Functional Differencing


  • Stéphane Bonhomme

    1. CEMFI, Casado del Alisal 5, 28014 Madrid, Spain;
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    • I thank the co-editor and four anonymous referees for very useful comments. I also thank Manuel Arellano, Alan Bester, Marine Carrasco, Gary Chamberlain, Bryan Graham, Jin Hahn, Chris Hansen, Jim Heckman, Joel Horowitz, Yingyao Hu, Konrad Menzel, Ulrich Müller, Jim Powell, Elie Tamer, Harald Uhlig, and seminar participants at Berkeley, Boston University, Brown University, CEMFI, University of Chicago, Chicago Booth, Harvard University, Université de Montréal, New York University, Northwestern University, Toulouse School of Economics, University College London, and University of Toronto. Support from the European Research Council Grant agreement 263107 is gratefully acknowledged. All errors are mine.


In nonlinear panel data models, the incidental parameter problem remains a challenge to econometricians. Available solutions are often based on ingenious, model-specific methods. In this paper, we propose a systematic approach to construct moment restrictions on common parameters that are free from the individual fixed effects. This is done by an orthogonal projection that differences out the unknown distribution function of individual effects. Our method applies generally in likelihood models with continuous dependent variables where a condition of non-surjectivity holds. The resulting method-of-moments estimators are root-N consistent (for fixed T) and asymptotically normal, under regularity conditions that we spell out. Several examples and a small-scale simulation exercise complete the paper.