Causal Forests for Heterogeneous Effects

• Causal forests are tree-based methods that estimate conditional average treatment effects by partitioning covariate space and comparing treated and control units.
• They utilize honest tree construction and adaptive kernel weighting with orthogonal scoring to improve inference and reduce bias in heterogeneous effect estimation.
• Extensions include survival analysis, instrumental variable adaptations, and continuous treatment frameworks, with ongoing debates about honesty and aggregation trade-offs.

A causal forest is a tree-based method for estimating heterogeneous treatment effects under the potential outcomes framework. Rather than targeting an outcome regression such as $\mu(x)=\mathbb{E}[Y\mid X=x]$, it targets the conditional average treatment effect (CATE),

$\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$

and uses a forest of treatment-effect-oriented trees to define adaptive local neighborhoods in covariate space. In the modern formulation, causal forests combine honest tree construction, local weighting, orthogonalization, and semiparametric scores, and they are typically interpreted as adaptive kernel estimators with asymptotic inference. The method originated as an extension of random forests for treatment-effect estimation and was later embedded in the generalized random forest framework, with subsequent extensions to clustered data, survival outcomes, manifold covariates, variable-importance analysis, and panel or continuous-treatment settings (Wager et al., 2015).

1. Foundations and estimands

In the potential outcomes setup, each unit $i$ has potential outcomes $Y_i(0)$ and $Y_i(1)$, observed treatment $W_i\in\{0,1\}$, and observed outcome

$Y_i=Y_i(W_i).$

The core estimand is the CATE,

$\tau(x)=\mathbb{E}[Y_i(1)-Y_i(0)\mid X_i=x],$

with the average treatment effect

$\tau=\mathbb{E}[Y_i(1)-Y_i(0)]$

as an aggregate target (Athey et al., 2019).

The foundational causal-forest literature frames the task as nonparametric estimation of $\tau(x)$ under unconfoundedness and overlap. In the 2015 formulation, the identification conditions are

$\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$0

and the existence of $\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$1 such that

$\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$2

for all $\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$3 (Wager et al., 2015). In the application note based on the National Study of Learning Mindsets, the same logic is expressed as

$\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$4

with the data analyzed as observational because the synthetic treatment assignment depends on a measured covariate, $\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$5 (Athey et al., 2019).

Causal forests differ from ordinary random forests in the object they localize. A regression forest defines neighborhoods to estimate $\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$6, whereas a causal forest defines neighborhoods in which treated and control observations can be compared to estimate treatment effects. In the original tree-based version, a leaf-specific effect is estimated by the treated-control difference in means within the leaf,

$\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$7

and the forest aggregates many such local estimates (Wager et al., 2015).

This basic estimand-centered view persists across later variants. Causal survival forests replace $\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$8 by a right-censoring-adjusted survival score while still targeting a conditional treatment effect, for example on restricted mean survival time or survival probability (Cui et al., 2020). Instrumental-variable forests target a conditional local average treatment effect rather than a CATE under unconfoundedness (Cordier, 3 Jan 2026). Difference-in-differences Bayesian causal forests target dynamic treatment effects indexed by event time, $\tau(x)=\mathbb{E}[Y(1)-Y(0)\mid X=x],$9, rather than a purely cross-sectional CATE (Souto et al., 14 May 2025). This suggests that “causal forest” now denotes a broader family of forest-based local estimators built around treatment-effect moment conditions rather than a single fixed algorithm.

2. Forest construction, honesty, and orthogonalization

The modern causal-forest workflow is usually described in two layers: nuisance estimation and forest-based local effect estimation. In the generalized random forest implementation used in grf, one first estimates

$i$0

using regression forests, and obtains out-of-bag predictions $i$1 and $i$2 for orthogonalization (Athey et al., 2019).

The motivation is the Robinson or R-learner formulation. When the treatment effect is constant, the efficient Robinson estimator is

$i$3

For heterogeneous treatment effects, the R-learner generalizes this to

$i$4

and causal forests implement a forest-based approximation to this objective (Athey et al., 2019).

The forest itself is interpreted as an adaptive kernel. A regression forest prediction can be written as

$i$5

where the weights $i$6 are determined by leaf co-membership across trees. In the causal setting these weights are combined with orthogonalized residuals to yield the local Robinson estimator

$i$7

This adaptive-kernel interpretation is central to generalized random forests and underlies later extensions to manifold data and other semiparametric targets (Athey et al., 2019).

A defining design feature is honesty. In the foundational theory, honest trees use separate data for choosing splits and for estimating leaf effects, or more generally ensure that each observation’s outcome is used either for splitting or for leaf estimation but not both (Wager et al., 2015). In the 2019 application note, the same idea appears as separate subsamples for split selection and leaf estimation, producing approximate independence between the weight structure $i$8 and the outcome noise (Athey et al., 2019). Honesty is the main device behind asymptotic theory, but later work emphasizes that it is also a regularization choice with a bias-variance trade-off: it reduces variance by preventing overfitting, but can increase bias by limiting the model’s ability to discover and exploit meaningful heterogeneity when the signal-to-noise ratio is high (Hou et al., 16 Jun 2025).

