Rounding Errors
Just a quick note on language, but I noticed a number of deal critics throughout the day refer to the bailout package as involving “nearly $1 trillion.” I’m outraged, too, but you need to be careful when rounding very large numbers. If somebody was trying to sell you a $7 hamburger, you might get upset and complain that it cost “nearly $10″ but you certainly wouldn’t complain that it cost “nearly $300 billion.” And yet, $7 is closer to $300 billion than $700 billion is to $1 trillion.
Now obviously rounding $700 billion up to $1 trillion isn’t as bad as rounding $7 up to $300 billion — orders of magnitude count for something. But actual quantities actually count for something, too. It’s not a good idea to wave hundreds of billions of dollars away as a shorthand.
51 Responses to “Rounding Errors”
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September 23rd, 2008 at 8:18 pm
You are allowed to complain about sloppy rounding as soon as you start proofreading your posts.
September 23rd, 2008 at 8:20 pm
“We do not support government bailouts of private institutions. Government interference in the markets exacerbates problems in the marketplace and causes the free market to take longer to correct itself,” – Republican Party Platform, 2008.
September 23rd, 2008 at 8:25 pm
and the total bailout package so far is a trillion is it not???
September 23rd, 2008 at 8:25 pm
Matt is right.
With the AIG bailout and the Fannie and Freddie rescue, it is OVER 1 trillion.
Epic fail, Yglesias.
September 23rd, 2008 at 8:29 pm
Matthew, in the (original) Paulson bill, they raised the debt ceiling more than 1.8 trillion dollars (I believe it was 1.8 and not 1). In both the Dodd and Paulson bills, 700 million refers to how much debt can be on the Federal books at any one time, not how much it will cost.
Presumably they needed to raise the debt ceiling that much because they intended to spend that much.
max
['So calling it a trillion dollar bailout is actually more accurate than calling it a 700 million dollar bailout.']
September 23rd, 2008 at 8:33 pm
If Matthew is checking the posts, he should have seen my point –made several times — that the bailout is closer to $2 Trillion. Roughly $700 Billion so far (Bear, Fannie,Freddie, AIG, Emergency Loans to Banks etc) plus an additional $700 Billion.
The Bailout Bill includes raising the federal debt limit to $11.3 Trillion, $1.5 Trillion above what it was just ($9.8 Billion) a few months ago.
Plus, as I noted, the Interest cost on the $1.5 Trillion will run to around $500 Billion over the next 5 years. (6 percent, compounded).
Hence, the HIGHLY DECEITFUL language is referring to the bailout as only $700 Billion.
September 23rd, 2008 at 8:37 pm
CLARIFICATION to post 6 above– Sentence 1 should end
“plus an additional $700 Billion that Paulson is only now asking for as Stage 2 of the Bailout.”
September 23rd, 2008 at 8:44 pm
It’s great that the Republican Party wants to protect babies’ right to be born alive, and into extraordinary Republican Party-induced debt.
September 23rd, 2008 at 8:49 pm
Matt would have a good point if people were using the term “quadrillion”.
September 23rd, 2008 at 8:52 pm
Matt, this post is just too much. First, what’s wrong with figuring in the FM/FM and AIG bailouts into the figure? Second, stop seeming so condescending!
September 23rd, 2008 at 8:58 pm
We now have Japanese financial analysts (who I trust to know a little more about debt deflation and systematic bank failure than Paulson) claiming that it will cost cost 5 trillion if it is to be successful.
September 23rd, 2008 at 8:59 pm
I don’t care about the typos. When I need my fill of pedantry I come directly here, and posts about rounding are exactly what I’m hungry for. One of the classic pieces of pedantry was just recently when we were informed that, technically, a $700 billion bailout cannot be a blank check. But it might well beoome a blank check!
September 23rd, 2008 at 8:59 pm
Mostly what Max said. The other point is that it’s hard to figure out what number to use. They’re talking about holding $700 Billion in shitty mortgages at any one time. As they roll over the better debt, the plan is to buy new debt. So they’ll probably spend upwards of a trillion on this part, but never more than $700 billion at a time.
September 23rd, 2008 at 9:01 pm
And mathematics is only second to your proofreading (as blah has already pointed out) as the most consistent weakness of your posts. Remember this
September 23rd, 2008 at 9:01 pm
As others have said, the $700,000,000,000 is the limit on the line of credit at any one time, not the amount available. And doesn’t include the other bailouts.
