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Can someone please explain what type of vcov (standard errors) argument is best for the following model:

$Y_{g,t, i} = \alpha + \beta Treat_g + \delta (Treat_g \times After_t) + \gamma Month + u_{g,t}$

where $Treat$ equals 1 for the treatment group, 0 otherwise. The DiD-estimator $Treat \times After$ equals 1 in the post-treatment period, 0 otherwise. And finally, $Month$ is a set of 15 dummies (I believe time-effects is the correct term, but I am not sure).

The dependent variable is employment. Note that I actually have 12 different models with 12 different dependent variables. Each model contains different income quartiles or workers in different sectors.

My question to you is, how do I correct the standard errors? I've tried a few, and they change the standard errors quite a bit. Just FYI, I use R to estimate these models.

Just two examples:

  1. Using "robust" gives me 3 out of 12 models with a significance of at least 95%
  2. If I use "HC2", I get 8 out of 12!

Here's a screenshot of (parts of) number 2:

enter image description here

Let me know if I can add or clarify something!

EDIT:

Another note. The data I have is on employment (among other things), from all US states. I have created a new database with only a treatment group and a control group, where the employment is the mean for each group. However, it is possible to keep the data as is and maybe cluster standard error on state -- if that is the better solution.

Tomas R
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  • Hi, in DiD models, it is common to use cluster robust inference & to cluster at the state level, see e.g. here: https://stats.stackexchange.com/questions/458862/difference-in-difference-fixed-effect-vs-clustered-standard-error. If you have few states (<50), your cluster robust inference might be biased, and you might want to have a look at the wild cluster bootstrap [main paper here](https://www.jstor.org/stable/40043157) (implemented in Stata via boottest & R in fwildclusterboot, clusterSEs and sandwich). – A.Fischer Dec 22 '21 at 13:23
  • Also, note that 'HC2' standard errors are just a specific type of 'robust' standard errors, see [this datacolada post](http://datacolada.org/99). The different types of standard errors differ in their 'finite sample' properties, e.g. it is often argued that for small samples, HC3 standard errors should be used. – A.Fischer Dec 22 '21 at 13:29
  • Very interesting @A.Ficher. I few follow-up questions if you have the time and don't mind. I'm actually a bit unsure on what counts as a small sample in this case. For example, the database I'm using is based on millions of individual observations on employment status. However, the actual data I have on my computer is just the mean change in employment for all US states (actually just 40 states, because some data is unavailable). In this example, is my sample size in the millions or just 40? If it's 40, should I use HC3 or should I cluster at the state level? – Tomas R Dec 22 '21 at 13:42
  • You should use cluster-robust inference. While the number of observations N is likely large enough, your data is clustered within 40 states. Using only 'robust' inference might potentially lead to over-rejection of the null hypothesis, which means that the chance to find an effect when in reality there is no effect is too high when using 'robust' inference. Cluster robust inference is more 'conservative'. – A.Fischer Dec 22 '21 at 13:51
  • For a recent treatment on cluster robust inference, have a look at this survey: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1456.pdf – A.Fischer Dec 22 '21 at 13:56
  • What do you mean when you say you’re using ‘robust’ to estimate your standard errors? Are you using the `robust` package in R? Also, your regression output suggests you have 20 period effects, not 15. – Thomas Bilach Dec 22 '21 at 21:41
  • @Thomas Bilach. I'm using the modelsummary package: https://vincentarelbundock.github.io/modelsummary/index.html. About the periods: its just a slight coding error. Period 5 is actually the first period. – Tomas R Dec 23 '21 at 22:53

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