Dynamic incentive problems show up repeatedly in macroeconomics. Examples include dynamic public finance questions about the design of unemployment insurance, disability insurance, or life-cycle income and savings taxation; lending relationships between investors and entrepreneurs; sovereign borrowing; or dynamic wage contracts in firms. Unlike complete-markets models or standard (exogenously) incomplete markets models (e.g., risk-free bond + exogenous borrowing limit), in these problems markets are endogenously incomplete in that the extent of risk sharing is determined endogenously by information or enforcement frictions (Golosov et al., 2016). The essential insight is that these problems can be made recursive by adding appropriate "forward looking" state variables (Ljungqvist and Sargent, 2018)— e.g., a promise to deliver some utility to an agent in the future.

The objectives of the course are: (i) to understand how different frictions (limited commitment, moral hazard and private information) shape risk sharing; (ii) to learn how to formulate and analyze these problems recursively, and provide a brief introduction to numerical methods; (iii) to provide a broad overview of the many applications. Ideally, the course will be of interest to both macro and theory students. Below is a tentative outline.

Lecture 1. Introduction and limited commitment
• Overview; exogenously vs endogenously incomplete markets.
• Limited commitment (Thomas and Worrall, 1988) and discussion of applications

Lecture 2. Dynamic moral hazard
• Dynamic moral hazard with an application to optimal unemployment insurance (Spear and Srivastava, 1987)
• Somediscussion on the hidden savings problem

Lecture 3. Private information and introduction to dynamic public finance
• Dynamic insurance with private information (Thomas and Worrall, 1990; Atkeson and Lucas Jr, 1992); Long-run immiseration
• Introduction to new dynamic public finance (NDPF): (i) Mirrleesian taxation, (ii) adding dynamics, (iii) Inverse Euler Equation, (iv) Implications of persistent private information
Lecture 4. Continue NDPF and introduction to computational methods
• Continue NDPF
• Discussion of computational challenges and introduce the recursive Lagrangian method (Marcet and Marimon, 2019). The issues and methods presented here apply to more problems beyond the dynamic contract ones studied in the course, such as Ramsey optimal policy
problems. 

Lecture 5. Cover some applications based on interests and/or student presentations
Ideally, we will focus more quantitative papers that try to bring these methods closer to data. Some topics/papers that could be covered (to be expanded):
• Sovereigndebt/International risk sharing: KehoeandPerri(2002), Aguiaretal. (2009), Dovis (2019), Abrahám et al. (2025)
• Quantitative macro-labor: Schaal (2017), Balke and Lamadon (2022), Souchier (2022)
• Further public finance topics (including unemployment and disability insurance): Golosov
and Tsyvinski (2006)
• Development: Ligon et al. (2002), Morten (2019)
• Corporatefinance/firmdynamics/entrepreneurship/CEOcompensation: ClementiandHopenhayn (2006), DeMarzo and Sannikov (2006), Edmans et al. (2012)
• Asset pricing: Kehoe and Levine (1993), Alvarez and Jermann (2000), Alvarez and Jermann (2001)

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