Research

Working papers and submissions

"Storage games" (with Sergei Balakin)

We study a long-horizon, oligopolistic market with random shocks to demand that can be arbitraged by two large storage operators with finite capacity. The application we speak to is electricity but our results extend to any storable commodity – that is,  most commodities. Because the arbitrage spread is so sensitive to market power, storage units face very strong incentives to restrain quantities by tacitly colluding. This cooperation takes new forms thanks to the multiplicity of actions they must take: selling, buying or both. We construct payoff-maximizing equilibria, and uncover a new form of partial collusion that trades off quantities and delay. Head-on competition is not always an equilibrium of the long-horizon game, unlike many standard games, when market power becomes large enough. We present some robustness checks. We also draw implications for policy and suggest poorly competitive storage is a negative externality to the development of the underlying commodity – for example, renewable energy.

"Near-optimal storage strategies in electricity markets" (with Sergei Balakin)

We model the dynamic trading of electricity by a storage operator in an oligopolistic market with demand shocks that make room for intertemporal arbitrage. We must restrict attention to heuristics for tractability reasons.  The dynamics of the stochastic game  are driven with the interaction of the heuristic, the exogenous stochastic process and the constraints on capacity and on short-selling.  We uncover a strong precautionary motive that we call the continuation risk.  A storage operator balances arbitrage revenue and the continuation risk.

"Supply Function Equilibrium with non-convexity" (with Ningyi Sun)

We study existence and characterisation of supply function equilibrium when players have fixed costs. As often the case in Walrasian markets, equilibrium fails to exist in general because of the non-convexities introduced by fixed costs. Here they manifest themselves in a novel way through point deviations off supply schedules. Existence is restored when demand is large enough, and players are constrained to use monotone schedules only to rule out these point deviations. Under these conditions we characterise the symmetric equilibrium, which is unique. This work informs market design.

"Is the clean energy transition making fixed-rate electricity tariffs regressive?" (with Gordon Leslie and Armin Pourkhanali, revisions requested)

This is a first: empirical work on an applied problem!  We decompose electricity consumption and tease out implicit subsidies that arise naturally in fixed-rate tariffs.  The value of electricity differs across households and over time, but fixed-rate tariffs fail to reflect these facts.  Perhaps surprisingly we find that more vulnerable households cross-subsidise wealthier one.  Moving to real-time pricing would unwind these subsidies and also foster efficiency.

"Designing incentive contracts under adverse selection and moral hazard." (submitted)

This paper revisits an old question of mixed model under a new lens.  It is rooted in moral hazard and so departs from the well-established "false moral  hazard" models; therefore only the transfer function can be used to steer agents.  In equilibrium it is distorted for all agents; the high type receives a rent and works less, the low type is exposed to more  risk and works more.  This stands in contrast to known results.

"Adverse selection in competitive search equilibrium: a comment."

In a paper that is well known in the literature, Guerrieri, Shimer and Wright (2010) claim it is equivalent for principals to all post a full vector of contracts and to segment the market by offering each only one type of contract. This assertion is only true under a condition that is very restrictive, which renders it mostly impractical. 

"Incentive contracts and efficiency in a frictional market." (with Benoit Julien, working paper only)

Principals seek to trade with agents by posting incentive contracts in a search environment. A contract solves the ex ante search problem, and adverse selection and moral hazard ex post. We fully characterise the equilibrium for quasi linear preferences, and derive some comparative statics. If using appropriate transfers the equilibrium allocation is constrained welfare optimal, in contrast to the one-to-one principal-agent problem. Search frictions thus correct that inefficiency because searching requires internalizing the utility of agents. Incentives are weaker than in bilateral contracting, and agents enjoy more efficient risk sharing. With a constraint on transfers search and moral hazard interact and may induce an inefficient allocation; principal competition results in over-insurance of the agents and too little effort in equilibrium.

