...against fictions and other tall tales

Tuesday, 19 November 2013

On the (ir)relevance of the money multiplier model: The Fed view

It has long been known within the Federal Reserve System -- especially among economists who worked in the FRS in the 1970s and 1980s when much of the research agenda was directed at issues of monetary control -- that the money multiplier model of money stock determination is not the most realistic (or useful) way to understand how central banks conduct monetary policy.

Here is the former Fed Governor, the late Sherman Maisel, during a conference on the theme of 'Controlling Monetary Aggregates' in 1971:
It is clear that, as a matter of fact, the Federal Reserve does not attempt to increase the money supply by a given amount in any period by furnishing a fixed amount of reserves on the assumption that they would be multiplied to result in a given increase in money [...] 
Many unsophisticated comments and theories speak as if the Federal Reserve purchases a given quantity of securities, thereby creating a fixed amount of reserves, which through a multiplier determines a particular expansion in the money supply. Much of modern monetary literature is actually spent trying to dispel this naive elementary textbook view which leads people to talk as if (and perhaps to believe) the central bank determines the money supply exactly or even closely--in the short run-through its open market operations or reserve ratio. This incorrect view, however, seems hard to dislodge. (1971:153, 161)
Briefly, the money multiplier is basically a relationship between deposits (D) and reserves (R), D = mR, (or M = mB) where m is called the money multiplier (or M is money stock and B is the monetary base). According to the model, if banks keep excess reserves to a minimum and reserve requirements are applied to all deposits, then the multiplier can be constant and the central bank -- if it retains control of the volume of reserves -- can control the amount of deposits (Goodfriend and Hargraves, 1983:5). However, if the central bank does not exercise control over the amount of reserves, the multiplier model is inoperable and cannot be exploited for monetary control purposes.

The Classic Fed View

In the US, the Fed's inability to control the quantity of reserves in recent decades (before October 2008) is said to be because of the introduction of lagged reserve requirements in the late 1960s and the Fed's almost continuous use of an interest rate operating procedure.

Former St. Louis Fed economist, R. Alton Gilbert, discussed the impact of lagged reserve accounting on Fed operations in his article "Lagged Reserve Requirements: Implications for Monetary Control and Bank Reserve Management" (1980):
[Lagged reserve accounting] breaks the link between reserves available to the banking system in the current week and the amount of deposit liabilities that banks can create in the current week. If banks increase aggregate demand deposits liabilities in response to an increase in loan demand, they are under no immediate pressure to reduce their deposit liabilities...Under LRA, the Federal Reserve tends to adjust total reserves each week in response to the total deposit liabilities that banks created two weeks earlier. (1980:12)
With lagged reserve requirements in effect the volume of reserves is determined by banking system demand. Reserve demand is simply accommodated and required reserves serve only to enlarge the demand for reserves at any given level of deposits. Under LRA, the change in R occurs as a result of changes in D, the exact opposite of the money multiplier model.

