March 2023. "Social Learning in a Network Model of Covid-19" (with Allan Davids, Gideon du Rand, Tina Koziol, and Joeri Schasfoort) [abstract] [paper] [github] - Journal of Economic Behaviour and Organization 213, (2023)
This paper studies the effects of social learning on the transmission of Covid-19 in a network model. We calibrate our model to detailed data for Cape Town, South Africa and show that the inclusion of social learning improves the prediction of excess fatalities, reducingthe best-fit squared difference from 20.06 to 11.28. The inclusion of social learning both flattens and shortens the curves for infections, hospitalizations, and excess fatalities. This result is qualitatively different from flattening the curve by reducing transmission probability through non-pharmaceutical interventions. While social learning reduces infections, this alone is not sufficient to curb the spread of the virus because learning is slower than the disease spreads. We use our model to study the efficacy of different vaccination strategies and find that a risk-based vaccination strategy--vaccinating vulnerable groups first--leads to a 50% reduction in fatalities and 5% increase in total infections compared to a random-order benchmark. By contrast, using a contact-based vaccination strategy reduces infections by 9% but results in 64% more fatalities relative to the benchmark.
We introduce social learning into an epidemiological network model of Covid-19 and show that this significantly improves the forecast of excess fatalities. We use the model to study different vaccination strategies.
November 2022. "Exit Spirals in Coupled Networked Markets" (with Christoph Aymanns and Ben Golub) [abstract] [paper] - Operations Research 71(5), (2023)
Strategic agents choose whether to be active in networked markets. The value of being active depends on the activity choices of specific counterparties. Several markets are \emph{coupled} when agents' participation decisions are complements across markets. We model the problem of an analyst assessing the robustness of coupled networked markets during a crisis---an exogenous negative payoff shock---based only on partial information about the network structure. We give conditions under which \emph{exit spirals} emerge---abrupt collapses of activity following shocks. Market coupling is a pervasive cause of fragility, creating exit spirals even between networks that are individually robust. The robustness of a coupled network system can be improved if one of two markets is replaced by a centralized one, or if links become more correlated across markets.
The extent of exit spirals in coupled over-the-counter markets depends on the structure of the networked markets.
We study the role of informal collaboration in academic knowledge production using published research papers previously presented and discussed at the NBER Summer Institute. We show that papers that have a discussant are published in highly-ranked journals and are more likely to be published in a top journal. Conditional on having a discussant, the quality of a paper's journal outlet increases in the discussant's prolificness and editorial experience. This supports the idea that discussants help reduce information asymmetries that are inherent in the academic publication process. Conversely, using social network analysis we find no evidence that citations accumulate because discussants diffuse information about the paper.
Having a discussant reduces asymmetric information inherent in the academic publishing process.
February 2021. "What 5,000 Acknowledgements Tell Us About Informal Collaboration in Financial Economics" (with Michael Rose) - Research Policy 50(6) (2021) [abstract] [paper] [data repo]
[voxeu].
Formal collaboration between researchers via co-authorship has been shown to have a positive impact on academic productivity. But most academic collaboration is informal, e.g. in the form of commentary on research papers. We present and discuss a novel dataset on informal collaboration in Financial Economics obtained from the acknowledgement sections of over 5,000 published research papers. We construct the social network of informal collaboration connecting authors and commenters and show that a researcher’s position in this network is predictive of her future productivity and the scholarly impact of the papers she comments on. We study the characteristics of the network using various measures from network theory and characterize what determines a researcher’s position in it.
Financial economists collaborate by commenting on each other's papers. We use the information captured in acknowledgements, construct the social network of informal collaboration, and highlight several interesting stylized facts.
