Chaotic Behavior in Monetary Systems: Comparison among Different Types of Taylor Rule
The aim of the present study is to detect the chaotic
behavior in monetary economic relevant dynamical system. The
study employs three different forms of Taylor rules: current, forward,
and backward looking. The result suggests the existence of the
chaotic behavior in all three systems. In addition, the results strongly
represent that using expectations in policy rule especially rational
expectation hypothesis can increase complexity of the system and
leads to more chaotic behavior.
[1] Banks, J., V. Dragan and A. Jones, Chaos: A Mathematical Introduction.
Cambridge University Press, Cambridge, 2003.
[2] Barkoulas, John T., “Testing for Deterministic Monetary Chaos: Metric
and Topological Diagnostics”, Chaos Solutions and Fractals, vol. 38,
2008, pp.1013-1024.
[3] Benhabib, Jess, S. Schmitt-Grohe and Martin Uribe, “Chaotic Interest
Rate Rules”, The American Economic Review, vol. 92, no.2, 2002, pp.
72-78.
[4] Bensaïda, Ahmed, “Noisy Chaos in Intraday Financial Data: Evidence
from the American Index”, Applied Mathematics and Computation, vol.
226, 2014, pp. 258-265.
[5] Bensaïda, Ahmed, and Houda Litimi, “High Level Chaos in the
Exchange and Index Markets”, Chaos, Solitons & Fractals, vol. 54,
2013, pp. 90-95.
[6] Clarida, Richard. Jordi Gali and Mark Gertler,” Optimal Monetary
Policy in Open versus Closed Economies: An Integrated Approach”,
American Economic Review, vol. 91, no. 2, 2001, pp. 248-252. [7] Clarida, Richard. Jordi Gali and Mark Gertler, “Monetary Policy Rules
and Macroeconomic Stability: Evidence and Some Theory”, the
Quarterly Journal of Economics, vol. 115, no. 1, 2000, pp. 147-180.
[8] Clarida, Richard. Jordi Gali and Mark Gertler, “Monetary Policy Rule in
Practice: Some International Evidence”, European Economic Review,
vol. 42, 1998, pp. 1033-1067.
[9] DeCoster, G. P. and D. W. Mitchwell, “Dynamic Implications of
Chaotic Monetary Policy”, Journal of Macroeconomics, vol. 14, no. 2,
1992, pp. 267-87.
[10] DeCoster, G. P. and D. W. Mitchwell, “Nonlinear Monetary Dynamics”,
Journal of Business and Economic Statistics, vol. 9, no. 4, 1991, pp.455-
461.
[11] Devany, R. L., A First course in Chaotic Dynamical System: Theory and
Experiment, Addison-Wesely, Menlo Park California, 1992.
[12] Devany, R. L., An Introduction to Chaotic Dynamical System, 2nd
edition, Addison-Wesely. Menlo Park California, 1989.
[13] Lynch, Stephen, Dynamical System with Application using MATLAB, 2nd
edition, Birkhäuser, 2014.
[14] May, Robert M., “Simple Mathematical Models with very Complicated
Dynamics”, Nature, vol. 261, 1976, pp. 459-67.
[15] Moosavi Mohseni, Reza and Adem Kilicman, “Hopf Bifurcation in an
Open Monetary Economic System: Taylor versus Inflation Targeting
Rule”, Chaos, Solitons & Fractals, vol. 61, 2014, pp. 8-12.
[16] Moosavi Mohseni, Reza and Adam Kilicman, Bifurcation in an Open
Economic System: Finding Chaos in Monetary Policy Rules,
International Conference on Mathematical Science and Statistics, 5-7
February, 2013, Kuala Lumpur, Malaysia.
[17] Muth, John F., Rational Expectations and the Theory of Price
Movements, Econometrica, vol. 29, no. 3, 1961, pp. 315-335.
[18] Park, Joon Y. and Yoon Jae Whang, “Random Walk or Chaos: A Formal
test on the Lyapunov Exponent”, Journal of Econometrics, vol. 169,
2012, pp. 61-74.
[19] Ruelle, David, and Floris Takens, “On the Nature of Turbulence”,
Communications in Mathematical Physics, vol. 20, 1971, pp. 167-92.
[20] Smale, S., “A Survey of some Recent Developments in Differential
Topology”, Bulletin of the American Mathematical Society, vol. 73,
1963, pp. 747-817.
[21] Smale, S., “Differentiable Dynamical Systems”, Bulletin of the
American Mathematical Society, vol. 73, 1967, pp. 747-817.
[22] Taylor, John B., “Discretion versus Policy Rule in Practice”, Carnegie-
Rochester Conference Series on Public Policy, vol. 39, 1993, pp. 195-
214.
[23] Turnovsky, Stephen J., Methods of Macroeconomic Dynamics, 2nd
Edition, Cambridge. Massachusetts: The MIT Press, 2000.
[24] Vald, Sorin, “Investigation of Chaotic Behavior in Euro-Leu Exchange
Rate”, Journal of Computer Science and Mathematics, vol. 8, no. 4,
2010, pp. 67-71.
[25] Yousefpoor, P., M. S. Esfahani and H. Nojumi, “Looking for Systematic
Approach to Select Chaos Tests”, Applied Mathematics and
Computation, vol. 198, 2008, pp. 73-91.
[26] Zivot, Eric, and Donald W. K. Andrews, “Further Evidence on the Great
Crash, the Oil-Price Shock, and the Unit-Root Hypothesis”, Journal of
Business & Economic Statistics, vol. 10, no. 3, 1992, pp. 251-70.
[1] Banks, J., V. Dragan and A. Jones, Chaos: A Mathematical Introduction.
Cambridge University Press, Cambridge, 2003.