Published work

"Electricity consumption, ethnic origin and religion." (with Gordon Leslie and Armin Pourkhanali, accepted for publication, Energy Economics)

This paper documents the average electricity consumption of households in neighbourhoods with a substantial minority presence and contrasts it to otherwise similar neighbourhoods, thereby establishing a correlation between consumption and variables such as country-of-birth (“ethnicity”). Controlling for standard socio-economic variables, we find systematic departures from the population mean, however not always in the same direction: some minority groups consume more, others less. The method we use is a non-invasive way to obtain electricity use patterns by cultural groups. We discuss how this may inform public energy use programs and perhaps motivate cultural adaptation of energy efficiency messaging at the local community level.

"Moral hazard and efficiency in a frictional market" (with Benoit Julien, accepted for publication, AEJ: Micro)

Principals seek to enter into a productive relationship with agents by posting incentive contracts in a market with competitive search. A contract solves the ex post moral hazard in production and the ex ante search problem, and introduces a trade off between incentives and participation. The optimal contract includes compensatory transfers to agents who fail to contract. In this frictional market the equilibrium allocation is constrained welfare optimal, in contrast to the standard principal-agent problem, which delivers a solution that is not welfare optimal. Principal competition forces them to internalize the agents' utility. There is also perfect risk sharing of the matching risk thanks to the compensatory transfers. These transfers are sufficient, and sometimes necessary, for welfare optimality.

"Scale effects in dynamic contracting" (with Shiley Bromberg-Silverstein and Santiago Moreno-Bromberg, accepted for publication, Mathematics and Financial Economics)

We study a continuous-time contracting problem in which size plays a role. The agent may take on excessive risk to enhance the drift; doing so exposes the principal to large, infrequent (Poisson) losses. An incentive-compatible contract must include size as an instrument: there is downsizing along the equilibrium path to preserve incentive compatibility. The problem is not homogeneous because liquidation is affine in size.  We characterize the value function and the optimal contract, including the downsizing process. There is an optimal liquidation size that is strictly positive and is selected by the principal. This pins an endogenous boundary of the problem, which we construct. In the special case of homogeneity this optimal liquidation size plays no role. The optimal contract is implemented using the full array of financial securities plus debt covenants; holding equity is essential to curb risk taking. Conflicts emerge between classes of security holders and explain phenomena like priority of claims. Firms for which  risk taking is less attractive can afford a higher leverage.
For really keen readers, we construct the endogenous boundary upwards from the optimal liquidation size. Therefore, at any point along this boundary except at the liquidation point, the continuation value strictly exceed liquidation. 
This paper replaces and supersedes an earlier version titled "Leverage and Risk Taking". It includes results from that earlier paper as well as new ones, contained in another draft called "Optimal liquidation value in dynamic contracting " -- see below. "Leverage and risk taking" was presented at the Stanford Institute of Theoretical Economics, July 2015 and awarded best paper award (doted prize), Paul Woolley Centre for Capital Market Dysfunctionality annual conference, October 2015.

"Bidding for incentive contracts" (with Benoit Julien, 2018,  Journal of Mathematical Economics)

Principals seek to enter into a productive relationship with agents by posting mechanisms in a market with competitive search. A mechanism includes an  incentive contract if the meeting is bilateral, and an ex post bidding process, in which agents make contract offers, if several agents meet the same principal. In equilibrium, the bidding process induces a lottery over two contracts. The main result is that the equilibrium allocation is not constrained welfare optimal, precisely because of this contracting risk. This stands in contrast to known results. Hence the optimality of such ex post bidding mechanism is sensitive to the extensive form, as well as to risk aversion. Correcting the allocation is possible, but heavy-handed.

"Two-sided competition with differentiation" (2016, Journal of Economics)

Two platforms compete in vertical differentiation for consumers and advertisers. There is no bottleneck, which implies that competition is fierce on both sides and induces a lack of quasi-concavity of the payoff function. The point of the paper is to show that the bottleneck assumption is substantive. In its absence the payoff function lacks quasiconcavity and equilibria are always asymmetric. They are also more difficult to characterize.

