A Causal Latent Transition Model With Multivariate Outcomes and Unobserved Heterogeneity: Application to Human Capital Development

In order to evaluate the effect of a policy or treatment with pre- and post-treatment outcomes, we propose an approach based on a transition model, which may be applied with multivariate outcomes and accounts for unobserved heterogeneity. This model is based on potential versions of discrete latent variables representing the individual characteristic of interest and may be cast in the hidden (latent) Markov literature for panel data. Therefore, it can be estimated by maximum likelihood in a relatively simple way. The approach extends the difference-in-difference method as it is possible to deal with multivariate outcomes. Moreover, causal effects may be expressed with respect to transition probabilities. The proposal is validated through a simulation study, and it is applied to evaluate educational programs administered to pupils in the sixth and seventh grades during their middle school period. These programs are carried out in an Italian region to improve non-cognitive skills (CSs). We study if they impact also on students' CSs in Italian and Mathematics in the eighth grade, exploiting the pretreatment test scores available in the fifth grade. The main conclusion is that the educational programs aimed to develop noncognitive abilities help the best students to maintain their higher cognitive abilities over time.