Introduction

Economists are well aware of the fact that the behavior of economic agents often is critically conditioned by latent (unobservable) variables. It is, therefore, hardly surprising that latent variable models have received increased attention over recent years (made possible by impressive advances in computing power). A few references are Aigner et al. (1983), Heckman (1981), Heckman and McCurdy (1980), McFadden (1989), and Pakes and Pollard (1989).

Estimation of latent variable models requires the elimination of the latest variables by marginalization, i.e., by integration of the joint sampling density of the observables and unobservables, in the case of continuous variables. Analytical solutions for such integrals generally are not available (with the important exception of linear Gaussian models for whose evaluation there exist analytical recurrence relationships).

In general one has to rely upon numerical integration. The problem is further complicated by the fact that latent variables often are inherently dynamic to the effect that their elimination requires interdependent (high-dimensional) numerical integration.

Until recently high-dimensional numerical integration could not be evaluated with sufficient numerical accuracy at any level of generality. This explains why a number of techniques had been developed over the years which circumvent this problem. For expository purposes we can usefully regroup these contributions into three broad categories:

1. Autocorrelation: the dynamics of the model are captured in the form of autocorrelated errors which can lead to operational likelihood functions (see, e.g., Laffont and Monfort (1979) for an innovative example in the context of disequilibrium models);

2. […]