Tuesday, September 8, 2015

Do NGDP futures markets already exist?

Unfortunately forex markets don't know they're NGDP markets.

Scott Sumner's big idea is that we should have a high-volume, liquid NGDP futures (prediction) market and use that to determine monetary policy. He frequently suggests that the existence of such a market would help understand macroeconomic conditions (for example, here with Australia).

Now I am not as convinced about the utility of prediction markets [1], but I had the random thought the other day while I was on a flight to New Mexico: Scott's high-volume, liquid futures market exists and is called the forex market.

The exchange rate between two countries is effectively (proportional to) a ratio of their aggregate demands [4]. The ratio of the price of a dollar to the price of a Euro depends not just on the supply, but the demand for both currencies -- the exchange rate is a general equilibrium solution, not partial equilibrium [2]. That is to say, you can look at the exchange rates between each pair of currencies and get a measure the relative NGDP of the two countries. Since exchange rate data is typically available immediately, that gives a forecast of the NGDP number that comes out usually a month (first estimate) to three months (third estimate) after the quarter it represents. You could measure any given currency against a basket of currencies to approximate an absolute measure.

Is there are problem with this?

Yes. Yes, there is.

Forex markets are notoriously volatile (see e.g. the Dornbusch overshooting model). And one of the reasons, at least from the information equilibrium perspective [3], is that it seems traders might have a sign error in their mental model leading to corrections that go the wrong way at first and only gradually return to a normal level (see the picture at the top of this post which is from [5]). For example, in a supply and demand diagram an expansion of the monetary base leads to a price drop for a currency. However, in general equilibrium an expansion of the monetary base is (usually) accompanied by a (relative) expansion in the economy. That is to say additional money isn't printed unless there is demand for it. And demand may rise a little bit, just the right amount or too much -- leading to excess inflation, trend inflation or below trend inflation/deflation.

It is possible to fix this by convincing forex markets that they are NGDP futures markets. But that is dependent on the "wrong model" theory [3, 5] accounting for most of the volatility.

Update + 10 min

I should add that this is relevant. Potentially exchange rates are measuring long run NGDP ratios in the same way P/E ratios measure long run returns which are volatile.

References (from this blog)

[1] Is the market intelligent?
[2] What do exchange rates measure?
[3] Is market monetarism wrong because the market is wrong?
[4] Exchange rates and monetary policy
[5] Exchange rates and irrational markets


  1. This is very interesting. However, I’d like to add a slightly different perspective.

    One of the major problems that I have with mainstream economics (and your version) is that GDP seems to be assumed to be a synonym for the economy. However, that is not correct. If you start by asking what choices we can make regarding money, we can see at least the following five options:

    Spend money on new goods and services (part of GDP)
    Spend money on creating new assets e.g. a new factory or house (part of GDP)
    Spend money on existing assets e.g. an existing factory or house (not part of GDP)
    Save money in a bank as insurance against unexpected future events e.g. breakdown of household heating system, need to buy healthcare in old age (focused saving - not part of GDP)
    Save / do nothing with money until / unless a better idea comes along (default saving - not part of GDP).

    You think of the economy as a box filled with gas molecules. You could see the above options as five separate boxes of gas molecules (with some restricted leakage between the boxes).

    You are suggesting that the forex market is like an NGDP prediction market. I’d suggest that it is more like a prediction market for the combined five boxes. That might be a part explanation of why forex markets are volatile.

    For example, the UK is normally seen as a safe haven for money (my insurance box). However, the UK has a large finance sector so in 2010 it was exposed to potential bank failures to a larger extent than many other countries. Hence, its safe haven status was threatened leading to a fall in value of the GBP against the Euro. This might explain the deviation from normal in your chart. A return to normal represents a resumption in safe haven status.

    The five boxes also provide an explanation of why some economic policies work better than others. When central banks change interest rates they directly impact behaviour in all five boxes including the GDP boxes. However, policies like QE act mainly on the existing asset box and the do nothing box. Any impact on the GDP boxes is a second or third level effect at best.

