Causal Inference for Experiments with Latent Outcomes: Key Results and Their Implications for Design and Analysis

TL;DR

This paper addresses how to analyze randomized experiments with latent outcomes measured in multiple ways, proposing design-based methods to improve causal inference and interpretability.

Contribution

It introduces design-based approaches and optimal weighting strategies for multiple outcome measures, enhancing causal estimation in experiments with latent variables.

Findings

Optimal weighted index improves estimate efficiency

Multiple measures increase robustness and precision

Empirical application demonstrates practical gains

Abstract

How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in existing methods for handling multiple measurements, which often rely on strong modeling assumptions or arbitrary standardization. Such approaches render the resulting estimands noncomparable across studies. To address the problem, we describe design-based approaches that enable researchers to identify causal parameters of interest, suggest ways that experimental designs can be augmented so as to make assumptions more credible, and discuss empirical tests of key assumptions. We show that when experimental researchers invest appropriately in multiple outcome measures, an optimally weighted scaled index of these measures enables researchers to obtain efficient and interpretable estimates of causal parameters by applying standard regression. An empirical application illustrates the gains in precision and robustness that multiple outcome measures can provide.