Fixed Effects, Invariance, and Spatial Variation in Intergenerational Mobility

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.