This dissertation consists of three essays. The first essay analyzes the effects of fixed costs in generating country pairs that do not trade or do foreign direct investment, and how incorporating such country pairs changes the welfare gains one computes from policy reform. Despite the enormous growth over the past several decades in global trade and investment, most countries still do not trade or invest with one other. Using a recently commissioned dataset, I document that 80% of bilateral trade and FDI relationships are zeros. I construct a model that rationalizes these zeros and allows bilateral relationships to form (aggregate zero-to-one transitions) following policy reform. Exact equilibria do not generically exist in the resulting multidimensional discrete-choice fixed point problem. I develop an algorithm that computes an approximate equilibrium where (1) countries engage in more than 99% of all profitable bilateral relationships available to them, and (2) where 99% of the bilateral relationships they engage in yield positive profits. Relative to models with no aggregate entry or exit, the gains from openness in the model where zeros matter are higher by 30% on average, with the discrepancy larger for countries in the developing world.In the second essay, I study the impact of international trade on the rise of the service economy. Services now constitute the majority of both value added and labor in the developed world, and its share is rising still. Trade in services, however, comes nowhere near that level as a fraction of aggregate trade, with few service providers exporting to foreign destinations. Moreover, while productivity growth in services as a whole has lagged behind the rest of the economy, service exporters are more productive, sell more, and hire more workers than their domestic counterparts. I construct a Heckscher-Ohlin model where firms have heterogeneous productivity levels and show that the asymmetric lowering of trade barriers across sectors can qualitatively account for all these facts. The model predicts that labor in skill-abundant countries should move into services. It also features endogenous selection into export markets, with exporters being more productive, selling more, and making more profits than domestic producers. Furthermore, as barriers to service trade remain high relative to non-services, the positive effect that foreign competition in the model has on sector-level average productivity is weaker, generating slower growth in service productivity. These results are shown to be robust to the introduction of intermediates and capital.In the third essay, I examine the role of debt auctions on quantitative models of sovereign default. Government bonds with default risk are often sold by auction, whether competitive or discriminatory. In standard models of sovereign default, the pricing protocol stipulates the existence of perfectly informed risk-neutral foreign creditors with flat demand curves that price bonds uniformly so they break even in expected value. In contrast, this paper follows the auction literature in assuming that creditors face downward sloping demand curves and uncertainty over the stop-out price at which bonds are sold. The interaction of this auction component with default risk has a significant impact on both the level of government borrowing and probability of default. Further, the auction mechanism matters: if bonds are sold using a competitive auction, it is optimal for lenders to bid their true valuation; in contrast, agents have an incentive to understate their valuation under a discriminatory auction protocol. Understanding the tradeoffs inherent in the choice between competitive and discriminatory bond auctions in the presence of default are particularly pertinent for countries that have historically been vulnerable to sovereign debt crises.