The Uselessness of the Money Multiplier as Brilliantly Elucidated by Nick Rowe

Not long after I started blogging over two and a half years ago, Nick Rowe and I started a friendly argument about the money multiplier. He likes it; I don’t. In his latest post (“Alpha banks, beta banks, fixed exchange rates, market shares, and the money multiplier”), Nick attempts (well, sort of) to defend the money multiplier. Nick has indeed figured out an ingenious way of making sense out of the concept, but in doing so, he has finally and definitively demonstrated its total uselessness.

How did Nick accomplish this remarkable feat? By explaining that there is no significant difference between a commercial bank that denominates its deposits in terms of a central bank currency, thereby committing itself to make its deposits redeemable on demand into a corresponding amount of central bank currency, and a central bank that commits to maintain a fixed exchange rate between its currency and the currency of another central bank — the commitment to a fixed exchange rate being unilateral and one-sided, so that only one of the central banks (the beta bank) is constrained by its unilateral commitment to a fixed exchange rate, while the other central bank (the alpha bank) is free from commitment to an exchange-rate peg.

Just suppose the US Fed, for reasons unknown, pegged the exchange rate of the US dollar to the Canadian dollar. The Fed makes a promise to ensure the US dollar will always be directly or indirectly convertible into Canadian dollars at par. The Bank of Canada makes no commitment the other way. The Bank of Canada does whatever it wants to do. The Fed has to do whatever it needs to do to keep the exchange rate fixed.

For example, just suppose, for reasons unknown, the Bank of Canada decided to double the Canadian price level, then go back to targeting 2% inflation. If it wanted to keep the exchange rate fixed at par, the Fed would need to follow along, and double the US price level too, otherwise the US dollar would appreciate against the Canadian dollar. The Fed’s promise to fix the exchange rate makes the Bank of Canada the alpha bank and the Fed the beta bank. Both Canadian and US monetary policy would be decided in Ottawa. It’s asymmetric redeemability that gives the Bank of Canada its power over the Fed.

Absolutely right! Under these assumptions, the amount of money created by the Fed would be governed, among other things, by its commitment to maintain the exchange-rate peg between the US dollar and the Canadian dollar. However, the numerical relationship between the quantity of US dollars and quantity of Canadian dollars would depend on the demand of US (and possibly Canadian) citizens and residents to hold US dollars. The more US dollars people want to hold, the more dollars the Fed can create.

Nick then goes on to make the following astonishing (for him) assertion.

Doubling the Canadian price level would mean approximately doubling the supplies of all Canadian monies, including the money issued by the Bank of Canada. Doubling the US price level would mean approximately doubling the supplies of all US monies, including the money issued by the Fed. Because the demand for money is proportional to the price level.

In other words, given the price level, the quantity of money adjusts to whatever is the demand for it, the price level being determined unilaterally by the unconstrained (aka “alpha”) central bank.

To see how astonishing (for Nick) this assertion is, consider the following passage from Perry Mehrling’s superb biography of Fischer Black. Mehrling devotes an entire chapter (“The Money Wars”) to the relationship between Black and Milton Friedman. Black came to Chicago as a professor in the Business School, and tried to get Friedman interested in his idea the quantity of money supplied by the banking system adjusted passively to the amount demanded. Friedman dismissed the idea as preposterous, a repetition of the discredited “real bills doctrine,” considered by Friedman to be fallacy long since refuted (definitively) by his teacher Lloyd Mints in his book A History of Banking Theory. Friedman dismissed Black and told him to read Mints, and when Black, newly arrived at Chicago in 1971, presented a paper at the Money Workshop at Chicago, Friedman introduced Black as follows:

Fischer Black will be presenting his paper today on money in a two-sector model. We all know that the paper is wrong. We have two hours to work out why it is wrong.

Mehrling describes the nub of the disagreement between Friedman and Black this way:

“But, Fischer, there is a ton of evidence that money causes prices!” Friedman would insist. “Name one piece,” Fischer would respond.The fact that the measured money supply moves in tandem with nominal income and the price level could mean that an increase in money casues prices to rise, as Friedman insisted, but it could also mean that an increase in prices casues the quantity of money to rise, as Fischer thought more reasonable. Empirical evidence could not decide the case. (p. 160)

Well, we now see that Nick Rowe has come down squarely on the side of, gasp, Fischer Black against Milton Friedman. “Wonder of wonders, miracle of miracles!”

But despite making that break with his Monetarist roots, Nick isn’t yet quite ready to let go, lapsing once again into money-multiplier talk.

