Temporal discounting is not about time
Economists doing cost-benefit analysis normally make use of temporal discounting, i.e. benefits further in the future count for less than those nearer to the present. In part this is done to reflect the availability of positive investment returns, but normally analysis also include an additional element of pure temporal preference.
Say that I set up a sealed habitat for some plants and cute bunny rabbits. The rabbits are placed in suspended animation, and the habitat is rocketed out of the Solar System by an automated spacecraft which will never return to interact with our world again. At a predesignated time, the rabbits will be revived and go on to live happy lives in the sealed habitat for a time and then die. With significant pure temporal preference this spacecraft is much more valuable if it is set to revive the isolated rabbits after 5 years rather than 50.
Indeed, economists typically make use of constant exponential discounting, e.g. reducing the valuation of benefits by 3% per year. At a 3% annual discount rate the value of future benefits will be cut by more than half every 23 years. After 230 years a good would be valued at less than a thousandth of an immediate counterpart. But to most people the change in activation time does not make such an overwhelming difference. Further, constant exponential discounting makes strong distinctions between different far-future periods: benefits received in 1 million years are still more than a thousand times as valuable as benefits received in 1,000,230 years.
But real humans mostly don't care about such distinctions. A difference of a few centuries added onto a million years is a negligible change in time: in either case they lie far beyond the current era and the proportional change is small. Favoring the earlier time for a thousandfold reduction in the goods achieved seems absurd in that context. Humans may be impatient within our own lives, care more about our children than distant descendants, and so forth, but the constant exponential discounting framework just doesn't make sense of our attitudes towards the further future.
Because of cases like this philosophers tend to reject the idea of pure temporal preference for social cost-benefit analysis, e.g. with respect to climate change, and often critique economists for persisting in making use of it. But economists are not fools, and the reasons why so many continue to do so are worth thinking about.
Temporal discounting is a hack to make utilitarian models less demanding
The Stern Review on the Economics of Climate Change offers a good illustration of the demand for models with exponential pure temporal preference. The Review, citing philosophers and arguments such as those above, rejected pure temporal preference, although they included a 0.1% annual discount rate intended to model the chance of human extinction. As a result, they estimated the benefits of averting climate change as several times as great as economists using typical rates of pure time preference, enough to justify large sacrifices by the present generation. In their model climate change would have harms lasting for centuries which could not be undone even at great cost. The lasting harms could be mostly ignored with standard discount rates, but with the Stern rate the greater duration and population of the future made it more important than the present.
However, if the same same discount rate and economic model were applied to other policy questions, they would have radical implications, e.g. that the present generation should divert the great majority of its income into investment and research an development to benefit future generations, slashing current living standards for the benefit of the future. But current voters, and thus politicians, don't want to cut most of their consumption to help future generations!
Likewise, if we drop the implausible assumption of a fixed 0.1% annual risk of extinction and allow some probability of successful space colonization or the creation of a stable society, averting existential risk would have even higher benefits, and standard cost-benefit analysis would prioritize existential risk reduction far ahead of current living standards, e.g. cutting current living standards 50% to reduce long-term existential risk by 1% . As climate economist William Nordhaus notes in a paper on cost-benefit analysis of catastrophic risk, voters probably wouldn't be very enthusiastic about such a policy.
Some people supported the methodology of the Stern Review because its argument provided a soldier, but far fewer were ready to embrace the broader implications of its principles, namely overwhelming focus on the welfare of future generations and existential risk. Many economists who supported strong action to reduce climate change, aside from those favoring slower policy responses, objected to the implicit fanaticism of the Stern approach. After all, if economists routinely gave extreme utilitarian recommendations to policymakers that involved sacrificing current voters for future generations, policymakers would ignore them. Pure temporal preference could help to hack models that were basically utilitarian in form (adding up the discounted benefits across people) to produce conclusions that were politically more acceptable.
But not a very good hack
Temporal discounting provides exponentially extreme discounts for far future benefits, but this still allows for extremely large social welfare numbers to appear in cost-benefit analysis. For instance, if human brain emulations or de novo artificial intelligence were developed populations and wealth could increase. As long as we assigned even a modest probability to such a scenario in the next century or so, it could dominate cost-benefit calculations, and again the models would demand large sacrifices from current people to improve the likelihood or quality of such a development.
