Course Plan

All lectures and exercise classes will be online through Zoom!

Zoom-Link: https://ucph-ku.zoom.us/j/3538047316

Zoom-Link exercises: https://ucph-ku.zoom.us/j/62125688670

Exercises

Deadlines:

• TBA: Submit project description here.
• TBA: Project presentations?
• June 10 (10AM): Submit project. 8-12 pages per person (font size 12, double spacing and 3 cm margins).
• Thursday 24 and Friday 25 of June (week 25): Oral exam (20 min).

Term paper:

You can find some previous papers and some ideas under "Files" -> "term paper".

Books:

• Adda, Jerome, and Cooper, Russell. Dynamic economics: quantitative methods and applications, MIT press, 2003 (download (Links to an external site.)Links to an external site.).

• Judd, Kenneth L. Numerical methods in economics. MIT press, 1998.

Python resources:

• Course by Jeppe Druedahl here: https://numeconcopenhagen.netlify.com/ Links to an external site.
  • Follow the installation guide from this webpage!
  • We will be using the same work-flow as suggested in this course
• Quant Econ: https://quantecon.org/ Links to an external site.
• Data Camp: https://www.datacamp.com/ Links to an external site.
• Python and Dynamic Programming by Fedor Iskhakov: https://fedor.iskh.me/compecon Links to an external site.

Venue:

• Wednesday from 10:00-12:00.
• Thursday from 10:00-12:00.

Schedule:

TJ: Thomas Jørgensen Links to an external site.

BS: Bertel Schjerning

JD: Jeppe Druedahl (guest lectures)

