Reader in Economics, Cambridge University
Fellow, Jesus College
Email: mle30 [at] cam.ac.uk
Address: Faculty of Economics, Austin Robinson Building, Sidgwick Avenue, Cambridge, CB3 9DD.
(with Ben Golub)
Journal of Political Economy, 2019
Suppose each of several agents can exert costly effort that creates nonrival, heterogeneous benefits for some of the others. How do negotiated outcomes depend on the heterogeneities? To study this question, we construct a matrix---or a weighted, directed network---that describes the marginal benefits agents can confer on one another. We first show that an outcome is Pareto efficient if and only if the largest eigenvalue of the marginal benefits matrix evaluated at that outcome is equal to 1. A corollary describes the players whose participation is essential for any Pareto improvement. We then show that an agent's contribution in any Lindahl equilibrium corresponds to his eigenvector centrality in the benefits network. This provides a new market foundation and interpretation for widely-used network statistics, and, conversely, a network perspective on price equilibria. Finally, we discuss strategic foundations for Lindahl outcomes in our setting, explaining when negotiations will result in contributions that correspond to network centralities.
(This paper includes results previously circulated in a paper titled “A network centrality approach to coalitional stability”)
(with Francesco Nava)
Theoretical Economics, 2019
This paper studies market clearing in matching markets. The model is non-cooperative, fully decentralized, and in Markov strategies. Workers and firms bargain with each other to determine who will be matched to whom and at what terms of trade. Once a worker-firm pair reach agreement they exit the market. Alternative possible matches provide endogenous outside options. We ask when do such markets clear efficiently and find inefficiencies — mismatch and delay — to be pervasive. Mismatch occurs whenever an agent is at risk of losing a binding endogenous outside option. Delay occurs, instead, when the market evolves in favor of an agent. Delay can be extensive and structured with vertically differentiated markets endogenously clearing form the top down.
(This paper includes results previously circulated in a paper titled “Decentralized Bargaining: Efficiency and the Core”)
American Economic Journal: Microeconomics, 2015.
In many markets, relationship specific investments are necessary for trade. These formed relationships constitute a networked market in which not all buyers can trade with all sellers. We show that networked markets can be decomposed to identify how alternative trading opportunities affect who trades with whom and at what price. This uncovers agents’ investment incentives. In some markets a buyer and seller must make different, separate investments to trade, while in others investments are jointly negotiated. Either way, inefficiencies can be severe and consume all the gains from trade, but for different reasons. We consider three applications in detail: high-skill labor markets, merger markets when industries are consolidating, and the international market for natural gas.
American Economic Review, 2014.
We model financial contagions and cascades of defaults among organizations that have a network of cross holdings. We first identify a network-based measure that captures the impact of changes in one organization's value on other organizations' values. We use the measure to study both integration (the increasing of cross holdings) and diversification (the spreading out of cross holdings). We show that diversification initially increases the probability and extent of cascades as a network of interdependencies grows, and eventually the probability and extent of cascades decreases once organizations become less tied to specific other organizations. Integration also faces tradeoffs: increased dependence on other organizations versus less sensitivity to own investments. We briefly discuss incentives to seek bailouts, and associated moral-hazard issues. We also show that once an organization approaches a bankruptcy threshold, there are no trades of cross holdings or assets at fair prices that can lower the probability of its failure, and that unduly favorable trades for that organization and/or a direct injection of capital are necessitated. Finally, we illustrate some aspects of the model with European debt cross holdings.
(with Jun Chen, Draft date: April 2019)
The past twenty years have witnessed the emergence of internet conglomerates fuelled by acquisitions. We provide a simple theoretical model to shed light on this. We follow a large literature in management (Wernerfelt, 1984) and endow firms with a set of scarce capabilities that drive their competitiveness across markets. This information is naturally represented as a hypergraph (a generalization of a network). Firms can combine their capabilities by merging and also spin-off new firms to partition them. We study the stable industry structures, where there no longer exist any profitable mergers or demergers. Positing that recent changes have caused markets to value new capabilities, particularly those held by internet firms, we show this can explain the conglomeratization of internet firms. Moreover, we find that as markets value more of the same capabilities, changes in industry structure can be abrupt. There is a sharp phase transition in the potential size of the largest firms at a key threshold.
