David R. Henderson  

The Importance of Numeracy

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When I was the senior economist for health policy under Martin Feldstein, chairman of President Reagan's Council of Economic Advisers, one of his biggest criticisms of politicians was their innumeracy. I agree that that matters a lot, and it's not just politicians but also many pundits who are innumerate.

I started teaching a 45-minute segment on numeracy about 25 years ago in every class I teach at the Naval Postgraduate School. What caused me to do it was a comment I made in class one day that, if the students had had any idea of the U.S. population, should have caused them to gasp or, at least, raise their eyebrows. (I don't remember my comment.) When I saw basically zero reaction, I asked them to take a scrap of paper and, without putting their names on the paper, write down their estimate of the U.S. population. At the time, it was about 250 million.

The median answer was great and so was the mode--both within about 2% of the right answer. But the range? The low end was 1.5 million. The high end was 1 billion. I pointed out that if the low end were right, it would mean that everyone in the United States was in the U.S. military.

What caused me to think of this was this comment by Jonah Goldberg:

The Left's identity-politics game is a bit like the welfare states of Europe, which exist solely by living off borrowed capital and unrequited generosity. Europeans can only have their lavish entitlements because they benefit from our military might and our technological innovation. Left to their own devices, they'd have to live quite differently.

It's the "our military might" that grabbed my attention. I'm sure that Goldberg has in mind the fact that the U.S. government is spending a higher percent of U.S. GDP on the military than the welfare states of Europe do. But even if the welfare states raised their percent to equal the percent that the U.S. government spends, that would be an increase of about 2 percentage points of GDP. That's a substantial number and doing that would require either an increase in taxes or a reduction in, most likely, welfare state spending. But it wouldn't mean that they would have to live "quite differently," not when government spending in those countries is typically over 40 percent of GDP. Goldberg's innumeracy here is not nearly as bad as that of the outliers in my class. Still, though, it would be hard to make his case if one had the right numbers.


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CATEGORIES: Political Economy




COMMENTS (17 to date)
Jason writes:

Is it possible that Goldberg, instead of meaning "without us they'd raise taxes to build up their military" meant "without us they'd suffer the consequences of having an undersized military"?

The latter is still a statement in need of further defense, but seems more plausible than the innumerate interpretation you presume.

John Thacker writes:
But even if the welfare states raised their percent to equal the percent that the U.S. government spends, that would be an increase of about 2 percentage points of GDP... But it wouldn't mean that they would have to live "quite differently," not when government spending in those countries is typically over 40 percent of GDP.

It would be manageable in the particular example, but your phrasing almost seems a little misleading to me. With your emphasis, it almost sounds like you're saying that since government spending is so high, raising it by another 2 percentage points wouldn't matter much. If it comes from cutting state spending in other areas that is likely true. However, if the choice is raising taxes, then the higher they are, the greater effect on how one lives there is to raise them more. That's because for people what matters is the money you have left.

To see this, take a very simplistic thought experiment of a flat tax with no dynamic effects on GDP whatsoever, so that raising the tax rate by 2% raises the same amount of money regardless of the starting rate. (A dynamic assumption would be worse for raising taxes. OTOH, I'm ignoring any argument that the spending would have stimulus effects superior to that of American spending for the country's benefit.)

Scenario A: Tax rate of 2%, increased to 4%. The tax rate is doubled, which seems like a lot. But it also means that the money left to the taxpayer decreases from 98% to 96%, which means that it is 98% of what it used to be. (.96/.98 = .97959)

Scenario B: Tax rate of 40%, increased to 42%. The tax rate only increased by 5% of its previous value. But the money left to taxpayer decreases from 60% to 58%, which means that it is 96.7% of what it used to be.

Scenario C: Tax rate of 90%, increased to 92%. The tax rate would increase by only 2.22% of its previous value. The money left to the taxpayer decreases from 10% to 8%, which means that after tax it is only 80% of what it used to be before the increase.

So if the average tax rate is higher already in Europe, then raising taxes to pay for an additional 2% of GDP in defense spending should be more painful in Europe than in the US, not less. It's a smaller proportion of what you're already paying, but a larger proportion of what you have left after taxes. The effects are pretty small until you get to extraordinarily high tax rates, so it's not much more painful, but it's certainly not less painful based on tax rates.

Josh Wexler writes:

It seems to me Goldberg's point comes off as more respectable if you consider the absolute level of military spending. Let's say the US spends 4% of its gdp on defense and France 2%. Yes it's only a couple percentage points of difference, but that's 4% of ~15 trillion compared to 2% of ~3 trillion, or... a LOT more.

So a more charitable reading of Goldberg's point would be: The US is spending hundreds of billions of dollars on a military that is committed to also defending France. If that generosity were withdrawn, France would have to raise their defense spending as a % of gdp to FAR HIGHER than the U.S.'s spending level in order to gain back some of that security. That could have a severe effect on their ability to spend on domestic welfare programs.

