Testing identification in mediation and dynamic treatment models

TL;DR

This paper introduces a new test for causal effect identification in mediation and dynamic treatment models, utilizing observed covariates and instruments, with a machine learning approach for covariate control, validated through simulations and real data.

Contribution

It extends existing tests to models with sequential treatments and mediators, incorporating machine learning for covariate adjustment and addressing attrition issues.

Findings

Testable conditions for causal effect identification are established.

The machine learning-based test performs well in finite samples.

Application to Slovak labor data shows no rejection of testable implications.

Abstract

We propose a test for the identification of causal effects in mediation and dynamic treatment models that is based on two sets of observed variables, namely covariates to be controlled for and suspected instruments, building on the test by Huber and Kueck (2022) for single treatment models. We consider models with a sequential assignment of a treatment and a mediator to assess the direct treatment effect (net of the mediator), the indirect treatment effect (via the mediator), or the joint effect of both treatment and mediator. We establish testable conditions for identifying such effects in observational data. These conditions jointly imply (1) the exogeneity of the treatment and the mediator conditional on covariates and (2) the validity of distinct instruments for the treatment and the mediator, meaning that the instruments do not directly affect the outcome (other than through the treatment or mediator) and are unconfounded given the covariates. Our framework extends to post-treatment sample selection or attrition problems when replacing the mediator by a selection indicator for observing the outcome, enabling joint testing of the selectivity of treatment and attrition. We propose a machine learning-based test to control for covariates in a data-driven manner and analyze its finite sample performance in a simulation study. Additionally, we apply our method to Slovak labor market data and find that our testable implications are not rejected for a sequence of training programs typically considered in dynamic treatment evaluations.