Money demand slopes downward. Higher interest rates raise velocity. Period. End of story.

I suppose I should not have been shocked.  Economics is full of obvious truths that sound odd when expressed in an unfamiliar way.  Everyone knows that the real demand for money slopes downward, as a function of the nominal interest rates.  It’s in all the textbooks.  If you raise the opportunity cost of holding base money (the interest rate) people will hold less base money.  It’s basic supply and demand.

But people seem shocked by the implications.  Higher interest rates raise velocity.  In a moment I’ll show you some evidence.  And there is a mountain of academic studies that show this to be true (Cagan, etc.)  But what it implies is that holding the money supply constant, higher interest rates will raise not just V, but also NGDP and inflation.  And that’s what shocks people.

They are not always shocked by this relationship.  They understand that fiscal stimulus can raise interest rates and raise inflation, holding M constant.  Ditto for greater animal spirits leading to more investment.  It’s the tight money that throws people off.  How can tight money raise inflation?  It doesn’t, but the higher short term interest rates caused by tight money do raise inflation.  We don’t notice it because the overall effect is for lower inflation.  The reduction in M reduces NGDP and inflation by more than the higher interest rates from tight money raises V and inflation.  There is nothing at all controversial in what I am saying here.  Indeed this is an argument that Keynesians frequently make to criticize monetarism.  The gains from more M will be offset by less V.

I could not find a time series of base velocity, but I did find it’s inverse, the base/GDP ratio.  And I found short term interest rates since 1934.  Note that between 1929 and 1934 (not shown on graph) the short term rate plunged from about 6% to little more than zero.  That explains the huge surge in the base/GDP ratio during 1929-34, and the resulting plunge in base velocity.  There is a drop in the base/GDP ratio in 1937 as rates rose slightly above zero in a premature exit from the zero rate trap (coming soon to theatres near you.)  Then rates go right back to zero, and the base/GDP ratio shoots up again peaking in 1940, when T-bill yields hit bottom.  After the war, interest rates trended upward all the way to 1981, and the base/GDP ratio falls, bottoming out in 1981 (i.e. velocity peaks).  Then interest rates fall gradually, and velocity falls as well, as the base/GDP ratio rises.  Recent years are a repeat of the 1930s.  I would add that after 2008 you don’t want to look at the nominal interest rate alone, rather the velocity of bank reserves depends on the short term interest rate minus IOR, which is actually negative.  The last 4 years are the least costly time in all of world history to hold reserves.


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34 Responses to “Money demand slopes downward. Higher interest rates raise velocity. Period. End of story.”

  1. Gravatar of Tyler Joyner Tyler Joyner
    18. January 2013 at 08:51

    It’s easy to see why there is confusion. Framed as the opportunity cost of holding money, it’s intuitive that higher interest rates increase V and cause inflation.

    But there are two sides to every transaction. Higher interest rates also increase the cost of borrowing money. In that light, it would seem that the question of how interest rates and inflation interact comes down to differing elasticities, no?

  2. Gravatar of 32 cent stamp 32 cent stamp
    18. January 2013 at 09:09

    Earlier you claimed there was no such thing as ‘inflation’.

  3. Gravatar of Doug M Doug M
    18. January 2013 at 09:18

    “If you raise the opportunity cost of holding base money (the interest rate) people will hold less base money.”

    Do they? What do I do with that excess chash when rates are high? I lend it to someone — someone who has a strong demand for money even in this higher rate environment. But now my borrower is holding the base money. Base money has not changed.

    Regarding the relationship between M, V, interest rates, and inflation. If you said that an increase in V with an unchanged M will increase iterest rates and inflation, I think that is pretty unambiguous. You are loosing people when you run that backwards (and the math says it can run backwards). Economists teach that rates rise because of falling M, and ignrore any other drivers of rates. A rate rise because of a declinging M is not inflationary.

