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Spurious correlation


Relationships between macroeconomic time series are not usually straightforward enough to establish with a simple graph. The problem is that almost all time series tend to grow in the long term as an economy grows. So, any measure in nominal terms will grow even more, since inflation rates are almost always positive. Because time series can exhibit a common trend, it becomes difficult to interpret whether there is a relationship between them beyond that common trend. We call this spurious correlation. There are various ways one can isolate the common trend, and we show some here using M2 and total federal debt. Above, with just the raw series, all we can see is that they both tend to increase in the long run at roughly the same rates.

In the second graph, we simply take growth rates of both series. Now the trend is gone, and it is much more difficult to argue that there is some correlation here, positive or negative. (Remember also that correlation does not mean causation: Even if we saw some relationship, we wouldn’t be able to tell whether one series is affected by the other. That requires more substantial statistical analysis.)

In the third graph, we remove the trend in another way: by dividing each series by another series that also has this trend. In this case, we take nominal GDP: GDP because it measures the size of the economy, and nominal because both M2 and the federal debt are measured in nominal terms. The picture of the two ratios now looks different, but it is still difficult to claim that there is a systematic relationship between them. Looking only at the first graph, one would not have concluded that.

How these graphs were created: Search for “M2” and “federal debt” to find the series: Be sure one of the series has its y-axis on the right. For the second graph, select “Percent change from year ago” for both series. For the third graph, change units to levels and add “Gross Domestic Product” to “M2” and apply the transformation “a/b”; then replace federal debt with the debt/GDP ratio available in the database (or create that ratio yourself).

Suggested by Christian Zimmermann

View on FRED, series used in this post: GDP, GFDEBTN, GFDEGDQ188S, M2NS


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