This dissertation consists of three chapters. The first chapter examines Robert Shimer’s 2005 paper and the important puzzle in labor economics it documented: Conventional models which use Mortensen-Pissarides undirected search with Nash Bargaining over wages are unable to match the volatility of market tightness seen in the data. Although some headway has been made in resolving the puzzle, the main solutions have involved fundamental changes to the base framework of Shimer’s original model via changes in both bargaining and search protocols. This paper resolves the puzzle within the original framework through the introduction of agent heterogeneity. The second chapter presents a model of international transmission of financial shocks where the country of origin is fundamental to the transmission of the shock. A country is defined by the quality of its financial markets, with financially-developed countries better able to insure against idiosyncratic shocks. Highly developed countries tend to accumulate larger positions in riskier, but more productive, capital flows, as seen in the data. When a financial shock occurs, the ability to insure is impaired, which lessens demand for risky foreign capital, which lowers production abroad. We interpret the Financial Crisis of 2008 as a change in the ability of financial market quality and calibrate the model to match the change in capital flows. Importantly, the calibrated model matches not only changes in capital flows, but also relative movements in interest rates as well as changes in debt flows. The third chapter proposes a modification to the endogenous grid method that allows it to be used in multi-dimensional problems. It provides a background on interpolation problems, and various standard solutions. The paper then uses a Gaussian basis function for estimation of the standard economics utility problems, and compares the performance of this modification to standard methods of value function iteration. The solution method yields higher accuracy for lower grid point levels, but suffers from slower performance as the number of grid points increases. Further work is required to investigate the effectiveness of alternative basis functions for a variety of other utility forms.