Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model

Yasuyuki Nishigaki; Daiki Maki; Mitsuhiko Satake

doi:doi:10.11648/j.ijebo.s.2015030201.19

| Peer-Reviewed

Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model

Yasuyuki Nishigaki, Daiki Maki, Mitsuhiko Satake

Published in International Journal of Economic Behavior and Organization (Volume 3, Issue 2-1)

Received: 13 March 2015 Accepted: 31 March 2015 Published: 11 April 2015

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this study, we investigate the non-linearity of the Japanese business cycle based on the theoretical concept of the limit cycle. To analyze the time series of capital stock and GDP simultaneously based on the theoretical relationships predicted by the limit cycle, we incorporate the capital coefficient into a Kaldor-type dynamic model and apply the threshold autoregressive (TAR) model to it to investigate fluctuations in the coefficient that are concurrent to the underlying oscillation of the limit cycle. The estimation results indicate that these time series are subject to the three-regime TAR model and that the middle regime has divergence and the outside regimes have convergence, suggesting that the process has a non-linear phenomenon typically caused by limit cycles.

Published in	International Journal of Economic Behavior and Organization (Volume 3, Issue 2-1) This article belongs to the Special Issue Recent Developments of Economic Theory and Its Applications
DOI	10.11648/j.ijebo.s.2015030201.19
Page(s)	52-59
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Business Cycle, Limit Cycle, Capital Coefficient, Threshold Autoregressive Model

References

[1]	Agliari, A., R. Dieci, and L. Gardini, (2007), “Homoclinic Tangles in a Kaldor-like Business Cycle Model,” Journal of Economic Behavior and Organization, Vol. 62, pp. 324-347.
[2]	Bec, F., M. Ben Salem, and M. Carrasco, (2004) “Tests for Unit-root Versus Threshold Specification with an Application to the Purchasing Power Parity Relationship,” Journal of Business and Economic Statistics, Vol. 22, pp. 382-395.
[3]	Bischi, G. I., R. Dieci, G. Rodano, and E. Saltari, (2001), “Multiple Attractors and Global Bifurcations in a Kaldor-type Business Cycle Model,” Journal of Evolutionary Economics, Vol. 11, pp. 527-554.
[4]	Chang, W. W. and D. J. Smith, (1971), “The Existence and Persistence of Cycles in a Non-linear Model: Kaldor's 1940 Model Re-examined,” Review of Economic Studies, Vol. 38, pp. 37-44.
[5]	Hansen, B. E., (1999), “Testing for Linearity,” Journal of Economic Surveys, Vol. 13, No. 5, pp. 551-576.
[6]	Kaldor, N., (1940), “A Model of the Trade Cycle,” Economic Journal, Vol. 50, pp. 78-90.
[7]	Kapetanios, G. and Y. Shin, (2006) “Unit Root Tests in Three-regime SETAR Models,” Econometrics Journal, Vol. 9, pp. 252-278.
[8]	Koop, G. and S. M. Potter, (1999), “Bays Factors and Nonlinearity: Evidence from Econometric Time Series,” Journal of Econometrics, Vol. 88, pp. 251-281.
[9]	Kraeger, H. and P. Kugler, (1993), “Non-linearities in Foreign Exchange Market: A Different Perspective,” Journal of International Money and Finance, Vol. 12, pp. 195-208.
[10]	Lefschetz, S., (1962), Differential Equations: Geometric Theory 2nd ed., Interscience Publishers.
[11]	Lorentz, H. W., (1993), Non-linear Dynamical Economics and Chaotic Motion, Springer-Verlag.
[12]	Maki, D., (2009) “Tests for a Unit Root using Three-regime TAR Models: Power Comparison and some Applications, Econometric Reviews, Vol. 28, pp. 335-363.
[13]	Maki, D., and S. Kitasaka, (2014), “Residual-based Tests for Cointegration with Three-regime TAR Adjustment,” Empirical Economics, forthcoming.
[14]	Nishigaki Y., Y. Ikeda, and M. Satake, (2007), “A Non-Linear Approach to the Japanese Business Cycles,” Global Business and Finance Review, Vol. 12, No. 3, pp. 41-50.
[15]	Park, J. Y., and M. Shintani, (2014) “Testing for a Unit Root Test against Transitional Autoregressive Models,” International Economic Review, forthcoming.
[16]	Potter, S. M., (1995), “A Non-linear Approach to U.S. GDP,” Journal of Applied Econometrics, Vol. 10, pp. 109-125.
[17]	Sarantis, N., (1999), “Modeling Non-linearities in Real Effective Exchange Rates,” Journal of International Money and Finance, Vol. 18, pp. 27-45.
[18]	Satake, M., Maki, D., and Y. Nishigaki, (2009) “Limit Cycles in Japanese Macroeconomic Data: Policy Implications from the View of Business Cycles,” International Journal of Economic Policy Studies, Vol. 4, pp. 37-54.
[19]	Tong, H., (1983), Threshold Models in Non-linear Time Series Analysis: Lecture Notes in Statistic 21, Springer-Verlag. and K. S. Lim, (1980), “Threshold Autoregression, Limit Cycles and Cyclical Data,” Journal of the Royal Statistical Society, Series B (Methodological), Vol. 42, No. 3, pp. 245-292.
[20]	Varian, H. R. (1979), “Catastrophe Theory and the Business Cycle,” Economic Inquiry, Vol. 17, pp. 14-28.

