The FRED® Blog

Constructing “ex ante” real interest rates on FRED

Interest rates are some of the most popular series on FRED. Almost all the interest rates on FRED are nominal interest rates, which reflect the annual cost of borrowing money. A nominal interest rate doesn’t account for the effects of inflation, though. For example, if a lender lends \$100 for a year at 5% interest, the borrower repays the lender with \$105 at the end of the year. But, if inflation has been 10% over that same year, the lender is actually able to buy less with the \$105 repayment at the end of that year than they could have bought with the \$100 originally loaned at the beginning of that year.

A real interest rate is an inflation-adjusted interest rate. You might think of a real interest rate as the price of borrowing in goods, not money. Because people and firms make decisions based on real quantities, not nominal quantities, real interest rates are more useful than nominal interest rates. For example, real interest rates are much more informative than nominal interest rates about the stance of monetary policy.

Technically, a gross real interest rate (1+r) is calculated as the ratio of gross nominal rates (1+i) to the gross inflation rate (1+π):

(1+r) = (1+i) / (1+π)

Suppose that candy bars cost \$1 on January 1, 2022. The lender could use the \$100 to buy 100 candy bars, but forgoes the purchase to make a loan of \$100 instead. When the borrower repays the loan at 5% interest on January 1, 2023, the lender receives \$105 dollars. If inflation has raised the price of candy bars by 10% by January 1, 2023, then each candy bar costs \$1.10 and the lender can buy only 95 candy bars: 105/1.1 = 95.4545. The gross real rate of return equals the real goods one can buy with the payoff from the loan (95.4545 candy bars) over the initial real value of the loan (100 candy bars). So, the gross real rate of interest is 95.4545/100 = 1.05/1.10 = (1+i)/(1+π).

This is often approximated as the interest rate minus the inflation rate.

r ≅ i – π

This approximation is generally useful for relatively low rates of interest and inflation. With the example above, it would be -5% = 5% – 10%. And yes, real interest rates can be negative.

To calculate historical real interest rates, one can either use a forecast of inflation or the average rate of inflation that actually occurred over the period of the loan/bond. When one uses a forecast of inflation to construct a real rate, that measure is called an “ex ante” real rate, while using realized inflation produces “ex post” real rates. Because forecasts of inflation will generally differ from each other and from the average rate of inflation realized over a period, estimates of real interest rates for the same date and same horizon can differ from each other.

Despite the usefulness of real interest rates, FRED only has a few real interest rates: 1-month, 1-year, and 10-year real rates, all at the monthly frequency, constructed by the Cleveland Fed with a variety of data to estimate the expected rate of inflation.

FRED users can also construct daily historical series for real rates of interest with market-implied forecasts of inflation, called “breakeven” inflation rates derived from options prices. There are breakeven inflation rates on FRED for 5-, 7-, 10-, 20-, and 30-year horizons.

The FRED graph at the top compares the monthly Cleveland Fed 10-year real interest rate with a daily 10-year real rate derived from breakeven inflation. The two series track each other reasonably well for most of the sample, but diverge at times when the breakeven inflation rate is particularly volatile, such as during the Financial Crisis of 2008 and the COVID-19 pandemic of 2020-2021.

Using the methods to construct the above graph, FRED users can investigate real interest rates in several ways.

• It would be easy to compare the exact formula for a real interest rate r = ((1+i)/(1+π)-1) with the approximation (r ≅ i – π) by using the “add line” and “formula” functions to create another series. You will see that the lines are difficult to distinguish.
• One could also compare the 10-year real interest rate above with the implied 5-year real interest rate from the 5-year constant maturity Treasury yield and 5-year breakeven inflation rate.
• One could download yield and inflation data to construct “ex post” real interest rates in Excel or another application.

How this graph was created: Search for and select “10-year constant maturity Treasury yield” and choose “Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity (DGS10).” From the “Edit Graph” panel, use the “Customize data” field to search for “10-year” and select “10-year breakeven inflation rate.” The 10-year yield (i.e., nominal interest rate) will be series “a” and the 10-year break-even inflation rate will be series “b”. From the formula bar, type in the following formula for a real interest rate: 100*((1+a/100)/(1+b/100) – 1) and click “Apply.” To compare this series with the Cleveland Fed 10-year real rate, use the “Add Line” tab at the top of the editing box to search for and select “10-year real interest rate” and click “Add data series.” The two series should now be displayed from 1982, but there will be no values for the constructed real rate until 2003. To see them over a common sample, set the sample to start on January 1, 2003.

