Thanks for the points, I should have done more due diligence into the arguments for each framework. That said, I don’t see these as fatal flaws:
I don’t know if I see this as a problem. I think it’s good for considerations about policy with international spillovers to be dominated by their effect on low-income countries. For example, I think that the welfare effects of US tariffs should be primarily judged by their impact on exporters in low-income countries, and that economic growth in the US is valuable primarily because of spillovers to the rest of the world. Insofar as log utility brackets this effect away, it doesn’t seem like the right reasoning process.
* Even if you’re uncomfortable with that philosophical commitment, you can still use high etas to evaluate policies that focus on low-income countries, such as growth advocacy. That is considerably narrower than I would like, because I think we should make that philosophical commitment, but it’s still a useful set of scenarios.
Sharpening the tradeoff between life and income is a much bigger problem to me, as I agree that it would be unattractive to place a low value on life. But I don’t think that high etas intrinsically imply a low total welfare. Utility functions are not normalized to scale. We can introduce a large constant for the baseline welfare of being alive, as is done in this framework which has a subsistence welfare s. A high value of s would increase the value of life relative to income, while still maintaining the intuition that each doubling of income is worth less than the last. That s would also be irrelevant for monetary considerations since it would cancel out when looking at the change in utility. Moreover, I think it should be possible to estimate s from IDinsight’s work on beneficiary preferences which retains tractability.
I have to admit that I did not scrutinize the studies and I am very open to them being flawed. But I think almost everyone would agree that 10% income increase is worth much more to a poor person than a rich person. The median economist in the Dropp survey might disagree, but I don’t really place a high weight on a survey of economists, who are a) very attached to log utility as a tractable model and thus incentivized to post-hoc justify it by saying eta = 1, b) not the arbiters of people’s utility functions.
I don’t think that aggregating over implied welfare levels is necessarily the right approach either, since isoelastic utility functions with reasonable values of η are inherently smaller in magnitude than log utility functions. If we arbitrarily squared all welfare levels (utility is invariant to strictly increasing transformations) before averaging them, we would also place a lot more weight on low η, even though nothing has intrinsically changed. More generally, the fact that isoelastic utilities give small numbers is not morally meaningful, because it can be changed by having a normalizing constant.
The simplicity of η=1 may be useful if we don’t know the whole distribution of income, but this kind of exercise for when we do know the whole distribution can produce discounting factors that we can use even when we don’t know the whole distribution of income. So I don’t think that higher η sacrifices much tractability.
Tl, dr; I think most of the features of high η that you identify can be solved by having a high baseline welfare component of the utility function, and the others are not problems.
Thanks Karthik. I think we might be talking past each other a bit, but replying in order on your first four replies:
My key issue with higher etas isn’t philosophical disagreement, it’s as guidance for practical decision-making. If I had taken your post at face value and used eta=1.5 to value UK GDP relative to other ways we could spend money, I think I would have predictably destroyed a lot of value for the global poor by failing to account for the full set of spillovers (because I think doing so is somewhere between very difficult and impossible). Even within low-income countries there are still pervasive tax, pecuniary, other externalities from high-income spending/consumption on lower-income co-nationals, that are closer to linear than logarithmic in $s. None of this is to deny the possibility or likelihood that in a totally abstract pure notion of consumption where it didn’t have any externalities at all and it was truly final personal consumption, it would be appropriate to have a log or steeper eta, it’s to say that that is a predictably bad approximation of our world and accordingly a bad decision rule given the actual data that we have. I think the main reply here has to be a defense of the feasibility of explicitly accounting for all relevant spillovers, and having made multiple (admittedly weak!) stabs in that direction, I’m personally pessimistic, but I’d certainly love to see others’ attempts.
In the blog post I linked in my #2 above we explicitly consider the set point implied by the IDInsight survey data, and we think it’s consistent with what we’re doing. We’re open to the argument for using a higher fixed constant on being alive, but instead of making you focus more on redistribution of income, the first order consequence of that decision would be to focus more on saving poor people’s lives (which is in fact what we predominantly do). It’s also worth noting that as your weight there gets high, it gets increasingly out of line with people’s revealed preferences and the VSL literature (and it’s not obvious to me why you’d take those revealed preferences less seriously than the revealed preferences around eta).
