The Doomsday Argument, Market Version

We're all going to die soon. And global GDP is a trainwreck. Really. Let me explain via the Doomsday Argument (DA).

For those of you not familiar with the Doomsday Argument, it goes something like this: Imagine two urns, one containing 10 balls numbered 1 thru 10; and a second urn containing a million balls, numbered 1 thru 1,000,000. If you pull a ball at random from one of the urns and you obtain a "3", the likelihood, according to Bayesian prior/posterior probabilities, is much higher that you have pulled from the 10-ball urn than the 1,000,000-ball urn.

The argument is ordinarily used to posit that we are closer to Doomsday than we know. After all, if we assume the humans are spread randomly through history, and you are here now making the observation -- sixty thousand years and fifty billion humans into our collective existence -- then what is the likelihood that we are closer to Doom, as opposed to being further away? Well, to think in urn-ish terms, you are either in a small urn -- there will never be more than 100 billion humans alive -- or we will go on to populate the multiverse -- thus there eventually being hundreds of billions of people alive. Given that you are "merely" number 50 billion, the likelihood is that we are in the smaller urn (by the [loose] Bayesian reasoning above), so Doomsday is closer than any of us think.

Fun, huh? Before turning to Doomsday Argument criticisms, let's do a markets variant. If you take global GDP as $18 trillion, or so, many wonder whether this is as good as it gets. Do we ever see much higher global GDP, like well above $30 trillion? Or do things begin to run down, as the catastrophists say, in a world of diminishing resources, warming, trade wars, strife, etc.

To put it in DA terms, we are comparing an urn with $30 trillion in GDP in it, and an urn with some much larger number. How big? Well, let's say in 100 years that 75% of the world's population of 9.4 billion has a GDP/capita of around what the U.S.'s is now, albeit inflated forward for 100 years at 1%. That would mean, by my rough calculations, global GDP of $873,360 trillion by the year 2109, which is a Big Urn indeed.

According to the Doomsday Argument, given that we are alive now and observing a global GDP of $18 trillion, the likelihood is high that we are drawing from the $30 trillion GDP urn as opposed to the $873,360 trillion urn. In other words, global GDP is unlikely to ever get to that much larger number, so sell, sell, sell, etc.

--------------

In case it's not obvious, I'm (mostly) kidding in applying the Doomsday Argument to markets. For starters, there are many lethal criticisms of the Doomsday Argument, including that the key postulate that we observers are randomly distributed is simply untrue. That criticism and others are ably presented here. Feel free to add your own criticisms, or, if you really want to get your apocalyptic freak on, suggest that things are even worse than DA sorts say -- or even propose that the world ended in 1962 and everything since has been a simulation.

Comments

[sg hammer:]

Good points. Clearly, if the global economy chugged along at $18 trillion and needed X level of debt to do it, cut X by 1/2 and where does that leave global GDP? Well, a lot lower and in no condition to reach back to $18 trillion anytime soon.

It's going to be a trader's market for quite awhile and the increased volatility makes it easier to achieve trading goals.

Feb 03 12:42 PM

[bcncv:]

Without digging into the logic and probabilities, this is just a silly argument from a common sense perspective. This exact same logic could have been used in ancient Rome, the middle ages, or in the 1950's. What makes now any different?

Without trying to argue times are good (they're not), how many people in 1900 thought that we would see an $18 Trillion global economy?

Feb 03 12:54 PM

[Nick Waddell:]

One thing is for sure: I have never read so many financial articles that mentioned stocking up on canned food or making sure you have a loaded gun before. There was even a New Yorker article recently that profiled a guy that sold his house, bought a boat and was reestablishing trade routes -in New England!

I take all this as a contrarian indicator. Surely a person who has bought 1500 cans of Spam and a Winchester rifle has no more stock left to sell....

Feb 03 01:00 PM

[Crank Monkey:]

This argument has all the clarity of six impossible things before breakfast.

Feb 03 01:06 PM

[Saul Albom:]

How can you predict something that you have never seen. None of us have seen a Dooms Day, apocalypse or end of the world. In order to make a prediction you need to have observational evidence. For example, if events X, Y and Z occur then Dooms Day will occur, because we have observed it.

You might as well say we are closer or father from aliens coming down and asking to see our leader, or the world suddenly slipping in time reverse. There is no empirical evidence for anything you have posted.

If there is any evidence at all is that events occur in a tangent function and not a sign-wave (randomly distributed). Look at hour our VAR models all broke down, when we needed them the most.

I like your thinking but we have no idea in even knowing how to place the odds of a doomsday or any super events like that. We might as well try to predict the odds of the messiah coming too or an alien messiah.

Feb 03 01:39 PM

[Orlando:]

Hey Paul: Global GDP is around $50 trillion. Could this comparison have been better made say in 1929 at the beginning of the last big contraction and compared to now? Or maybe 1980?

