The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Velocity of Circulation

  • J. S. Cramer
Reference work entry


The velocity of circulation of money is V in the identity of exchange
$$ MV\equiv PT $$
which is due to Irving Fisher (1911). On the left-hand side, M is the stock of money capable of ready payment, i.e. currency and demand deposits, or, in modern parlance, M1, on the right, P is the price level and T stands for the volume of trade. PT is usually identified with total transactions at current value, which must be identically equal to total payments. All these variables are aggregates. The identity defines V as PT/M, that is the ratio of a flow of payments to the stock of money that performs them; its dimension is time−1.
The velocity of circulation of money is V in the identity of exchange
$$ MV\equiv PT $$
which is due to Irving Fisher (1911). On the left-hand side, M is the stock of money capable of ready payment, i.e. currency and demand deposits, or, in modern parlance, M1, on the right, P is the price level and T stands for the volume of trade. PT is usually identified with total transactions at current value, which must be identically equal to total payments. All these variables are aggregates. The identity defines V as PT/M, that is the ratio of a flow of payments to the stock of money that performs them; its dimension is time−1.

Apart from defining V, the identity (1) also serves for rudimentary quantity theories of money. If V is assumed constant, we have a theory of money demand, with PT determining M. Again, with both V and T constant, changes in M imply changes in P; this is still a popular explanation of inflation, with ‘too much money chasing too little goods’. The above quantity theory of money demand has however long been replaced by a more sophisticated argument, whereby money demand is determined along with demand for other assets by yield and liquidity differentials and by net wealth or income Y. This has led, by analogy, to the unfortunate term income velocity for the ratio Y/M. It should not be thought that Y here acts as a proxy for PT of the earlier theory: the underlying argument is quite different, and if Y is a proxy at all it represents net wealth. The term velocity is inappropriate in this context. We shall here reserve it for the transactions velocity V as defined above, and for its constituents parts.

This V has no place in modern economic analysis; it attracted some interest in the decades before 1940. When we divide M into currency Mc and demand deposits Md, and acknowledge that there are several different types of transaction, (1) becomes
$$ {M}_c{V}_c+{M}_d{V}_d=\sum_j{P}_j{T}_j. $$
Among the variables in this expression, Md and Vd are in principle observable at short notice, and in the absence of production indices and of national income estimates MdVd (or MdVd/P) is a useful indicator of economic activity. It was used as such by authors like Angell (1936), Edie and Weaver (1930), Keynes (1930) and Snyder (1934). As for the data, Md is demand deposit balances, available from banking returns, and Vd is the ratio of debits to balances, which can also be obtained from banks. The US Federal Reserve Board has long published monthly statistics of this debits ratio or deposit turnover rate, and still does so; there have been some drastic changes in definition and coverage over the years. The Bank of England provided a similar series from 1930 to 1938. Comparable statistics are available for several other countries.

The main trouble with this approach is that there is more than one type of transaction, and that (bank) payments are not limited to transactions in connection with current production. Some debits even have no economic meaning at all, as when a depositor has several accounts, and shifts funds between them, or when currency is withdrawn. Moreover bank debits can also reflect the sale of capital assets, income transfers, and money market dealings. The latter are by far the largest single category of turnover. These elements hinder the interpretation of Vd, and various attempts have been made to identify and remove them. We refer to Keynes’ distinction between industrial and financial circulation, and to the Federal Reserve’s practice of separately recording turnover in major financial centres. Failing a detailed classification of debits by the banks, however, all corrections are limited to approximate adjustments.

The observed value of Vd thus varies considerably with the definition of the relevant payments. For the US we quote the overall annual Vd, inclusive of financial transactions and the money market. This gross Vd, inclusive Vd rose from just under 30 in 1919 to about 35 in 1929, and then declined until 1945 when it was under 15. After the war it started on a long rise. It was about 50 by 1965, and from then onwards it soared to over 400 in 1984 (Garvy and Blyn 1970; Federal Reserve Bulletin). In Britain, net velocity, exclusive of the money market, was roughly stable at values between 15 and 20 from 1920 to 1940; later it rose from 20 in 1968 to 40 in 1977 (Cramer 1981). In the Netherlands, similarly defined net debits series show a Vd of between about 40 in 1965 and 45 in 1982 (Boeschoten and Fase 1984).

It is hard to find a single common interpretation of these movements. The development in the US until the 1960s suggests strong business cycle effects, but the enormous later increase of gross Vd must in large part be due to new techniques like overnight lending and repurchase agreements. These generate a huge amount of debits on the basis of quite small average balances. New banking techniques that go hand in hand with improved cash management explain increases in Vd outside the money market, too. The process is induced by the pressure of rising interest rates. Increased speed and precision of bank transfers permit a reduction of working balances at a given turnover level, and the reduction of demand moreover calls forth additional debits, as when idle funds are shifted to time deposits. Debits may thus increase because balances are reduced, and the rise of Vd is accentuated.

As regards currency payments, the currency stock Mc is well documented, but the estimation of velocity Vc or payments McVc presents intractable problems. There are two solutions, but both use major assumptions that defy verification.