I don't know if that's dispositive in Goldberg's favor. But I imagine it's more of what he had in mind, and it's a more forceful argument.

David R. Henderson writes:

@John Thacker,
With your emphasis, it almost sounds like you're saying that since government spending is so high, raising it by another 2 percentage points wouldn't matter much.
I can see how it sounds that way, but I wasn’t saying that.
If it comes from cutting state spending in other areas that is likely true.
Yes, that’s what I was saying. But your numerical example is absolutely spot on to make the point that an additional 2% is a big deal.
Good point, as always.
@Josh Wexler,
If that generosity were withdrawn, France would have to raise their defense spending as a % of gdp to FAR HIGHER than the U.S.'s spending level in order to gain back some of that security. That could have a severe effect on their ability to spend on domestic welfare programs.
Good point also. Further discussion would get us further into the weeds of military spending. I would point out that the F-35 is such a colossal spending project and that if the French avoided programs like that, they could achieve a lot without raising spending by more than 2% of GDP.

Bill Conerly writes:

David, I'm curious how you teach numeracy. Maybe you could give us a brief outline.
Bill

mike shupp writes:

Your remarks on numeracy are excellent.

And since they're the point, rather than Mr. Goldberg, I'll stop here.

Kendall writes:
if the French avoided programs like that, they could achieve a lot without raising spending by more than 2% of GDP.
Why do you think that is a reasonable expectation? Isn't it a given on this board that government spending is always inefficient? Why would we expect the French to be better at it than we are?
Tom West writes:

it's not just politicians but also many pundits who are innumerate.

Actually, it was finding out how many doctors are innumerate that shocked me (here).

If I think about it, one can probably do a decent job as a GP while being innumerate, but it's still left me feeling kind of worried. A lot of base assumptions about statistics become general rules of thumb. And if you've got bad statistics, then you end up with a bad rule of thumb.

Charlie writes:

It's very charitable of you to assume he's innumerate.

mico writes:

"But even if the welfare states..."

I think this hard distinction is becoming increasingly untenable as the US's spending has risen and that of many (most of the previously biggest spending) European states, along with Canada, has fallen.

Some European countries, though probably not the ones you mean, are actually more capitalist than the US. Some of the Baltic states have (low) flat taxes, as does Bulgaria. Heritage ranks Estonia, Ireland, and Denmark ahead of the US for economic freedom. Bulgaria outranks the US on every "Limited Government" and "Open Markets" metric, falling below it on aggregate only due to poor scores in "Rule of Law" and "Regulatory Efficiency", i.e. the country has better policies than the US but its Stalin-legacy government doesn't implement them fairly. I suspect that's true of most of Europe East of the Elbe.

The US is a welfare state. Alternatively, there are no welfare states. You are completely right that the 2% of GDP on the military more or less is not a qualitative difference between the US and European countries.

It is however a little more relevant to the social debate, where it is true that European populations generally feel themselves above military and foreign policy matters that they would have to take much more seriously if not for the US's blank cheque. It is a gift in terms of diplomatic freedom of action rather than literal money. It also removes what might otherwise be the need for conscription in countries like the Baltics and Poland.

mico writes:

@Josh Wexler,
"If that generosity were withdrawn, France would have to raise their defense spending as a % of gdp to FAR HIGHER than the U.S.'s spending level in order to gain back some of that security. That could have a severe effect on their ability to spend on domestic welfare programs."

Total EU GDP is larger than US GDP, so the EU as a whole would not need to raise its spending above that of the US as a proportion of GDP. Sharing the burden between the EU and US would probably permit both to drop their spending into the 2-3% range, or lower.

Boonton writes:

The US is spending hundreds of billions of dollars on a military that is committed to also defending France. If that generosity were withdrawn, ...

If it was withdrawn what exactly would happen? Germany would invade? The UK? Russia?

I suspect the US could withdraw entirely and France wouldn't have to raise its military budget a penny. Yes France wouldn't be able to provide a lot of support to, say, invading Iran but I'm skeptical France would find it 'needed' to replace US military spending.

Todd Kreider writes:
" If that generosity were withdrawn, France would have to raise their defense spending as a % of gdp to FAR HIGHER than the U.S.'s spending level in order to gain back some of that security."

I think some may have forgotten that France has 300 nuclear warheads and an army that is pretty integrated with Germany's army.

Thomas Bartlett writes:

The second sentence of the second paragraph reads, "What caused me to do it was a comment I made in class one day that, if the students had had any idea of the U.S. population, should have caused them to gasp or, at least, raise their eyebrows." Reading this suggests that the writer could benefit from some supplementary sessions on basic English grammar; that's called "literacy".

David R. Henderson writes:

@Thomas Bartlett,
I’m always open to learning that I made a mistake in basic grammar. On rereading my sentence, however, I can’t find it. Please identify it.

Thiago Ribeiro writes:

"The low end was 1.5 million. The high end was 1 billion."
Interesting.

scott writes:

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