3. Inference, asymptotics, and statistical interpretation

The first general asymptotic results established pointwise consistency and asymptotic normality for honest subsampled forests under regularity conditions. In the regression case, the theory shows that there exists $i$9 such that

$Y_i(0)$0

with a consistent infinitesimal jackknife variance estimator. The same Gaussian theory is then extended to causal forests (Wager et al., 2015). The paper presents this as the first set of results allowing random forests, including classification and regression forests, to be used for provably valid statistical inference (Wager et al., 2015).

In the generalized random forest formulation, inference is tied to orthogonal scores. The local estimating equation can be written as

$Y_i(0)$1

which is a local version of the orthogonal score used in double/debiased machine learning (Athey et al., 2019). The 2019 note further stresses that if $Y_i(0)$2 and $Y_i(0)$3 converge at $Y_i(0)$4 rates, orthogonalization implies first-order insensitivity to nuisance-estimation error and supports $Y_i(0)$5-rate inference for average effects (Athey et al., 2019).

For average treatment effects and related aggregates, the same note uses an augmented inverse-propensity weighted score,

$Y_i(0)$6

and then averages these scores at the cluster or sample level (Athey et al., 2019). This score is described there as doubly robust and orthogonal.

Subsequent theory has clarified how the rate can depend on intrinsic rather than ambient complexity. For a suitably defined forest estimator on manifold-supported covariates, the pointwise mean squared error satisfies

$Y_i(0)$7

where $Y_i(0)$8 is the intrinsic manifold dimension rather than the ambient dimension $Y_i(0)$9. Under extreme honesty and optimal bandwidth,

$Y_i(1)$0

and a pointwise central limit theorem is available with consistently estimable variance (Huo et al., 2023). This suggests that, under the stated manifold assumptions, causal forests behave like optimal local smoothers in intrinsic dimension.

Inference has also been extended to nonstandard outcomes. Causal survival forests use a doubly robust score for right-censored data and then plug that score into the generalized random forest machinery. Under regularity conditions, the resulting local estimator is asymptotically normal and supports pointwise confidence intervals for treatment effects on restricted mean survival time or survival probability (Cui et al., 2020).

4. Applied workflow and empirical use

A methodological review of 133 peer-reviewed applied papers finds that emerging practice relies heavily on the grf implementation and on workflows introduced by the original authors (Rehill, 2024). In that sample, grf is the dominant reported software, applied researchers usually work with relatively low-dimensional covariate sets, and most applications rely either on experiments or on observed controls for identification (Rehill, 2024).

The same review identifies a recurring empirical workflow. Researchers often estimate an ATE with average_treatment_effect, inspect the univariate distribution of predicted CATEs, report forest variable importance, and then graph treatment effects against a small set of theoretically salient or highly ranked covariates (Rehill, 2024). In the learning-mindsets application, the implementation follows exactly this logic: encode covariates, fit nuisance forests for $Y_i(1)$1 and $Y_i(1)$2, fit a pilot causal forest, compute variable importance, retain variables with above-average importance, and then fit a final forest with samples_per_cluster increased and tune.parameters = TRUE (Athey et al., 2019).

The same application also illustrates the gap between visible variation in predicted CATEs and statistically credible heterogeneity. Using $Y_i(1)$3 students in $Y_i(1)$4 schools, the authors report an ATE of approximately $Y_i(1)$5 with standard error approximately $Y_i(1)$6 and a positive 95% confidence interval. Yet a median-split comparison of high-$Y_i(1)$7 and low-$Y_i(1)$8 groups yields a difference of $Y_i(1)$9, and a calibration test gives coefficient approximately $W_i\in\{0,1\}$0, standard error approximately $W_i\in\{0,1\}$1, and $W_i\in\{0,1\}$2, providing no strong cluster-robust evidence of high-dimensional heterogeneity (Athey et al., 2019). This is a recurring applied lesson: a dispersed CATE histogram is not itself evidence of stable effect modification.

The review also documents several common deviations from best practice. In randomized experiments, many papers estimate propensities instead of supplying the known assignment probability; for observational studies, overlap diagnostics are often underreported; and some papers run post-forest linear regressions on predicted CATEs with standard regression standard errors, which the review treats as methodologically problematic (Rehill, 2024). By contrast, the review treats best linear projection, calibration tests, and RATE-type summaries as more principled tools for communicating heterogeneity (Rehill, 2024).

A plausible implication is that the applied literature has converged on a standardized “forest + diagnostic + targeted visualization” workflow, but not yet on equally standardized practices for overlap assessment, policy evaluation, or subgroup-level validity checks.

