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A lesson in measuring the federal debt

The many ways to calculate how much the U.S. federal government owes

What’s the debt level of the U.S. federal government? The answer isn’t as straightforward as it may seem. A quick search on FRED for “federal debt” delivers the graph above, which shows the total level of the federal debt, in millions of dollars, at a quarterly frequency since first quarter 1966. The latest figure, as of the writing of this post, corresponds to second quarter 2019 and amounts to over $22 trillion. We can also express the federal debt as a percentage of GDP, like so:

The federal debt reached 103% of GDP in second quarter 2019. These numbers, however, don’t properly reflect the amount owed by the federal government to private bondholders, since certain federal agencies (primarily, the Social Security trust funds) also hold federal debt. These agency bond holdings are liabilities the federal government owes to itself and therefore should be netted out. This adjustment is made in a series called “Federal Debt Held by the Public,” which FRED has both in millions of dollars and as a percentage of GDP. The latter is below:

As we can see, these adjusted amounts are substantially lower than the ones previously shown. Federal debt held by the public amounted to roughly $16 trillion or 76% of GDP in second quarter 2019. However, since the Federal Reserve Banks are actually private banks, they’re included in the government’s definition of “public.” Since Federal Reserve Banks remit their profits to the Treasury, any interest earned on their federal debt is rebated to the federal government. Thus, debt held by Federal Reserve Banks constitutes liabilities that the federal government owes to itself. FRED has a series called “Federal Debt Held by Federal Reserve Banks”:

If we deduct this value above from the federal debt level, we can create a more accurate series of federal debt held by the public, excluding the holdings by Federal Reserve Banks. (Simply subtract “Federal Debt Held by Federal Reserve Banks” from “Federal Debt Held by the Public” after making sure they’re both expressed in the same units.)

So, as of second quarter 2019, federal debt is $13.7 trillion or 64% of GDP, much smaller than the figures we started with before netting out the holdings of federal agencies and Federal Reserve Banks.

How these graphs were created: For all but the last one, search for the series name and click on the relevant result. For the last, take the next-to-last graph, click on “Edit Graph,” add a series by searching for “federal debt held by the public as percent of GDP,” and apply formula b-a.

Suggested by Fernando Martin.

View on FRED, series used in this post: FYGFGDQ188S, GFDEBTN, GFDEGDQ188S, HBFRGDQ188S

The cost of owing

How rising interest rates can affect the federal government's debt payments

Rising interest rates mean higher interest rates on debt payments, which means it becomes more expensive to buy a home, buy a car, or even go to college. It also becomes more expensive for the federal government to finance its debt.

As interest rates rise, payments on federal government debt also increase. The FRED graph above shows federal government expenditures with interest payments since January 1990: As federal debt has risen, expenditures on interest payments have also risen. These expenditures also depend on interest rate movements: When interest rates fall, payments decrease for the same level of federal debt. The Federal Reserve tends to lower interest rates during recessions, and this translates to lower payments, as seen in 2001 and 2008. (The gray shaded bars represent recession periods.)

Conversely, when economic conditions improve, the Federal Reserve tends to raise interest rates and this leads to higher interest payments. The second graph illustrates these two forces behind the movements in federal interest payments: The blue line is the secondary market rate on the 3-month Treasury bill, a measure of the federal government cost of borrowing that tracks very closely the interest rate set by the Federal Reserve (the federal funds rate). The red line is a measure of total public debt.

In principle, these two series can help us disentangle the main driving forces behind increasing interest payments. But doing this is more complicated than it sounds: The reason is that the federal government issues debt at different maturities, and the Fed typically sets only short-term rates. The behavior of interest rates at longer maturities depends on market forces and expectations of future inflation, among other factors.

How these graphs were created: For the first graph, search for and select “federal government expenditures: interest payments”; set the starting date to 1990-01-01. For the second graph, search for and select “3-month treasury bill: secondary market rate” (the monthly series); set the starting date to 1990-01-01. From the “Edit Graph” menu, select “Add Line.” Search for “federal debt: total public debt” and click on “Add data series.” From the “Edit Lines” tab, under “Units,” select “Index (Scale value 100 for chosen date)” and set that date to 1990-01-01. Then, under “Customize data” in the “Formula” field, type “a/100” and click “Apply.”

Suggested by Miguel Faria-e-Castro.

View on FRED, series used in this post: A091RC1Q027SBEA, GFDEBTN, TB3MS

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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