Using Fixed Effects in Difference-in-Differences

[Cansu Oymak]

Dear Stata Intellectuals,

I am interested in exploring the effect of terrorism (events constantly took place between 2013 and 2015) on child health, which is measured by BMI.
I have 2018 and 2013 waves of the Turkish Demographic and Health Survey, both of which are individual level cross-sectional datasets. I pooled them.

I will capture the effect of terror events by conducting dif-and-dif analysis. While some cities of Turkey were affeced by those events, some cities were not affected and this allows me to run dif-and-dif.
I have a year dummy to run dif-and-dif. It takes value 1 if the year is 2013 (it shows the exposure) and it takes value 0 if the year is 2018 (it indicates that there is no exposure to terrorism).

In addition, I can capture city-level differences by adding city-level GDP, number of schools, number of hospitals and etc. However, due to presence of so-called "unoberseved third factors" that I cannot control (such as innate ability, genetic endowments, or heterogeneity in time preferences of families) I need to add a fixed effect estimator. Yet, I am confused about how to do it.

As far as I know, one solution is to use "dummy variable regression". I read it from Wooldridge's book which suggests that add a dummy variable for each individual (i>1 = omitting the first individual because of multicollienarty). I do not understand how to do it. How my data look like? and how can i run the regression? I have some difficulties in visualising the data on STATA.

If any of you can help me, I will be appreciated.

Thank you in advance!

[Jeff Wooldridge]

Cansu: I think you're describing a pooled cross section analysis. Or, do you see the same children in both years? If you have two pooled cross sections then there is no using individual fixed effects. If you are referring to my introductory econometrics book, you need to use the material on diff-in-diffs for pooled cross sections. You can, if you prefer, include city fixed effects and the year dummy for 2018, along with the treatment indicator and the control variables.

reg bmi terror i.cityid i.year control variables, vce(robust)

If you have a sufficient number of control and treatment cities you can replace vce(robust) with vce(cluster cityid) to fully account for uncertainty generated by the uncertainty of terrorist attacks.

JW

[Cansu Oymak]

Dear Jeff Wooldrigde,

First of all, thank you very much for answering my question. This is very explanatory.

The individuals interviewed in years 2013 and 2018 are completely different. That is, childrens are not the same. In other words, I am working with pooled cross sections. I did not realized the fact that I do not need to use individual level fixed effects.

I cautiously analyzed the example explaining the dif-and-dif in your book. It is the example of Construction of Garbage Incinerator. To capture its effect on house prices, the book uses a year dummy. For my case, I can only use a year dummy (0=2018; 1=2013) to capture the effect of terrorism. The increases in terror activities stems from a policy change in TR between 2013 and 2015. That is why I only added a year dummy to capture its effect.

Yet, now I am confused about how to include "terrorism" into my data set. According to your code;
"reg bmi terror i.cityid i.year control variables, vce(robust)" I need an indicator of "terrorism" as well as year dummy. If you have any suggestions, I will definitely try it. Thank you in advance.

[Cansu Oymak]

Dear Jeff Wooldrigde,

First of all, thank you very much for answering my question. This is very explanatory.

The individuals interviewed in years 2013 and 2018 are completely different. That is, childrens are not the same. In other words, I am working with pooled cross sections. I did not realized the fact that I do not need to use individual level fixed effects.

Let me explain it in a more detailed manner.

The Turkish governmennt implemented a policy change between 2012 and 2015. This resulted in a drastic increase in the terrorist attacks during this period. Between 2012 and 2015, these terrorist attacks were highly prevalent in Southeastern cities of Turkey. That is, the Southeastern cities account for my "treatment group". The number of Southeastern cities is 10. On the other hand, the Aegean cities were not affected by the terrorist attacks between 2012 and 2015. The Aegean cities are my "control group". The number of Aegean cities is 9. For each and every city, variables such as GDP, schooling ratio, hospital beds per ten thousand capita, migration rate, and urbanization rate are available. Now, I am re-writing your incinerator equation by changing it to my case:


bmi = B0 + s0 (year2018) + B1 (exposed_cities) + s1 (year2018*exposed_cities) + ut

if this is the equation,

B0 is the intercept showing the average bmi of children who were residing in Southeastern cities (terror-exposed cities); s0 captures changes in all children's bmi from 2013 to 2018; B1 measures the location impact not due to the prevelance of terror activities, and year2018 is a dummy taking value of 0; exposed_cities is a dummy taking value of 1. If I construct the model like that with the control variables, does the parameter of interest on the interaction term year2018*exposed_cities measure decline in bmi due to terror events?.

If yes, I am confused about how to include "terrorism" into my data set. According to your code; "reg bmi terror i.cityid i.year control variables, vce(robust)" I need an indicator of "terrorism" as well as year dummy. Am I right? Do year dummy and city dummy capture the effect of terrorism? Or Should I include "terrorism" in my dataset by using another technique (because it is only a policy chance and I though that year and city dummies will capture its effects)?

Thank you very much !

[Jeff Wooldridge]

Hi Cansu: By "terror" I simply meant your interaction term year2018*exposed_cities. The rest seems fine.

[Cansu Oymak]

Totally got it. Thank you very much !