Former Richmond Fed economist, Marvin Goodfriend, discussed the relevance of the money multiplier model when lagged reserve requirements are in effect in his paper "A model of money stock determination with loan demand and a banking system balance sheet constraint(1982):
...[T]he discussion has shown that the money multiplier is not generally a complete model of money stock determination and is actually irrelevant to money stock determination for some monetary control procedures. Specifically, the money multiplier is irrelevant to determination of the monetary aggregates if lagged reserve requirements are in effect. (1982:15)
As for the other institutional factor relating to the Fed's use of an interest rate operating procedure, Robert Hetzel of the Richmond Fed highlighted the following in his paper "A Critique of Theories of Money Stock Determination(1986):
Deposits and reserve demand are determined simultaneously with credit creation. As a consequence of defending its rate target, the monetary authority, by creating an infinitely elastic supply of reserves, accommodates whatever reserve demand emerges...In a regime of rate targeting, neither the quantity of reserves nor the desired reserves-deposits ratio of the banking system exercises a causal role in the determination of the money stock (1986:6) [...]
Interest rate smoothing by the monetary authority makes reserves and the money stock endogenous...Since [Chester] Phillips (1921), reserves-money multiplier formulas have been derived from a model of the banking sector summarized in the multiple expansion of deposits produced by an injection of reserves. The existence of markets for bank reserves, however, renders this model untenable. Phillips' model assumes that the individual bank is constrained by the quantity of its reserves and that its asset acquisition and deposit creation are driven by discrepancies between actual and desired reserves. Given the existence of markets for bank reserves, such as the fed funds and CD markets, however, individual banks are constrained by the price, rather than the quantity, of reserves they hold. (1986:20) (emphasis added)
A succinct and detailed discussion of the problems associated with multiplier models of money stock determination is found in the excellent article "Understanding the remarkable survival of multiplier models of money stock determination(1992) by former Fed economist, Raymond Lombra:
Assuming textbook authors reveal their intellectual and pedagogical preferences and beliefs, a careful survey of the leading intermediate textbooks in money and banking and macroeconomics reveals a uniform and virtually universal consensus – the multiplier model of money stock determination is widely viewed as the most appropriate and presumably most correct approach to the topic...Since such consensus is not, in general, an enduring characteristic of monetary economics, one is tempted to “let sleeping dogs lie”. The problem is that the multiplier model, whether viewed from an analytical or empirical perspective, is at best a misleading and incomplete model and at worst a completely misspecified model. (Lombra, 1992:305) (emphasis added)
Lombra's article is especially useful because it groups together the different critiques of the multiplier approach into two categories (the article discusses a third set of critiques relating to the predictive accuracy of multiplier models but this issue is less relevant for this post). 

The first set of critiques identified by Lombra is that the multiplier model "is not structural but rather is a reduced-form", a point first made in the 1960s by proponents of the "New View" (including James Tobin in "Commercial banks as creators of "money")*. Lombra summarizes this critique as follows:
Succinctly stated, the critique emphasizes that the multiplier approach abstracts from the short-run dynamics of adjustments by banks and the public, leaves the role of interest rates implicit rather than explicit, and proceeds that the movements in the monetary base (or reserves) are orthogonal to fluctuations in the multiplier. The multiplier model, it is argued, implies that deposit expansion is quantity constrained through the Fed's control over the sources of bank reserves (chiefly, the Fed portfolio of securities). One of the most forceful and articulate crafters of the critique, Basil Moore, concludes that "as a result, the money multiplier framework is of no analytical or operational use".

The consensus view of the staff and policymakers within the Federal Reserve, as revealed in numerous publications, embraces much, if not all, of the critique advanced by Moore and others. In particular, the Fed adheres to the view that the system is equilibrated through the movements of interest rates, which through their effects on bank revenues and costs, determine banks' and the public's desired asset and liability positions. In this view, money is controlled by using open market operations to affect interest rates which in turn affect demand and thus the uses of bank reserves (chiefly, required reserves).  (307)
The second set of critiques discussed by Lombra concerns the issue of the endogeneity of reserves, that is, the notion that the quantity of reserves is in practice determined by the banking system:
This contention, which is related to the lagged reserve accounting scheme...and the Fed's interest rate operating procedure in effect for virtually all of the post-Accord period, implies the multiplier model is completely irrelevant for the determination of the money supply. (308)
Lombra's article concludes with a discussion on why, despite these important flaws, the multiplier approach continues to be popular among economists. The reason, he argues, is that when applied to longer term horizons the models track monetary growth reasonably well:
The model lives on with model-builders who are confirmed adherents to the Law of Parsimony and skilled in the use of Occam's Razor. The high correlations and identities so tightly linking reserves (or the base) and money over the longer run provide all the comfort most empiricists need to proceed as if the concerns noted above matter little. (312)
Still irrelevant?

Recently, Fed economists Seth Carpenter and Silva Demiralp concluded in their paper "Money, Reserves, and the Transmission of Monetary Policy: Does the Money Multiplier Exist?" that the money multiplier is not a useful means of assessing the implications of monetary policy for money growth or bank lending in the US.

Not only does their paper discuss the institutional factors that render the money multiplier inoperable (including those discussed above), it also demonstrates empirically that the relationships between reserves and money implied by the money multiplier model do not exist.