And as El Cid hints, this is where the triumph of the American billion over its British cousin has problems. Say it like this: seven hundred thousand million dollars. Or ‘a seven with eleven zeroes after it’. Or 7 × 10^11.
September 23rd, 2008 at 9:06 pm
I like you Matt but this is one of your silliest posts
There are too many figures involved, it depends on what exactly you’re talking about. Throwing 1 trillion around is a reasonable figure if there’s no reason to get into the math of adding up Paulson’s request with the other bailouts.
If people know enough to be more specific, they should be more specific, but for those of us who aren’t Bernanke-level experts and are just trying to get a reasonable idea of what’s going on, speaking of 1 trillion is fine
September 23rd, 2008 at 9:12 pm
Contention: calling 700 billion almost 1 trillion is, pace Matt, exactly the same as saying $7 is almost $10. In making statements like that, absolute value don’t matter at all – what matters is percentages. Matt would be appear to be contending that it is more correct to say that 25 cents is “almost $1″ than to say that $95 is “almost $100″. This seems incorrect.
September 23rd, 2008 at 9:18 pm
One of the zillions of articles I’ve read about this over the past few days suggested that the $700 billion figure was a rough average of two scientific wild-assed guesses (SWAG). The bottom-end SWAG was $500B, the top-end was $1T. In short, all of these numbers are so completely pulled out of Treasury and the Fed’s ass that rounding is irrelevant.
September 23rd, 2008 at 9:21 pm
Everyone is being really hard on Matthew here, but I think this post is just adorable. In the midst of this very serious crisis, I’m glad to have something gently diverting like this. Rounding!
September 23rd, 2008 at 9:33 pm
A trillion here, a trillion there–pretty soon you’re talking about real money . . .
September 23rd, 2008 at 9:38 pm
This is an example of a typical misuse of language when applied to numbers. For some reason Americans hate giving specific numbers and instead try to compare it to some more round number.
One example is the daily change in the DOW. If it goes up 7.91, this is changed to “up almost 8 points”. If it goes up 8.01, this is changed to “up over 8 points”. Since “almost” and “over” imply upward momentum these are positive statements about the movement. But these could be reformulated as “up less than 8 points” or “up just over 8 points”. A completely neutral formulation would be “up around 8 points”. But all of these formulations are devoid of scale, so the use of these colourful terms obscures the importance of the movement.
The BBC reports either exact movements or percentage movement. Percentage is probably the best way to combine both scale and movement. Percentage is very helpful when you report the performance of multiple averages.
But if someone request 700,000,000,000 dollars, the number of significant digits is 12. You should not round this to a figure with one significant digit.
September 23rd, 2008 at 10:04 pm
There is some skepticism that $700 billion is all that it will cost. What did they estimate the Iraq war would cost?
September 23rd, 2008 at 10:04 pm
Adding up all the promised bailout money now adds up to $1.8 trillion. Admittedly the money may not be sent but it’s on the table and could be.
http://globaleconomicanalysis.blogspot.com/2008/09/how-congress-intends-to-waste-18.html
September 23rd, 2008 at 10:11 pm
Re Walker’s comment “We now have Japanese financial analysts (who I trust to know a little more about debt deflation and systematic bank failure than Paulson) claiming that it will cost cost 5 trillion if it is to be successful ”
—————
Kenchi Ohmae! A Blast from the Past — I liked his book “Mind of the Strategist”
Although in this situation, I think Lao Tzu laid down first principles over 2400 years ago:
“He who wishes to unravel the tangled and confused does not grasp the entire skein”
September 23rd, 2008 at 10:14 pm
If you had done a degree in a real subject such as some form of engineering instead of an “ology” degree you would have come across the concept of scale and then all would be clear.
For example, for several years I worked in an office where I looked out on a sign which said max headroom = 4.4196 metres which suggested that arch above which it was positioned was never less than 4.4195m high and never more than 4.4197m high. The imperial equivalent, 14ft 6 inches, made far more sense.
September 23rd, 2008 at 10:23 pm
Barney Frank is an idiot.
September 23rd, 2008 at 10:31 pm
I like the British convention of referring to 1 billion as 1,000 million, and 1 trillion as 10,000 million. Adds a little perspective.
September 23rd, 2008 at 10:31 pm
This is honestly one of the worst posts I’ve seen from Matt yet. The number of pedantic “yes, but” posts on trivial semantic issues over the last few days has been ridiculous.
