How Hard Are Fractions, Really: Elizabeth Warren Scares Her/Megan McArdle Is Always Wrong Chronicles, Cont’d.

Update: some edits to make the post read like someone without a grudge against English syntax wrote this post. Nothing substantive — a couple of cuts, a couple of verbs supplied to verbless “sentences.”

I guess I just can’t quit that Ms. McArdle.

I vowed to give myself a break from looking at the work of someone who seems to me to be trying to live up to fitness report number 12 on this list (or perhaps, better, number 4…oh hell, actually, a whole bunch of them).*

But then I read on, and I can’t help myself.

In my last post on this subject, I compared elements of her hatchet job on Warren to the techniques Andrew Breitbart uses in his war on progressives, Obama, and random African Americans who drift into his sights.

This time, it’s a little different:  McArdle is here simply trying to confuse the issue, apparently in the hopes that each bit of noise and nonsense that she can generate around Elizabeth Warren will damage her chances to become the first director of the he new Consumer Financial Protection Agency.  It’s an example of what I’ve called in the past McArdle’s monkey-in-the-zoo approach, in which she flings anything that comes to hand against the wall and hopes some fraction of it will stick..

To recap McArdle has promised the world a second part to that first post that attracted much uncomplimentary attention, but, as Susan of Texas notes it’s been a while.  In the meantime, she has outsourced the task, excerpting a Wall St. Journal op-ed of some years ago, which she presents under the title, “More Weird Metrics for Elizabeth Warren.”

What is so weird to McArdle?

Expressing tax liabilities as percentages of income.

No, really.

As in:  a single-earner family with an income of $38,700 facing a tax burden that claims 24% of that total.

As in: a two-earner family with earnings of $67,800 facing a tax burden of 33%.

Stating tax bills in this manner is apparently a dreadful sin, a willingness to mislead or a confusion about the underlying data.

Or so says the WSJ item’s author, Todd Zywicki, who in the passage quoted by McArdle complains that Elizabeth Warren and her co-author Amelia Warren Tyagi express certain items in raw dollar terms — $5,140 on car expenses for the single earner example, for example, vs. $8,000 in the two income family — but state tax liabilities only as percentages.

To Zywicki, this amounts to an obvious attempt to confound “an “apples to apples” comparison of all expenses.”

He corrects this, in his mind, by performing what he seems to regard as the utterly impenetrable magic act of performing two calculations:  .24*38,700 and .33*67,800, to yield dollar figures for the tax bills the two families in these examples owed.**

But beyond this en passant swipe at the eternal mystery that is the Wall St. Journal op-ed operation, our real concern here is McArdle.

She too, apparently, finds expressing a quantity as percentage of another, specified quantity, somehow suspect, a “weird metric.”

More, she regards this example as somehow dispositive of a systematic misuse of data, a demonstration of either Warren’s incompetence or her dishonesty.  McArdle writes,

Does it matter if we have a regulator who can use data consistently?  A lot of commenters seem angry that I would suggest it might.  As for me, I don’t know which is worse:  the notion that Elizabeth Warren understood what she was doing, or the notion that she didn’t.

My question would be, were I the publisher of The Atlantic, does it matter if we have an economics writer who can, apparently, neither read nor count?

Now that’s harsh, and I know it, but look at what happens if you read Warren’s and Tyagi’s examples in good faith, with a view to understanding what they are actually trying to say.

Well, long ago I wrote about the importance of such simple calculations as percentages to raw data in the context of Iraq War casualties.

The point there was that doing so allowed one to make comparisons across disparate bodies of data or historical examples.  If you want to understand the implications of  600,000 casualties among Iraqis, it helps to express that as a percentage of the population affected, which then allows you to compare it to, say, the deaths suffered by combatant nations in World War I or the American Civil War.  Thinking about the comparisons those enabled provided the frame for the moral of that post:  that the application of even veryy simple arithmetical/mathematical ideas to the raw experience of the world can prove enormously useful.

So, what might persuade Warren and Tyagi to present housing expenses or car costs as dollar numbers but  tax burdens as percentages?

Well, if I were to guess, it would be to make a point central to their larger argument:  that there are systematic increases in costs that accompany the increase in earnings in as you move from one income to two — but that different kinds of cost increases behave differently, have different scales of impact on the outcome for a two-earner family.

That is — increase in car costs like most family expenditures are basically linear:  if you go from one car to two, you pay a bit more in payments, insurance, and maintence, and that’s it.  If you take on a larger mortgage, the same applies and so on.  As Zywicki notes, apparently with some sense of being deceived, this results in such costs consuming a smaller percentage of the gross family income for two-earner households compared with single earner ones.***

Update:   note commenter Jim Bales analysis below.  Zwicki’s sins are worse than what I, in my haste to get this up, fully recognized; Jim does the due diligence.