These conclusions should, however, be viewed with caution given that the period under investigation in the paper ends in 2008, just prior to the Fed's shift toward the use of unconventional monetary policies.

Interestingly, Robert Hetzel now believes that the money multiplier model has actually gained relevance since the Fed started with its large-scale asset purchases in 2008.

Here is an excerpt from Hetzel's recent book, The Great Recession:
Starting in mid-December 2008 when the FOMC lowered its funds-rate target to near zero with payment of interest on bank reserves, the textbook reserves-money multiplier framework became relevant for the determination of the money stock. The reason is that the Fed's instrument then became its asset portfolio, the left side of its balance sheet, which determined the monetary base, the right side of its balance sheet. As a result, from December 2008 onward, the nominal (dollar) money stock was determined independently of the demand for real money. Although the reserves-money multiplier increased because of the increased demand by banks for excess reserves, the Fed retained control of M2 growth. Even if banks hold onto increases in excess reserves, the money stock increases one-for-one with open market purchases. (2012:237) (emphasis added)
In other words, Hetzel is saying that, as a result of its ability to determine the monetary base (B), the Fed now exercises considerable control over the change in deposits (D). And by doing so, Hetzel is suggesting that the Fed -- in one way or another -- is currently exploiting the money multiplier framework.

Here's a chart that appears to support Hetzel's claim:

The chart shows that since 2008 changes in B -- resulting from Fed asset purchases -- are clearly associated with changes in M**. For the period prior to 2008, there is no such relationship.

Hetzel's claim about the relevance of the multiplier approach could help to explain why some commentators have found causal relationships between changes in the monetary base and other variables for the period since December 2008.

For instance, Market Monetarist proponent Mark Sadowski recently pointed to empirical evidence that changes in the monetary base have had some causal role since December 2008:
I’ve done Granger causality tests on the monetary base over the period since December 2008 and find that the monetary base Granger causes the real broad dollar index, the S&P 500, the DJIA, commercial bank deposits, commercial bank loans and leases, the PCEPI, and 5-year inflation expectations as measured by TIPS.
So what's the bottom line? Does this mean the money multiplier model is now relevant?

On the one hand, I'm not convinced the model is entirely applicable (for instance, the textbook treatment implies that banks keep excess reserves to a minimum, which is obviously not the case today). On the other hand, it's unlikely that Hetzel is somehow wrong here.

Fortunately, I don't think it matters much one way or another, unless perhaps you are a Fed technician or an econometrician. What does matter is that the Fed currently exercises control over the monetary base. This, in itself, is a significant development for understanding the policy options now available to the Fed.

One thing is for sure, this recent development provides an excellent illustration of a crucial point often highlighted in Raymond Lombra's work:
The specific procedures ("policy rule") employed by the Fed and the reserve accounting regulations governing bank reserve management play a crucial role in determining causal relationships and system dynamics. (1992:309)

* The 'New View' focused on the role of assets, both real and financial, and the relative price mechanism in monetary analysis. From an operational standpoint, it contended that the Fed has little control over the money stock and that the money stock plays only a minor role in the transmission mechanism linking Fed actions to the real sectors of the economy.

** It's clear that the monetary base is not pulled upward due to increased deposit creation by banks.


Carpenter, S and S. Demiralp, Money, Reserves, and the Transmission of Monetary Policy: Does the Money Multiplier Exist?", Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs, Federal Reserve Board, Washington, D.C.2010

Gilbert, R.A., Lagged Reserve Requirements: Implications for Monetary Control and Bank Reserve Management", Monthly Review, Federal Reserve Bank of St.Louis, 1980:

Goodfriend, M., A model of money stock determination with loan demand and a banking system balance sheet constraint", Federal Reserve Bank of Richmond Working Paper, 1982

Goodfriend, M. and M. Hargraves, A historical assessment of the rationales and functions of reserve requirements, Federal Reserve Bank of Richmond Working Paper, 83-1, 1983

Hetzel, R., A Critique of Theories of Money Stock Determination, Federal Reserve Bank of Richmond Working Paper, 86-6, 1986

Hetzel, R., The Great Recession: Policy Failure or Market Failure, Cambridge University Press, 2012

Lombra, Raymond. Understanding the remarkable survival of multiplier models of money stock determination, Eastern Economics Journal, Vol 18, No 3, 1992

Maisel, S., Controlling Monetary Aggregates, Federal Reserve Bank of Boston Conference Proceedings, 1971

Tobin, J., Commercial banks as creators of "money" 1963


  1. Nice post!

    There's also Lombra and Torto from the mid 70s.