“I think almost everyone would agree that 10% income increase is worth much more to a poor person than a rich person”—I don’t think that’s right as a descriptive claim but again even if it were the point I’m making in #1 above still holds—if your income measure is imperfect as a measure of purely private consumption without any externalities, and I think they all are, then any small positive externalities that are ~linear in $ will dominate the effective utility calculation as eta gets to or above 1. I think there are many such externalities—taxes, philanthropy, aid, R&D, trade… - such that very high etas will lead to predictably bad policy advice.
You can add a constant normalizing function and it doesn’t change my original point—maybe it’s worth checking the Weitzman paper I linked to get an intuition? There’s genuinely more “at stake” in higher incomes when you have a lower eta vs a higher eta, and so if you’re trying make the correct utilitarian decision under true uncertainty, you don’t want to take a unweighted mean of eta and then run with it, you want to run your scenarios over different etas and weight by the stakes to get the best aggregate outcome. (I think how you specify the units might matter for the conclusion here though, a la the two envelope problem; I’m not sure.)
Got it, I think I misunderstood that point the first time. Yes, I am convinced that this is an issue that is worth choosing log over isoelastic for.
Yes, I agree with the first order consequence of focusing more on saving lives. The purpose of this is just to compare different approaches that only increase income, and I was just suggesting that a high set point is a sufficient way to avoid having that spill over into unappealing implications for saving lives. It is true that a very high set point is inconsistent with revealed preference VSLs, though. I don’t have a good way to resolve that. I have an intuition that low VSLs are a problem and we shouldn’t respect them, but it’s not one I can defend, so I think you’re right on this.
Agreed
I’m on board with the idea of averaging over scenarios ala Weitzman, my original thinking was that a normalizing constant would shrink the scale of differences between the scenarios and thus reduce the effect of outlier etas. But I was confusing two different concepts—a high normalizing constant would reduce the % difference between them, but not the absolute difference between them which is the important quantity for expected value.
Thanks, appreciate it! I sympathize with this for some definition of low FWIW: “I have an intuition that low VSLs are a problem and we shouldn’t respect them” but I think it’s just a question of what the relevant “low” is.
Thanks for the points, I should have done more due diligence into the arguments for each framework. That said, I don’t see these as fatal flaws:
I don’t know if I see this as a problem. I think it’s good for considerations about policy with international spillovers to be dominated by their effect on low-income countries. For example, I think that the welfare effects of US tariffs should be primarily judged by their impact on exporters in low-income countries, and that economic growth in the US is valuable primarily because of spillovers to the rest of the world. Insofar as log utility brackets this effect away, it doesn’t seem like the right reasoning process. * Even if you’re uncomfortable with that philosophical commitment, you can still use high etas to evaluate policies that focus on low-income countries, such as growth advocacy. That is considerably narrower than I would like, because I think we should make that philosophical commitment, but it’s still a useful set of scenarios.
Sharpening the tradeoff between life and income is a much bigger problem to me, as I agree that it would be unattractive to place a low value on life. But I don’t think that high etas intrinsically imply a low total welfare. Utility functions are not normalized to scale. We can introduce a large constant for the baseline welfare of being alive, as is done in this framework which has a subsistence welfare s. A high value of s would increase the value of life relative to income, while still maintaining the intuition that each doubling of income is worth less than the last. That s would also be irrelevant for monetary considerations since it would cancel out when looking at the change in utility. Moreover, I think it should be possible to estimate s from IDinsight’s work on beneficiary preferences which retains tractability.
I have to admit that I did not scrutinize the studies and I am very open to them being flawed. But I think almost everyone would agree that 10% income increase is worth much more to a poor person than a rich person. The median economist in the Dropp survey might disagree, but I don’t really place a high weight on a survey of economists, who are a) very attached to log utility as a tractable model and thus incentivized to post-hoc justify it by saying eta = 1, b) not the arbiters of people’s utility functions.
I don’t think that aggregating over implied welfare levels is necessarily the right approach either, since isoelastic utility functions with reasonable values of η are inherently smaller in magnitude than log utility functions. If we arbitrarily squared all welfare levels (utility is invariant to strictly increasing transformations) before averaging them, we would also place a lot more weight on low η, even though nothing has intrinsically changed. More generally, the fact that isoelastic utilities give small numbers is not morally meaningful, because it can be changed by having a normalizing constant.