But I think every sentient American knows that taxes don’t behave like housing or car payments.

In fact, I find it hard to believe –absurd, in fact — that McArdle, of all people, a self proclaimed libertarian, doesn’t grok the point Warren and Tyagi are trying to make as clearly as possible by using an expression for the tax burden faced by their two families in percentages.

After all, the book is about the two income trap.  And one of critical elements of that trap, as we all know, is that marginal tax rates go up at higher income levels.  This is, of course, something that McArdle has written about –notoriously quite recently, in her “calculatorgate” post.

In fact, in every context but the one in which she attacks Warren, McArdle grasps the implications of a progressive income tax, and she should, of course, given the fact, noted above, that every American who has ever looked at a tax table recognizes that the last dollar of income above minimum thresholds is taxed at a higher rate, a higher percentage than is the first.

So, quite the contrary to the charges leveled against them by Zwicki and McArdle:  Warren and Tyagi weren’t obscuring a fact that anyone — probably even McArdle’s calculator! — could obtain in seconds from the raw data they povided in full.  Rather, they were making the point that their own argument required in the best form they could — which, I meekly say, as the writer of this and that myself, is the essential core of an author’s job.

And that argument, the one that Warren and Tyagi developed across a couple of hundred pages, turned on explicating the fact that two incomes do not bring wealth proportional to the effort expended to acquire them.

Which is what would be understood, pretty clearly, I believe, by any reader unburdened by a willed desire not to get it.  How hard is to grasp that marginal tax rates in progressive taxation systems — which are generally pretty well expressed as percentages — act as a drag on the aspirations of two earner families?

This is not a raving radical position.

I believe I’ve heard some conservatives lament this very fact.

All of which is to say that there was nothing “weird’ about Warren and Tyagi’s metrics– unless asking a reader to do a quick bit of mental arithmetic (what’s one quarter of 39K vs. one third of 68) is somehow a malicious act by authors bent on deceit.

That McArdle might find that task daunting I find plausible, barely, given her recent trouble with long division.

But really, I know that she’s perfectly capable of handling fractions.  This is pretty clearly a case of willful misreading to a malicious end,  a baffle with bullsh*t moment.

So, with that,  I’m left here with is her own question, again rephrased for those in charge at The Atlantic. Does it matter if your “Business and Economics Editor” cannot consistently grasp the simplest of calculations, the most elementary of analyses?  Is it worse that McArdle understands what she is doing, or that she doesn’t?

*My personal favorite has always been number 2, but that’s just me.

**…Then, seemingly oblivious of the hilarity that thus ensues, Zywicki converts a number of the other quantities into percentages to make comparisons of the relative weight of different expenses possess in the two family’s budgets.  Seriously.  Oh well.  That was long ago, in a country far, far away, and besides, the kvetch is dead.

***He seems to think Warren and Tyagi are concealing this fact, as if it is beyond the ken for someone to notice that $8,000 is a smaller chunk of around 68K than roughly $5,200 is of $39,000. Truly, this just isn’t that hard.

Images:  Jan Massys, “At the Tax Collector,” 1539

The title pages to two arithmetic texts published in Germany in 1514

Explore posts in the same categories: Arithmetic, bad behavior, bad writing, Journalism and its discontents, libertarian nonsense, numbers, Stupidity, Uncategorized

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12 Comments on “How Hard Are Fractions, Really: Elizabeth Warren Scares Her/Megan McArdle Is Always Wrong Chronicles, Cont’d.”

  1. BruinKid Says:

    Actually, what Zywicki did, IMO, was even more deceptive. He took the pre-tax income to show the housing, mortgage, etc., payments decreased. Except… Warren’s point was about the amount of disposable income a family has to spend, and last I checked, disposable income is total income MINUS taxes.

    And when you take away the money owed to taxes, the numbers do indeed show that those rates have gone up in the last 30 or so years.

    My problem with Zywicki (and McArdle) is he HAD to have known this. You can’t tell me that Zywicki somehow suddenly forgot the DEFINITION of what disposable income is. So for him to write what he did, I would say amounts to willful deception of what I like to call “useful idiots” who don’t know any better, and will swallow his stuff hook, line, and sinker.

  2. Downpuppy Says:

    Megan has a longstanding problem reading tax tables –

  3. Jim Bales Says:

    It is interesting that Mr. Zywiki complains about Warren et al. switching from dollar amounts to percentages in mid-argument, then does so himself.

