Approximate Functional Differencing

TL;DR

This paper introduces an approximate functional differencing method that unifies existing solutions to the incidental parameter problem in panel data models, effective even with small T.

Contribution

It develops a unified framework connecting fixed-T differencing and large-T bias correction, enabling approximate solutions for a broader range of models.

Findings

Provides a new approximate functional differencing technique.

Unifies existing methods for incidental parameter problem.

Applicable to models with small T.

Abstract

Inference on common parameters in panel data models with individual-specific fixed effects is a classic example of Neyman and Scott's (1948) incidental parameter problem (IPP). One solution to this IPP is functional differencing (Bonhomme 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 2002 and Hahn and Newey 2004), but this is only guaranteed to work well when T is sufficiently large. This paper provides a unified approach that connects those 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.