However I would advise a recheck of some of your numbers: I checked your citation to erdil(2024) on page 23 and I think you made errors there? Compared to erdil page 21, you say r is “1.51 in the case of linear programming”, whereas if I’m reading table 8 correctly, the actual 50th percent value is 1.077. Also you say the 90% confidence interval is ”.082 to 2.42″, I think it’s actually .82 to 2.42.
Also, Are you sure Erdil is using the same model as yours for his estimation of r? In that section he cites back to an earlier section describing the “feller diffusion model”, which has some similarities to your semi-endogenous model but has extra terms. Is it valid to use his beta as yours?
Really glad to hear from you, since I greatly appreciated your work on the AI 2027 material!
You’re right that there are two errors here that need to be corrected. One is that it should be .82 rather than .082. The other is that I intended to be using the numbers from the “naive estimate” column of Table 8 on page 21 in the Erdil paper, which are calculated using a simple process which (to my mind) is likely to be less subject to errors introduced by model choice, but the 1.58 is the 50% estimate from their more complex model — the naive estimate is 1.66. The Feller diffusion model is relevant to their more complex calculations, about which I am a little suspicious, but not to their naive calculations.
Interesting work!
However I would advise a recheck of some of your numbers: I checked your citation to erdil(2024) on page 23 and I think you made errors there? Compared to erdil page 21, you say r is “1.51 in the case of linear programming”, whereas if I’m reading table 8 correctly, the actual 50th percent value is 1.077. Also you say the 90% confidence interval is ”.082 to 2.42″, I think it’s actually .82 to 2.42.
Also, Are you sure Erdil is using the same model as yours for his estimation of r? In that section he cites back to an earlier section describing the “feller diffusion model”, which has some similarities to your semi-endogenous model but has extra terms. Is it valid to use his beta as yours?
Really glad to hear from you, since I greatly appreciated your work on the AI 2027 material!
You’re right that there are two errors here that need to be corrected. One is that it should be .82 rather than .082. The other is that I intended to be using the numbers from the “naive estimate” column of Table 8 on page 21 in the Erdil paper, which are calculated using a simple process which (to my mind) is likely to be less subject to errors introduced by model choice, but the 1.58 is the 50% estimate from their more complex model — the naive estimate is 1.66. The Feller diffusion model is relevant to their more complex calculations, about which I am a little suspicious, but not to their naive calculations.