Antoine Mandel

We develop an additive Cox proportional hazard model with time-varying covariates, including spatio-temporal characteristics of weather events, to study the impact of weather extremes (heavy rains and tropical cyclones) on the probability of mortgage default and prepayment. We compare the survival model with a flexible logistic model and an extreme gradient boosting algorithm. We estimate the models on a portfolio of mortgages in Florida, consisting of 69,046 loans and 3,707,831 loan-month observations with localization data at the five-digit ZIP code level. We find a statistically significant and non-linear impact of tropical cyclone intensity on default as well as a significant impact of heavy rains in areas with large exposure to flood risks. These findings confirm existing results in the literature and also provide estimates of the impact of the extreme event characteristics on mortgage risk, e.g. the impact of tropical cyclones on default more than doubles in magnitude when moving from a hurricane of category two to a hurricane of category three or more. We build on the identified effect of exposure to flood risk (in interaction with heavy rainfall) on mortgage default to perform a scenario analysis of the future impacts of climate change using the First Street flood model, which provides projections of exposure to floods in 2050 under RCP 4.5. We find a systematic increase in risk under climate change that can vary based on the scenario of extreme events considered. Climate-adjusted credit risk allows risk managers to better evaluate the impact of climate-related risks on mortgage portfolios.

This paper develops a network economy model to study the propagation of the COVID lockdown shock. Firms are related to each other through buyer–seller relations in the market for intermediate inputs. Firms choose production levels and input combinations using prices that emerge from local interactions. Nothing forbids trade at out-of-equilibrium prices. In such a setting, disequilibrium spills over from one market to another due to the interconnections between markets. These disequilibrium dynamics are capable of generating unemployment when workers released by contracting firms are not frictionlessly absorbed by expanding firms. We calibrate the model to the US economy using a data set with more than 200,000 buyer–seller relations between about 70,000 firms. Computational experiments on the calibrated economy suggest that the COVID lockdown generates a sizeable decline in GDP. The endogenously generated unemployment dynamics is a primary determinant of the cost of the lockdown.

We propose a model of the joint evolution of opinions and social relationships in a setting where social influence decays over time. The dynamics are based on bounded confidence: social connections between individuals with distant opinions are severed while new connections are formed between individuals with similar opinions. Our model naturally gives raise to strong diversity, i.e., the persistence of heterogeneous opinions in connected societies, a phenomenon that most existing models fail to capture. The intensity of social interactions is the key parameter that governs the dynamics. First, it determines the asymptotic distribution of opinions. In particular, increasing the intensity of social interactions brings society closer to consensus. Second, it determines the risk of polarization, which is shown to increase with the intensity of social interactions. Our results allow to frame the problem of the design of public debates in a formal setting. We hence characterize the optimal strategy for a social planner who controls the intensity of the public debate and thus faces a trade-off between the pursuit of social consensus and the risk of polarization. We also consider applications to political campaigning and show that both minority and majority candidates can have incentives to lead society towards polarization.

We analyze whether random network formation processes, such as preferential attachment, can emerge as the outcome of strategic behaviour. We represent network formation as an extensive game in which players sequentially form links as they enter the network. In this setting, we investigate under which conditions subgame perfect equilibria of the game are observationally equivalent with random network formation process. We put forward two structural conditions that are necessary in this respect. First, players must have some form of imperfect information as randomization is purposeful only if its realization is not perfectly observed by the other players. Second, there must be some form of competition between a player and its successors: a player has incentives to reduce the information available to its successors only to the extent that their objectives are in opposition. Accordingly, we put forward a class of games where players compete with their predecessors and their successors for the costs and benefits induced by link formation and show that subgame perfect equilibria of this game are observationally equivalent with random network formation process. In particular, when linkage costs are inversely proportional to the degree of a node, equilibrium play induces a preferential attachment process. This provides a positive answer to the question of the existence of strategic foundations for preferential attachment. However the very specific conditions requiredfor the observational equivalence to hold suggest that preferential attachment can be explained by strategic considerations only in a limited number of situations.