  4. Gravatar of Saturos Saturos
    18. January 2013 at 10:09

    *coming soon to theatres near you*

    That sounds like a prediction, Scott…

  5. Gravatar of John John
    18. January 2013 at 11:22

    Then how come when Volcker wanted to lower inflation/NGDP, he raised interest rates?

  6. Gravatar of Nuksukow Nuksukow
    18. January 2013 at 11:38

    John,

    “The reduction in M reduces NGDP and inflation by more than the higher interest rates from tight money raises V and inflation. “

  7. Gravatar of Mike Sax Mike Sax
    18. January 2013 at 11:40

    This discussion is always tough for me to wrap my head around. Whats tough is to differntiate between causation as opposed to just correlation and also cause and effect.

    I think why I find it hard is because when the Fed wants to damp down on inflation it raises rates.

    So the rates raise because inflation is already high rather than rates causing inflation-or so it seems to me.

    I’m just thinking about the Fed here, but on the market, as inflation rises, creditors raise interst rates to mitigate what they lose from higher inflation.

    So you wouldn’t raise rates to get higher inflation or higher output, etc.

    If you raise inflation and output then in time you would get higher rates.

    To get higher inflation you lower rates which lowers costs to borrowers which in time would lead to inlfation.

  8. Gravatar of jsalvatier jsalvatier
    18. January 2013 at 12:51

    The concept of demand for money is intuitive, but thinking about it, it doesn’t seem to make sense. A demand curve is quantity of a good demanded at a given price, in terms of another good. Usually the second good is money, but we can’t use that for money demand curves. You might be able to use “all other goods” in some way, but I don’t see an obvious one.

    Plus, the way money works, everyone is a *seller* of money (sellers mostly don’t actively choose the transactions they participate in), rather than a buyer.

    Even if the concept of money demand isn’t a good one. Monetary disequilibrium still works and does what you’d expect if you build a model where money is in the utility function of agents (perhaps with a term like log((M-T)/M); M = money held, T = expected nominal transactions). See here for a model (http://goodmorningeconomics.wordpress.com/2012/04/07/the-backrub-economy-a-simple-mathematical-model-of-monetary-disequilibrium/) )

    But it’s kind of clumsy to talk bout utility functions directly. Is there a simpler concept we can talk about? I haven’t found one, and I don’t think demand for money is it since that seems to disintegrate under inspection.

  9. Gravatar of Ron Ronson Ron Ronson
    18. January 2013 at 13:08

    Higher animal spirits -> more demand for investment funds -> higher interest rates -> more incentive to put cash balances in a bank -> higher velocity as demand to hold money is lower -> inflation and NGDP increase.

    is that it ?

    However while the initial rise in spirits causes the demand for loanable fund curve to move, isn’t the change in velocity just part of the move along the supply for loanable funds curve ?

  10. Gravatar of o. nate o. nate
    18. January 2013 at 14:11

    I think Tyler Joyner has a good point. Perhaps the answer is that it depends on inflation. The opportunity cost of holding money is the nominal interest rate, whereas the cost of borrowing money is the real interest rate (since loans are repaid with future money). So in times of high inflation, high interest rates are inflationary. In times of low inflation, they are neutral.

  11. Gravatar of ssumner ssumner
    18. January 2013 at 14:34

    Tyler, Don’t confuse money and credit.

    Doug, You said;

    “Do they? What do I do with that excess chash when rates are high? I lend it to someone “” someone who has a strong demand for money even in this higher rate environment. But now my borrower is holding the base money. Base money has not changed.”

    Time to review the hot potato effect. Society gets rid of excess cash balances by bidding up the level of prices and NGDP.

    John, Read the very next commenter.

    jsalavtier, Lots of problems in your comment. In upper level economics all demand curves are defined in terms of all other goods–so money is no different.

    And no, every transaction involves one person selling money and another buying money.

    Ron, No, the nominal interest rate is the opportunity cost of holding money. Studies confirm it has a powerful effect.

