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The velocity of money

The velocity of money played an important role in monetarist thought. For example, monetarists argued that there exists a stable demand for money (as a function of aggregate income and interest rates). In some formulations, that translates into a stable relationship between the velocity of money and a nominal interest rate—for example, the short-term Treasury bill rate.

The velocity of money is defined by

V = (PY)/M,

where V is velocity, P is the price level, Y is real output, and M is a measure of the money stock.

The graph shows the velocity of M1, with nominal gross domestic product as the chosen measure of PY. There are at least two interesting features in the graph: First, before the early 1980s, there was a more-or-less predictable trend increase in velocity. But after 1980, velocity exhibits wide swings. Basically, this reflects a fairly stable money demand relationship before 1980 and an unstable one afterward. Second, there’s a dramatic decrease in velocity starting at the beginning of the Great Recession, shown as the shaded area in 2008-09 in the graph. This is perhaps surprising, as short-term nominal interest rates have been essentially zero since late 2008. If the demand for M1 had been stable, velocity would be roughly constant; but since the beginning of the Great Recession, M1 has grown at a much faster rate than nominal GDP. This can be explained partly by a flight to the safety of insured bank deposits during the financial crisis.

How the graph was created: There are measures of the velocity of money available in FRED, but we can learn some useful things about FRED by constructing M1 velocity ourselves. First, go to the Categories menu, look under the category “Money Banking and Finance,” and select the subcategory “Monetary Data”: There you’ll find “M1 and Components.” Select “M1 Money Stock, Monthly, Seasonally Adjusted” and the graph will appear. Because we use quarterly GDP as our nominal income measure, we need M1 to be quarterly as well. So in the Frequency box, select “Quarterly.” This will convert the raw monthly M1 data to a quarterly frequency. Next, select ADD DATA SERIES and check the “Modify existing series” box. In the search box, type “gross domestic product” and add it to the graph. (Make sure you select “gross domestic product” and not “real gross domestic product.”) Now click “EDIT DATA SERIES 1” and select “Create your own data transformation.” M1 is series “a” and PY is series “b,” so enter the formula “b/a.” (See the V = (PY)/M equation above.) Next, under “Create your own data transformation,” scale the result by selecting “Index (Scale value to 100 for chosen period)” and then add the initial date of the series, 1959-01-01, in the Observation Date box.

Suggested by Stephen Williamson

View on FRED, series used in this post: GDP, M1SL

Fertility in FRED

FRED recently added fertility data from the World Bank’s World Development Indicators. A few examples are listed above, and they show a general trend toward lower fertility. The measure used here is the average number of children a woman has in her lifetime. A rate just above two is necessary to replenish a population, taking into account that some children die before becoming fertile and having children of their own. In the graph above, a few observations are remarkable: 1. The United States remains at just two children per woman. 2. China experienced a big drop, no doubt due to the one-child policy; but the number is still quite a bit above one child, as the policy does not apply to everyone. 3. Mexico also exhibits a sharp decline. 4. This decline is more recent for Benin, which has still quite a ways to go.

How this graph was created: Look for the fertility series, select the countries you’re interested in, and add them to the graph. There are several pages of listings, so you may need to add some from the graph page itself.

Suggested by Christian Zimmermann.


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