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Measuring income inequality as a ratio

Typically, the most affluent earn 13 times more than the least affluent

U.S. Census data in FRED has helped us examine income inequality before, including mean and median income and the Gini ratio. Here, we examine income inequality through a different lens.

The GeoFRED map above shows the level of income inequality across U.S. counties. This particular measure is the ratio of average (mean) income for the highest earners (top 20%) divided by the average income of the lowest earners (bottom 20%) for each county. The Census data track the average income over a five-year period, in this case 2014 to 2019, to account for the fact that people’s income changes from year to year.

Measured this way, income inequality can be as high as 90 or as low as 5. That means that the most-affluent households in a particular county can earn as much as 90 times or as little as 5 times what the least-affluent households do. But those are the two extremes of income inequality. The typical (median) value is 13 times.

Because income levels vary widely across counties, two counties with similar degrees of income inequality can have very different economic profiles. For example, both Bath County, KY, and Ocean County, NJ, have a typical income inequality ratio, but the percentage of persons below the poverty line is 2.4 times higher in the Kentuckian county than in the New Jerseyan county.

How this map was created: From GeoFRED, click on “Build new map” (green button, northeast corner of the screen) and then click on “Tools” (orange cogwheel button, northwest corner). Under “Region” select “County,” under “Data” select “Income Inequality,” and under “Date” select 2019. Note that you can also edit the colors, legend, and labels.

Suggested by Diego Mendez-Carbajo.

Comparing unemployment rates by race: The Great Recession vs. COVID-19

During the Great Recession, between 2008 and 2010, the unemployment rate climbed gradually and then slowly declined over nearly a decade. During the COVID-19 pandemic, between February and April 2020, the unemployment rate spiked to historically high levels but quickly dropped and had largely returned to pre-pandemic levels by April 2022, just two years later.

These are overall patterns, but do they hold across different racial and ethnic groups? To see how the unemployment rate differs by race and ethnicity within each recession, we can look to FRED. Our FRED graph above plots the unemployment rate for Black, White, Latino, and Asian workers—in blue, red, green, and purple, respectively—from October 2006 to the latest available data. Historically, Black workers have usually faced the highest unemployment rate, followed by Latino workers. The unemployment rates of White and Asian workers closely track one another, with Asian workers generally facing the lowest unemployment rate.

COVID-19 recession

During the COVID-19 recession, Latino workers suffered the largest shock: Their unemployment rate skyrocketed from 4.3% in January 2020 to 18.8% by April 2020—a 14.5-percentage-point increase. Asian workers suffered the second highest increase (11.4 percentage points), followed by White workers (11 percentage points) and Black workers (10.3 percentage points). Unemployment rates have since been on a rapid and steady decline. By April 2022, rates had dipped below January 2020 levels for Black and Latino workers, while remaining only 0.1 percentage point above for both White and Asian workers.

Great Recession

On the other hand, unemployment rates gradually climbed over the Great Recession period. Consistent with historical patterns, Black workers faced the highest unemployment rate throughout the episode, followed by Latino workers. By June 2009, the two groups had seen comparable increases in unemployment rates (from pre-recession levels in November 2007) of 6.3 and 6.2 percentage points, respectively. Even though unemployment rates increased by over 4 percentage points for both White and Asian workers over the same period, they faced low unemployment relative to Black and Latino workers. The gradual recovery pattern holds, with unemployment rates stabilizing around pre-recession levels in mid to late 2016 for all four groups.

How this graph was created: In FRED, search for the seasonally adjusted unemployment rate for one group, e.g. “Unemployment Rate – Black or African American.” From this graph, click “Edit Graph” at the top right corner and navigate to the “Add Line” tab. Search for the unemployment rate of next group, e.g. “Unemployment Rate – White,” and click “Add data series.” Repeat for the remaining groups.

Suggested by Serdar Birinci and Ngân Trần.

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.

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