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The theory of interstellar trade
By Paul Krugman, circa 1978. He considers the arbitrage conditions for interstellar trade, given that not all traders will inhabit the same frame of temporal reference. There is much humor in this piece.
My own puzzling focuses on the determinants of real interest rates, given how time dilation changes the meaning of time preference. As you approach the speed of light you move into the future relative to more stationary observers. So can you not leave a penny in a savings account, take a very rapid spaceflight, and come back to earth "many years later" as a billionaire? Hardly any time has passed for you. In essence we are abolishing time preference, or at least allowing people to lower their time preference by spending money on fuel. I believe that in such worlds the real interest rate cannot exceed the costs at which more fuel can "propel you into the future through time dilation."
Whether the individual arbitrage conditions translate into economy-wide arbitrage conditions is a difficult puzzle. What if everyone gets into a fast spaceship? Do the savings accounts still bear positive interest? How does the price of robots enter into this equation?
Is monetary policy neutral in such a world, with time travelers arbitraging against any attempt by the Fed to shift real interest rates? Does the Fed have to subsidize the price of fuel to stimulate the economy? Does everyone just end up in the future?
Posted by Tyler Cowen on March 11, 2008 at 05:50 PM in Economics | Permalink
Comments
What happens to human capital during faster-than-light travel. Investing in specific skills training before travel would seem pointless. People would have to be trained in how to learn skills once reaching destination. How markets would value labour in an environment like this would be very interesting.
Posted by: Mark at Mar 11, 2008 6:37:38 PM
Supposing for the moment that short-term rates were previsible, they would be vectors (or their dual), not scalars; the "law of one price" should allow a consistent definition of discount factors as a function of space and time, and the interest rate is the gradient of the log of this figure. Such a vector ought to be time-like, I would think.
Allowing interest rate markets to move naturally complicates things, but I can't imagine that that would change. You would want to move relative to the "time" direction of the interest rate at as fast a speed as possible to maximize the interest rate in your frame; conversely borrowers would wish to be in the reference frame in which the interest rate has no spacial component.
Posted by: dWj at Mar 11, 2008 6:49:28 PM
Don't you get roughly the same effect by freezing yourself or putting yourself into some form of suspended animation?
Posted by: RobbL at Mar 11, 2008 6:53:51 PM
I always think that, if you go to a planet one light year away at the speed of light you will arrive at a time which is 2 years ahead of what it was when you looked at the planet from earth (if you see year 2008 in planet X, the actual year there would currently be 2009, and you would arrive in 2010).
If at the day you left data was sent to the branch of your bank in that planet regarding your balance, and if this data traveled at the speed of light, when you arrive on planet X you will still have the balance you left with, accumulating 0 interest in a year.
Now, if you withdraw this money and return back to earth (along with the data from the foreign branch saying that you made the withdrawal), then you will have accumulated 2 years interest in a balance you kept for only 1 year (and you would have been able to spend that money on the spaceship).
So my point is, even if you move into the future relative to everyone on earth when you travel away, by the time you come back the time lapsed will be the time you spent travelling.
As for the data, we have to find a way to make it travel at twice the speed of light to avoid the mis-match mentioned above, or adjust the inter-planetary exchange rate accordingly.
Posted by: Recep Peker at Mar 11, 2008 6:57:51 PM
Whether the individual arbitrage conditions translate into economy-wide arbitrage conditions is a difficult puzzle. What if everyone gets into a fast spaceship? Do the savings accounts still bear positive interest?
I'm assuming that Cowen is thinking about this in a standard Fisherian way, where the subjective time preference schedules interact with objective real returns on capital to establish the market-clearing interest rate.
In that framework, yes, I think the possibility of everybody "skipping" 50 years would indeed allow them all to grow that much wealthier. As RobbL noted above, it's basically a way for people to reduce the discomfort of waiting. Assuming we could keep some robots (or a few stragglers who get paid for being isolated their whole lives) to build up the capital stock etc., everybody could indeed be fantastically rich if they took a nap for a century. And so there would be nothing inconsistent with them all accumulating a fantastic bank balance, in terms of its purchasing power.
Posted by: Bob Murphy at Mar 11, 2008 7:05:18 PM
I think if real interest rates are to remain positive, you'd have to criminalize this sort of time traveling arbitrage that you mention. If everyone tries to move forward 50 years, then there will be no consumers or producers, and the economy will go to crap. The only other alternative is to build robots to manage the economy while we do our great leap forward, but then wouldn't we worry that the robots would wise up and take the economy from us? If the robots are smart enough to run the economy in our absence, wouldn't they be smart enough to also figure out that we're screwing them over? So yeah, the only alternatives, I think, are to have interest rates at zero or to criminalize time travel arbitrage.
