Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model
International Journal of Economic Behavior and Organization
Volume 3, Issue 2-1, April 2015, Pages: 52-59
Received: Mar. 13, 2015;
Accepted: Mar. 31, 2015;
Published: Apr. 11, 2015
Views 4142 Downloads 141
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
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.
Capital Adjustment and Limit Cycles: An Empirical Analysis Based on the Threshold Autoregressive Model, International Journal of Economic Behavior and Organization. Special Issue: Recent Developments of Economic Theory and Its Applications.
Vol. 3, No. 2-1,
2015, pp. 52-59.
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.
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.
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.
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.
Hansen, B. E., (1999), “Testing for Linearity,” Journal of Economic Surveys, Vol. 13, No. 5, pp. 551-576.
Kaldor, N., (1940), “A Model of the Trade Cycle,” Economic Journal, Vol. 50, pp. 78-90.
Kapetanios, G. and Y. Shin, (2006) “Unit Root Tests in Three-regime SETAR Models,” Econometrics Journal, Vol. 9, pp. 252-278.
Koop, G. and S. M. Potter, (1999), “Bays Factors and Nonlinearity: Evidence from Econometric Time Series,” Journal of Econometrics, Vol. 88, pp. 251-281.
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.
Lefschetz, S., (1962), Differential Equations: Geometric Theory 2nd ed., Interscience Publishers.
Lorentz, H. W., (1993), Non-linear Dynamical Economics and Chaotic Motion, Springer-Verlag.
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.
Maki, D., and S. Kitasaka, (2014), “Residual-based Tests for Cointegration with Three-regime TAR Adjustment,” Empirical Economics, forthcoming.
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.
Park, J. Y., and M. Shintani, (2014) “Testing for a Unit Root Test against Transitional Autoregressive Models,” International Economic Review, forthcoming.
Potter, S. M., (1995), “A Non-linear Approach to U.S. GDP,” Journal of Applied Econometrics, Vol. 10, pp. 109-125.
Sarantis, N., (1999), “Modeling Non-linearities in Real Effective Exchange Rates,” Journal of International Money and Finance, Vol. 18, pp. 27-45.
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.
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.
Varian, H. R. (1979), “Catastrophe Theory and the Business Cycle,” Economic Inquiry, Vol. 17, pp. 14-28.