AØKK08207U Dynamic Programming - Theory, Computation, and Empirical Applications
MSc programme in Economics – elective course
The PhD Programme in Economics at the Department of Economics:
- The course is an elective course with research module. PhD students must contact the study administration AND the lecturer in order to register for the research module and write the research assignment.
The overall purpose of the course is to provide a fundamental understanding of dynamic programming (DP) models and their empirical application. The dynamic programming 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. During exercise classes students will obtain hands on experiences and programming skills.
The students are going to write a project paper, where the purpose is to make students combine many of the simplified building blocks covered in the computer exercises. By combining these building blocks, students should be able to solve and estimate more sophisticated models later on.
After completing the course the student is expected to be able to:
- Account for 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.
- Account for estimation methods for dynamic structural models.
- Evaluate integrals involved in evaluating expectations future states of the world and to integrate unobservable out of the sample criterion used in estimation.
- Account for the numerical approximation and interpolation techniques required to approximate value functions over continuous state variables.
- Reflect on how to evaluate policy initiatives by means of counter factual simulations.
- Solve unique and multiple equilibria in general equilibrium models and simple dynamic games.
- Solve and/or estimate relatively simple models (cake eating, stochastic growth, consumption/savings, investment, labor demand/supply.
- Solve and estimate dynamic games or single agent models and test hypotheses using solution and estimation methods discussed in the course.
- Investigate the consequences policy proposals by means of counterfactual simulations program the estimators applied in the paper using Python (or MATLAB, GAUSS, FOTRAN and C)
- Discuss papers and master empirical analysis of a (simple) dynamic structural model
- Present an analysis in a short, structured and focused exam paper.
- Implement dynamic programming solution and estimation techniques on new economic problems.
- Carry through 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.
The courses Econometrics I from the Bachelor of Economics, University of Economics, or equivalent must have been completed.
Past experience with programming (preferable Python) is also recommended but not required. Programming in Python will mostly be self-study if students have no past experience with this.
In case of a pandemic like Corona the teaching in this course may be changed to be taught either fully or partly online. For further information, see the course room on Absalon.
2x2 hours lectures a week during 10½-11 weeks (from week 6 to 16 except holidays).
2 hours of exercise classes during 12 weeks (from week 6/7 to 17/18 except holidays).
The overall schema for the Master courses can be seen at KUnet:
MSc in Economics => "courses and teaching" => "Planning and overview" => "Your timetable"
KA i Økonomi => "Kurser og undervisning" => "Planlægning og overblik" => "Dit skema"
Timetable and venue:
To see the time and location of lectures and exercise classes please press the link/links under "Timetable"/"Se skema" at the right side of this page (F means Spring). The lectures are shown in each link.
You can find the similar information in English at
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-F21; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Forår/Spring – Week 5-30”
Press: “View Timetable”
Please be aware regarding exercise classes:
- The schedule of the exercise classe is only a pre-planned schedule and can be changed until just before the teaching begins without the participants accept. If this happens it can be seen in the personal schema, at the app myUCPH and at the links in the right side/above link.
- The student is not allowed to participate in an exercise class that the student is not registered.
- That the study administration allocates the students to the exercise classes according to the principles stated in the KUnet.
- That it is the students´s own responsibility to continuously update themselves about their studies, their teaching, their schedule, their exams etc. through the study pages, the course description, the Digital Exam portal, Absalon, KUnet, myUCPH app, the curriculum etc.
- Class Instruction
The lecturer will give collective oral feedback at a workshop at which students present their project descriptions for their exam paper.
The teaching assistant will give individual oral feedback during the exercise class.
For gæste- og enkelfagsstuderende: Tilmelding via Uddannelse i Økonomi.
- 7,5 ECTS
- Type of assessment
- Oral examination, 20 minWritten assignment, 4 weeksThe exam is an individual oral exam defending a project paper.
Please be aware of:
• The project paper can be written individually or in groups up to 3 students. The plagiarism rules must be complied and please be aware of the rules for co-writing assignments.
• The project paper and the oral defence must be written in English.
In the event that this summer's exams have to be conducted as online exams due to COVID-19, the exam form will be a take-home exam with an online oral exam without preparation. The reexam will be the same as the rescheduled ordinary exam, but possibly online orally if only few students register.
- Exam registration requirements
There are no requirements that the student has to fulfill during the course to be able to sit the exam.
- All aids allowed
for the project paper.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
The oral defence may be with external assessment.
- Exam period
The regular exam:
The project paper must be uploaded no later than:
10 June 2021 at 10 AM to Digital Exam
Oral defence without preparation:
24th and/or 25th of June 2021
Only the project paper is allowed at the oral examination.
Note: The dates can change in special circumstances.
In case of COVID-19 restrictions, please refer to "Type of assessment".
In Digital Exam from the middle of the semester.
The reexam: In week 32, August 2021
as an individual oral exam defending the project paper, without preparation time. Only the project paper is allowed at the oral examination. The project paper must be uploaded no later than: 30 July 2021 at 10 AM to Digital Exam
The paper can be based on the same material as the non-passed paper. Note: The dates can change in special circumstances. In case of COVID-19 restrictions, please refer to "Type of assessment".
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 with no or only a few minor weaknesses be able to demonstrate an excellent performance displaying a high level of command of all aspects of the relevant material and can make use of the knowledge, skills and competencies listed in the learning outcomes.