Parallel Trends (The Effect, Videos on Causality, Ep 52)

Please visit www.theeffectbook.net to read The Effect online for free, or find links to purchase a physical copy or ebook.
The Effect is a book about research design and causal inference. How can we use data to learn about the world? How can we answer questions about whether X causes Y even if we can't run a randomized experiment? The book covers these things and plenty more. These videos are meant to accompany the book, although they can also be viewed on their own.
This video relates to material found in Chapter 18 of the book.
A version of this video without background music can be found here: • Parallel Trends (The E...
For difference-in-differences to work, you need to make an important assumption: the parallel trends assumption! This assumption says that the change over time you see in the control group is the change over time you would have seen for the treated group, if the treatment hadn't occurred. How can we understand this assumption, and how can we make it as plausible as possible?

[@rxsieexxx]

Omg thanks so much for the great video!!

[@mylifeisinhishandsamen4167]

This is a special request from me....could you please make a video about how to use lead-lag analyses to ascertain parallel trends assumption in R?

[@NickHuntingtonKlein]

Try this video kzbin.info/www/bejne/lZ_On3WYrJJ7fLM As a note, this method is (like every other test) a test of *prior* trends. It can only make parallel trends more or less plausible, it doesn't actually prove or disprove parallel trends. There is no test that does that, since parallel trends is inherently not observable in the data.

[@NickHuntingtonKlein]

And for R code check the accompanying chapter section in the book theeffectbook.net/ch-DifferenceinDifference.html#long-term-effects

[@RobertWF42]

Thanks Nick! Am I correct that we cannot empirically test the parallel trends assumption because we can't control for all the possible differences between the treatment and control groups? (Although the synthetic control method claims to equalize non-parallel trends.)

[@NickHuntingtonKlein]

You can't empirically test the parallel trends assumption because it's inherently about a counterfactual - what the treated group's outcome would have been post-treatment if the treatment had not occurred. What some people call a test of parallel trends is actually a test of prior trends (i.e. whether trends seem to be the same before treatment occurs), which can be suggestive that those trends would have remained equal in the period after treatment, but it's only suggestive, it doesn't actually test the thing you really want (similarly, it's entirely possible to violate prior trends even if parallel trends holds). Synthetic control is capable of equalizing *prior* trends. If you want to say that synthetic control gives you the causal effect of treatment, you still have to assume that the changes beyond that period are only because of the treatment (the analogous assumption in synthetic control to DID's parallel trends).

[@NickHuntingtonKlein]

Plenty more detail in my book chapter on DID by the way: theeffectbook.net/ch-DifferenceinDifference.html

[@RobertWF42]

@NickHuntingtonKlein This is helpful, thank you. When learning about DiD, my first impression was why worry about parallel trends at all? Aren't we more interested in comparing relative trend changes of trmt and ctrl groups after the intervention time? For instance, you could simply regress Y on the variables Time (continuous), Period (pre or post), and Cohort (trmt or cntrl) with main effect & interaction terms for all three variables. If the coefficient for the interaction term Time×Period×Cohort is statistically significant, then the treatment group time trend has a different % change in the post period relative to the control group.

[@NickHuntingtonKlein]

@@RobertWF42 some people do this but it ends up being super super sensitive to the functional form you pick for your time trend, and there are other issues too

[@RobertWF42]

@NickHuntingtonKlein So dropping the parallel trends assumption and going with the ANCOVA approach instead of DiD isn't necessarily wrong as long as linear trends holds true? I haven't come across pre/post studies that take this approach - DiD seems to be preferred.