ECO529: Fall 2022
- Syllabus
- Lecture Notes (preliminary and evolving)
- Lecture Zoom Video Links
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Outline
1. Introduction
2. Why Continuous Time Modeling
- 02slides
- 02video
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3. Continuous Time Stochastic Optimization (Consumption, Portfolio)
- 03slides
- Stochastic Calculus Basics
- Differential Equations Basics
- Problem Set Basics
- 03video_a, 03video_b
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4. A Simple Macro-Finance Model with Heterogeneous Agents
- 04slides
- 04video
- TA Session 01
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5. Endogenous Risk Dynamics with Log utility
- 05slides
- 05video_a, 05video_b
- TA Session 02
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6. ... with CRRA and Epstein-Zin utility, ValueFcn Backwards Iteration
- 06slides
- 06video
- TA Session 03
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7. Kolmogorov Forward Equation
- 07slides
- 07video
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8. Numerical Methods (Andrey Alexandrov)
- 08slides
- 08video
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Videos by Yuliy Sannikov
- 8.01 Introduction: General Class of Equations
- 8.02 Example: Valuation Equation and HJB
- 8.03 Forward and Backward Equations: HJB, KFE
- 8.04 Finite Difference Schemes: Key Principles
- 8.05 Finite Difference Operator and sign of Matrix M
- 8.06 Explicit Scheme
- 8.07 Implicit Scheme
- 8.08 Stationary Value Function in a Single Step
- 8.09 KFE using Matrix M
- 8.10 General Class of HJB in One Dimension
- 8.11 Solving HJB
- 8.12 Non-monotone Schemes (what can go wrong?)
- 8.13 Valuation Equation in m Dimensions
- 8.14 Convex Positive Semidefinite Cone
- 8.15 Some Geometry Details in Two Dimensions
- 8.16 The Algorithm for the 2nd-order Term in Two Dimensions
- 8.17 Assembling M and Solving the Valuation Equation
- 8.18 Solving HJB Equation in m Dimensions
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9. Endogenous Risk Dynamics with Jumps
- 09slides
- 09video
- TA Session 04
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10. Monetary Model with one Sector
- 10slides
- 10video_a_Overview
- 10video_b_constant idiosyncratic risk
- 10video_c_FTPL_stochastic idiosyncratic risk
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11. Cash vs. Cashless + I Theory of Money
- 11slides
- 11video_a
- 11video_b
- TA Session 05
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12. Welfare and Optimal Policy
- 12slides (from 2021)
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13. International Finance, Exchange Rate, Sudden Stops
- 13slides (from 2021)
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13. Digital Money and Digital Currency Areas
Description
In models with financial frictions, a setting with heterogeneous agents is paramount. In addition to the consumption choice, the portfolio choice of the various agents is the focus of this course. The risk itself is endogenous and so is the price of risk leading to a time-varying risk premia. Agents save for precautionary reasons in the safe asset, which consists of money and government bonds – possibly priced as a bubble. The course draws a link to leading monetary theories. As idiosyncratic risk rises, flight-to-safety flows kick in leading to endogenous consumption demand shocks. Monetary policy is necessary to avoid deflationary and liquidity spirals. The safe asset perspective sheds new light on debt sustainability analysis, currency competition, international capital flows, also in the light of emergence of new digital forms of money. New concepts like Digital Currency Areas and digital dollarization will be discussed.
Past Semesters
- Fall 2021
- Fall 2020
- Spring 2019
- Fall 2019