Yuliy Sannikov, Clark Medalist 2016
American Economic Association Honors and Awards Committee
Yuliy Sannikov is a theorist who has developed new methods for analyzing continuous time dynamic games using stochastic calculus methods. His work has not only broken new ground in methodology, it has had a substantial influence on applied theory. He has significantly altered the toolbox available for studying dynamic games, and as a result of his contributions, new areas of economic inquiry have become tractable for rigorous theoretical analysis. The areas of application include the design of securities, contract theory, macroeconomics with financial frictions, market microstructure, and collusion.
Sannikov’s work is impressive. It is elegant, powerful, and it paves the way for further analysis on lots of problems. The early successes highlighted how even simple and well-studied models could yield new insight. His most recent work has tackled more complex models in finance and macroeconomics. Previous models abstracted from crucial economic forces in the name of tractability, but Sannikov’s methods allow models to include the most important forces and thus deliver results that are much more relevant. He is one of the few theorists in many years to have introduced a truly novel tool that changed the way theory is done.
Foundations and Applications to Contract Theory
Sannikov’s dissertation (“Games with Imperfectly Observable Actions in Continuous Time,”Econometrica, 2007) was a breakthrough, introducing tools for analyzing repeated games. At a time when the vast majority of the literature used discrete time models, the paper showed how continuous time tools allowed otherwise intractable games to be analyzed elegantly and neatly. The paper characterized the set of equilibrium values obtainable in perfect public equilibrium as a function of the discount factor. This characterization is more challenging and more interesting than simply analyzing what happens in the limit as players get patient, where tradeoffs between efficiency and incentives often disappear and all feasible payoffs can be obtained; in contrast, with less patient players, real tradeoffs arise, and a characterization of the set of equilibrium payoffs highlights those tradeoffs. This work was immediately recognized as being path-breaking, a truly significant advance in a literature that had for years been characterized by incremental improvements.
In an application to incentive theory (“A Continuous-Time Version of the Principal-Agent Problem,” Review of Economic Studies, 2008), Sannikov analyzes a continuous time model in which an agent controls the drift of a diffusion process. The paper characterizes the optimal contract in this environment, providing new insights that were not available with existing models. As in traditional models, eliciting higher effort from an agent comes at the cost of exposing the agent to additional risk, so the underlying tradeoff is familiar. However, the dynamics are much richer in this modeling framework. One result is that agents eventually “retire,” either because they have had a series of bad luck leading their utility to be so low that it is too expensive to provide additional incentives, since the agent can’t be hurt any further; or else because they have had a series of good luck leading the utility to be so high that additional rewards are not effective relative to their cost to the principal.
Reputation, Collusion and Game Theory
A paper that looks at a classic problem through the new lens of continuous time (“Reputation in Continuous-Time Games,” with Eduardo Faingold, Econometrica, 2011) studies the problem of a “large” individual attempting to establish a reputation with a set of “small” players who react to the large player’s behavior, but do not individually influence outcomes. The tractability enabled by the continuous-time modeling approach allows the paper to characterize equilibria for a range of discount factors.
Another pair of papers examines collusion with imperfect monitoring. In the first (“Impossibility of Collusion under Imperfect Monitoring with Flexible Production,” with Andrzej Skrzypacz, American Economic Review, 2007), the authors examine what happens when you take the limit as the frequency of actions gets large, showing that frequent actions can undermine collusion in games with imperfect monitoring. As actions become more frequent, information quality per period is assumed to deteriorate. “The Role of Information in Games with Frequent Actions” (with Andrzej Skrzypacz, Econometrica, 2010) looks more deeply at how different types of information affect players’ ability to cooperate, and how different types of information can be used to provide incentives to players in a moral hazard context. The paper incorporates both “lumpy” information that arrives infrequently (e.g. an accident in a factory) and “smooth” information that arrives continuously. The paper shows that player strategies should use smooth information to transfer utility across players without sacrificing efficiency, while “lumpy” information may lead to players taking inefficient actions (value burning).
Dynamic Contracts, Security Design, and Firm Financing
A line of research on incentives in finance with Peter DeMarzo has been highly influential and widely recognized. “Optimal Security Design and Dynamic Capital Structure in a Continuous-Time Agency Model” (Journal of Finance, 2007) studies how optimal dynamic contracts can be implemented with a capital structure (credit line, long-term debt, and equity). In the model, the agent undertakes a project that experiences fluctuations in cash flows and thus requires investment. The agent’s effort shifts the mean of cash flows (which can be interpreted as the agent diverting cash for private benefit), and the output is observed in real time by the principal. The principal designs the optimal contract. A first result is that the optimal contract can be implemented with a capital structure. The use of credit versus debt varies with features of the environment such as volatility. Another result is that the level of debt declines with past profitability, and the contract may require a firm to hold a compensating cash balance while borrowing (at a higher rate) through the credit line. Thus, the model provides a justification for behavior that might seem irrational absent incentive problems—the cash balance ensures that the firm will have cash flow in future states where investors may not be willing to provide funds. The contract also allows the agent to choose which debts to pay off first. The agent chooses to pay off the credit line before paying dividends, but once the credit line is paid off, will pay dividends rather than “hoard cash” (that is, increase the cash balance, which would have the benefit of cushioning against future shocks). The total financing available to the firm is primarily determined by the expected value of the project and the agent’s outside options, rather than the project’s volatility, but the volatility affects the capital structure of the firm, with more volatile firms using a larger credit line relative to long term debt. Surprisingly, the usual conflicts between debt and equity (asset substitution, strategic default) need not arise—that is, neither equity holders nor the agent have the incentive to increase risk, increase dividends to induce default, or to contribute more capital to postpone default. This model is a substantial improvement beyond the existing literature in terms of both matching real-world observations and providing compelling but subtle explanations for them. A follow-up paper (“Learning, Termination and Payout Policy in Dynamic Incentive Contracts,” joint with Peter DeMarzo, 2014 working paper) enriches the previous paper’s model to allow for dynamic learning about the profitability of the project on behalf of both the principal and the agent.