Posted by: jhbjhb at Mar 11, 2008 7:12:40 PM
As long as it costs more than zero to travel, that will place limits on the ability to try to outrun everyone else. Even as travel costs drop, for reasons pointed out, productivity of capital would start to drop if large numbers of people started doing this, and so would demand for borrowing for consumption, so that interest rates should drop, but an equilibrium should exist before they necessarily get to zero.
Posted by: dWj at Mar 11, 2008 7:21:34 PM
tyler, there is no free lunch!
the cost of the fuel needed for your ponzi scheme would outstrip by far the gains from time dilation!
Posted by: DIS at Mar 11, 2008 7:44:12 PM
There are also some practical considerations if you try to go a lot of years into the future. (What an odd sentence.) You will have to establish your identity when you return. Maybe the DNA bank will have been hit by an earthquake. The bank where you made your deposit might not exist. Indeed, the country where you made it might not exist, at least not in the same form as when you left.
What would have been the safest investment available, without hindsight, five hundred years ago? Suppose you could go back and make it. What would it be worth to you today?
Posted by: Bernard Yomtov at Mar 11, 2008 8:10:03 PM
Bernard: One quick safe investment that comes to mind is Gold. If you put it in a chest and left it somewhere no one would find...
Some fungible goods with universal value.
Posted by: Recep Peker at Mar 11, 2008 8:30:49 PM
What would be the point of coming back in a 1000 years and having everyone you've ever known be dead? Everyone except Robin Hanson perhaps...
Posted by: Sam at Mar 11, 2008 8:36:02 PM
Now this is amazing: Krugman (1978) mentions ET on page 5 -- four years before the movie was released!
Posted by: Phil Maymin at Mar 11, 2008 8:55:27 PM
http://www.amazon.com/gp/reader/0471135615/ref=sib_dp_pt#
Check Page 243: "The Economics of Interstellar Commerce". While it certainly doesn't predate Krugman, the notion has been explored before, at least superficially.
Posted by: Adam Hyland at Mar 11, 2008 9:00:05 PM
Wouldn't the state prevent this from happening by declaring the people who have disappaeared to be dead and seize their assets, or just by instituting a wealth tax for assets above a certain astronomically high amount?
Posted by: Hei Lun Chan at Mar 11, 2008 9:10:26 PM
On a note, I recall reading that section of the book. It comes at the end of "island in the Sky", a remarkably sober book about colonizing space (sober in light of crazier scifi/colonization books). For some reason I read it first and the pessimism of the article stuck with me, setting the tone for the whole book. That's not bad--our views about space travel and the future need pessimism, but I felt that it was the overriding theme.
In the end, there is no free lunch. While you could predict that interstellar travel would change time preference for some, there are a few caveats to make here:
1. Perhaps travel is so expensive that the change in time preference for some doesn't impact the market as a whole. If you have a vanishingly small group of people pushing the discount rate down, does it affect the prevailing rate? You could argue that the income effect of the billionaires of the world might be analogous. While Bill Gates may have the latitude to spend more money on small purchases than they might be worth to him systematically, that does not do much to change the price I pay for those same products.
2. Travellers will face a STEEP opportunity cost. There isn't any other way to describe it. They may (as the article in "islands in the sky" suggests) spend their wealth ENTIRELY on acclimating themselves to a radically different world or insulating themselves from that new world.
3. In the longer term, risk dominates. Inflation risk and default risk historically rise to 1.0 as time marches on. There are vanishingly view equity or debt instruments that are still valid from 200 years ago. they exist, most notably in the low countries and england, but they are few and far between. What happens in the event of hyperinflation, panics or fraud (although the last one could be accounted for given a persistent third party overseer)?
4. Adverse selection. This is a corrolary of the risk argument. What bank would be likely to write a contract to make an astronomical payment in the far future? A bank that is likely to be solvent that whole time (assuming the bank knows with certainty) might, but would be FAR less likely to do so than a bank who might default on the contract.
5. Explicit cost. While this might eventually become a non-issue, we have to be real about what is at stake. A long term space voyage is basically one way in the eyes of the company chartering the craft. Unlike a 767 from NY to London, when the space ship returns, it will be obsolete, or at least at the end of its viable life. Each trip presents a large fixed cost for the charter company. This may not translate directly as a large enough cost to a consumer if the flight manifest is big enough, but it isn't trivial.
