2
$\begingroup$

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 my 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 applies 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?

$\endgroup$

1 Answer 1

0
$\begingroup$

My advice is to do a stacked diff-in-diff. For each treated unit, randomly assign a control unit. This forms a group, $g$. There will be several such groups.

$$y_{igt} = \sum_{s}\beta_sT_{ig}d_{gs}+\lambda_i +\lambda_{gt}+\varepsilon_{igt}$$

where $\beta_s$ is the effect of being $s$ periods after (or before) treatment. $T_{ig}$ is a binary variable that individual $i$ in group $g$ was treated. $d_{gs}$ is a binary variable for being $s$ time periods from treatment for group $g$, $\lambda_i$ are individual FE, $\lambda_{gt}$ are fixed effects for group and being $t$ time periods from treatment.

Gardner 2021 shows the stacked diff-in-diff returns a weighted average of the ATT for each treated unit.

I personally find this much more desirable than the De Chaisemartinand d'Hautfoeuille or Sun and Abraham estimators because it is straightforward and similar in spirit to baseline diff-in-diff.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.