This essay takes a narrow view of the debate; does the central bank set the level of the “money supply” or an interest rate? However, some authors take a wider definition of what constitutes the “endogenous money debate,” but I view those to be separate questions. These wider definitions are more relevant to understanding recent macro arguments, as it would be difficult to find a trained economist under the age of 40 who follows the strict definition of exogenous money that I use. These more general definitions are more abstract, relying on unmeasurable concepts like the expected money supply. Since the assertions in those debates cannot be compared to empirical results, there is no way of resolving them one way or another.
Exogenous Versus EndogenousThis an old debate (described further below), the exact terms of debate have changed over time. Since I believe that the debate is over, I will not worry about the exact phrasings used historically, and offer a simplified explanation.
- The “money supply” is exogenous if we believe that it is set directly by the central bank; private agents within the economy will set interest rates on instruments in response to the supply of money. (Exo- is the Greek root that indicates that something is external; in this case, the money supply is set externally to the model of the private sector.)
- The “money supply” is endogenous if we believe that the central bank sets the policy rate of interest; the level of money is determined by factors within the private sector. (The root endo- implies that it is an internal property; that is, the level of the money supply is determined within the model of the private sector.)
For example, take the discussion in the paper Money Creation in the Modern Economy (a working paper by Bank of England Researchers McLeah, Radia and Thomas )
Neither step in that story [exogenous monetary base and a money multiplier] represents an accurate description of the relationship between money and monetary policy in the modern economy. Central banks do not typically choose a quantity of reserves to bring about the desired short-term interest rate. Rather, they focus on prices — setting interest rates [emphasis in original – BR].Previously, central banks kept their operations veiled in opacity. Furthermore, during the early 1980s, they announced that they were following the Monetarist policy of forcing the money supply to grow at a target rate. (Monetarist economists had been the primary believers in exogenous money, a view that has been absorbed by many in the mainstream, even those that do not consider themselves Monetarist.)
Killing “Money” In Economic Theory Kills Exogenous MoneyIf we follow my prescription of abolishing “money” from economic theory, the debate is even easier to deal with. Instead of discussing whether the central bank can set some nebulously-defined “money supply,” we have to ask ourselves: can the central bank set the level of various instruments?
- There is no mechanism for the central bank to set the level of currency in circulation. It cannot force people to withdraw currency from banks. It could attempt to stop people from doing so (by stopping the delivery of new currency to banks), but this would trigger something resembling a bank run, and so the financial stability mandate of central banks would prevent that action.
- Loans are created voluntarily within the private sector, in response to economic conditions. There is normally no mechanism to force banks to increase lending (which creates deposits), although the central bank could attempt to reduce growth rates by imposing quantitative limits on credit growth. In modern economies, credit rationing has been eliminated, so this no longer applies. (In other words, in an economy with effective quantitative credit controls, exogenous money might be viewed as correct. That said, Hyman Minsky’s analysis of the evolution of the post-war banking system in the United States underlined the extreme difficulty of enforcing quantitative credit controls outside of an emergency.)
- Since deposit growth is not controlled by the central bank, required reserves are also outside of their control. (See comment below.)
- The only real freedom of action the central bank has it so buy assets (or lend against assets) so as to create excess reserves within the system. This does allow the central bank to grow its balance sheet relative to a certain minimum size (currency in circulation plus required reserves), but that minimum size is still determined by private sector actions. (This was made apparent by the policy of Quantitative Easing.)
The top panel shows the level of excess reserves in the United States banking system during that era. Up until the mid-1980s, it was well below $1 billion. Although $1 billion was a lot of money for an individual in those days, that is minuscule relative to required reserves. The bottom panel shows the magnitude (that is, absolute value) of monthly changes in total reserves as well as the changes in required reserves. The monthly changes in total reserves dwarfed that of excess reserves. Since excess reserves were essentially a small constant amount, the Federal Reserve had no choice but to supply almost exactly the amount of reserves required by the banking system each month. Notably, this was also true for the early 1980s, which was when the Federal Reserve was allegedly targeting the money supply (see below).
In summary, the policy-making committee at the central bank sets a target level (range) for the interbank rate, and the open market desk injects/drains reserves until the market rate of interest hits the target level (range). (Historically, the Federal Reserve allowed for a relatively wide variation around the target rate; once banks grew accustomed to the framework of an explicitly announced policy rate, the market rate was very tightly tied to the target.) The open market desk had very little leeway in setting the magnitude of the operations, since they had to provide enough reserves to cover required reserves, plus the small excess.
One could try to claim that the money supply is influenced by central bank policy; but the same thing is allegedly true of the price level when the bank targets inflation. Nobody sensible believes that the central bank has the power to set the price level in the economy to whatever level it wishes each month  (which is what a belief in an exogenous price level/inflation rate implies).
BackgroundThe previously cited text by Marc Lavoie introduces this debate. In Section 4.1.2, he notes that this idea could be traced back to the debate between the Currency School and the Banking School in England in the early 1980s. 
Ricardo and the Currency School argued that only coins and Bank of England notes could be considered as money, that this stock of money determines aggregate demand, and that aggregate money determined the price level, thus giving support to the quantity theory of money.The Banking School position was that the situation was more complicated in that bank deposits were involved.
The debate flared up during the hearings of the Radcliffe Commission in the late 1950s. Entertainingly enough, academics refused to listen to testimony of central bankers, under the theory that people who do something all day still know less about their area of expertise than academic economists. (Interest rate strategists are well acquainted with this phenomenon.)
