous factor in the long run (because it eventually reacts to changes in the base -- i.e. long run neutrality of money).

    4. Jason, that's a very interesting paragraph! However, can you use the ITM to determine if a country is ripe for hyperinflation or not? For example Vincent has predicted that Japan may reach 26% annual inflation for multiple months (perhaps as much as a year?) by ~2016. He bases that on the idea that the Japanese CB (BoJ) is the primary government bond buyer currently, that the debt is large (over 100% of GDP) and the deficit has been large, and (I think) that BoJ bond buying continues at a high rate. He estimates a positive feedback loop may develop which proves to be difficult to get out of which ultimately results in hyperinflation. He defines the hyperinflation threshold as 26% annual rate (several economists dispute his threshold, some saying 50% a month is a better figure, but whatever). Marcus Nunes is on record as predicting this will not happen by 2016. Also, Vincent thinks the US is in danger of hyperinflation for much the same reasons that Japan is, but he has not made any concrete predictions that I'm aware of. He acknowledges that in any case, it's very difficult to predict when the feedback loop into hyperinflation will begin. He has had interesting responses from Nunes, Sadowski and Cullen Roche: none of whom share his concern about hyperinflation in Japan or the US in the near term.

      The way I read where your model of where the US and Japan are on your plot of log(P/P0) vs log(MB/MB0) indicates to me that hyperinflation is not likely to occur in either the US or Japan in the near term (say w/in the next 5 years or so?). Would that be reasonable read of your model?

    5. Would that be reasonable read of your model?


      Barring any major political change (e.g. war, Chavez-style populist takeover) there won't be any inflation. But maybe hyperinflation might be preferable to zero inflation.

    6. Thanks Jason. Why do you say hyperinflation might be preferable to zero inflation?

      There are many places that get hyperinflation without war. Certainly 26% is easy to get to. I think Brazil and Argentina are doing that right now.

      You have said that, "a constant rate of increase in the monetary base results in accelerating inflation". Japan is increasing their money supply by around 0.7% every 10 days. How does your theory say the previous but that this does not lead to accelerating inflation? I don't see where "war" is mentioned in your theory. Can you work through how you would use your theory to predict if Japan or the UK were headed for hyperinflation?

    7. I said that wrong, is "war" in any way key to your theory or just one way that governments go overboard in printing money?

    8. Why would hyperinflation be preferable to zero inflation? I only said that it might be and it is highly politically dependent. Hyperinflation can return us to the status quo where monetary policy is the primary tool of demand management. But maybe we'd rather have fiscal policy be that primary tool -- then zero inflation would be preferable.

      Constant rate of increase. By this I meant something like a k-percent rule that ignores economic indicators. Japan's monetary base/currency have "constantly" increased in the common usage of the word, but not the mathematical usage where dMB/dt = constant (Friedman's k-percent rule). Japan may be increasing its money supply by 0.7% every 10 days, but it is not bound by law to do so, nor is there an ongoing war or populist government that is distributing that additional money to the population. The BoJ is trying to meet inflation targets. That is why inflation goes to zero and monetary policy becomes ineffective.

      Brazil, Argentina and War. In both cases, the government appeared (appears) to be printing currency to pay the government's bills (and support populist measures). War is just another potential way that governments will print currency in a way that ignores economic indicators.

      The key point is if the central bank makes the (currency component of the) monetary base endogenous by using some target like inflation, NGDP, interest rates, then inflation goes to zero as the base becomes large relative to NGDP. If the base is exogenous due to paying for a government's fiscal policy or war (or adopting a k-percent rule), then accelerating inflation will result.

    9. I'd also like to emphasize this is all very theoretical at this point. But it does give an explanation for why the BoJ could print so much money and still not be able to meet its inflation targets. Theories of expectations lack explanatory power (how much money could they print before expectations suppressing inflation?) much like theories of eventual inflation (when will inflation take off?). Inflation in Japan really should have taken off by now -- either because markets should realize Japan isn't going to cut its base by a factor of 5 or because 25 years is a long time for a delayed effect.

  3. Jason, Japan is spending twice what it gets in taxes. The extra money is coming from the central bank monetizing bonds. How do you decide that the central bank is not funding the deficit? Just because the head of the central bank says he is using some other policy? I think the central bankers with hyperinflation always say they are working on some reasonable sounding policy and not funding the government. So how can you make any prediction for Japan?

  4. Thanks!... I tried out the search box just now (I look this particular one up a lot).


Comments are welcome. Please see the Moderation and comment policy.

Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.

Note: Only a member of this blog may post a comment.