Selman Erol
Tepper School of Business, Carnegie Mellon University
Papers
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Interbank Networks in the Shadows of the Federal Reserve Act
Central banks provide public liquidity (through lending facilities and promises of bailouts) with the intent to stabilize the financial system. Even though this provision is restricted to member (regulated) banks, an interbank system can provide indirect access to nonmember (shadow) banks. We construct a model to understand how a banking network may change in the presence of central bank interventions and how those changes affect financial fragility. We provide evidence showing that the introduction of the Fed’s liquidity provision in 1913 increased systemic risk through three channels; it reduced aggregate liquidity, created a new source of financial contagion, and crowded out private insurance for smoothing cross-regional liquidity shocks (manifested through the geographic concentration of networks).
I develop a novel framework for studying network formation with continuum populations. I use the framework to examine contagion and resilience in endogenous networks, with applications to misinformation, supply chains, financial contagion, and epidemics. I examine the equilibrium effects of policies that mitigate contagion externalities and find that interconnectedness and concentration increase in response to interventions. This general equilibrium response negates the benefits of interventions and creates a “network hazard.” Despite interventions that mitigate contagion ex post, contagion and volatility are exacerbated and welfare and resilience are reduced ex ante.
Regulating Clearing in Networks
Recent U.S. and European regulations promote centrally clearing derivatives to reduce complexity and systemic risk in the financial system. With a network model, we show that their effectiveness depends on clearing patterns. More clearing does not guarantee less systemic risk. Systemic risk can increase if multilateral netting increases at the expense of bilateral netting. We study confidential derivatives regulatory data and find evidence that contagion is less likely to start in the core but more likely to spread from the core. We introduce concepts of complexity and centrality within the financial network, exploring their implications for stability and regulatory oversight.
Financial System Architecture and Technological Vulnerabilities
This paper presents a framework to study of technological resiliency of financial system architecture. Financial market infrastructures, or platforms, compete with services critical functions along various stages in the lifecycle of a trade, and make investments in technological resiliency to guard against attackers seeking to exploit system weaknesses. Platforms’ financial network effects attenuate competition between platforms on security. Exposure to vulnerabilities is magnified in the presence of strategic adversaries. Private provision of technological resiliency is generally sub-optimal, with over- and underinvestment in security depending on market structure. Vulnerabilities evolve over the maturity of a financial system, but there generically exists a tipping point at which technological resiliency diverges from optimal and creates technological drag on the financial system. We find supportive evidence in tri-party repo settlement: the exit of duopolist resulted in a significant drop in IT-related investment by the sole provider, even as peer firms ramp up investment.
Contagion in Graphons
The analysis of threshold contagion processes in large networks is challenging. While the lack of accurate network data is often a major obstacle, finding optimal interventions is computationally intractable even in well-measured large networks. To obviate these issues we consider threshold contagion over networks sampled from a graphon—a flexible stochastic network formation model—and show that in this case the contagion outcome can be predicted by only exploiting information about the graphon. To this end, we exploit a second interpretation of graphons as graph limits to formally define a threshold contagion process on a graphon for infinite populations. We then show that contagion in large but finite sampled networks is well approximated by graphon contagion. This convergence result suggests that one can design interventions for large sampled networks by first solving the equivalent problem for an infinite population interacting according to the limiting graphon. We show that, under suitable regularity assumptions, the latter is a tractable problem and we provide analytical characterizations for the extent of contagion and for optimal seeding policies in graphons with both finite and infinite agent types.
This paper introduces a model of endogenous network formation and systemic risk. In it, firms form joint ventures called ‘links’ which are subsequently subjected to either good or bad shocks. Bad shocks incentivize default. Links yield full benefits only if the counter-party does not subsequently default on the project. Accordingly, defaults triggered by bad shocks render firms insolvent and defaults propagate via links. The model yields three insights. First, stable networks with ex-ante identical agents exhibit a core–periphery structure. Second, an increase in the probability of good shocks increases systemic risk. Third, because the network formed depends on the correlation between shocks to links, an observer who misconceives the correlation will underestimate the probability of system-wide default by a factor of a half.
Relationship Externalities
We propose a model of network formation where agent’s payoffs depend on the connected component they belong to in a way that is specific enough to be tractable yet general enough to accommodate a number of economically relevant settings. Among them are formation in the presence of contagion via links and collaboration with spillovers. A key feature of this setting is that the externalities stem from links rather than nodes. We characterize stable and efficient networks. Under negative externalities, disjoint cliques are stable and efficient. Under positive externalities complete networks and star networks are stable. Efficient networks feature a mix: pineapple networks which consist of one large clique and a star network appended to each other.
Optimal regulatory restrictions on banks have to solve a delicate balance. Tighter regulations reduce the likelihood of banks’ distress. Looser regulations foster the allocation of funds toward productive investments. With multiple banks, optimal regulation becomes even more challenging. Banks form partnerships in the interbank lending market in order to face liquidity needs and to meet investment possibilities. We show that the interbank network can suddenly collapse when regulations are pushed beyond a critical level, with a discontinuous increase in systemic risk as the cross-insurance of banks collapses.