Lavoie argues that the post-Keynesian view was still not that much different from the mainstream, at least until the 1970s – when the Monetarist fad regarding “money supply targeting” took hold. (I discuss that episode below.)
Outside of the scattered remnants of Monetarism, there really is not a lot of support for exogenous money. Most mainstream economists interpret their models in terms of the central bank setting the rate of interest. (This is outside of peculiarities such as Quantitative Easing, which is not easily modelled within DSGE models. The analysis of Quantitative Easing that has been done have been ad hoc empirical studies that have demonstrated whatever the authors wanted to believe about Quantitative Easing.)
However, the picture is muddied by the relatively simple money demand equations that exist. (In many models, there is no term that forces a demand for money, and so the models predict zero money holdings when interest rates are positive. In such a model, the money supply is obviously endogenous, since the central bank has no means whatsoever to change its level.) From a mathematical perspective, there exists an invertible function that relates interest rates to the money supply. Therefore, we can specify a “reaction function” for the central bank either as a rule on interest rates or as rule on money supply growth. As a result, using those models, one could argue either way regarding whether the money supply is endogenous. The issue is what happens when some extra complexities are introduced into the model, which would break the symmetry between specifying monetary policy in terms of interest rates or the level of the money stock. As my discussion notes, the analysis of how the various instruments are used within the economy in the real world breaks that symmetry.
The Monetarist ExperimentMonetarists argued that the central banks should control the growth of the money supply, following the logic of the Quantity Theory of Money. This position was translated into a belief that the central bank operated by setting the quantity of “money” in the economy. Various countries experimented with money supply targeting, including Canada (in the 1970s), the United Kingdom (until the early 1970s), and the Volcker Fed. (I am less familiar with the German Bundesbank’s experience, which was the less negative than the cases I discuss here. The Bundesbank was the only central bank that paid much attention to money growth when I started my career in finance in the late 1990s. This translated into the early European Central Bank discussing M3 growth, but attention to that aggregate has waned as the euro area turned to the more urgent question of not having the common currency disintegrate.)
There is a large literature on how money supply targeting worked in practice. However, I was unable to find a modern reference that greatly differs from my characterisation above: the central bank set the interest rate so that money growth would be near some target level.
One good example is the Bank of Canada working paper “The Quantity of Money and Monetary Policy” by David Laidler  , where he writes:
Simplifying somewhat, but without misrepresenting the essence of the case: a money-demand function was estimated using monthly data; values of its real income and price level arguments over a rather short policy horizon were forecast and plugged in, along with the lagged values dictated by the econometrics of an equation based on monthly data; a target value for the money supply became the equation’s left-hand-side variable; the resulting expression was solved for the value of the interest rate that would set money demand moving towards that target value over some desired time horizon; and the Bank then set its interest rate instrument at that value.His paper covers the Canadian experience, but there were strong parallels to the situations in the United States and the United Kingdom, but perhaps not Germany. The article is an interesting reference for my purposes as the author was relatively sympathetic to the objectives of the money supply targeting regime. (He also positions the debate in a somewhat different fashion than I do here, which makes the discussion more nuanced.) In the article, he states:
In light of this evidence, the widely held view that money-growth targeting was a failure is a little too pat. This is not to deny that genuine problems of interpreting the behaviour of M1, the aggregate on which the experiment focused, arose during the course of money-growth targeting, particularly from late 1979 onwards, or that these problems raised important doubts, still relevant today, about the usefulness of monetary aggregates as policy guides. It is, however, to question the common interpretation of this earlier episode, namely that it demonstrates a degree of inherent unreliability in these variables that should disqualify them from anything but a subordinate position in policy formation.I admit to a bias against the use of monetary aggregates in analysis, but I have no strong reason to believe that they are useless. Like other credit aggregates, they should provide some information about the evolution of the economy; however, the behaviour is dependent upon the current institutional framework. In other words, the usefulness of monetary aggregates in analysis is an empirical question.
Concluding RemarksThe debate between endogenous and exogenous money is one that would have been resolved a long time ago if economic theory did not assume the existence of some magical entity called “money” within its models, and instead confined itself to the analysis of the instruments that appear in the real world. Although the historical debate covered more territory than I discuss here, the most interesting part can be dealt with by accepting that the central bank sets the rate of interest, and the “money supply” is determined by the reaction of the private sector to macroeconomic developments.
 “Money creation in the modern economy,” by Michael McLeay, Amar Radia and Ryland Thomas, Bank of England Quarterly Bulletin, 2014 Q1. URL: https://www.bankofengland.co.uk/quarterly-bulletin/2014/q1/money-creation-in-the-modern-economy (I would like to thank an alert reader who found that the original link was broken.)
 Purists who think in terms of continuous time economic models would object that this would only be true for price level targeting, and not inflation targeting. However, in the real world, the inflation rate is defined relative to the fixed level from a year before, and so inflation targeting is equivalent to price level targeting in the near run.
 Page 184 of Post-Keynesian Economics: New Foundations, Marc Lavoie, Edward Elgar Publishing Limited, 2014. ISBN 978-1-78347-582-7.
 “The Quantity of Money and Monetary Policy,” by David Laidler, Bank of Canada Working Paper 99-5, April, 1999. URL: http://www.bankofcanada.ca/wp-content/uploads/2010/05/wp99-5.pdf