Non parametric analysis of panel data models with endogenous variables

This paper considers the estimation of panel data models by first differences in the presence of endogenous variables and under an instrumental variables condition. This framework leads to the resolution of linear inverse problems solved using a Tikhonov regularization with L2 or Sobolev penalty. Rates of convergence and data driven selection of the regularization parameters are proposed. The practical implementation of our estimators is presented and some Monte Carlo simulations show the potential of the method.