I think many economists justify discount rates for more pragmatic reasons, including uncertainty over the future. Your hypothetical in which a civilization 10,000 years from now is given extremely little weight isn’t necessarily a reductio in my opinion, since we know very little about what the world will be like in 10,000 years, or how our actions now could predictably change anything about the world 10,000 years from now. It is difficult to forecast even 10 years into the future. Forecasting 10,000 years into the future is in some sense “1000 times harder” than the 10 year forecast.
An exponential discount rate is simply one way of modeling “epistemic fog”, such that things further from us in time are continuously more opaque and harder to see from our perspective.
Do economists actually use discount rates to account for uncertainty? My understanding was that we are discounting expected utilities, so uncertainty should be accounted for in those expected utilities themselves.
Maybe it’s easier to account for uncertainty via an increasing discount rate, but an exponential discount rate seems inappropriate. For starters I would think our degree of uncertainty would moderate over time (e.g. we may be a lot more uncertain about effects ten years from now than today, but I doubt we are much more uncertain about effects 1,000,010 years from now compared to 1,000,000 or even 500,000 years from now).
If you think that the risk of extinction in any year is a constant γ, then the risk of extinction by year t is γt, so that makes it the only principled discount rate. If you think the risk of extinction is time-varying, then you should do something else. I imagine that a hyperbolic discount rate or something else would be fine, but I don’t think it would change the results very much (you would just have another small number as the break-even discount rate).
I think there’s a non-negligible chance we survive until the heat death of the sun or whatever, maybe even after, which is not well-modelled by any of this.
The reason it seems reasonable to view the future 1,000,010 years as almost exactly as uncertain as 1,000,000 years is mostly myopia. To analogize, is the ground 1,000 miles west of me more or less uneven than the ground 10 miles west of me? Maybe, maybe not—but I have a better idea of what the near-surroundings are, so it seems more known. For the long term future, we don’t have much confidence in our projections of either a million or a million an ten years, but it seems hard to understand why all the relevant uncertainties will simply go away, other than simply not being able to have any degree of resolution due to distance. (Unless we’re extinct, in which case, yeah.)
I agree that in short-term contexts a discount rate can be a reasonable pragmatic choice to model things like epistemic uncertainty, but this seems to somewhat obviously fall apart on the scale of tens of thousands of years. If you introduce space travel and uploaded minds and a world where even traveling between different parts of your civilization might take hundreds of years, you of course have much better bounds on how your actions might influence the future.
I think something like a decaying exponential wouldn’t seem crazy to me, where you do something like 1% for the next few years, and then 0.1% for the next few hundred years, and then 0.01% for the next few thousand years, etc. But anything that is assumed to stay exponential when modeling the distant future seems like it doesn’t survive sanity-checks.
Edit: To clarify more: This bites particularly much when dealing with extinction risks. The whole point of talking about extinction is that we have an event which we are very confident will have very long lasting effects on the degree to which our values are fulfilled. If humanity goes extinct, it seems like we can be reasonably confident (though not totally confident) that this will imply a large reduction in human welfare billions of years into the future (since there are no humans around anymore). So especially in the context of extinction risk, an exponential discount rate seems inappropriate to model the relevant epistemic uncertainty.
Perhaps worth noting that very long term discounting is even more obviously wrong because of light-speed limits and the mass available to us that limits long term available wealth—at which point discounting should be based on polynomial growth (cubic) rather than exponential growth. And around 100,000-200,000 years, it gets far worse, once we’ve saturated the Milky Way.
Hyperbolic discounting, despite its reputation for being super-short-term and irrational, is actually better in this context, and doesn’t run into the same absurd “value an extra meal in 10,000 years more than a thriving civilization in 20,000 years” problems of exponential discounting.
Here is a nice blog post arguing that hyperbolic discounting is actually more rational than exponential: hyperbolic discounting is what you get when you have uncertainty over what the correct discount rate should be.
