What’s New in DiD? On Flexibility, Heterogeneity, and Robustness

Two recent papers and one guide that stretch, reframe, and strengthen what we thought we knew about DiD

I have three new updates, I’ll list them first and then we move on to talk about them. I’ll try to keep it short.

1. Difference-in-Differences Designs: A Practitioner's Guide, by Andrew Baker, Brantly Callaway, Scott Cunningham, Andrew Goodman-Bacon, and Pedro H. C. Sant'Anna.

2. Finitely Heterogeneous Treatment Effect in Event-study, by Myungkou Shin.

3. Difference-in-Differences Meets Synthetic Control: Doubly Robust Identification and Estimation, by Yixiao Sun, Haitian Xie, Yuhang Zhang.

Difference-in-Differences Designs: A Practitioner's Guide

It seems like the literature keeps moving mainly thanks to the efforts of these guys in particular (+ prof Wooldridge The Great). Their collective productivity is not only boosting the US TFR, but also expanding our understanding of how to better set up DiD studies and what to actually consider when doing so.

You can’t use the excuse that you don’t know how to do stuff if there’s so much material online and offline nowadays. This guide is particularly useful because it brings together all the efforts they put along the years. It is straight-forward and very rich in details. They are putting the “science” in “social science” by proposing an organizing framework that conceptualizes complex DiD designs as aggregations of multiple 2x2 comparisons. This guide does for DiD what a microscope does for biology, it zooms into the essential building blocks, helping you understand and construct better causal inference models. They emphasize that even “intricate” DiD studies can be broken down into simpler components, each relying on the fundamental parallel trends assumption.

The guide further explores practical considerations such as the use of covariates, weighting schemes, and strategies for handling multiple periods and staggered treatments. They want to provide us with the tools to implement DiD methods more effectively and interpret our results with a greater clarity. It’s packed with clear examples, organizing frameworks, and even code references to help us implement modern DiD designs properly (we love tools that we can immediately apply).

Save it, print it, enjoy it!

(Also thank them!)

Finitely Heterogeneous Treatment Effect in Event-study

I know most of us sometimes stumble on the pivotal parallel trends assumption, the idea that untreated units provide a valid counterfactual for treated units. It can be hard to justify (someone will ask you about it at a seminar), especially when conditions aren’t ideal, like short time horizons or pre-treatment trends that don’t quite line up.

Others might say: “This should’ve been an event study.” This paper brings both worlds together: it bridges the traditional DiD and event-study approaches by proposing a more flexible way to handle heterogeneity in time trends across units.

신명구 교수님 shows how event-study designs implemented via DiD can be made more robust when natural groupings exist in the data even if we can’t observe them directly. It’s especially useful when there isn’t a clean natural experiment, but you suspect there are distinct patterns of heterogeneity in your data.

The key idea is the “type-specific parallel trends” assumption. It allows for heterogeneous time trends by introducing a latent type variable - an unobserved characteristic that assigns each unit (person, firm, region) to a group or “type” based on underlying traits we can’t observe directly, but that affect their outcomes over time.

In traditional DiD, we assume all units (treated and untreated) would have followed similar trends absent treatment. But what if some units are natural fast improvers, while others stagnate or decline - even without treatment? And what if that variation reflects some unobserved group structure? In that case, the standard DiD estimate can be biased - because the untreated trend isn’t a valid counterfactual for the treated group.

This paper’s innovation is to allow for finitely many latent types - and assume that units of the same (even unobserved) type would have followed the same trajectory absent treatment. This relaxes the classic parallel trends assumption and gives us a more robust framework to deal with hidden heterogeneity in DiD designs.

Definitely worth a read if you’re working with DiD or event-study designs in applied settings - especially when you’re concerned about hidden heterogeneity or shaky pre-trends. It’s a thoughtful contribution that expands what we can credibly identify in non-experimental data.

Difference-in-Differences Meets Synthetic Control: Doubly Robust Identification and Estimation

Ok, so we discussed event-study and DiD settings - now let’s talk SC and DiD (so much content today. What’s next, IV and DiD? Don’t be crazy).

DiD is great, but it relies on the parallel trends assumption - that treated and control groups would have evolved similarly in the absence of treatment. SC doesn’t assume parallel trends; instead, it builds a weighted combination of control units to replicate the treated unit’s pre-treatment path. Both methods can fail if their core assumptions don’t hold - and in practice, we often don’t know which one is more believable.

This paper’s innovation is an integrated approach that offers a doubly robust identification strategy for causal effects in panel data with group structures. It identifies the average treatment effect on the treated (ATT) if either the parallel trends assumption or a group-level synthetic control assumption holds. Sun, Xie and Zhang 老师 focus on typical micro panel data settings where individuals are observed repeatedly over time and grouped into larger units (e.g. households in states), with treatment assigned at the group level.

They develop a doubly robust estimator that blends the strengths of DiD and SC. You get a consistent estimate of the treatment effect as long as one of the two assumptions holds, you don’t need both. The method works with panel data, repeated cross-sections, and staggered adoption, making it highly versatile for applied researchers working with micro-level datasets like surveys, administrative records, or digital trace data.

In more technical terms, Sun, Xie and Zhang 老师 introduce a moment function φ - a carefully constructed combination of outcome changes in treated and control groups. It’s adjusted for covariates and treatment probabilities, and weighted using synthetic control logic. This structure ensures that φ delivers a valid ATT estimate as long as either the DiD or SC assumptions are satisfied.

In more “math” terms, a moment function is an expression that, when averaged over the sample, gives an estimate of a parameter (here the ATT). The authors work in a semiparametric estimation framework, where the parameter of interest (ATT) is finite-dimensional, while the nuisance components (e.g., the propensity score, conditional outcomes, and synthetic weights) are modeled nonparametrically. This allows for flexible estimation without overcommitting to functional form assumptions, and inference is handled via a multiplier bootstrap.

Speaking of bootstrapping, they provide a recipe for implementation (hopefully a package soon?). To compute the estimator in practice, they describe using cross-fitting (a form of sample-splitting common in double machine learning) to estimate nuisance functions like mΔ(X)m_\Delta(X)mΔ​(X) (the expected change in outcome given covariates), pg(X)p_g(X)pg​(X) (the group-level propensity scores, and weights wg(X)w_g(X)wg​(X) for SC. These can be estimated using nonparametric or machine learning methods, like local polynomial regression, RF, boosted trees, neural nets, and any other “flexible” method. Sun, Xie and Zhang 老师 specifically mention that their estimator is compatible with DML-type algorithms, which makes it relatively plug-and-play if you’re using packages like DoubleML (in R or Python) or custom estimators in scikit-learn, grf, etc.

It is great paper for anyone working with messy pre-trends, fuzzy treatment timing, or “almost good” quasi-experiments. Their doubly robust approach can help us to identify and estimate the ATT as long as either the parallel trends assumption or the synthetic control condition holds, which is a significant step forward in settings with imperfect designs.

The End (?)

That’s a lot of causal inference in one sitting but honestly it’s exciting to see how far we’ve moved from “just run a DiD” to actually thinking hard about assumptions, heterogeneity, and design. If you’re doing applied work, these papers are well worth saving, reading, and probably thanking the authors for later.

Next time: maybe IV and DiD?