Tim Harford The Undercover Economist

Outside EdgeOutside Edge

The FT’s quirky comment column, published on Saturdays.

Outside Edge

Of foxes, hedgehogs and the art of financial forecasting

The fantastic Mr Fox is on course for another famous victory. FT Money has a tradition of holding a year-end competition to forecast some key financial indicator, and easily the most distinctive competitor is a fox in the garden of the columnist Kevin Goldstein-Jackson, who gives his forecasts by consuming one of a variety of appropriately labelled pieces of chicken. (I refer not to Mr Goldstein-Jackson but to the fox.)

If the method is quirky, there’s no arguing with the results: the fox was the most accurate forecaster in 2008 and 2009 and, barring a year-end rally, the fox will win again in 2011. Such repeated success is an outstanding achievement against fields of about a dozen rivals.

Since the fox is a taciturn competitor, we cannot directly ask it for forecasting tips. A few lessons do, however, suggest themselves. The first is that extreme forecasts have an excellent chance of winning such contests because professional forecasters will huddle together for protection and the eventual outcome is rarely close to the cosy consensus.

Most competitors predicted a bloodbath in UK housing for 2009, for example. The fox predicted a modest fall and scooped the plaudits when house prices actually rose. This year, the fox predicted a 19 per cent fall in the FTSE 100. That looks far too pessimistic, but since every single professional pundit predicted a rise of at least 3 per cent, the fox may well win again. Intriguingly, when a new fox cub took up the challenge and lost in 2010, it made the rookie error of plumping for a forecast in the middle of the field.

The second lesson follows from the first. Professional pundits are not usually paid to make correct forecasts. They are paid to sound convincing, whether they are columnists or figureheads for asset managers. An extreme-sounding forecast can occasionally pay off – those who predicted disaster in the mid-2000s will be set up for the next few years at least – but there is safety in the consensus, especially when coupled with slick patter.
“The fox eschews the consensus and peddles no patter. Its results speak for themselves”

The fox eschews consensus and peddles no patter. Its results speak for themselves. Yet has the fox been offered any prestigious City jobs? Exactly.

The fox has, perhaps, been lucky, but nobody who studies the subject of forecasting will be surprised. The psychologist Philip Tetlock, author of the modern classic Expert Political Judgement, conducted a two-decade investigation into the accuracy of expert forecasts in social sciences. He discovered that regardless of academic field, practical experience, gender or political persuasion, experts make very poor forecasts. By some measures, the “chimp strategy” of randomly predicting that things will get better, or get worse, or stay much the same, matches the best the experts can do. Mr Goldstein-Jackson’s fox is in good company.

Mr Tetlock did find one way of dividing up his experts in a way that correlated with less-awful forecasting ability: that of “cognitive style”. Harking back to an essay by Isaiah Berlin, and before him to the Greek poet Archilochus, Mr Tetlock points to the “hedgehogs”, people who view the world through the lens of a single, powerful, logical idea. They make hopeless forecasters. Less hopeless are intellectually promiscuous, self-doubting dabblers. They are called, of course, “foxes”.

Also published at ft.com.

Outside Edge

Wed with a bang not a whimper

We can’t all have a wedding that costs tens of millions – or even £5bn, the amount Prince William and Kate Middleton’s nuptials will reportedly (and implausibly) knock off Britain’s struggling economy. But even if most of us are untroubled by bills for carriage rides from the palace and the hiring of Westminster Abbey, the rising cost of getting hitched appears to be a global issue.

Reports suggest that tying the knot is now a $30,000 affair in the US, with price tags also rising to £20,000 in the UK; not far short of income per capita in each country. Celebrity weddings are now so expensive they almost rival the cost of celebrity divorces. And nor is this just a rich-world phenomenon. Abhijit Banerjee and Esther Duflo, authors of Poor Economics, note that even households in poverty in north-west India typically spend 10 per cent of their income on weddings and other festivals.

What could be the return on such lavish spending? It becomes easier to comprehend when you realise that most of us do pay a good deal less. Headlines about the rocketing costs of solemn vows are often gathered from surveys of readers in fancy wedding magazines, exactly the kind of people who might arrange a fancy wedding. Indeed, if they weren’t tempted by a blow-out for the big day before they subscribed, they soon will be.