    1. Nice nod Ram, but wasn't it Circuit and FRB that dug up the youngsters from the Fed. No need to remind him. Looks to me like MMTers had forgotten where the parameters originally came from; in fact I believe they had never heard of Lombra and Torto.

      At least, you praise the pioneers!!! Most others MMTers don't even acknowledge their contribution

    2. Right yeah I have seen the reference to it in this blog. I actually found the reference in Moore's book Horizontalists and Verticalists.

  2. with QE the ultimate sellers of treasuries are largely non-banks. The primary dealers buy from these non-bank sources and then sell to the Fed. As such Fed QE purchases increase non-bank deposits as well as bank reserves. This doesn't mean that a money multiplier process from reserves to deposits is at work though.

    1. I think your point is generally consistent with the second Hetzel quote. Note also that models are useful because they simplify complex processes. Note that he's not looking at it from a single bank's perspective (the loan and deposit expansion process of a single bank). His focus is at the macro level (total money supply).

  3. !!! Circuit. I like the way you assembled your references,. esp Goodfriend, Hetzel (any monetarist rolling and rantng) and Tobin. Since nothing with you is accidental, you assembled quite a roster for the Fed to match up with in terms of publications. I think one of your readers, a while back, had emphasized that the Fed economists play second fiddle to no one. Lombra and Torto certainly showed that by paving the road for operatives. StatsCan, before the reorg was like that: talent to spare. What a shame.

    !! stay the course Circuit. great work.

    1. Thanks Swells. Nod!!

      Caught it all (youngsters, fiddles, Goodfriend, StatsCan(!)). How could I? Someone told me a while back to "pay attention to every word".
      It'd be great to hear from a monetarist. In fact, I'm looking for good Harry Johnson references.

  4. Excellent post.

    I think Hetzel is wrong though.

    What is at work in QE is better described as a money duplication process rather than a money multiplier process. It's entirely different.

    The correlation between base changes and M2 changes during QE has nothing to do with the reserve ratio calculation that is part of the money multiplier math.

    It has to do with the fact that non-banks were the ultimate source for most of the assets acquired by the Fed under QE. To the degree that's the case, there is a 1:1 duplication of reserve expansion and M2 expansion at the point of transaction origin. Non-bank bond sellers basically convert their bonds to M2 at source.

    Subsequent commercial bank balance sheet changes may change the one-to-oneness that appeared at origination, but that also has nothing to do with money multiplier dynamics.

    So in total this has nothing to do with a standard money multiplier argument. The two should not be confused.

    1. I see y said about the same thing above, which I agree with

      Again, IMO it's a very bad idea to conflate this with the money multiplier concept - two completely different levels of monetary operations logic

  5. Very good work. I am particularly fond of your Tobin insertion. I would add a most important contribution that has inspired, in its own way, both Hetzel (sometimes difficult) and Ben Friedman; Lombra/ Moran: Policy Advice and Policymaking in the Fed Res. It has very valuable insights.

    I enjoyed all your posts but took nostalgic pleasure in seeing Samuelson at his sensible best and noting Steindl's name reappearing and being very seriously considered.


    1. "...sensible best..." LOL!

      Also, I like Steindl's "Stagnation Theory and Stagnation Policy". Some parts read as though it was written today. Covers topics like austerity and debt.

  6. I agree with JKH's nice comment.

    In the quote you quote by Hetzel, there isn't any mutliplier and he just says that the Federal Reserve has more influence on the stock of money.

    However Hetzel is wrong that the Fed actually determines the stock and that it is not demand determined. Economic units still hold money balances as per their desire. The stock of money is still demand determined because of reflux, asset allocation mechanism etc.

    1. As in I should say that even though Hetzel says money multiplier framework, his mechanism - whether his reasoning is right or wrong - is that it is determined by the monetary authority and that itself is wrong even if money multiplier is wrong (which it is ie wrong).