Cite This Article

Plain Text BibTeX RIS

APA Style

Yasuyuki Nishigaki, Daiki Maki, Mitsuhiko Satake. (2015). Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model. International Journal of Economic Behavior and Organization, 3(2-1), 52-59. https://doi.org/10.11648/j.ijebo.s.2015030201.19

Copy | Download

ACS Style

Yasuyuki Nishigaki; Daiki Maki; Mitsuhiko Satake. Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model. Int. J. Econ. Behav. Organ. 2015, 3(2-1), 52-59. doi: 10.11648/j.ijebo.s.2015030201.19

Copy | Download

AMA Style

Yasuyuki Nishigaki, Daiki Maki, Mitsuhiko Satake. Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model. Int J Econ Behav Organ. 2015;3(2-1):52-59. doi: 10.11648/j.ijebo.s.2015030201.19

Copy | Download

@article{10.11648/j.ijebo.s.2015030201.19,
  author = {Yasuyuki Nishigaki and Daiki Maki and Mitsuhiko Satake},
  title = {Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model},
  journal = {International Journal of Economic Behavior and Organization},
  volume = {3},
  number = {2-1},
  pages = {52-59},
  doi = {10.11648/j.ijebo.s.2015030201.19},
  url = {https://doi.org/10.11648/j.ijebo.s.2015030201.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijebo.s.2015030201.19},
  abstract = {In this study, we investigate the non-linearity of the Japanese business cycle based on the theoretical concept of the limit cycle. To analyze the time series of capital stock and GDP simultaneously based on the theoretical relationships predicted by the limit cycle, we incorporate the capital coefficient into a Kaldor-type dynamic model and apply the threshold autoregressive (TAR) model to it to investigate fluctuations in the coefficient that are concurrent to the underlying oscillation of the limit cycle. The estimation results indicate that these time series are subject to the three-regime TAR model and that the middle regime has divergence and the outside regimes have convergence, suggesting that the process has a non-linear phenomenon typically caused by limit cycles.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model
AU  - Yasuyuki Nishigaki
AU  - Daiki Maki
AU  - Mitsuhiko Satake
Y1  - 2015/04/11
PY  - 2015
N1  - https://doi.org/10.11648/j.ijebo.s.2015030201.19
DO  - 10.11648/j.ijebo.s.2015030201.19
T2  - International Journal of Economic Behavior and Organization
JF  - International Journal of Economic Behavior and Organization
JO  - International Journal of Economic Behavior and Organization
SP  - 52
EP  - 59
PB  - Science Publishing Group
SN  - 2328-7616
UR  - https://doi.org/10.11648/j.ijebo.s.2015030201.19
AB  - In this study, we investigate the non-linearity of the Japanese business cycle based on the theoretical concept of the limit cycle. To analyze the time series of capital stock and GDP simultaneously based on the theoretical relationships predicted by the limit cycle, we incorporate the capital coefficient into a Kaldor-type dynamic model and apply the threshold autoregressive (TAR) model to it to investigate fluctuations in the coefficient that are concurrent to the underlying oscillation of the limit cycle. The estimation results indicate that these time series are subject to the three-regime TAR model and that the middle regime has divergence and the outside regimes have convergence, suggesting that the process has a non-linear phenomenon typically caused by limit cycles.
VL  - 3
IS  - 2-1
ER  -