Also, there is some nonzero probability that unexpected developments in physics or the like may allow for growth to outpace discount rates, e.g. by creating baby universes. So long as some probability is assigned to these outcomes they would dominate, and indeed would make the expected welfare infinite (see Bostrom's Infinite Ethics for more).
Economists don't like it when their models give infinite expected utility for every policy, or when they require fanatical focus on the possibility of infinite outcomes at the expense of the interests of their policymaker paymasters, so they produce models that assume with questionable infinite certainty that such possibilities won't happen. Combining such assumptions with temporal discounting, they can generate convergent utilities and the 'common sense' recommendations policymakers want while using analytically convenient utilitarian formalism.
Unfortunately, one side effect of these hacks is that they create confusions like those mentioned in the first section, and fail to map onto human preferences (such as they are). People are not willing to make arbitrary sacrifices to avert astronomical waste, but they also don't think that colonizing the galaxy is practically worthless. They don't want to cut living standards to produce somewhat greater gains to distant future people, but would be willing to pay meaningful amounts to prevent the otherwise certain destruction of the Earth in 200 years. Common intuitions seem to reflect an attitude of "Shut Up and Divide" which assigns some importance to total future population, civilization duration, average welfare, and the like, but only up to some bound (requiring diminishing marginal value for additional people added to future history). Such a function would lose some of the elegance and convenience of (pretending to) combine benefits additively, but could still be quite tractable and better reflect human attitudes than the existing hacks, let alone their selective and opportunistic application.
Economists doing cost-benefit analysis normally make use of temporal discounting, i.e. benefits further in the future count for less than those nearer to the present. In part this is done to reflect the availability of positive investment returns, but normally analysis also include an additional element of pure temporal preference.
Say that I set up a sealed habitat for some plants and cute bunny rabbits. The rabbits are placed in suspended animation, and the habitat is rocketed out of the Solar System by an automated spacecraft which will never return to interact with our world again. At a predesignated time, the rabbits will be revived and go on to live happy lives in the sealed habitat for a time and then die. With significant pure temporal preference this spacecraft is much more valuable if it is set to revive the isolated rabbits after 5 years rather than 50.
Indeed, economists typically make use of constant exponential discounting, e.g. reducing the valuation of benefits by 3% per year. At a 3% annual discount rate the value of future benefits will be cut by more than half every 23 years. After 230 years a good would be valued at less than a thousandth of an immediate counterpart. But to most people the change in activation time does not make such an overwhelming difference. Further, constant exponential discounting makes strong distinctions between different far-future periods: benefits received in 1 million years are still more than a thousand times as valuable as benefits received in 1,000,230 years.
But real humans mostly don't care about such distinctions. A difference of a few centuries added onto a million years is a negligible change in time: in either case they lie far beyond the current era and the proportional change is small. Favoring the earlier time for a thousandfold reduction in the goods achieved seems absurd in that context. Humans may be impatient within our own lives, care more about our children than distant descendants, and so forth, but the constant exponential discounting framework just doesn't make sense of our attitudes towards the further future.
Because of cases like this philosophers tend to reject the idea of pure temporal preference for social cost-benefit analysis, e.g. with respect to climate change, and often critique economists for persisting in making use of it. But economists are not fools, and the reasons why so many continue to do so are worth thinking about.
Temporal discounting is a hack to make utilitarian models less demanding
The Stern Review on the Economics of Climate Change offers a good illustration of the demand for models with exponential pure temporal preference. The Review, citing philosophers and arguments such as those above, rejected pure temporal preference, although they included a 0.1% annual discount rate intended to model the chance of human extinction. As a result, they estimated the benefits of averting climate change as several times as great as economists using typical rates of pure time preference, enough to justify large sacrifices by the present generation. In their model climate change would have harms lasting for centuries which could not be undone even at great cost. The lasting harms could be mostly ignored with standard discount rates, but with the Stern rate the greater duration and population of the future made it more important than the present.
However, if the same same discount rate and economic model were applied to other policy questions, they would have radical implications, e.g. that the present generation should divert the great majority of its income into investment and research an development to benefit future generations, slashing current living standards for the benefit of the future. But current voters, and thus politicians, don't want to cut most of their consumption to help future generations!