The money issued by the Bank of Canada (mostly currency, with a very small quantity of reserves) is a very small share of the total Canadian+US money supply. What exactly that share would be would depend on how exactly you define “money”. Let’s say it’s 1% of the total. The total Canadian+US money supply would increase by 100 times the amount of new money issued by the Bank of Canada. The money multiplier would be the reciprocal of the Bank of Canada’s share in the total Canadian+US money supply. 1/1%=100.

Maybe the US Fed keeps reserves of Bank of Canada dollars, to help it keep the exchange rate fixed. Or maybe it doesn’t. But it doesn’t matter.

Do loans create deposits, or do deposits create loans? Yes. Neither. But it doesn’t matter.

The only thing that does matter is the Bank of Canada’s market share, and whether it stays constant. And which bank is the alpha bank and which bank is the beta bank.

So in Nick’s world, the money multiplier is just the reciprocal of the market share. In other words, the money multiplier simply reflects the relative quantities demanded of different monies. That’s not the money multiplier that I was taught in econ 2, and that’s not the money multiplier propounded by Monetarists for the past century. The point of the money multiplier is to take the equation of exchange, MV=PQ, underlying the quantity theory of money in which M stands for some measure of the aggregate quantity of money that supposedly determines what P is. The Monetarists then say that the monetary authority controls P because it controls M. True, since the rise of modern banking, most of the money actually used is not produced by the monetary authority, but by private banks, but the money multiplier allows all the privately produced money to be attributed to the monetary authority, the broad money supply being mechanically related to the monetary base so that M = kB, where M is the M in the equation of exchange and B is the monetary base. Since the monetary authority unquestionably controls B, it therefore controls M and therefore controls P.

The point of the money multiplier is to provide a rationale for saying: “sure, we know that banks create a lot of money, and we don’t really understand what governs the amount of money banks create, but whatever amount of money banks create, that amount is ultimately under the control of the monetary authority, the amount being some multiple of the monetary base. So it’s still as if the central bank decides what M is, so that it really is OK to say that the central bank can control the price level even though M in the quantity equation is not really produced by the central bank. M is exogenously determined, because there is a money multiplier that relates M to B. If that is unclear, I’m sorry, but that’s what the Monetarists have been saying all these years.

Who cares, anyway? Well, all the people that fell for Friedman’s notion (traceable to the General Theory by the way) that monetary policy works by controlling the quantity of money produced by the banking system. Somehow Monetarists like Friedman who was pushing his dumb k% rule for monetary growth thought that it was important to be able to show that the quantity of money could be controlled by the monetary authority. Otherwise, the whole rationale for the k% rule would be manifestly based based on a faulty — actually vacuous — premise. The post-Keynesian exogenous endogenous-money movement was an equally misguided reaction to Friedman’s Monetarist nonsense, taking for granted that if they could show that the money multiplier and the idea that the central bank could control the quantity of money were unfounded, it would follow that inflation is not a monetary phenomenon and is beyond the power of a central bank to control. The two propositions are completely independent of one another, and all the sturm und drang of the last 40 years about endogenous money has been a complete waste of time, an argument about a non-issue. Whether the central bank can control the price level has nothing to do with whether there is or isn’t a multiplier. Get over it.

Nick recognizes this:

The simple money multiplier story is a story about market shares, and about beta banks fixing their exchange rates to the alpha bank. If all banks expand together, their market shares stay the same. But if one bank expands alone, it must persuade the market to be willing to hold an increased share of its money and a reduced share of some other banks’ monies, otherwise it will be forced to redeem its money for other banks’ monies, or else suffer a depreciation of its exchange rate. Unless that bank is the alpha bank, to which all the beta banks fix their exchange rates. It is the beta banks’ responsibility to keep their exchange rates fixed to the alpha bank. The Law of Reflux ensures that an individual beta bank cannot overissue its money beyond the share the market desires to hold. The alpha bank can do whatever it likes, because it makes no promise to keep its exchange rate fixed.

It’s all about the public’s demand for money, and their relative preferences for holding one money or another. The alpha central bank may or may not be able to achieve some targeted value for its money, but whether it can or can not has nothing to do with its ability to control the quantity of money created by the beta banks that are committed to an exchange rate peg against  the money of the alpha bank. In other words, the money multiplier is a completely useless concept, as useless as a multiplier between, say, the quantity of white Corvettes the total quantity of Corvettes. From now on, I’m going to call this Rowe’s Theorem. Nick, you’re the man!

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45 Responses to “The Uselessness of the Money Multiplier as Brilliantly Elucidated by Nick Rowe”


  1. 1 Greg Ransom March 27, 2014 at 2:15 pm

    Excellent and helpful discussion, David.

