  We provide estimation methods for nonseparable panel models based on low-rank
factor structure approximations. The factor structures are estimated by
matrix-completion methods to deal with the computational challenges of
principal component analysis in the presence of missing data. We show that the
resulting estimators are consistent in large panels, but suffer from
approximation and shrinkage biases. We correct these biases using matching and
difference-in-differences approaches. Numerical examples and an empirical
application to the effect of election day registration on voter turnout in the
U.S. illustrate the properties and usefulness of our methods.
