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Came across this paper that does panel regressions of Y (Covid growth rates) ~ P (adopted polices) + fixed effects. The elementary modeling mistake is not to control for past growth rates and new recent cases. Call these variables I (information variables). 1/n
2/n I determine adoption of policies (P) and peoples private behavioral (B) reactions to Covid-19. That's documented empirical fact in the US data. Even if (I) doesn't affect outcome directly , they I's are powerful confounders that should be controlled for. 2/n
3/n The confounding backdoor path is P <- I -> B -> Y. The confounding path should be blocked by conditioning on I, hence requiring this variable (lagged dependent variables) to be in the model: Y ~ P + I + other controls W. (See Figure attached from our paper with Paul & Hiro.
n/n When we control for information variables (I), we find, using US cross-state data, that policies (P) do matter. https://www.medrxiv.org/content/10.1101/2020.05.27.20115139v6
Last, but not the least, graphical way of thinking helps (as much as traditional old-school structural econometrics (SE) way of thinking). I highly recommend the Book of Why for developing graphical way of thinking, along with SE paper Arellano & Bond in JoE for panel data.
