In a paper soon to be published in the Journal of Applied Corporate Finance I do a back of the envelope calculation of the velocity of currency, C, using US data. I start with the Fed’s periodic Diary of Consumer Payment Choice (DCPC). In the October 2016 survey, consumers reported using cash for 7.9 percent of their payments by value. Applying that percentage to 2016 US data on personal consumption expenditures yields about $1 trillion in cash payments made during that year (5.4 percent of US GDP).
On the surface it would appear easy to calculate the average number of times the average banknote changes hands. Simply divide estimated spending with cash by the average amount of currency in circulation (outside the US Treasury and Federal Reserve vaults). There are two primary problems with this naïve approach, one particularly important in the US case: the quantity of US currency circulating outside the US—not used by US consumers—is large and unknown, and the amount of currency that is being hoarded and/or used for transactions not recorded in official statistics is also unknown.
If we compare our estimated US cash payments with the average 2016 currency figure included in M1, we arrive at an average turnover of .729, that is, the average “dollar” changes hands less than once per year. Even if we assume that 60 percent of US currency is circulating abroad and/or used in the underground economy, we arrive at 1.2 times per year. This number seems exceptionally low compared to common experience. Indeed, while the 2016 DCPC survey suggests the median US consumer holds only 4 bills (primarily $1s, $5s, and $20s) totaling $24 on their person, data from the US Treasury and Fed on the composition of currency issued implies that only 15 percent of US currency by value comprises denominations from $1 - $20 and 85 percent $50s and $100s and that average US per capita currency outstanding is roughly $4,500! Even after adjusting for currency held abroad, the only plausible reconciliation of the statistics and practical experience is that the turnover of low denominations is fairly “high”, say 24X per year while the turnover of high denominations, $50s and $100s is extremely low, i.e., large denomination bills are largely outside effective circulation.
Physical currency is, of course, only part of what economists call “money”. Indeed, the fraction of payments made with currency is exceedingly small, so when considering money turnover we need to turn our attention to forms of money that are used more intensively and have higher turnover rates.
In all modern financial systems, the vast bulk of payments is effected using bank reserves, R. Taking the US for illustration, in 2016 the two US large-value transfer systems (which settle in R) handled 259 million payments instructions, about 1 million per business day, for a total yearly value equivalent of $1,131 trillion—over one quadrillion dollars. This compares with 2016 US GDP of $18.7 trillion.
Since reserves are used for more than 1,000 times more payments by value than currency, it is tempting to imagine that at the quantity of R must necessarily be much larger than the quantity of C but that would be quite wrong. Operating in the background of the minds of most economists is that the turnover rate of C and R must be roughly the same, that is, to make more payments the stock of money must be higher regardless of the form of payment. But that is quite incorrect. In their defense, empirical monetary concepts, such as M0 and M1, combine quite different money types, C and R in the former, and C and demand deposits at banks, D, in the latter although they have wildly different transactions velocities.
In the case of the R component of M0, advanced technology, sophisticated matching algorithms netting payments among participants, the time deferral between payment and settlement, and efficient cash management techniques operating in conjunction allow modern banking systems to handle large volumes of payments with scant settlement balances. Roughly speaking, prior to the GFC-related expansion in settlement balances that was primarily a side effect of the expansion of central bank asset purchases, the US banking system handled on average about $5 trillion in payments daily despite holding average settlement balances of less than $20 billion. Thus, the average bank reserve balance turned over 250 times per day. Assuming 250 working days in a year yields an annual turnover rate of 62,500 times. So, what does the average turnover rate of M0 tell us, combining the average turnover rates of C and R? Not much I would say. It is a bit like trying to extract information from the average of the speeds of the average horse and the average rocket ship.
These turnover rates are not unique to the US. In a 2004 speech, Paul Tucker, former Bank of England Board Member, stated: “The whole [interbank] system now rests on the banking system targeting aggregate balances [R] of just £45 (million not billion), compared with average daily flows in the CHAPS payment system of over £150 billion (more than three thousand time greater).”
Apart from the factors mentioned above, many central banks operating real time bank reserve settlement systems (RTGS) provide daylight overdrafts, intra-day loans of reserves against collateral. This permits banks to target very low levels of end-of-day balances. Tucker describes the UK system operation: “The RTGS machine determines how wholesale payments (CHAPS payments) are effected amongst the dozen or so settlement banks. All such transfers are made in real time across the Bank’s balance sheet. Where a settlement bank’s balance is too small to fund a payment, it borrows from us intra-day—at a zero interest rate and in amounts limited only by how much eligible collateral it has available.” Indeed, these systems allowed countries to either eliminate reserve requirements or set them at zero as Canada did in June 1994 (the Fed finally did so in 2020).
Consequently, the idea that more payments with reserves requires more end-of-day reserve balances is completely wrong and has been for decades. Nevertheless, defenders of the notion that there is a relation between money and payments and thereby to an important macroeconomic variable will tend to fall back on other measures of money, such as M1.
M1, the sum of C and D, suffers from a quite similar conceptual muddle. The turnover of currency, as we have seen, is quite low, and simple reflection suggests that the technology of payments using physical media has not changed all that much from the days of buying snacks at the amphitheater in ancient Athens to doing so pre-COVID at the Old Vic in London. Meanwhile the turnover of bank deposits increased significantly in the 20th century. Although the Fed stopped calculating US demand deposit turnover rates in 1996, the available data show that the average annual turnover rate of demand deposits at New York banks increased from 50 in 1957 to 6,289 in 1996, even before the digitalization of checks and widespread adoption of automated clearinghouse transfers (ACH).
Like the case with M0, one might think that in a modern economy the quantity of deposit money must be much higher than currency since the latter is so quantitatively insignificant in the payments system. But again, this is wrong. As I show in the paper mentioned above, the currency component of US M1 was larger than the deposit component from December 1993 until January 2010 and during the roughly 16 years between September 1991 and November 2007, fully 99.7 percent of the growth of M1 was accounted for by growth in currency in circulation.
The assumptions underlying the “theory” of monetary velocity have long lain in the dust left behind by accelerating technological developments in payments systems yet the archaic mental representations of the role money plays in payments remain. Stories based on the notions that money velocity will return to a historical average, or even a historical average growth rate and that changes in observed velocity provide insight into predictable changes in significant macroeconomic variables may be entertaining for certain audiences but really are much ado about nothing.