# Difference-in-difference robust to heterogeneous treatment effect - extension of an article

I am trying to extend the results of Gendron-Carrier et al. (2022) article published in the American Economic Journal : Applied Economics which is about the effect of subway opening on pollution.

I want to use an estimation method robust to heterogeneous treatment effects (meaning that the effect of subway opening on air pollution may have a different trend throughout the different cities where it is implemented).

I cannot understand if the recent robust estimator proposed by De Chaisemartin and d'Hautfoeuille (2020) which is for two-way fixed estimation can be used in this case.

The specification of Gendron-Carrier is as follows :

$$AOD_{it} = \beta_i + \alpha_1D_{it} + \gamma'X_{it} + \epsilon_{it}$$

Where $$AOD$$ is a measure of air pollution, $$D_{it}$$ is a dummy variable equal to 1 when the subway has opened 18 months ago, $$X_{it}$$ is a set of controls consisting of year-by-continent indicators to flexibly account for regional trends in AOD, and city-by-calendar month (1–12) indicators to capture seasonality in pollution patterns as well as climate controls. $$\epsilon_{it}$$ is the error term of the equation.

Do you think the De Chaisemartin and d'Hautfoeuille estimator can be used in this case?

Is this a two-way fixed effects estimation?

In our case how can we apply an estimation method robust to heterogeneous treatment effects?

• Welcome. These are great questions. Do you want to know if this new estimator is applicable to their case or yours, or both? Jun 27, 2022 at 22:47
• Thank you ! Sorry if it wasn't clear, I edited the question. I want to know if the econometric specification of Gendron-Carrier can be considered as a two-way fixed effects estimation and if it's the case, can we apply de Chaisemartin et al. . If it's not the case I'd like to know if there's another estimation method robust to heterogeneous treatment effects we could use on this specification. Jun 27, 2022 at 23:03