Imagine velocity were a constant

When John Lennon wrote his famous song about utopia, he should have also asked us to imagine a world where velocity was constant. Here are some characteristics of such a world:

1. No long and variable lags in monetary policy. Indeed no lags at all.

2. Money supply targeting would be identical to NGDP targeting.

Many people wrongly assume that “monetarists believe velocity is constant”. And yet we are also told that “monetarists believe in long and variable lags.” These people must think monetarists are pretty stupid, as a constant velocity implies no lags at all. So which is it? What do monetarists actually believe?

The answer is simple. Monetarists believe in long and variable lags and they don’t believe that velocity is constant. Rather monetarists believe that velocity would be relatively stable if monetary policy were stable. They believe that actual real world movements in velocity are mostly due to unstable monetary policy. More specifically, a highly expansionary monetary policy will often cause velocity to fall in the short run and rise in the medium to long run. It depends on the persistence of the monetary expansion—is it one time increase in M, or a permanent (inflationary) increase in the money supply growth rate?

It would be wonderful if velocity were constant, especially base velocity. All of Keynesian economics would immediately collapse. The entire ideology would become essentially useless. Fiscal policy would have no impact on NGDP. There would be no paradox of thrift. Animal spirits would not affect aggregate demand. The IS/LM model would become meaningless.

The reason I don’t favor monetary aggregate targeting is not because monetarism was tried and failed—it was never tried for an extended period of time—rather because my reading of the evidence is that velocity would not be stable enough to produce good results even were the Fed to stabilize growth in the monetary aggregates over a period of many decades. Thus I prefer using market forecasts as a guidepost.

Some monetarists disagree with me, but pointing to unstable real world velocity doesn’t really address this question.



25 Responses to “Imagine velocity were a constant”

  1. Gravatar of Effem Effem
    1. February 2022 at 12:37

    Agree, however I wonder if the case for something like targeting monetary aggregates is strengthening in the presence of a central bank that believes it’s inflation mandate is asymmetric?

    If the lag is sufficiently long then money creation in one period will produce inflation in a future period – but the Fed will not react at that point because it will see inflation as a current phenomenon to be ignored rather than overly easy policy in a past period.

  2. Gravatar of Richard A. Richard A.
    1. February 2022 at 13:30

    I have said this before–nominal GDP figures need to be released in as much a timely fashion as the money supply figures.

  3. Gravatar of Benoit Essiambre Benoit Essiambre
    1. February 2022 at 13:52

    This means it’s likely impossible to create a stable decentralized cryptocurrency.

  4. Gravatar of Tristan Sinha Tristan Sinha
    1. February 2022 at 17:38

    Do you mean using monetary aggregates as an intermediate target as opposed to the short run nominal interest rate, or in a K-percent rule fashion? I assume since you favor an NGDP target that you mean the former, but weren’t there problems with that back in the 80s such as which aggregate to target and measurement issues (I think josh hendrickson recognized this and suggested using divisia aggregates as an intermediate tool).

  5. Gravatar of rwperu34 rwperu34
    1. February 2022 at 19:27

    Quick somewhat off topic question;

    What is you take on the market signal of 30 year treasuries yielding 2%? To me that is the clearest signal that the market thinks the current bout of inflation is transitory and Powell is doing a good job.

    I also try and imagine the effects of a long period with low interest rates and high inflation. This is obviously great for all borrowers. I’d think it would be good for workers (fast growing wages in a low interest environment makes borrowing easier via a better debt:income ratio). It wouldn’t be terrible for big business since the higher inflation doesn’t lead to higher borrowing costs or a lower PE multiple on stocks. Which leads to my final question;

    This situation can’t persist, can it? Either interest rates get higher or inflation gets lower, but something’s gotta give.

  6. Gravatar of Matthias Matthias
    1. February 2022 at 19:55

    Doesn’t George Selgin argue (eg in Less than Zero) that free banking with privately issued bank notes will turn a stable base (like gold) into a stable nominal GDP?

    If I remember right the argument right, it goes roughly as follows:

    Velocity of notes and deposits is rather variable. A low velocity is equivalent to more demand for money. But in this system money is just a bank liability, and banks can create more of them.

    Even without a legal reserve requirement, banks keep some precautionary reserve around to settle interbank balances and redemption requests.

    Empirically, the amount of precautionary reserves required is basically proportional to the amount of total spending. Or viewed the other way round: a fixed amount of total reserves gives rise to a stable total amount of spending. (But a highly variable amount of notes and deposits.)

