1 Introduction

The credibility revolution transformed empirical economics [Angrist and Pischke, 2010]. Instrumental variables, regression discontinuity, difference-in-differences, and randomised experiments are now routine in top journals. Yet as these methods matured, they revealed new layers of complexity. What seemed settled turns out to be contested; what seemed simple turns out to require assumptions that can fail badly.  

This article surveys six open problems that define the frontier of causal inference research in 2025. These are not obscure technical puzzles. Each one bites researchers working on real policy questions, and each one has attracted serious theoretical and empirical attention in recent years. The goal is not to resolve these problems—that would require a much longer article—but to map the terrain clearly enough that empirical researchers understand what is at stake.  

2 Problem 1: Identification Under Interference and Network Spillovers

The workhorse framework of causal inference assumes the Stable Unit Treatment Value Assumption (SUTVA): one unit's potential outcome depends only on its own treatment assignment, not on the assignments of others. This assumption is implausible in an enormous range of settings. Vaccines create herd immunity. Conditional cash transfers change prices in local markets. Policing in one neighbourhood displaces crime to the next.  

The study of interference asks: what can we identify when SUTVA fails? Early theoretical work by Hudgens and Halloran [2008] distinguished direct effects (on treated units) from indirect effects (on untreated units via spillovers), but required strong partial-interference assumptions that the population is divided into groups within which units interact but not across. This is often unrealistic in social networks.  

Aronow and Samii [2017] proposed the exposure mapping framework: define a unit's "exposure" as a function of the full treatment vector, and estimate effects of switching from one exposure to another. Under a correctly specified exposure mapping, standard Horvitz-Thompson estimators recover causal effects of interest. The difficulty lies in specifying the exposure mapping without error.  

Leung [2022] developed an alternative for settings where interference decays with network distance—"approximate neighbourhood interference"—and derived asymptotic theory for treatment effect estimation under weak interference. Recent work has extended these ideas to bipartite experiments [Pouget-Abadie et al., 2019] and to settings where the network itself is endogenous.

The open frontier: most results are for static networks. Dynamic networks, where treatment can reshape who interacts with whom, remain largely uncharted. And in many applied settings—social media platforms, financial markets—the network is itself an outcome, making the identification problem circular.

3 Problem 2: Causal Discovery with Latent Variables

Causal discovery algorithms—PC, FCI, GES, LINGAM—attempt to learn causal structure from observational data [Spirtes et al., 2000, Chickering, 2002]. Under sufficiently strong assumptions (Markov, faithfulness, and correct functional form), such algorithms can recover the Markov equivalence class of the true DAG from the conditional independence structure of the data.

The challenge of latent confounders is severe. The FCI algorithm extends PC to handle latent common causes, returning a Partial Ancestral Graph (PAG) that encodes uncertainty about latent structure. But PAGs can be highly non-informative in practice. When many latent variables are possible, the equivalence class of compatible causal structures can be very large.

Recent work has asked whether data from interventional settings can sharpen identification. Hauser and Bühlmann [2012] showed that combining observational data with a small number of perfect interventions can identify the full DAG, not just a Markov equivalence class. But perfect interventions are rare; most empirical variation is "imperfect" or "soft" [Eberhardt and Scheines, 2007].

A separate frontier is the use of non-Gaussianity and non-linearity for identification. Linear non-Gaussian Acyclic Models (LiNGAM) achieve full identifiability without interventions when the noise is non-Gaussian [Shimizu et al., 2006]. Nonlinear additive noise models extend this to nonlinear functional forms [Peters et al., 2014]. But both require strong assumptions about the data-generating process that are difficult to test.

The open frontier: combining automated causal discovery with domain knowledge in a principled way. LLMs have been proposed as a source of prior causal knowledge [Kıcıman et al., 2023], but their tendency to confabulate structure that sounds plausible is a serious concern. Hybrid approaches that use data-driven discovery for the local structure and prior knowledge for the global orientation remain underdeveloped.

4 Problem 3: Dynamic Treatment Regimes

Most of the causal inference literature focuses on a single, binary, static treatment. But many policy questions are inherently dynamic: a patient receives a sequence of drugs, each chosen based on their evolving health state; a worker transitions through multiple jobs and training programmes; a country experiences a sequence of trade shocks.

The potential outcome framework for sequential treatments was developed by Robins [1986], who introduced G-computation and marginal structural models to handle time-varying confounding. The central difficulty is that standard regression models "block the effect" of past treatment by conditioning on intermediate variables that are themselves affected by treatment—a classic bad-control problem in a longitudinal setting.

Marginal structural models (MSMs) use inverse-probability-of-treatment weighting to estimate the effect of a treatment regime (a pre-specified rule for mapping histories to treatments) on a terminal outcome [Robins et al., 2000]. The identifying assumption is sequential ignorability: conditional on the observed history, treatment is as good as randomly assigned at each period.

Recent work has begun to combine machine learning with dynamic causal inference. The key challenge is that cross-fitting—essential for DML's bias reduction—must be applied sequentially across time periods, which introduces complications from the temporal dependence structure. Lines and van der Laan [2016] showed how to estimate optimal dynamic treatment rules under sequential ignorability using efficient influence function arguments. Connecting this to the DML framework of Chernozhukov et al. [2018] is an active area of research.