[2] Barkoulas, John T., “Testing for Deterministic Monetary Chaos: Metric
and Topological Diagnostics”, Chaos Solutions and Fractals, vol. 38,
2008, pp.1013-1024.
[3] Benhabib, Jess, S. Schmitt-Grohe and Martin Uribe, “Chaotic Interest
Rate Rules”, The American Economic Review, vol. 92, no.2, 2002, pp.
72-78.
[4] Bensaïda, Ahmed, “Noisy Chaos in Intraday Financial Data: Evidence
from the American Index”, Applied Mathematics and Computation, vol.
226, 2014, pp. 258-265.
[5] Bensaïda, Ahmed, and Houda Litimi, “High Level Chaos in the
Exchange and Index Markets”, Chaos, Solitons & Fractals, vol. 54,
2013, pp. 90-95.
[6] Clarida, Richard. Jordi Gali and Mark Gertler,” Optimal Monetary
Policy in Open versus Closed Economies: An Integrated Approach”,
American Economic Review, vol. 91, no. 2, 2001, pp. 248-252. [7] Clarida, Richard. Jordi Gali and Mark Gertler, “Monetary Policy Rules
and Macroeconomic Stability: Evidence and Some Theory”, the
Quarterly Journal of Economics, vol. 115, no. 1, 2000, pp. 147-180.
[8] Clarida, Richard. Jordi Gali and Mark Gertler, “Monetary Policy Rule in
Practice: Some International Evidence”, European Economic Review,
vol. 42, 1998, pp. 1033-1067.
[9] DeCoster, G. P. and D. W. Mitchwell, “Dynamic Implications of
Chaotic Monetary Policy”, Journal of Macroeconomics, vol. 14, no. 2,
1992, pp. 267-87.
[10] DeCoster, G. P. and D. W. Mitchwell, “Nonlinear Monetary Dynamics”,
Journal of Business and Economic Statistics, vol. 9, no. 4, 1991, pp.455-
461.
[11] Devany, R. L., A First course in Chaotic Dynamical System: Theory and
Experiment, Addison-Wesely, Menlo Park California, 1992.
[12] Devany, R. L., An Introduction to Chaotic Dynamical System, 2nd
edition, Addison-Wesely. Menlo Park California, 1989.
[13] Lynch, Stephen, Dynamical System with Application using MATLAB, 2nd
edition, Birkhäuser, 2014.
[14] May, Robert M., “Simple Mathematical Models with very Complicated
Dynamics”, Nature, vol. 261, 1976, pp. 459-67.
[15] Moosavi Mohseni, Reza and Adem Kilicman, “Hopf Bifurcation in an
Open Monetary Economic System: Taylor versus Inflation Targeting
Rule”, Chaos, Solitons & Fractals, vol. 61, 2014, pp. 8-12.
[16] Moosavi Mohseni, Reza and Adam Kilicman, Bifurcation in an Open
Economic System: Finding Chaos in Monetary Policy Rules,
International Conference on Mathematical Science and Statistics, 5-7
February, 2013, Kuala Lumpur, Malaysia.
[17] Muth, John F., Rational Expectations and the Theory of Price
Movements, Econometrica, vol. 29, no. 3, 1961, pp. 315-335.
[18] Park, Joon Y. and Yoon Jae Whang, “Random Walk or Chaos: A Formal
test on the Lyapunov Exponent”, Journal of Econometrics, vol. 169,
2012, pp. 61-74.
[19] Ruelle, David, and Floris Takens, “On the Nature of Turbulence”,
Communications in Mathematical Physics, vol. 20, 1971, pp. 167-92.
[20] Smale, S., “A Survey of some Recent Developments in Differential
Topology”, Bulletin of the American Mathematical Society, vol. 73,
1963, pp. 747-817.
[21] Smale, S., “Differentiable Dynamical Systems”, Bulletin of the
American Mathematical Society, vol. 73, 1967, pp. 747-817.
[22] Taylor, John B., “Discretion versus Policy Rule in Practice”, Carnegie-
Rochester Conference Series on Public Policy, vol. 39, 1993, pp. 195-
214.
[23] Turnovsky, Stephen J., Methods of Macroeconomic Dynamics, 2nd
Edition, Cambridge. Massachusetts: The MIT Press, 2000.
[24] Vald, Sorin, “Investigation of Chaotic Behavior in Euro-Leu Exchange
Rate”, Journal of Computer Science and Mathematics, vol. 8, no. 4,
2010, pp. 67-71.
[25] Yousefpoor, P., M. S. Esfahani and H. Nojumi, “Looking for Systematic
Approach to Select Chaos Tests”, Applied Mathematics and
Computation, vol. 198, 2008, pp. 73-91.
[26] Zivot, Eric, and Donald W. K. Andrews, “Further Evidence on the Great
Crash, the Oil-Price Shock, and the Unit-Root Hypothesis”, Journal of
Business & Economic Statistics, vol. 10, no. 3, 1992, pp. 251-70.
@article{"International Journal of Business, Human and Social Sciences:70550", author = "Reza Moosavi Mohseni and Wenjun Zhang and Jiling Cao", title = "Chaotic Behavior in Monetary Systems: Comparison among Different Types of Taylor Rule", abstract = "The aim of the present study is to detect the chaotic
behavior in monetary economic relevant dynamical system. The
study employs three different forms of Taylor rules: current, forward,
and backward looking. The result suggests the existence of the
chaotic behavior in all three systems. In addition, the results strongly
represent that using expectations in policy rule especially rational
expectation hypothesis can increase complexity of the system and
leads to more chaotic behavior.", keywords = "Chaos theory, GMM estimator, Lyapunov Exponent,
Monetary System, Taylor Rule.", volume = "9", number = "8", pages = "2761-4", }