Feb 03 01:53 PM

[Ed's perspe...:]

never is a long time. the tortoise eventually wins .... world gdp will someday account for MANY more in the middle class and the result will be fine. the 1929 reference above is a good one .... S&P went to low double digits from lofty numbers and look where it came back to. albeit, we may see a VERY NASTY drop even from here, the human condition(s) fear and GREED will still prevail ...and there will be a counter to these tough times. don't bet it all ... as in golf live to play the next hole. good luck.

Feb 03 02:12 PM

[Adam Hayes:]

all we need is progress to push global economic growth. What i mean is some new technology that will create jobs and move humanity forward.
The internet & mobile telecomm was the last such push forward. Without the internet the stock market wouldve never had the internet bubble.. but even still it created wealth and propelled us all forward.
Before that it was the personal computer and increases in processing power for computers in general.
look throughout history.. just as economies falter something comes out of the blue and wham! accelerated growth occurs once more.
There was television and radio before that
Air travel, interstate highways, and its grandaddy the railroads.
There was oil and before that coal.
All of these produced great wealth for investors and speculators, created 1000s upon 1000s of jobs..

So what's our next push forward as once again we are petering out?
Clean technology such as solar, nuclear fusion or fuel cell?
Is it in neuro-technology applications such as controlling video games etc. with a mere thought?
Is it a nano-tech biomedical revolution?
Is it going to be space travel/tourism?

Most likely it will be something none of us can even fathom. It will spawn spontaneously as if out of nowhere. Nobody expected the internet or the airplane or the railroad etc. etc.

Any ideas what this might be??

Feb 03 02:45 PM

[The Good Ne...:]

And for the "eternal" optimists, the world actually *ends* on a positive note.

Feb 03 02:51 PM

[Big Al45:]

Paul.

You must have had a lot of extra time on your hands. If we're so bored with stocks that we're doing this sort of analysis, maybe the market bottom is imminent.

Feb 03 03:17 PM

[Firat Ünlü:]

I don't see how this has anything to do with markets to be blatantly honest. The only thing determining markets and GDP growth is business. What drives business is work-force, education level, entrepreneurship and a decent government. As long as these are given there a doomsday scenario is way off.
The US provides to biggest chunk to global GDP figures, should it fall by 'only' ten percent it would India and Argentina would have to double their respective economies to make up for the loss.
Global GDP rise is based on sound government first and foremost as most people throughout the world could be so much more productive and contributing if only the business environment was better, but that's a topic for another day.

Feb 03 03:25 PM

[Firat Ünlü:]

"The argument is ordinarily used to posit that we are closer to Doomsday than we know."

To make it more succint doomsday doesn't come knocking "Oh, hey time's up, gotta go through this, it's your turn..."
Time is quite simply irrelevant, what matters is cause. Time can't be causal as it does not change the way society is run. In fact you could make a good argument that with each passing day the doomsday scenario becomes less probable as learning and capability increases.

Feb 03 03:39 PM

[Mr. Cynical:]

Funny stuff. "Apocalyptic freak on." I'm going to use that, thanks.

Feb 03 03:39 PM

[Chuch:]

even if you are kidding there is still some doom, definitely with banks, see here crashmarketstocks.com

Feb 03 03:43 PM

[Conan the B...:]

World GDP is only $18 Trillion... I thought it was higher.

Oh well, with World debt still above $700 Trillion, I imagine there is still some deleverging left somewhere.

My favorite is Ragnarok.

The Super volcano is due, the Skulls are loose and an asteroid may take the planet out within 30 years.

An important quote by an astute notable of the 60's:
"What, Me Worry?"

Feb 04 04:50 AM

[speculari:]

As one who is certified as an asteroid avoidance technologist, I am happy to clear up this little (and I do mean little in the relative sense) problem. For any cogent argument to be made on the premise of the "10 - ball" versus "1,000,000 - ball" scenarios.... one must "know" the precise size of each and every ball, as well as the size and type of the "urns" containing them. Additionally, I hasten to add, there is no need to "number" any of the balls in either of the vessels containing (or not containing) them. In his book "Smoothing, Forecasting & Prediction of Discrete Time Series" , Brown worked this out for all of mankind around 1959. The answer is... 20 minutes! What was the question?

Feb 04 09:49 AM

[Jason Rines...:]

There were two scientists in the 1960's. One stated that Doomsday would happen in 40-50 years as population exploded and mankind would run out of natural resources. The other argued absolutely not. The one who argued no made a wager. He told doomsday to pick a commodity, any commodity and stated that the price and availability of the commodity would be exactly the same 10 years from then including median inflaion rates. Doomsday picked Aluminum. Doomdsay was wrong, other scientists was right and won the wager. Other scientist also compiled 100 years of data of food, water availability proving that mankind's living quality continues to increase, not decrease as Doomsday would proclaiming. I still have this case study if anyone wants me to dig it out and email it to them. The point? Man is improving his quality of life. Perhaps we shall see one more World War but even this event and the rebuilding of society would only delay the improvement of quality of life for 20-30 years, not end our species as many claim in a nuclear exchange. 1/3 of mankind would die in such an event, most through sickness and starvation, effects of radiation. I don't lose sleep over it.

Feb 05 10:02 AM