In a third paper on dynamic incentives (“Moral Hazard and Long Run Incentives,” 2014 working paper), Sannikov analyzes optimal contracts in an environment where agent effort has a long run impact on the stochastic process of output, rather than just shifting the mean of contemporaneous payoffs. The paper provides a characterization of the optimal contract, which has some quite interesting features. First, despite the long-term impact of the agent’s effort, the agent’s control over current outcomes drives the agent’s exposure to firm risk. Indeed, risk exposure starts small but adjusts towards a target level of risk exposure over time. Second, the contract includes consumption smoothing features, so that incentive effects of current performance are distributed over time, both on the positive side on the negative side, to give the most “bang for the buck” in terms of providing incentives. Third, due to limited liability, pay for performance has bounded sensitivity and an agent is terminated if performance is too poor.
Financial Frictions in Macroeconomic Models
Most recently, Sannikov has developed a new line of research in macroeconomics. His paper with Markus Brunnermeier, “A Macroeconomic Model with a Financial Sector” (American Economic Review, 2014), illustrates the fruitfulness of the kind of techniques that he has perfected in another area of application. An important issue for modeling fluctuations in aggregate economic activity, and one that has received renewed attention following the recent financial crisis, concerns the role of distortions in the financial sector as a source of economic contractions. For technical reasons, the prior literature on financial-accelerator models generally had to make assumptions that apply mean-reverting dynamics for the net worth of the leveraged investors, so that, under the assumption that exogenous aggregate disturbances are small enough, this variable will forever fluctuate over a fairly small range around a constant “long-run steady-state” value. This property allows equilibrium dynamics to be linearized around that steady state, which in turn renders tractable the calculations needed to characterize optimal equilibrium behavior. While this approach has allowed some degree of understanding of financial accelerator mechanisms, it also has unfortunate limitations.
The paper characterizes the global dynamics of a model in response to a continuing series of small random aggregate disturbances, using continuous-time methods that allow the equilibrium dynamics to be characterized by solving an ordinary differential equation, and without requiring any linearization. Using the global characterization of equilibrium dynamics, it becomes possible to solve for the amount of time that the key state variable (the net worth of leveraged investors as a share of total wealth) is predicted to spend in excursions far from its long-run average value, under any given values of the model’s parameters. In this way it is possible to describe how significant “crises” (when financial distortions are much greater than usual as a result of an unusually low net worth of leveraged investors) should be expected to occur endogenously with a certain frequency, and to analyze how the frequency and severity of such crises should be affected by parameter variations. In particular, the introduction of financial innovations (such as securitization or derivatives contracts) that improve risk-sharing among individuals can have undesirable consequences by generating equilibrium dynamics in which crises are more frequent.
The nonlinear solution for the model dynamics also makes it possible to analyze how both average behavior, and the way that behavior should respond to further small shocks, change depending on the current value of the net-worth state variable; this makes it possible to identify different “phases” of a “financial cycle,” and to consider how desirable policy might differ depending on such a state variable. An important consequence is that it is possible to distinguish between a situation in which risk is high for endogenous reasons (i.e., because of how the level of leveraged investors’ net worth has evolved in response to past shocks) and one in which risk is high for exogenous reasons (i.e., because the distributions from which future disturbances are expected to be drawn have high variance). Indeed, a decline in the amount of exogenous risk can actually increase endogenous risk (as a result of increased equilibrium leverage)—a result that they call the “volatility paradox,” and that arguably helps to explain how a period of apparent macroeconomic calm in the period 1985-2005 could have ended with an unusually severe financial crisis.
A second paper in this line (“The I-Theory of Money,” with Markus Brunnermeier, working paper, 2014) analyzes the effects of monetary policy in their dynamic model of the financial accelerator, extended to include intermediaries that take deposits and lend them out. A central result of the model shows how the supply of both credit and liquid short-term assets varies depending on the net worth of intermediaries (which becomes the key state variable). This provides an amplification mechanism for business fluctuations: when final borrowers are hit with shocks and default on loans, the banks must both reduce their lending and supply less “inside money,” with effects that reduce spending and thus further increase the number of defaults.
Yuliy Sannikov’s research agenda is truly remarkable. He has an innovation uniquely associated with him, which has led to a variety of truly novel analyses. He has new ideas, and almost all of his papers can be considered to have taken the existing literature to new levels, opening up new lines of inquiry. His contributions stand out particularly strongly in an era where there have been very few breakthroughs in microeconomic theory, and also when macroeconomic theory models have been limited by tractability constraints that substantially affect the economic conclusions.