# Meta-Learners for Estimation of Causal Effects: Finite Sample Cross-Fit Performance

arXiv: https://arxiv.org/abs/2201.12692 · HTML: https://mlsanity.com/paper/2201.12692/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 146 references that are in the map.
- First posted on arXiv 30 Jan 2022.

## Builds on (most cited first, 30 of 39)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [A Random Forest Guided Tour](https://mlsanity.com/paper/1511.05741/) (2015)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [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)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Machine Learning Methods Economists Should Know About](https://mlsanity.com/paper/1903.10075/) (2019)
- [Perfect Match: A Simple Method for Learning Representations For Counterfactual Inference With Neural Networks](https://mlsanity.com/paper/1810.00656/) (2018)
- [Learning When-to-Treat Policies](https://mlsanity.com/paper/1905.09751/) (2019)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife](https://mlsanity.com/paper/1311.4555/) (2013)
- [The State of Applied Econometrics - Causality and Policy Evaluation](https://mlsanity.com/paper/1607.00699/) (2016)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [A unified survey of treatment effect heterogeneity modeling and uplift modeling](https://mlsanity.com/paper/2007.12769/) (2020)
- [How Important is the Train-Validation Split in Meta-Learning?](https://mlsanity.com/paper/2010.05843/) (2020)
- [Program Evaluation and Causal Inference with High-Dimensional Data](https://mlsanity.com/paper/1311.2645/) (2013)
- [A comparison of methods for model selection when estimating individual treatment effects](https://mlsanity.com/paper/1804.05146/) (2018)
- [Estimating Individual Treatment Effect in Observational Data Using Random Forest Methods](https://mlsanity.com/paper/1701.05306/) (2017)
- [Response Transformation and Profit Decomposition for Revenue Uplift Modeling](https://mlsanity.com/paper/1911.08729/) (2019)
- [Assessing Treatment Effect Variation in Observational Studies: Results from a Data Challenge](https://mlsanity.com/paper/1907.07592/) (2019)
- [A Representation Learning Perspective on the Importance of Train-Validation Splitting in Meta-Learning](https://mlsanity.com/paper/2106.15615/) (2021)
- [Machine learning for causal inference: on the use of cross-fit estimators](https://mlsanity.com/paper/2004.10337/) (2020)
- [Machine learning in policy evaluation: new tools for causal inference](https://mlsanity.com/paper/1903.00402/) (2019)

## Built on by (most cited first, 4 of 4)

- [Comparison of meta-learners for estimating multi-valued treatment heterogeneous effects](https://mlsanity.com/paper/2205.14714/) (2022)
- [Multiple Treatments Causal Effects Estimation with Task Embeddings and Balanced Representation Learning](https://mlsanity.com/paper/2511.09814/) (2025)
- [Scalable Vision-Guided Crop Yield Estimation](https://mlsanity.com/paper/2511.12999/) (2025)
- [Assessment of the conditional exchangeability assumption in causal machine learning models: a simulation study](https://mlsanity.com/paper/2510.26700/) (2025)

## Abstract (arXiv)

Estimation of causal effects using machine learning methods has become an active research field in econometrics. In this paper, we study the finite sample performance of meta-learners for estimation of heterogeneous treatment effects under the usage of sample-splitting and cross-fitting to reduce the overfitting bias. In both synthetic and semi-synthetic simulations we find that the performance of the meta-learners in finite samples greatly depends on the estimation procedure. The results imply that sample-splitting and cross-fitting are beneficial in large samples for bias reduction and efficiency of the meta-learners, respectively, whereas full-sample estimation is preferable in small samples. Furthermore, we derive practical recommendations for application of specific meta-learners in empirical studies depending on particular data characteristics such as treatment shares and sample size.