Answer: No.
But it has become increasingly common for people, even otherwise numerate analysts, to write as if it can.
Consider a recent instance. In the Spring 2014 issue of Regulation, Sam Batkins and Mitch Boynton discuss a case in which an estimate of a regulatory cost fell from $672 million to $89 million. That’s a drop of 87 percent.
But that’s not what they wrote. They call this “a 750 percent drop in costs.” How did they get that? It looks as if they take the drop as a percent, not of the number from which it dropped, but of the number to which it dropped. The drop was $583 million. That’s 655 percent of the number it dropped to. Then, for some reason, they add another approximately 100 percentage points.
READER COMMENTS
Matt
Apr 17 2014 at 11:46am
What they mean is “the new budget number would need to be increased ~7.5x to reach the old budget number” (ie, ~89 million increased by 750% is ~667).
However, that is indeed a bizarre way to make the point.
David R. Henderson
Apr 17 2014 at 11:48am
@Matt,
Right. I know that’s what they meant. But notice that they got even that wrong–by about 100 percentage points.
Greg Heslop
Apr 17 2014 at 11:51am
Annoying, that. Maybe they had in mind $672 million’s being approximately 750 per cent of $89 million? 89*7.5 is not much less than 672.
At least they did not call it a drop of 750 percentage points.
Martin Ringo
Apr 17 2014 at 12:07pm
“Drops,” “increases” and the like have an arrow of time implied. And if we are semantically honest — probably an all to rare occurrence in policy debates — the arrow of time implies a base for percentage calculations. Maybe we — the semantically honest — could flaunt our virtue by always using constructions like “and 87 percent drop from $672 million.”
David R. Henderson
Apr 17 2014 at 12:33pm
@Martin Ringo,
Maybe we — the semantically honest — could flaunt our virtue by always using constructions like “and 87 percent drop from $672 million.”
I think you meant “an,” not “and.”
I don’t have reason to think they were dishonest. I doubt they were. They were just unclear and incorrect. For me, it’s not primarily about virtue: it’s about correctness and clarity.
Big Dubya
Apr 17 2014 at 1:41pm
In a similar vein, a radio ad for a residential alarm company asserts: “Homes with an alarm system are three times less likely to be robbed.”
I take them to be representing that my odds of being robbed will drop to less than zero. Very impressive protection!
David Cushman
Apr 17 2014 at 2:43pm
You’re all wrong! It’s a 202% decline!
ln(89) – ln(672) = -2.02.
Furthermore, I like my answer because it’s sorta Solomonic, being (very, very) roughly half way between 750% and 87%!
Or we could use use the midpoint formula like they do with elasticities in Principles books, but that only gets us a 153% decline, so I’m stickin’ with my log approach.
John Jenkins
Apr 17 2014 at 3:43pm
David:
I believe you are wrong about how they calculated their erroneous number. It’s much simpler than you are giving them credit for:
89/672=0.1324
1-0.1324=0.8676 or ~87%
John Jenkins
Apr 17 2014 at 3:50pm
Sorry, I completely misread this. please disregard my prior post.
Rob Rawlings
Apr 17 2014 at 4:19pm
I think they just mean that 672 is (roughly) 750% of 89.
It incorrect to say this is a “drop” of 750%” but its not (as far as I can see) out by 100.
NZ
Apr 17 2014 at 4:57pm
Just for clarity, so it’s all in one spot:
655% of 89 is 582.95
750% of 89 is 667.5
755% of 89 is 671.95
Sam Batkins
Apr 17 2014 at 9:29pm
As the author, I’ll note that we never claimed the drop between those two numbers was 750%. The two numbers David references were from the previous paragraph. Anyway, our language there was not precise.
David R. Henderson
Apr 17 2014 at 11:42pm
@Sam Batkins,
Thanks for replying. The bigger question is: how can any number fall by 750% and still be positive?
emerich
Apr 18 2014 at 5:55am
I thought it was a trick question and answered, well, a number could fall by 1% 87 times and still be positive (or by 8.7% 10 times…)…
emerich
Apr 18 2014 at 6:33am
Sorry, should have said a number could fall by 1% 750 times, etc.
Eli
Apr 18 2014 at 12:08pm
Wouldn’t that make any fall by any amount a fall of more than 100%?
My weight dropped 108% in the last 8 weeks. Frames can make you feel so good.
Jay
Apr 18 2014 at 3:23pm
@Sam Batkins
Thanks for responding, but then what two numbers were you referring to when stating the 750% number if it wasn’t the values David posted?
Jay
Apr 18 2014 at 3:28pm
David,
I believe you have the 2 values Sam was referring to in the article wrong. Within the same paragraph he mentioned the cost being $70 million versus $529 million.
529 = 755% of 70
These are the numbers I think the author was referring to.
This won’t change your conclusion any, it is still bad language.
Sam Batkins
Apr 18 2014 at 3:51pm
The article was about changes in costs and benefits during the life of rulemakings. The word “drop” was inaccurate and I thank everyone for their feedback. This is an ongoing project and we will be more precise in our next iteration.
Comments are closed.