What You Observe Determines How You Identify Causal Effects: Evaluating Causal Models across Observational Views

Heejin Jung; Gyeongdeok Seo; Hoyoon Byun; Joseph Lee; Kyungwoo Song

cs.LGSep 29, 2026

What You Observe Determines How You Identify Causal Effects: Evaluating Causal Models across Observational Views

Authors: Heejin Jung, Gyeongdeok Seo, Hoyoon Byun, Joseph Lee, Kyungwoo Song

Organizations: Yonsei University · University of Illinois Urbana–Champaign

Abstract

Causal foundation models (CFMs) pre-trained on data generated from various structural causal models (SCMs) have been proposed for estimating causal effects from observational data. However, differences in pre-training environments and evaluation protocols make it difficult to assess how their performance depends on the information available for causal identification. To enable controlled comparisons, we introduce CausalIDView, a multi-view benchmark that holds fixed SCM realization and target estimand while varying only the observational view available to the estimator. Each observational view corresponds to a distinct identification regime under the benchmark's maintained causal assumptions. Across these matched views, no CFM consistently performs best and model rankings vary substantially. Under controlled structural changes, CFMs exhibit model-specific failures to maintain stable estimates when true effects are unchanged and to track genuine effect changes. We also examine whether combining explicit identification with strong predictive estimation is effective. A modular approach that pairs a predictive tabular foundation model with regime-specific identification procedures is competitive with CFMs and outperforms several of them. These findings motivate cross-regime comparisons to assess the empirical value of CFMs.

Figures & tables

Figure 1: Overview of CausalIDView . Each realized SCM is mapped to matched observational views while preserving the query units and target CATE. We can also compare the Hidden Confounding (HC) view, described in Appendix B.5 .

Figure 2: Point estimation across observational views. We compare the evaluated model configurations under (a) Back-Door, (b) Front-Door, (c) IV, and (d) Proximal views. Bars show mean

\mathrm{sPEHE}^{2}

across 40 SCM worlds, decomposed into mean squared query-sample ATE error (dark blue) and mean

\mathrm{c\text{-}sPEHE}^{2}

(light blue). Shading marks the lowest observed mean in each panel. CausalPFN and Do-PFN receive the auxiliary variables available in each view as ordinary covariates, except for the post-treatment mediator.

Figure 3: Structural-response audit across observational views. We evaluate model responses under (a) Back-Door, (b) Front-Door, (c) IV, and (d) Proximal views. Top: Bars show mean

\mathrm{sPEHE}^{2}

under the Original, Stay, and Move conditions. Bottom: Each point represents an evaluated model configuration, positioned by its mean spurious-response error

E_{\mathrm{stay}}

on the horizontal axis and mean change-tracking error

E_{\mathrm{move}}

on the vertical axis.

Estimator	ACIC 2016			LaLonde-PSID ( $\times 10^{6}$ )			LaLonde-CPS ( $\times 10^{6}$ )
Estimator	$\mathrm{sPEHE}^{2}$	$\mathrm{ATE\ error}^{2}$	$\mathrm{c\text{-}sPEHE}^{2}$	$\mathrm{sPEHE}^{2}$	$\mathrm{ATE\ error}^{2}$	$\mathrm{c\text{-}sPEHE}^{2}$	$\mathrm{sPEHE}^{2}$	$\mathrm{ATE\ error}^{2}$	$\mathrm{c\text{-}sPEHE}^{2}$
CausalPFN	$3.24$ $\pm 3.45$	$0.1074$ $\pm 0.2224$	$3.13$ $\pm 3.34$	$44.0$ $\pm 61.5$	$27.2$ $\pm 41.7$	$16.7$ $\pm 21.6$	$11.2$ $\pm 8.03$	$7.55$ $\pm 8.10$	$3.65$ $\pm 0.782$
Do-PFN	$31.48$ $\pm 20.02$	$12.19$ $\pm 9.29$	$19.29$ $\pm 18.65$	$373$ $\pm 37.2$	$213$ $\pm 34.8$	$160$ $\pm 7.20$	$80.6$ $\pm 4.70$	$43.6$ $\pm 3.81$	$37.0$ $\pm 1.77$
CausalFM	$23.56$ $\pm 17.52$	$5.49$ $\pm 4.84$	$18.08$ $\pm 17.49$	$423$ $\pm 7.50$	$212$ $\pm 6.85$	$211$ $\pm 4.49$	$85.6$ $\pm 1.31$	$44.4$ $\pm 0.711$	$41.2$ $\pm 1.42$
Causal Tree	$11.43$ $\pm 9.75$	$1.30$ $\pm 1.41$	$10.14$ $\pm 9.86$	$181$ $\pm 23.7$	$2.23$ $\pm 4.34$	$179$ $\pm 22.9$	$61.2$ $\pm 8.83$	$12.4$ $\pm 8.83$	$48.8$ $\pm 0.0000$
TARNet	$9.44$ $\pm 8.15$	$0.2352$ $\pm 0.3589$	$9.20$ $\pm 8.09$	$131$ $\pm 212$	$46.6$ $\pm 90.2$	$84.4$ $\pm 130$	$49.2$ $\pm 21.3$	$23.4$ $\pm 6.55$	$25.7$ $\pm 21.2$

