# Estimation of Local Average Treatment Effect by Data Combination

arXiv: https://arxiv.org/abs/2109.05175 · HTML: https://mlsanity.com/paper/2109.05175/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 70 references that are in the map.
- First posted on arXiv 11 Sep 2021.

## Builds on (most cited first, 9 of 9)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [Less Is Better: Unweighted Data Subsampling via Influence Function](https://mlsanity.com/paper/1912.01321/) (2019)
- [Trimmed Density Ratio Estimation](https://mlsanity.com/paper/1703.03216/) (2017)
- [Efficient nonparametric causal inference with missing exposure information](https://mlsanity.com/paper/1802.08952/) (2018)
- [Uplift Modeling from Separate Labels](https://mlsanity.com/paper/1803.05112/) (2018)
- [Estimation of local treatment effects under the binary instrumental variable model](https://mlsanity.com/paper/2007.14458/) (2020)
- [Instrumented Difference-in-Differences](https://mlsanity.com/paper/2011.03593/) (2020)

## Built on by (most cited first, 2 of 2)

- [Orthogonal Series Estimation for the Ratio of Conditional Expectation Functions](https://mlsanity.com/paper/2212.13145/) (2022)
- [Online Data Collection for Efficient Semiparametric Inference](https://mlsanity.com/paper/2411.03195/) (2024)

## Abstract (arXiv)

It is important to estimate the local average treatment effect (LATE) when compliance with a treatment assignment is incomplete. The previously proposed methods for LATE estimation required all relevant variables to be jointly observed in a single dataset; however, it is sometimes difficult or even impossible to collect such data in many real-world problems for technical or privacy reasons. We consider a novel problem setting in which LATE, as a function of covariates, is nonparametrically identified from the combination of separately observed datasets. For estimation, we show that the direct least squares method, which was originally developed for estimating the average treatment effect under complete compliance, is applicable to our setting. However, model selection and hyperparameter tuning for the direct least squares estimator can be unstable in practice since it is defined as a solution to the minimax problem. We then propose a weighted least squares estimator that enables simpler model selection by avoiding the minimax objective formulation. Unlike the inverse probability weighted (IPW) estimator, the proposed estimator directly uses the pre-estimated weight without inversion, avoiding the problems caused by the IPW methods. We demonstrate the effectiveness of our method through experiments using synthetic and real-world datasets.