    Nevertheless, I like the idea of forex markets as prediction markets for national economies.

    Regarding prediction markets in general, they are just an example of the wisdom of the crowd. Here is a Lars Syll post containing a video which tries to explain why a diverse set of views leads to more accurate predictions. It makes sense to me but I have no expertise in this area. What do you think of this, particularly the maths?


    If this video is correct, then this type of logic would also apply to the study of the macro-economy and other complex systems. An academy which encouraged diverse methods and views would likely be more accurate than one which tries to impose uniformity. It is a lack of appreciation for diversity by economists that makes it so hard for someone like you to get a hearing for your non-mainstream views from the econo-Borg collective.

    In the wider world, three of the most successful social mechanisms we have are democracy, markets and trial by jury. All of these rely on the wisdom of the crowd to assess the products / opinions proposed by specialists. These mechanisms are at their weakest when there is an insufficiently diverse choice of options from which the crowd can choose.

    1. Hi Jamie,

      Your comment ended up in the spam filter for some reason so I fished it out. Actually, when I read your comment in the email notification I thought it was on this post:


      which actually addresses exactly this.

      Let's count your examples that contribute to GDP as "consumption" C and those that don't as "other". If we have two time periods 1 and 2 the consumption by people is going to be constrained by

      C₁ + C₂ ≤ GDP

      The actually realized consumption in an economy is likely to be less -- if C₁ = σ₁ and C₂ = σ₂, then we have:

      σ₁ + σ₂ < GDP


      σ₁ + σ₂ + ɛ = GDP

      where ɛ is that "other spending" on things not a part of GDP. I drew a picture of this scenario here:


      In the two period case, the ensemble average would give you a point in the middle of the triangle with ɛ > 0 and σ₁ + σ₂ < GDP.

      However! (And this is pretty neat -- it depends on the mathematical properties of higher dimensional spaces.)

      If you have a lot of consumption periods C₁, C₂, C₃, ... Cn subject to the budget constraint Σ Ci ≤ GDP, then the ensemble average is

      ɛ' + Σ σi = GDP

      with ɛ' ≈ 0 simply because most of the points in the higher dimensional space are near the budget constraint (a hyperplane). This is the second picture at the twitter link above.

      The ensemble average (the "representative agent") spends all of their consumption on things that count towards GDP, but individual agents do not necessarily do so.

    2. Thanks for the reply. I've read this and your later posts. However, I am now confused (probably my fault rather than yours). I will have a think and then reply to the separate post you wrote on this.

      In the meantime, do you have any comments on the wisdom of crowds element of my previous comment?

    3. Hi Jamie,

      Regarding the video you linked to on the wisdom of crowds, there are a couple of important caveats to the examples: the underlying predictions are unbiased, the underlying distribution isn't skewed and that the predictions occur on a linear scale.

      The "theorem" -- that the individual errors are larger than the error of the mean -- is just a basic property of an average ... given those caveats on the distribution above.

      When a distribution meets those caveats (and using the central limit theorem), the standard deviation of the mean goes as 1/√N where N is the number of observations. In the example with 3 observations, we'd expect the error of the average to be about half the error of single observations (60% of the time).

      Effectively, the "diversity prediction theorem" is a consequence of the central limit theorem.

      In the diner example, we don't know how many seats are in it, but that's the kind of example that meets our requirements. We know the number has to be less than some maximum Xmax (set by size of diner and number of seatings). The scale is linear (you're not guessing something that could go over several orders of magnitude .. like the size of planets) -- i.e. we know the answer will be α Xmax with α = o(1). Since we don't know Xmax, we can't really tell if the guesses are unbiased. And with only three guesses, you just have the bare minimum to define a normal distribution.

      [As an aside, the maximum entropy guess would be α = 1/2.]


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