Synthetic difference in differences with repeated cross sectional data

[Nadia Ahm]

Hi All,

I want to get a better understanding of synthetic difference in differences and use the method in my research. My data set is a repeated cross-sectional survey with 10 provinces over 18 years. For each of the provinces and years, I have individual-level responses. I am seeking some clarification on sDID before I plan my data analysis, as I read a few posts which indicate that sdid may not ideal for my kind of dataset.

1. Is it possible to run sDID with the type of data set I have, i.e., individual-level data for each province over time?

2. If I am to aggregate the data (e.g., take the average) by each province and year and use for sDID, how do I deal with categorical variables, e.g. binary and ordinal variables?

Any thoughts on my questions above will help me kick start my research.

Thanks and best regards,
Nadia

[Jared Greathouse]

So, no I do not think that this is viable here. I mean, short of aggregating that is. So let's say 2 of these provinces are treated but the others aren't. Okay, I suppose it's possible to aggregated these individual observations by taking the average, but this presumes that the intervention is at the aggregated level and that there aren't units treated and untreated within a state/area.

So here's the thing for the second point: you shouldn't care about the binary or ordinal variables. Rather, you should care about your outcome. So long as the intercept shifted control group lies within the convex hull/support of the treated unit, you don't need to worry about additional covariates. Let me give a real example.

Suppose we wish to estimate the impact of an anti tobacco law on consumption. Theoretically we could adjust for additional covariates. But, in some cases we do not need to. If we can pick the optimal control group that's as parallel as possible to the treated unit in the pre-policy period, then I do not need to adjust for additional predictors.

[Nadia Ahm]

Hi Jared,

Thank you very much for helping me to understand the method better. I will trouble you with another question. If my outcome variable is binary, for aggregation should I take the proportion values? How do I deal with my ordinal outcome variable for aggregation?

Again, thanks a lot for your help!

[Jared Greathouse]

You can't really use SCM for binary outcomes. Well, I lied, you can, but that will take more programming than you are likely to be willing to do. For the standard estimator anyways, how would this even look in practice, fitting to 0s and 1s in the pre period? I mean not impossible since this is technically differentiable, but you don't wanna do this.

My advice to you is to find a different outcome of interest. I've never seen anyone do SCM with proportions, nevermind ordinal data (until I saw the hyperlinked paper anyways), but in the interest of your sanity, find a better outcome to study the policy with. I wish I had better news.

[Nadia Ahm]

Thanks Jared, really appreciate the help.

[Jared Greathouse]

You're quite welcome!!!!!