Estimation of Local Average Treatment Effect by Data Combination
This work addresses a practical challenge in causal inference for researchers and practitioners dealing with fragmented data, though it is incremental as it builds on existing direct least squares methods.
The paper tackles the problem of estimating local average treatment effects (LATE) when data is split across separate datasets due to technical or privacy constraints, proposing a weighted least squares estimator that simplifies model selection and avoids issues with inverse probability weighting, showing effectiveness in synthetic and real-world experiments.
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.