But the mooted £20,000 tag is not even typical for a flashy wedding-magazine-reader’s wedding. Instead it is the average, where a few major extravagances inflate the figure well beyond what most couples would recognise. Just 10 £100,000 weddings in a survey of 1,000 people notch up average costs by £1,000.

If Will and Kate’s wedding did cost £5bn (which it will not), it would raise the average for everyone else by over £30,000. But the cost of the median wedding – that which is more expensive than half of all weddings, but less expensive than the other half – is certain to be much lower. (I am grateful to colleagues on BBC Radio 4’s More or Less for pointing this out.)

Fine. Let’s say the true cost of a typical British wedding is a generously proportioned £10,000. Carve off enough for a honeymoon, a couple of thousand more for the basics – a dress, a suit, a couple of rings, and a venue for the ceremony – and suddenly you’re looking at spending an average of 50 quid a head on food, wine, and entertainment for a hundred guests. This is hardly absurd.

Indeed, it may be a bargain. Andrew Oswald, a professor at Warwick University and a specialist in the economics of happiness, thinks that a happy marriage brings as much life satisfaction as an extra £70,000 a year. Even without this, get your gift registry right and you could even make a profit. And if you don’t, you’ll still be paid back in the long run. Zsa Zsa Gabor aside, most of us can expect to be guests at a wedding rather more often than we are hosts.

The writer is married. He regards his wife as cheap at twice the price.

Also published at ft.com.

Outside Edge

Outside Edge: Date tips for the lovelorn stats nerd

The basket of goods and services chosen by Britain’s Office for National Statistics to calculate inflation provides a geek’s-eye view of the way we live. But it also reveals a kind of truth. Each year the list is updated to reflect spending habits, providing a glimpse of the nation’s changing soul, as expressed through its wallet.

This week, online dating was included for the first time. That feels right. Dating agencies were once the place losers went to date other losers: who else chooses to seek professional help in meeting people who have themselves been forced to resort to professional help? But now internet dating is YouTube to conventional dating’s three-channel TV, while speed dating provides a chance to quite legitimately make a pass at 20 people, in less time than it takes to watch a film.

But I detect a hidden agenda. Might not Britain’s lonely and lovelorn statisticians have an ulterior motive for combing over the mountains of data churned out by these dating media? Indeed, knowing the romantic insights these might allow them to exploit, might they not have lobbied hard to include them in the basket?

For let us be clear: these are data to bring a flush of passion to any statistician’s cheeks. Speed dating generates reams of evidence about who says “yes” to a second date, and why. Previously, such gold dust for the lonely-hearted required decades of covert surveillance, and a persuasive lawyer.

Web dating offers even larger troves, as researchers comb digital profiles. From this, the psychologist Dan Ariely, and economists Ali Hortaçsu and Günter Hitsch, discovered that those in search of romance online claim to be implausibly rich, slim, blonde and beautiful; that men don’t reply to women who claim to earn high salaries; and that everyone should post a photograph – otherwise suitors draw their own conclusions.

Surely it is no coincidence that the nation’s lecherous statisticians have alighted on such data-driven tips for dating success. The number-crunchers are looking for love too, and they, of all people, know that numbers are their friends.

Yet, for real insight, these impassioned bean counters should turn to economists Michèle Belot and Marco Francesconi, whose work digs into the dos and don’ts of speed dating. Some conclusions may not be surprising: the women liked rich men; the men liked slim women. But their true insight is in showing how users react to market conditions. If pickings are slim, both men and women will quickly lower their standards, taking the best of whatever is on offer, even if the best is not terribly good.

This, then, is one sure-fire dating tip even the unloved of the ONS can take to heart. Forget about surreptitiously combing spreadsheets in search of that perfect romantic gambit. Instead, go speed dating – but bring a short, ugly friend with you.

The writer is a tall, blond non-smoking millionaire with above average looks and a GSOH.

Also published at ft.com.

Outside Edge

Outside Edge: A bonus in his fingertips

Minutes of the March 11 2011 meeting of the remuneration committee of HotShots Bank

The committee approved the minutes of the previous meeting.

The committee contemplated the conclusions of Project Merlin, under which it had promised to pay exactly the bonuses it had been planning to pay all along, before moving on to its main business: the pay and conditions of star trader, Mr Charles Sheen, following recent complaints about his highly unusual behaviour.