(with Eduard Talamas, Draft Date: March 2019)
Different types of agents make non-contractible investments before bargaining over both who matches with whom and the terms of trade. In thin markets, the holdup problem---that is, underinvestment caused by agents receiving only a fraction of the returns from their investments---is ubiquitous. However, we show that holdup need not be a problem in markets that attract traders over time---even when only a few traders are present in the market at any point in time. In particular, we characterize---for all sufficiently high discount factors---the type-symmetric Markov perfect equilibria of a non-cooperative investment and bargaining game with sequential entry, and we show that, in every such equilibrium, everyone receives the full returns from her marginal investments. Intuitively, future entry creates present competition---so even intratemporally thin markets can be competitive. This provides non-cooperative foundations for the standard price-taking assumption in the literature investigating investment efficiency in competitive matching markets.
(with Attila Ambrus, Draft date: August 2018)
Revise and resubmit, Review of Economic Studies
This paper provides a framework to study the formation of risk-sharing networks through costly social investments, in particular the inefficiencies and resulting inequality associated with such processes. First, individuals invest in relationships to form a network. Next, neighboring agents negotiate risk-sharing arrangements. There is never underinvestment, but overinvestment is possible and we find a novel trade-off between efficiency and equality. The most stable efficient network also generates the most inequality. When the income correlation structure is generalized by splitting individuals into groups, such that incomes across groups are less correlated but these relationships are more costly, there can be underinvestment across group but not within group. We find that more central agents have better incentives to form across-group links, reaffirming the efficiency inequality trade-off. In general, endogenous network formation in the risk sharing context tends to result in highly asymmetric networks and stark inequalities in consumption levels.
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.
(with Marina Agranov, Draft date: September 2017)
Revise and resubmit, Journal European Economic Association
We conduct an experimental investigation of decentralized bargaining over the terms of trade in matching markets. We study if/when efficient matches are reached, and the terms of trade agreed upon. We find that mismatch is extensive, and persists as we change the nature of bargaining by moving from a structured experimental protocol to permitting free-form negotiations. We identify two sources of inefficiencies. Inefficiencies are driven by (a) players' rational responses to their bargaining positions changing as others reach agreement, and (b) the existence of players who are unwilling to accept low, inequitable payoffs.
(with Ben Golub, Draft date: February 2015)
Consider a negotiation in which agents will make costly concessions to benefit others -- e.g., by implementing tariff reductions, environmental regulations or nuclear disarmament. An agenda specifies which issue or dimension agents will make concessions on; after an agenda is chosen, the negotiation comes down to the magnitude of each agent's contribution. We seek a ranking of agendas based on the marginal costs and benefits they each generate at the status quo, which are captured in a Jacobian matrix. In a transferable utility (TU) setting, there is a simple ranking based on the best available social return per unit of cost (measured in the numeraire). When transfers are not available, the problem of ranking agendas is more difficult, and we take an axiomatic approach. First, we require the ranking not to depend on economically irrelevant changes of units. Second, we require that the ranking be consistent with the TU ranking on problems that are equivalent to TU problems in a suitable sense. The unique ranking satisfying these axioms is represented by the spectral radius (Frobenius root) of a matrix closely related to the Jacobian, whose entries measure the marginal benefits per unit marginal cost agents can confer on one another.
(Draft date: Nov 2015)
Workers' labor market participation decisions and firms' vacancy creation decisions are studied in a model where different matches generate different surpluses. An immediate consequence of these heterogeneities is that better matches are possible in thicker markets. This creates a thick market externality: when additional workers and firms enter the market, they confer net benefits on the other workers and firms by improving the expected quality of their matches. As a consequence, there is always too little entry by both workers and firms. The thick market externality has further implications. Quite generally labor markets will be fragile. Considering shocks to average match productivities, there will be a critical threshold at which a labor market suddenly collapses from supporting multiple workers and multiple firms in equilibrium to supporting no workers or firms in any equilibrium. All but one agent will suffer discontinuous losses as this threshold is passed and the market collapses.
We model two experts who must make predictions about whether an event will occur or not. The experts receive private signals about the likelihood of the event occurring, and simultaneously make one of a finite set of possible predictions, corresponding to varying degrees of alarm. The information structure is commonly known among the experts and the recipients of the advice. Each expert's payoff depends on whether the event occurs, her prediction, and possibly the prediction of the other expert. Our main result shows that when either or both experts receive uniformly more informative signals, their predictions can become unambiguously less informative. We call such information improvements perverse. Suppose a third party wishes to use the experts' recommendations to decide whether to take some costly preemptive action to mitigate a possible bad event. The third party would then trade off the costs of two kinds of mistakes: (i) failing to take action when the event will occur; and (ii) needlessly taking the action when the event will not occur. Regardless of how this third party trades off the associated costs, he will be worse off after a perverse information improvement. These perverse information improvements can occur when each expert's payoff is independent of the other expert's predictions and when the information improvement is due to a transfer of technology between the experts.