# BOHANON & CUROTT: Tossing around statistics can quickly lead to trouble

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We’ve all heard the quip: “Figures don’t lie, but liars can figure,” along with, “There are “lies, damn lies and statistics.”

True enough. But misunderstandings about common economic statistics are often more a matter of statistical complexity than of intentional dishonesty. Take the online article that stated: “The U.S. economy shrank by a record 32.9% in the second quarter of 2020.” As articulated, the statement is incorrect. The correct statement is “shrank at a record annual rate of 32.9%.” What? Six of one, half a dozen of the other? Well, no, and here’s why.

U.S. gross domestic product, or GDP, is the value of production of final goods and services over a given time frame—typically one year. Let’s say GDP is \$20 trillion per year. This can be equivalently expressed over other time frames: U.S. GDP is \$5 trillion per quarter or \$1.66 trillion per month.

So, let’s suppose GDP is \$5 trillion in the first quarter of the year and then some disaster, like a lethal and highly infectious virus, afflicts the economy. In the second quarter, GDP is \$4.5 trillion. That’s a 10% decline, right?

Well, yes, from quarter-to-quarter. But GDP is conventionally reported in annual terms. To convert the above-mentioned quarter-to-quarter percentage decline to an annual percentage decline, one calculates what GDP’s percentage decline would be for a full year if the current quarter-to-quarter percentage decline were to persist for a full year.

You can do the arithmetic on your cell phone. If initial GDP is \$5 trillion per quarter, and GDP were to decline 10% per quarter—or be 90% of what it was in the previous quarter—for four quarters, GDP would be \$3.2805 trillion per quarter one year from now. That’s a 34.4% annual rate of decline—much larger than the 10% quarterly rate of decline.

It ends up these easy-to-calculate hypotheticals are pretty close to the actual numbers. But the major takeaway is a 10% GDP decline, which is bad news but not as bad as a 34.4% decline. We did NOT suffer a shrinkage in GDP of 32.9% between the first and second quarters of 2020—more like a 9.5% shrinkage.

The lesson, as usual, is to never trust a statistic if you don’t know where it comes from. And never repeat a statistic that you can’t calculate yourself.•

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Bohanon and Curott are professors of economics at Ball State University. Send comments to ibjedit@ibj.com.

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