Using an exogenous but non-random event for DiD

[Jun Park]

Hi everyone,

I have a quick question regarding whether the following event might pose any issues for my study.

I am interested in exploring perceptions of climate change. In the early 1970s, former dictator Park of South Korea selected nine regions in Korea and established heavy chemical factories in them, subsidizing their development. Now, I am interested in investigating whether individuals who resided in those regions during that time, and who directly or indirectly benefited from this initiative (as these regions experienced rapid growth compared to others), exhibit greater tolerance towards climate change.

However, the challenge lies in the fact that these regions were likely not chosen randomly (although I am not 100% sure). I am encountering difficulty in gathering evidence on the allocation process, which could have involved strategic decisions or political connections.

If I were to compare these nine regions with similar ones, would that introduce any problems? Typically, it would. However, for my purposes, I don't believe there are endogeneity issues, as it is improbable that regions more tolerant of pollution were intentionally selected due to the dictator's regime. The main concern is that individuals tolerant of pollution may not be so due to economic benefits, but rather because the targeted regions were chosen based on political affiliations. Loyalty to the dictator, stemming from political connections, might influence respondents to exhibit greater tolerance of pollution (though I consider this scenario unlikely. I would also control for political affiliation).

Would the non-random selection process of these regions pose a problem for my study?

[George Ford]

some sort of matching is an option.

[Jun Park]

George Ford Thanks for your reply. But do you think I would encounter bias if I don't do matching?

[George Ford]

Maybe, maybe not. But if you plan to publish, you'd better address the possibility.

[Jeff Wooldridge]

Jun: The method of diff-in-diffs allows for nonrandom assignment. At the most basic level, that's why two-way fixed effects is used so often. You account for differences across regions by including region fixed effects along with time fixed effects. With a common intervention timing, that tends to work well. You can include controls and interact them with time period dummy variables, and also with the treatment variable to estimate heterogeneous effects.

The key assumption is the parallel trends assumption, which means the assignment of treatment cannot depend on trend differences. But level differences is fine. As another example that I'm working with, opportunity zone designation in the United States was clearly far from random. Census tracts with high unemployment were more likely to be assigned special status. Given at least two years of data, DiD handles that. It doesn't handle the case where the assignment was based on the trend in unemployment but it allows arbitrary differences in pre-intervention levels.

It is easy to include the term i.evertreat*c.year to account for differences in pre-treatment trends.

I probably wouldn't match with the small N that you have. But if you want to, let me recommend my paper with Soo Jeong Lee that shows how to properly extend DiD to cases where you want to use matching after removing pre-treatment means or trends from each unit.

Lee and Wooldridge (2023)