Time for another #Econometrics thread!
Today I want to talk about my paper with Jun Zhao (absolutely great PhD candidate from Vanderbilt ), "Doubly robust difference-in-differences estimators", which is now forthcoming at the Journal of Econometrics!
sciencedirect.com/science/articl…
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Today I want to talk about my paper with Jun Zhao (absolutely great PhD candidate from Vanderbilt ), "Doubly robust difference-in-differences estimators", which is now forthcoming at the Journal of Econometrics!
sciencedirect.com/science/articl…
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Before I go on, let me make it clear that everything that I say here or that we proposed in the paper can be easily implemented in #R via the package DRDID: pedrohcgs.github.io/DRDID/
I hope you find this easy to use!
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I hope you find this easy to use!
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Now to the paper. First, why should you pay attention to *another* Difference-in-Differences paper?
I think we propose a cool set of new tools that can be very handy. We talk about robustness, efficiency, and inference.
I'll cover the main points here, one-at-a-time!
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I think we propose a cool set of new tools that can be very handy. We talk about robustness, efficiency, and inference.
I'll cover the main points here, one-at-a-time!
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When parallel trends plausibly hold after conditioning on covariates, there are 2 modelling approaches to estimate the ATT:
a) Outcome-reg: model the evol. of outcomes.
b) IPW: model the prob. of being in the treated group.
Hard to choose btw a-b as they are non-nested!
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a) Outcome-reg: model the evol. of outcomes.
b) IPW: model the prob. of being in the treated group.
Hard to choose btw a-b as they are non-nested!
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So instead of choosing btw the 2, we propose to combine them in a way such that we get additional *robustness*. This is the birth of the DR DID estimator.
Interestingly, the DR DID estimator shares the strengths of each procedure and can avoid some of their weakness.
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Interestingly, the DR DID estimator shares the strengths of each procedure and can avoid some of their weakness.
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More specifically, to implement the DR DID, you'll model both the outcome evolution and the pscore. However, the resulting estimator only requires one of the working models to be correctly specified!
In other words, you get two chances of pinning down the ATT in DID setups!
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In other words, you get two chances of pinning down the ATT in DID setups!
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But robustness is not the only game in town. We also want to form (regular) DID estimators that efficiently exploit all the available information compatible with our assumptions.
But how do the most efficient DID estimators look like?
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But how do the most efficient DID estimators look like?
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To anwser this q., we derive the semiparametric efficient bound for the ATT under DID setups when panel or repeated cross-section (RCS) data are available.
Good news: our DR DiD estimators attain these bounds when the working out. reg and pscore models are correct!
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Good news: our DR DiD estimators attain these bounds when the working out. reg and pscore models are correct!
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The "best" DD estimators when panel or RCS data are available are different! But which one is "better"?
Intuition tell us that panel should be better. We confirm that and characterize the lost of efficiency associated with only having assess to RCS.
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Intuition tell us that panel should be better. We confirm that and characterize the lost of efficiency associated with only having assess to RCS.
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All the above results are generic in the sense they hold for a family of estimators/estimation procedures.
But in practice, you need to choose an specific estimation method, right?!
The final cont. of our paper is to show that paying attention to this step can also help!
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But in practice, you need to choose an specific estimation method, right?!
The final cont. of our paper is to show that paying attention to this step can also help!
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Simply speaking, we highlight that sometimes you can tailor the estimation method such that the resulting improved DR DiD estimator is now also *doubly-robust for inference*.
In practice, this usually translates to narrower conf. int. when one working model is misspecified.
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In practice, this usually translates to narrower conf. int. when one working model is misspecified.
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In the paper we also have simulations and an empirical illustration, but I'm sure you can check that out!
That's all I have! Hope you enjoyed the ride!
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That's all I have! Hope you enjoyed the ride!
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Tagging my great co-author Jun Zhao here: @ZhaoBean