The open frontier: valid inference on dynamic causal effects when the number of time periods is large and the nuisance functions are estimated with machine learning. Standard asymptotic theory applies to fixed time horizons; the behaviour under long panels or high-dimensional treatment histories is much less understood.

5 Problem 4: Distributional Causal Effects

Average treatment effects are a coarse summary. Policies that raise average wages may compress the distribution for some workers and expand it for others. A drug that raises average survival may harm the most vulnerable patients. Economic inequality is fundamentally a distributional question.

The distributional treatment effect (DTE)—the mapping from quantiles under control to quantiles under treatment—is not point-identified without additional assumptions [Manski, 1990]. The quantile treatment effect (QTE)—the difference in quantiles between two distributions—is identified in randomised experiments [Firpo, 2007], but unlike the ATE, it does not have a clean structural interpretation without the rank invariance assumption.

Instrumental variable quantile regression [Chernozhukov and Hansen, 2005] allows identification of the structural quantile function under rank invariance, but this assumption—that individuals maintain their relative rank in the outcome distribution regardless of treatment—is hard to justify in many applications.

Callaway and Li [2019] extended the DiD framework to distributional outcomes, identifying the quantile treatment effect on the treated under a distributional parallel trends assumption. More recently, Cattaneo and Titiunik [2025] developed an RDD framework for distributional outcomes, using local polynomial estimation of the conditional CDF at the cutoff.

The open frontier: inference on full distributional treatment effects under weak assumptions in IV and DiD settings. The partial identification approach of Fan and Park [2010] provides bounds on the joint distribution of potential outcomes, but inference on these bounds in applied-sized samples remains computationally demanding.

6 Problem 5: Combining Experimental and Observational Evidence

Randomised experiments have high internal validity but are often small, expensive, and conducted on selected populations. Large observational datasets have broad coverage but suffer from confounding. Can we systematically combine both?

The problem of external validity formalises this: even when an experiment identifies a LATE for a particular complier population, extrapolating to a broader population requires modelling the relationship between treatment effect heterogeneity and selection into the experiment [Hartman et al., 2015]. The marginal treatment effect (MTE) framework [Heckman and Vytlacil, 2005] provides one approach: if we can estimate the MTE as a function of the propensity score, we can construct target estimands that weight differently across the population.

Data fusion approaches [Bareinboim and Pearl, 2016] use graphical criteria to identify when and how experimental evidence from one domain can be transported to another. The key requirement is that selection into the experiment is captured by observed covariates—an assumption that may fail if experiments recruit volunteers from specific institutions or geographic areas.

Recent work by Kallus and Puli [2018] showed that when experimental data and observational data are jointly available, doubly robust estimators that combine the two can recover the ATE in the target population, under conditions weaker than either source alone would require.

The open frontier: valid inference when the overlap between the experimental and observational populations is limited, and when the selection mechanism differs across observed and unobserved dimensions. This remains an open problem both theoretically and in terms of practical software tools.

7 Problem 6: Sensitivity Analysis as a Default

Perhaps the most underappreciated open problem is not a new identification challenge but a missing norm: the absence of systematic sensitivity analysis as a standard part of empirical practice.

Every causal estimate rests on untestable assumptions. Parallel trends can fail. Instruments can be invalid. Matching can miss unobserved confounders. The key question is not whether these assumptions hold exactly, but how large a violation would be needed to qualitatively overturn the main conclusion.

Rosenbaum [2002] developed the classical framework for sensitivity analysis in matching, quantifying how strong unobserved confounding (Γ) would need to be to render a finding non-significant. Oster [2019] proposed a coefficient-stability approach for OLS: if selection on unobservables is proportional to selection on observables, how large must this proportionality factor be to drive the treatment effect to zero?

For DiD, Rambachan and Roth [2023] developed sensitivity analysis that relaxes the parallel trends assumption by allowing pre-period trends to extrapolate into the post period within specified bounds. For instrumental variables, Conley et al. [2012] proposed inference that remains valid when instruments have small direct effects on the outcome.

The open frontier: a unified framework for sensitivity analysis that applies across identification strategies, is computationally tractable, and produces comparably interpretable summary statistics (analogous to a p-value or confidence interval). The HonestDiD package [Rambachan and Roth, 2023] is a step in this direction for DiD. Extending this to IV, RD, and matching in an integrated toolkit remains a gap in the literature.

8 Discussion: Common Threads

Several themes run through these six problems. First, finite-sample behaviour diverges sharply from asymptotic theory in many causal inference settings: weak instruments, few treated units, high-dimensional nuisance estimation, and small within-treatment-arm cell sizes all create challenges that standard large-sample approximations do not capture well.

Second, the interaction between identification and estimation is increasingly central. It is no longer sufficient to establish point identification under a set of assumptions; the estimator must be robust to departures from those assumptions, and the uncertainty quantification must reflect the actual sources of uncertainty rather than just sampling noise.

