And the recovery is well under way.
Real gross domestic product (GDP) increased at an annual rate of 33.1 percent in the third quarter of 2020 (table 1), according to the “advance” estimate released by the Bureau of Economic Analysis. In the second quarter, real GDP decreased 31.4 percent.
This is from a news release from the U.S. Department of Commerce’s Bureau of Economic Analysis, October 29, 2020.
A 33.1 percent annual rate of increase means that that would be the rate if the rate of increase of the summer quarter continued for 3 more quarters. Of course, that won’t happen. To put it in perspective, a 33.1 percent annual increase implies that real GDP in the summer quarter increased by 7.4 percent. That’s a record increase for a quarter.
Of course it comes after the huge decline of 31.4 percent (annual) in the spring quarter, which happened due to Covid-19 and the lockdowns.
That doesn’t make it even. If a number falls by 31.4 percent, then to get back to where we where, we need an increase of 45.8 percent.
To help with the math on the second point a little, here’s how I put it after a tutorial during which I watched myself on video in prepping for my first distance-learning class way back in 2002: “The camera loses 1/4 of my energy; therefore I need to increase my energy by 1/3.”
Here’s the math on both if you’re interested and, for that matter, even if you aren’t interested.
Let x be the quarterly rate of growth.
Then (1+x)^4 = 1.331.
4 ln(1+x) = ln(1.331) = 0.2859
ln(1+x) – 0.2859/4 = 0.07148
1+x = e(0.07148) = 1.074
Therefore x = 0.074. Growth rate = 7.4 percent.
On the second one.
If a number falls by 31.4 percent, it falls to 68.6 percent of what it was.
To get from 68.6 percent to 100 percent, it must rise by 1/0.686 = 45.8 percent.