November 2020. "Systemic Risk-Shifting in Financial Networks" (with Matthew Elliott and Jonathon Hazell), Journal of Economic Theory 191 (2021). [abstract] [paper]
Banks face different but potentially correlated risks from outside the financial system. Financial connections can help hedge these risks, but also create the means by which shocks can propagate. We examine this tradeoff in the context of a new stylised fact we present: German banks are more likely to have financial connections when they face more similar risks—potentially undermining the hedging role of financial connections and contributing to systemic risk. We find that such patterns are socially suboptimal, but can be explained by risk-shifting. Risk-shifting motivates banks to correlate their failures with their counterparties even though it creates systemic risk.
We provide a novel mechanism why banks would lend to other banks that have similar real exposures and show that predictions of our model are in line with empirical evidence from Germany.
May 2017. "Information Contagion and Systemic Risk" (with Toni Ahnert), Journal of Financial Stability 35 (2017). [abstract] [paper]
We examine the effect of ex-post information contagion on the ex-ante level of systemic risk defined as the probability of joint default of banks. Because of counterparty risk or common exposures, bad news about one bank reveals valuable information about another bank and trigger information contagion. When banks are subject to common exposures, information contagion induces small adjustments to bank portfolios and therefore increases systemic risk overall. When banks are subject to counterparty risk, by contrast, information contagion induces a large shift toward more prudential portfolios and therefore reduces systemic risk.
Information contagion can reduce systemic risk if banks lend to each other because ex-post counterparty risk leads to more prudent ex-ante portfolio choice.
January 2015.
"Contagious Synchronization and Endogenous Network Formation in Financial Networks" (with Christoph Aymanns), Journal of Banking and Finance 50(1) (2015). [abstract] [paper] [code available upon request]
When banks choose similar investment strategies the financial system becomes vulnerable to common shocks. We model a simple financial system in which banks decide about their investment strategy based on a private belief about the state of the world and a social belief formed from observing the actions of peers. Observing a larger group of peers conveys more information and thus leads to a stronger social belief. Extending the standard model of Bayesian updating in social networks, we show that the probability that banks synchronize their investment strategy on a state non-matching action critically depends on the weighting between private and social belief. This effect is alleviated when banks choose their peers endogenously in a network formation process, internalizing the externalities arising from social learning.
Banks act based on a private and a social signal in a simple extension of Bayesian learning. The social signal is stronger if banks observe a larger group of peers which leads to correlated investment strategies of highly interconnected banks.
February 2013.
"The Effect of the Interbank Network Structure on Contagion and Common Shocks", Journal of Banking and Finance 37(7) (2013). [abstract] [paper] [code]
This paper proposes a dynamic multi-agent model of a banking system with central bank. Banks optimize a portfolio of risky investments and riskless excess reserves according to their risk, return, and liquidity preferences. They are linked via interbank loans and face stochastic deposit supply. Evidence is provided that the central bank stabilizes interbank markets in the short-run only. Comparing different interbank network structures, it is shown that money-center networks are more stable than random networks. Systemic risk via contagion is compared to common shocks and it is shown that both forms of systemic risk require different optimal policy responses.
A dynamic multi-agent model of the financial system. The interbank network structure does not always affect financial stability and central bank liquidity provision can stabilize the interbank market in the short-run only.
We propose a framework to study regulatory complexity, based on concepts from computer science. We distinguish different dimensions of complexity, classify existing measures, develop new ones, compute them on three examples—Basel I, the Dodd-Frank Act, and the European Banking Authority’s reporting rules—and test them using experiments and a survey on compliance costs. We highlight two measures that capture complexity beyond the length of a regulation. We offer a quantitative approach to the policy trade-off between regulatory complexity and precision. Our toolkit is freely available and allows researchers to work on other texts and test alternative measures.
The amount of (financial) regulation has increased significantly over the past decades. But has regulation really become more complex? We propose to use measures of software complexity to provide a more nuanced answer to this question and test our measures empirically for a range of financial regulations.
