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.

Consider an individual making a portfolio choice at date T involving two assets. The (gross) returns at t per unit invested at t 1 are Yit and Y2t* The individual has observed these returns from t = 0 to t = T. He has also observed the values of the variables Y3t',... YKt, which are thought to be relevant in forecasting future returns. Thus, the information available to him when he makes his portfolio choice is z = {(Yt ... YKt)} t=0. He invests one unit, divided between an amount a in asset 1 and an amount 1 a in asset 2, and he then holds on to the portfolio until date T + H. Let w = {(Yit, Y2t)}T:H+ 1 and let h(w, a) denote the value of the portfolio at t T + H: