Instrumental variable estimation with observed and unobserved heterogeneity of the treatment and instrument effect: a latent class approach

This article introduces a latent class approach to estimate the impact of a continuous and endogenous treatment on a continuous outcome, incorporating observed and unobserved heterogeneity in both the treatment and instrument effects, and relaxing the monotonicity assumption across groups of individuals. Our approach, based on a fully parametric model estimated via maximum likelihood, allows the parameters to vary across different classes (groups) of individuals. Given that the membership of each individual to a given class is unknown, we jointly estimate it alongside class-specific parameters assuming a discrete distribution. We perform a Monte Carlo experiment to evaluate the performance of our estimator under assumptions similar to those of the traditional instrumental variables model. Our results indicate that when the model is well specified, our proposed estimator accurately estimates the true degree of unobserved heterogeneity across classes and the population average treatment effect. We illustrate the practical implementations of our approach with two empirical examples.