"Participation problems under moral hazard" (2016, Games and Economic Behavior)

The standard principal-agent problem is embedded in a Hotelling model of spacial competition. The agent's location is private information and defines her reservation utility, which is thus stochastic. The optimal transfer function must both provide incentives and secure participation; there is a "participation-incentive trade off" which results in weaker incentives and lower welfare. Competition for the agent exacerbates this result, but the participation-incentive trade off mitigates the effect of competition.

"Risky Utilities" (with Jean-Charles Rochet, online 2015, Economic Theory)

We develop a theory of “risky utilities”, i.e. any private firm that manages an infrastructure for public service, and that may be tempted to engage in excessively risky activities, such as reducing maintenance expenditures (at the risk of provoking a break-down of the system) or engaging in speculative activities (at the risk of incurring massive losses it cannot bear). These include financial utilities like exchanges, clearinghouses or payment systems, as well as standard utilities like electricity transmission networks. We focus specifically on the survival risk of these  firms, whose closure would generate very large externalities. The optimal regulatory contract minimizes the social cost among the contracts that steer the firm away from risky activities. It is simple and implemented with a capital (equity) adequacy requirement and a restructuring rule when that requirement is breached. The social cost function is explicitly computed and         comparative statics can be simply derived.

"A revelation mechanism for soft information under moral hazard" (2016, JPET)

This paper constructs a revelation mechanism to address a problem of moral hazard under soft information. The agent alone observes the stochastic outcome of her action, which she reports to the principal. Therefore the principal also faces a problem of ex post adverse selection. Economically relevant restrictions induce constraints on the principal’s choice of mechanism and Revelation Principle fails to apply. Specifically, a direct mechanism induces some pooling, which does not  replicate the allocation obtained using a larger message space. Pooling also weakens the ex ante incentives. The Revelation Principle is extended to obtain type separation.  A better audit relaxes frictions.

"Investing in Skill and Searching for Coworkers: Endogenous Participation in a Matching Market" (with Chris Bidner and Jessica Moses, 2016, AEJ: Micro) Best paper award, AEJ: Micro -- 2017.

Agents must invest in skill acquisition before entering a market to match with potential trading partners (complementary agents or firms). The combination of search frictions and the (costly) entry decision generates a new class of equilibria that we call "acceptance constrained equilibria". These equilibria mayy be multiple, may co-exist with the better known "cost-constrained" equilibria (whereby the investment constraint is saturated) and cannot be selected away. In addition, their comparative statics diverge from known results and standard corrective action (e.g. taxes or subsidies) have no bite.

"Platform pricing structure with moral hazard", with Luis Vasconcelos JEMS (2014)

(Winner of the ANACOM Award for best paper at the second Workshop on the Economics of ICTs; Scientific committee: Gary Biglaiser, Luis Cabral, Marc Ivaldi, Bruno Jullien, Martin Peitz)

"Optimal contract under moral hazard with soft information" AEJ: micro (2013)

"Moral hazard with discrete soft information" Economic Record (2013)

“Media concentration with free entry”, The Journal of Media Economics (2009)

Technical reports

Work-in-progress

"Contracting with imperfect observations." (with Ben Goldys)

A principal contracts with an agent over an infinite horizon in continuous time.  Although the production process is continuous, the observation process of the principal is discrete.  This generates asymmetric information; the filtration of the agent is an enlargement of that of the principal.  We provide an alternative representation of the continuation value of the agent based on the discrete observation of the principal, and solve a mixed control problem with continuous, deterministic controls and impulse controls.  Incentive compatibility always holds, however at the cost of delayed payments and premature payments.  We implement the contract in securities, which display real-world phenomena such as premature dividends and special dividends.