Insider Networks
How do insiders respond to regulatory oversight on the use of insider information? History suggests that they form more sophisticated networks to circumvent regulation. We develop a theory of the formation and regulation of insider information networks. We show that agents with sufficiently complex networks bypass any given regulatory environment. In response, regulators employ broad regulatory boundaries to combat gaming. Tighter regulation induces agents to migrate activity from existing social networks to a core-periphery insider network. A small group of agents endogenously arise as intermediaries for the bulk of transmissions.
Civil Liberties and Social Structure
Governments use coercion to aggregate distributed information relevant to governmental objectives –from the prosecution of regime-stability threats to terrorism or epidemics–. A cohesive social structure facilitates this task, as reliable information will often come from friends and acquaintances. A cohesive citizenry can more easily exercise collective action to resist such coercion, however. We present an equilibrium theory where this tension mediates the joint determination of social structure and civil liberties. We show that segregation and unequal treatment sustain each other as coordination failures: citizens choose to segregate along the lines of an arbitrary trait only when the government exercises unequal treatment as a function of the trait, and the government engages in unequal treatment only when citizens choose to segregate based on the trait. We characterize when unequal treatment against a minority or a majority can be sustained, and how equilibrium social cohesiveness and civil liberties respond to the arrival of widespread surveillance technologies, shocks to collective perceptions about the likelihood of threats or the importance of privacy, or to community norms such as codes of silence.
Dillenberger (2010) introduced the negative certainty independence (NCI) axiom, which captures the certainty effect phenomenon. He left open the question of whether there are continuous and monotone preference relations over simple lotteries that satisfy NCI but do not belong to the betweenness class of preferences considered by Chew (1989) and Dekel (1986). We answer this question in the affirmative.
Existence, Optimality and Dynamics of Equilibria with Endogenous Time Preference
This paper studies the dynamic implications of the endogenous rate of time preference depending on the stock of capital, in a one-sector growth model. The planner’s problem is presented and the optimal paths are characterized. We prove that there exists a critical value of initial stock, in the vicinity of which, small differences lead to permanent differences in the optimal path. Indeed, we show that a development trap can arise even under a strictly convex technology. In contrast with the early contributions that consider recursive preferences, the critical stock is not an unstable steady state so that if an economy starts at this stock, an indeterminacy will emerge. We also show that even under a convex–concave technology, the optimal path can exhibit global convergence to a unique stationary point. The multipliers system associated with an optimal path is proven to be the supporting price system of a competitive equilibrium under externality and detailed results concerning the properties of optimal (equilibrium) paths are provided. We show that the model exhibits globally monotone capital sequences yielding a richer set of potential dynamics than the classic model with exogenous discounting.
Various blockchain systems have been designed for dynamic networked systems. Due to the nature of the systems, the notion of “time” in such systems is somewhat subjective; hence, it is important to understand how the notion of time may impact these systems. This work focuses on an adversary who attacks a Proof-of-Work (POW) blockchain by selfishly constructing an alternative longest chain. We characterize optimal strategies employed by the adversary when a difficulty adjustment rule alà Bitcoin applies.
This paper studies a model of firms with endogenous bilateral exposures and government bailouts. It is shown that the anticipation of bailouts makes firms less concerned with the counterparty choices of their counterparties. This “network hazard” gives rise to large central firms. Bailouts can mitigate contagion but they can not restore output losses. Consequently, idiosyncratic bad shocks to large central firms generate large welfare losses. As such, bailouts create welfare volatility and systemic risk. Surprisingly, moral hazard on risk-return dimension is mitigated by bailouts. Ex-ante regulations can induce discontinuous changes in the network.
Higher availability and efficacy of protective measures against infectious diseases, such as vaccines, increases individuals’ propensity to socialize. Consequently, the number of visits to central points of interest (e.g., schools, gyms, grocery stores) and the rate of interactions with the agents employed therein (e.g., teachers, trainers, cashiers) increase. This opens more channels for the virus to transmit through the central agent or location. This leads to a manifestation of network hazard (Erol 2019). The infection rates can increase as protective measures become more effective and more available. Testable predictions of the theory are confirmed by the foot traffic data from 2019-2022 and historical COVID-19 vaccination and community transmission rates.
During the 1920-1921 recession, the Richmond Fed provided liquidity to its member banks to prevent a banking crisis. Using newly digitized data on interbank borrowing and deposits for Virginia state banks, we analyze how the Richmond Fed’s liquidity provision affected the interactions between the funding role and the payment role of the interbank system and financial stability. We show that the Richmond Fed’s liquidity provision enabled members to lend discount window liquidity to nonmembers that experienced large deposit outflows and prevented the mass withdrawal of interbank deposits. Interestingly, the banks with interbank borrowing reduced interbank deposits placed in lending banks, implying that these correspondents provided liquidity to nonmembers through both interbank loans and deposits. Our study shows that understanding the interaction between different types of networks is important to promote the stability of the banking system.
Dealing with pandemics, such as the recent COVID-19 virus, has highlighted the critical role of social distancing to avoid contagion and deaths. New technologies that allow replacing in-person for at-distance activities have blurred the mapping between social and economic distancing. In this paper we model how individuals react to social distancing guidelines by changing their network of economic relations, affecting total output, wealth inequality, and long-term growth.