Suggested by Christopher Neely.

Gauging spending on gasoline and other energy goods

Prices for gasoline and other energy goods had already been rising before they spiked in the first quarter of 2022, after the Russian invasion of Ukraine. Personal consumption expenditures on gasoline and other energy goods (excluding natural gas and electricity) in that quarter were \$451 billion, which is about \$150 billion more than in the first quarter of 2021.

Since 2005, personal consumption expenditures on gasoline and other energy goods have averaged \$343 billion per quarter. These expenditures are highly variable, however. Not surprisingly, they usually fall during recessions, which was especially clear during the recent recessions of 2008-09 and 2020. Many households curtailed travel when the COVID-19 pandemic struck in 2020, which reduced the demand for gasoline and pushed sales down precipitously. Gasoline sales have since rebounded, and nominal consumer expenditures on gasoline and other energy goods were already above average before the invasion of Ukraine.

The first FRED graph shows that these personal consumption expenditures on energy have risen significantly since World War II in nominal terms. Of course, the general level of prices has risen significantly as well, and consumer expenditures on all goods and services have grown with household income. (For more on real versus nominal gas prices, see this recent FRED Blog post.)

One indicator of the burden of higher energy prices on households is reflected in the share of total consumer expenditures devoted to gasoline and other energy goods. So, the second FRED graph plots the ratio of personal consumption expenditures on gasoline and other energy goods to total personal consumption expenditures. We see that the share of consumption devoted to energy has generally declined since World War II.

This trend was significantly interrupted during the 1970s and again before the 2008-09 recession. War in the Middle East and the Arab oil embargo in 1973, the Iranian revolution in 1978, and Iraq’s invasion of Iran in 1980 all fueled oil price spikes as well as spikes in the share of personal consumption expenditures devoted to energy purchases. Since then, the share of personal consumption expenditures devoted to energy purchases has consistently been below the share that prevailed before the 1970s.

Despite the sharp increase in gasoline prices in the first quarter of 2022, purchases of gasoline and other energy goods comprised just 2.7% of total consumer expenditures in that quarter, which is about average for the period since 2010. Additional energy price increases could drive the expenditure share higher than it was in the first quarter. But currently, the share of personal consumption expenditures has been well below the peak of 6% reached in 1980.

How these graphs were created: First graph: Search FRED for “Personal consumption expenditures: Nondurable goods: Gasoline and other energy goods.” The chart appears as is with the default dates. Second graph: Search FRED for “Personal consumption expenditures: Nondurable goods: Gasoline and other energy goods.” From the “Edit Graph” panel, add a series to the workspace by searching for “PCEC” under “Customize data.” Add the series. For the formula,  enter a/b*100 to express as percentage and click “Apply.”

Suggested by Jason Dunn and David Wheelock.

Referring to the interest paid on reserves

A rate by any other name...

The Fed’s monetary policy tools are used to promote maximum employment, stable prices, and moderate long-term interest rates in the U.S. economy. These tools evolve over time as the economy evolves, and so it makes sense the terms that describe these tools also change.

The FRED graph above shows three different interest rates the Board of Governors has set on the reserve balances commercial banks keep at their corresponding Federal Reserve Banks. The time frame is between October 9, 2008, and when this post was written:

• The interest rate on required reserves (the dashed red line) and the interest rate on excess reserves (the solid orange line) were identical. The former applied to balances kept in fulfillment of reserve requirement ratios, and the latter applied to balances kept in excess of those requirements. On March 26, 2020, the reserve requirement ratios were lowered to zero, so the distinction in the type of reserves lost any practical significance. Both of these interest rate data series were discontinued on July 28, 2021.
• As of July 29, 2021, the “interest rate on reserve balances” (the solid blue line) became the new name of the interest rate paid by the Federal Reserve on all reserve balances kept by commercial banks.

The FRED Team uses an automated process to name many of its data series. This process makes tracing the current data back to their sources easier. For information on series name changes, copyright statements, and much more, check the metadata in the notes below every FRED graph.

How this graph was created: Search for and select “Interest Rate on Excess Reserves (DISCONTINUED).” From the “Edit Graph” panel, use the “Add Line” tab to search for and select “Interest Rate on Required Reserves (DISCONTINUED).” Repeat the last step to add “Interest Rate on Reserve Balances” to the graph. To change the style and color of the lines in the graph use the “Format” panel.

Suggested by Diego Mendez-Carbajo.