|
課程名稱 |
經濟與非線性動態理論
Economic Complexity and Nonlinear Dynamics |
|
開課學期 |
110-2 |
|
授課對象 |
社會科學院 經濟學研究所 |
|
授課教師 |
裴尼科 |
|
課號 |
ECON5182 |
|
課程識別碼 |
323EU7520 |
|
班次 |
|
|
學分 |
3.0 |
|
全/半年 |
半年 |
|
必/選修 |
選修 |
|
上課時間 |
星期二3,4(10:20~12:10)星期三3(10:20~11:10) |
|
上課地點 |
社科407社科407 |
|
備註 |
本課程以英語授課。
限學士班三年級以上 或 限碩士班以上 或 限博士班
總人數上限：30人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1102ECON5182 |
|
課程簡介影片 |
|
|
核心能力關聯 |
核心能力與課程規劃關聯圖 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
課程概述 |
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). |
|
課程目標 |
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:
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. Deterministic Chaos and 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 |
|
課程要求 |
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. |
|
預期每週課後學習時數 |
|
|
Office Hours |
|
|
指定閱讀 |
|
|
參考書目 |
Required readings:
-Bischi, G. I., Panchuk, A., & Radi, D. (2016). Qualitative Theory of Dynamical Systems. Tools and Applications for Economic Modelling. Springer. (chapters 1 and 6)
-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. |
|
評量方式
(僅供參考) |
|
|
週次 |
日期 |
單元主題 |
|
Week 4 |
3/08,3/09 |
Introduction to dynamical systems and general definitions.
Eigenvalues and eigenvectors. Complex numbers. |
|
Week 5 |
3/15,3/16,3/18 |
One-Dimensional systems in continuous time: from linear to nonlinear differential equations. Applications: the cobweb model, the SI model.
Local bifurcations. Applications: Lux (1995) model, Solow model, Allee effect. |
|
Week 6 |
3/22,3/23,3/25 |
Two-dimensional linear systems of differential equations. Application: the IS-LM model.
2D nonlinear systems of differential equations. Application: the Kaldor business cycle model. |
|
Week 7 |
3/29,3/30,4/01 |
N-dimensional systems in continuous time. Deterministic chaos.
Introduction to difference equations: 1D linear models. Applications: cobweb model, a simple financial market model
Nonlinear 1D discrete time systems: local bifurcations. Logistic map and deterministic chaos. |
|
Week 8 |
4/06,4/08 |
2D linear and nonlinear maps.
Applications: the Cournot model, a financial market model with trend extrapolators |
|
Week 9 |
4/12,4/13 |
Dynamic models of order 2 and higher.
Basins of non-invertible maps. Lyapunov exponents.
Application: duopoly models with gradient dynamics |
|
Week 10 |
4/19,4/20 |
Bounded rationality and economic models.
Applications to a monopolistic and a cobweb model with reference dependent price. |
|
Week 11 |
4/26,4/27 |
Heterogeneous expectations in economics: the case of the cobweb |
|
Week 12 |
5/03,5/04 |
Asset pricing models with heterogeneous beliefs.
A financial market model with market sentiment. |
|
Week 13 |
5/10,5/11 |
Behavioral macro-models and policy analysis |
|
Week 14 |
5/17,5/18 |
Heterogeneous expectations and housing market dynamics |
|
Week 15 |
5/24,5/25 |
Heterogeneous expectations and laboratory experiments |
|
Week 16 |
5/31,6/01 |
Final presentations and discussion |
|