Latent Variables and Propensity Score Matching

Abstract

This paper examines how including latent variables can benefit propensity score matching. A researcher can estimate, based on theoretical presumptions, the latent variable from the observed manifest variables and can use this estimate in propensity score matching. This paper demonstrates the benefits of such an approach and compares it with a method more common in econometrics, where the manifest variables are directly used in matching. We intuit that estimating the propensity score on the manifest variables introduces a measurement error that can be limited when estimating the propensity score on the estimated latent variable. We use Monte Carlo simulations to test how various matching methods behave under distinct circumstances found in practice. Also, we apply this approach to real data. Using the estimated latent variable in the propensity score matching increases the efficiency of treatment effect estimators. The benefits are larger for small samples, for non-linear processes, and for a large number of the manifest variables available, especially if they are highly correlated with the latent variable.