The committee heard that, at Mr Sheen’s most recent performance review, he was asked by his line manager whether he had been abusing prohibited substances.

He replied: “I am on a drug. It’s called Charlie Sheen. It’s not available because if you try it, you will die. Your face will melt off and your children will weep over your exploded body.”

It was suggested to Mr Sheen at the time that, in fact, “Charlie Sheen” was not the only drug he was taking. He replied, “I probably took more drugs than anyone could survive. I was banging seven-gram rocks, because that’s how I roll. I have one speed, I have one gear: Go.”

When it was further put to Mr Sheen that this was incompatible with HotShots Bank’s code of ethical business practices, he blamed the bank “for giving me this much dough knowing who they were giving it to.”

When asked to comment on his business performance, Mr Sheen replied, “I’ve got magic. I’ve got poetry in my fingertips. Most of the time – and this includes naps – I’m an F-18.”

Noting grave concerns about his deportment in the office environment, the remuneration committee moved to the matter of Mr Sheen’s behaviour in front of the parliamentary working group on banking reform, at which he had waved a machete and declared himself to be “winning”. His convictions for domestic violence were also officially recorded in his personnel file, and it was noted that his wife had recently been awarded a restraining order against him.

The committee then considered objective measures of Mr Sheen’s performance. These were impressive: Mr Sheen’s trading had contributed tens of millions of pounds to the bank’s bottom line over the previous year.

At this point the committee was minded to view Mr Sheen’s transgressions as a private matter, and not one over which it behoved HotShots Bank to take an excessively paternalistic line.

It was also noted that Mr Sheen, a self-pronounced “total freakin’ rock star from Mars” appeared to regard himself as very mobile. If not paid a bonus in line with his compensation expectations, he would surely quit.

It was not clear exactly how Mr Sheen’s compensation expectations were formed, nor what psychological condition he was in when he formed them. Nevertheless the remuneration committee concluded that Mr Sheen was “winning” and unanimously decided to award him £48m plus a guaranteed bonus of the same size next year.

There being no other business, the committee concluded the meeting.

Also published at ft.com.

Outside Edge

Outside Edge: Priced out of an alcoholic stupor

“Supermarkets will no longer be allowed to sell alcohol as a loss leader under minimum pricing measures expected to be announced by the government on Tuesday. The UK coalition has been looking into minimum pricing to tackle alcohol abuse.” (Financial Times, January 17)

I wasn’t always an alcoholic tramp. I am a man of letters. I studied Philosophy, Politics and Economics at Oxford, like that David Cameron fellow. But when I looked at the options open to me – over-worked banker, castrated civil-servant or, worst of all, parliamentarian – I decided that the optimal course of affairs would be to begin building up my stock of addictive capital.

I don’t want to romanticise life as a rough-sleeping bum. It gets cold and lonely. I’m not sure what is keeping my underpants together, though I’m sure they wouldn’t survive contact with suds and warm water. But my boozy existence has a cool, calculating logic. I know that seems odd, but thankfully Gary Becker and Kevin Murphy, two of the University of Chicago’s most celebrated economists, have worked out the details in their theory of rational addiction.

For sure, not everything is perfect. But I’m a rational addict; a utility-maximising old soak. I drink because it makes sense to do so – by following an ex-ante optimal inter-temporal consumption plan, as they say. Speaking of which, let me crack open a bottle of strong cider … that’s better.

Where was I? Oh yes: you see, every drink I have contributes to my stock of addictive capital. I feel bad if I drink, but I feel worse if I don’t. Alcohol thus acquires what another drinking buddy once told me was a negative own-price elasticity across time. Put another way: Fred Astaire is a complement to Ginger Rogers; strawberries are a complement to cream; and Special Brew on your cornflakes today makes it quite rational to want to have even more Special Brew on your cornflakes tomorrow.

But I digress. The real problem for we rational drinkers is that, even if you don’t buy the idea, the evidence that people drink less when the price goes up is pretty strong. Even cirrhosis of the liver falls when liquor duty rises. So I’m in a bit of a state about these plans to put a floor under the price for booze. Admittedly, it’s not much of a floor, but it’s the thin end of the wedge. (Forgive the mixed metaphors. I am drunk.)

It isn’t that I’m cheap, or not just that. It’s that these plans threaten to impinge on my optimal consumption path. For a rational addict, every swig of Smirnoff planned for tomorrow reinforces the case for drinking Smirnoff today. I’m sure I don’t need to spell out the corollary: if prices will rise in the future, the time to quit is now.