Third, the role of domain knowledge—economic theory, biological mechanisms, legal institutional rules—is paradoxically both more important and more difficult to formalise as methods become more data-driven. The challenge of embedding subject-matter knowledge into causal analyses without contaminating them is one that the field has not yet resolved.

9 Conclusion

Causal inference has never been more sophisticated. The problems surveyed here are not symptoms of a field in crisis but of a field in productive maturity—the stage where foundational assumptions are tested, edge cases are mapped, and the limits of identification become clear. Researchers who grapple with these open problems will produce work that is more honest about what it can and cannot establish. That is progress.

References

1. Angrist, J. D. and Pischke, J.-S. (2010). The credibility revolution in empirical economics: How better research design is taking the con out of econometrics. Journal of Economic Perspectives, 24(2):3-30.
2. Aronow, P. M. and Samii, C. (2017). Estimating average causal effects under general interference, with application to a social network experiment. Annals of Applied Statistics, 11(4):1912-1947.
3. Bareinboim, E. and Pearl, J. (2016). Causal inference and the data-fusion problem. Proceedings of the National Academy of Sciences, 113(27):7345-7352.
4. Callaway, B. and Li, T. (2019). Quantile treatment effects in difference in differences models with panel data. Quantitative Economics, 10(4):1579-1618.
5. Cattaneo, M. D. and Titiunik, R. (2025). Distributional regression discontinuity designs. arXiv preprint, 2504.03992.
6. Chernozhukov, V. and Hansen, C. (2005). An IV model of quantile treatment effects. Econometrica, 73(1):245-261.
7. Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., and Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. Econometrics Journal, 21(1):C1-C68.
8. Chickering, D. M. (2002). Optimal structure identification with greedy search. Journal of Machine Learning Research, 3:507-554.
9. Conley, T. G., Hansen, C. B., and Rossi, P. E. (2012). Plausibly exogenous. Review of Economics and Statistics, 94(1):260-272.
10. Eberhardt, F. and Scheines, R. (2007). Interventions and causal inference. Philosophy of Science, 74(5):981-995.
11. Fan, Y. and Park, S. S. (2010). Sharp bounds on the distribution of treatment effects and their statistical inference. Econometric Theory, 26(3):931-951.
12. Firpo, S. (2007). Efficient semiparametric estimation of quantile treatment effects. Econometrica, 75(1):259-276.
13. Hartman, E., Grieve, R., Ramsahai, R., and Sekhon, J. S. (2015). From sample average treatment effect to population average treatment effect on the treated: Combining experimental with observational studies to estimate population treatment effects. Journal of the Royal Statistical Society: Series A, 178(3):757-778.
14. Hauser, A. and Bühlmann, P. (2012). Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs. Journal of Machine Learning Research, 13:2409-2464.
15. Heckman, J. J. and Vytlacil, E. (2005). Structural equations, treatment effects, and econometric policy evaluation. Econometrica, 73(3):669-738.
16. Hudgens, M. G. and Halloran, M. E. (2008). Toward causal inference with interference. Journal of the American Statistical Association, 103(482):832-842.
17. Kallus, N. and Puli, A. M. (2018). Removing hidden confounding by experimental grounding. Advances in Neural Information Processing Systems, 31.
18. Kıcıman, E., Ness, R., Sharma, A., and Tan, C. (2023). Causal reasoning and large language models: Opening a new frontier for causality. arXiv preprint, 2305.00050.
19. Leung, M. P. (2022). Causal inference under approximate neighborhood interference. Econometrica, 90(1):267-293.
20. Luedtke, A. R. and van der Laan, M. J. (2016). Optimal individualized treatments in resource-limited settings. International Journal of Biostatistics, 12(1):283-303.
21. Manski, C. F. (1990). Nonparametric bounds on treatment effects. American Economic Review Papers and Proceedings, 80(2):319-323.
22. Oster, E. (2019). Unobservable selection and coefficient stability: Theory and evidence. Journal of Business and Economic Statistics, 37(2):187-204.
23. Peters, J., Mooij, J. M., Janzing, D., and Schölkopf, B. (2014). Causal discovery with continuous additive noise models. Journal of Machine Learning Research, 15:2009-2053.
24. Pouget-Abadie, J., Saint-Jacques, G., Saveski, M., Duan, W., Ghosh, S., Xu, Y., and Airoldi, E. M. (2019). Testing for arbitrary interference on experimentation platforms. Biometrika, 106(4):929-940.
25. Rambachan, A. and Roth, J. (2023). A more credible approach to parallel trends. Review of Economic Studies, 90(5):2555-2591.
26. Robins, J. M. (1986). A new approach to causal inference in mortality studies with a sustained exposure period application to control of the healthy worker survivor effect. Mathematical Modelling, 7(9-12):1393-1512.
27. Robins, J. M., Hernan, M. A., and Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11(5):550-560.
28. Rosenbaum, P. R. (2002). Observational Studies. Springer, 2nd edition.
29. Shimizu, S., Hoyer, P. O., Hyvärinen, A., and Kerminen, A. (2006). A linear non-Gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7:2003-2030.
30. Spirtes, P., Glymour, C., and Scheines, R. (2000). Causation, Prediction, and Search. MIT Press, 2nd edition.