    O. Nate. No, Tyler confused money and credit. It is true that a rise in interest rates has no predicatble effect on the quantity of credit—it depends entirely on which curve shifted.

  12. Gravatar of John John
    18. January 2013 at 14:46

    Nuksukow and Scott,

    Scott says, “How can tight money raise inflation? It doesn’t, but the higher short term interest rates caused by tight money do raise inflation. We don’t notice it because the overall effect is for lower inflation.”

    What the heck is the definition of inflation here? If you’re defining it as a rise in prices, this is saying that tight money (how are you defining this, in terms of NGDP?) raises short term rates. Higher short term rates raise prices higher than they would be otherwise but the net effect is for prices to fall because of a reduction in the money supply.

    There are some problems here. First, if you’re defining tight money in terms of the monetary base or M1, M2, then you’re contradicting a great number of things you’ve said earlier. If you’re defining tight money in terms of NGDP as you’re likely to do, lower NGDP should, ceteris paribus, reduce interest rates across the board.

    The biggest problem I see is that if you’re arguing that higher rates raise inflation but have the net effect of prices falling due to less money, then higher interest rates are not raising prices on net and therefore not causing inflation. My point stands that if prices don’t rise on net as a result of raising short term interest rates, then short term interest rates are not causing inflation.

  13. Gravatar of Gabriel Gabriel
    18. January 2013 at 14:51

    John, as long as Volcker reduced the monetary base (by selling bonds to reduce their price and raise short-term rates) the long run (and dominant) effect is lower inflation, even though the higher rates raise velocity.
    Thus, the way the Fed goes about about making rate changes produces larger changes in M than V and are therefore effective at moving inflation (up or down). This doesn’t seem that contentious .
    I really hope I didn’t mess that up.

  14. Gravatar of John John
    18. January 2013 at 14:58

    I think it’s mistaken to talk about the effect of interest rates exclusively on inflation. It makes perfect sense that higher interest rates would decrease the demand to hold base money where it doesn’t earn interest but it doesn’t at all follow that an decrease in the demand for base money would lead to higher consumer prices.

  15. Gravatar of Geoff Geoff
    18. January 2013 at 15:00

    Dr. Sumner:

    “How can tight money raise inflation? It doesn’t, but the higher short term interest rates caused by tight money do raise inflation. We don’t notice it because the overall effect is for lower inflation. The reduction in M reduces NGDP and inflation by more than the higher interest rates from tight money raises V and inflation.”

    There is no way to empirically test this theory.

    You are saying that increasing A causes an increase to B, but alongside this, an increase in A also causes an increase in C which itself causes a reduction to B, but that reduction is overwhelmed by the increase caused by A.

    C can be unicorns, pandabears, hot dogs, or fiddleheads, and the theory can never be falsified.

  16. Gravatar of o. nate o. nate
    18. January 2013 at 16:09

    I’m not sure that Tyler and I are confusing money and credit any more than Keynesians are when they put IS and LM curves on the same chart (perhaps you would say that they are). I guess my point is just a restatement of the old criticism that IS/LM confuses nominal and real variables (as well as short- and long-term rates).

  17. Gravatar of Doug M Doug M
    18. January 2013 at 16:17

    “Time to review the hot potato effect. Society gets rid of excess cash balances by bidding up the level of prices and NGDP.”

    Then you haven’t played hot potato. I grab the pototato, but it is hot, so I throw it to Bob, and Bob passes it to Carol, who passes it back to me, and I pitch it to Alice.

    Despite 4 transactions we still have 1 potato. The temprature of the potato does not change the number of potatos in circulation.

  18. Gravatar of Max Max
    18. January 2013 at 16:29

    The reduction is the quantity of money caused by higher seignorage is a “supply side” effect. It raises the cost of doing business.

    It all goes back to Milton Friedman’s “optimal quantity of money”.

    If you can’t set seignorage independently of interest rates, then the quantity of money will be too low, except in a liquidity trap.

