The equilibrium relationship among money, income, prices, and interest rates: evidence from a threshold cointegration test

Abstract

The long-run equilibrium relationship among money, income, prices, and interest rates in Japan is investigated by the threshold cointegration test, which allows for asymmetric adjustment, introduced by Enders and Siklos (2001). The threshold cointegration approach provides clear evidence of the cointegration relationship characterized by asymmetric adjustment. By allowing for asymmetric adjustment, results are obtained showing the stability of the money demand function, similar to Lucas (1988), who pointed out that the money demand function is stable if unit income elasticity is imposed. In particular, the estimated results show that the adjustment process toward equilibrium is highly persistent above an appropriately estimated threshold, whereas the adjustment process toward equilibrium quickly converges below it. This finding indicates that deviations from equilibrium resulting from increases in money or decreases in income and prices are highly persistent.

Acknowledgements

We would like to thank Ryuzo Miyao, Tutomu Miyagawa, Yoshiyasu Ono, Kazuo Ogawa, Charles Yuji Horioka, Hisahiro Naito, and the seminar participants at Institute of Social and Economic Research Osaka University for helpful comments.

Notes

¹ According to Friedman and Kuttner (1992), intermediate target and information variable are defined as follows: The former is to determine the money growth rate ex ante to be consistent with the central bank's macroeconomic policy objectives. The latter is to adjust policy operations during some interval in response to actual money growth that departs from the ex ante path.

² In addition to the TAR model, as an alternative model, Enders and Siklos (2001) proposed the momentum threshold (MTAR) model which can capture the properties such that the threshold depends on the previous period's change in μ _{t −1}, i.e., whether the Δ μ _{t −1} is increasing or decreasing. Here only the TAR model is employed in order to directly compare TAR with the Engle–Granger method from the viewpoint of asymmetry.

³ More accurately, to begin with, the equation with the maximum lag is estimated (here, the maximum lag = 8). The lag length is employed if the absolute t-statistic of the parameter of the lag = 8 is larger than 1.65. If the absolute t-statistic in the lag = 8 is smaller than 1.65, the equation is estimated with the lag = 7. That is, when the absolute t-statistic of the parameter of the lag = k − q is significant, the lag length is used.

⁴ When testing for a cointegration relationship, incorrect results may be obtained if processes of each variable is a non-linear mean-reverting process including asymmetric adjustment. Therefore, unit root tests are used, taking into account linear and non-linear adjustment. Breitung (2002) provided the results of the high power of the non-parametric test under an asymmetric process assumed by Enders and Granger (1998).

⁵ Those additional results are available from the authors upon request.

⁶ For System 2 with other sample sizes, the test statistics of t-max and Φ are obtained from Enders and Siklos (2001). For both systems with other sample sizes, the test statistics of the Engle and Granger's (1987) method are obtained from e.g. Phillips and Ouliaris (1990).