Network formation and its Impact on Systemic Risk

In the aftermath of the financial crisis of 2008, many policy makers and researchers pointed to the interconnectedness of the financial system as one of the fundamental contributors to systemic risk. The argument is that the linkages between financial institutions served as an amplification mechanism: shocks to smaller parts of the system propagate through the system and result in broad damage to the financial system. In my dissertation, I explore the formation of networks when agents take into account systemic risk. The dissertation consists of three complementary papers on this topic. The first paper titled ``Network Formation and Systemic Risk\u27\u27, joint with Professor Rakesh Vohra. We set out the framework and construct a model of endogenous network formation and systemic risk. We find that fundamentally `safer\u27 economies with higher probability of getting good shocks generate higher interconnectedness, which leads to higher systemic risk. This provides network foundations for ``the volatility paradox\u27\u27 arguing that better fundamentals lead to worse outcomes due to excessive risk taking. Second, the network formed crucially depends on the correlation of shocks to the system. As a consequence, an observer, such as a regulator, facing an interconnected network who is mistaken about the correlation structure of shocks will underestimate the probability of system wide failure. This result relates to the ``dominoes vs. popcorn\u27\u27 discussion by Edward Lazear. He comments that a fundamental mistake in addressing the crisis was to think that it was ``dominoes\u27\u27 so that saving one firm would save many others in the line. He continues to argue that it was ``popcorn in a pan\u27\u27: all firms were exposed to same correlated risks and saving one would not save many others. We complement his discussion by arguing that the same mistake might have been the reason behind why sufficient regulatory precaution was not taken prior to the crisis. The third result is that the networks formed in the model are utilitarian efficient because the risk of contagion is high. This causes firms to minimize contagion by forming dense but isolated clusters that serve as firebreaks. This finding is suggestive that, the worse the contagion, the more the market takes care of it. In the second paper, titled ``Network Hazard and Bailouts\u27\u27, I ask how the anticipation of ex-post government bailouts affects network formation. I deploy a significant generalization of the model in the first paper and allow for time-consistent government transfers. I find that the presence of government bailouts introduces a novel channel for moral hazard via its effect on network architecture, which I call ``network hazard\u27\u27. In the absence of bailouts, firms form sparsely connected small clusters in order to eliminate second-order counterparty risk: expected losses due to defaulting counterparties that default because of their own defaulting counterparties. Bailouts, however, eliminate second-order counterparty risk already. Accordingly, when bailouts are anticipated, the networks formed become more interconnected, and exhibit a core-periphery structure (many firms connected to a smaller number of central firms, which is observed in practice). Interconnectedness within the periphery leads to higher extent of contagion with respect to the networks formed in the absence of intervention. Moreover, solvent core firms serve as a buffer against contagion by increasing the resilience of the many peripheral firms that are connected to the core. However, insolvent core firms serve as an amplifier of contagion since they make peripheral firms less resilient. This implies that in my model, ex-post time-consistent intervention by the government, while ex-ante welfare improving, increases systemic risk and volatility, solely through its effect on the network. A remark is that firms, in my model, do not make riskier individual choices regarding neither their choice of investment risk, nor the number of their counterparties they have. In this sense, network hazard is a genuine form of moral hazard solely through the formation of the detailed network. On another note, the model can also be viewed as a first attempt towards developing a theory of mechanism design with endogenously formed network externalities which might be useful in various other scenarios such as provision of local public goods. In the final paper, titled “Network Reactions to Banking Regulations”, joint with Professor Guilermo Ordonez, we consider the role of liquidity and capital requirements to alleviate network hazard and systemic risk. In the model, financial firms set up credit lines with each other in order to meet their funding needs on demand. Accordingly, higher liquidity requirements induce firms to form higher interconnectedness in order to be able to find deposits as needed. At a tipping point of liquidity requirements, the network discontinuously jumps in its interconnectedness, which contributes discontinuously to systemic risk. On the other hand, the reaction to capital requirements is smooth. Capital requirements indirectly work as an upper bound in the interconnectedness firms would form. This way, interconnectedness can be effectively reduced to a desired level via capital requirements. Yet capital requirements cannot be used to induce higher interconnectedness. Thusly, in times of credit freeze, capital requirements may not help promote circulation of credit. A conjunction of both liquidity and capital requirements is more effective in promoting desired circulation while reducing systemic risk. The work in this dissertation suggests that endogenous network architecture is an essential component of the study of financial markets. In particular, network hazard is a genuine form of moral hazard that will be overlooked unless network formation is taken into account, while it has implications about systemic risk. Moreover, this work illustrates how the reaction of networked financial markets to both fundamentals of the economy and to the policy can be non-trivial, featuring non-monotonicity and discontinuity

Analyzing Large Network Dynamics with Process Hitting

In this chapter, we introduce the Process Hitting framework, which provides the methodology of constructing the most permissive dynamics and then using successive refinements to fine tune the model. We present static analysis methods designed to identify fixed points or answer successive reachability questions, and introduce the stochastic semantics of Process Hitting too