Need help with marginal effect after DID test

[Liyu He]

Hi all,

Let’s say I am studying the impact of a new global training program on employee productivity on a specific mega-corporation’s franchises over time. The training program was implemented in 2015, and I want to understand its effect in the two years leading up to its implementation (t-2) and in the two years following its implementation (t+2).

I am using the below code for a DID test after propensity score matching where emb is coded “1” for US franchises/firms or “0” for non-US franchises/firms.
t is the year indicator for 2013, 2014, 2016, 2017

reg index i.emb##i.t
margins emb#t, noestimcheck
marginsplot, xdimension(t)

I receive the following results.

Questions:

In the regression result, the co-efficients of the interaction terms (emb#t) are significant suggesting that the new training program has a stronger effect on the treatment firms. However, the marginal effect result shows that the control firms have a stronger marginal effect than the treatment firms. What I don’t understand is why the marginal effect for non-US firms is higher, when the interaction term for non-US firms is insignificant as per the linear regression above.

2^nd question is about the marginal effect plot. One of the DID assumptions is the treatment and control group should have parallel trends before the treatment occurs.
However, I don’t understand why the marginal effect of the control group (pre-treatment) is significant and stronger than the treatment group (pre-treatment), even before receiving the treatment. To prove the parallel trend assumption is met, should the marginal effects of the control group be insignificant as well, in the plot?

Also, I understand that marginal effects are usually used for continuous variables. However, when both indicators are dummy variables in this case, how would I interpret the marginal effect plot?

Thank you very much and appreciate any assistance on this topic.

[Clyde Schechter]

However, the marginal effect result shows that the control firms have a stronger marginal effect than the treatment firms.

You do not know what the marginal effect results shows, because you have not calculated it. The -margins- output you show is not marginal effects, it is predictive margins. To get the marginal effects of emb in each year run -margins t, dydx(emb)-. If you want an average marginal effect of emb across all years, run -margins, dydx(emb)-.

Concerning parallel trends, because you have only two pre-intervention time periods in your data, it is really difficult to assess this. But the trends in each group prior to intervention would, in your case, be shown by -margins emb, dydx(2014.t)-. And if you want to formally test those for equality, -margins emb, dydx(2014.t) pwcompare- will do that. And, no, it does not matter whether the pre-intervention trends in the control group are "significant." In fact, it doesn't matter at all what the pre-intervention trends in the control group are. All that matters is whether the pre-intervention trends in the two groups are, for practical purposes, the same.