Just some thoughts.
Posted by: Adam Hyland at Mar 11, 2008 9:17:42 PM
..given how time dilation changes the meaning of time preference"
But at light speed there is no time so interest rate ,is zero or oo?
Posted by: karl at Mar 11, 2008 9:21:17 PM
I think several people have raised good objections to the original scenario. But what if we didn't view it as people doing their enhanced waiting in one fell swoop? E.g. suppose there is a colony on Mars, and the flight crew who make the back-and-forth only age a three days for every work week. They don't view humanity as slipping away from them, because they still get weekends off and live normally during them.
From their point of view, their ship is incredibly fast, and weeks consist of Sunday, Monday, Wednesday, Friday, and Saturday. Yet their monthly dividend payments are the same as before.
Posted by: Bob Murphy at Mar 11, 2008 9:42:58 PM
In one of the Ender's Game novels, Ender relies on just this property: his accumulated savings compound over millenia during interstellar voyages at relativistic speeds, allowing him to advance the plot at a later date using this wealth.
Posted by: Andrew at Mar 11, 2008 10:04:45 PM
recep,
What has been the growth in the real value of gold since, say, 1508, and how much fluctuation has there been? Is it really the best alternative?
Posted by: Bernard Yomtov at Mar 11, 2008 10:07:18 PM
@ Bob Murphy
I think the real change in time preference comes from major relativistic change--the kind of time dilation occurring at speeds >0.2c. In the case of that crew on mars, we have current analogues. A ship at sea represents the same situation or an astronaut in the ISS.
The issue is what happens when travel to other stars at high speeds becomes (if it ever does) as cheap as transatlantic travel is now. Those travelers will see a dramatically different time horizon than people on earth. That is the distinction.
Posted by: Adam Hyland at Mar 11, 2008 10:15:04 PM
the real problem is that if all the savers are off in space, the remaining earthbound voters will be sure to vote for inflationary monetary policy and confiscatory taxation. problem solved. and if you think you can fight it, you'd have to start paying lawyers and lobbyists with present dollars, before you've become superwealthy.
Posted by: DK at Mar 11, 2008 11:10:21 PM
The real question is what you'll name your space ship as you zip off for your round trip of a couple of Earth-centuries. The Wild Goose is already taken, how about The Black Swan?
Posted by: Matt C at Mar 11, 2008 11:38:21 PM
In "The Forever War" I think the soldiers returning from combat were confronted with such high taxes and over-crowded world that the real interest gains were not especially significant. In addition upon returning the 2nd time everyone on Earth was gay and homogenous, and the 3rd time there was just one person's genetic type replicated billions of times over.
In "Star Trek The Next Generation" a 20th century businessman with a previously uncurable disease is found, unfrozen, and cured. He thinks he should be magnificantly rich, but money doesen't exist in the future like it did in the past since everyone's needs are easily met.
So after taxes, chances of a new super flu which the future world is immune to but you are not, government revolutions (future world = socialist), human extinction scenarios, and changes in society which make life unendurable, the EV of such a trip could easily be negative.
Posted by: mm at Mar 11, 2008 11:41:09 PM
To gain a substantial reward from the banker's twin paradox, you'd need to spend several Earth decades on board ship, for perhaps a couple of elapsed years of your personal time.
As a result, you will abandon any of your family and friends that you don't take with you. This should make the trick sufficiently unpopular that there will always be a modest profit for time-travelling arbitragors.
I think we can probably eliminate the planetary "great leap forward" as a realistic option. Practical considerations aside, there will be someone who is bound to stay behind and steal all the robots.
Posted by: Sam at Mar 11, 2008 11:44:28 PM
Bernard,
I actually don't know, but here is where I was coming from:
If you went to the mint today and bought a gold coin and just normal coins/notes of the same value (fresh out of the mint), I expect the gold coin to be the better investment over 500 years.
Posted by: Recep Peker at Mar 12, 2008 12:09:39 AM
Recep,
why? I mean, we have a fascination with the notion of intrinsic value. It dominates the language and makes speaking about economics especially difficult. What sort of evidence do we have to say that gold as an asset is a better investment than anything else?
Of course, I will grant you that as a dead hand investment, gold is strictly better than most debt or equity structures because you need to have someone around to manage and guide investments. As I said before, a "fire and forget" investment is liable to backfire. But I would imagine that given a sufficient amount of wealth one could set a trust up and have that managed over time. I would put my money on a set of paper investments loosely shepherded over gold coins.