  2. 2 Rob Rawlings March 27, 2014 at 3:59 pm

    As long as you recognize that the money multiplier is itself an endogenous variable it seems a very useful concept.

    The money multiplier helps to understand the relationship between base and credit money. And to understand the multiplier you have to understand something about the demand for loans, and the demand to hold money.

    Plus its fun to annoy Post-Keynsians by bringing up the money multiplier whenever they talk about endogenous money. It appears that opposition to the use of the very words has symbolic importance in their framework.

  3. 3 Mike Sproul March 27, 2014 at 4:57 pm

    “the discredited real bills doctrine”

    Unkind words about the real bills doctrine? Now you gone and done it. How can you see Friedman’s other mistakes so clearly, and still not see that he was wrong about the real bills doctrine?

  4. 4 David Glasner March 27, 2014 at 5:04 pm

    Mike, Sorry to touch a sore spot, but I was merely conveying Friedman’s response to Black, not expressing my own view.

  5. 5 Nick Rowe March 27, 2014 at 5:49 pm

    David: Wow! That way of phrasing my thought-experiment was a throw-away line.

    Suppose I double the target speed of my car. Does that cause the gas pedal to go down? Or vice versa? Yes.

    Sometimes it is easier to solve a model backwards,

    If I push the gas pedal down by one cm, what happens to the speed of my car?

    If I increase the speed of my car by 50km/hr, what needs to happen to the gas pedal?

    If an Old Keynesian says that increasing the target level of Y by 200 means G increases by 100 (because the multiplier is 2), he is not asserting that causality runs from Y to G. Though, in a sense, causality does run from *target* Y to the government’s choice of G.

  6. 6 JP Koning March 27, 2014 at 5:50 pm

    David, my guess is that Nick hasn’t entirely converted to your corner.

    For instance, if we imagine that all banks suddenly emit an excess supply of deposits, you usually say that these deposits will very quickly reflux back to the issuer with no effect on the price level, the redeemability commitment being the mechanism that brings this about.

    Nick would say (hopefully he verifies this for me) that this excess supply of deposits would probably push the price level up. However, an inflation-targeting central bank will see this and quickly tighten policy. Since deposits are redeemable in base money, the rise in the value of base money inspired by tightening will lead to a 1:1 rise in the value of deposits, and a more normal price level.

    But I could be wrong in my interpretation of you two. Good post. I also liked that bit from Mehrling’s book.

  7. 7 PeterP March 27, 2014 at 6:15 pm

    I think endogenous money does mean the CB doesn’t control prices, because the only tool left are interest rates. And those act only weakly apart from the housing channel.

    As to the multiplier it is a weird inability to differentiate a cause and effect. Gas pedal causes speed not the other way round. It makes no sense to call speed “pedal depressor”. Speed doesn’t depress the pedal, it is as simple as that.

  8. 8 Nick Rowe March 27, 2014 at 6:25 pm

    Typo?: “The post-Keynesian exogenous money movement…”
    should I think be “endogenous”.

    “The two propositions are completely independent of one another, and all the sturm und drang of the last 40 years about endogenous money has been a complete waste of time, an argument about a non-issue.”

    Totally agree. We take the central bank’s target as exogenous, and anything which depends on that target is endogenous. Unless the central bank has an M target, M is endogenous.

    In general equilibrium, it is not helpful to say that Base affects P only via its effect on M. Base affects both P and M simultaneously. Given neutrality of money, the money multiplier must be stable *in the long run*, since M/Base is a real variable. But in the short run, when money is non-neutral, who knows?

  9. 9 Nick Rowe March 27, 2014 at 6:32 pm

    JP: “Nick would say (hopefully he verifies this for me) that this excess supply of deposits would probably push the price level up.”

    Yes. Anything that increases the supply of something that is a substitute for base money would increase the price level, for a given base.

  10. 10 Nick Rowe March 27, 2014 at 8:23 pm

    A simple thought-experiment: holding the base constant, suppose the government subsidised commercial bank deposits. Would the price level rise? I say yes, provided we assume deposits are an (imperfect) substitute for base money. The (real) stock of deposits would increase, leading to an excess supply of deposits and/or base at the existing price level, leading to an increase in the equilibrium price level. Just like if you subsidise pears, the price of apples will fall.

  11. 11 Max March 28, 2014 at 3:32 am

    Nick, doesn’t that depend on reserves paying a below-market interest rate? If reserves are paying a competitive rate, then it doesn’t matter whether the public exchanges $100 bills for bank accounts.