"A comprehensive characterization of a value function." (with Santiago Moreno-Bromberg)

In dynamic P-A models under moral hazard,  it is often claimed, rather than proven, that the value function of the principal is globally concave.  In  conducting our work we never found a comprehensive proof of this claim; in particular, most papers ignore potential discontinuity sets in the controls,  over which jumps may occur.  This note corrects this deficiency.  The proof is actually simple and applies to all papers currently published in this literature.

"Contracting on unobserved volatility." (with Ben Goldys)

This paper is concerned with a dynamic contracting problem in which the agent may alter both the drift and volatility of output under moral hazard. Diversion can always be deterred, but that introduces incentive for the agent to manipulate the drift, which increases the volatility and is therefore costly to the principal. When the continuous process is observed discretely only, the strategy selected by the agent can only be imperfectly inferred by the principal, hence (i) penalties are necessary to enforce incentive compatibility and are raised on the equilibrium path (by mistake),  (ii) incentive compatibility cannot be enforced path-wise and requires a new definition and (iii)  the control problem is not Markovian because of the inference that is required. We fully characterise the contract. To minimize the impact of the penalties the principal must select their timing optimally; this is a problem of stochastic impulse control. The model speaks to delegated portfolio management.

"Dynamic contracting with a mean-reverting process" (with Ben Goldys and Jiezhong Wu)

We extend the simple model of DeMarzo and Sannikov (2006) by allowing for the output process to follow an Ornstein Uhlenbeck (mean-reverting) process , which better describes the behaviour of asset returns.  Whether the principal induces effort depends on the state of the process, which leads to rich dynamics. 

"Dynamic moral hazard under soft information."

This paper is concerned with a dynamic contracting problem in which the agent controls the drift of a diffusion under moral hazard and the principal never observes the outcome. Instead the principal elicits a message from the agent. This is a soft information problem. To overcome it, the principal runs an audit and terminates the agent upon discovering a lie. The ability to defer compensation greatly helps. It mutes the incentives to lie, which has at best a delayed benefit but an instantaneous cost. It also affords a simple mechanism: misreporting is cheap at low continuation utilities, and its costs increases in the continuation value of the agent. Therefore to have bite, the mechanism requires terminating the agent at a positive continuation value -- a golden parachute; it is socially costly because premature. The optimal contract is fully characterized; it trades off the drift with the expected cost of an audit at each instant. The contract is implemented in standard securities; the cost of finance is explicitly connected to the governance problems of the firm.

"Risk taking under limited liability." (with Santiago Moreno-Bromberg)

We study a continuous-time contracting problem in which both principal and agent are protected by limited liability and size plays a role. The agent may take on excessive risk; doing so exposes the principal to losses from which he may be shielded by limited liability. The principal prefers to not deter risk taking only when the project is large enough; that is, leverage induces risk taking by the principal. These incentives interact with those of the agent, who accepts to take risk only when her continuation utility is low enough to be guaranteed by the liquidation value of the firm. Limited liability effectively reduces the commitment power of the principal, and the incentives of the agent discipline the principal. The model features multiple regimes depending on size, and rich dynamics. We suggest implications for regulatory policy when risk is deemed undesirable for a planner.

"Moral hazard and non-monotonicity" (with Martin Byford)

We study a one-shot principal-agent problem with two-dimensional moral hazard. Their interaction induces non-monotonicity of the likelihood ratio, which vhallenges the first-order  approach. In equilibrium, the transfer function must be non-responsive over some range of outcomes (flat), like an option. Unlike in Jewitt, Kadan and Swinkels (2008) however, this is a feature of equilibrium and not a constraint. We discuss effort levels as well as their interactions.

Work-in-no-progress

Never spoken about...

Writing tip from Mark Colvin (1952-2017), journalist and master broadcaster

"You must always use short, sharp sentences. Keep them active, never passive. No sub-clauses. You need to keep the story moving so the reader [listener]  doesn't switch off. And always, always choose a single-syllable word — usually of Anglo-Saxon origin — over a three-syllable word derived from Latin origin. So 'fuck' over 'fornicate'."