So assuming that both investments exist after 500 years, meaning that the gold isn't physically stolen or destroyed and the paper still resolves to something of worth, why is gold better?
Posted by: Adam Hyland at Mar 12, 2008 12:28:44 AM
The best investment would be to start a religion. If you can prove you're the religion's founder, upon your return you get more or less everything owned by the believers.
Posted by: jb at Mar 12, 2008 12:29:41 AM
Adam,
The way you put it, yes, a managed investment is much better than the gold (though the trust isn't immune to theft or destruction either). Plus for all we know we might find a vast and accessible gold deposit (in space or on earth) which makes gold cheaper than copper.
I was merely thinking about Bernard's question (albeit with some hindsight).
"What would have been the safest investment available, without hindsight, five hundred years ago?"
Since I'm writing to you, I also wanted to say that I liked the points you made in the above post, the last point had never occured to me.
Posted by: Recep Peker at Mar 12, 2008 2:01:05 AM
Recep,
Thanks. I don't mean to impugn you by making general comments about gold, investment and intrinsic value. I do agree that without the prospect of at least minimal management, a physical commodity is probably a better choice than a corporate investment.
I vote for Hafnium. :)
Adam
Posted by: Adam Hyland at Mar 12, 2008 2:41:28 AM
Watch out.
We've been linked to /.
http://science.slashdot.org/article.pl?sid=08/03/12/0112205
Posted by: Adam Hyland at Mar 12, 2008 3:03:18 AM
A more likely scenario is that a con-artist would convince people of the wealth they could earn by traveling light years into space. Or a government deals with overpopulation by sending citizens on a journey with promises of wealth.
If I killed everyone you know, how much would I have to pay you? I think the interest rate of a normal "time traveler" would be much higher than the rate we see today. Maybe the only willing travelers, who would accept a low rate, would be extreme narcissists or very naive people who fail to calculate the risks.
Posted by: 8 at Mar 12, 2008 7:17:35 AM
Am I the only one who was reminded of Douglas Adams here? You put a penny in a bank account in your own time so that, with the power of compound interest, you can afford the fabulously expensive cost of the meal at the _Restaurant at the End of the Universe_.
Posted by: MCJ at Mar 12, 2008 9:09:30 AM
Recep,
I asked two questions. Let's say gold was safe. What return would you realize? (Though I don't know why gold would be safe. Maybe it would be found and stolen. Maybe the place you hid it would become inaccessible for some reason. Or maybe someone will build a huge structure like a stadium right on top of your hiding place, so retrieval costs are enormous.)
Posted by: Bernard Yomtov at Mar 12, 2008 9:15:27 AM
MCJ,
I was also reminded of Douglas Adams, but a different bit. The custom-made-planet builders of Magrathea produce a luxury good. When the galactic economy crashes, the Magratheans go into hibernation waiting for the galactic economy to recover and for demand in their product to reappear.
Posted by: Aldo at Mar 12, 2008 9:30:07 AM
Heh heh! ". . . this is a serious analysis of a ridiculous subject, which is of course the opposite of what is usual in economics."
Posted by: bob at Mar 12, 2008 10:05:21 AM
there wouldn't be a problem. when you deposit the penny in a bank and blast off into space to travel near the speed of light the bank, after a few months of inactivity on your account, would start charging monthly maintenance fees. by the time you got back you'd owe them several million dollars and would go bankrupt.
Posted by: c at Mar 12, 2008 10:42:48 AM
Krugman's paper has some gems. I've only read the first couple pages, but here are two so far:
From the abstract.... "A solution is dervied from economic theory, and two useless but true theorems are proved."
"Interplanetary trade...raises no major theoretical problems, since it can be treated in the same framework as interregional and international trade. Among the authors who have not pointed this out are Ohlin (1933) and Samuelson (1947)."
Anyway, I saw the title and thought it was going to be a reference to trade in the world of Eve Online, a game where some people make their virtual living conducting interstellar arbitrage.
Posted by: brian at Mar 12, 2008 1:11:43 PM
In that framework, yes, I think the possibility of everybody "skipping" 50 years would indeed allow them all to grow that much wealthier.
If everyone skipped into the future, no one would be putting their capital to work in the meantime. Presumably interest rates would fall until emigrating to the future was no longer profitable.
Posted by: ad at Mar 12, 2008 1:58:00 PM
If everyone skipped into the future, no one would be putting their capital to work in the meantime.
