Bitcoins are a medium of exchange, perhaps even money, but not “M”

When economists have models containing “M”, aka ‘money,’ they are not referring to the medium of exchange.  Rather M is the medium of account.  Here’s a very simple model:

NGDP = M*v(i, z)     where v is a function of the nominal interest rate (i) and the share of transactions using money (z).

In that model we are trying to explain changes in a nominal aggregate that is measured in terms of some medium of account, like dollars.  But not Bitcoins—at least not yet.

Monetary models basically have two purposes; explaining nominal aggregates like P and NGDP, and explaining business cycles.  Nominal GDP shocks create business cycles because nominal hourly wages are very sticky.  But wages are denominated in dollars, not Bitcoins.  Hence wages are sticky in terms of dollars, not Bitcoins.

As long as wages and NGDP are denominated in terms of dollars, then the “money” in macro models should be dollars, even if Bitcoins become a large share of the media of exchange.



14 Responses to “Bitcoins are a medium of exchange, perhaps even money, but not “M””

  1. Gravatar of Tyler Joyner Tyler Joyner
    4. March 2013 at 08:15

    Surely there must be countries that use more than one type of currency interchangeably. How do models handle that?

  2. Gravatar of ssumner ssumner
    4. March 2013 at 08:51

    Tyler, Which one is the medium of account for wages and NGDP? Use that one.

  3. Gravatar of TravisV TravisV
    4. March 2013 at 09:09

    Phenomenal post by Ryan Avent on Bernanke’s recent speech:

    “The low rate conundrum”

  4. Gravatar of Michael Michael
    4. March 2013 at 09:36

    Here is John Cochrane on problems of monetary policy with large debts:

    ” Monetary policy depends on fiscal policy in an era of large debts and deficits. Suppose that the Fed raises interest rates to 5% over the next few years. This is a reversion to normal, not a big tightening. Yet with $18 trillion of debt outstanding, the federal government will have to pay $900 billion more in annual interest.

    Will Congress and the public really agree to spend $900 billion a year for monetary tightening? Or will Congress simply command the Fed to keep down interest payments, as it did after World War II, reasoning that “Fed independence” isn’t worth that huge sum of money?”

  5. Gravatar of Nick Nick
    4. March 2013 at 10:00

    I thought nominal shocks created business cycles because of debt too (in addition to wage stickiness). Just like the wage earner is anchored on his last nominal wage, a lender sticks with the nominal face value of debt, causing a transfer of real value from the borrower to the lender (unless the borrower takes some back by defaulting). Is this not really a factor? If it is, then borrowings in bitcoins could someday create recessions too.

  6. Gravatar of ssumner ssumner
    4. March 2013 at 11:38

    TravisV, Thanks, I did a post.

    Michael, Thanks, I’ll do a post.

    Nick, No, debt transfers are a zero sum game and do not cause people to work less. Sticky wages (and to a lesser extent sticky prices) are the reason NGDP matters.

  7. Gravatar of Geoff Geoff
    4. March 2013 at 13:34

    A commodity being a medium of account derives from that commodity being a medium of exchange. The same cannot be said for the vice versa.

    This equation:

    NGDP = M*v(i, z)

    is an equation that is based on medium of exchange (M is surrounded by NGDP and velocity, both of which are medium of exchange concepts).

    “Nominal GDP shocks create business cycles because nominal hourly wages are very sticky.”

    This doesn’t address why, absent Fed inflation, NGDP would suddenly fall.

    I think it’s more accurate to say that nominal NGDP shocks are a symptom of that which causes business cycles.

  8. Gravatar of Steve Steve
    4. March 2013 at 19:17

    Bitcoin is worthless and will go to zero. Worthless securities trading for a price is one of the shortcomings of EMH, due to the limits of arbitrage.

  9. Gravatar of Saturos Saturos
    4. March 2013 at 21:16

    Just quickly (since you know I had to comment on this one) – logical fallacy: from “not MOA -> no business cycles -> no model significance” it does not follow “MoA -> business cycles -> model significance”.

