# Is my model right ? DiD FE

A week ago I already asked a question to my first project, unfortunately it was not realy clear what I wanted. Now I am a few steps further..

What I want to know is if my model is correct. It's a mix of difference-in-differences and Fixed Effects

I want to measure the "(medium-term)-effect of smoke cessation on BMI".. the panel data set includes the questions about bmi and smoking every other year 2002, 2004, ... , 2012 By "medium term" I mean that I am also interessted how the weight gain looks in 2 years, 4 years and maybe in 6 years

I droped a few oberservation and have three groups
a) Neversmokers.. they never smoked
b) Ex-smoker.. they smoked 2002, 2004, 2006 and did not smok ein 2008, 2010, 2012 (the exact moment when they stopped it not clear)
c) Alwayssmokers.. they always smoked

First of all I plotted the average BMIs of the groups and the results are what I expected, "smokers have lower bmi and after smoke cessation people gain weight"

Then I tried normal D-i-D, but I am afraid that the results may be wrong because the treatment is endogenous, its not a political policy, people decide to stop smoking

So I did Fixed Effects:

// did = post2006 * exsmokerdummy
xtreg bmi did i.year manyvariables, robust fe cluster(id)
xtreg bmi_t2 did i.year manyvariables, robust fe cluster(id)
xtreg bmi_t4 did i.year manyvariables, robust fe cluster(id)


The results look promising: did coefficients are 1.01, 0.74 and 0.034 (all significant) which I guess are similiar to the results in the picture below But the R-squared overall is only 0.0049

So do you think the model might show this effect I am looking for? I welcome every answer.

• can you show how you egened this variable "did"? that doesn't make sense to me. What are these data? Are they aggregate time series data or are they from a panel study where you can map from participant to participant overtime (is this addhealth?) – AdamO Jan 4 '18 at 21:56
• egened ? do you mean gen post06 = year >= 2008 gen did = post08 * exsmoker exsmoker is 1 if group b) , else 0 ´ ... I got the idea from link .. its a normal panel data set.. SOEP from germany – JK31 Jan 4 '18 at 22:05
• Yes. I presume you mean gen post08 in the code example. This will help construct an answer thanks. – AdamO Jan 4 '18 at 22:06
• sorry mate I edited while you made the next answer ;D – JK31 Jan 4 '18 at 22:08

It's not the right analysis.

Putting aside the issues from self-report, and even the issue that smokers rarely "quit" indefinitely, and even the issue of what a terrible measure BMI is, this is not a difference-in-difference analysis.

A difference in difference requires that crossover cases have a control group that does not cross over. For instance, in a matched experiment of physical fitness, two athletes lifting weights will expectedly gain muscle mass as a function of their routine exercise, but if one athlete supplements with protein and creatine, I need to calculate difference-in-difference to see what the incremental effect (eq. interaction) of supplementation is on physical fitness. It matters not, by contrast, whether the crossover period was set administratively or out of one's own volition. A method similar to difference in difference is interrupted time series which follows the approach I'll outline below.

Approach 1: case cohort design: You can make a difference-in-difference analysis out of cohort data using a case-cohort design. I am assuming, as I said, you have a reliable measure of those who definitely did quit smoking and those who continued smoking continuously. Here you match a quitter to a non-quitter 1:1 using similar baseline covariates (age, sex, socioeconomic status, site, etc.) you can compare trends in a participant who quit smoking to those of a person who did not quit. Fit in this subsample a model with a random effect for the pair ID, a time trend as a numeric or categorical variable, baseline BMI, smoking status as a time varying covariate, and the interaction of smoking status and time trend. Test this against the statistical model which does not adjust for smoking status.

Approach 2: APC time smoking interaction As before, adjusting for confounding variables (age, sex, SES, and such), fit a time series model with random intercepts for repeated measures within participant, BMI at the start, and a fixed effect for time (either linear or categorical). Such a model can carefully claim to capture the effects of age, period, and cohort (APC) on BMI. As before adjust for smoking and its interaction with time. Test against the null model which does not adjust for smoking.

• thanks for the quick answer ! yes the bmi is a terrible measure, I already mentioned it in my report ;), I have never heard about your approaches before since I had only a few statistics/econometrics classes, but I will check them.. do you have any good resources ?... Well, I would really like to use some regression models since this is the goal of the class, according to my prof the models dont have to be perfect – JK31 Jan 4 '18 at 22:37
• @F.Aires I think doing literature review of actual published papers on the subject will be most helpful. There are too many to count. Make use of a good scholarly search like PubMed or Google Scholar. – AdamO Jan 4 '18 at 22:44
• I already did my lit review, read about 50-60 papers and couldnt find any good method that I am able to use (or for my data set), most of them have RCT with anova, a few had regressions but they never explained it truly – JK31 Jan 5 '18 at 9:54
• it would be enough for me to have a simple FE model which can measure the t+2 t+4 effecs – JK31 Jan 5 '18 at 11:55
• and what exactly do you mean by "requires that crossover cases have a control group that does not cross over." ? if we assume that group a), the control group, realy never smokes and we remove group "alwayssmokers" (I did it firstly like this but then added them them to see their line) would DiD work somehow ? – JK31 Jan 5 '18 at 13:54