In this paper Heider, Florian, and Alexander Ljungqvist. "As certain as debt and taxes: Estimating the tax sensitivity of leverage from state tax changes." Journal of financial economics 118.3 (2015): 684-712.
on p. 705, it says: "Since the treatment varies within state across time, we cannot include state-year fixed effects to remove such confounds directly. This is a general feature of diff-in-diff tests using policy variation. The only way to address confounds of this kind is to be explicit about what they are and investigate them one by one. In this section, we consider three potential confounds,..."
One of the confounds was investigated via including it as a control, how is it guaranteed that that the estimated effect of the this potential confounds do not include the treatment effect (i.e. the same problem which would result from including state-year fixed effects (since the confound and the treatment might influence each other))?
Is the difference between controls and fixed effect: while controls are continuous variables, fixed effect are not?