Update.June 2025. "Contagious Zombies" (with Christian Bittner and Falko Fecht) [abstract] [paper] - Revision requested, Journal of Financial Stability
Does banks' zombie lending induced by unconventional monetary policy also allow zombie firms to leverage their trade credit borrowing? We first provide evidence suggesting that—even in Germany—particularly weak banks used the European Central Bank's very long-term refinancing operations (VLTROs) to evergreen exposures to zombie firms, which in turn elevated credit risk. Second, we show that zombie firms, which obtained additional funding from banks relying to a larger extent on VLTRO funding, also increased their accounts payable and advance payments received from downstream and upstream firms. And third, zombie firms that obtained further bank funding and such trade credit after the VLTROs had an elevated expected default probability even compared to average zombie firms. This suggests that suppliers relying on banks' lending decisions as a signal about borrowers' credit quality might be misled by banks' zombie lending to extend more trade credit to zombie firms exposing suppliers to elevated contagion risk.
Particularly weak German banks make use of the ECB's long-term refinancing operations to evergreen exposures to zombie firms. These firms, in turn, obtain more trade credit from other firms.
We test the prediction that investors divest from an asset in anticipation of large liquidation costs when their portfolio similarity with other asset holders is high. We provide evidence supporting this hypothesis using detailed data on money market funds that invest in the debt securities of financial institutions. We develop an instrument that exploits variation in portfolio similarity driven by idiosyncratic redemptions from other funds to confirm our results. Consistent with our hypothesis, the effect of portfolio similarity on divestment is stronger for ex-post illiquid securities, for more illiquid and diversified funds, and for actively managed institutional funds.
Mutual funds reduce their exposure to a security issuer more if they are more similar to other funds investing in the same security issuer. This increases issuers' liquidity risk.
November 2024. "Vulnerability Webs: Systemic Risk in Software Networks" (with Cornelius Fritz, Angelo Mele, and Michael Schweinberger) [abstract] [paper]
Modern software development is a collaborative effort that re-uses existing code to reduce development and maintenance costs. This practice exposes software to vulnerabilities in the form of undetected bugs in direct and indirect dependencies, as demonstrated by the Crowdstrike and HeartBleed bugs. The economic costs resulting from such vulnerabilities can be staggering. We study a directed network of 52,897 software dependencies across 16,102 Python repositories, guided by a strategic model of network formation that incorporates both observable and unobservable heterogeneity. Using a scalable variational approximation of the conditional distribution of unobserved heterogeneity, we show that outsourcing code to other software packages by creating dependencies generates negative externalities. Modeling the propagation of risk in networks of software packages as an epidemiological process, we show that increasing protection of dependencies based on popular heuristics is ineffective at reducing systemic risk. By contrast, AI-assisted coding enables developers to replace dependencies with in-house code and reduces systemic risk.
Reusing code creates dependencies between software packages. We present a model of strategic network formation to describe how directed dependency networks form and study how susceptible these networks are to vulnerability contagion.
How likely is financial contagion when banks anticipate an aggregate liquidity shock and what are the consequences for bank choices, welfare, and regulation? We study an economy with two regional banks that insure risk-averse consumers against their idiosyncratic liquidity shocks and hold interbank deposits to co-insure against regional liquidity shocks. An aggregate liquidity shock hits one of the banks with positive probability and can lead to contagion---the mutual default of banks. We numerically characterize the equilibrium and show that contagion is rare: it occurs in approximately 5% of the parameter space and its ex-ante probability is below 1%. For likely aggregate liquidity shocks, the decentralized economy achieves the same expected utility as a global bank benchmark, which we fully characterize analytically. For less likely liquidity shocks, the economy is constrained inefficient. To shield themselves from contagion, banks hold inefficiently low interbank positions (co-insurance) and excessive liquidity (self-insurance). Efficiency is restored via an alternative bank resolution scheme.
We revisit the seminal Allen and Gale (2000) paper and show that, when banks with interbank linkages anticipate an aggregate liquidity shock, financial contagion only occurs in about 5% of the parameter space.
