Levels or Growth Rates? Specification Choice, the Infection-to-Death Pipeline, and COVID-19 Mortality in the United States

Abstract

The empirical literature on COVID-19 lockdowns and mortality has produced strikingly divergent findings. This paper argues that a central driver of this divergence is the choice between modeling mortality in levels and modeling it in growth rates. The infection-to-death pipeline spans approximately four weeks; a lockdown that reduces transmission today cannot reduce death counts for several weeks, making level specifications mechanically biased against detecting effects in the short run. Using a state-week panel of 50 U.S. states from January 2020 through April 2021, I estimate event-study specifications comparing 44 states that adopted statewide stay-at-home orders to 6 that did not. Level specifications produce significantly positive post-treatment coefficients regardless of estimator, including a Poisson model that handles zeros without any log transformation, confirming that the divergence is structural. The preferred log-growth specification produces a negative average post-treatment coefficient with four individually significant negative coefficients and a clean pre-trend (p = 0.838), and the directional finding survives a restricted sample excluding early zero-dominated weeks. The Callaway and Sant'Anna (2021) estimator, the primary inferential result, yields an ATT of -0.322 (p = 0.001) with dynamic effects that are null at weeks 0 through 2 and negative from week 3 onward with most individual periods individually significant, closely aligned with the pipeline prediction. Unlike the TWFE specification, the CS ATT remains significantly negative (p < 0.01) under both IHS and log(y + 1) transformations, providing evidence that the finding is robust to transformation choice even though the magnitude is not. A case growth rate specification confirms the pipeline timing, and a cancer mortality falsification produces a clean null. The paper provides evidence for the direction and mechanism of the specification-choice divergence 6 rather than a precise causal magnitude, which is sensitive to transformation choice. Specification choice is a central driver of the lockdown literature's divergence, and log-growth specifications are more consistent with the biological mechanism of transmission reduction.