    However, since the vast majority of transactions are consummated without using currency, this is probably not terribly important.

  19. Gravatar of Lorenzo from Oz Lorenzo from Oz
    18. January 2013 at 17:47

    jsalvatier: Goods and services have consumption and/or production utility. Money qua money only has transaction utility. Makes a difference.

    The demand to hold money is the demand to defer transacting/retain future transacting capacity. Either because we expect money to increase in swap value or as a risk hedge or for intended transactions we are not yet able or willing to make or some combination thereof. Hence the failure to anchor income expectations is why normal inflation targeting can come to badly apart.

    Money is why Say’s Law (simple version) does not apply in a monetary economy — Supply does not generate equivalent Demand, since money allows Demand to be deferred, permitting general gluts of goods and services.

    So, money demand is different in an important sense. But that does not get in the way of defining money demand in terms of all goods and services; on the contrary, what else is on offer for money, which (qua money) only has transaction utility but, in a monetised economy, has general transaction utility?

  20. Gravatar of Lorenzo from Oz Lorenzo from Oz
    18. January 2013 at 17:49

    That should be “can come apart so badly”. Low blood sugar, must eat.

  21. Gravatar of Mike Sax Mike Sax
    18. January 2013 at 19:58

    I was hoping for an answer-is this question somehow unrelated to the poast too?

    It does seem like high interest rates result from inflation-creditors raise them for protection-but not inflation from high interest rates.

    So it seems as if cause and effect go from inflation to higher rates.

  22. Gravatar of Mike Sax Mike Sax
    18. January 2013 at 19:58

    I was hoping for an answer-is this question somehow unrelated to the poast too?

    It does seem like high interest rates result from inflation-creditors raise them for protection-but not inflation from high interest rates.

    So it seems as if cause and effect go from inflation to higher rates.

  23. Gravatar of RebelEconomist RebelEconomist
    19. January 2013 at 03:35

    “How can tight money raise inflation? It doesn’t, but the higher short term interest rates caused by tight money do raise inflation. We don’t notice it because the overall effect is for lower inflation.”

    So this is a bit of a pointless post then. Like explaining that pressing the accelerator on a car has the effect of slowing the engine a little since the fuel pump drains some power, but we don’t notice because effect of the additional fuel supply dominates.

    Aren’t you too busy to waste your time on posts like this, Scott.

  24. Gravatar of ssumner ssumner
    19. January 2013 at 07:32

    John, You are taking things out of context. I was discussing the way Keynesians look at things. They regard an increase in the money supply that reduces short term rates as “easy money.”

    And a decrease in the demand for money obviously does cause inflation. Money is the MOA.

    Gabriel. Yup, I think everyone should agree with that.

    Geoff. The theory can be tested and has been tested. Higher rates raise V.

    Doug, That’s the whole point, the number of potatoes don’t change but their velocity does.

    Mike, I’ve already answered that–causation goes both ways.

    Rebeleconomist. I’m too busy to waste time on commenters who don’t take the time to try to understand what the post is about. Go back and read the original post, and then look at the comments to that post. Then you’ll see why I did this post.

  25. Gravatar of Mike Sax Mike Sax
    19. January 2013 at 08:06

    So if the Fed raised rates that would increase inflation?

  26. Gravatar of Saturos Saturos
    19. January 2013 at 08:27

    Mike, no you’ve completely misunderstood the discussion here. Let me talk you through the concrete steppes. The Fed sells Treasury bills. It receives Federal reserves in exchange. This reduces the total amount of money in circulation (all forms, except currency). More importantly, it is interpreted as a signal that the Fed intends to lower the growth path over time of the money supply – which also increases the demand for holding money today, and lowers its velocity of circulation.

