Difference in difference with time variant treatment

[Suat Cubukcu]

I am currently working on district-month level data and interested in examining how the use of police body-worn cameras influences the disposition of citizen complaints against police. I am expecting less dismissed complaints when the body-worn cameras are present during a problematic interaction.

I am working on Chicago data, there are 25 different districts and the data covers 2005-2018. I set the data as time-series at the district-month level. The Chicago police started their full implementation of BWCs in June 2016 with a few districts. However, all districts had BWC at the end of 2017. So, I have time-variant treatment. I've used the following code:

xtreg notsustained BWC##post complaint i.year arrest, fe

notsustained: the number of dismissed complaints at district-month level
BWC (0/1): whether the district had BWC in a given month
Post (0/1): Post is 1 if it's after the first full implementation of BWC in Chicago (Post = 1 if mdate > June2016)
complaint: number of total complaints at the district month level
arrest: number of total arrests at the district-month level

I used traditional difference-in-difference model. However I don't have the same intervention dates for all districts, so I think it may not be appropriate.
Looking forward to your comments.

Best,
Suat

[Clyde Schechter]

This model is not correct, because the intervention begins at different times in different locations, and your post variable does not reflect that. Even if you had an intervention that began at the same time everywhere, the BWC variable, as you have defined it, would not be the correct one to use in a classical DID model: you would want the BWC variable to be 1 in every observation for a district which eventually adopted body-worn cameras, and 0 in those that never used a body worn cameras.

But no point fretting over how you would do a classical DID analysis because your data requires a generalized DID analysis. For that, the BWC variable that you show in #1 (not the different BWC variable I described in the preceding paragraph) is precisely what you need. Modifying your current model, it would look like this:

xtreg notsustained i.BWC complaint i.year arrest, fe

That said, I'm not sure that -xtreg- is the best way to go here. Your outcome variable is a count variable, and I would imagine that the numbers are fairly small. So I think a model that is closer to the real data-generating process might be:

xtpoisson notsustained i.BWC i.year arrest, fe exposure(complaint) irr

You also might want to think about other substantive aspects of the model: does the number of arrests really belong there, or should it be, pfor eample, the ratio of arrests to district population? I have no expertise in this content area, so don't be too influenced by this particular concern I have raised, but my "common sense" suggests it's worth at least thinking about.

[Clyde Schechter]

Additional thought. It dawns on me that your outcome variable, notsustained, is a count of complaints that were not sustained, and is therefore a subset of the set of all complaints. Consequently, the model specification with -xtpoisson- that I suggested, although probably workable, is still not quite right. A better model might be:

xtgee notsustained i.BWC i.year arrest, family(binomial complaint) link(logit)

[Suat Cubukcu]

Thanks Clyde. Your suggestions are amazing.
In specific, I am interested in how BWCs change the proportion of non-sustained complaints among total number of complaints. Initially, I used proportion of non-sustained complaints, however, there are several cases with zero complaints, so the proportion turns out to be missing since the denominator is zero. This is why I used the number of not-sustained cases as dependent and include the total number of complaints as a control variable in the model.

[Suat Cubukcu]

Dear Clyde,

The codes that you provided on xtgee and xtpoisson are not working with the data since there are zero complaints in some districts. To test, I only included districts with 1 or more complaints, however, I am losing observations, then.

[Clyde Schechter]

You are losing observations, but you are not losing information! If a district has zero complaints, then it has no information whatsoever about how anything impacts the proportion of complaints that are notsustained. There is no valid analysis of those observations, and Stata (and every statistical package) will automatically omit them from the calculations.