6.17 How Does Treatment Effect Heterogeneity in Time Affect TWFE?

As we have seen earlier, the TWFE estimator is baised even in cases where the parallel trend assumption holds given that the treatment effect varies over time. As of VWATT, this is a weighted version of each \(2 \times 2\) DD estimate and the weights are dependent on treatment timing as well as treatment heterogeneity across groups. For example, states with high anti-smoking sentiments have increases cigarette taxes earlier; increases in cigarette taxes can affect populace living in state with higher anti-smoking sentiments more compared to states with low anti smoking sentiments. Now given that states with relatively lower of anti-smoking sentiments increased cigarette taxes later (and if this falls in the middle of the panel), the VWATT will provide higher weights to the states with lower anti-smoking sentiments. In this case, the estimate of cigarette taxes will be underestimated.