💡Econometrics Thread: 💡Going beyond average effects with Diff-in-Diff. Recently, DiD methods became very popular and many excellent papers showed up! But, today, I want to talk about two papers that are not that recent, but are super interesting!
@Susan_Athey and Imbens (2006, AI, onlinelibrary.wiley.com/doi/abs/10.111…) and Bonhomme and Sauder (2011, BS, jstor.org/stable/23015949) discuss how to extend the DiD framework to identify not only average effects, but also effects on other parts of the distribution.
Comparing counterfactual distributions is very important to understand not only heterogeneous treatment effects, but also to evaluate whether policies are increasing or fighting inequality.
Doing so in a DiD framework is not that simple because the parallel trends assumption is additive and quantiles are not linear operators. This poses a challenge! What can we do?
AI and BS propose two different solutions, but both of them require independence assumptions. So their models are a bit more restrictive then the usual DiD. But those extra assumption buy us a lot! We can now analyze entire counterfactual distributions!
There are a few important differences between AI and BS. AI has a production function of outcomes that is fully non-linear on time effects and unobserved ability. However, the unobserved ability has the same distribution over time within a group.
They need this assumption to use trends over time for the same quantile of the control group to capture time effects for an agent with a specific value of the unobserved ability.
BS allow for unobserved ability shocks to evolve over time, allowing for general distributional effects. But they pay a cost: an additive structure on the production function of outcomes, implying that their model is not invariant to monotone transformations of the outcome.
So, those two approaches are non-nested. If you want to be creative and analyze distributional effects with a DiD framework, you have at least two alternatives and must think about which assumptions are more plausible in your context.
Overall, two excellent papers that I find very useful for applied research. So, let’s be a Pokémon master and catch all the cool poke methods! PS: BS illustrate that the scary characteristic function from our first year metrics class can be useful in the real world!