Copy | Download

Author Information

Yasuyuki Nishigaki

Faculty of Economics, Ryukoku University, Kyoto, Japan
Daiki Maki

Faculty of Economics, Ryukoku University, Kyoto, Japan
Mitsuhiko Satake

Faculty of Economics, Doshisha University, Kyoto, Japan

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Yasuyuki Nishigaki, Daiki Maki, Mitsuhiko Satake. (2015). Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model. International Journal of Economic Behavior and Organization, 3(2-1), 52-59. https://doi.org/10.11648/j.ijebo.s.2015030201.19

Copy | Download

ACS Style

Yasuyuki Nishigaki; Daiki Maki; Mitsuhiko Satake. Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model. Int. J. Econ. Behav. Organ. 2015, 3(2-1), 52-59. doi: 10.11648/j.ijebo.s.2015030201.19

Copy | Download

AMA Style

Yasuyuki Nishigaki, Daiki Maki, Mitsuhiko Satake. Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model. Int J Econ Behav Organ. 2015;3(2-1):52-59. doi: 10.11648/j.ijebo.s.2015030201.19

Copy | Download

@article{10.11648/j.ijebo.s.2015030201.19,
  author = {Yasuyuki Nishigaki and Daiki Maki and Mitsuhiko Satake},
  title = {Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model},
  journal = {International Journal of Economic Behavior and Organization},
  volume = {3},
  number = {2-1},
  pages = {52-59},
  doi = {10.11648/j.ijebo.s.2015030201.19},
  url = {https://doi.org/10.11648/j.ijebo.s.2015030201.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijebo.s.2015030201.19},
  abstract = {In this study, we investigate the non-linearity of the Japanese business cycle based on the theoretical concept of the limit cycle. To analyze the time series of capital stock and GDP simultaneously based on the theoretical relationships predicted by the limit cycle, we incorporate the capital coefficient into a Kaldor-type dynamic model and apply the threshold autoregressive (TAR) model to it to investigate fluctuations in the coefficient that are concurrent to the underlying oscillation of the limit cycle. The estimation results indicate that these time series are subject to the three-regime TAR model and that the middle regime has divergence and the outside regimes have convergence, suggesting that the process has a non-linear phenomenon typically caused by limit cycles.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model
AU  - Yasuyuki Nishigaki
AU  - Daiki Maki
AU  - Mitsuhiko Satake
Y1  - 2015/04/11
PY  - 2015
N1  - https://doi.org/10.11648/j.ijebo.s.2015030201.19
DO  - 10.11648/j.ijebo.s.2015030201.19
T2  - International Journal of Economic Behavior and Organization
JF  - International Journal of Economic Behavior and Organization
JO  - International Journal of Economic Behavior and Organization
SP  - 52
EP  - 59
PB  - Science Publishing Group
SN  - 2328-7616
UR  - https://doi.org/10.11648/j.ijebo.s.2015030201.19
AB  - In this study, we investigate the non-linearity of the Japanese business cycle based on the theoretical concept of the limit cycle. To analyze the time series of capital stock and GDP simultaneously based on the theoretical relationships predicted by the limit cycle, we incorporate the capital coefficient into a Kaldor-type dynamic model and apply the threshold autoregressive (TAR) model to it to investigate fluctuations in the coefficient that are concurrent to the underlying oscillation of the limit cycle. The estimation results indicate that these time series are subject to the three-regime TAR model and that the middle regime has divergence and the outside regimes have convergence, suggesting that the process has a non-linear phenomenon typically caused by limit cycles.
VL  - 3
IS  - 2-1
ER  -

Copy | Download