Understanding Bias in Nonlinear Panel Models: Some Recent Developments∗

The purpose of this paper is to review recently developed bias-adjusted methods of estimation of nonlinear panel data models with fixed effects. Standard estimators such as maximum likelihood estimators are usually inconsistent if the number of individuals n goes to infinity while the number of time periods T is held fixed. For some models, like static linear and logit regressions, there exist fixed-T consistent estimators as n →∞ (see, e.g., Andersen, 1970). Fixed T consistency is a desirable property because for many panels T is much smaller than n. However, these type of estimators are not available in general, and when they are, their properties do not normally extend to estimates of average marginal effects, which are often parameters of interest. Moreover, without auxiliary assumptions, the common parameters of certain nonlinear fixed effects models are simply unidentified in a fixed T setting, so that fixed-T consistent point estimation is not possible (see, e.g., Chamberlain, 1992). In other cases, although identifiable, fixed-T consistent estimation at the standard root-n rate is impossible (see, e.g., Honoré and Kyriazidou, 2000; Hahn, 2001). The number of periods available for many household, firm-level or country panels is such that it is not less natural to talk of time-series finite sample bias than of fixed-T inconsistency or underidentification. In this light, an alternative reaction to the fact that micro panels are short is to ask for approximately unbiased estimators as opposed to estimators with no bias at all. That is, estimators with biases of order 1/T 2 as opposed to the standard magnitude of 1/T . This alternative approach has the potential of overcoming some of the fixed-T identification difficulties and the advantage of generality. The paper is organized as follows. Section 2 describes fixed effects estimators and the incidental parameters problem. Section 3 explains how to construct analytical bias correction of estimators. Section 4 describes bias correction of