Non-linear adjustment in the term structure of interest rates: a cointegration analysis in the non-linear STAR framework

Abstract

The term structure of interest rates in Japan is analysed by means of a cointegration test in a non-linear smooth transition autoregression (STAR) framework. The STAR approach tests for the null hypothesis with no cointegration against cointegration including a globally stationary process. The results of the STAR cointegration test, differing from the results of cointegration tests assuming linear adjustment, show that the long-run equilibrium relationship between long-term and short-term interest rates is stable with non-linear adjustment. The results indicate non-linear adjustment in the term structure of Japanese interest rates.

Acknowledgements

The author is grateful to Takayoshi Kitaoka, Hiroshi Kamae, Shin-ichi Kitasaka, Yoshitomo Kiyokawa, and Mikiyo Niizeki for helpful comments and discussions.

Notes

¹ Although Enders and Granger (1998) and Enders and Siklos (2001) also proposed threshold autoregressive (TAR) model, which allows the degree of autoregressive decay to depend on the state of the variables, they did not find the TAR adjustment of the US term structure between federal funds rates and the ten-year interest rate on government securities.

² As an alternative model, Kapetanios et al . (2003b) also proposed a test based on the error correction model. In the present paper, only the residual-based test is employed to directly compare it in the non-linear STAR framework with residual based-tests with linear adjustment including those described by Engle and Granger (1987) and Perron and Rodriguez (2001).

³ This cointegration test is consistent with the unit root test introduced by Kapetanios et al . (2003a) when the variable is one. Kapetanios et al . (2003a) showed that their proposed test had greater power under the alternative hypothesis of a globally stationary process than did the standard Dickey and Fuller (1979) unit root test and the unit root test allowing for asymmetric adjustment as developed by Enders and Granger (1998).

⁴ More accurately, to begin with, the equation is estimated with the maximum lag (here, the maximum lag k = int[12∗(T/100)^1/4]). The lag length is employed if k_t  ≥ 1.65, where k_t is the absolute t-statistic of the parameter of the lag = k. If k_t  < 1.65, the equation is estimated with lag = k − 1. That is, when the absolute t-statistic of the lag = k − q is significant at a conventional level, the lag length is used.

⁵ See Schwert (1989) and Ng and Perron (1995) for details regarding the selection of a maximum lag.

⁶ First differences of variables were significant at conventional levels. In addition, even when AIC criterion is used (for GLS, MAIC proposed by Ng and Peron, 2001 is employed), the results were similar to those of t-sig. These additional results are available upon request.

⁷ The reason that γ = −1 is imposed is that, as pointed out by Kapetanios et al . (2003b), joint estimation of γ and θ incurs severe identification problems and makes the convergence of non-linear algorithms difficult. Therefore, a minus unit coefficient is imposed on γ. The other estimation of γ such that γ = −1.5 and γ = −0.5 did not affect the significance of θ. These additional results are available upon request.