Table 1: Back-door evaluation on semi-synthetic benchmarks. Mean squared errors over 40 repeated realizations. Lower is better. For each dataset–metric column, the lowest value is shown in red and the second-lowest value in orange . Values are reported as mean

\pm

standard deviation. LaLonde-PSID and LaLonde-CPS results are shown in units of

\times 10^{6}

Estimator	ACTG 175 ( $n_{C}=768$ )			Pennsylvania ( $n_{C}=1024$ )			Illinois ( $n_{C}=2048$ )
Estimator	$\mathrm{sPEHE}^{2}$	$\mathrm{ATE\ error}^{2}$	$\mathrm{c\text{-}sPEHE}^{2}$	$\mathrm{sPEHE}^{2}$	$\mathrm{ATE\ error}^{2}$	$\mathrm{c\text{-}sPEHE}^{2}$	$\mathrm{sPEHE}^{2}$	$\mathrm{ATE\ error}^{2}$	$\mathrm{c\text{-}sPEHE}^{2}$
CausalPFN	$0.0146\,{\scriptstyle\pm 0.0086}$	$0.0028\,{\scriptstyle\pm 0.0035}$	$0.0118\,{\scriptstyle\pm 0.0068}$	$0.0166\,{\scriptstyle\pm 0.0089}$	$0.0030\,{\scriptstyle\pm 0.0036}$	$0.0136\,{\scriptstyle\pm 0.0064}$	$0.0051\,{\scriptstyle\pm 0.0040}$	$0.0011\,{\scriptstyle\pm 0.0019}$	$0.0039\,{\scriptstyle\pm 0.0031}$
Do-PFN	$0.0203\,{\scriptstyle\pm 0.0113}$	$0.0113\,{\scriptstyle\pm 0.0094}$	$0.0090\,{\scriptstyle\pm 0.0062}$	$0.0177\,{\scriptstyle\pm 0.0080}$	$0.0099\,{\scriptstyle\pm 0.0052}$	$0.0077\,{\scriptstyle\pm 0.0037}$	$0.1249\,{\scriptstyle\pm 0.0220}$	$0.0960\,{\scriptstyle\pm 0.0210}$	$0.0289\,{\scriptstyle\pm 0.0069}$
CausalFM	$0.0053\,{\scriptstyle\pm 0.0028}$	$0.0009\,{\scriptstyle\pm 0.0010}$	$0.0045\,{\scriptstyle\pm 0.0029}$	$0.0023\,{\scriptstyle\pm 0.0011}$	$0.0016\,{\scriptstyle\pm 0.0010}$	$0.0007\,{\scriptstyle\pm 0.0003}$	$0.0016\,{\scriptstyle\pm 0.0008}$	$0.0004\,{\scriptstyle\pm 0.0005}$	$0.0011\,{\scriptstyle\pm 0.0005}$
Causal Tree	$0.0416\,{\scriptstyle\pm 0.0485}$	$0.0022\,{\scriptstyle\pm 0.0028}$	$0.0394\,{\scriptstyle\pm 0.0484}$	$0.0173\,{\scriptstyle\pm 0.0352}$	$0.0042\,{\scriptstyle\pm 0.0058}$	$0.0131\,{\scriptstyle\pm 0.0308}$	$0.0082\,{\scriptstyle\pm 0.0197}$	$0.0017\,{\scriptstyle\pm 0.0026}$	$0.0065\,{\scriptstyle\pm 0.0193}$
TARNet	$0.0692\,{\scriptstyle\pm 0.0308}$	$0.0037\,{\scriptstyle\pm 0.0038}$	$0.0655\,{\scriptstyle\pm 0.0306}$	$0.0993\,{\scriptstyle\pm 0.0345}$	$0.0040\,{\scriptstyle\pm 0.0053}$	$0.0953\,{\scriptstyle\pm 0.0324}$	$0.0239\,{\scriptstyle\pm 0.0142}$	$0.0016\,{\scriptstyle\pm 0.0022}$	$0.0223\,{\scriptstyle\pm 0.0137}$

