Estimation of a Nonlinear Panel Data Model with Semiparametric Individual Effects ∗ Wayne-Roy Gayle † , Soiliou Daw Namoro ‡ March 2, 2012 Abstract This paper explores identification and estimation of a class of nonlinear panel data single-index models, which includes a class of single-index panel discrete-choice models. The model allows for unknown time-specific link functions, and semipara- metric specification of the individual-specific effects. We develop an estimator for the parameters of interest that may be computed with any appropriate smoother, be it sieves or kernel smoothers. We propose a powerful new kernel-based modified back- fitting algorithm to compute the estimator. The algorithm fully implements the identi- fication restrictions of the model. We derive uniform rates of convergence results for the estimators of the link functions, and show the estimators of the finite dimensional parameters are root-N consistent with a Gaussian limiting distribution. We study the small sample properties of the estimator via Monte Carlo techniques. The results indi- cate that the estimator performs well in recovering the finite-dimensional parameters of interest. Keywords: Semiparametric estimation, modified backfitting, panel data, nonlinear models. JEL classification: C13, C14, C23 ∗ The authors are grateful to Jean-Francois Richard, Mehmet Caner, Robert Miller, Holger Sieg, George- Levi Gayle, and three anonymous referees for insightful comments and discussions. Comments by the partic- ipants of the 12th Conference on Panel Data at Copenhagen, Denmark, 2005, were greatly appreciated. All remaining errors are our own. † Department of Economics, University of Virginia, Monroe Hall, McCormick Rd, Room 208A, Char- lottesville VA 22903; E-mail: wg4b@virginia.edu. ‡ Economics Department, University of Pittsburgh, 230 S. Bouquet St., Pittsburgh, PA. 15260; E-mail: snamoro@pitt.edu. 1