    First, he performs the calculation that Ms McArdle finds daunting, and gets the taxes for the two cases in constant (inflation-adjusted) dollars. He then calculates that the tax burden on our hypothetical family increases by 140% (from $9.3k to $22.4k) and asserts that the non-discretionary post-tax expenses increase by “less than [75%]” (Zywiki is wrong in his assertion — see below).

    Because the taxes went up by a larger percentage than the discretionary post-tax expenses, he claims that “[Taxes are] the most important contributor to the purported household budget crunch.”

    But Mr. Zywiki had earlier insisted that “to conduct an “apples to apples” comparison of all expenses” required working in dollars, not percentages. So:

    Between 1970 and 2000
    – Non-discretionary expenses increased by $16,840 (from $11,480 to $28,320)
    – Taxes increased by $13,086 (from $9,288 to $22,374)

    In other words, Ms McArdle believes that Warren cannot “use data consistently” because Ms McArdle believes that an increase of $13,086 is more important than an increase of $16.840!

    But, it is even worse than that. Mr. Zywiki did not calculate the percentage increase in the non-discretionary expenses, so I will do that for him here.

    ($28,320 – 11,480)/11,480 x 100% = 147%

    Note that:
    1) The percentage increase in non-discretionary expenses is 147%, not the “less than [75%]” Zymiki asserted.
    2) The percentage increase in non-discretionary expenses is greater than the percentage increase in taxes, unlike Zymiki asserted.

    (FWIW, Zywiki does better than McArdle here, in that her last big error was a factor of 10, while his is more like a factor of 2.)

    In other words, even by Zywiki’s standards, the increase in non-discretionary expenses was more important than the increase in taxes (although not by much).

    Shorter Zywiki: “Elizabeth Warren is wrong because I didn’t bother to do the math.”

    Shorter McArdle: “Elizabeth Warren is unfit to be a regulator because Tod Zywiki didn’t bother to do the math.”

    Shorter Jim Bales: “Warren was right. McArdle and Zywiki were wrong. Nothing new here.”

    This shows how one must be careful in comparing percentages that use different bases. What happened was the following.

    Taxes went up from 24% to 33% of gross income
    Non-discretionary expenses went from 30% to 42% of gross income
    Discretionary funds went down from 46% to 25% of gross income

    Notice that this approach, using the same base (gross income) to express all percentages you wish to intercompare, avoids the confusion that tripped up Mr. Zywiki and Ms McArdle.

    And that is why we feel poorer than our parents. Compared to them, we are working harder in the work place and spending less time with our kids. Yet they got to spend 46 cents of each dollar that Dad earned, where as we only get to spend 25 cents of each dollar that we jointly earn with our spouse. That feels like being poorer.

    Jim Bales

    • Downpuppy Says:

      Jim, you missed the pea in the hand. Zywiki said:

      “Although income only rose 75%, and expenditures for the mortgage, car and health insurance rose by even less than that, the tax bill increased by $13,086 — a whopping 140% increase. The percentage of family income dedicated to health insurance, mortgage and automobiles actually declined between the two periods”

      by specifying 3 expenses, he can ignore the $9700 daycare bill. It’s not that he didn’t calculate – its that he hid the result.

      • Jim Bales Says:


        Many thanks for noting the sleight of hand, I had simply missed it.

        Let me paraphrase Ms McArdle:
        “As for me, I don’t know which is worse: the notion that Mr. Zywiki understood what he was doing, or the notion that he didn’t.”


  4. Jim Bales Says:

    A short follow up to my “ASIDE” at the end of the last comment.

    Note that the right way to use percentages — using the same base (gross income) to express all percentages you wish to compare — is exactly what Warren did, and Zywki did not.

    Also, I suspect that “intercompare” is new usage, as it’s not in the OED. Thoughts? Am I making this up?

    Jim Bales

    • Tom Says:

      Thanks for both of these comments Jim. Sure you don’t want to start blogging?

    • Jonathan Livengood Says:

      It’s not in the OED, but it is in some other dictionaries, e.g. Random House’s 2010 dictionary, as a “related form” of “compare” to be used when the verb has an object.

      • Jim Bales Says:

        Many thanks — the next question is, I suppose, is the sentence clearer with “intercompare” than it would be with “compare”.

        I think so, but would love to hear how others read it.


  5. The Atlantic (James Fallows, who links to you, and Joshua Green) have now voiced their approval of Warren.

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  7. […] Friends Cite The Atlantic’s “Business and Economics Editor” by Tom Levenson, and “How Hard Are Fractions, Really: Elizabeth Warren Scares Her/Megan McArdle Is Always Wrong Chr…, also by […]

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