This isn’t what I wanted, but when prices change, so does the optimal response. So I’m drying out, with immediate effect. I’ll get a job. I wonder if Mr Cameron needs a fresh voice on the frontbenches?

The writer is a recovering economics commentator

Also published at ft.com.

Outside Edge

Outside Edge: Of turtle doves and inflation hawks

The UK’s coalition put up value added tax by 2.5 percentage points last week, guaranteeing a day of bad headlines about rising prices. But anyone buying products dependent on the price of oil, or gold, or copper, or wheat, doesn’t need George Osborne to experience a world of sharp increases in prices.

Even Christmas was more expensive. According to PNC, an American company which calculates these things, the cost of buying the items mentioned in The Twelve Days of Christmas rose by a painful 9.2 per cent last year.

Doubtless inflation doves would point out that this was caused by a punitive jump in the price of major “non-core” components in the indicators, including lords-a-leaping, swans and gold rings.

I don’t buy this for a second: it’s all very well for central bankers to split hairs over core and non-core inflation. But if your true love wants nine ladies dancing, the price increase of 15 per cent is very real. And if you are feeding a family of five in Dhaka, Mexico City or Casablanca, the increase in the price of food is more real yet.

Yet for those of us not living hand to mouth, there is something rather bracing about sharp price rises. Consider petrol, which follows a “rocket and feather” trajectory. Prices shoot up at the hint of an increase in the price of crude oil, but fall back at the gentlest of rates, long after crude prices themselves have subsided.

There’s no mystery about the “rocket”: in a competitive market, wholesale price increases will be passed through to consumers promptly. But the “feather” is more ticklish, because the same argument should work in reverse, and so wholesale price falls ought to be passed on just as quickly. That means that markets are less competitive when prices are falling than when they are rising – a rather baffling suggestion.

A plausible explanation comes from Matthew Lewis, an economist at Ohio State University: falling prices make us complacent, while rises bring out the bargain hunter inside us, even when there are no bargains to be had.

As long as the price of a product is a little lower today than yesterday, we relax. We assume there’s no need to shop around. Retailers then take their sweet time cutting prices, knowing that we consumers are immensely relaxed, addled by the fact that at least prices are moving in the right direction. Paradoxically, their profits may be higher when prices are falling than when they are rising.

Falling prices may do odd things to consumers’ judgment. The price of computers and clothes has fallen for years, which may explain our otherwise inexplicable love for iPads and bumster jeans. But while the current rising prices will sting, by golly, they’ll keep us sharp. It’s just a shame that we won’t stay sharp when they start to drift down.

The writer would like to clarify that his true love has had no dalliance with any lords-a-leaping.

Also published at ft.com.

8th of January, 2011Outside EdgeComments off
Outside Edge

Outside Edge: Sleepless in Seoul

As I write this paragraph, it’s midnight. Or possibly lunchtime. I’m in a hotel room in a city which, I am reliably informed, is Seoul. I got here too late for breakfast but in plenty of time to go to bed at 3pm. Does that make any sense? I really am extraordinarily jet lagged.
The South Koreans are very proud that the G20 summit was held in Seoul, but perhaps that is mostly relief that they didn’t have to negotiate in the wrong time zone – no such luck for most of their guests.
This is in the nature of summitry: leaders whose powers of decision are so indispensable they fly all over the globe, exercise those powers of decision in what can only be described as a highly impaired state.
I have become very concerned – possibly this is just an insomniac’s paranoia – at the amount of important business that seems to be conducted by people who are equally sleep-deprived. The German finance minister called American monetary policy “clueless” last week. I am not sure it was fair then. But it seems a pretty accurate description of how many of the sleepless summiteers must have been feeling last night.
Powers of decision? Even my eyeballs are indecisive. Every time I stop concentrating on them – I was going to write “looking at them”, but how can you look at your own eyeballs? – they start drifting around, sometimes bumping into each other and sometimes edging apart. Is this a common symptom of sleep deprivation, or is it just me?
You’re also going to have to forgive the odd tpyo, I’m afraid.
Don’t get me wrong. I can handle jet lag. It’s just that I’m not sure it’s a terribly good idea to do anything important in this state. Should the future of the world economy really be decided by men and women so tired they just want to curl up in a corner?
This may account for some of the summit’s disappointments. For example, the Americans and Koreans have failed to agree a bilateral trade deal, the whole point of which was to create an impression of progress which the summit proper was always likely to lack.
Jet lag explains all. I get very ratty myself when I’m short of sleep. At least nobody has repeated the performance of the late Shoichi Nakagawa, the Japanese finance minister who managed almost simultaneously to sign away a colossal sum of money to the International Monetary Fund, and slur his words at a G7 press conference last year.
Mr Nakagawa blamed medication for a cold, and others speculated that he had been at something stronger. The way I feel, I can assure you all that the jet lag would have been enough to cause his incoherence. Now we hear that grumpy late-night discussions about currency wars at the G20 were only resolved by an agreement to pass the buck to the IMF. That makes some sense. Say what you like about IMF staff, they always try to get a good night’s sleep.
The writer is going to bed