    2. Oh inspired a post:


    3. Like Ramanan and JKH, I disagree with Hetzel's view. But I'm not sure I agree with JKH's alternate theory. The correlation between M2 and the base could be due to a third causal factor -- namely outbreaks of fear and panic. When bad events happen investors rebalance their portfolios away from shadow banking deposits (and/or riskier European deposits) into M2 deposits. Thus the rise in M2. At the same time the Fed reacts to these outbreaks by initiating a new round of QE, driving up the base. So they are separate phenomena. Assuming that I'm right and there is no causal relationship between base and M2, then an outbreak of panic not met by a new round of QE would still be met by a rise in M2.

    4. Hi JP,

      I approach this stuff from the starting point of other things equal logic.

      So if most of the bonds sold into QE originate from non-bank balance sheets (which they did), then QE increases reserves and M1 at origin 1:1. That’s pretty close to an accounting/operational tautology according to how the payment system works.

      As I said in my comment above, there may be subsequent changes in balance sheet composition for a variety of reasons. For example, new equity issued by banks during the QE period would be paid for by debit to M1 deposits – so that would result in a recomposition of the funding side of the banking system while reserves remained in tact on the asset side. That’s just one example. There are probably a zillion of them.

      Regarding your point on panic rebalancing from shadow banking into M2, I’d use the same approach from the start. In order for that to happen, there has to be an accompanying shift in which shadow banks sell their assets to banks – somehow. Other things equal, system balance sheets won’t balance otherwise. I haven’t thought about that, but you’d have to come up with a thesis that would explain the order of magnitudes involved in such a shift so as to:

      a) Correlate that asset expansion materially with that M2 expansion

      b) Explain what happened to the original M1 creation attributable to QE at origin

      What your thesis suggests is a double flow of assets into the banking system – QE reserves and shadow banking asset imports – matched by a double flow of deposit creation for the two reasons I’ve suggested.

      So there would seem to be a duplication of balance sheet expansion required at origination with a subsequent messy disentangling of that in order to explain where we finally got to. But I’m not sure that story works, because you have what are essentially two strong cyclical forces – QE and asset migration – working in parallel, both requiring bank balance sheet expansion, other things equal.

      In all cases, one must explain with some sort of summary model how balance sheets end up balancing. That’s what the story must be about.

      Not saying you’re wrong – just that I would be interested in your alternative balancing story.

    5. Yes, I see what you mean. I originally discounted (b) but having worked through the accounting, I get it. There is a one-to-one effect, as you describe it, between each dollar of QE and each dollar of deposits, and this could explain the correlation.

  7. These are all great comments so thanks to everyone. As I wrote, I'm not altogether convinced about Hetzel's claim so I'm glad I stayed on the fence on this one.

    In fact, I thought a lot about this issue before writing the post, but I figured Hetzel thought it through. It seems to me he's using the expression 'reserve-money multiplier' as short-hand to express the fact that the Fed now has influence over both B and growth in M. I suppose he's saying that once that happens, then "the deed is done", the model applies.

    I've seen some textbooks with decent multiplier models that take into account complicating realities. They're still 'sausage grinder' models but they seem to allow for adjustments by banks and the public. Perhaps Hetzel is suggesting that with Fed actually exercising influence over B and growth in M, the models work better.

    @Ram: Nice follow-up on your blog.

    @GC: Thanks. The Lombra/Moran book is excellent. In fact, I really got a kick out of this part from Lombra's introduction on the monetarist critique of keynesianism: "While it is tempting to examine each of the above premises, there is a considerable risk of getting bogged down in analytic details which may not be essential to understanding policy advice and policy-making. A more productive route may be to focus on the key economic, social, and political aspects of the critique and the reaction to it". The analysis that follows is excellent. I enjoyed the part about the supposed harm associated with inflation vs unemployment. It includes some nice quotes by Tobin and Okun.