    There’s also a pretty simple mathematical model based on random walks of money transfers between people banking with different banks, that reproduces the empirical finding.

    (I hope I did George Selgin’s argument justice here.)

    So in a free banking regime, the velocity of ngdp / base money is stable, but the velocity of ngdp / (notes + deposits) is rather variable (but variable in just the right way to stabilise the former).

    Scott, just to double check my understanding:

    Market monetarists like you don’t believe in long and variable lags? You guys believe in long and variable anticipation via expectations? Or less poetically: near instant effects once future monetary policies get credibly announced or even just leaked?

  7. Gravatar of Matthias Matthias
    1. February 2022 at 19:58

    rwperu34, don’t bother trying to read tea leaves of inflation expectations from bond yields like that.

    Just look directly at the spread between inflation adjusted and non-inflation adjusted bonds. Also knows as the TIPS spread.

    That gives you a much clearer signal of market inflation expectations.

    Fred calculates the 5 year and 10 year TIPS spread for you, ie the 5 year and 10 year market inflation expectations.

    (Not sure if inflation adjusted bonds come in long enough duration to calculate a 30 year TIPS spread.)

  8. Gravatar of Matthias Matthias
    1. February 2022 at 20:22

    Benoit, see what I wrote above and look directly at George Selgin’s work of how the gold standard worked in Scotland and Canada.

    Bitcoin can be seen as similar enough to gold. So the same mechanisms of privately issued fiduciary notes that made the gold standard work would also work for bitcoin.

    You’d have bitcoin as the base money and unit of account, but people would hold ‘notes’ and balances denominated in bitcoin and with a fractional reserve at competing providers, and redeemable on demand.

    That system could produce stable total nominal spending.

    Different providers could offer balances either off the Blockchain, or in smart contracts on a block chain. (It would likely not be the bitcoin blockchain, even if the assets are denominated in bitcoin. But eg Ethereum provides enough machinery to make this work.)

    We might be seeing a glimpse of that future already via existing bitcoin futures. The futures allow market participants to essentially manufacture assets with very low credit risk that are denominated in bitcoin.

    And these assets can be backed with your general balance sheet, not necessarily with a bitcoin reserve. (In fact, you can’t directly back them with a bitcoin reserve, since they are USD settled and your margin requirements are also in USD.)

    Of course, these futures are otherwise even harder to use to pay for a pizza than bitcoin. So they are even less useful as a medium of transaction at the moment.

    See also synthetic stable coins:

    You can take a big pot of something valuable but volatile, like bitcoin, and slice it in multiple tranches. Just like what people used to do to mortgages.

    If you have a million USD worth of bitcoin, you can sell people a senior claim to that pot that you promise to redeem for 500k USD, and you keep a junior claim on the rest.

    The junior claim essentially behaves like 2x leveraged bitcoins.

    If bitcoin goes up, you make a 2x profit on your junior claim. If bitcoin goes down, you make a 2x loss. If bitcoin goes down by more than 50%, your junior claim gets wiped out, and the senior claim starts to take losses.

    You could go with 3x over capitalisation instead of a mere 2x, to be more secure in the senior tranche. You can also denominate the senior tranch in something other than USD. Eg in gold, or in percentage of US ngdp, or in Facebook stock.

    Critically, this whole contraption can live as a smart contract somewhere on a blockchain and doesn’t have to touch the regular financial system.

    Also, you can acquire another pot of bitcoin and replicate this scheme, if there’s sufficient demand. And you can wind these pots down, too. Thus providing for stabilising mechanisms.

  9. Gravatar of Thaomas Thaomas
    1. February 2022 at 21:09

    Of course anything that prevented aggregated demand recessions would make Keynesian “theory” useless. But so long as there are periods of aggregated demand recessions, an income maximizing fiscal policy will increase deficit financed investment, Keynesian theory or no Keynesian theory.
    [Interesting to wonder if in an excess demand inflation an income maximizing government would reduce investment and increase the surplus, replicating both implications of Keynesian theory w/o Keynes? I suppose it would if the central bank monetary policies resulted in a rising real borrowing rate for the government.]

  10. Gravatar of Harry Harry
    1. February 2022 at 23:37

    The best economist is an unemployed economist! My company never hires them! And we never will!

    Human nature will never fit cleanly inside a model.

    If you get rid of the Fed, the IMF, and people like Sumner the US economy would be so much better off.

