Parker_Whitfill comments on Estimating the Substitutability between Compute and Cognitive Labor in AI Research

[Parker_Whitfill]

Here is a fleshed out version of Cheryl’s response. Lets suppose actual research capital is $qK$ but we just used $K$ in our estimation equation.

Then the true estimation equation is

$\ln \frac{qK}{L}=\sigma \ln \frac{\gamma }{1-\gamma }+\sigma \ln \frac{w}{r}$

re-arranging we get

$\ln \frac{K}{L}=\sigma \ln \frac{\gamma }{1-\gamma }-\ln q+\sigma \ln \frac{w}{r}$

So if we regress $\ln \frac{K}{L}$ on a constant and $\ln \frac{w}{r}$ then the coefficient on $\ln \frac{w}{r}$ is still $\sigma$ as long as q is independent of $w/r$.

Nevertheless, I think this should increase your uncertainty in our estimates because there is clearly a lot going on behind the scenes that we might not fully understand—like how is research vs. training compute measured, etc.