  12. 12 Nick Rowe March 28, 2014 at 4:41 am

    Max: what constitutes a “competitive rate” depends on the relative quantities of each.

    This is the easiest way to think about it:

    An “excess supply of apples” means there is an excess supply of apples in the market where apples trade for money. That is one market. “Excess supply of apples” in unambiguous.

    But in an economy with n goods, plus one money, there are n markets in which money is traded, and n different excess supplies (or demands) for money. There could be an excess supply of money in the apple market, and an excess demand for money in the banana market.

    Given asymmetric redeemability, there cannot be an excess supply of beta money in the market where it trades for alpha money. But there can be an excess supply of beta money in all the other markets. People cannot wish to hold a different ratio (share) of alpha/beta money than they actually hold. But they can wish to hold a different sum of alpha+beta money than they actually hold. The Law of Reflux ensures the shares of different monies are always in equilibrium against each other; it does not ensure the quantities of different monies are always in equilibrium against goods. If one money is in excess supply against apples, all monies are in excess supply against apples.

    If money is convertible on demand into peanuts, there cannot be an excess demand or supply of money in terms of peanuts, but there can be an excess demand or supply of money in terms of all the other goods. The peanut theory of recessions is false.

  13. 13 Nick Edmonds March 28, 2014 at 6:52 am

    Nick

    “We take the central bank’s target as exogenous, and anything which depends on that target is endogenous. Unless the central bank has an M target, M is endogenous.”

    I presume by this you mean that it’s the target itself that is exogenous, rather than the outcome. So, even if the central bank has an M target, M will still tend to be endogenous. I’d say that even for an measure like base money, which the central bank can theoretically control precisely, in practice it’s only the target that is endogenous, as the central bank also has to meet other targets such as not letting the financial system collapse.

  14. 14 Max March 28, 2014 at 6:58 am

    In your scenario, some people are substituting from currency into bank accounts, right? But when that happens, the composition of base money shifts from currency into reserves. If reserves pay interest at the safe overnight rate, then the base quantity can remain constant without creating a disequilibrium. It would be like “QE”, only arising from a drop in currency demand rather than from CB asset purchases.

  15. 15 Nick Rowe March 28, 2014 at 8:09 am

    Nick E: “I presume by this you mean that it’s the target itself that is exogenous, rather than the outcome.”

    Correct. Only if we assume that control is perfect can we treat them as being the same. And that will depend on what we have built the model for. Sometimes I will assume inflation is always and everywhere 2%, if I am not interested in explaining how closely the BoC hits its target.

    Max: it depends why people want to shift from currency into deposits.

    David: I have a response, which I hope makes it clearer what I think:

    http://worthwhile.typepad.com/worthwhile_canadian_initi/2014/03/there-can-be-an-excess-supply-of-commercial-bank-money.html

  16. 16 Mike Sproul March 28, 2014 at 9:08 am

    Nick:

    “Anything that increases the supply of something that is a substitute for base money would increase the price level, for a given base.”

    If the base money is worth more than its backing, then the issuer got a free lunch. If private banks issue derivative moneys (checking accounts, credit cards, gift cards, etc) then the base money loses value and the issuer of the base money loses some of his free lunch. This should make the issuer of base money angry at the private banks. But where is the anger?

    On the other hand, if base money is worth its backing, then there’s no free lunch, and nothing for the issuer of base money to be angry about.

  17. 17 Max March 28, 2014 at 9:17 am

    “Max: it depends why people want to shift from currency into deposits.”

    I’m just going with your thought experiment, where the government is subsidizing bank accounts.

  18. 18 David Glasner March 28, 2014 at 9:45 am

    Greg, Thanks.

    Rob, My point is precisely that its precisely because it’s endogenous that it’s useless. It’s just a reduced form relationship, not a structural one. It doesn’t tell us anything about how the system operates, just that in equilibrium there is a relationship between the monetary base and the total amount of deposits. And there is no reason to believe that the relationship is stable. So what good is it? Annoying post-Keynesians is not a reason, it’s an excuse.

    Nick, What happens to the speed of your car when you push down the gas pedal depends on a whole bunch of stuff, like the horsepower in your engine, the transmission, the road that you’re driving on. The money multiplier pretends to be a structural relationship that tells us something useful about the relationship between the supply of broad money and the monetary base, but it is just a summary of the combined effects of a bunch of structural demand and supply relationships. It purports to enlighten, but it simply distracts attention from relationships that are important.