We develop a tractable model of price dynamics in a general equilibrium economy with cash-in-advance constraints. The dynamics emerge from local interactions between firms that are governed by the production network underlying the economy. We analytically characterise the influence of network structure on the propagation of monetary shocks. In the long run, the model converges to general equilibrium and the quantity theory of money holds. In the short run, monetary shocks propagate upstream via nominal changes in demand and downstream via real changes in supply. Lags in the evolution of supply and demand at the micro level can give rise to arbitrary dynamics of the distribution of prices. Our model provides an explanation of the price puzzle: a temporary rise in the price level in response to monetary contractions. In our setting, the puzzle emerges under two assumptions about downstream firms: they are disproportionally affected by monetary contractions and they account for a sufficiently small share of the wage bill. Empirical evidence supports the two assumptions for the US economy. Our model calibrated to the US economy using a data set of more than fifty thousand firms generates the empirically observed magnitude of the price level rise after monetary contractions.

We investigate the containment of epidemic spreading in networks from a normative point of view. We consider a susceptible/infected model in which agents can invest in order to reduce the contagiousness of network links. In this setting, we study the relationships between social efficiency, individual behaviours and network structure. First, we characterise individual and socially efficient behaviour using the notions of communicability and exponential centrality. Second, we show, by computing the Price of Anarchy, that the level of inefficiency can scale up to linearly with the number of agents. Third, we prove that policies of uniform reduction of interactions satisfy some optimality conditions in a vast range of networks. In setting where no central authority can enforce such stringent policies, we consider as a type of second-best policy the implementation of cooperation frameworks that allow agents to subsidise prophylactic investments in the global rather than in the local network. We then characterise the scope for Pareto improvement opened by such policies through a notion of Price of Autarky, measuring the ratio between social welfare at a global and a local equilibrium. Overall, our results show that individual behaviours can be extremely inefficient in the face of epidemic propagation but that policy can take advantage of the network structure to design welfare improving containment policies.

There is increasing concern among financial regulators that changes in the distribution and frequency of extreme weather events induced by climate change could pose a threat to global financial stability. We assess this risk, for the case of floods, by developping a simple model of the propagation of climate-induced shocks through financial networks. We show that the magnitude of global risks is determined by the interplay between the exposure of countries to climate-related natural hazards and their financial leverage. Climate change induces a shift in the distribution of impacts towards high-income countries and thus larger amplification of impacts as the financial sectors of high-income countries are more leveraged. Conversely, high-income countries are more exposed to financial shocks. In high-end climate scenarios, this could lead to the emergence of systemic risk as total impacts become commensurate with the capital of the banking sectors of countries that are hubs of the global financial network. Adaptation policy, or the lack thereof, appears to be one of the key risk drivers as it determines the future exposure of high-income coun

Dans cet ouvrage, deux chercheurs aux extrêmes du conceptuel, Yann Toma, artiste, et Antoine Mandel, mathématicien, proposent des rencontres improbables entre art et mathématiques. Ils initient un itinéraire par une série d’analogies entre raison mathématique et créativité esthétique, entre images et sons dans les algorithmes, entre logique et esthétique. De ces rencontres sont nés les textes présentés ici – un ensemble de contributions de nombreux artistes et mathématiciens – qui mettent en lumière de nouvelles formes de création, de représentation et d’action sur le réel.

This paper estimates the cost of the lockdown of some sectors of the world economy in the wake of COVID-19. We develop a multi sector disequilibrium model with buyer-seller relations between agents located in different countries. The production network model allows us to study not only the direct cost of the lockdown but also indirect costs which emerge from the reductions in the availability of intermediate inputs. Agents determine the quantity of output and the proportions in which to combine inputs using prices that emerge from local interactions. The model is calibrated to the world economy using input-output data on 56 industries in 44 countries including all major economies. Within our model, the lockdowns are implemented as partial reductions in the output of some sectors using data on sectoral decomposition of capacity reductions. We use computational experiments to replicate the temporal sequence of the lockdowns implemented in different countries. World output falls by 7% at the early stage of the crisis when only China is under lockdown and by 23% at the peak of the crisis when many countries are under a lockdown. These direct impacts are amplified as the shock propagates through the world economy because of the buyer-seller relations. Supply-chain spillovers are capable of amplifying the direct impact by more than two folds. Naturally, the substitutability between intermediate inputs is a major determinant of the amplification. We also study the process of economic recovery following the end of the lockdowns. Price flexibility and minor technological adaptations help in reducing the time it takes for the economy to recover. The world economy takes about one quarter to move towards the new equilibrium in the optimistic and unlikely scenario of the end of all lockdowns. Recovery time is likely to be significantly greater if partial lockdowns persist.