Note on Selection Bias in Observational Estimates of Algorithmic Progress

Ho et. al (2024) attempts to estimate the degree of algorithmic progress from language models. They collect observational data on language models' loss and compute over time, and argue that as time has passed, language models' algorithmic efficiency has been rising. That is, the loss achieved for fixed compute has been dropping over time. In this note, I raise one potential methodological problem with the estimation strategy. Intuitively, if part of algorithmic quality is latent, and compute choices are endogenous to algorithmic quality, then resulting estimates of algorithmic quality will be contaminated by selection bias.