⚡ TL;DR

Develops a design-based framework for analyzing quasi-experimental settings (DiD, IV, RDD) where treatment assignment can be viewed as the realization of a stochastic process and there is concern about unobserved selection into treatment. Provides conditions under which popular quasi-experimental estimators correspond to interpretable finite-population causal parameters. The natural complement to Athey-Imbens (2022, J Econometrics) design-based DiD framework.

🧩 Setup & motivation

Traditional quasi-experimental inference is sampling-based: the researcher imagines drawing a random sample from a super-population and asks how the estimate would vary across hypothetical samples. The design-based alternative treats the units as fixed and inference comes from the randomness in treatment assignment — much like analysis of a randomized experiment.

For RCTs the design-based framework is standard. For quasi-experiments (where assignment is not literally randomized) it requires articulating the assignment mechanism: the probability with which each unit could have been treated under different counterfactuals. Rambachan-Roth formalize this for the DiD/IV/RDD class.

📐 Main results

The framework

Units are indexed \(i = 1, \dots, n\). Each unit has potential outcomes \(Y_i(0), Y_i(1)\). The treatment assignment \(D_i\) is the realization of a stochastic process; let \(\pi_i = P(D_i = 1)\) be the unit-specific treatment probability. The target estimand is some finite-population causal parameter, e.g., the sample ATT \(\hat\tau_{\text{ATT}} = \frac{1}{n_1} \sum_i D_i (Y_i(1) - Y_i(0))\).

Conditions for interpretability

The paper provides conditions on the assignment process under which standard quasi-experimental estimators (TWFE DiD, two-stage IV, local-linear RD) consistently estimate interpretable finite-population causal parameters. Key conditions: (i) regularity of the assignment probabilities; (ii) limited dependence across units (rules out general-equilibrium effects); (iii) finite-sample bias control.

Inference

The paper derives design-based standard errors that account for the variance induced by random treatment assignment — even when units are not drawn from a super-population. Standard CR1/CR3 cluster-robust SEs typically overcover (too conservative) in finite samples; design-based SEs are tighter.

🛠️ Implications for practice

• When the units in your sample are the population (states, countries, industries), design-based inference is more natural than sampling-based.
• Use design-based SEs as a robustness check against cluster-robust SEs.
• The framework is the formal underpinning for randomization-inference robustness checks (Conley-Taber 2011 style).

🧭 Where this sits in the broader DiD literature

Complements Athey-Imbens (2022, J Econometrics) "Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption." Rambachan-Roth extends the framework to RDD and IV. Together they form the design-based wing of the modern DiD literature.

📥 Read the paper

• Local PDF (2.9 MB) — instant, no external request
• arXiv 2008.00602
• JASA