# Two Layers of Instability in Causal Estimation

arXiv: https://arxiv.org/abs/2606.21185 · HTML: https://mlsanity.com/paper/2606.21185/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [What can be estimated? Identifiability, estimability, causal inference and ill-posed inverse problems](https://mlsanity.com/paper/1904.02826/) (2019)
- [Towards Bounding Causal Effects under Markov Equivalence](https://mlsanity.com/paper/2311.07259/) (2023)
- [Partial Transportability for Domain Generalization](https://mlsanity.com/paper/2503.23605/) (2025)
- [Nonparametric identification is not enough, but randomized controlled trials are](https://mlsanity.com/paper/2108.11342/) (2021)

## Abstract (arXiv)

There is a precise sense in which drawing causal inferences from observational data is hard, even when identifiability is assumed. In particular, Robins and Ritov (1997) and Robins et al. (2003) showed that causal effects can be discontinuous as a function of the data distribution: two arbitrarily close data distributions might correspond to different causal effects. This is a fact independent of the choice of estimator; however, not all estimators are equally unstable. Our contribution is to surface a second layer of instability that depends on the choice of estimator. We show that many standard point estimates can be read as point summaries of multimodal distributions over the space of structural causal models. As such, estimators can jump discontinuously in the data distribution. This defines a taxonomy of estimators that admits a decision-theoretic reading: stability depends on whether the implicit loss function an estimator optimizes is aligned with the causal effect itself. Specifically, inverse propensity weighted estimators and regression estimators are examples of discontinuous summaries, while explicit posterior means and medians are shown to be continuous.