Raking for estimation and inference in panel models with nonignorable attrition and refreshment

In panel data subject to nonignorable attrition, auxiliary (refreshment) sampling may restore full identification under weak assumptions on the attrition process. Despite their generality, these identification strategies have seen limited empirical use, largely because the implied estimation procedure requires solving a functional minimization problem for the target density. We show that this problem can be solved using the iterative proportional fitting (raking) algorithm, which converges rapidly even with continuous and moderately high-dimensional data. This resulting density estimator is then used as input into a parametric moment condition. We establish consistency and convergence rates for both the raking-based density estimator and the resulting moment estimator when the distributions of the observed data are parametric. We also derive a simple recursive procedure for estimating the asymptotic variance. Finally, we demonstrate the satisfactory performance of our estimator in simulations and provide an empirical illustration using data from the Understanding America Study panel.