Recession Math for People Who Don’t Like Math

That headline is easy to misinterpret. If you’re just tuning into economics journalism, you might assume that Deutsche Bank is predicting that U.S. economic output will be 13% smaller in the second quarter than it was in the first quarter. But that’s not what the bank is forecasting.

As the body of the story explains, 13% is the predicted annual rate of decline—that is, how much the economy would shrink over a full year if it kept shrinking for four straight quarters as quickly as it’s expected to in the second quarter. Deutsche Bank doesn’t think the contraction will continue at that pace. In fact, it’s looking for a second-half rebound.

 You can do a little math to figure out how much the economy would have to shrink from the first quarter to the second quarter to produce a 13% annual rate of decline. The answer is 3.4%. Still a lot, but not quite as shocking.

Space is at a premium in headlines, so headline writers often (usually?) leave out “annual rate,” saving that information for the story. If you read a lot of economics news, you’re used to the convention. But many people who are focusing on economic news for the first time because of the pandemic-induced recession could be mystified.

(Math detour here: Because of compounding, the quarterly change is not exactly a quarter of the annual change. The difference is easier to see with unrealistically big changes. An annual rate of decline of 80% in the second quarter—perish the thought—implies a one-quarter output decline of 33.1%. Conversely, an annual rate of increase of 80% in the second quarter implies a one-quarter output increase of 15.8%.)

Actually, it’s not just the annual rate that Wall Street economists forecast, but the seasonally adjusted annual rate. This factors in predictable fluctuations, such as the increase in retail sales during the Christmas shopping season, to get at the underlying growth trend.

And, of course, all predictions of gross domestic product strip out the effects of inflation. If you didn’t do that, you couldn’t tell whether reported growth was caused by an increase in the volume of production or an increase in prices.

You wouldn’t need to adjust for seasonality or for the annual rate if you just reported how big you expect the economy to be in, say, the second quarter of 2020, vs. the second quarter of 2019. That’s how China, for one, officially reports its GDP. But that approach fuzzes up what’s happening now. For example, China is finishing up an awful first quarter, but output doesn’t look so weak when compared with a year earlier because there’d been decent growth until the Covid-19 outbreak.

If this is too much to digest, just remember that when economists and headline writers talk about economic growth rates, they’re almost certainly citing a number that’s a bit imaginary: the growth that would occur if the quarterly rate of change continued for an entire year. Which it almost certainly won’t.

©2020 Bloomberg L.P.