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

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.