First published on ft.com
13th of November, 2010Outside EdgeComments off
Outside Edge

Robo-rage at the trading frontier

Outside Edge: Robo-rage at the trading frontier

Day One: Everybody is talking about this “robo-trading” business. It sounds like money for old rope. You plug a fast computer into the stock exchange and buy and sell huge numbers of shares using an automatic trading program. How hard can it be? Get the computer, get the software, go for three-pint lunch.
Day Two: My phrase of the day is “quote-stuffing”. This apparently refers to the practice of sending hundreds of millions of little offers per second to a trading platform in an effort to get its computers to seize up, meanwhile exploiting that fact to make big trading gains elsewhere. You know, it may be time to upgrade my ageing Dell and get rid of Windows Vista.
Day Five: New laptop has arrived and it rocks. Meanwhile I have been learning about the “Boston Zapper”. It’s a pattern that sometimes appears in share trading data, if you view it at the microsecond level of detail. It might be an automated trading program trying to manipulate the market. Or it might be the product of two or more bots interacting. Or it might be a programming error. The great thing is that no one seems to know. This market is obviously full of amateurs. It will be like shooting robofish in an electronic barrel!
Day Six: Note to self: switch off the screen-saver before attempting to quote-stuff the Nasdaq. My screen suddenly filled up with animated goldfish. Before I could retype the password, I’d lost $100m.
Day 11: My attempt to unleash a “Bandsaw” trading pattern has been repeatedly foiled by the Windows auto-update. Damn you, Bill Gates! I’m going to get a Mac.
Day 20: Change of tack. I am standing outside the London Stock Exchange with an iPhone 4 trying to figure out whether there’s an App to execute the “Flag Repeater” strategy. Why do I keep losing signal?
Day 21: Steve Jobs says I AM HOLDING THE PHONE WRONG? Seriously?
Day 24: The iTunes “Genius” has categorised all my automated trading strategies according to album and year of release and is now suggesting an algorithm that provides the rhythm to a hilarious treadmill routine featuring Lady Gaga. I feel like Steve Jobs is camping out in my brain.
Day 30: I am back with Windows. The Mac was vanity. I’m not in the robo-trading business to look good, but to make money. Nothing can now go wrong.
Day 31: I was hoping that when the screen went blue, that was my auto-trader doing something clever. Apparently not. Reboot.
Day 41: Wall Street has just experienced a “flash crash”. The Dow has nothing on my computer, which has its own private flash crash every time I start up Internet Explorer.
Day 52: Mary Schapiro of the Securities and Exchange Commission says she’s going to regulate the high-frequency trading industry. Apparently it’s bad for the little guy. Tell me about it.
The writer has just given up on his first iPad
26th of September, 2010Outside EdgeComments off
Outside Edge

