# What is the best way to visualize difference-in-differences (multi-period) regression?

What's the best way to visualize difference-in-differences for both binary and continuous treatment?

Do I regress the outcome variable on the set of controls but exclude the treatment variable and plot the residuals in each group (binary case)?

Is there a way to see the "dynamics" of the ATE parameter over time?

I want to show that the parallel trend assumption is reasonable.

• For the continuous treatment you also have a observations that have zero treatment intensity or is everyone affected to some degree? By "dynamics" of the ATE you mean that you want to see whether there are long-run effects of the treatment that fade out over time? – Andy May 17 '15 at 19:11
• Yes, let's say we have some zero treatment intensity. I've read this in a paper, but I'm not sure what the author is doing exactly "Each figure interacts the effect of being incorporated in a treated state with monthly indicator variables in event time. The figures exhibit level changes at the event date, rather than any differential trends separating the treated and untreated groups". Any idea how to implement this? – sazuhabe May 17 '15 at 19:45
• Ah I just posted the answer before seeing the update of your comment. Do you have a link to the paper? – Andy May 17 '15 at 19:52
• This is similar to what the paper by Autor does which I have referenced in the answer. Your guy regresses the outcome (patents) on the treatment and interacts the treatment with time dummies. The top panel does this for the control group, the bottom panel for the treatment group. So you see that the outcome jumps only for the treated after the treatment date (not for the control) and that the effect increases over time. – Andy May 17 '15 at 20:29

To estimate the fading-out time of the treatment you can follow Autor (2003). He includes leads and lags of the treatment as in $$Y_{ist} = \gamma_s + \lambda_t + \sum^{M}_{m=0}\beta_{-m} D_{s,t-m} + \sum^{K}_{k=1}\beta_{+k} D_{s,t+k} + X'_{ist}\pi + \epsilon_{ist}$$ where he has data on each individual $i$, in state $s$ at time $t$, $\gamma$ are state fixed effects, $\lambda$ are time fixed effects, and $X$ are individual controls. The $m$ lags of the treatment estimate the fading out effect from $m=0$, i.e. the treatment period. You can visualize this by plotting the coefficients of the lags over time:
You can do the same with the $k$ leads. However, those should be insignificant because otherwise this hints towards anticipatory behavior with respect to the treatment and therefore the treatment status may not be exogenous anymore.