
How an arcane statistical law could have prevented the Greek disaster - zalthor
http://economicsintelligence.com/2011/07/28/how-an-arcane-statistical-law-could-have-prevented-the-greek-disaster/?blogsub=confirming#subscribe-blog
======
jgrahamc
Other fun I've had with Benford's Law.

1\. Spotting odd things in MPs' expenses: [http://blog.jgc.org/2009/06/its-
probably-worth-testing-mps.h...](http://blog.jgc.org/2009/06/its-probably-
worth-testing-mps.html)

2\. Spotting odd things in BBC executives' expenses:
[http://blog.jgc.org/2009/06/running-numbers-on-bbc-
executive...](http://blog.jgc.org/2009/06/running-numbers-on-bbc-
executives.html)

3\. The Iranian election: [http://blog.jgc.org/2009/06/benfords-law-and-
iranian-electio...](http://blog.jgc.org/2009/06/benfords-law-and-iranian-
election.html)

4\. New Age mumbo jumbo: [http://www.jgc.org/blog/2008/02/any-sufficiently-
simple-expl...](http://www.jgc.org/blog/2008/02/any-sufficiently-simple-
explanation-is.html)

~~~
ars
Benford's law does not apply to some of those things! In particular not to
expenses.

Benford's law only applies to things that experience exponential growth,
things that obey a power law distribution, and things that are totals of
random processes.

Expenses are none of those.

~~~
Symmetry
How could expenses not have a power law component to their distribution?
Sometimes you're buying an expensive thing, and sometimes a cheap thing, and
you don't buy something between $999 and $200 dollars nine times as often as
you buy something between $199 and $100.

~~~
onemoreact
If you have a 40$ meal limit on your expence reports you would expect to see a
lot more 3X$ meals than 1X$ meals.

~~~
Symmetry
Yes, you will certainly get artifacts at the top of what you can expense. You
will probably also get distortions at the bottom where you'll have some
threshold of "not worth expensing." There will almost certainly be distortion
around the boundaries, but as long as you have a big enough range you should
be able to see a Benford's law effect in the middle.

------
Estragon
Benford's law would not have stopped the groupthink, willful ignorance and
corruption which actually drove the Greek disaster. It's not like Greece's
problem with tax collection was a well-kept secret, it's just that nobody
wanted to face the facts.

~~~
zwischenzug
I seem to remember at the time there was widespread reported skepticism about
a number of countries' data. It was just accepted that the central European
elite wanted to expand to sell their wares to these dodgy countries and
prevent conflict. It shows how dependent the lender is to the lendee and how
both sides don't face up to the reality.

~~~
sethg
Also, Greece’s original accession to the EU was motivated in part by
geopolitical considerations; Greece applied for membership shortly after a
democratic government replaced seven years of harsh military rule.

------
ColinWright
The Tim Harford article mentioned in this submission was submitted and
discussed a couple of days ago:

<http://news.ycombinator.com/item?id=3008848>

The similarly mentioned Ben Goldacre article was also submitted, but that got
no discussion:

<http://news.ycombinator.com/item?id=3007964>

A detailed discussion by Terry Tao of Benford's Law (and more) can be found
here:

[http://terrytao.wordpress.com/2009/07/03/benfords-law-
zipfs-...](http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-
and-the-pareto-distribution/)

------
aqrashik
The issue with using Benford's Law with analysis is that as soon as people
realize that you're using it, data can easily be manipulated to make it
compatible.

The previous article by Tim Harford mentioned that Madoff's financial data was
Benford compatible. So I doubt that using it would have actually prevented the
Greek or any other disaster.

~~~
ramchip
The article says the opposite, though it's hard to put a lot of credibility on
something starting with "according to statisticians"...

 _According to statisticians, it is almost impossible to manipulate data in a
way that a certain outcome is guaranteed and Benford’s Law is met at the same
time. Hence, tax authorities in several countries are using Benford’s Law as a
default testing device._

~~~
aqrashik
I re-read the article and you're right. The article seems to imply Madoff as
an exception rather than the common case, but I still feel that if data is
being manipulated at such a vast scale where an entire countries economic
activity is misrepresented, you will be able to find people as smart as Madoff
to 'fit' the data as per requirements.

~~~
waitwhat
You certainly _can_ find people smart enough to make sure that their
fraudulent statistics will meet Benford's Law (or any other data model you
wish). The article points out that Greece _didn't_ find people this smart.

Not meeting Benford's Law is a good indicator that there has been some dodgy
dealing. However, meeting Benford's Law is not a good indicator that
everything is above board.

