| Data available to economists is often incomplete. Frequently values of the explanatory variables cannot be observed or are observed with a noise. To deal with the data limitation problems, various latent variable models have been considered in the econometric and statistic literature. In this thesis, we examine two categories of these models and propose new approaches to estimation and inference. The first category consists of regression models with unobserved explanatory variables, such as expectational variables. The second category contains models of financial time series with a latent process of stochastic volatility. In the first essay, we focus on inference in regression models while the stochastic volatility models are discussed in essays two and three.;Finite sample tests and confidence sets for models with unobserved and generated regressors as well as various models estimated by instrumental variable method are first proposed. We study two distinct approaches for various models considered by Pagan (1984). The first one is an instrument substitution method which generalizes an approach proposed by Anderson and Rubins (1949) and Fuller (1987) for different (although related) problems, while the second one is based on splitting the sample. The instrument substitution method uses the instruments directly, instead of generated regressors, in order to test hypotheses about the "structural parameters" of interest and build confidence sets. The second approach relies on "generated regressors", which allows a gain in degrees of freedom, and a sample split technique. A distributional theory is obtained under the assumptions of Gaussian errors and strictly exogenous regressors.;In the second essay, we study stochastic volatility models with time deformation. Such processes relate to early works by Mandelbrot and Taylor (1967), Clark (1975), Tauchen and Pitts (1983), among others. In our setup, the latent process of stochastic volatility evolves in an operational time which differs from calendar time. The time deformation can be determined by part volume of trade, part price changes, possibly with an asymmetric leverage effect, and other variables setting the pace of information arrival.;We finally study trading patterns, time deformation and stochastic volatility in foreign exchange markets. One way to model such phenomena is to adopt a framework where market volatility is tied to the intensity of (world) trading through a subordinated stochastic process representation. (Abstract shortened by UMI.). |
