Essays in Computational Macroeconomics and Finance
This dissertation examines three topics in computational macroeconomics and finance. The first two chapters are closely linked; and the third chapter covers a separate topic in finance. Throughout the dissertation, I place a strong emphasis on constructing computational tools and modeling devices; and using them in appropriate applications. The first chapter examines how a central banks choice of interest rate rule impacts the rate of mortgage default and welfare. In this chapter, a quantitative equilibrium (QE) model is constructed that incorporates incomplete markets, aggregate uncertainty, overlapping generations, and realistic mortgage structure. Through a series of counterfactual simulations, five things are demonstrated: 1) nominal interest rate rules that exhibit cyclical behavior increase the average default rate and lower average welfare; 2) welfare can be substantially improved by adopting a modified Taylor rule that stabilizes house prices; 3) a decrease in the length of the interest rate cycle will tend to increase the average default rate; 4) if the business and housing cycles are not aligned, then aggressive inflation targeting will tend to increase the mortgage default rate; and 5) placing a legal cap on loan-to-value ratios will lower the average default rate and lessen the intensity of extreme events. In addition to these findings, this paper also incorporates an important mechanism for default, which had not pre- viously been included in the QE literature: default spikes happen when income falls and home equity is degraded at the same time. The paper concludes with a policy recommendation for central banks: if they wish to crises where many households default simultaneously, they should either adopt a rule that generates interest rates with slow-moving cycles or use a modified Taylor rule that also targets house price growth. The second chapter generalizes the solution method used in the first and compares it to more common techniques used in the computational macroeconomics literature, including the parameterized expectations approach (PEA), projection methods, and value function iteration. In particular, this chapter compares the speed and accuracy of the aforementioned modifications to an alternative method that was introduced separately by Judd (1998), Sutton and Barto (1998), and Van Roy et al. (1997), but was not developed into a general solution method until Powell (2007) introduced it to the Operations Research literature. This approach involves rewriting the Bellman equation in terms of the post-decision state variables, rather than the pre-decision state variables, as is done in standard dynamic programming applications in economics. I show that this approach yields considerable performance benefits over common global solution methods when the state space is large; and has the added benefit of not forcing modelers to assume a data generating process for shocks. In addition to this, I construct two new algorithms that take advantage of this approach to solve heterogenous agent models. Finally, the third chapter imports the SIR model from mathematical epidemiol- ogy; and uses it to construct a model of financial epidemics. In particular, the paper demonstrates how the SIR model can be microfounded in an economic context to make predictions about financial epidemics, such as the spread of asset-backed securities (ABS) and exchange-traded funds (ETFs), the proliferation of zombie financial institutions, and the expansion of financial bubbles and mean-reverting fads. The paper proceeds by developing the 1-host SIR model for economic and financial contexts; and then moves on to demonstrate how to work with the multi-host version of the model. In addition to showing how the SIR framework can be used to model economic interactions, it will also: 1) show how it can be simulated; 2) use it to develop and estimate a sufficient statistic for the spread of a financial epidemic; and 3) show how policymakers can impose the financial analog of herd immunity-that is, prevent the spread of a financial epidemic without completely banning the asset or behavior associated with the epidemic. Importantly, the paper will focus on developing a neutral framework to describe financial epidemics that can be either bad or good. That is, the general framework can be applied to epidemics that constitute a mean-reverting fad or an informational bubble, but ultimately yield little value and shrink in importance; or epidemics that are long-lasting and yield a new financial in- strument that generates permanent efficiency gains or previously unrealized hedging opportunities.