~~~
aqrashik
You're looking at it from the opposite point of view than the one I'm making.

The reason Greece didn't find people smart enough to satisfy Benford's is that
Benford's wasn't being used in the audit.

If it was common knowledge that audits utilize this Law, you can bet that
Greece's data would have been compatible.

------
skrebbel
Nice geek porn, but the title and the premise is basically nonsense.

EU politicians knew for many years that Greece was scamming things. Maybe not
so much when the Euro started, but well before it all blew up. All kinds of
circumstances, however (such as the need for Greece's vote on some other hot
issue of the moment) made sure that no one had the will to really do something
about it.

Statistics is nice and dandy, but it doesn't help a dime in fixing the broken
mess that is EU politics.

ps. Fun trivia: if the EU applied for EU membership, it wouldn't get in
because it's too undemocratic.

------
kaneraz
It's nice that they made sure the data set contained the key data to their
collapse. The pensions of retirees. Would the results have been the same if it
weren't included? I don't have access to the paper but I'd be curious what
their justification for their choice was.

Among other things, they looked at the total level of debt, the cash reserves
of the government and the pensions of retired civil servants.

------
KeepTalking
Radiolabs had a segment dedicated to such analysis. It appears the
IRS/accountants use Benford law patterns to audit tax evaders.

<http://www.radiolab.org/2009/nov/30/from-benford-to-erdos/>

------
VaedaStrike
Are there numbers from other nation's economies/ledgers that someone's run by
Benford's Law?

~~~
waitwhat
Not sure if you skimmed the linked article and missed this or not:

 _statistics from the Czech Republic, Sweden and the UK meet the Benford
distribution particularly close and hence appear unsuspicious. All those
countries have no interest in joining the Euro and therefore do not have to
meet the convergence criteria. On the other hand, statistics from Latvia,
Belgium and Romania (the latter notorious for its corruption) appear very
suspicious, as well._

And from Tim Harford's article in the FT:
[http://www.ft.com/cms/s/2/171aaa36-d8f1-11e0-aff1-00144feabd...](http://www.ft.com/cms/s/2/171aaa36-d8f1-11e0-aff1-00144feabdc0.html)

 _Romania, Latvia and Belgium also have abnormally distributed data, while
Portugal, Italy and Spain have a clean bill of health._

------
ilcavero
can you apply Benford's law to only 130 samples?? that's not a large set of
data according to my book

~~~
msellout
As I read it, they examined 130 different time series. The article did not say
how many observations were in the sample for each time series.

~~~
ilcavero
"They looked at 130 different values per country and year", they don't say how
many years were studied but I assume the greece book fixing lasted only a few
years so we are looking at ~500 samples. I honestly don't know if that's
enough or not, on wikipedia they show examples of the distribution on less
than 100 samples so I guess I'm on the wrong.

------
aneth
The article says:

> According to statisticians, it is almost impossible to manipulate data in a
> way that a certain outcome is guaranteed and Benford’s Law is met at the
> same time. Hence, tax authorities in several countries are using Benford’s
> Law as a default testing device.

I'd be very interested in evidence to support this. This doesn't sound
correct. "Almost impossible?"

------
dramaticus3
Arcane ?

~~~
ArbitraryLimits
My thoughts exactly. Between reddit and HN I see a Benford's Law post every
month or so.

~~~
waqf
Although in this instance I agree, I think the bigger point is that you
shouldn't call _anything_ "arcane" on HN. Because it'll be well known to
_someone_ and that someone—who is probably someone who could contribute a lot
to the HN discussion—will think poorly of you.

------
zerostar07
Come on, this is not even a real law, and the data are really shaky to justify
the title of this post. 5% significance threshold means that Luxembourg or
Austria satisfy the criteroa. So what? The EU is a large political
organization, not a NYSE index. The real trouble for greece is not the fake
accession data (Italy had similarly manipulated data), but the squandering of
public money that followed.

I get it, geeks love to play with empirical laws, but this paper is at best
interesting trivia. I could go on analyzing what could really prevent the
disaster forever ...

