Chetty et al. (2014) document variation across commuting zones in intergenerational mobility. With over 700 commuting zones, the task of estimating place effects involves a high-dimension parameter space. I develop a fixed-effects model along with an oracle bound on the risk of invariant estimators. The oracle estimator uses an invariant prior, which I have incorporated into a random-effects model to obtain a feasible estimator. This estimator almost achieves the oracle bound over the relevant part of the (fixed-effects) parameter space in the empirical application. There is substantial reduction in risk compared with the least-squares estimator.