In the first chapter, the authors propose a new Bayesian synthetic control framework to overcome limitations of extant synthetic control methods (SCMs). The proposed Bayesian synthetic control methods (BSCMs) do not impose any restrictive constraints on the parameter space a priori. Moreover, the proposed model provide statistical inference in a straightforward manner and a natural mechanism to deal with the “large p, small n” and sparsity problems through Markov Chain Monte Carlo (MCMC) procedures. The authors find via simulations that for a variety of data generating processes, the proposed BSCMs almost always provide better predictive accuracy and parameter precision than extant SCMs. They demonstrate an application of the proposed BSCMs to a real-world context of a tax imposed on soda sales in Washington state in 2010. As in the simulations, the proposed models outperform extant models, as measured by predictive accuracy in the post-treatment periods. They find that the tax led to an increase of 5.7% in retail price and a decrease of 5.5\sim5.8% in sales. They also find that retailers in Washington over-shifted the tax to consumers, leading to a pass-through rate of about 121%. In the second chapter, the authors develop a utility-based multiple discrete-continuous model of charitable giving that provides insights into potentially large differences in individuals' giving behaviors across forms of giving. The model also incorporates via Bayesian Gaussian processes changes in givers’ preferences for forms of giving, as the relationship with the NPO evolves. The authors apply their model to five years of giving data of a cohort of individuals. They find that the effects of lifetime, recency, seasonality, and responsiveness to appeals of donation and membership options change non-monotonically over time in distinctive ways. Moreover, they find substantial individual heterogeneity in preference for forms of giving. The authors demonstrate that the model estimates help to predictively identify who will give in multiple forms in the future, and to build appeal targeting strategies. In the third chapter, the authors try to answer two questions: i) What are the long-term impacts of the Philadelphia beverage tax on sales and prices of taxed beverage categories?, and ii) Do the impacts of the beverage tax spill over to other non-taxed product categories? They plan to empirically investigate various healthy and unhealthy potential complements and substitutes of the beverage category to study the spillover effects of the beverage tax in Philadelphia. The goal of essay 3 is to propose a research idea for which the empirical analysis would be completed subsequent to the Ph.D.