Yuliy Sannikov

A Macroeconomic Model with a Financial Sector

This paper studies the full equilibrium dynamics of an economy with financial frictions. Due to highly non-linear amplification effects, the economy is prone to instability and occasionally enters volatile episodes. Risk is endogenous and asset price correlations are high in down turns. In an environment of low exogenous risk experts assume higher leverage making the system more prone to systemic volatility spikes - a volatility paradox. Securitization and derivatives contracts leads to better sharing of exogenous risk but to higher endogenous systemic risk. Financial experts may impose a negative externality on each other and the economy by not maintaining adequate capital cushion.

Macroeconomics with Financial Frictions: A Survey

This article surveys the macroeconomic implications of financial frictions. Financial frictions lead to persistence and when combined with illiquidity to non-linear amplification effects. Risk is endogenous and liquidity spirals cause financial instability. Increasing margins further restrict leverage and exacerbate downturns. A demand for liquid assets and a role for money emerges. The market outcome is generically not even constrained efficient and the issuance of government debt can lead to a Pareto improvement. While financial institutions can mitigate frictions, they introduce additional fragility and through their erratic money creation harm price stability.

Impossibility of Collusion under Imperfect Monitoring with Flexible Production

We show that it is impossible to achieve collusion in a duopoly when (1) goods are homogenous and firms compete in quantities, (2) new, imperfect information arrives continuously, without sudden events and (3) firms are able to respond to this new information quickly. The result holds even if we allow for asymmetric equilibria or monetary transfers. The intuition is that the flexibility to respond to new information quickly unravels any collusive scheme and that signals about the aggregate behavior only cannot be used effectively to provide individual incentives via transfers. Our result applies both to a simple stationary model and a more complicated one with prices following a mean-reverting Markov process.

The Role of Information in Repeated Games With Frequent Actions

We show that in repeated interactions the avenues for effective provision of incentives depend crucially on the type of information players observe. We establish this conclusion for general repeated two-player games in which information arrives via a continuous-time stationary process that has a continuous multidimensional Brownian component and a Poisson component, and in which the players act frequently. The Poisson jumps can be used to effectively provide incentives both with transfers and value burning, while continuous Brownian information can be used to provide incentives only with transfers.

A Continuous-Time Agency Model of Optimal Contracting and Capital Structure

We consider a principal-agent model in which the agent needs to raise capital from the principal to finance a project. Our model is based on DeMarzo and Fishman (2003), except that the agents cash flows are given by a Brownian motion with drift in continuous time. The difficulty in writing an appropriate financial contract in this setting is that the agent can conceal and divert cash flows for his own consumption rather than pay back the principal. Alternatively, the agent may reduce the mean of cash flows by not putting in effort. To give the agent incentives to provide effort and repay the principal, a long-term contract specifies the agents wage and can force termination of the project. Using techniques from stochastic calculus similar to Sannikov (2003), we characterize the optimal contract by a differential equation. We show that this contract is equivalent to the limiting case of a discrete time model with binomial cash flows. The optimal contract can be interpreted as a combination of equity, a credit line, and either long-term debt or a compensating balance requirement (i.e., a cash position). The project is terminated if the agent exhausts the credit line and defaults. Once the credit line is paid off, excess cash flows are used to pay dividends. The agent is compensated with equity alone. Unlike the discrete time setting, our differential equation for the continuous-time model allows us to compute contracts easily, as well as compute comparative statics. The model provides a simple dynamic theory of security design and optimal capital structure.

Learning, Termination, and Payout Policy in Dynamic Incentive Contracts

We study a principal-agent setting in which both sides learn about future profitability from output, and the project can be abandoned/terminated if profitability is too low. With learning, shirking by the agent both reduces output and lowers the principals estimate of future profitability. The agent can exploit this belief discrepancy and earn information rents, reducing his incentives to exert effort. The optimal contract controls information rents to improve incentives by distorting the termination decision. Our results capture the transition from a young, financially constrained firm to a mature firm that pays dividends. For young firms, poor performance permanently raises the termination threshold, as doing so lowers information rents. Mature firms pay smoothed dividends and have a fixed termination threshold. Dividend smoothing occurs because earnings surprises are used to adjust financial slack in line with profitability. When profitability only reflects the agents private ability, a simple equity contract is optimal.

An Algorithm for Two Player Repeated Games with Perfect Monitoring

Consider repeated two-player games with perfect monitoring and discounting. We provide an algorithm that computes the set V* of payoff pairs of all pure-strategy subgame perfect equilibria with public randomization. The algorithm provides significant efficiency gains over the existing implementations of the algorithm from Abreu, Pearce and Stacchetti (1990). These efficiency gains arise from a better understanding of the manner in which extreme points of the equilibrium payoff set are generated. An important theoretical implication of our algorithm is that the set of extreme points E of V* is finite. Indeed, |E| ≤ 3|A|, where A is the set of action profiles of the stage game.