Table 2: RCT negative-control null-CATE benchmarks. Mean squared null-CATE error over 40 repeated context/query realizations. Lower is better. For each dataset–metric column, the lowest value is shown in red and the second-lowest distinct value in orange . Tied values receive the same color. Each dataset uses its primary context size

n_{C}

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Taxonomy of identification. The three identification status categories are defined by the identified set. The assumptions and identification approaches shown are representative examples, including those relevant to our benchmark, rather than an exhaustive enumeration of possible identification regimes.

View	Observed context variables
Back-door (BD)	$X,U,T,Y$
Front-door (FD)	$X,M,T,Y$
Instrumental variable (IV)	$X,I,T,Y$
Proximal (PX)	$X,Z_{\mathrm{p}},W_{\mathrm{p}},T,Y$
Hidden Confounding (HC)	$X,T,Y$

Appendix

Table 3: Observational contexts constructed from each complete causal world. All views share the same context and query units, treatment assignments, factual outcomes, and oracle effects.

Quantity	Value
Number of world-generation seeds	40
Baseline dimension	50
Context / query units per world	1,024 / 100
Calibration sample size	50,000
Calibration CATE mean / standard deviation	0.5 / 0.5
Treatment covariate / latent / instrument loading	0.55 / 0.75 / 1.50

Appendix

Table 4: Main SCM numerical configuration.

Check	Result
Shared-field mismatches	$0$
Master-projection mismatches	$0$
Query-order mismatches	$0$
Target identity: $\max_{i}\|Y_{i}(1)-Y_{i}(0)-\tau_{0}(X_{i})\|$	$1.55\times 10^{-15}$
Saved Stay target: $\max_{i}\|\tau_{0}^{\mathrm{S}}(X_{i})-\tau_{0}(X_{i})\|$	$0$
Saved Move target: $\max_{i}\|\tau_{0}^{\mathrm{M}}(X_{i})-2\tau_{0}(X_{i})\|$	$0$

Appendix

Table 5: Construction integrity. Pairing checks cover all 40 worlds and their five observational views. The potential-outcome target check uses all 44,960 units. Saved Stay/Move target checks use 4,000 paired queries. Maximum errors are taken over all applicable worlds and units.

Diagnostic	Criterion	Result
Complete propensity $P(T=1\mid X,U,I)$	$[0.01,0.99]$	$[0.02998,0.98115]$
FD standardized shift $\|\delta\|/\sigma_{M}$	$\geq 0.75$	$1.3333$
FD support score $\exp\{-\delta^{2}/(8\sigma_{M}^{2})\}$	$\geq 0.60$	$0.8007$
IV first-stage fifth percentile	$\geq 0.10$	$[0.2601,0.2737]$
PX minimum singular value	$\geq 0.01$	$[0.4139,0.4655]$
PX maximum condition number	$\leq 250$	$[2.2484,2.5821]$

Appendix

Table 6: Regime diagnostics and analytic functional consistency. Diagnostics use the certification populations described in the text. Bracketed values give ranges of world-level statistics, except for complete propensity, which gives the global range over checked probabilities. FD diagnostics are identical across worlds. Oracle reconstruction uses 4,000 shared queries per regime.

Figure 5: Effect of auxiliary-variable inputs for CausalPFN and Do-PFN. We compare

X

-only inputs with inputs augmented by the regime-specific auxiliary variables in the front-door (FD), instrumental-variable (IV), and proximal (PX) views. The auxiliary-input FD configurations condition on the factual mediator and are included as input-sensitivity diagnostics, not as front-door estimators of the total effect.

r^{\mathrm{raw}}_{ai}=M_{i}-\widehat{g}_{a,-k(i)}(X_{i}),\qquad T_{i}=a

Appendix

Algorithm 3 Front-door plug-in estimator

\widetilde{q}_{T_{i}}(Z_{p,i},X_{i})=\operatorname{clip}_{[-25,25]}\bigl(q_{T_{i}}(Z_{p,i},X_{i})\bigr)

