Bayesian Model Selection and Dynamic Factor Models
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Bayesian Model Selection and Dynamic Factor Models


This dissertation focuses on bringing to light several innovations to models typically used by Bayesian econometricians. In the world of statistics, one can take either the Classical Neyman-Pearson Frequentist approach, or the subjectivist view advocated, first by the Reverend Thomas Bayes and formalized more recently, most notably by De Finetti. The methods are of particular interest to economists, however, the techniques are applicable to any discipline relying on statistics. Additionally there is substantial attention given to estimating the model evidence for each of these novel models, so that competing models can be compared and contrasted. A strength of the Bayesian paradigm is the ease with which one can compare models, even those that are non-nested. The applications used in this dissertation make use of this fact. The first chapter provides improvement to the traditional methods of estimating multilevel dynamic factor models (MLDFMs). MLDFMs have been used in economics as a popular way of estimating global, regional, and country business cycles. The use of factors, especially in macroeconomics, is a useful way to estimate correlation between multiple data series. Using them to estimate multiple simultaneous factors is an extension given by Kose (2003), but which I extend in this chapter. In addition, I discuss how useful a global factor is to the model when observables are included. The findings from this research are helpful to the synchronization or decoupling debate extant in the LDV (Limited Dependent Variable) literature. Decoupling and convergence has been debated in the macroeconomic literature since at different times and by different researchers the amount of explanatory power arising from a global factor has differed in a significant manner. Because of the flexibility of the Bayesian approach I am also able to derive a method of testing for breakpoints in the sample period using the Bayes factors. The second chapter uses the methods from the second chapter but in an entirely new setting, the multivariate probit model (MVP). The MVP is a suitable way to model correlated binary data. For instance, the way an individual votes on several issues, or the binary choice of features in a vehicle would be obvious situations to use this model. The difficulty with the MVP model is its identification requires a correlation matrix. The problem is then producing suitable draws from a correlation matrix since the typical Wishart or inverse Wishart distribution would give a covariance matrix. Generating draws meeting the restrictions of between -1 to 1 and also positive definiteness requires some creative approaches. Factor models, however, are suitable for just this kind of situation. They can summarize the correlation between equations quite well, and reduce the parameter space significantly. However, until this research factor models have not been used in LDV models before, as far as I could tell by a review of the literature in this area. This research opens up the door of possibility for much larger dimensional LDV models than have previously been considered since factor models can parsimoniously estimate correlation matrices, given the underlying stochastic process can be written in factor form. The last chapter handles a type of modeling situation which arises due to constraints upon the parameters space that are necessary either because of theoretical or practical reasons. Research in this area was inspired from the Bayesian limited dependent variable literature (LDV), which for its own reasons developed methods of integration that are also useful in calculating marginal likelihoods. Taking those methods and adapting them to the situation of a truncated parameter space is a natural connection between the two seemingly unrelated literatures.

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