    Shock to MoA (when it exists) is sufficient but not necessary for recessions. A bitcoin shock however has minimal effect on output and employment, as wages are not generally paid in bitcoins. We can imagine another non-MoA MoE which is used to pay workers, that would definitely have to go into macro-models.

    If a monetary shock to MoA affects the nominal value of bitcoins, then because they are MoE this will have some (tiny) effect on RGDP. If half of output was and could only be sold with bitcoins (with employment thus dependent on those sales), then bitcoins would certainly have to be put in the models. In fact the models would probably have to start explicitly distinguishing between MoA and Moe, thus properly refocussing economists’ attention on money in general…

    (Nick and Bill can clarify further.)

  10. Gravatar of J.V. Dubois J.V. Dubois
    5. March 2013 at 01:32

    Scott: imagine that everything except wages would be denominated in Bicoins. Wages are denominated in dollars. Employees are actually paid in Bitcoins according to exchange rate on the only bitcoin -> dollar market there is.

    Can we even say that the dollar price of wage is sticky in this environment? Does it actually have any meaning? If wages would be denominated in dollars, but contracts would contain bitcoin-inflation clause (automatic wage changes according to bitcoin dollar exchange rate changes) would you say that dollar is medium of account?

    I think that you are too much focused on assumption of sticky wages (in terms of medium of account) without considering how such phenomena comes to be about. We are back in the MoA vs MoE debate that you had with Nick Rowe some time ago. My take is that considering pure MoA does not have any meaning because it assumes some Walrasian auctioneer waving his magic wand and setting prices. In the real world (market) prices are set by the act of exchange of the MoE.

    Anyways, this may still be interesting topic for research. For instance, what is the most important money in small and open economy where large part of the employees have their contracts (and are paid) in different currencies? There were (and are) such thing in Europe, where large swaths of population regularly work abroad but send money and/or directly spend money back at home.

  11. Gravatar of Geoff Geoff
    5. March 2013 at 03:44


    “Bitcoin is worthless and will go to zero. Worthless securities trading for a price is one of the shortcomings of EMH, due to the limits of arbitrage.”

    Bitcoin demonstrably is given “worth”. Bitcoins carry a price. People are paying the price.

    If by “worthless” you mean there is no “inherent” value in them, then you’ll have to say everything conceivable is worthless. Why? Because nothing has “inherent” value. Value comes from us humans via our minds and activity. It isn’t “inside” the objects. Value is applied to otherwise inherently worthless objects.

    I mean, surely you will agree that pieces of paper with pictures of dead Presidents are inherently worthless, but their use and price derives from humans attaching value to them.

  12. Gravatar of ssumner ssumner
    5. March 2013 at 09:06

    Geoff, I’m afraid you are totally wrong. There is no “medium of exchange concept” in MV=PY. V does not refer to the average number of times money is spent. It’s the ratio of PY/M, nothing more.

    I do agree with your second post.

    Saturos, the issue is not whether workers are paid in bitcoins, it’s whether nominal wages are denominated in bitcoins.

    JV, I’m not sure I follow, but see my answer to Saturos. The key is what MOA wages are denominated in.

  13. Gravatar of Geoff Geoff
    5. March 2013 at 09:15

    Dr. Sumner:

    “There is no “medium of exchange concept” in MV=PY. V does not refer to the average number of times money is spent. It’s the ratio of PY/M, nothing more.”

    You can’t have a ratio of PY and M unless money is turned over in exchange. P implies exchange (since you can’t have prices of goods unless there are exchanges of goods against money), and Y implies exchange as well.

    Imagine I discovered a pile of dollars in my basement, and I hold it for one year. What is the “equation of exchange” that would characterize this year? It would be undefined, because there is no exchanging taking place.

  14. Gravatar of Geoff Geoff
    5. March 2013 at 09:17

    Why else would they call it “equation of exchange” anyway? It’s rather funny reading “There is no medium of exchange concept in the equation of exchange.”

Leave a Reply