We model the spread of news as a social learning game on a network. Agents can either endorse or oppose a claim made in a piece of news, which itself may be either true or false. Agents base their decision on a private signal and their neighbors' past actions. Given these inputs, agents follow strategies derived via multi-agent deep reinforcement learning and receive utility from acting in accordance with the veracity of claims. Our framework yields strategies with agent utility close to a theoretical, Bayes optimal benchmark, while remaining flexible to model re-specification. Optimized strategies allow agents to correctly identify most false claims, when all agents receive unbiased private signals. However, an adversary's attempt to spread fake news by targeting a subset of agents with a biased private signal can be successful. Even more so when the adversary has information about agents' network position or private signal. When agents are aware of the presence of an adversary they re-optimize their strategies in the training stage and the adversary's attack is less effective. Hence, exposing agents to the possibility of fake news can be an effective way to curtail the spread of fake news in social networks. Our results also highlight that information about the users' private beliefs and their social network structure can be extremely valuable to adversaries and should be well protected.
We model the spread of fake news as a learning game on a social network and use deep learning methods to solve the model. When an attacker has access to information about the strength of users' private beliefs, fake news spread faster.
Interdisciplinary, Policy, and Other Publications
"Central Bank Digital Currency Global Interoperability Principles" (World Economic Forum Whitepaper) [whitepaper]
"A System to Manage Digital Rights Tokens" [whitepaper]
"Issuing Central Bank Digital Currency Using Algorand" (with Andrea Civelli, Pietro Grassano, and Naveed Ihsanullah) [whitepaper]
"Interbank Intermediation" (with Marcel Bluhm and Jan-Pieter Krahnen) [abstract] [paper]
This paper explores the economics of interbank lending and borrowing using bank-balance sheet data for Germany, the largest European economy. Our 2002-2014 panel data set allows us to analyze the cross section and the dynamics of the observed interbank exposures. Our findings suggest a genuine intermediation process within the banking system, with implications for allocative efficiency and financial stability. A typical bank in our sample holds a significant amount of term and overnight interbank positions on both sides of the balance sheet simultaneously, and at any point in time. The average contract length in the German interbank market is well above one year, which stands in contrast to the widely held view that interbank exposures are largely overnight. Based on panel regressions, we find the build-up of the interbank book to be driven by innovations in the client book (i.e. non-bank deposit taking and lending). The resulting interbank book affects the bank’s duration gap, the maturity disparity between bank assets and bank liabilities. A bank’s duration gap is often seen as its major macroeconomic risk factor. Overall our findings lend support to a theory of banking that involves leverage stacks, i.e intermediation among banks.
"Revealing patterns of local species richness along environmental gradients with a novel network tool" (with Mara Baudena, Utrecht, Angel Sanchez, UC3M, Paloma Ruiz-Benito, Alcala, Miguel A. Rodriguez, Alcala, Miguel A. Zavala, Alcala, and Max Rietkerk, Utrecht), Nature Scientific Reports 5 (2015). [paper]
"A Network View on Interbank Liquidity" (with Silvia Gabrieli) [abstract] [paper]
The euro area overnight interbank market is best described as a network of over-the-counter lending relationships. We study liquidity reallocation in this interbank network using a novel dataset of all interbank loans settled between European banks. We show the existence of a centrality premium when banks act as intermediaries of liquidity: banks with a one standard deviation higher betweenness centrality capture a 30% larger intermediation spread. Our results are in line with predictions from models of intermediation and bargaining in networks, but are difficult to reconcile with search based models of over-the-counter markets.
"Seven Questions on Financial Interconnectedness" (with Camelia Minoiu, IMF), IMF Research Bulletin, (2014), March. [.pdf]
"Complex Derivatives" (with Stefano Battiston, Guido Caldarelli, Robert M. May, and Joseph E. Stiglitz), Nature Physics Vol.9, No.3, (2013). [abstract] [focus]
The intrinsic complexity of the financial derivatives market has emerged as both an incentive to engage in it, and a key source of its inherent instability. Regulators now faced with the challenge of taming this beast may find inspiration within the budding science of complex systems..