Likewise, if we drop the implausible assumption of a fixed 0.1% annual risk of extinction and allow some probability of successful space colonization or the creation of a stable society, averting existential risk would have even higher benefits, and standard cost-benefit analysis would prioritize existential risk reduction far ahead of current living standards, e.g. cutting current living standards 50% to reduce long-term existential risk by 1% . As climate economist William Nordhaus notes in a paper on cost-benefit analysis of catastrophic risk, voters probably wouldn't be very enthusiastic about such a policy.
Some people supported the methodology of the Stern Review because its argument provided a soldier, but far fewer were ready to embrace the broader implications of its principles, namely overwhelming focus on the welfare of future generations and existential risk. Many economists who supported strong action to reduce climate change, aside from those favoring slower policy responses, objected to the implicit fanaticism of the Stern approach. After all, if economists routinely gave extreme utilitarian recommendations to policymakers that involved sacrificing current voters for future generations, policymakers would ignore them. Pure temporal preference could help to hack models that were basically utilitarian in form (adding up the discounted benefits across people) to produce conclusions that were politically more acceptable.
But not a very good hack
Temporal discounting provides exponentially extreme discounts for far future benefits, but this still allows for extremely large social welfare numbers to appear in cost-benefit analysis. For instance, if human brain emulations or de novo artificial intelligence were developed populations and wealth could increase. As long as we assigned even a modest probability to such a scenario in the next century or so, it could dominate cost-benefit calculations, and again the models would demand large sacrifices from current people to improve the likelihood or quality of such a development.
Also, there is some nonzero probability that unexpected developments in physics or the like may allow for growth to outpace discount rates, e.g. by creating baby universes. So long as some probability is assigned to these outcomes they would dominate, and indeed would make the expected welfare infinite (see Bostrom's Infinite Ethics for more).
Economists don't like it when their models give infinite expected utility for every policy, or when they require fanatical focus on the possibility of infinite outcomes at the expense of the interests of their policymaker paymasters, so they produce models that assume with questionable infinite certainty that such possibilities won't happen. Combining such assumptions with temporal discounting, they can generate convergent utilities and the 'common sense' recommendations policymakers want while using analytically convenient utilitarian formalism.
Unfortunately, one side effect of these hacks is that they create confusions like those mentioned in the first section, and fail to map onto human preferences (such as they are). People are not willing to make arbitrary sacrifices to avert astronomical waste, but they also don't think that colonizing the galaxy is practically worthless. They don't want to cut living standards to produce somewhat greater gains to distant future people, but would be willing to pay meaningful amounts to prevent the otherwise certain destruction of the Earth in 200 years. Common intuitions seem to reflect an attitude of "Shut Up and Divide" which assigns some importance to total future population, civilization duration, average welfare, and the like, but only up to some bound (requiring diminishing marginal value for additional people added to future history). Such a function would lose some of the elegance and convenience of (pretending to) combine benefits additively, but could still be quite tractable and better reflect human attitudes than the existing hacks, let alone their selective and opportunistic application.
7 comments:
I think most people would feel, as I do, that the state of the universe, and of our civilization in a million years, has little correlation with any action we could take today. Yes, we could wipe ourselves out, but this would affect the nearer future. It would be hard to argue that some action today would be benign for a million years and suddenly become toxic. The number of possible universes in a million years is so large that all predictions are meaningless.
If we insist on reasoning about infinite time it's inevitable that we will run up against infinite benefits. I think it's probably a better idea, and more honest, to put in some sort of time horizon beyond which the theory breaks down. down.
What's clearer to accuse economics of under this spotlight, is overblown present-centrism. The present has no special solidarity with the future, it's just eager to consume most of it over a single human lifetime. Exponential discounting is also unacceptable because it appears to forbid reading values off a the horizon (and a fortiori writing any onto it).
> However, if the same same discount rate and economic model were applied to other policy questions, they would have radical implications, e.g. that the present generation should divert the great majority of its income into investment and research an development to benefit future generations, slashing current living standards for the benefit of the future. But current voters, and thus politicians, don't want to cut most of their consumption to help future generations!
