I’m still not sure how they ended up with 84x and 8.7x
the answer is discounting for time and productivity. Consider the 84x for research scientists. With a 20% annual research discount rate, the average value of otherwise-identical research relative to the present is a bit less than 0.9. And productivity relative to peak is very slightly less than 1. These forces move the 100 to 84.
Regarding
why the two numbers [84x and 8.7x] are so different from each other
the answer is mainly differences in productivity relative to peak and scientist-equivalence. As in the plots in this section, PhD students midway through their PhD are ~0.5x as productive as they will be at their career peak. And, as in this section, we value PhD student research labor at 0.1x that of research scientists. The other important force is the length of a PhD—the research scientist is assumed to be working for 1 year whilst the PhD student is funded for 5 years, which increases the duration of the treatment effect and decreases the average time value of research.
Very roughly: 100x baseline you identified * ~0.5x productivity * 0.1x scientist-equivalence * 5 years * ~0.5 average research discount rate = 12.5. (Correcting errors in these rough numbers takes us to 8.4.)
This is broadly correct!
Regarding
the answer is discounting for time and productivity. Consider the 84x for research scientists. With a 20% annual research discount rate, the average value of otherwise-identical research relative to the present is a bit less than 0.9. And productivity relative to peak is very slightly less than 1. These forces move the 100 to 84.
Regarding
the answer is mainly differences in productivity relative to peak and scientist-equivalence. As in the plots in this section, PhD students midway through their PhD are ~0.5x as productive as they will be at their career peak. And, as in this section, we value PhD student research labor at 0.1x that of research scientists. The other important force is the length of a PhD—the research scientist is assumed to be working for 1 year whilst the PhD student is funded for 5 years, which increases the duration of the treatment effect and decreases the average time value of research.
Very roughly: 100x baseline you identified * ~0.5x productivity * 0.1x scientist-equivalence * 5 years * ~0.5 average research discount rate = 12.5. (Correcting errors in these rough numbers takes us to 8.4.)