|
Course title |
Economic Complexity and Nonlinear Dynamics |
|
Semester |
109-2 |
|
Designated for |
COLLEGE OF SOCIAL SCIENCES GRADUATE INSTITUTE OF ECONOMICS |
|
Instructor |
NICOLO PECORA |
|
Curriculum Number |
ECON5182 |
|
Curriculum Identity Number |
323EU7520 |
|
Class |
|
|
Credits |
3.0 |
|
Full/Half
Yr. |
Half |
|
Required/
Elective |
Elective |
|
Time |
Tuesday 3,4(10:20~12:10) Thursday 3(10:20~11:10) |
|
Remarks |
Restriction: juniors and beyond OR Restriction: MA students and beyond OR Restriction: Ph. D students
The upper limit of the number of students: 30. |
|
Ceiba Web Server |
http://ceiba.ntu.edu.tw/1092ECON5182_ |
|
Course introduction video |
|
|
Table of Core Capabilities and Curriculum Planning |
Table of Core Capabilities and Curriculum Planning |
|
Course Syllabus
|
|
Please respect the intellectual property rights of others and do not copy any of the course information without permission
|
|
Course Description |
The economy is a complex system with nonlinear interactions. The complexity modeling paradigm has been strongly sustained since the 1980s by economists and multidisciplinary scientists from various fields, and has also drawn the attention of policy makers dealing with complex phenomena and unpredictable market transitions. The linear and stable view of the economy was criticized in the 1940s and 1950s, mainly because it did not offer an economic explanation of observed fluctuations. Instead, according to the nonlinear viewpoint, the economy may be intrinsically unstable and, even in the absence of external shocks, fluctuations and complex dynamics can arise in the evolution of the economic variables.
This course introduces students to the dynamic analysis of economic phenomena by means of appropriate mathematical methods and with the eventual use of software for the numerical simulations of the models that describes such phenomena. Traditional frontal classes will be complemented with practical lessons, in which the use of some open-source software for the analysis of dynamical systems is presented (e.g. Maxima, E&F chaos). |
|
Course Objective |
Course Objective:
The course has the objective of introducing quantitative and numerical instruments for the formalization and the study of dynamic models that describe complex nonlinear dynamic phenomena in a wide range of economic fields, such as macroeconomics, microeconomics, finance, industrial organization, etc. Additionally, the applications of complexity modeling to economics and finance is also of relevance. Finally, the course aims at proposing a critical analysis of a selected literature on economic dynamics, in particular on behavioural models with heterogeneous boundedly rational agents.
Course outline (Course Schedule of 16 weeks):
Week 1: Eigenvalues, Eigenvectors, complex numbers. Basic Definitions of dynamical systems theory (fixed point, local stability, global stability).
Week 2: One-Dimensional systems: from linear to nonlinear differential equations. Application: the cobweb model.
Week 3: Local bifurcations: Saddle-Node, Transcritical, Pitchfork, Flip. Application: the Solow growth model.
Week 4: Two-dimensional systems: from linear to nonlinear systems of differential equations. Application: the IS-LM model.
Week 5: Local bifurcations: Andronov-Hopf bifurcation. Application: the Kaldor model.
Week 6: N-dimensional systems: from linear to nonlinear systems of differential equations. Economic applications to macro, microeconomics and finance.
Week 7: Difference between continuous-time and discrete-time formulation of dynamic models.
Week 8: One-Dimensional maps: from linear to nonlinear difference equations. Application: the cobweb model.
Week 9: The Logistic map and Deterministic Chaos in discrete time.
Week 10: Local bifurcations: Saddle-Node, Transcritical, Pitchfork, Flip. Examples.
Week 11: Two-dimensional maps: from linear to nonlinear systems of difference equations. Application: the Cournot model.
Week 12: Local bifurcations: Neimark-Sacker bifurcation. Global bifurcations and basins of attractions.
Week 13: Piecewise-linear maps. Applications to financial markets.
Week 14: Expectations feedbacks and dynamics: the nonlinear cobweb model.
Week 15: Modelling complexity through behavioral models with boundedly rational agents: heterogeneous agents models, behavioral macroeconomics and evolutionary finance.
Week 16: Final project |
|
Course Requirement |
Grading:
Grading consists in two parts. The first part regards three assignments, that will be provided every four weeks, and that have to be resubmitted individually or in pairs.
The assignments contribute for 30% of the final grade.
The second part regards the final project. Students need to choose one selected research paper (e.g. among those of the extension readings, or to be agreed among others that deal with the topics addressed in the course), replicate and discuss the main results as their final project. The final project has to be done individually.
Requirements for students after the class:
At the end of the course students should:
1. have acquired the knowledge and the comprehension of the tools of nonlinear systems theory and be able to apply the mathematical methods described in the program in order to analyze economic problems;
2. be able to understand the translation of a real world situation into a mathematical model.
3. be able to deal with complex problems by using the mathematical tools.
4. analyse and eventually perform simulations of periodic and chaotic solutions and provide interpretation of the numerical results;
5. have learned a rigorous and essential language that allows them to communicate the knowledge on economic dynamics clearly and effectively, with a special focus on behavioural models with boundedly rational agents. |
|
Student Workload (expected study time outside of class per week) |
|
|
Office Hours |
Thu. 13:30~14:30 |
|
Designated reading |
G.I. Bischi, F. Lamantia, D. Radi, Lecture notes on Dynamical Systems in Economics and Finance.
(these lecture notes will be directly provided in class)
|
|
References |
Further readings:
-Brock, W. A., & Hommes, C. H. (1997). A rational route to randomness. Econometrica: Journal of the Econometric Society, 1059-1095.
