Does velocity of money explain growth and inflation?

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The quantity of money available in the economy is a better indicator of economic activity than the speed with which money moves.

Policymakers, in Mauritius as elsewhere, have been pumping money into the economy in a bid to mitigate the disastrous impact of the Covid- 19, let alone to restore economic growth. Such a policy is based on the monetarist assumption that more money always leads to more spending. Still, Mauritius’ real gross domestic product (GDP) would contract by 7.0% in the fiscal year 2020-2021, would rebound moderately by 4.5% in 2021-2022 and would be back to pre-pandemic level only in 2022-2023, according to projections made in the national budget. 

For policymakers, interest rates are an instrument of intervention in the economy, but central banks cannot just change the policy interest rate: they must also manage the monetary base, which includes the currency circulating in the public, the currency physically held in the vaults of commercial banks and the reserves of banks held at the central bank. In Mauritius, the monetary base more than doubled from Rs 71.6 billion end-June 2015 to Rs 148.3 billion end-June 2020. Yet, this drastic increase led to a relatively subdued price inflation (an average year-on-year inflation of 2.2% in that period) and to a mild economic growth (from +3.9% in 2015-2016 to -6.3% in 2019-2020).

Similarly, broad money liabilities (BML), which comprise cash, deposits and debt securities, jumped by a hefty 54% while nominal GDP rose by only 14%. Two reasons can explain why national output grows much slower than money supply: the commercial banking sector transforms only a part of the base money into money in circulation (maybe because of increased risk aversion), hence a drop in the average broad money multiplier (BML/monetary base); and holders of money, both physical and digital, reduce their frequency of transaction – what economists call the velocity of circulation of money. 

Velocity plummets when businesses and consumers spend less and hold their money assets for a longer period of time. A fall in velocity may defeat the purpose of stimulus measures (which push up the money supply) whereas its increase may raise expectations about future price inflation. Now the question remains whether the speed with which money moves is a reliable indicator of economic activity.

The equation of exchange

The idea of velocity is that the money a person spends for goods and services is used later by the recipient of that money to purchase other goods and services. For example, a 100-rupee note is used during a year as follows: a shoemaker pays the 100 rupees to a tomato farmer. The latter uses the 100-rupee note to buy juice from a shopkeeper who uses the money to purchase bread from a baker. The 100 rupees have thus served in three transactions: the velocity is 3. A 100-rupee note circulating with a velocity of 3 finances 300 rupees worth of transactions.

Overall, the money stock is boosted by means of a velocity factor to establish the value of transactions in an economy in a particular year:

Money supply (M) x Velocity (V) = Value of transactions

Value of transactions = Average prices (P) x Volume of transactions (T)

This gives the famous equation of exchange set out by Irving Fisher in 1911:

MV = PT.

Since T is a measure of the real GDP, it follows that money times velocity equals nominal GDP:


If velocity is assumed to be stable, then for a given stock of money, the nominal value of GDP can be determined. Central banks track velocity (GDP/M) for several definitions of money, but the Bank of Mauritius seems to focus on broad money liabilities. The velocity of BML dipped below one in 2015-2016, which means that the average rupee was exchanged less than once in that year. From 1.01 in 2014-2015, it trended lower to 0.76 in 2019-2020, despite aggressive cuts in the Key Repo Rate. For currency with public, the velocity also tumbled, from 17.15 to 13.73, reflecting to some extent the use of cash during the lockdown. 

The decline in velocity is a matter of concern for those who, from the equation of exchange, view money together with velocity as a source of funding: for a given stock of money, an increase in velocity helps finance a greater value of transactions than money can do by itself. In fact, neither money nor velocity has anything to do with financing transactions.

Consider a shoemaker who sells a pair of shoes to a tomato farmer for Rs 100, and then exchanges the Rs 100 to buy juice from a shopkeeper. How does the shoemaker pay the juice? He has financed the purchase of juice not with money but with the shoes he produced. He has used money to facilitate the exchange: money fulfils here the role of the medium of exchange. The number of times the unit of money (the rupee) changes hands (the velocity of circulation) does not bear on the capacity of the shoemaker to fund his purchase of juice: shoes have been exchanged for juice by means of money. 

Money velocity does not have a life of its own. It is not an independent variable and therefore cannot cause anything. Velocity is just PT/M and is dependent on the other terms to maintain the balance of the equation of exchange. This mechanistic equation is not a truism but merely represents a tautology: that the income and expenditure involved in all transactions must be equal.

Demand for money

A crucial defect of the velocity concept is that it is an aggregate average that looks at the whole economic system – a holistic concept that disregards the actions of individuals. From an individual point of view, prices are determined in every transaction, each time money changes hands, so an “average velocity of circulation” does not make sense. Moreover, while a “general price level” can be considered at a certain point in time, it is absurd to measure prices over a time period as goods and services vary in quantity and quality in time and space. 

Everyone needs to keep an amount of ready cash on hand: this desire creates the demand for money, i.e., the demand for cash holding. Changes in the purchasing power of the monetary unit are brought about by changes arising in the relation between the demand for money and the quantity of money available (money supply). The value of money originates from humans’ subjective desire to maintain certain cash balances. 

No one ever has cash holdings more than he wants. If he thinks that his cash holdings are excessive, he will invest the excess in buying goods and services or in lending it through bank deposits, shares or securities. Cash holdings are not idle money (hoarding), but they render the service of being ready for any future use. While money changes hands, it is always in someone’s possession, in the cash balance of an economic agent.

In a weakening economy, people normally wish to increase their cash holdings instead of spending their money. Recessions, let alone anxiety or uncertainty about the economy, tend to dampen the velocity of money by making money as a store of value more attractive than alternative investments. Since the Mauritian economy had contracted during the first two quarters of 2020, it would be interesting to know whether domestic saving subsequently shot up. 

In any case, households are not flush with cash, and there is currently no glut of savings. As soon as the pandemic ends, Mauritians will not go on a spending spree because the economy will recover only slowly. Nevertheless, consumer demand may rebound, more money will change hands, and this will contribute to the rise in inflation which has already started following the monetary stimulus.

Money unevenly distributed

For sure, the expansion of money supply has not raised the general price level as proportionally as monetarists would have us believe. This is because the velocity of circulation has not been relatively constant over time, and the GDP has not approximated that of full employment (output gap). It remains that inflation is a monetary phenomenon which, however, does not affect uniformly all sectors and so disrupts the productive structure. 

When more money is injected into the economy, an excess of spending over production results. When spending grows faster than production, price inflation happens. The latter may also arise without an expansion in money supply if the volume of goods shrinks (supply shock). 

Variations in the quantity of money have also microeconomic effects on relative prices, besides the fact that new money enters the economic system at specific points (via public expenditure or credit creation) and at different moments (in a sequential manner), favouring certain economic agents to the detriment of the rest. Thus begins a process of income redistribution in which the first to receive the newly-created monetary units can purchase goods at prices not yet affected by monetary growth, at the expense of late receivers who find themselves buying goods at rising prices. Money unevenly distributed not only widens income inequality but also distorts the structure of relative prices: money is not neutral. 

Some economists make a distinction between cost-push inflation, of which exchange rates are a key determinant, and demand-pull inflation. Actually the two types of inflation are two sides of the same coin as, at the end of the day, it is effective demand that counts. That said, one cannot fully understand inflation with the velocity of money. The process by which money comes into the economy, the credit policy of the commercial banks, the central bank’s management of the monetary base, the rates of change of the money supply and the discrepancy between demand and supply of goods and services are all major factors of inflation.

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