    There are only three “economists” worth reading (I put “economist” in quotes because these three men are more or less philosophers). Henry Hazlitt, Thomas Sowell and Walter Williams. The rest are clueless barbarians who are front men for thug bankers and MNC’s.

  11. Gravatar of Ankh Ankh
    2. February 2022 at 01:42

    And the left says they care about the working class.

    Hmmm….seems like all that “free stuff” they promise is more about control than true empathy for the working class.

    Take the red pill america.

  12. Gravatar of Todd Ramsey Todd Ramsey
    2. February 2022 at 08:08

    It seems to me that “Fiscal policy would have no impact on NGDP” is not literally true?

    If low-productivity increases in “G” are funded by a reduction in more-productive “I”, that would lower NGDP by lowering RGDP? Although the effect might be quite small in the short run.

    Picking nits, and not really relevant to your main point, I suspect.

  13. Gravatar of ssumner ssumner
    2. February 2022 at 08:52

    Effem, I think it’s too early to assume the inflation mandate is seen as asymmetric.

    Tristan, In this post I’m contemplating using the aggregates in a K-percent rule fashion.

    rwperu, Yes, I expect either interest rates will rise or inflation will fall (Probably the latter, if not both.)

    Matthias, You said:

    “Empirically, the amount of precautionary reserves required is basically proportional to the amount of total spending.”

    That’s where I disagree. The issue is not the amount of reserves “required”, the issue is what do banks view as the profit maximizing quantity of reserves. That will vary as interest rates fluctuate.

    The effect on money on asset prices is immediate, the effect on sticky goods prices is delayed.

    Todd, If NGDP is 100% determined by the monetary base, how does a change in RGDP affect NGDP?

  14. Gravatar of rinat rinat
    2. February 2022 at 10:41

    Look at those Canadian Nazi’s and fascists playing a game of hockey.

    I never knew Nazi’s were so polite and peaceful.

    For the readers who forgot history, or think the neo-marxists are smarter than the old marxists, all you have to do is look at SFO and L.A.: massive homelesness, looting, drugs and crime. That is Nancy Pelosi and Scott Sumner’s vision playing out in real time. No history book needed to view that cesspool of destruction. Indeed, hundreds of thousands have left the state for greener pasters (hopefully they don’t bring Sumner’s politics with them).

    How about an article with a backbone; how about displaying a bit of courage, like denouncing the CCP, BLM, and neo marxist academics. How about an article that shows support for the blue collar truckers and farmers.

    If it wasn’t for them, you’d be hunting for food in your wellingtons.

  15. Gravatar of Spencer Bradley Hall Spencer Bradley Hall
    2. February 2022 at 11:14

    RE: “No long and variable lags in monetary policy. Indeed no lags at all.”

    There’s not a single Ph.D. in economics that understands monetary lags. NO, velocity can’t remain the same. The bottom fell out of velocity in the 4th qtr. of 2008 not simply because there were lags.

    RE: “The effect on money on asset prices is immediate, the effect on sticky goods prices is delayed.”

    For example, the price of oil troughed in Jan 2016 as long-term money flows fell by 80 percent from 1/2013 to 1/2016. Oil fell by 70 percent during the same period.

    You are too quick to supply an opinion without providing any evidence. You’re a terrible teacher. You never define your terms.

  16. Gravatar of Matthias Matthias
    2. February 2022 at 17:17

    Scott, yes, of course, the amount of precautionary reserves is subject to profit maximisation. Assuming you have a solid balance sheet in general and that you roughly know the probability distribution of interbank flows and redemption requests, you balance the cost of holding reserves against the inconveniences and contract penalties and cost of emergency borrowing of reserves for settling.

    Your argument about interest rates going into that calculation is a good one. I wonder how that played out historically in Scotland and Canada (and the other countries with free banking episodes).

    In the model I sketched, we took the gold reserves as given endogenously and fixed. In the short run that approximately true for the global economy. But small economies like Scotland and Canada decide how much gold they want to export and import.

    Would be interesting to see how that interplay worked out.

    We know for a fact that Scotland and Canada had pretty stable economies during the relevant time. So I’m curious to see whether they just had luck and encountered mostly stable enough interest rates? Or whether they had another mechanism to keep spending stable despite varying interest rates? Or whether they had mechanisms to stabilise interest rates endogenously? Of something else I haven’t thought of.

    About the immediate effects and delays: I assume the effect on sticky prices is delayed as measured from the announcement, which might still overall be long before the implementation? Depending on how far in advance they announce or how far in advance the market guesses with confidence.