    1. @GC: Apologies...Looks like I am referring to a different article (not the Lombra/Moran). The quote comes from Lombra's "Policy advice and policy making: Economic, political and social issues" from the book "The Political Economy of policymaking: essays in honor of W.E Mason"

  8. @Ram:

    In your post, you mention:

    "In Post-Keynesian monetary theory, economists say that the stock of money is “demand-determined” and Hetzel’s arguments seems to be against this view. However what Hetzel forgets is that while the Federal Reserve influences the stock of money, it is still demand-determined."

    About the last sentence, surely the central bank can control money growth within a certain range, especially on a longer-term horizon. Doesn't that mean the supply side matters just as much?

    1. True it matters a bit but "control" is another thing. Control is moving it in the desired direction without difficulty. It may move it in one direction sometimes but this doesn't mean always.

      So let us consider the opposite case where the central bank is behaving like the 70s. If bond holders fear losses, the non-bank sector may sell bonds to the banks (who are prepared to buy and sell) and the stock of money can actually increase even if central banks try to reduce it. In this case it is true that the supply mattered but the result was opposite of what is intended.

    2. That's why they explain that control is "within a certain range or band". It implies the CB doesn't have complete control but it has significant influence over time.

  9. This is an interesting post! Thanks for the useful links and references.

  10. Very good article - thanks for all the enlighting citations! Nevertheless, I still think money multiplier or fractional reserve model is wrong. Banks can still create money by expanding the two sides of their balance sheet simultaneously. However, in crises when interbank market for reserves dries up, they are more careful and many of them need to be sure they have enough reserves on hand before they land. Also, excess reserves in the Fed system does not automaticaly imply that there is now a causal relationship between reserves and lending. For example, ECB in it's may 2012 Monthly Bulletin states that:

    "The large increase in Eurosystem lending to euro area credit institutions was mirrored by a significant increase in base money (see Chart B). Base money consists of currency in circulation, the deposits that credit institutions are required to maintain with the Eurosystem in order to cover the minimum reserve requirement (required central bank reserves) and credit institutions’ holdings of highly liquid deposits with the Eurosystem over and beyond the level of required central bank reserves (excess central bank reserves and recourse to the deposit facility), which can be considered “excess central bank liquidity”. The increase in base money is mainly attributable
    to an expansion of the excess central bank liquidity held by some euro area credit institutions. The occurrence of signifi cant excess central bank liquidity does not, in itself, necessarily imply an accelerated expansion of MFI credit to the private sector. If credit institutions were constrained in their capacity to lend by their holdings
    of central bank reserves, then the easing of this constraint would result mechanically
    in an increase in the supply of credit. The Eurosystem, however, as the monopoly
    supplier of central bank reserves in the euro area, always provides the banking system with the liquidity required to meet the aggregate
    reserve requirement. In fact, the ECB’s reserve requirements are backward-looking, i.e. they depend on the stock of deposits (and other
    liabilities of credit institutions) subject to reserve requirements as it stood in the previous period, and thus after banks have extended the credit demanded by their customers." (page 21)


    Any thoughts on that?


    1. Ales,

      Thanks for your comments and for the link. The excerpt you provide is certainly consistent with the Fed mechanism prior to December 2008 (and Japan during the QE phases in the 2000s). The system works through the upward pull of reserves by deposit creation. Since December 2008, additional reserves creates deposits, one for one. In other words, there is a 'multiplier' of one. Under such circumstances, the central bank has the ability to exogenously control the money supply. Some folks disagree with this because the public is constantly rebalancing its portfolio, which implies that the money supply can't be controlled...My view is that the central bank has considerable influence. That said, whether or not that influence is helpful is another story...

    2. OOps!

      I meant to say (and Japan BEFORE the QE phases in the 2000s)

  11. Hi,

    Thanks for you reply. My view is that the banks are just careful and once the conomiy recovers and confidence sets in, we will again see that there is no causal relationship between reserves and lending. However, I may be wrong.



  12. Hello Circuit. I enjoy reading your blog. I have a similar blog at http://savingsandinvestment.blogspot.ca/. The reason I am writing is that I live in Ottawa as well and because of our similar interests, perhaps we can meet over coffee and chat. My personal email address is beichenlaub@gmail.com. Thanks

    1. Welcome Bernhard! I'll drop you an email soon. Thanks for reaching out.