Predicting Unobserved Individual-level Causal Effects

Abstract:

Measuring accurately heterogeneous effects is key for the design of efficient public
policies. This paper focuses on predicting unobserved individual-level causal effects
in linear random coefficients models, conditional on all the available data. In the
application I consider, these “posterior effects” are the average effects of teachers’
knowledge on their students’ performance, conditional on both variables. I derive
two nonparametric strategies for recovering these posterior effects, assuming inde-
pendence between the effects and the covariates. The first strategy recovers the
distribution of the random coefficients by a minimum distance approach, and then
obtains the posterior effects from this distribution. The corresponding estimator can
be computed using an optimal transport algorithm. The second approach, which
is valid only for continuous regressors, directly expresses the posterior effects as a
function of the data. The corresponding estimator is rate optimal. I discuss several
extensions, in particular the relaxation of the independence condition. Finally, the
application reveals large heterogeneity in the effect of teachers’ knowledge, suggest-
ing that we could substantially improve the cost-effectiveness of their training.