Bayesian analysis of some pricing and discounting models
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The dissertation comprises an introductory Chapter, four papers and a summary Chapter. First, a new class of Bayesian dynamic partition models for the Nelson- Siegel family of non-linear state-space Bayesian statistical models is developed. This class is applied to studying the term structure of government yields. A sequential time series of Bayes factors, which is developed from this approach, shows that term structure could act as a leading indicator of economic activity. Second, we develop a class of non-MCMC algorithms called “Direct Sampling”. This Chapter extends the basic algorithm with applications to Generalized Method of Moments and Affine Term Structure Models. Third, financial economics is characterized by long-standing problems such as the equity premium and risk free rate puzzles. In the chapter titled “Bayesian Learning, Distributional Uncertainty and Asset-Return Puzzles” solutions for equilibrium prices under a set of subjective beliefs generated by Dirichlet Process priors are developed. It is shown that the “puzzles” could disappear if a “tail thickening” effect is induced by the representative agent. A novel Bayesian methodology for retrospective calibration of the model from historical data is developed. This approach shows how predictive functionals have important welfare implications towards long-term growth. Fourth, in “Social Discounting Using a Bayesian Nonparametric model” the problem of how to better quantify the uncertainty in long-term investments is considered from a Bayesian perspective. By incorporating distribution uncertainty, we are able to provide confidence measures that are less “pessimistic” when compared to previous studies. These measures shed a new and different light when considering important cost-benefit analysis such as the valuation of environmental policies towards the resolution of global warming. Finally, the last Chapter discusses directions for future research and concludes the dissertation.