    Also any Cantillon effects should be more about sticky prices and perhaps information flow, and not about flow of money?

    (Btw, Scott, do you have an opinion on the Austrian business cycle theory? The naive version I read always struck me as requiring entrepreneurs to be too stupid to anticipate a very well expected future.)

  17. Gravatar of ssumner ssumner
    3. February 2022 at 08:52

    Matthias, I don’t think we have enough data on NGDP in Canada during the 1800s to know how stable things were.

    I’m not a fan of ABC theory, and don’t view Cantillon effects as being very important in most developed countries.

  18. Gravatar of Ivan Ivan
    3. February 2022 at 10:52

    Scott, I think that Bundesbank had officially targeted M2 in Germany in the 80s or so. I would be interested to learn how did their overall record look on that target.

  19. Gravatar of Michael Rulle Michael Rulle
    3. February 2022 at 13:16

    Velocity of M2 was very constant between 1959-1990. Why was that the case?

  20. Gravatar of Rajat Rajat
    4. February 2022 at 03:12

    “Rather monetarists believe that velocity would be relatively stable if monetary policy were stable.” It seems to me that the endogeneity of velocity is the key reason behind the lack of progress in macroeconomic thought in the last 50 years. Endogeneity makes complicated structural models pointless. The only or best way to account for this endogeneity is – as you’ve suggested – by using market expectations as an input into policy-making by targeting market forecasts. While Friedman was able to say “we have gone one derivative beyond Hume”, arguably the only innovation since (1960s) Friedman was Lucas/Sargent’s RE plus Fama’s EMH.

  21. Gravatar of William Peden William Peden
    4. February 2022 at 03:31

    Even if velocity was fairly stable, there would still be a good case for a Market Monetarist approach rather than an Old Monetarist approach.

    Central banks would still face knowledge problems and incentive problems. There would be cases where they would have to “look through” certain increases/decreases in the money supply caused by regulatory changes, financial disruptions etc.

    Since almost all monetarists generally favour markets over government agencies as ways of addressing knowledge problems and incentive problems, they should expect that using futures/prediction markets to determine monetary policy would be best, even in an Old Monetarist economy. The stability of velocity would make the speculators’ job easier, but it would be no reason to nationalise it.

  22. Gravatar of Todd Ramsey Todd Ramsey
    4. February 2022 at 07:02

    Duh, stupid question, thanks for responding.

  23. Gravatar of ssumner ssumner
    4. February 2022 at 10:43

    Ivan, I heard something about that, but I doubt it was a strict money targeting policy.

    Michael, I wouldn’t say “very” constant.

    Rajat, I agree.

    William, But if V were constant then steady growth in M would produce steady growth in NGDP. Why do you need markets?

  24. Gravatar of Michael Rulle Michael Rulle
    6. February 2022 at 04:00

    Admittedly, “very” is not very (heh) precise. But it ranged in ‘59-90, says Fred, from absolute low of 1.65 to absolute high of 1.93–-with 70-80% of time between about 1.7 and 1.8. Compared to straight down level from a spike up to 2.2 in ‘96 to Covid level of 1.1 seems pretty constant. And, of course M2 supply increased accordingly. Frankly, I always though one of the key changes you made from Friedman, was recognizing monetary policy needed always adjust for this.

    I now wonder if this is part illusion——I.e., maybe these two simply adjust to each other semi automatically, without much Fed intervention.

    I have no idea why we have inflation now. Prices should adjust to supply and demand and vice versa—-thus keeping prices within narrow ranges—-hence Friedman’s “inflation is always and everywhere a monetary phenomenon”—-which you have adjusted to account for velocity—-which makes sense to me.

    So I assume, that has happened. But Powell also must believe that——so he must believe output will catch up——and he hates the idea of short circuiting growth (or accelerating negative growth)——first guy in a while who feared no to low growth more than inflation. So he takes his risk on the inflation side.

  25. Gravatar of William Peden William Peden
    6. February 2022 at 15:18


    If velocity were constant, then markets would be unnecessary. However, even in an Old Monetarist model and even with a k percent rule, it’s not constant. Ditto the base money multiplier: under some conditions, it could be stable, but a constant money multiplier is not going to occur in e.g. a world where there’s a fluctuating international demand for dollars.

    So, by “stable,” I mean “roughly stable,” e.g. velocity changes are mean-reverting and have a low (but nonzero) variance.

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