    JP, Whether an increase in the quantity of money emitted by banks increases the price level depends on why the bank money has been increased. If the quantity of bank money outstanding increases because of a shift in demand away from base money to bank money (because banks have made it cheaper to hold their moneys– say, by increasing the interest they pay on deposits — than holding currency), then, yes, the reduction in demand for base money will cause an increase in the price level unless the central bank reduces the amount of base money. However, it the amount of bank money increases because some or all banks increase the amount of lending, unless banks have a way of inducing the public to increase the amount of deposits they want to hold, banks will experience a drain on their reserves and will have to reduce their lending, and there will be no effect on the price level.

    PeterP, The interest rate affects the amount of base money demanded, and the amount of base money in the system affects the price level.

    Nick, Yes, thanks, it should have been endogenous. Fixed it. Yes, base affects both M and P simultaneously. The point of the money multiplier was to say that base affects M and M affects P. The money multiplier was a structural relationship determining the supply of money, not the reduced form that we now understand it to be. Once we understand that it’s a reduced form, we understand that we have no reason to care about it. We agree about your thought experiment. Here’s my question. Given an equilibrium, let the supply of bank money increase, holding everything else constant. I say, the excess money refluxes back to the banks and the price level doesn’t change. You are assuming, as in your response to
    Max, that there is no market mechanism by which unwanted money is returned to the banks. Holders of money can exchange their money for assets held by the bank (e.g., liabilities previously used to obtain money from the banks). If you are saying that a necessary and sufficient condition for a persistent excess demand or supply of bank money is a persistent excess demand for or supply of base money, I will not argue. But that means that you can’t have a persistent excess demand for or supply of bank money in the absence of a persistent excess demand for or supply of base money.

    Nick Edmonds, There is always a question about how much to include within a model. For purposes of policy evaluation, we are interested in letting policy be exogenous and comparing the effects of alternative policies. From another perspective, we may be interested in predicting how policy evolves over time and we posit a policy reaction function of some sort. No variable is intrinsically exogenous or endogenous.

    Max, If the central bank chooses to pay competitive interest on reserves, the elasticity of demand for base money increases, and its ability to determine the price level is attenuated. That’s a problem with the policy of paying interest on reserves.

    Nick, Great, thanks. I saw it, but haven’t read it yet.

  19. 19 Tom Brown March 28, 2014 at 10:05 am

    David, if we have

    r = “the reserve ratio” = (total reserves)/(checkable deposits)
    c = “the currency ratio” = (currency in circulation [not bank vaults])/(checkable deposits)

    And we take

    money multiplier = (1+c)/(r+c) = M1/MB

    What do you think of these descriptions of r, c, and MB, which apparently appear in Mishkin’s text book:

    “The currency ratio is always portrayed as the depositors’ choice, the reserve ratio (above required, if any) is always the lenders’ choice, and the total amount of currency and reserves (the monetary base) is the central bank’s choice (even if supplied through the discount window)”

  20. 20 Tom Brown March 28, 2014 at 10:07 am

    MB = (currency in circulation) + (total reserves)

  21. 21 JKH March 28, 2014 at 10:08 am

    “No variable is intrinsically exogenous or endogenous.

    That could be a good starting point for “a theory of everything” about economics

  22. 22 Nick Rowe March 28, 2014 at 10:32 am

    David: ” But that means that you can’t have a persistent excess demand for or supply of bank money in the absence of a persistent excess demand for or supply of base money.”

    Agreed.

    “Given an equilibrium, let the supply of bank money increase, holding everything else constant. I say, the excess money refluxes back to the banks and the price level doesn’t change.”

    If “everything else” includes things like the rate of interest paid on bank money, we very nearly agree there. (It won’t be strictly correct if bank money is a perfect substitute for base money). But even if banks raise the interest rate paid on bank money to prevent reflux, that will mean there is an excess supply of both monies against other goods, holding the base constant.

    Closing in on agreement.

  23. 23 Tom Brown March 28, 2014 at 11:38 am

    David, can we safely substitute “paper notes and coins” for all occurrences of “currency” in your post? Thanks.

  24. 24 Blue Aurora March 28, 2014 at 7:04 pm

    Since we are on the subject of endogenous credit creation…IIRC, some Post Keynesian economists have argued that J.M. Keynes “understood endogenous money and used it in A Treatise on Money, but reverted back to exogenous money in The General Theory“. On closer inspection, I’m not so sure. J.M. Keynes does acknowledge that money can be created via endogenous and exogenous processes, and points to Industrial Fluctuations by A.C. Pigou as another author aware of this fact.

