Matching in a linear DiD setup

Question

I am trying to determine (if any) the effect of an economics shock on a number of outcomes. In order to do this, I use the usual difference in differences setup, i.e. estimate a model of the form:

$Y = \beta_0 + \delta_1 \cdot year_2 + \gamma_1 \cdot treatment + \beta_1 treatment \cdot year_2 + u$

For two time periods.

I am getting the effect that I expect. Economics shocks are not a good thing. However one concern (which I suppose every researcher faces in such studies), is that I am just picking a “generic” (in lack of better word) difference between the two groups. To overcome this, I have looked into matching as a mean of overcoming the obstacle. But I am having doubts about how to preprocess the data properly (I use MatchIt in R).

As I understand it I would have to determine the following:

1. Determine which variable that should be used for the basis of the matching.

2. Tie these variables to the DiD data sample I have. (my data is panel-set, such that each individual is uniquely identified - so the merge should be simple enough).

3. Use a matching scheme from MatchIt, check the balance, and extract the matched dataframe.

4. Estimate the above model, using the sample from (3).

So far so good?

Is it correct that for the t/f statistics to have nice properties, I would have to assume the either the matching procedure or the model is correctly specified? But not (necessarily) both?

Also the variables used for matching should not influenced by the economics shock? Therefore, if I wanted to use educating as one the variables for matching, I could do so if A) Educating is not influenced by the shock or B) Use education from before the shock?

Is it really this “simple”, or am I missing something?

Answer 1

There is a study which shows that DiD matching performs well only under certain conditions. That's the paper by Chabé-Ferret (2014) "Why does Difference in Difference Matching work?". Your idea with the matching is correct but you want to match on the time-invariant controls. Citing from the abstract:

"One intuitive explanation for this success is that DID & Matching combine their strengths: DID differences out the permanent confounders while Matching on pre-treatment outcomes captures transitory shocks. I show that this intuitive explanation is incorrect: it is both inconsistent theoretically and does not perform well in simulations of a model of earnings dynamics and selection into a Job Training Program (JTP). I show that DID Matching performs well when it is implemented symmetrically around the treatment date and does not condition on pre-treatment outcomes."

Since you only have one period the matching should be straight forward. With more than one pre-treatment period the matching becomes more difficult because you move from a simple cross-sectional match to panel matching. Conventional matching algorithms will not take the panel structure into account meaning that for individual $a$ in year one you get a match with individual $b$, but in year two you get a match with individual $c$. That's because the usual matching methods look for the best cross-sectional fit. In case of panel data have a look at the question propensity score matching with panel data and the helpful answers therein.

Remember though that the main assumption in difference in differences is that both treatment and control group have the same trend in the outcome before the treatment (see here for more information on this). With only one pre-treatment period this will not be very convincing because with a single data point you can't show that the parallel trends assumption holds. So this will probably be the main criticism of your work then.