Grouped effects estimators in fixed effects models

We consider estimation of nonlinear panel data models with common and individual specific parameters. Fixed effects estimators are known to suffer from the incidental parameters problem, which can lead to large biases in estimates of common parameters. Pooled estimators, which ignore heterogeneity across individuals, are also generally inconsistent. We assume that individuals in the data are grouped on multiple levels where groups are defined by some observable external classification. We consider “group effects” estimators, where individual specific parameters are assumed common across groups at some level. We provide conditions under which group effects estimates of common parameters are asymptotically unbiased and normal. The conditions suggest a tradeoff between two sources of bias, one due to incidental parameters and the other due to misspecification of unobserved heterogeneity.