    It seems to me that the question of how the money is created isn’t so important – after all, both scenarios of money creation still require the retention of liquidity. Perhaps it is how the money is used that is the real problem…

  25. 25 Tom Brown March 28, 2014 at 7:39 pm

    Blue Aurora, I am not an economist (not even close!), but I do my best to digest some concepts here. One of the things that’s been a little confusing to me has been endogeneity vs exogeneity and how various econ bloggers use those terms. I try to summarize my views here a bit and sort out where Nick Rowe stands vs David Beckworth for example:

    http://pragcap.com/crickets/comment-page-1#comment-171571

    It occurs to me, in my non-econ brain, that we could actually measure a degree of endogeneity of one variable wrt another. For example, the magnitude of their correlation coefficient might be a good candidate. So for example, suppose a fixed inflation rate were targeted exogenously at 2%. Then if we wanted to measure the degree of endogeneity of say the monetary base wrt the inflation rate, we measure the magnitude of it’s correlation coefficient with the inflation rate achieved. If rho = 0, we could say MB is “fully endogenous.” If |rho| is on (0,1) then it’s partially endogenous. And if |rho| = 1, then MB is fully determined by the inflation rate, and thus it’s just as exogenous as the inflation rate.

    I have a couple more comments on that underneath the one I link to above (both before and after Frances Coppola’s response to me). I’d appreciate any feedback. Thanks!

  26. 26 Dustin March 28, 2014 at 8:22 pm

    David,

    You said: “but it is just a summary of the combined effects of a bunch of structural demand and supply relationships”

    Absolutely true (not sure who claims otherwise). But aren’t summaries alone interesting? If the multiplier (really just a ratio) changes, it means something. And things that mean something are, well, meaningful in some way.

  27. 27 PeterP March 28, 2014 at 8:31 pm

    “PeterP, The interest rate affects the amount of base money demanded, and the amount of base money in the system affects the price level.”

    Yes, affects, but is the effect strong enough to be measurable? Or is it an article of faith? I’d say incomes and net worth affect the price level a lot more than the amount of base money, because everyone knows their income and their balance sheet, and very few can sense what the level of base money is.

  28. 28 Tom Brown March 29, 2014 at 9:06 am

    Nick writes,

    “But even if banks raise the interest rate paid on bank money to prevent reflux, that will mean there is an excess supply of both monies against other goods, holding the base constant.”

    But “other goods” does NOT include bank assets, for which there can be neither an excess supply nor demand, true?

  29. 29 Nick Rowe March 30, 2014 at 1:32 am

    Tom Brown: “But “other goods” does NOT include bank assets, for which there can be neither an excess supply nor demand, true?”

    False. Sometimes beta banks’ assets include fixed term loans, which you cannot pay off any time you want, unless beta banks agree. And sometimes beta banks may ration loans.

  30. 30 David Glasner March 30, 2014 at 7:32 am

    Tom, I don’t believe that depositors are choosing a ratio of deposits to currency, I believe they are choosing how much currency to hold and how much deposits to hold. I agree that central bank chooses how much currency and how much reserves to create when currency and reserves are non-interest bearing and when nominal rates are positive. When nominal rates are zero, demand for currency and reserves becomes very elastic and it is hard to specify what the demand is.

    JKH, Not much of a starting point, but let me know if you make any progress.

    Nick, I think that you have to distinguish between perfect substitutes and indistinguishability. My bank deposit may be a perfect substitute for my Federal Reserve notes, but that doesn’t mean I can’t tell them apart. If I have a larger bank balance than I would like, I can reduce that bank balance to the desired amount without any repercussions on my holdings of currency. Also if banks raise the interest rate on deposits when there is an excess supply of money to induce the public to hold an increased quantity of deposits, the excess supply of deposits has been eliminated, so I don’t know what you mean by saying:

    “if banks raise the interest rate paid on bank money to prevent reflux, that will mean there is an excess supply of both monies against other goods, holding the base constant.”

    Tom, Yes, I think so.

    Blue Aurora, My understanding is simply that in the Treatise on Money, Keynes did not assume that the quantity of money was fixed; he recognized that the amount of money created by banks responded to economic incentives including the public’s demand for liquidity. In the GT, however, Keynes, in hyper-Monetarist fashion, assumed that the quantity of money was a constant determined by the monetary authority, without any discussion of the incentives of the banking system to create more or less money in response to fluctuation in the public’s demand for liquidity.

    Tom, Your suggestion has some merit as a test of exogeneity, but you also need to adjust for the amount of variation. If the rate of inflation is not varying very much, and the measured coefficient is low, you can’t really make any inference about the degree of endogeneity/exogeneity.

    Dustin, I didn’t say that the money multiplier is meaningless; I said it’s useless.