-Brock, W. A., & Hommes, C. H. (1998). Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic dynamics and Control, 22(8-9), 1235-1274.
-Agliari, A., Massaro, D., Pecora, N., & Spelta, A. (2017). Inflation targeting, recursive inattentiveness, and heterogeneous beliefs. Journal of Money, Credit and Banking, 49(7), 1587-1619.
-Assenza, T., Bao, T., Hommes, C., & Massaro, D. (2014). Experiments on expectations in macroeconomics and finance. Experiments in macroeconomics, 17(2014), 11-70.
Eventual further study material will be made available.
Extension readings
-Hommes, C.H. (2013). Behavioral rationality and heterogeneous expectations in complex economic systems. Cambridge University Press, Cambridge, UK
-Day, R. H., & Huang, W. (1990). Bulls, bears and market sheep. Journal of Economic Behavior & Organization, 14(3), 299-329.
- Wegener, M., Westerhoff, F., & Zaklan, G. (2009). A Metzlerian business cycle model with nonlinear heterogeneous expectations. Economic Modelling, 26(3), 715-720.
-Naimzada, A., & Sodini, M. (2010). Multiple attractors and nonlinear dynamics in an overlapping generations model with environment. Discrete Dynamics in Nature and Society, 2010.
-Dieci, R., & Westerhoff, F. (2012). A simple model of a speculative housing market. Journal of Evolutionary Economics, 22(2), 303-329.
- Fanti, L., & Gori, L. (2012). The dynamics of a differentiated duopoly with quantity competition. Economic Modelling, 29(2), 421-427.
-Naimzada, A. K., & Tramontana, F. (2012). Dynamic properties of a Cournot–Bertrand duopoly game with differentiated products. Economic Modelling, 29(4), 1436-1439.
-Anufriev, M., Assenza, T., Hommes, C., & Massaro, D. (2013). Interest rate rules and macroeconomic stability under heterogeneous expectations. Macroeconomic Dynamics, 17(8), 1574-1604.
- Naimzada, A., & Pireddu, M. (2014). Dynamics in a nonlinear Keynesian good market model. Chaos: An Interdisciplinary Journal of Nonlinear Science, 24(1), 013142.
-Flaschel, P., Charpe, M., Galanis, G., Proano, C. R., & Veneziani, R. (2018). Macroeconomic and stock market interactions with endogenous aggregate sentiment dynamics. Journal of Economic Dynamics and Control, 91, 237-256.
-Sordi, S., & Davila-Fernandez, M. J. (2020). Investment behaviour and “bull & bear” dynamics: modelling real and stock market interactions. Journal of Economic Interaction and Coordination, 1-31.
-Wegener, M. (2020). Exchange rate speculation and heterogeneous expectations in a small open economy. Nonlinear dynamics, psychology, and life sciences, 24(1), 105. |
|
Grading |
|
No. |
Item |
% |
Explanations for the conditions |
|
1. |
Assignments |
30% |
Three assignments, provided every four weeks, and that have to be resubmitted individually or in pairs. |
2. |
Final project |
70% |
Students need to choose one selected research paper (e.g. among those of the extension readings, or to be agreed among others that deal with the topics addressed in the course), replicate and discuss the main results as their final project. The final project has to be done individually. |
|
|
Week |
Date |
Topic |
|
Week 1 |
2/23,2/25 |
Introduction to dynamical systems.
Complex numbers. Eigenvalues and eigenvectors |
|
Week 2 |
3/02,3/04 |
One-Dimensional systems in continuous time: from linear to nonlinear differential equations. Application: the cobweb model. |
|
Week 3 |
3/09,3/11 |
Local bifurcations: Saddle-Node, Transcritical, Pitchfork. Application: the Solow growth model, the Allee effect. |
|
Week 4 |
3/16,3/18 |
Two-dimensional linear systems of differential equations. Application: the IS-LM model. |
|
Week 5 |
3/23,3/25 |
2D nonlinear systems of differential equations. Application: the Kaldor business cycle model. |
|
Week 6 |
3/30 |
Multi-dimensional systems in continuous time.
Deterministic chaos.
Introduction to difference equations: 1D linear models. Applications: cobweb model, a simple financial market model |
|
Week 8 |
4/13,4/14,4/15 |
Nonlinear 1D discrete time systems: local bifurcations. Logistic map and deterministic chaos. |
|
Week 9 |
4/20,4/22 |
2D linear and nonlinear maps.
Applications: the Cournot model, a financial market model with trend extrapolators |
|
Week 10 |
4/27,4/29 |
Dynamic models of order 2 and higher.
Basins of non-invertible maps. Lyapunov exponents.
Application: duopoly models with gradient dynamics |
|
Week 11 |
5/04,5/06 |
Piecewise linear maps with one discontinuity.
Applications to growth models and financial markets. |
|
Week 12 |
5/11,5/13 |
Bounded rationality and economic models.
Applications to a monopolistic and a cobweb model with reference dependent price. |
|
Week 13 |
5/18,5/20 |
Heterogeneous expectations in economics: the case of the cobweb |
|
Week 14 |
5/25,5/27 |
Asset pricing models with heterogeneous beliefs.
A financial market model with market sentiment. |
|
Week 15 |
6/01,6/03 |
Behavioral macro-models and policy analysis |
|
Week 16 |
6/08,6/10 |
Heterogeneous expectations and housing market dynamics |
|
Week 17 |
6/15,6/17 |
Heterogeneous expectations and laboratory experiments |
|