Dynamic Macroeconomics
ataozk@yahoo.com
Content
Objective
The aim of the Dynamic Macroeconomics course is to provide students with the theoretical and mathematical tools required to analyze the intertemporal optimization behavior of economic agents (households, firms, and the government) and its implications for macroeconomic equilibrium. To this end, the course applies dynamic optimization methods (calculus of variations, optimal control, dynamic programming) to core macroeconomic problems such as consumption-saving decisions, capital accumulation, growth, and business cycles; examines concepts such as equilibrium, stability, and multiplicity of equilibria; and develops and solves standard dynamic macroeconomic models, including the Solow model, the Ramsey-Cass-Koopmans model, and endogenous growth models. Ultimately, the course seeks to equip students with an analytical foundation that goes beyond static analysis, enabling them to model the time evolution of economic variables and to engage with the contemporary dynamic macroeconomics literature.
Course Content
1- Introduction to the calculus of variations and optimal control.
2- Study of elementary optimal dynamical systems. Problems of existence, multiplicity, and stability of equilibria.
3- Working through several examples and exercises.
4- Introduction to endogenous growth.
Course Learning Outcomes
By the end of this course, the student will be able to:
Explain the distinction between static and dynamic optimization and formulate intertemporal optimization problems
Apply the calculus of variations (Euler-Lagrange equation) and optimal control theory (Hamiltonian, Pontryagin's maximum principle, transversality conditions) to macroeconomic problems
Solve optimization problems using the dynamic programming approach (Bellman equation)
Model the household's intertemporal consumption-saving decision and the firm's capital accumulation/investment decision within a dynamic framework
Formulate and solve the Solow growth model, and analyze its steady-state equilibrium and comparative dynamics
Formulate the Ramsey-Cass-Koopmans (representative household) model and interpret its equilibrium conditions, phase diagram, and transitional dynamics
Explain the core logic of endogenous growth models and how they differ from exogenous growth models Romer and Lucas.
Analyze the existence, multiplicity, and stability of equilibria in dynamic systems (local/global stability, saddle-path property)
Relate the results obtained from theoretical models to the contemporary dynamic macroeconomics literature and policy debates
Teaching and Learning Methods
Theoretical and applied exercisesIn the Dynamic Macroeconomics course, instruction combines the presentation of the theoretical framework with applied problem-solving:
Theoretical lectures: presentation of the mathematical foundations of dynamic optimization methods (calculus of variations, optimal control, dynamic programming), derivation of the Euler-Lagrange equation, the Hamiltonian, and the Bellman equation, and theoretical treatment of equilibrium and stability concepts
Model building: step-by-step construction of the Solow, Ramsey-Cass-Koopmans, and endogenous growth models, derivation of equilibrium conditions, and their interpretation through phase diagrams
Applied problem-solving sessions: exercise sessions in which students apply the theoretical tools covered to concrete macroeconomic problems (consumption-saving decisions, capital accumulation, growth paths)
Weekly homework: consolidation of theoretical concepts and independent application of the mathematical tools (optimization, differential/difference equations)
Numerical/analytical examples: illustration of the existence, multiplicity, and stability of equilibria through simple dynamical systems; visualization of phase diagrams using computational software (MATLAB, Python) when needed
Discussion and case studies: relating theoretical results to the contemporary dynamic macroeconomics literature and policy examples
Assessment: evaluation of both theoretical understanding and problem-solving ability through a midterm exam, homework/exercises, and a final exam
References
Barro, R. J., Sala-i-Martin, X. — Economic Growth, MIT Press
Blanchard, O. J., Fischer, S. — Lectures on Macroeconomics, MIT Press
Romer, D. — Advanced Macroeconomics, McGraw-Hill
Acemoglu, D. — Introduction to Modern Economic Growth, Princeton University Press
Ljungqvist, L., Sargent, T. J. — Recursive Macroeconomic Theory, MIT Press
Chiang, A. C. — Elements of Dynamic Optimization, McGraw-Hill
Kamien, M. I., Schwartz, N. L. — Dynamic Optimization, North-Holland (Dover yeniden basımı)
Weekly Contents
| Week | Weekly Contents |
|---|---|
| 1 | Calculate variations. 1st order necessary conditions for fixed and free terminal point. |
| 2 | Exercices. |
| 3 | The optimal order. 1st order necessary conditions for fixed and free terminal point. |
| 4 | Exercices. |
| 5 | Sufficient conditions for the given final time. |
| 6 | Sufficient conditions for infinite horizon. |
| 7 | Exercices. |
| 8 | The neoclassical optimal model. |
| 9 | A simulation of the neoclassical optimal model. |
| 10 | The optimal neoclassical model with exogenous technical progress. The role of the condition of transversality. |
| 11 | Endogenous technical progress: Romer's model. Existence of equilibrium growth rates. |
| 12 | Endogenous technical progress: Lucas' model. Existence of equilibrium growth rates. Equivalence with the model of Romer. |
| 13 | A superficial introduction to the problem of existence, uniqueness and stability in the models of Romer and Lucas. |
| 14 | The conditions of transversality in the models of Romer and Lucas. |
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 0 | 0 |
| Contribution of final exam to overall grade | 0 | 0 |
| Total | 0 | 0 |
| Activities | Number | Contribution |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 0 | 0 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Total | 0 | 0 |
Relation of Proficiency
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Demonstrate a basic knowledge of different economic theories and main discussions driving current theoretical approaches | |||||
| 2 | Demonstrate ability to use basic qualitative and quantitative methods to asses different economic questions of applied fields | |||||
| 3 | Show a sound understanding of current economic discussions and problems | |||||
| 4 | Have an effective and clear communication in written and oral formats in different public and professional contexts. | |||||
| 5 | Demonstrate basic knowledge of the world economic history and a sound knowledge of the Turkish economic history | |||||
| 7 | Demonstrate knowledge of standard quantitative techniques and empirical models used in economics | |||||
| 8 | Show ability to apply basic economic theory to an applied topic | |||||
| 9 | Show a basic understanding of analytical methods, both theory- and model-based | |||||
| 10 | Show ability to use economic concepts to discuss current economic issues | |||||
| 11 | Reason logically and work analytically | |||||
| 12 | Show awareness on social aspects of the economics in different applied and theoretical fields | |||||
| 13 | Identify appropriate economic models to analyse problems | |||||
| 16 | Show understanding of basic statistical and econometric concepts and ability to apply basic concepts to own empirical work | |||||
| 17 | Demonstrate a sound knowledge of the current economic issues in Turkey and a general knowledge of the issues in the world economy | |||||
ECTS
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 3 | 42 |
| Working Hours out of Class | 14 | 2 | 28 |
| Assignments | 0 | 0 | 0 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 30 | 60 |
| Project | 0 | 0 | 0 |
| Laboratory | 2 | 10 | 20 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 0 | 0 | 0 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Make-up | 0 | 0 | 0 |
| Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Bütünleme | 0 | 0 | 0 |
| Total Workload | 150 | ||
| Total Workload / 25 | 6.00 | ||
| Credits ECTS | 6 | ||