Editing Money multiplier (section)

===The importance of excess reserves===

In some presentations of the money multiplier theory, the further simplification is made that commercial banks only hold the reserves that are legally required by the monetary authorities so that the R/D ratio is determined directly by the central banks.<ref name="krugmacro"/> In many countries the monetary authorities maintain [[reserve requirement]]s that secure a minimum level of reserves at all times. However, commercial banks may often hold [[excess reserves]], i.e. reserves held in excess of the legal reserve requirements. This is for instance the case in countries that do not impose legal [[Reserve requirement#Reserve requirements by country|reserve requirements]] at all like the United States,<ref name="RIP MM">{{cite web |last1=Ihrig |first1=Jane |last2=Weinbach |first2=Gretchen C. |last3=Wolla |first3=Scott A. |title=Teaching the Linkage Between Banks and the Fed: R.I.P. Money Multiplier |url=https://research.stlouisfed.org/publications/page1-econ/2021/09/17/teaching-the-linkage-between-banks-and-the-fed-r-i-p-money-multiplier |website=research.stlouisfed.org |publisher=Federal Reserve Bank of St. Louis |access-date=4 August 2023 |language=en |date=September 2021}}</ref><ref>{{Cite web|url=https://www.forbes.com/sites/bobhaber/2020/03/16/the-fed-fires-the-big-one/|title=The Fed Fires 'The Big One'|first=Bob|last=Haber|website=Forbes|accessdate=30 June 2023}}</ref> the United Kingdom, Canada, Australia, New Zealand and the Scandinavian countries.<ref name="imf.org">{{cite web|url=https://www.imf.org/external/pubs/ft/wp/2011/wp1136.pdf|title=Central Bank Balances and Reserve Requirements|author=Simon Gray |website=IMF|access-date=19 July 2023}}</ref><ref>Even in those countries that do, the reserve requirement is as a ratio to deposits held, not a ratio to loans that can be extended.{{cite web
|url=http://www.bis.org/publ/bcbs189.pdf |title=Basel III: A global regulatory framework for more resilient banks and banking systems |date=December 2010|website=bis.org|access-date=19 July 2023}} [[Basel III]] does stipulate a liquidity requirement to cover 30 days net cash outflow expected under a modeled stressed scenario (note this is not a ratio to loans that can be extended); however, liquidity coverage does not need to be held as reserves but rather as any high-quality liquid assets.{{cite web|url=http://www.bis.org/publ/bcbs238.pdf|title=Basel III: The Liquidity Coverage Ratio and liquidity risk monitoring tools |date=January 2013|website=bis.org|access-date=19 July 2023}}{{cite web |url=http://www.bis.org/bcbs/basel3/b3summarytable.pdf|title=Basel Committee on Banking Supervision reforms - Basel III|website=bis.org|access-date=19 July 2023}}</ref> The possibility of banks voluntarily choosing to hold excess reserves, in amounts that may change over time as the opportunity costs for banks change, are one reason why the monetary multiplier may not be stable. For instance, following the introduction of interest rates on excess reserves in the US, a large growth in excess reserves occurred in the [[2008 financial crisis]], US bank excess reserves growing over 500-fold, from under $2 billion in August 2008 to over $1,000 billion<!-- Please leave as 1,000 billion, not as 1 trillion, as otherwise the scale of increase is unclear, because one does not mentally compare “billion” to “trillion”; please see http://xkcd.com/558/ for an illustration. --> in November 2009.<ref>[http://research.stlouisfed.org/fred2/series/EXCRESNS EXCRESNS] series, St. Louis Fed</ref><ref>{{cite news | url=https://krugman.blogs.nytimes.com/2009/12/14/followup-on-samuelson-and-monetary-policy/ | title=Followup on Samuelson and monetary policy | first=Paul | last=Krugman | authorlink=Paul Krugman | newspaper=[[New York Times]] | date=14 December 2009}}</ref>

The insight that banks may adjust their reserve/deposit ratio endogenously, making the money multiplier unstable, is old. [[Paul Samuelson]] noted in his [[Economics (textbook)|bestselling textbook]] in 1948 that:

{{blockquote|By increasing the volume of their government securities and loans and by lowering Member Bank legal reserve requirements, the Reserve Banks can encourage an increase in the supply of money and bank deposits. They can encourage but, without taking drastic action, they cannot ''compel.'' For in the middle of a deep depression just when we want Reserve policy to be most effective, the Member Banks are likely to be timid about buying new investments or making loans. If the Reserve authorities buy government bonds in the open market and thereby swell bank reserves, the banks will not put these funds to work but will simply hold reserves. Result: no 5 for 1, “no nothing,” simply a substitution on the bank’s balance sheet of idle cash for old government bonds.|{{Harv|Samuelson|1948|loc=pp. 353–354}}}}
Restated, increases in central bank money may not result in commercial bank money because the money is not ''required'' to be lent out – it may instead result in a growth of unlent (i.e. excess) reserves. This situation has been referred to as "[[pushing on a string]]": withdrawal of central bank money ''compels'' commercial banks to curtail lending (one can ''pull'' money via this mechanism), but input of central bank money does not compel commercial banks to lend (one cannot ''push'' via this mechanism).<ref>{{cite news |last1=Blyth |first1=Mark |author-link=Mark Blyth |title=The Last Days of Pushing on a String |url=https://hbr.org/2012/08/the-last-days-of-pushing-on-a |access-date=19 October 2023 |work=Harvard Business Review |date=7 August 2012}}</ref>

The amount of its assets that a bank chooses to hold as excess reserves is a decreasing function of the amount by which the market rate for loans to the general public from commercial banks exceeds the interest rate on excess reserves and of the amount by which the market rate for loans to other banks (in the US, the [[federal funds rate]]) exceeds the interest rate on excess reserves. Since the money multiplier in turn depends negatively on the desired reserve/deposit ratio, the money multiplier depends positively on these two opportunity costs. Moreover, the public’s choice of the currency/deposit ratio depends negatively on market rates of return on highly liquid substitutes for currency; since the currency ratio negatively affects the money multiplier, the money multiplier is positively affected by the return on these substitutes. Note that when making predictions assuming a constant multiplier, the predictions are valid only if these ratios do not in fact change. Sometimes this holds, and sometimes it does not; for example, increases in central bank money (i.e. base money) may result in increases in commercial bank money – and will, if these ratios (and thus multiplier) stay constant – or may result in increases in excess reserves but little or no change in commercial bank money, in which case the reserve–deposit ratio will grow and the multiplier will fall.<ref>{{Harv|Mankiw|2002|loc=[https://books.google.com/books?id=B-iNoOEoSnkC&pg=PA489&q=fall%20in%20the%20money%20multiplier p. 489]}}</ref>