Since the last decade we live in a digitalized world where many actions in human and economic life are monitored. This produces a continuous stream of new, rich and high quality data in the form of panels, repeated cross-sections and long time series. These data resources are available to many researchers at a low cost. This new era is fascinating for econometricians who can address many open economic questions. To do so, new models are developed that call for elaborate estimation techniques. Fast personal computers play an integral part in making it possible to deal with this increased complexity.
This chapter reviews econometric models for which statistical inference requires intensive numerical computations. A common feature of such models is that they incorporate unobserved (or latent) variables, in addition to observed ones. This often implies that the latent variables have to be integrated from the joint distribution of latent and observed variables. The implied integral is typically of high dimension and not available analytically. Simulation methods are almost always required to solve the computational issue, but they bring new problems. A general introduction on simulation based inference can be found in [27] and [38].
The organisation of this chapter is as follows. The first section deals with limited dependent variable models, with a focus on multi-period discrete choice dynamic models. The second section treats the stochastic volatility (SV) model, used in finance and financial econometrics to calibrate the volatility of asset returns, as an alternative to the class of generalized autoregressive conditional heteroskedastic (GARCH) models. It also reviews related dynamic duration models. The last section deals with finite mixture models. Illustrative applications drawn from the recent literature are used. Programs and data are on the web site www.core.ucl.ac.be/econometrics/Bauwens/HBCS/HBCS.htm.
All the models discussed in this chapter are parametric. Nonparametric and semiparametric models may induce additional computational complexity. We refer to [42], [32] and Chap. III.10 of this volume for examples on these methods.