AØKK08207U  Dynamic Programming - Theory, Computation, and Empirical Applications

Volume 2017/2018

The overall purpose of the course is to provide a fundamental understanding of dynamic programming (DP) models and their empirical application. The DP framework has been extensively used in economic modeling because it is sufficiently rich to model almost any problem involving sequential decision making over time and under uncertainty. Prominent examples are saving/consumption decisions, retirement behavior, investment, labor supply/demand, housing decisions. The course will first introduce participants to theoretical concepts, and then focus on empirical applications covering both discrete and continuous decision problems as well as the estimation of dynamic games.

Learning Outcome

The purpose of the lectures and the exercise classes is that the student should

Acquire knowledge, skills and competencies related to stochastic dynamic programming and the involved computational hurdles (curse of dimensionality, high dimensional integration, multiplicity of solutions, etc.)

After completing the course, the student should be able to:


  • Acquire knowledge about solution methods (backward recursion, value function iterations, policy iterations, endogenous grid method) for dynamic structural models of sequential decision making under uncertainty of both finite and infinite horizons and for single and multiple agents.

  • Acquire knowledge about solving for unique and multiple equilibria in general equilibrium models and simple dynamic games.

  • Acquire knowledge about estimation methods (full solution methods: Mathematical Programming with Equilibrium Constraints (MPEC) and Nested Fixed Point Algorithm (maximum likelihood, minimum distance, indirect inference, GMM and simulation versions of these); Non-full solution methods: CPP-estimator, Nested Pseudo likelihood (policy iteration estimators); GMM using Euler equations).

  • Acquire knowledge about numerical techniques to evaluate integrals (quadrature methods andMonte Carlo integration) involved in evaluating expectations future states of the world and to integrate unobservable out of the sample criterion used in estimation (e.g. the likelihood function).

  • Acquire knowledge about the numerical approximation and interpolation techniques required to approximate value functions over continuous state variables (splines, orthogonal polynomials, neural net).

  • Acquire knowledge about a variety of dynamic structural models

  • Acquire knowledge about how evaluate policy initiatives by means of counter factual simulations


Skills obtained through exercise classes

  • Students will obtain (programming) skills though hands on experiences with solving and/or estimating relatively simple models (cake eating, stochastic growth, consumption/savings, investment, labor demand/supply and simple dynamic games).

Skills obtained through Term paper

  • The purpose of the term paper is to make students combine many of the simplified building blocks we covered in the computer exercises. By combining these building blocks, students should be able to solve and estimate more sophisticated model. In particular the students should

  • Solve and estimate dynamic games or single agent models and test hypotheses using solution and estimation methods discussed in the course. Ideally students should be able to replicate the results from an already published paper and thereby get hands on experience with the involved techniques.

  • Investigate the consequences policy proposals by means of counterfactual simulations program the estimators applied in the paper using MATLAB (or GAUSS, FOTRAN and C)

  • Present the analysis in a short and focused term paper.


  • Hence, after completing the course, the student should have obtained the competencies in dynamic programming theory and practice and thereby be able to understand papers and undertake empirical analysis on a (simple) dynamic structural model and to present the analysis in a short and focused paper.


The acquired competencies in dynamic programming theory and practice provide a strong background that enable students to do empirical analyses at a high level suitable for a Master or even a PhD thesis.


  • Jérome Adda and Russell Cooper: “Dynamic Economics: Quantitative Methods and Applications” MIT Press 2003, ISBN: 978-0-262-01201-0

  • Kenneth Judd: “Numerical Methods in Economics” MIT Press 1998, ISBN: 978-0-262-10071-7

  • 15-20 papers: Ranging from classic seminal contributions to recent state of the art work from the research frontier.


Pre-requisites are Micro III, Macro III, Econometrics I-II. Strongly recommended is Advanced Microeconometrics. While the latter is essential as this course provides the necessary computational skills (MATLAB Programming) and knowledge about estimation techniques, it is not a formal requirement.
The lectures focus on theory whereas the class provides hands on knowledge of solution and estimation of the models. Ideally, the whole process of estimating a dynamic structural model empirically is learned by writing a term paper that has to be handed in at the end of the semester.
2x2 hours lectures a week from week 6 to 17 (except holidays).
2 hours of exercise classes from week 6 to 18

Timetable and venue:
The schedule for the semester spring 2018 will be available no later than 7th of November 2017
7,5 ECTS
Type of assessment
Oral examination, 25 min under invigilation
Written assignment
The exam is an oral defence of the project assignment. The project assignment and defence must be in English.

All aids can be used to the project assignment.

The student can only take the project assignment in to the oral examination, nothing els.



Marking scale
7-point grading scale
Censorship form
External censorship
if chosen by the Head of Studies.
Exam period

The schedule for the exam 2018 will be available no later than 7th of November 2017

For enrolled students more information about examination, rules, exam schedule etc. is available at the intranet for master students (UK) and master students (DK).



Oral exam in week 35-36 with the same assignment and examination in the hole syllabus.

Exact date and time will be made in agreement with the teacher and the Exam Office.


For enrolled students more information about reexamination, rules, schedule etc. is available at the intranet for master students (UK) and master students (DK).

Criteria for exam assesment

Students are assessed on the extent to which they master the learning outcome for the course.

To receive the top grade, the student must be able to demonstrate in an excellent manner that he or she has acquired and can make use of the knowledge, skills and competencies listed in the learning outcomes.

  • Category
  • Hours
  • Lectures
  • 42
  • Class Instruction
  • 24
  • Preparation
  • 140
  • Exam
  • 0,42
  • Total
  • 206,42