"Systemic Risk in the Financial Sector" (with Ian Goldin, Mike Mariathasan, and Tiffany Vogel), in: Ian Goldin and Mike Mariathasan: "The Butterfly Defect - Globalisation and Systemic Risk", Princeton University Press, (2014)
"Note on interlinkages in the South African interbank system" (with Nicola Brink), Special Note in the Financial Stability Review, South African Reserve Bank (March 2011). [abstract] [fsr]
This paper analyses the network structure of the South African overnight interbank market by employing measures from network theory. A unique data set of interbank transactions from the South African Multiple Options Settlement (SAMOS) system is used. It is shown that the South African interbank system has been largely stable and resilient over the period from March 2005 to June 2010, even in times of great distress on the international financial markets. The number of banks participating in the interbank market was approximately constant over the analysed period, as well as the high level of interconnectedness. A low average path length and high clustering coefficient indicate a high level of liquidity allocation and risk sharing in the system. Furthermore a Network Systemic Importance Index (NSII) is developed to assess the systemic importance of individual banks in South Africa. This index measures each banks size, interconnectedness and substitutability by employing network theory. It is a relative index in the sense that the systemic importance of any given bank does not only depend on the properties of the bank itself, but rather on the properties of the whole network. This approach is therefore less prone to moral hazard and can be used as a tool for macroprudential oversight in addition to microprudential supervision. The NSII addresses the cross-sectional dimension of systemic risk. It has to be stressed, however, that it gives no indication of the default probability of individual banks and has therefore be accompanied by other macroprudential tools for a full picture of systemic risk.
"Basel III and Systemic Risk Regulation - What Way Forward?", Global Financial Markets Working Paper Series 17-2011, (2011). [abstract] [paper] .
One of the most pressing questions in the aftermath of the financial crisis is how to deal with systemically important financial institutions
(SIFIs). The purpose of this paper is to review the recent literature on systemic risk and evaluate the regulation proposals in the Basel III framework with respect to this literature. A number of shortcomings in the current framework are analyzed and three measures for future reform are proposed: counter-cyclical risk-weights, dynamic asset value correlation multipliers, and enhanced transparency requirements for SIFIs.
Software and Web Projects:
We are developing Black Rhino, an open source financial network multi-agent model framework. You can find the latest release (including a short tutorial) in our github repository.
Michael Rose and I have developed a website to accompany our paper"What 5,000 Acknowledgements Tell Us About Informal Collaboration in Financial Economics", Research Policy 50(6) (2021). Here you will find a ranking of financial economists based on their centrality in the network of informal collaboration. To our website.
Team
I am fortunate to work with a group of outstanding students and postdoctoral researchers. If your contacts are missing or outdated, it is time to get in touch again!
University of Cape Town
Postdoctoral Researchers (#: First placement)
Marcin Borsuk (PhD Gdansk, 10/2019-10/2021, #: Postdoc, Oxford)
Joeri Schasfoort (PhD Groningen, 10/2019-10/2021, #: Lecturer, University of Groningen)
Suraj Shekhar (PhD Penn State, 08/2016-06/2019, #: Assistant Professor, Ashoka University)
Michael Rose (MSc Kiel, 04/2015-04/2018, #: Max Planck Institute for Innovation and Competition Munich)
Gideon du Rand (MSc Stellenbosch, 04/2015-02/2020, PhD Student at Stellenbosch, #: Senior Lecturer Stellenbosch)
Teaching
Important. I created a github repository for all my teaching material. In particular, I have uploaded the slides for my course on Financial Regulation and Fintech and Cryptocurrencies. Check out the wiki which contains tons of material. Comments welcome.
We have launched a fantastic online short course on Fintech: Disruption in Finance aimed at finance professionals in collaboration with GetSmarter. You can enroll here.
We are developing Black Rhino, an open source financial network multi-agent model framework. You can find the latest release (including a short tutorial) in our github repository.