September 23rd, 2008 at 10:39 pm
Blowback,
As a chemical engineer I have to agree with you. The imperial units are superior. Fortunately I live in the US so we use inches, feet, yards, ounces, pounds, etc.
Here is the issue: metric units require that things get divided into ten parts. Half of a meter is 50 centimeters. But what is one third of a meter? 33.3333… centimeters. What is a third of a yard? One foot. Half a foot? Six inches. Half an inch? Half an inch. Half of half an inch? Quarter inch.
Humans find it very easy to divide things into half or thirds, but dividing something into ten parts, and finding a new name for it is difficult.
Metric units are great for certain scientific calculations, but for instance, not for chemistry calculations. But humans don’t divide things into ten parts, and they don’t think in metric terms.
September 23rd, 2008 at 10:40 pm
I was thinking that Hank Paulson, Ben Bernanke and crew must have had a Louie DePalma moment recently.
Last Nov., Gregory Corcoran was thinking what I’m thinking now.
http://blogs.wsj.com/deals/2007/11/05/citis-math-problem/
“It all is reminiscent of the episode of “Taxi” when the apartment of cab master Louie DePalma (played by Danny DeVito) is burnt down by the Rev. Jim Ignatowski, a man who breathed too deeply the intoxicating air of the 60s. Jim’s wealthy father offers a blank check to cover the damages, thereby setting up Louie’s comedic conundrum: how to determine the exact amount for the check so that it isn’t too low, but isn’t so high that Jim’s dad rescinds his offer. An agonizing Louie finally picks a number, but proves the sucker when it turns out Jim’s father expected an amount nearly 10 times higher.”
September 23rd, 2008 at 10:54 pm
tomj,
If all I needed multiplication and dividing for was slicing pie and pouring ingredients, your line of reasoning might make sense. Human beings are just fine at multiplying and dividing by ten.
September 23rd, 2008 at 11:17 pm
Fortunately I live in the US
Yeah, because you’d find it pretty damn hard to get a job elsewhere.
September 23rd, 2008 at 11:50 pm
I’m not sure I follow. $7 is closer to $300 billion than $700 billion to $1 trillion by *seven dollars.* What’s the difference? And we all know the difference between projected and actual (as I recall, the original forecast for the cost of the gulf war was on the order or $70 billion.)
September 23rd, 2008 at 11:51 pm
Are you confusing the English and American definitions of trillion? Check the dictionary:
“1. in Great Britain – the number that is represented as a one followed by 18 zeros (1,000,000,000,000,000,000)
“2. one million million in the United States – the number that is represented as a one followed by 12 zeros (1,000,000,000,000).
Using the US definition – 700 billion plus 300 billion is 1 trillion – a reasonable rounding amount.
Using the English definition, you would have to add $999,999,300,000,000,000 to the 700 billion, making your comment correct.
September 24th, 2008 at 1:50 am
Did Iraq ($20 billion tops) teach you nothing?
If it only costs $7,000,000,000,000 I’ll shit myself with glee.
September 24th, 2008 at 9:57 am
Matt,
Your stupid points are really piling up after this post. Stop being so deferential to what your Big Daddies say. Sometimes they lie. I bet you would have jumped down anyone’s throat who suggested the Iraq war would cost more than $86 billion.
September 24th, 2008 at 10:58 am
Matt, love the blog, but this post offensively innumerate.
Consider the $7 trillion in per capita terms for Americans. Suddenly rounding is kosher. Or again, consider the fact that $7 is 700 pennies. Or such-and-such many pesos. Or convert it to a percentage of GDP.
The general point is that the magnitude of a coefficient has no bearing on whether it’s proper or improper to round. Never ever.
September 24th, 2008 at 12:29 pm
“offensively innumerate”
Followed by:
Consider the $7 trillion . . .
LOL!!!!!
January 31st, 2009 at 2:21 am
If it only costs $7,000,000,000,000 I’ll shit myself with glee.
I wasn’t kidding.
Now we’ve got another $850+ billion and for “average Joe” they’re predicting Wall Street may top $4 trillion, and it’s only January bitches.
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March 22nd, 2009 at 7:36 pm
Well, near the end of March, 2009. The feds are “infusing” even another $1.2 Trillion dollars into “the market” = bailouts. Obama is asking for $3.4 Trillion for the next year’s budget (some portion of which is for bailout and other stimulus.)
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