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 independence 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, suggesting that we could substantially improve the cost-effectiveness of their training.