Latent variables and propensity score matching: a simulation study with application to data from the Programme for International Student Assessment in Poland

Abstract

This paper examines how including latent variables can benefit propensity score matching. Latent variables can be estimated from the observed manifest variables and used in matching. This paper demonstrates the benefits of such an approach by comparing it with a method where the manifest variables are directly used in matching. Estimating the propensity score on the manifest variables introduces a measurement error that can be limited with estimating the propensity score on the estimated latent variable. We use Monte Carlo simulations to test how the proposed approach behaves under distinct circumstances found in practice, and then apply it to real data. Using the estimated latent variable in the propensity score matching limits the measurement error bias of the treatment effects’ estimates and increases their precision. The benefits are larger for small samples and with better information about the latent variable available.