2200-F21;Dynamic Programming - Theory, Computation, and Empirical Applications

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:

Python resources:

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 Download here!

)

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.

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.

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
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

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 Download Carroll (1997) Download Carroll (1997)
Download Carroll (2012) 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.
Download Aiyagari (1994)

Further reading:
Download Krussel and Smith (1998)
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  Download Gourieroux, Monfort and Renault (1993)

and Download Jørgensen (2013)

Have a look at this example: notebook Download notebook, with Download lec9_model.py

This notebook  illustrates "identification"/ informativeness of moments in estimation. Download This notebook  illustrates "identification"/ informativeness of moments in estimation.

Download Gourcinhas and Parker (2002)


Download Druedahl and Jørgensen (2017a)

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.

Download Iskhakov et. al. (2016)


Download Druedahl and Jørgensen (2017b)

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 Download this collection of model sectionsView in a new window. Read at least one of the model sections (the full papers are available under files)
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)