    PeterP, For the monetary base to be an effective instrument of monetary policy, the interest rate does not have to be the most powerful factor affecting the demand for the monetary base, it just has to affect the monetary base in a predictable way.

  31. 31 Tom Brown March 30, 2014 at 9:53 am

    David, thanks a ton! Very helpful. Of the three “choices” that Mishkin presents though

    1. c is deposits’ choice
    2. r is lenders’ choice
    3. MB is CB’s choice

    You’ve covered 1. and 3. but not 2. Unfortunately 2. was the one of greatest interest to me. :D

    So what do you say? Is

    r = reserves / (checkable deposits) = “reserve ratio”

    really well described as primarily or exclusively the “lender’s choice?”

    Of the three, I think that’s the one Mishkin is furthest off on. Keep in mind that by “reserves” I mean total reserves: required, excess, vault cash, and electronic. Briefly reviewing the other two (and why I don’t have a problem with Mishkin on those):

    Regarding 1. c = the currency ratio

    I agree that depositors’ don’t literally select a ratio but they pretty much do the equivalent, like you say: pick a numerator and a denominator. Unless something is forcing their hand (like bank failures in the 1930)… I think it’s an OK approximation to say that the currency ratio (or it’s equivalent) is primarily the depositors’ choice.

    Regarding 3. MB = monetary base = currency in circulation + reserves)

    I agree that this is the CB’s choice primarily: even though they may have chosen not to chose and instead let an algorithm or rule govern it (for example, say they are targeting inflation or a fixed overnight rate of interest). But it’s always the CB’s prerogative to change the rule. I don’t fully follow your point about elasticity though.

    Regarding 2.: r = the reserve ratio

    Here’s why I think describing this as primarily the lender’s choice is misleading: Imagine a country with no cash and reserve requirements = 0%. Then the money multiplier ratio identity (call it “mm”) reduces as follows:

    mm = (1+c)/(r+c) = 1/r = 1/(excess reserves)

    and thus

    M1 = mm*MB = MB/(excess reserves)

    Now say the CB targets a fixed MB. I don’t think it’s a good description to say that the lenders choose r at this point: I think it’s a three way choice and that lenders’, borrowers (borrowers NOT depositors) and the CB all play an important role: the lenders will buy loans (determining a demand curve for loans), the borrowers will sell them loans (determining a supply curve for loans), and the CB has a big influence too. For example, right now in the United States, why are all the lenders “choosing” such a large value for r? (lots of excess reserves relative to deposits means r is big). I think it’s as plain as day that the CB has a big role, and it’s not just the lenders’ making that choice, or even primarily making that choice.

  32. 32 W. Peden March 30, 2014 at 10:10 am

    It’s not too clear to me why Keynes made the exogenous broad money supply assumption in the GT (it may have just been for analytic ease) but I do find it always fascinating how Friedman’s liquidity theory (1956) is an extension and de-idealization of Keynes’s, and I think an improvement.

  33. 33 W. Peden March 30, 2014 at 10:11 am

    In fact, two of the thinkers of the 20th century whom I really admire (Friedman and Carnap) both saw Keynes as a forerunner. A man of some talents, that Keynes…

  34. 34 David Glasner March 30, 2014 at 10:31 am

    Tom, Sorry for not responding about r. My answer is largely the same as for the currency deposit ratio. Bankers don’t choose a ratio, they choose an amount of reserves that they want to hold in light of the circumstances they perceive and their expectations about future conditions at a given moment. You don’t think that there is much difference between saying that depositors choose the quantity of deposits they want to hold and the quantity of currency they want to hold and saying that they choose a currency deposit ratio. At the level of arithmetic there is no difference at the level of understanding the monetary system, there is a huge difference, and the same is true for the reserve ratio.

  35. 35 Tom Brown March 30, 2014 at 11:19 am

    David, re: my “measure of endogeneity” or “exogeneity” scheme, thanks for the feedback, and you make an excellent point: I get what you are saying about the inflation rate not moving much making it hard,… I thought that at first too, but I’m not sure that’s a big concern. I have a scheme worked out. Say we were looking at three variables at a series of regular sample periods:

    x1 = log(MB), x2 = log(P), and x3 = d(x2)/dt

    and we construct a vector X(t(n)) = X[n] = [x1[n] x2[n] x3[n]]‘ at regularly spaced sample times t(n).

    x3 might be the target (it’s essentially a linearized inflation rate). Then we could calculate a sample covariance from the set of differences, D[n] = X[n+1]-X[n]. Say C = sample_covariance(D) = [c(i,j)], a 3×3 matrix

    Assume that an adequate approximation for the transition from one sample time to the next is a fixed 3×3 transition matrix F (which we don’t have to know BTW, just that it’s fixed) such that X[n+1] = F*X[n]. We should be able to now use C to measure a degree of exogeneity between x3 and any other variable: |rho(i,j)| = |c(i,j)/sqrt(c(i,i)*c(j,j)) where i = 3 say, and j = 1 or 2.