Outside Edge: The art of pricing no-balls

First published on ft.com
If the problem is corruption in cricket, where to turn for the solution? Surely, my beloved field of economics.
For those whose attention has been distracted, the sad story is that two of Pakistan’s bowlers, and their captain, have been suspended on suspicion of bowling no-balls, or illegal deliveries, to order in a five-day Test match against England. (Betting on the outcome of a particular ball is, for some reason, oddly popular in certain gambling circles.)
Many cricket lovers would like to see such offenders banned for life, if guilt is established. This is where the theory of optimal punishment comes in. It began to occur to the Nobel laureate economist Gary Becker, as he contemplated whether to park illegally while running late for an important appointment. (When I interviewed him a few years ago, he parked illegally for the duration of our lunch.) At its core is the idea that if the waste and misery caused by a crime cost society the equivalent of £100, then a suitable fine for deterring offences is £100 – if all offenders are caught, that is. If one in a thousand is caught, then the appropriate fine is £100,000. If the offender doesn’t have £100,000, then less efficient punishments such as prison – or worse – must be considered. Prison is costly, but a length of rope is cheap. If hanging or flogging strike you as problematic punishments – I am not aware that Mr Becker has endorsed them either – then perhaps you care about more than efficiency.
Setting such niceties to one side, even the simplest version of the theory of optimal punishment forces us to ask a splendidly awkward question: how serious is the crime? To observe the hand-wringing in cricket circles one would assume a few allegedly staged no-balls have ruined not only the entire series but civilisation itself.
Hardly. In a five-day Test match about 3,000 balls will be bowled and a thousand runs scored. Bowling a no-ball means a one-run penalty and a chance to dismiss the batsman is forfeited. It is unlikely to affect the outcome. It’s the equivalent of throwing less than a thousandth of a Test match.
“I hope that 99.95% of the cricket I see is entirely genuine,” agonised Jonathan Agnew, the BBC’s cricket correspondent. I can reassure him. If a single deliberate no-ball is bowled in a Test match, then 99.95 per cent of that particular match is genuine.
Cricket fans will spend several million pounds on tickets for a popular Test. If 0.05 per cent of the match is crooked, then 0.05 per cent of five million pounds is £2,500. Or is the mental anguish caused to cricket lovers beyond price?
I’m no fan of cheats. Such crimes are so hard to detect that punishments must be much more severe than £2,500 to achieve optimal deterrence. But should the offending players be forever banished from the pavilion? I am not so sure about that.
The writer does not play cricket
4th of September, 2010Outside EdgeComments off
Outside Edge

Outside Edge: Learn to love that statistical feeling

First published in the Financial Times, 8 August 2009

Maligned and misunderstood, statisticians have at last found a spokesman: the Chinese author of a poem celebrating a life swimming in data.

“Why is it that statistics/Put a calm smile on my face?” the poet writes, responding to a morale-boosting campaign dubbed “Statistical Feelings” organised by China’s National Bureau of Statistics. “Because of statistics/ I can rearrange the stars in the skies above.”

Hmm. Slightly awkward, that one. In a week when China’s economic statistics have earned more scepticism than usual, it might not be wise to talk about astronomical manipulation.

Even the state-controlled Chinese media have admitted that 91 per cent of citizens do not believe official Chinese statistics. Statistically speaking, that may not be too bad. Another survey, published in Insight China, reckoned that 7.9 per cent of respondents think prostitutes are trustworthy. This figure seems low, but places prostitutes as the third most trusted group in China, well above politicians and scientists, let alone what China Daily describes as “the least credible category which consists of real estate developers, secretaries, agents, entertainers and directors”.

If you are following the statistical argument, Chinese statisticians are more trusted than its sex workers. Or perhaps I am relying on one of the 82 per cent of statistics invented on the spot. Or one of the 46.79842 per cent of statistics that claim an unjustifiable level of precision.

China’s official statisticians are not the only ones facing scepticism. In the UK, only 36 per cent of people believe that official figures are generally accurate. This is, however, an official figure, so 64 per cent of us would hesitate before placing much confidence in it.

“Some mock me for doing statistics/ Some loathe me and statistics”, writes China’s poet-statistician, but our relationship with statistics is more complex. We feel that no argument is complete without a gesture towards the data, yet few of us understand how they are compiled. We sense – rightly – that statistics are often abused through ignorance, or manipulated.

I am a non-statistician who deals with statistics and statisticians frequently, and in my view statisticians are unsung heroes. Statistics are essential to understanding the world, but statisticians get little credit. We accept the numbers in the news as fact, without considering the skill in producing them from small, non-representative samples.

The most striking statistical story I came across this year was that adding statistical information to a charitable appeal reduces donations. It seems that merely reading a statistic makes us meaner.

This is the kind of obstacle statisticians must overcome. So sing out, poet-statisticians of China. Bean-counters of the world, unite!

8th of August, 2009Outside EdgeComments off
Previous
Do NOT follow this link or you will be banned from the site!