Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 2012, Volume 80, Issue 4

Functional Differencing
p. 1337-1385

Stéphane Bonhomme

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‐ consistent (for fixed ) and asymptotically normal, under regularity conditions that we spell out. Several examples and a small‐scale simulation exercise complete the paper.

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Supplemental Material

Supplement to "Functional Differencing"

This zip file contains codes used to generate the numerical results.

Supplement to "Functional Differencing"

This appendix contains analytical and numerical results on various models.  It also presents a method to numerically compute information bounds and check the non-surjectivity condition. Lastly, it outlines a specification test of parametric random-effects models.

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