  This paper considers a nuclear norm penalized estimator for panel data models
with interactive effects. The low-rank interactive effects can be an
approximate model and the rank of the best approximation unknown and grow with
sample size. The estimator is solution of a well-structured convex optimization
problem and can be solved in polynomial-time. We derive rates of convergence,
study the low-rank properties of the estimator, estimation of the rank and of
annihilator matrices when the number of time periods grows with the sample
size. Two-stage estimators can be asymptotically normal. None of the procedures
require knowledge of the variance of the errors.
