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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