Appendix

Algorithm 5 Proximal P-Learner

Figure 6: Hidden-confounding and partial-identification evaluation. (a) Synthetic paired comparison of point-estimation error when the confounder is observed (BD) or unobserved (HC). (b) Full versus Hidden comparisons on IHDP-HC. (c) Endpoint RMSE for representative partially identified settings, including bounded-outcome, IV-based, and sensitivity-model leaves. The sensitivity comparison in panel (c) is evaluated at

\Gamma=2

. (d) Performance of B-Learner variants across sensitivity levels

\Gamma

. (e) Endpoint RMSE of sensitivity-aware estimators across

\Gamma

Back-door (BD): Overlap
	Stress severity
Method	Default	Mild	Moderate	Severe
CausalPFN	$0.208\,{\scriptstyle\pm\,0.062}$	$0.233\,{\scriptstyle\pm\,0.068}$	$0.253\,{\scriptstyle\pm\,0.074}$	$0.291\,{\scriptstyle\pm\,0.084}$
Do-PFN	$0.360\,{\scriptstyle\pm\,0.071}$	$0.338\,{\scriptstyle\pm\,0.066}$	$0.322\,{\scriptstyle\pm\,0.064}$	$0.310\,{\scriptstyle\pm\,0.061}$
CausalFM	$0.233\,{\scriptstyle\pm\,0.033}$	$0.232\,{\scriptstyle\pm\,0.033}$	$0.234\,{\scriptstyle\pm\,0.034}$	$0.235\,{\scriptstyle\pm\,0.034}$
TabPFN-v3.5 + X-Learner	$0.153\,{\scriptstyle\pm\,0.060}$	$0.166\,{\scriptstyle\pm\,0.066}$	$0.182\,{\scriptstyle\pm\,0.068}$	$0.212\,{\scriptstyle\pm\,0.078}$

Appendix

Table 7: Regime-specific stress tests across four identification regimes. We report

\mathrm{sPEHE}^{2}

(

\downarrow

) as the mean

\pm

standard deviation across 40 SCM worlds. Default, Mild, Moderate, and Severe denote increasing levels of regime-specific stress. These levels are not calibrated across regimes. Bold means indicate the lowest mean error within each regime and severity level.

Back-door (BD)
	Context length $n_{\mathrm{ctx}}$
Method	Default	Mild	Moderate	Severe
CausalPFN	$0.208\,{\scriptstyle\pm\,0.062}$	$0.249\,{\scriptstyle\pm\,0.063}$	$0.327\,{\scriptstyle\pm\,0.085}$	$0.451\,{\scriptstyle\pm\,0.134}$
Do-PFN	$0.360\,{\scriptstyle\pm\,0.071}$	$0.363\,{\scriptstyle\pm\,0.071}$	$0.370\,{\scriptstyle\pm\,0.079}$	$0.383\,{\scriptstyle\pm\,0.082}$
CausalFM	$0.233\,{\scriptstyle\pm\,0.033}$	$0.240\,{\scriptstyle\pm\,0.035}$	$0.253\,{\scriptstyle\pm\,0.044}$	$0.273\,{\scriptstyle\pm\,0.055}$
TabPFN-v3.5 + X-Learner	$0.153\,{\scriptstyle\pm\,0.060}$	$0.202\,{\scriptstyle\pm\,0.056}$	$0.261\,{\scriptstyle\pm\,0.069}$	$0.308\,{\scriptstyle\pm\,0.089}$

Appendix

Table 8: Context-length stress test across four identification regimes. We report

\mathrm{sPEHE}^{2}

(

\downarrow

) as the mean

\pm

standard deviation across 40 SCM worlds. Context lengths of 1,024, 512, 256, and 160 correspond to the Default, Mild, Moderate, and Severe settings, respectively. Bold means indicate the lowest mean error within each regime and context length.

Figure 7: Input and identification ablation for the modular approach. We compare three TabPFN configurations:

(X,T)

only, all variables available in each observational view provided as ordinary predictive features, and the corresponding regime-specific modular estimator. The first two configurations provide no annotations or information about the causal roles of the input variables.

Figure 8: Effect of the predictive backbone in modular approaches. We replace the predictive model in modular approaches while keeping the regime-specific identification procedure fixed within each panel.

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