The simplicity of η=1 may be useful if we don’t know the whole distribution of income, but this kind of exercise for when we do know the whole distribution can produce discounting factors that we can use even when we don’t know the whole distribution of income. So I don’t think that higher η sacrifices much tractability.
Tl, dr; I think most of the features of high η that you identify can be solved by having a high baseline welfare component of the utility function, and the others are not problems.
Thanks Karthik. I think we might be talking past each other a bit, but replying in order on your first four replies:
My key issue with higher etas isn’t philosophical disagreement, it’s as guidance for practical decision-making. If I had taken your post at face value and used eta=1.5 to value UK GDP relative to other ways we could spend money, I think I would have predictably destroyed a lot of value for the global poor by failing to account for the full set of spillovers (because I think doing so is somewhere between very difficult and impossible). Even within low-income countries there are still pervasive tax, pecuniary, other externalities from high-income spending/consumption on lower-income co-nationals, that are closer to linear than logarithmic in $s. None of this is to deny the possibility or likelihood that in a totally abstract pure notion of consumption where it didn’t have any externalities at all and it was truly final personal consumption, it would be appropriate to have a log or steeper eta, it’s to say that that is a predictably bad approximation of our world and accordingly a bad decision rule given the actual data that we have. I think the main reply here has to be a defense of the feasibility of explicitly accounting for all relevant spillovers, and having made multiple (admittedly weak!) stabs in that direction, I’m personally pessimistic, but I’d certainly love to see others’ attempts.
In the blog post I linked in my #2 above we explicitly consider the set point implied by the IDInsight survey data, and we think it’s consistent with what we’re doing. We’re open to the argument for using a higher fixed constant on being alive, but instead of making you focus more on redistribution of income, the first order consequence of that decision would be to focus more on saving poor people’s lives (which is in fact what we predominantly do). It’s also worth noting that as your weight there gets high, it gets increasingly out of line with people’s revealed preferences and the VSL literature (and it’s not obvious to me why you’d take those revealed preferences less seriously than the revealed preferences around eta).
“I think almost everyone would agree that 10% income increase is worth much more to a poor person than a rich person”—I don’t think that’s right as a descriptive claim but again even if it were the point I’m making in #1 above still holds—if your income measure is imperfect as a measure of purely private consumption without any externalities, and I think they all are, then any small positive externalities that are ~linear in $ will dominate the effective utility calculation as eta gets to or above 1. I think there are many such externalities—taxes, philanthropy, aid, R&D, trade… - such that very high etas will lead to predictably bad policy advice.
You can add a constant normalizing function and it doesn’t change my original point—maybe it’s worth checking the Weitzman paper I linked to get an intuition? There’s genuinely more “at stake” in higher incomes when you have a lower eta vs a higher eta, and so if you’re trying make the correct utilitarian decision under true uncertainty, you don’t want to take a unweighted mean of eta and then run with it, you want to run your scenarios over different etas and weight by the stakes to get the best aggregate outcome. (I think how you specify the units might matter for the conclusion here though, a la the two envelope problem; I’m not sure.)
Got it, I think I misunderstood that point the first time. Yes, I am convinced that this is an issue that is worth choosing log over isoelastic for.
Yes, I agree with the first order consequence of focusing more on saving lives. The purpose of this is just to compare different approaches that only increase income, and I was just suggesting that a high set point is a sufficient way to avoid having that spill over into unappealing implications for saving lives. It is true that a very high set point is inconsistent with revealed preference VSLs, though. I don’t have a good way to resolve that. I have an intuition that low VSLs are a problem and we shouldn’t respect them, but it’s not one I can defend, so I think you’re right on this.
Agreed
I’m on board with the idea of averaging over scenarios ala Weitzman, my original thinking was that a normalizing constant would shrink the scale of differences between the scenarios and thus reduce the effect of outlier etas. But I was confusing two different concepts—a high normalizing constant would reduce the % difference between them, but not the absolute difference between them which is the important quantity for expected value.
Thanks, appreciate it! I sympathize with this for some definition of low FWIW: “I have an intuition that low VSLs are a problem and we shouldn’t respect them” but I think it’s just a question of what the relevant “low” is.