Carnegie Mellon University
(Joint work with Christopher Sleet)
We analyze an equilibrium concept called revision-proofness for infinite-horizon games played by a dynasty of players. Revision-proofness requires strategies to be robust to joint deviations by multiple players and is a refinement of sub-game perfection. Sub-game perfect paths that can only be sustained by reversion to paths with payoffs below those of an alternative path are not revision-proof. However, for the important class of quasi-recursive games careful construction of off-equilibrium play can render many, and in some cases all, sub-game perfect paths revision-proof.
University of Pennsylvania
Why Doesn't Technology Flow from Rich to Poor Countries?
(Joint work with Jeremy Greenwood and Juan M. Sanchez)
What determines the choice of technology within a country? While there could be many factors, the efficiency of the country’s financial system may play a significant role. To address this question, a dynamic contract model is embedded into a general equilibrium setting with competitive intermediation. The ability of an intermediary to monitor and control the cash flows of a firm plays an important role in the decision to underwrite technology adoption. Can such a theory help to explain the differences in TFP and establishment-size distributions between India, Mexico and the U.S.? Some applied analysis suggests that answer is yes.
Simon Fraser University
Moral Hazard and Lack of Commitment in Dynamic Economies
(Joint work with Fernando M. Martin)
We revisit the role of limited commitment in a dynamic risk-sharing setting with private information. We show that a Markov-perfect equilibrium, in which agent and insurer cannot commit beyond the current period, and an infinitely-long contract to which only the insurer can commit, implement identical consumption, effort and welfare outcomes. Unlike contracts with full commitment by the insurer, Markov-perfect contracts feature non-trivial and determinate asset dynamics. Numerically, we show that Markov-perfect contracts provide sizable insurance, especially at low asset levels, and are able to explain a significant part of wealth inequality beyond what can be explained by self-insurance. The welfare gains from resolving the commitment friction are larger than those from resolving the moral hazard problem at low asset levels, while the opposite holds for high asset levels.
Queen Mary University
(Joint work with Victor Rios-Rull)
We develop a new theory of credit lines or long term unsecured credit contracts based on costly contracting and lack of commitment that matches the data in a variety of dimensions. Credit lines pre-specify a credit limit and interest rate in each period. Households can unilaterally default as in the U.S. Bankruptcy code, and can unilaterally switch credit lines. Lending firms can set a new credit limit at any time. Whether they must commit to the interest rate or not depends on the regulatory setting (a recent change in the US imposed such a commitment). We solve and characterize the equilibria, finding the resulting set of contracts as well as the distribution of households over interest rates, credit limits and wealth. We find that this model replicates the main properties of typical lending contracts. We use the model to assess the implications of the policy change and find it moderately, but not uniformly positive.
Wharton School, University of Pennsylvania
A Theory of Political and Economic Cycles
(Joint work with Laurence Ales and Pierre Yared)
We develop a theoretical framework in which political and economic cycles are jointly determined. These cycles are driven by three political economy frictions: policymakers are non-benevolent, they cannot commit to policies, and they have private information about rents. Our first main result is that, in the best sustainable equilibrium, distortions to production emerge and never disappear even in the long run. This result is driven by the interaction of limited commitment and private information on the side of the policymaker, since in the absence of either friction, there are no long run distortions to production. Our second result is that, if the variance of private information is sufficiently large, there is equilibrium turnover in the long run so that political cycles never disappear. Finally, our model produces a long run distribution of taxes, distortions, and turnover, where these all respond persistently to temporary economic shocks, and where periods of possible turnover are associated with the lowest equilibrium taxes and the highest equilibrium distortions. We show that many of these dynamics are consistent with the empirical evidence on the interaction of political and economic cycles.
UC Santa Barbara
Optimal Taxation in a Life Cycle Economy with Endogenous Human Capital Formation
(Joint work with Marek Kapicka)
We study efficient allocations and optimal policies in a life-cycle economy with risky human capital accumulation. The agents are ex-ante heterogeneous in their initial human capital and in their ability level. Ex-post, they also differ in their realization of shocks to human capital. The model incorporates two frictions. First, it assumes that ability and labor supply are both private information of the agents. Second, it adds a moral hazard component by assuming that schooling and realized rates of return to human capital are both private information. Since models with those three sources of heterogeneity are successful in replicating and explaining the distribution of earnings and consumption observed in the data, the model is thus both realistic enough to be useful for policy analysis, and tractable enough to carry out the analysis.
On the Dual Approach to Recursive Contracts
(Joint work with Matthias Messner and Christopher Sleet)
We bring together the theories of duality and dynamic programming. We show that the dual of an additively separable dynamic optimization problem can be recursively decomposed using summaries of past Lagrange multipliers as state variables. Analogous to the Bellman decomposition of the primal problem, we prove equality of values and solution sets for recursive and sequential dual problems. In nonadditively separable settings, the equivalence of the recursive and sequential dual is not guaranteed.