    Now, the present sale of securities on the open market has an insignificant temporary flow effect on the price of bonds, and upward pressure on yields (the interest rate). More significantly, because prices are sticky people find themselves with insufficient money balances relative to their requirement for holding money assets. They substitute from other assets towards money assets, selling bonds and creating the “liquidity effect” on bonds, what Keynes called the speculative demand for bonds. This is captured in the LM part of the ISLM model that all undergraduates are taught in economics schools everywhere.

    The liquidity effect involves a change in the demand for holding money to meet the reduced supply. It is an epiphenomenon, which is an unreliable signal of the change in the stance of money, as it is due to temporary non-neutralities associated with changes in the money stock, and is often dwarfed by many other forces acting on interest rates, which are usually driven be expectations of the future (the predominant influence on current yields). However, the change in money demand does mean that velocity has moved in an equal and opposite direction to money supply. The higher rates have induced a reduced demand for money, which pushes spending up, matching the negative influence on spending from less money available.

    What the Keynesians don’t understand is that this effect is necessarily quite temporary. If the asset sale and reduction in money is permanent, then as the supply and demand for holding money are driven into equilibrium by a change in bond yields, people stop selling bonds to get more money. That means bond prices have to come up again. The interest rate cannot permanently equilibriate demand and supply for money. There is strong pressure to increase money holding in other ways – such as by spending less on real goods and services, which eventually becomes possible in the medium run as prices adjust. So nominal spending (NGDP) falls, and either the price level or the level of real output is reduced until people no longer want to hold more money than there is, because their nominal incomes have fallen. So the ultimate effect of the monetary contraction is to reduce spending and inflation. But part of the process does involve a rate rise, which is a countervailing upward force on spending which opposes the downward force from less money in the system.

    And yes, this is all consistent with what the ISLM model says.

  27. Gravatar of Saturos Saturos
    19. January 2013 at 08:31

    Sorry, it would decrease currency in circulation too, obviously. (I’m such an idiot.)

  28. Gravatar of dtoh dtoh
    19. January 2013 at 09:12

    Scott,
    If you look at the last 30 years, there is certainly some correlation, but it could certainly be due to other factors. Growth of the gray economy. Higher ATM fees. More ATM, etc. I just think that given the cash balances held by most businesses and individuals are so small the opportunity cost of holding cash is negligible in absolute dollar terms.

  29. Gravatar of polymath polymath
    19. January 2013 at 11:29

    “But what it implies is that holding the money supply constant, higher interest rates will raise not just V, but also NGDP and inflation. And that’s what shocks people.”

    “Mike, I’ve already answered that-causation goes both ways.”

    I think one of the points of confusion is simply that the first quote, in English semantics, has causation going only one way. I’ve seen this in several posts recently. The thing that shocks people is talking about equilibrium shifts in terms of unidirectional causality.

    Maybe that’s a pedagogical device? Use the unfamiliar causal direction to get people to think about equilibrium shifts differently? I don’t think as a device it’s working reliably.

  30. Gravatar of Mike Sax Mike Sax
    19. January 2013 at 11:34

    Saturos, it does not suprise me at all if I have misunderstood it. Appreciate you taking the trouble to get me up to speed-LOL.

  31. Gravatar of Mike Sax Mike Sax
    19. January 2013 at 11:47

    Thanks for the concrete steppes. It was helpful. Normally when Scott says this I have no idea how we get from point A to point B.

    Do you have a econ background?

  32. Gravatar of Mike Sax Mike Sax
    19. January 2013 at 13:22

    Seriously Saturos, I’m curious how you understand econ so well-do you have a background in it or self-taught?

  33. Gravatar of Ray Lopez Ray Lopez
    13. January 2015 at 21:23

    This is not logical. Throughout human history velocity changes even with a fixed money supply due to “animal spirits”.

  34. Gravatar of Vincent Cate Vincent Cate
    16. December 2015 at 05:39

    The velocity of money using MZM seems to closely track the 10 year treasury interest rate:

    http://howfiatdies.blogspot.com/2015/09/punchbowl-removal-difficulties.html

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