Mapping Networks to Probability Distributions in the Economy

Abstract

This dissertation develops and applies a set of theoretical tools that allows us to explicitly map the topologies of networks in the economy to different probability distributions of interest. The first chapter, "The Distribution of Outcomes for a Networked Economy," develops a set of tools for mapping the topology of a network to a probability distribution of possible outcomes for the economy. I adapt these tools to study locally formed macroeconomic sentiment and how agents' interaction structure shapes the capacity for there to exist non-fundamental swings in aggregate macroeconomic sentiment, with implications for our understanding of animal spirits. I can apply these tools to analyze complex systems in closed form and to construct error bounds about the paths of aggregated networked economies. In the second chapter, "The Distribution of Multipliers in a Networked Economy," there is a policymaking actor who wants to increase the aggregate action in a networked population of N agents. To achieve that goal, the policymaker implements a policy targeting n < N agents. This second chapter studies how the topology of agents' interaction network shapes the distributions of possible policy-induced aggregate actions and economic multipliers. I study a general networked setting and three environments with network-based interaction: (1) strategic complements and substitutes, (2) coordination and anti-coordination, and (3) production. Given n, for each environment, I map the network topology to distributions of possible resulting aggregate actions and multipliers. The third chapter, "Comprehensively Stress Testing the Economy," addresses two main weaknesses in the Federal Reserve's stress testing approach: (1) the number of stress tests faced by each financial institution is quite small, and (2) the Federal Reserve's toolkit is not sufficiently macroprudential. Employing a macroprudential approach, this chapter shows how to massively increase the total number of stress tests without increasing the computational burden. I generate classes of stress tests with large cardinalities; for each class, I construct probability distributions that capture the full range of possible balance sheet effects for individual financial institutions and the overall financial system. This approach shows how the topologies of bipartite networks linking financial institutions to assets shape stress tests' effects.