University of Minnesota
(Joint work with Vincenzo Quadrini)
The 2007-2009 crisis was characterized by an unprecedented degree of international synchronization as all major industrialized countries experienced large macroeconomic contractions around the date of Lehman bankruptcy. At the same time countries also experienced large and synchronized tightening of credit conditions. We present a two-country model with financial market frictions where a credit tightening can emerge as a self-fulfilling equilibrium caused by pessimistic but fully rational expectations. As a result of the credit tightening, countries experience large and endogenously synchronized declines in asset prices and economic activity (international recessions). The model suggests that these recessions are more severe if they happen after a prolonged period of credit expansion.
University of Southern California
Risky Investments with Limited Commitment
(Joint work with Thomas Cooley and Ramon Marimon)
Over the last three decades there has been a dramatic increase in the concentration of income at the very top of the distribution. This increase in income inequality has been especially notable in the compensation of financial executives where it has often been associated with greater risk-taking using more complex financial instruments. Parallel to this trend, organizational forms in the financial sector have been transformed with the traditional partnership form of organization replaced by public companies that compete for managerial talent and have weaker forms of commitment between investors and managers. In this paper we describe the link between commitment, risk taking and competition for managers. We emphasize the increase in competition for human talents that followed domestic and international liberalization of financial markets and its interplay with different degrees of contract enforcement, representing different organizational forms. Because of the limited enforcement of contracts, the increase in competition raises the managerial incentives to undertake risky investment. Although this may have a positive effect on economic growth, the equilibrium outcome is not efficient and generates greater risk-taking and income inequality.
Federal Reserve Bank of St. Louis
Unemployment Insurance Fraud and Optimal Monitoring
(Joint work with David L. Fuller and Yuzhe Zhang)
In this paper, we study the optimal monitoring of fraudulent behavior in a model of unemployment insurance. An unemployed agent who finds a job can hide his true employment status and continue claiming unemployment benefits. While most of the existing literature focuses on hidden search effort, the evidence suggests that the benefits overpaid because of fraud are more than ten times the overpayments due to insufficient search. We use a model with constant absolute risk aversion preferences, where employment status is private information. The agent transits to employment according to a Poisson process and employment is an absorbing state. The unemployment insurance agency has a costly verification technology to detect the agent’s true employment status. We consider pre-commitment mechanisms, formulate the problem as one of optimal control and apply the Pontryagin minimum principle. Our optimal mechanism uses two instruments: insurance and monitoring. We show that the optimal monitoring mechanism consists of cycles: the interval between two consecutive monitoring periods is a constant, independent of history. For the unemployed agent to report the transition to employment truthfully and without delay, it must be the case that delaying the report yields a lower payoff. Thus, late reporters face a higher wage tax relative to early reporters within each monitoring cycle. However, the wage tax decreases immediately after verification: the wage tax is non-monotonic. The consumption of the unemployed decreases with the duration of unemployment. It starts below the consumption of the employed at the beginning of each monitoring cycle, but eventually exceeds the consumption of the employed before the end of each cycle. Our mechanism also prevents quitting and rejection of employment opportunities.
New York University
Agency Models with Frequent Actions: A Quadratic Approximation Method
(Joint work with Tomasz Sadzik)
The paper analyzes dynamic principal-agent models with short period lengths. The two main contributions are: (i) an analytic characterization of the values of optimal contracts in the limit as the period length goes to 0, and (ii) the construction of relatively simple (almost) optimal contracts for fixed period lengths. Our setting is ‡flexible and includes the pure hidden action or pure hidden information models as special cases. We show how such details of the underlying information structure affect the optimal provision of incentives and the value of the contracts. The dependence is very tractable and we obtain sharp comparative statics results. The results are derived with a novel method that uses a quadratic approximation of the Pareto boundary of the equilibrium value set.
University of Edinburgh
Dynamic Relational Contracts with Limited Liability
(Joint work with Jonathan P. Thomas)
This paper considers a long-term relationship between two agents who undertake costly actions or investments which produce a joint benefit. Agents have an opportunity to expropriate some of the joint benefit for their own use. The question asked is how to structure the investments and division of the surplus over time so as to avoid expropriation. It is shown that investments may be either above or below the efficient level and that actions and the division of the surplus converges to a stationary solution at which either both investment levels are efficient or both are below the efficient level.
Federal Reserve Bank of Chicago
Human Capital Risk, Contract Enforcement, and the Macroeconomy
(Joint work with Tom Krebs and Moritz Kuhn)
We develop a macroeconomic model with physical and human capital, human capital risk, and limited contract enforcement. We show analytically that young (high-return) households are the most exposed to human capital risk and are also the least insured. We document this risk-insurance pattern in data on life-insurance drawn from the Survey of Consumer Finance. We show that a calibrated version of the model can quantitatively account for the life-cycle variation of insurance observed in the US data and estimate the welfare costs of under-insurance for young households to be equal to a 4 percent reduction in lifetime consumption. A policy reform that makes consumer bankruptcy more costly leads to a substantial increase in the volume of credit and insurance.