Date	Content	Preparation	Material
Part I: Theory and tools (by Thomas Jørgensen)
wed feb 10	Lecture 1: Introduction You will learn why dynamic programming is an indispensable tool for developing realistic economic models and evaluating counter-factual policies. You will learn how the idea of backwards induction known from game theory can be applied to solve dynamic stochastic optimization problems. The example is the simplest consumption-saving model imaginable. You will be introduced to the basic vocabulary of dynamic programming (states, choices, transitions). You will get an overview of the plan and content of the course, and understand what you will be doing.	1: Survey Links to an external site. 2: look at this notebook. Download look at this notebook. (if you have trouble opening the notebook, see the pdf-version here! Download here! )	Slides Download Slides
thur feb 11	Lecture 2: The Bellman Equation You will learn how to turn a real world economic optimization problem into a Bellman equation using Bellman's principle of optimality. You will learn that the problem can have both discrete and continuous elements, and be deterministic or stochastic. You will understand the need for numerical interpolation in the continuous case. Examples are extensions of the model used in the first lecture.	1: Bellman + optimality (until 7:00mins) Links to an external site. 2: Cake-eating problem (using backward induction) (6mins) Links to an external site. 3: Extra (infinite horizon cake-eating and guess and verify) (6mins) Links to an external site.	Slides Download Slides
wed feb 17	Lecture 3: Numerical Integration + Simulation  You will learn how to handle continuous shocks by using numerical integration (Monte Carlo, equiprobable and Gaussian quadrature). You will learn to do counter-factual simulations and how to determine the accuracy of the policy function you have found.	Have a look at this notebook on Monte Carlo integration Download Have a look at this notebook on Monte Carlo integration 1: Gaussian Quadrature (example). A bit slow but good intro. (9.34 min) Links to an external site. 2: Euler equation (simple example) (13:39 mins -> speed up) Links to an external site. Extra Euler (variational argument) Links to an external site. Extra Gaussian 1 (finding Gaussian weights) Links to an external site. Extra Gaussian 2 (picking Gaussian points) Links to an external site.	Slides Download Slides notebook illustrating  nodes and weights Download notebook illustrating  nodes and weights
thur feb 18	Lecture 4: The Bellman Operator You will be introduced to infinite horizon optimization problems and the Bellman equation on operator form. You will learn fundamental theoretical results such at the contraction mapping theorem and Blackwell's theorem. You will learn how to use policy iteration as an alternative to value function iteration. You will learn how to translate a verbal economic problem into a Bellman equation		Slides Download Slides
wed feb 24	Lecture 5: Function Approximation + The Curse of Dimensionality You learn how to approximate functions with both finite element and spectral methods in one or multiple dimensions. You will understand the three curses of dimensionality inherent in solving large models by numerical dynamic programming. You will learn various tips and trics to allevate the curse of dimensionality.	1: Linear interpolation (5:19 mins) Links to an external site. 2: Notebook illustrating numerical accuracy on a computer Download 2: Notebook illustrating numerical accuracy on a computer 3: OLS interpolation Download 3: OLS interpolation 4: loop order Download 4: loop order	Slides Download Slides
thu feb 25	Lecture 6: RECAP: Write to me if there is something you would like me to recap. Otherwise it will be a workshop for you to work on the exercises with guidance from me. Extra exercise if done: Solve exercise 6 with policy iteration from lecture 4.
Part II: Consumption-saving models (By Thomas H. Jørgensen - and Jeppe Druedahl)
wed mar 3	Lecture 7: Buffer-Stock Consumption Model You will learn the canonical buffer-stock consumption model and how to solve it using the state-of-the-art endogenous grid method (EGM). You will learn to analyze the implied optimal consumption function and the importance of e.g. liquid constraints and income risk. Code: ConSavNotebooks Links to an external site. Required packages: ConSav Links to an external site.	Read section II of Carroll (1997) Download Carroll (1997)	Carroll (1997) Download Carroll (1997) Carroll (2012) Download Carroll (2012) ConsumptionSaving.pdf Download ConsumptionSaving.pdf
thu mar 4	Lecture 8: General Equilibrium You will learn to solve a stationary general equilibrium model with households behaving as described by a simple buffer-stock consumption model and a simple representative firm. You will also briefly hear about the Krusell-Smith algorithm to approximate the dynamic equilibrium when there are aggregate shocks.		Aiyagari (1994) Download Aiyagari (1994) Further reading: Krussel and Smith (1998) Download Krussel and Smith (1998) Algan et. al. (2014) Download Algan et. al. (2014)
tue mar 9 8-10	Lecture 9: Estimating the Buffer-Stock Model You will learn how to estimate the buffer-stock consumption model using either maximum likelihood or the method of simulated methods  (or e.g. indirect inference or minimum distance). You will also get an overview wrt. alternative estimations methods such as simulated maximum likelihood and MPEC.	Look at Gourieroux, Monfort and Renault (1993) Download Gourieroux, Monfort and Renault (1993) and Jørgensen (2013) Download Jørgensen (2013) Have a look at this example: notebook Download notebook, with lec9_model.py Download lec9_model.py This notebook  illustrates "identification"/ informativeness of moments in estimation. Download This notebook  illustrates "identification"/ informativeness of moments in estimation.	Gourcinhas and Parker (2002) Download Gourcinhas and Parker (2002) Druedahl and Jørgensen (2017a) Download Druedahl and Jørgensen (2017a) Slides Download Slides
thur mar 11	Lecture 10: Discrete-Continuous Choice Models You will learn to analyze consumption-saving models with non-convexities such as retirement or indivisible labor supply (none, half-time, full-time). You will learn how to apply generalizations of the EGM in this context.	Iskhakov et. al. (2016) Download Iskhakov et. al. (2016) Druedahl and Jørgensen (2017b) Download Druedahl and Jørgensen (2017b) Slides Download Slides
wed mar 17	Lecture 11: Extensions of the Buffer-Stock Consumption Model You will learn how to extend the buffer-stock consumption model yourself and build upon extensions found in the literature wrt. to e.g. durable goods, richer income dynamics, housing, richer balance sheets, and heterogeneity.	Download this collection of model sections Download Download this collection of model sections . Read at least one of the model sections (the full papers are available under files)	Slides Download Slides
PART III: Estimation of dynamic discrete choice models [DATES NOT UPDATED!]
thur mar 18:    Lecture 12: The Nested Fixed Point Algorithm (NFXP) wed mar 24:    Lecture 13: Constrained Optimization Approaches to Structural Estimation   thu mar 25:     Lecture 14:  Zurcher on Steroids: Residential and Work Location Choice  wed mar 31:   Lecture 15 ( Zurcher on Steroids II): Equilibrium Trade in Automobile Markets  thu apr 1:      Easter - NO lecture  wed apr 8:      Lecture 17: Nested Pseudo Likelihood (NPL) and CCP estimators.
Part IV:_ Solving and estimation of dynamic games
thu apr 9:        Lecture 18: Solving and estimating static games of incomplete information  thu apr 15:      Lecture 19: Structural Estimation of Dynamic Games using MPEC, NPL and 2-step-PML  wed apr 24     Lecture 20 and 21: Solving  and estimating directional dynamic games with multiple equilibria using RLS   thu apr 25     Lecture 20 and 21: Solving  and estimating directional dynamic games with multiple equilibria using RLS Endogenous date:  Meetings with individual/group supervision of term papers (8--14)