I maintain that the (net present) value of the delay does not depend on when farming becomes irrelevant. The counterfactual reduction in farming starts after the construction time of 5 years. So I think t0 in your expression should be equal to 5 years regardless of whether farming becomes irrelevant in 10 or 20 years.
Nitpick. Your formula includes 6 years from t0 to t0+5. The sum should start at t0+1 such that it only covers 5 years, which is the duration of the delay.
Fair point. Here is a notebook showing that, under 20 year timelines, saving 4 animals/year indefinitely is better than saving 5/year for 10 years, but that the order is reversed under 10 year timelines. Does this make sense now?
Thanks. Those values make sense. At the same time, I do not think they show “delaying tactics may be (relatively) more valuable in short-timelines worlds”. Holding the construction time constant, the net present value (NPV) of the delay would be the same because it would counterfactually reduce farming in the same years regardless of when farming becomes irrelevant.
I think we might be talking past each other. I’m just trying to make the point in the above table: the delaying tactic is not the most effective in a long timelines world, but it is the most effective in a short timelines world. (I think you agree?)
Thanks for being so patient! I understand what you mean now. You agree the cost-effectiveness of the delay is the same in both scenarios, but are pointing out that the difference between the cost-effectiveness of the delay and that of other tactics decreases if farming becomes irrelevant sooner. I got confused because whether tactics involve delays or not is not what really matters for how their cost-effectiveness is affected by the time when farming becomes irrelevant. What matters is that their (counterfactual) effects materialise soon such that they are not heavily discounted. An intervention delaying the construction of a farm for a super long time would be a delaying tactic, but short timelines would decrease the vast majority of its value. In contrast, buying beef does not involve any delays, but arguably helps soil animals via increasing agricultural land for a few years after the beef is bought, so it would not be affected by short timelines.
Thanks. I still do not get it. For a construction starting in year 1, and lasting 5 years, and a delay of 5 years:
If farming became irrelevant in 10 years, there would be farming from years 6 to 10 without the delay, and no farming with the delay.
If farming became irrelevant in 20 years, there would be farming from years 6 to 20 without the delay, and from years 11 to 20 with the delay.
In both cases, the delay would eliminate the farming from years 6 to 10.
Yes, but the earlier 5 years are more valuable!
Given some discount rate r, the value of preventing 5 years starting at t0 is ∑t0+5t=t0rt. Here is a plot with r=0.8:
You can see that increasing values of t0 (horizontal axis) result in less valuable outcomes.
I maintain that the (net present) value of the delay does not depend on when farming becomes irrelevant. The counterfactual reduction in farming starts after the construction time of 5 years. So I think t0 in your expression should be equal to 5 years regardless of whether farming becomes irrelevant in 10 or 20 years.
Nitpick. Your formula includes 6 years from t0 to t0+5. The sum should start at t0+1 such that it only covers 5 years, which is the duration of the delay.
Fair point. Here is a notebook showing that, under 20 year timelines, saving 4 animals/year indefinitely is better than saving 5/year for 10 years, but that the order is reversed under 10 year timelines. Does this make sense now?
Thanks. Those values make sense. At the same time, I do not think they show “delaying tactics may be (relatively) more valuable in short-timelines worlds”. Holding the construction time constant, the net present value (NPV) of the delay would be the same because it would counterfactually reduce farming in the same years regardless of when farming becomes irrelevant.
I think we might be talking past each other. I’m just trying to make the point in the above table: the delaying tactic is not the most effective in a long timelines world, but it is the most effective in a short timelines world. (I think you agree?)
Thanks for being so patient! I understand what you mean now. You agree the cost-effectiveness of the delay is the same in both scenarios, but are pointing out that the difference between the cost-effectiveness of the delay and that of other tactics decreases if farming becomes irrelevant sooner. I got confused because whether tactics involve delays or not is not what really matters for how their cost-effectiveness is affected by the time when farming becomes irrelevant. What matters is that their (counterfactual) effects materialise soon such that they are not heavily discounted. An intervention delaying the construction of a farm for a super long time would be a delaying tactic, but short timelines would decrease the vast majority of its value. In contrast, buying beef does not involve any delays, but arguably helps soil animals via increasing agricultural land for a few years after the beef is bought, so it would not be affected by short timelines.