Some strange properties of panel data estimators

We study the biases that are likely to arise in practice with panel data when parameters vary across individuals, but this is not allowed for in estimation. We consider both stationary and non-stationary regressors. We find that biases can be severe for relatively small parameter variation, and that this problem is hard to detect. We study in some detail by Monte-Carlo the performance of the Anderson-Hsiao estimator in the presence of this particular mis-specification.