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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.

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Tests for a unit root using three-regime threshold autoregressive (TAR) models play a significant role in the empirical analysis of some economic theories. This article compares the powers of recently proposed unit root tests in three-regime TAR models using Monte Carlo experiments. The following results are obtained from the Monte Carlo simulations: Kapetanios and Shin's (2006) Wsup, Wave, and Wexp statistics, which degenerate with respect to the threshold parameters under the null hypothesis, have a better power in the three-regime TAR process with a relatively narrow band of a unit root process and a small sample, whereas their statistics do not perform well when the threshold and sample size increase; Bec et al.'s (2004, BBC) sup W and Park and Shintani's (2005) inf-t statistics and their restricted models, which do not degenerate with respect to the threshold parameters in the limit, perform poorly in the three-regime TAR process with a small threshold even when compared with the Dickey-Fuller test, whereas their statistics perform better in the case of a large threshold; sup W, inf-t, and their restricted models perform much better when the sample size and threshold increase and the outer regimes have a rapid convergence. In order to substantiate the use of our Monte Carlo results for some of the applied work, we apply these tests to the real exchange rates for many countries.Power, Three-regime TAR model, Unit root test,

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.

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