Approximate functional differencing

Inference on common parameters in panel data models with individual-specific fixed effects is a classic example of Neyman and Scott's (Econometrica 36:1-32, 1948) incidental parameter problem (IPP). One solution to this IPP is functional differencing (Bonhomme in Econometrica 80(4):1337-1385, 2012), which works when the number of time periods T is fixed (and may be small), but this solution is not applicable to all panel data models of interest. Another solution, which applies to a larger class of models, is "large-T" bias correction [pioneered by Hahn and Kuersteiner (Econometrica 70(4):1639-1657, 2002) and Hahn and Newey (Econometrica 72(4):1295-1319, 2004)], but this is only guaranteed to work well when T is sufficiently large. This paper provides a unified approach that connects these two seemingly disparate solutions to the IPP. In doing so, we provide an approximate version of functional differencing, that is, an approximate solution to the IPP that is applicable to a large class of panel data models even when T is relatively small.