    If F is exact, then in this case rho(3,2) = 1 meaning x2 is fully co-exogenous with x3. rho(3,1) should be on (-1,1) though, meaning it (MB) has a degree of endogeneity wrt a fixed inflation rate.

    But now getting back to your concern: if we are perfectly targeting inflation, so that x3 is constant across time in our sample set, then we’ll have for D = [d1 d2 d3]‘ that d3 = 0, d1 > 0 and d2 is a constant > 0 at all time samples.

    In this case we can’t calculate any rhos because var(d3) = var(d2) = 0, but just the fact that they both are 0 tells us that P is a co-exogenous variable with inflation rate! … it’s pretty certain that c(1,1) = var(d1) > 0 (the only non-zero entry in C) in this case (meaning we can tell there’s a degree of endogeneity in MB still).

    So, you’re right: there are special cases, but it can still do the job.

    So maybe an easier and more general measure is just the variances of all the other variables assuming we’re doing a good job targeting one of them.

    This can be adapted for time varying F too.

  36. 36 Tom Brown March 30, 2014 at 12:19 pm

    David, thanks again! I’d propose we add a fourth category of “choosers” to the list: borrowers (as distinct from depositors). Then we might say:

    The numerator of c is chosen primarily by depositors, given a denominator.

    The numerator of r is chosen by the lenders and the CB in conjunction (witness the US now with the CB adding to the numerator of r every month via QE and IOR). Sometimes the CB doesn’t play as big a role (perhaps Canada currently?).

    The denominator of both r and c is chosen by the lenders and the borrowers in conjunction (the lenders setting the demand curve for buying loans and the borrowers setting the supply curve). Of course this is conditioned on depositors’ choice for the numerator of c.

    And MB is chosen by the CB (with above qualifications already noted).

    Shoot it’s a mess: I’m with you: it’s completely useless!

  37. 38 Nick Rowe March 31, 2014 at 6:34 am

    David: ” Also if banks raise the interest rate on deposits when there is an excess supply of money to induce the public to hold an increased quantity of deposits, the excess supply of deposits has been eliminated, so I don’t know what you mean by saying:…”

    Banks can raise the interest rate on deposits when there is an excess supply of bank money relative to base money (when the actual ratio of bank money to base money exceeds the desired ratio). If they do so, that ensures that nobody will want to get rid of bank money for base money. But it does not ensure that people will not want to get rid of both bank and base money for other goods. They hold the desired ratio, but they hold an excess total.

    The excess supply of deposits in the market where deposits are traded for currency has been eliminated. But the excess supply of deposits in the market where deposits are traded against all other goods has not been eliminated (if deposits and currency are close substitutes).

  38. 39 Nick Rowe March 31, 2014 at 6:38 am

    In the limit, as deposits become closer and closer substitutes for currency, the increase in interest rates on deposits needed to persuade people to hold a larger ratio of deposits to currency approaches zero, and raising the rate of interest on deposits does nothing to eliminate the excess supply of both monies relative to all other goods.

  39. 40 Jussi April 3, 2014 at 2:55 am

    “Banks can raise the interest rate on deposits when there is an excess supply of bank money relative to base money (when the actual ratio of bank money to base money exceeds the desired ratio). If they do so, that ensures that nobody will want to get rid of bank money for base money. But it does not ensure that people will not want to get rid of both bank and base money for other goods. They hold the desired ratio, but they hold an excess total.”

    But if there is an excess why they do not pay back loans to get rid off excess money (reflux)? There might be a hot potato in a way that not all have loans to pay back. Yet that should be short-lived and mostly cleared through asset prices?

    If currency and deposit market is cleared through interest rate, isn’t higher yield make them less substitutes? If deposits are yielding enough those are more resemblances with investment than currency? Thus at the same time altering also the supply of monies relative to all other goods?

  40. 41 Tom Brown April 3, 2014 at 9:20 pm

    This is a test

    of blockquoting text

    to see if it works here


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About Me

David Glasner
Washington, DC

I am an economist at the Federal Trade Commission. Nothing that you read on this blog necessarily reflects the views of the FTC or the individual commissioners. Although I work at the FTC as an antitrust economist, most of my research and writing has been on monetary economics and policy and the history of monetary theory. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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