Some Strange Properties of Panel Data Estimators

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.
1. INTRODUCTION
Econometric investigations often seek to exploit the extra information available in panel data,
e.g. panels of individual consumers, firms, etc., or panels of countries, provinces, regions, etc.
Inference often proceeds by imposing equality restrictions on parameters, across individuals
or through time: indeed this is the point of the exercise. Consider a fairly general specification
where i = 1, N indexes individuals, t = 1, T indexes time, xit is an exogenous regressor, &it is
some residual, and an individual-specific constant fixed through time. It is usually hoped that
f, will control for differences between individuals. The existing literature tends to stress the
case ai= a, all i, and explores consistent estimation of the above (Nickell, 1981, Anderson and
Hsiao, 1982). In this paper we investigate problems that arise when the restriction = a is
false, but imposed in estimation. We shall see this specification error can cause serious
problems, likely to be important in practice.