I think that's under the assumption they could have fully automated production processes. An incredibly big assumption, when you consider all of the natural corrosion that will occur, not just on materials, but the expansion of biological life. Is the system robust vs. meteor strikes?
Then there's the possibility of having a skeleton crew. But, as others have suggested in various ways, they could enact confiscatory redistribution on your gains in the meantime: you arrive, only to find out, "Hey, your gains are taxed at 100%, and we enacted a 'help the folks that actually did the work' program, that gives it all to them! Tough break. You can sue, but we're the judges too."
Posted by: Person at Mar 12, 2008 2:52:00 PM
You step off your space ship and walk into the nearest bar to celebrate your becoming a billionaire, unfortunately, the tab for your beer is $3 billion.
Posted by: Yancey Ward at Mar 12, 2008 4:39:23 PM
Yancey_Ward: You forgot the hedonic adjustments. Drinking the beer would be like a taste of pure heaven, something people on earth before your voyage could only dream about ;-)
And then you'd leave and go to a lower-grade automated bar that gives the exact same beer for $1000 but without all the branding :-P
Posted by: Person at Mar 12, 2008 4:59:33 PM
You step off your space ship and walk into the nearest bar to celebrate your becoming a billionaire, unfortunately, the tab for your beer is $3 billion.
And when you check your mail you find lots of notices from the IRS about your failure to file tax returns, with penalties and interest in, I think it is appropriate to say, astronomical amounts.
You made arrangements with a CPA before you left? How much did that cost, and are you sure it's a big, reliable firm, like Arthur Anderson used to be?
Posted by: Bernard Yomtov at Mar 12, 2008 6:44:39 PM
I think a number of complications raised here depend on people making productive use of capital while moving at a velocity near that of light. Krugman, if I understand him correctly, is assuming that all the production happens planetside--spaceships are merely transport.
There is, however, a much more serious problem with the piece, which suggests that Krugman is better at economics than at physics. For details, see my blog:
http://daviddfriedman.blogspot.com/
Posted by: David Friedman at Mar 12, 2008 10:46:20 PM
Once again, the dismal science is corrupting a truly beautiful science, astrophysics. Perhaps I'm galactically provincial in mindset.
Posted by: David at Mar 13, 2008 1:19:47 AM
Tyler, interesting post. Would you be interested in syndicating your content on the home page of my site? It's an online community of finance professionals ( http://www.wallstreetoasis.com ). I could add an RSS feed that will allow me to promote your blog posts to my home page (when i think it will lead to a good discussion and/or is appropriate), but I wanted to make sure you were comfortable syndicating first. The syndicated post would have a link back to your original post. Thanks, Patrick (you can reach me at wallstreetoasis@wallstreetoasis.com if you have any questions).
Posted by: Patrick at Mar 13, 2008 2:32:56 AM
HOW DO YOU DO…
TIME TRAVEL
21st century boring you?
Want a way to walk with dinosaurs that isn’t sitting really close to the TV to watch an unrealistic 3D diplodocus eat leaves?
You need a holiday in time, or dinoworld
Tick, tick, tick… tick
1.5 million years since fire was lit, 35,000 years after the birth of art, 16,000 years from the first mappings of stars and 600 years since the blueprints of the helicopter were drawn. We sit here thinking, “Y’know the 21st century could have been a bit more, well, silvery.” Aside from those metal toasters that’ll burn a farmyard animal into your bread and those credit cards with one of the corners cut off a bit. The 21st century has had:
No proper Robots. My house isn’t doing stuff for me when I go to work so when I get back it’s like a new house and the kitchens in the bathroom. Cars and skateboards don’t hover. We can’t holiday in space and the so called information super highway is still not bypassing my brain with an LCD screen in my eye and USB ports in my tippy toes.
AHHhhhh, yet as a time traveller you can go to the future where these things should have occurred with a few other things that you probably didn’t think about; like a chocolate bar called waffpinuts. A wafer, pineapple and nuts bar wrapped in Kevlar.
Then, go back in time to tell all those people on Tomorrows World that hoodwinked our innocent child eyes, “Hey hey, perm-head, that ain't going to happen you pre-foetus futurist fuck.”
And they’d have to believe your aggressive preaching cos you’d bring an almanac from 2008 with all the sports results and next weeks Eastenders from UK-GOLD, so there.
...continues at lifestyleguides.blogspot.com
Posted by: jollyroger at Mar 17, 2008 8:11:21 AM
