
In every course I taught in the last 20 years before I retired, I did about a 45-minute segment on numeracy. One point I emphasized is that there is typically a huge difference between a percent change and a percentage-point change. So, for example, when various proponents were advocating a one-percentage-point increase in our local sales tax, they would sometimes claim that it was a one-percent increase. A one-percent increase sounds trivial and, indeed, is trivial. But a one-percentage-point increase, which is what they were actually advocating, on top of an 8-percent sales tax, is a 12.5 percent increase. And that’s not trivial.
Which brings me to the Arizona Supreme Court. In a decision on Wednesday, the court disqualified an initiative from the Arizona ballot for the November elections. Here’s how Ricardo Cano of the Arizona Republic accurately describes the measure:
Prop. 207 would have raised income-tax rates by 3.46 percentage points to 8 percent on individuals who earn more than $250,000 or households that earn more than $500,000. It also would have raised individual rates by 4.46 percentage points to 9 percent for individuals who earn more than $500,000 and households that earn more than $1 million.
And here’s how he describes the complaint of the measure’s opponents:
The complaint alleged the petitions were misleading because they referred to the proposed tax-rate increase as a “percent” increase and not the more accurate “percentage point” increase. According to the complaint, the tax rate would have seen a 76 and 98 percent increase and not a 3.46 and 4.46 percent increase.
It really would have been a 76 and 98-percent increase, respectively. That’s huge.
Ed Kilgore of New York Magazine writes:
Considering the rare, massive attention the initiative was already receiving and would continue to receive until Election Day, the odds of a significant number of voters misunderstanding it was limited, to say the least.
I would bet, not that there’s any easy way to formulate a bet, that Kilgore is wrong. In my experience teaching MBA students who are military officers, I found that many hadn’t even thought about the percent/percentage-point distinction until I raised it. Also, Kilgore is leaving out the incredible ignorance voters have about the issues they’re voting on. I’m sure that he gave the initiative “massive attention.” I wouldn’t be surprised if at least 30 percent of the voters in November, enough to swing the vote, would have given the issue zero attention.
By the way, although Mr. Cano does a good job of presenting the issues, he makes his own numeracy mistake in another paragraph of his news story, writing:
The Arizona Chamber of Commerce, [Governor] Ducey and other state business leaders have largely ignored a proposal by former PetSmart CEO Phil Francis and several others to raise the sales tax by a cent to bring in more money for education.
A one-cent higher sales tax on a $20,000 car would, assuming a completely elastic supply of cars, raise the price of the car by one cent. That’s trivial. Francis et al are not advocating a one-cent increase in the sales tax. They’re pushing for a one-percentage-point increase in the sales tax rate. That’s substantial.
Here’s the Arizona Supreme Court’s decision.
Disclosure: One member of the Arizona Supreme Court, Clint Bolick, is a Facebook friend and, indeed, an actual friend. Given the numeracy I’ve observed in conversations with him, I would be surprised if he wasn’t one of the Justices who voted to knock the measure off the ballot.
READER COMMENTS
EconRob
Aug 31 2018 at 1:16pm
Nice post & good on you for getting in a lecture on numeracy for the benefit of your students – you should pen a blogpost summarizing these lectures.
AMW
Aug 31 2018 at 1:27pm
You should do more than write a blog post. You should make your lecture notes and/or slides available online. I would consider using them in my principles of micro course.
Phil
Aug 31 2018 at 2:34pm
I teach public budgeting and students struggle with large numbers: millions, billions, trillions. So I draw a line on the board that is a meter long. I tell the class that the line represents $1 billion. Then I ask a student to make a mark along that line that is where $1 million should be. Depending on the student, they have to think a bit and (often with some coaching) make a mark at the extreme left — 1 mm from the end.
Then we start talking about trillions, that is a km away. As a colleague of David’s, I also teach military officers, many of whom have no problem running a 10K or half-marathon. The look on their faces is priceless when they realize the national debt can be conceived as running a 20K (12.4 miles), where every millimeter of that run represents $1 million.
EconRob
Aug 31 2018 at 2:59pm
I do hope that you bring the running analogy into proper context stating that that the US economy and related debt as a road race is more akin to the ease with which a Tesla Roadster at 250MPH has in completing a 20K than does a human running 8mph. This as conceived by the extremely low interest rates the national debt is funded at (akin to the ease of a Tesla traveling 12.4 miles).
Mark Z
Sep 3 2018 at 8:39pm
That would actually be a rather misleading analogy, suggesting what we care about is who’s ‘winning the race’, in absolute terms (dollars). But that’s not what matters. If, in an economy of $1 trillion, national debt equals 50% of GDP, and GDP grows by 2 *percentage points* per year and debt grows by 3%, then sure, at the moment, gdp is growing by $20 billion per year while debt is growing by $15 billion. But in the long run, debt is catching up with GDP, and we should not breathe easy because the economy is outpacing debt. Debt is more likely to grow faster as it gets bigger than GDP is.
EconRob
Sep 5 2018 at 8:03am
I agree it isn’t a great analogy but it’s the analogy Phil chose so I extended it. Additionally, it isn’t suggesting anything about “winning the race” as I focused on the “ease… in completing”. My larger point was more that Phil’s approach seemed to me to no more than a scare tactic and not truly assisting in this blog post’s focus which is numeracy/economic literacy.
Peter Hurley
Aug 31 2018 at 7:42pm
Percentage point increase is the better measure to use for describing a tax increase, because it more accurately portrays the change in tax.
For example, the Arizona proposal would be an 11.26% increase if it were being applied to the top marginal rate applied by the Federal government. But there really isn’t that much difference between Arizona collecting 4.46 more percentage points of tax as opposed to the US Treasury collecting 4.46 more percentage points of tax. The pocketbook impact to taxpayers is the same.
And yet using percentage change would portray one as about 9x larger of a change than the other.
For things which are constrained to the range of 0% to 100% like tax changes, percentage points convey the information most accurately. For a ballot initiative, the way Mr. Cano phrased it for the Arizona Republic is the best way to accurately convey the information.
David Henderson
Aug 31 2018 at 10:15pm
Either way–percent or percentage-point–is good. The point is to do it correctly, not to do what the proponents did. They did it incorrectly.
Mark
Sep 2 2018 at 7:05pm
People also are unable to differentiate between, say, 50% off the price versus 50% more product for the same price. @ 4 for $1, 50% off (i.e., 4 for 50¢) comes out to 12.5¢ each. 50% more at the same price is 6 for $1, which comes out to 16.67¢ each.
Floccina
Sep 3 2018 at 6:20pm
This is important in stock mutual funds they quote there take as 1%/year but it is really close to 25% of the expected real return.
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