I think many economists justify discount rates for more pragmatic reasons, including uncertainty over the future. Your hypothetical in which a civilization 10,000 years from now is given extremely little weight isn’t necessarily a reductio in my opinion, since we know very little about what the world will be like in 10,000 years, or how our actions now could predictably change anything about the world 10,000 years from now. It is difficult to forecast even 10 years into the future. Forecasting 10,000 years into the future is in some sense “1000 times harder” than the 10 year forecast.
An exponential discount rate is simply one way of modeling “epistemic fog”, such that things further from us in time are continuously more opaque and harder to see from our perspective.
Do economists actually use discount rates to account for uncertainty? My understanding was that we are discounting expected utilities, so uncertainty should be accounted for in those expected utilities themselves.
Maybe it’s easier to account for uncertainty via an increasing discount rate, but an exponential discount rate seems inappropriate. For starters I would think our degree of uncertainty would moderate over time (e.g. we may be a lot more uncertain about effects ten years from now than today, but I doubt we are much more uncertain about effects 1,000,010 years from now compared to 1,000,000 or even 500,000 years from now).
If you think that the risk of extinction in any year is a constant γ, then the risk of extinction by year t is γt, so that makes it the only principled discount rate. If you think the risk of extinction is time-varying, then you should do something else. I imagine that a hyperbolic discount rate or something else would be fine, but I don’t think it would change the results very much (you would just have another small number as the break-even discount rate).
I think there’s a non-negligible chance we survive until the heat death of the sun or whatever, maybe even after, which is not well-modelled by any of this.
The reason it seems reasonable to view the future 1,000,010 years as almost exactly as uncertain as 1,000,000 years is mostly myopia. To analogize, is the ground 1,000 miles west of me more or less uneven than the ground 10 miles west of me? Maybe, maybe not—but I have a better idea of what the near-surroundings are, so it seems more known. For the long term future, we don’t have much confidence in our projections of either a million or a million an ten years, but it seems hard to understand why all the relevant uncertainties will simply go away, other than simply not being able to have any degree of resolution due to distance. (Unless we’re extinct, in which case, yeah.)
I agree that in short-term contexts a discount rate can be a reasonable pragmatic choice to model things like epistemic uncertainty, but this seems to somewhat obviously fall apart on the scale of tens of thousands of years. If you introduce space travel and uploaded minds and a world where even traveling between different parts of your civilization might take hundreds of years, you of course have much better bounds on how your actions might influence the future.
I think something like a decaying exponential wouldn’t seem crazy to me, where you do something like 1% for the next few years, and then 0.1% for the next few hundred years, and then 0.01% for the next few thousand years, etc. But anything that is assumed to stay exponential when modeling the distant future seems like it doesn’t survive sanity-checks.
Edit: To clarify more: This bites particularly much when dealing with extinction risks. The whole point of talking about extinction is that we have an event which we are very confident will have very long lasting effects on the degree to which our values are fulfilled. If humanity goes extinct, it seems like we can be reasonably confident (though not totally confident) that this will imply a large reduction in human welfare billions of years into the future (since there are no humans around anymore). So especially in the context of extinction risk, an exponential discount rate seems inappropriate to model the relevant epistemic uncertainty.
Perhaps worth noting that very long term discounting is even more obviously wrong because of light-speed limits and the mass available to us that limits long term available wealth—at which point discounting should be based on polynomial growth (cubic) rather than exponential growth. And around 100,000-200,000 years, it gets far worse, once we’ve saturated the Milky Way.
Hyperbolic discounting, despite its reputation for being super-short-term and irrational, is actually better in this context, and doesn’t run into the same absurd “value an extra meal in 10,000 years more than a thriving civilization in 20,000 years” problems of exponential discounting.
Here is a nice blog post arguing that hyperbolic discounting is actually more rational than exponential: hyperbolic discounting is what you get when you have uncertainty over what the correct discount rate should be.