Are time varying covariates necessary for staggered did or did in general?

[Zhiyong Huang]

I got an R&R. The reviewer suggested we include "time-varying confounders" in our did setting, where we have already included a bundle of control variables measured at baseline.

However, I think this may result in problems as the time-varing variables can be affected by treatment. As put by Sant'Anna et al., "It is also important to consider that the Panel data estimators assume that you are using time invariant variables. Even if those variables are time variant, only the pretreatment values are used for the outcome model estimator or the probability model estimation. It is possible to add time varying covariates with panel data estimators, adding covariate changes as controls, in addition to the pretreatment covariates. However, unless the controls are strictly exogenous (strong assumption), this may produce inconsistent results, because the changes that would otherwise be capture in the ATT would be absorbed by the varying covariates.

So is it possible/proper to include time-varying variables in staggered did setting, or did in general?

Reference
Sant'Anna, Pedro H. C., and Jun Zhao. 2020. "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics 219 (1): 101–22.

[George Ford]

https://nickchk.substack.com/p/controls-in-difference-in-differences

[Zhiyong Huang]

Thanks, George. It is a really detailed illustration of the issue. Now I have more confidence to persuade the reviewer.

[George Ford]

I think Wooldridge has some posts on here addressing this issue.

You don't want anything in X that might be affected by the treatment.

[George Ford]

New paper on this topic:

https://arxiv.org/pdf/2412.14447

[Jeff Wooldridge]

As with almost everything involving estimation and inference, these choices have to be made in the context of a specific setting. And, you have to be careful with words like "necessary." As George helpfully pointed out -- and as you are clearly aware -- a lot of DiD research assumes the controls do not change over time. But it is possible to include time-varying controls. Whether it is "necessary" is harder to determine. If the time-varying controls are something such as weather in a farm production function, it seems safe to conclude these controls are not influenced by a policy intervention. But if the policy intervention is not determined by weather, then controlling for weather is not necessary to estimate a causal effect. (It can, however, improve efficiency.) Generally, I would want to be sure that the covariates do not react to the policy intervention and that they don't react to past shocks to y (violating strict exogeneity). Both situations result in "bad controls."

If no time-varying, strictly exogenous controls suggest themselves, I might push back a bit on the reviewer's comments and conclude there are no obvious confounders that change over time that satisfy the strict exogeneity requirement.