The first method is based on the redemption rates of worn-out banknotes of different denominations. Under stationary conditions these rates are the reciprocal of average lifetime, and this turns out to be positively related to face value. While this may well be due to more careful handling of the larger notes, it is usually inferred from this that larger denominations circulate less rapidly and are hoarded more often, and for longer periods, than small notes. Laurent (1970) uses these specific redemption rates to estimate currency payments. He assumes that a banknote is redeemed if and only if it has completed G transfers. Assigning G transfers to notes that are redeemed, and ½G to notes still in circulation, he builds up cumulative estimates of the transfers performed by each US denomination from 1861 onwards. This yields annual transfers by denomination, and hence total currency payments per year, ignoring coins. All estimates are of course a multiple of the unknown G, which is regarded as a physical constant like the number of times a note can be handled. Laurent assumes implicitly that it equals the number of payments a note can perform in its lifetime. He constructs currency payments series for various G, adds bank debits, and examines the correlation of this sum with GNP over the period 1875 to 1967. The maximum correlation occurs at G = 129, and this value is adopted. Since currency in circulation, bank debits, and GNP all share the same real growth and price movements, the constructed payment series will be closely correlated with GNP for any G, and the maximum correlation is not a good criterion for determining this constant. It is moreover uncertain that G is, constant. Laurent’s estimates of currency payments imply that Vc is about 30 from 1875 to 1890; it then rises to a peak of 120 in 1928, and thereafter declines steeply to 32 in 1945, remaining at that level since. We shall argue that this level is too high.

The second method of estimating currency payments is due to Fisher (1909). He observes that most people obtain the currency they spend from banks, and that most recipients return their takings to banks. The currency circulation thus consists of loops of payments connecting withdrawals with deposits, and currency payments can be established by multiplying aggregate withdrawals (or deposits) by the average number of intervening payments, or the loop length. Withdrawals and deposits are of course recorded at the banks, and should be readily available statistics (although in fact they are not); as for the loop length, there is no way of measuring it, and it must be inferred from common sense considerations. In consumer spending the loop consists of a single payment, as households draw cash from the banks and spend it at retail shops that deposit all their takings. This is of course a minimum: some agents do not deposit their currency receipts, but spend them; some agencies, like post offices or stores that cash customers’ cheques, act in a double capacity, paying out currency they have received and thus doubling the number of payments it performs before returning to the banks. Such considerations together suggest an average loop length of about two for present-day industrialized countries.

In recent years, Vc has been estimated for two countries for which series or estimates of cash withdrawals could be established. Fisher’s method gives a constant Vc of about 18.5 for Britain over the period 1960–78 (Cramer 1981). For the Netherlands, a combination of Laurent’s and Fisher’s methods gives a constant value of about 15.3 for the years 1965–82 (Boeschoten and Fase 1984). These results suggest that currency velocity is a constant, as if it were set by physical limitations to the speed of currency circulation, and that it lies between 15 and 20.

This estimate often arouses strong feelings, as casual observation suggests that currency performs far more than 15 or 20 payments a year. A higher value of Vc does however mean higher currency payments McVc, and it is not at all clear where these take place. Even with a velocity of 15 this is a problem, for at this value currency payments in most countries far exceed consumer spending, let alone retail sales. Yet consumer spending is commonly believed to be the major repository of cash. A fair proportion must by our estimate take place elsewhere, and it appears that crime or the informal economy cannot account for this vast amount. Over and again the currency stock is much larger than common sense would suggest. Where are these payments made? Where is all the currency used or hoarded? The plain answer is that no one knows, and that very few people care. Attempts to find the answer by a sample survey have failed (Cramer and Reekers 1976).

The above results suggest that even for current transactions (excluding the money market) bank velocity is larger than currency velocity, so that the steady and continuing shift from currency to demand deposits must mean a gradual increase in the overall velocity V.

See Also


  1. Angell, J.W. 1936. The behaviour of money. New York: McGraw-Hill.Google Scholar
  2. Boeschoten, W.J., and M.M.G. Fase. 1984. The volume of payments and the informal economy in the Netherlands 1965–1982, Monetary Monographs no. 1. Amsterdam/Dordrecht: de Nederlandsche Bank/Nijhoff.Google Scholar
  3. Cramer, J.S. 1981. The volume of transactions and of payments in the United Kingdom, 1968–1977. Oxford Economic Papers 33(2): 234–255.CrossRefGoogle Scholar
  4. Cramer, J.S., and G.M. Reekers. 1976. Money demand by sector. Journal of Monetary Economics 2(1): 99–112.CrossRefGoogle Scholar
  5. Edie, L.D., and D. Weaver. 1930. Velocity of bank deposits in England. Journal of Political Economy 38: 373–403.CrossRefGoogle Scholar
  6. Fisher, I. 1909. A practical method for estimating the velocity of circulation of money. Journal of the Royal Statistical Society 72: 604–611.CrossRefGoogle Scholar
  7. Fisher, I. 1911. The purchasing power of money, 2nd ed, 1922. Reprinted New York: Kelley, 1963.Google Scholar
  8. Garvy, G., and M.R. Blyn. 1970. The velocity of money. New York: Federal Reserve Bank, available from Microfilm International, Ann Arbor and London.Google Scholar
  9. Keynes, J.M. 1930. A treatise on money. London: Macmillan.Google Scholar
  10. Laurent, R.D. 1970. Currency transfers by denomination. PhD Dissertation, University of Chicago.Google Scholar
  11. Snyder, C. 1934. On the statistical relation of trade, credit, and prices. Revue de I’Institut international de Statistique 2: 278–291.CrossRefGoogle Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • J. S. Cramer
    • 1
  1. 1.