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)

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* 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.

References

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