In this chapter we briefly consider some miscellaneous topics. We shall first consider statistical inference using simulation methods (Section 10.1). We shall then consider panels with both large N and large T (Section 10.2), leading to the discussion of the specific issue of unit-root tests (Section 10.3). Section 10.4 will discuss panels with more than two dimensions. Section 10.5 considers issues of measurement errors and indicates how one can take advantage of the panel structure to identify and estimate an otherwise unidentified model. Finally, we discuss proposals for relaxing the cross-section independence assumption apart from the specification of the individual-invariant time-varying factors.

SIMULATION METHODS

Panel data contain two dimensions – a cross-sectional dimension and a time dimension. Models using panel data also often contain unobserved heterogeneity factors. To transform a latent variable model involving missing data, random coefficients, heterogeneity, etc., into an observable model often requires the integration of latent variables over multiple dimensions (e.g., Hsiao (1989, 1991b, 1992c)). The resulting panel data model estimators can be quite difficult to compute. Simulation methods have been suggested to get around the complex computational issues involving multiple integrations (e.g., Gourieroux and Monfort (1996); Hsiao and Wang (2000); Keane (1994); McFadden (1989); Pakes and Pollard (1989)).

The basic idea of the simulation approach is to rely on the law of large numbers to obtain the approximation of the integrals through taking the averages of random drawings from a known probability distribution function.