Are COVID-19 fatalities large when a federal government does not enforce containment policies and instead allow states to implement their own policies? We answer this question by developing a stochastic extension of a SIRD epidemiological model for a country composed of multiple states. Our model allows for interstate mobility. We consider three policies: mask mandates, stay-at-home orders, and interstate travel bans. We fit our model to daily U.S. state-level COVID-19 death counts and exploit our estimates to produce various policy counterfactuals. While the restrictions imposed by some states inhibited a significant number of virus deaths, we find that more than two-thirds of U.S. COVID-19 deaths could have been prevented by late November 2020 had the federal government enforced federal mandates as early as some of the earliest states did. Our results quantify the benefits of early actions by a federal government for the containment of a pandemic.

This thesis presents new developments in the literature of non-negative affine interest rate models. The first chapter is devoted to the introduction of the main mathematical tools used in the following chapters. In particular, it presents the so-called affine processes which are extensively employed in no-arbitrage interest rate models. Chapter 2 provides a new filtering and estimation method for linear-quadratic state-space models. This technique is exploited in the 3rd chapter to estimate a positive asset pricing model on the term structure of Euro area interbank spreads. This allows us to decompose the interbank risk into a default risk and a liquidity risk components. Chapter 4 proposes a new recursive method for building general multivariate affine processes from their univariate counterparts. In particular, our method does not impose the conditional independence between the different vector elements. We apply this technique in Chapter 5 to produce multivariate non-negative affine processes where some components can stay at zero for several periods. This process is exploited to build a term structure model consistent with the zero lower bound features.