Hey Carl, I've heard people (Arrow?) talk about how there'd be a very high savings and investment rate under zero pure time preference. What would this actually look like, and how much worse off would present people be under the policy? Is the scenario lots more investment in basic science and technology, and less consumption of things that don't produce much general human empowerment?
I agree that not doing pure time preference + limiting costs to the present generation is the right hack.
Nick,
We'd have to specify the counterfactual a bit: if the government suddenly started enacting policies based on equal concern for future generations while the citizenry remained the same, it would have to worry about electoral defeat, rebellion, and so forth.
With the standard economic hypothetical of a fantasy benevolent despot who doesn't have to worry about rebellion I'd expect some of the following, pretty weird items:
1. Eliminate policies that increase present consumption at the expense of society's productive capabilities. E.g. cut Social Security to subsistence levels (in cheap overseas retirement communities), subsidized medical care for the retired and those permanently unable to work. Eliminate tax subsidies to large homes, medical expenditures, etc. This would free up most government budgets for long-term investments.
1a. On the taxation side, increase taxes until the uses for available revenue are outweighed by disincentives on productive activity like entrepreneurship. The experience of places like Sweden shows that this can be very high, although in this fantasy world the money is going towards investments in the future, rather than the standard welfare/social security state (in the real world this would diminish its legitimacy).
2. Policies to increase labor participation in the economy (this has gone down steadily in rich countries as increasing wealth and redistribution made life less desperate). Less generous benefits for the unemployed, active stigmatization of unemployment, cutting education subsidies for programs with poor employment placement for their students, shift of taxation from labor and productive investment to other areas (carbon emissions, luxury taxes, consumption taxes, height taxes, genetic endowment taxes).
3. Efforts to increase the size and productivity of the population. Allowing unlimited immigration, at least for those who make net contributions to tax revenues (if not as citizens, then as guest workers with minimal logistical hassle, although since we are imagining a benevolent despotism, any effects of immigration on the democratic process can be ignored). Paying for people to have babies, and for others to adopt them. Paying more for babies that have been enhanced using biotechnology to be more productive. More of some kinds of education, less of others.
4. Large investments in capital goods (although the chance of technological obsolescence and similar factors will still give us a discount rate on long-term investments: it's silly to spend a lot of resources on high-speed trains right before robocars make the investment useless): roads, ports, high-voltage electricity lines, sewerage and other connections for new construction.
5. Much more attention to generating scientific knowledge that can improve performance over long periods and large scopes. Most medical subsidy funding might take the form of medical trials. Everyone's medical records might be required to be available for scientific studies. New policy interventions would be carefully tested, etc.
6. Huge investments in averting immediate risks: adequate countermeasures for celestial impacts, big efforts to prevent artificial pathogens and nuclear war. However these would be limited by the tradeoff with increasing general capacities (deploying too early with inefficient methods can reduce total quality-weighted deployment). Huge isolated bunkers would be constructed to let humanity survive a catastrophe.
7. R&D investment would skyrocket, with more effort on getting value for money. More programs supporting smart kids in accelerating through early education to become scientists, more pro-science propaganda, more favorable tax rates for scientists vs other professions, etc. R&D would especially flow to areas that might otherwise result in civilization getting derailed without them. Probably tighter security measures on some fields.
Overall, from the perspective of a typical rich country person, this would involve the use of the tax and transfer system to take away most of your current consumption (higher taxes, plus loss of benefits) and direct it to investment, R&D, and increasing population.
You would probably live in a substantially smaller house or apartment (although pro-construction policies could drive down housing costs a lot, see Texas or Matt Yglesias), eat more cheaply, drive or share cheaper cars or transit, only get the most cost-effective medical care, and would need to scrimp and save to avoid a precipitous drop in SOL upon retirement. You would still have a nutritious diet, clean water, comfortable living quarters, cheap electronic entertainment, and a not much reduced life expectancy. You also wouldn't face the pathologies of poverty in our society (exposure to crime and dysfunctional people, low relative status), so you would be less happy, but not miserable.
Things would be much worse for you than average if you were unable to work, but better if you were willing to raise lots of children (perhaps not blood relatives) or were well suited to suddenly favored fields of R&D and investment.
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