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

[Parker_Whitfill]

Note that if you accept this, our estimation of $\sigma$ in the raw compute specification is wrong.

The cost-minimization problem becomes

${min}_{H,K}wH+rKs.t.F(AK,H)=\overline{F}$.

Taking FOCs and re-arranging,

$\frac{K}{H}=\sigma \frac{\gamma }{1-\gamma }+\sigma \ln \frac{wA}{r}$

So our previous estimation equation was missing an A on the relative prices. Intuitively, we understated the degree to which compute was getting cheaper. Now A is hard to observe, but let’s just assume its growing exponentially with an 8 month doubling time per this Epoch paper.

Imputing this guess of A, and estimating via OLS with firm fixed effects gives us $\sigma =.89$ with $.10$standard errors.

Note that this doesn’t change the estimation results for the frontier experiments since the $A$ in $\frac{A{K}_{res}}{A{K}_{train}}$ just cancels out.