# Dynamic Programming - Theory, Computation, and Empirical Applications

### Course content

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.

Education

MSc programme in Economics – elective course

The PhD Programme in Economics at the Department of Economics - elective course with resarch module (PhD students must contact the study administration and the lecturer in order to write the research assignment)

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:

Knowledge:

• 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:

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.

Competencies:

• 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.

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.

• 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.

Schedule:
2x2 hours lectures a week from week 6 to 18 (except holidays).
2 hours of exercise classes from week 6 to 18

The overall schema for the Master can be seen at
https:/​/​intranet.ku.dk/​ECONOMICS_MA/​COURSES/​COURSECATALOGUE-F18/​Pages/​default.aspx

Timetable and venue:
To see the time and location of lectures and exercise classes please press the link/links under "Se skema" (See schedule) at the right side of this page (E means Autumn, F means Spring). The lectures is shown in each link.

You can find the similar information partly in English at
https:/​/​skema.ku.dk/​ku1718/​uk/​module.htm
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-F18; [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 will be informed at the intranet or can be seen in the app myUCPH and at the above link.
- The student is not allowed to participate in an exercise class not registered, because the room has only seats for the amount of registered student.
- That the study administration allocates the students to the exercise classes according to the principles stated in the KUnet.

ECTS
7,5 ECTS
Type of assessment
Oral examination, 25 min under invigilation
Written assignment
The exam is an individual oral exam, without preparation, defending the project paper. The project assignment 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 paper and the oral defence must be in English.
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Aid

All aids can be used to the project assignment.

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

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Marking scale
Censorship form
No external censorship
The course can be selected for external assessment.
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##### Criteria for exam assessment

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.

Single subject courses (day)

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