| The comparison of alternative econometric models is a problem of significant interest in statistical theory and applied work. This dissertation consists of three essays that develop new simulation-based techniques for estimation and comparison of competing parametric, semiparametric, and nonparametric models.;The first essay examines the problems of estimation and model comparison in the setting of a model for binary panel data with state dependence, serial correlation, unobserved heterogeneity, and an unknown covariate functional form. Efficient MCMC methods are developed for posterior simulation, estimation of the marginal likelihood, and calculation of the average covariate effects. A simulation study suggests that the estimation techniques perform well. An application to women's labor force participation illustrates that the methods are practical and useful in uncovering important features of the data. In particular, Bayes factors strongly support a two-lag semiparametric model, where, in addition to a random intercept, the effects of pre-school children on female labor supply are unit-specific and are correlated with the husband's earnings.;The second essay considers the specification, estimation, and comparison of nonparametric additive models. A new scheme is used to identify the unknown covariate functions; estimation of these functions and the model parameters is by a new efficient MCMC sampling procedure. In contrast to previous applications, the smoothness priors and identification approach enable Bayesian model comparison with marginal likelihoods and Bayes factors instead of asymptotic criteria such as BIC and AIC. The methods in this essay thus lead to a complete inferential toolkit for the important class of semiparametric and nonparametric additive models. Applications of the techniques to simulated and real data are also presented.;The final essay of this dissertation tackles the model comparison problem for models in which the posterior distribution is simulated via the accept-reject Metropolis-Hastings algorithm. A method for estimating the marginal likelihood is developed from the building blocks of that simulation algorithm, even though its proposal density has an unknown normalizing constant. The method is straightforward, efficient, and economical in terms of programming, additional tuning effort, and computational intensity. The approach is widely applicable as it can accommodate single- and multi-block samplers. |
