Dynamic Programming - Theory, Computation, and Empirical Applications
Course content
The overall purpose of this advanced 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. In order to register for the research module and to be able to write the research assignment, the PhD students must contact the study administration AND the lecturer.
The course is open to:
- Exchange and Guest students from abroad
- Credit students from Danish Universities
- Open University students
After completing the course the student is expected to be able to:
Knowledge:
- 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.
Skills:
- 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.
Competences:
- 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.
- 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, Econometrics II, Introduction to Programming
and Numerical Analyses, or Programming for Economists at the
Economics Program, University of Copenhagen, or similar courses,
have been followed.
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 strongly
recommended.
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 enrolled students: Rules etc at Master(UK) and Master(DK)
When registered you will be signed up for exam.
- Full-degree students – sign up at Selfservice on KUnet
- Exchange and guest students from abroad – sign up through Mobility Online and Selfservice- read more through this website.
- Credit students from Danish universities - sign up through this website.
- Open University students - sign up through this website.
The dates for the exams are found here Exams – Faculty of Social Sciences - University of Copenhagen (ku.dk)
Please note that it is your own responsibility to check for overlapping exam dates
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral examination, 20 minHome assignment, 4 weeks
- Type of assessment details
- Individual oral examination (20 minutes) defending a project
paper (4 weeks).
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. - Examination prerequisites
-
There are no requirements that the student has to fulfill during the course to be able to sit the exam.
- Aid
- All aids allowed
Use of AI tools is permitted. You must explain how you have used the tools. When text is solely or mainly generated by an AI tool, the tool used must be quoted as a source.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
- Exam period
-
Exam information:
The examination date can be found in the exam schedule here
More information is available in Digital Exam from the middle of the semester.
More information about examination, rules, aids etc. at Master (UK) and Master (DK).
- Re-exam
-
Same as the ordinary exam.
Reexam information:
The reexamination date/period can be found in the reexam schedule here
More information in Digital Exam in August. More information at Master UK) and Master DK)
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)
- Category
- Hours
- Lectures
- 42
- Class Instruction
- 24
- Preparation
- 100
- Project work
- 40
- English
- 206
Kursusinformation
- Language
- English
- Course number
- AØKK08207U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
Ph.D.
- Duration
-
1 semester
- Placement
- Spring
- Price
-
Information about admission and tuition fee: Master and Exchange Programme, credit students and guest students (Open University)
- Studyboard
- Department of Economics, Study Council
Contracting department
- Department of Economics
Contracting faculty
- Faculty of Social Sciences
Course Coordinator
- Bertel Schjerning (17-4e717e8071783a5f6f7476717e7a757a734c716f7b7a3a77813a7077)
Teacher
See ‘Course Coordinators’
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Kursusinformation for indskrevne studerende