5. Extensions and variants

Several later papers generalize the causal-forest paradigm to settings that violate the canonical cross-sectional, binary-treatment, uncensored setup. One major line extends the method to right-censored survival outcomes. Causal survival forests define a doubly robust survival score that adjusts for both treatment selection and censoring, then use honest forests and pseudo-outcome splitting to estimate heterogeneous effects on restricted mean survival time or survival probability (Cui et al., 2020).

A second line studies geometric structure in the covariates. The manifold-adaptation analysis shows that a suitably defined causal forest estimator can achieve the optimal convergence rate determined by the intrinsic manifold dimension, not the ambient dimension, and that it admits a pointwise central limit theorem with consistently estimable variance (Huo et al., 2023). The estimator analyzed there uses separate trees for treated and control units, regression-adjusted imputation of missing potential outcomes, and an explicit kernel smoothing step over the forest-imputed pseudo-outcomes (Huo et al., 2023).

A third line concerns interpretation. The variable-importance paper proposes a drop-and-relearn importance measure for causal forests, targeting

$W_i\in\{0,1\}$3

so that irrelevant variables have asymptotically zero importance and relevant heterogeneity drivers have positive importance (Bénard et al., 2023). The paper also shows that naive variable deletion can break identification when a dropped variable is also a confounder, and introduces a corrective term to recover consistency (Bénard et al., 2023). A distinct interpretability-oriented proposal, the Causal Rule Forest, uses stacked causal-tree layers to convert learned patterns into multi-level Boolean rules and then feeds those rule-based representations to interpretable causal models such as a single causal tree (Hsu et al., 2024).

Other variants change the identification strategy. DiD-BCF adapts the Bayesian causal forest parameterization to panel difference-in-differences with staggered adoption by modeling

$W_i\in\{0,1\}$4

so that treatment effects vary over covariates and event time under a parallel-trends assumption rather than cross-sectional unconfoundedness (Souto et al., 14 May 2025). Instrumental causal forests replace the ignorability-based score by an IV-based local effect estimand to study endogenous treatments (Cordier, 3 Jan 2026).

The family has also been pushed toward more specialized decision problems. Generalized causal forest for online marketplaces replaces scalar binary-treatment effects by nonparametric dose-response functions for continuous treatments and uses a distance-based splitting criterion between treatment-effect curves (Wan et al., 2022). Large-Scale Budget-Constrained Causal Forest estimates a vector of treatment effects for multiple treatments and combines the forest with a knapsack-style policy optimizer under a global budget constraint (Ai et al., 2022).

6. Limitations, controversies, and methodological debates

Several recurrent limitations are explicit in the literature. First, the standard causal forest still relies on unconfoundedness and overlap; it does not solve hidden confounding. The 2019 application note states directly that causal forests cannot address unobserved confounding and that alternative strategies such as IVs or sensitivity analysis would be needed to relax the assumption (Athey et al., 2019).

Second, clustering can be decisive. In the learning-mindsets application, ignoring school-level clustering underestimates standard errors, produces a much more dispersed distribution of out-of-bag CATE estimates, and turns a heterogeneity calibration test strongly significant ($W_i\in\{0,1\}$5), whereas cluster-robust analysis shows much of the apparent heterogeneity to be school-level noise (Athey et al., 2019). The paper therefore advocates cluster-aware subsampling, cluster-based out-of-bag definitions, and cluster-level aggregation when clusters are the units of independence (Athey et al., 2019).

Third, honesty is no longer treated as an unqualified virtue. The recent analysis of honesty in causal forests argues that honest estimation should be viewed as a form of regularization: it helps when effect heterogeneity is hard to detect, but hurts when the signal is strong, because it reduces the model’s ability to discover and exploit heterogeneity (Hou et al., 16 Jun 2025). In that account, honesty improves individual-level effect estimation in low signal-to-noise regimes and worsens it in high signal-to-noise regimes, so it should be tuned for out-of-sample performance rather than adopted by default (Hou et al., 16 Jun 2025).

Fourth, standard aggregation itself has been questioned. The LILI clustering proposal argues that independent tree aggregation may repeat misclassification errors across trees and introduces a post-processing scheme based on stable leaf co-occurrence across trees. The paper claims that this clustering reduces bias in ATE estimation and proves convergence of the LILI-based estimator under its assumptions (Dong et al., 4 Jul 2025). This suggests an alternative view of forests as randomized mechanisms for discovering stable partitions rather than only as averaging devices.

Finally, methodological reviews emphasize that many applied uses remain exploratory even when the software output looks formally inferential. Researchers frequently summarize CATE distributions, variable importance, and covariate-specific plots, but more limited attention is paid to overlap, subgroup-level design validity, and the distinction between predictive and causal use of forest summaries (Rehill, 2024). Taken together, these debates indicate that causal forests are best understood not as a finished method but as a modular semiparametric framework whose practical validity depends on design assumptions, tuning choices, dependence structure, and the target of inference.