Approximate functional differencing

Abstract 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 functional differencing (Bonhomme Econometrica 80(4):1337–1385, 2012), which works when the number time periods T (and may be small), but not applicable all interest. Another solution, applies larger class models, “large- ” bias correction [pioneered by Hahn Kuersteiner 70(4):1639–1657, 2002) Newey 72(4):1295–1319, 2004)], only guaranteed work well sufficiently large. This paper provides unified approach that connects these two seemingly disparate solutions IPP. In doing so, we provide an approximate version differencing, is, large even relatively small.