AØKK08207U Dynamic Programming - Theory, Computation, and Empirical Applications

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

• 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.)

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.
• 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 and  Monte 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).

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:

• 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.