Can I lag my independent variable to avoid reverse causality bias?

[Adam Sadi]

Hello! I am quite new on econometrics, so I apologize if this question is quite simple. I am trying to explain the variation of the stringency index during the COVID-19 pandemic across countries using panel regression. Of course, I suspect the number of infected people to be a reason why countries choose to adopt more stringent policies. However, I read that one should be careful about reverse causality and I believe there might be chances that the level of stringency of a country's policies could also cause less infected people. I would like to address this bias properly, but I'm not sure how.

I was thinking about lagging my variable infected that is defined monthly, with something like :

xtset country month
xtreg str_index L1.infected, fe

(of course this is just a simplified model with just my variables of interest)

but I'm not sure if this is a good idea. Any expert on the topic that might be willing to guide me?

[Sebastian Kripfganz]

By lagging your independent variable, you are specifying a model in which the number of infected people only have a one-period delayed effect on more stringent policies. This could be reasonable if you assume that there is lag in policy implementations. If you want to allow for an instantaneous effect, you should not lag the independent variable. In the latter case, concerns of reverse causality should be handled by using instrumental variables. The lagged number of infected people could be an instrument, although in the fixed-effects world this only works if your time dimension is large. If T is small, you might have to switch to IV or GMM estimation in first differences.