Dynamic Programming - Theory, Computation, and Empirical Applications
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.
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.
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.
The lectures focus on theory where as the exercise classes
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 the exam paper.
Restrictions due to pandemic crisis:
The teaching in this course may be changed to be taught either fully or partly online due to a pandemic crisis like COVID-19. In case of changes and further information, please read the study messages in KUnet or the announcements in the course room on Absalon (for enrolled students).
- 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.
It is strongly recommended that Macroeconomics III,
Microeconomics III and Econometrics II at the Study of Economics,
University of Copenhagen, or similar courses, has been followed
prior taking Dynamic of Programming.
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.
2x2 hours lectures a week from week 6 to 16.
2 hours of exercise classes from week 6/7 to 17/18.
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-F22; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Forår/Spring – Week 5-30”
Press: “View Timetable”
Please be aware:
- The study administration allocates the students to the exercise classes according to the principles stated in the KUnet.
- If too many students have wished a specific class, students will be registered randomly at another class.
- It is not possible to change class after the second registration period has expired.
- If there is not enough registered students or available teachers, the exercise classes may be jointed.
- The student is not allowed to participate in an exercise class not registered.
- All exercise classes will be taught in English.
- The schedule of the lectures and the exercise classes can be changed without the participants´ acceptance. If this happens you can see the new schedule in your personal timetable at KUnet, in the app myUCPH and through the links in the right side and the link above.
- It is the students´s own responsibility continuously throughout the study to stay informed about their study, their teaching, their schedule, their exams etc. through the curriculum of the study programme, the study pages at KUnet, student messages, the course description, the Digital Exam portal, Absalon, the personal schema at KUnet and myUCPH app etc.
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.
Foreign students and guests: Information about admission requirements, application, tuition fee, registration at Study Economics.
Please read the curriculum before enrolment.
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 that:
• The project paper can be written individually or in groups up to 3 students.
• The plagiarism rules and the rules for co-writing assignments must be complied.
• The project paper and the oral defence must be in English.
- All aids allowed
for the project paper.
Information about allowed aids for the re-examination, please go to the section "Re-exam".
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
for the written exam.
The oral examination may be with external assessment.
Criteria for exam assessment
Students are assessed on the extent to which they master the learning outcome for the course.
In order to obtain the top grade “12”, 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.
In order to obtain the passing grade “02”, the student must in a satisfactory way be able to demonstrate a minimal acceptable level of the knowledge, skills and competencies listed in the learning outcomes.
Single subject courses (day)
- Class Instruction
- Project work
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Go to 'Signup' for
information about registration and enrollment.
Information about admission and tuition fee: Master and Exchange Programme, credit students and guest students (Open University)
- For teaching: Go to 'Remarks'.
- For exam and re-sits: Go to 'Exam'.
- Department of Economics, Study Council
- Department of Economics
- Faculty of Social Sciences
- Bertel Schjerning (17-44677476676e3055656a6c6774706b70694267657170306d7730666d)
Lectures: See ‘Course Coordinators’
Teacher for exercise classes;
Ex. class 1: Jeppe Elholm Madsen
Ex. class 2: Jeppe Elholm Madsen
Please read "Remarks" regarding the schedule of the teaching.
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Courseinformation of students