The Constant Velocity of Money

When estimating the effect of changes in the money supply to changes in nominal GDP, it is common to assume that the velocity of money is constant.

The velocity of money is a measure of average number of times per year that a dollar is exchanged.

The quantity theory of money states that the money supply multiplied by the velocity of money is equal to the price level multiplied by output.

( )

Price level multiplied by output is the nominal output. Therefore, a percent change in the money supply added to a percent change in the velocity is equal to a percent change in nominal output.

( ).

In order to make calculations easier it is often assumed that the velocity of money is constant. If this is true, any changes in the money supply would directly and proportionately change nominal GDP. If the economy is at full employment it can further be assumed that real output is fixed. Therefore any change in the money supply will subsequently change the price level. Unfortunately real output is not fixed, and even at full employment, will fluctuate with the business cycles.

To test the constancy of velocity I compiled data on nominal GDP and the money supply for the last forty years. I had to decide whether to use M1 or M2 for the money supply. M1 is defined as currency in circulation plus demand deposits. M2 is M1 plus savings accounts, money market accounts, and smaller certificate of deposit accounts. I ended up calculating the data for both. M1 shows how the velocity of money typically used for everyday purchases has changed. On the other hand, M2 is the best representation of the money supply targeted by the Fed in its operations. For example, when the Fed sells treasury bonds on the open market this would theoretically reduce the M2 money supply because bonds are most likely paid for with money formerly held in saving and money market accounts. The same logic holds when the Fed buys bonds, the increase in the money supply would be reflected in the buyers’ savings and money market accounts. I found the historical data on the money supply from the Federal Reserves website. (http://www.federalreserve.gov/releases/) I found the data on GDP form the Economic History website. (http://eh.net/hmit/gdp/)

Rearranging the quantity theory of money equation, the percent change in velocity can be found by subtracting the percent change in the money supply from the percent change in the nominal GDP ( ). The results of my calculations are as follows:

Overall Change Last Twenty Years Mean Standard Deviation

M1 80.32% 43.57% 1.959% 0.047

M2 17.09% 12.24% 0.417% 0.032