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Real interest rate parity in the Pacific Rim countries: new empirical evidence

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Abstract

This paper revisits the real interest rate parity (RIP) hypothesis for the Pacific Rim countries under considerations of structural breaks in the auxiliary regression. To this end, we make use of a set of state-of-the-art unit root tests. We find strong evidence in favor of the RIP hypothesis by using the unit root tests considering smooth structural breaks. The empirical results are almost unchanged using the unit root test incorporating abrupt structural breaks. The smooth-break models have better goodness of fit than the abrupt-break models in characterizing the long-run trend of real interest rate differentials of the countries examined. The results of the simulation experiments show that the smooth-break unit root test can capture the feature of the abrupt unit root test, but not vice versa. Empirical evidence reveals a high degree of market integration for the Pacific Rim countries over time allowing for structural breaks.

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Notes

  1. Please see Edison and Pauls (1993) for the theoretical derivation of the nonzero mean in the real interest rate differential. The nonzero mean of the rid could be due to the existence of non-traded goods and transaction costs as emphasized by Goodwin and Grennes (1994).

  2. Readers are referred to Table 1 of Sirichand et al. (2015) for a brief summary of empirical studies on the RIP hypothesis. See Table 1 of Neely and Rapach (2008) for a summary of previous empirical studies on the issue of real interest rate persistence.

  3. Ferreira and León-Ledesma (2007, p. 380) suggested that capital market liberalization and financial crisis may have generated structural changes in real interest rate differential.

  4. The Fourier-type unit root tests are popular with researchers and applied in many empirical applications. See Ferreira and León-Ledesma (2007), Su et al. (2012), Gulcu and Yildirim (2019) and Bahmani-Oskooee et al. (2019) on the real interest rate parity and Yilanci and Eris (2013), Zhou and Kutan (2014), Kutan and Zhou (2015) and Bahramian and Saliminezhad (2021) on the purchasing power parity.

  5. Fountas and Wu (1999) and Holmes (2002) defined strong RIP and weak RIP using the concept of cointegration. They defined weak RIP when domestic and foreign ex post real interest rates are cointegrated in the following manner

    $$\begin{aligned} r_t=\alpha +\beta r_t^* +\varepsilon _t, \end{aligned}$$

    where \(\alpha \ne 0\), \(\beta \ne 1\) and \(\varepsilon _t\) is I(0). If both domestic and foreign ex post real interest rates are non-stationary but cointegrated with \(\alpha = 0\), \(\beta = 1\) and \(\varepsilon _t\) is stationary, then strong RIP holds within a long-run cointegration. Fountas and Wu (1999) and Camarero et al. (2010) pointed out that the weak version of RIP hypothesis may arise theoretically from the nonzero country-specific risk premium, the presence of transaction costs, the existence of non-traded goods, and differential national tax rates.

  6. Let \(q_t\) denote the logarithm of real exchange rate, and it is assumed that \(q_{t+1}-q_t=\gamma t,\,\) where \(\gamma >0\). That is, the appreciation rate of real exchange rate grows at \(\gamma \)% over time. By substituting \(q_{t+1}=s_{t+1}+p_{t+1}^*-p_{t+1}\) and \(q_t=s_t+p_t^*-p_t\) into \(q_{t+1}-q_t=\gamma t\), and using the uncovered interest parity allowing risk premium \( i_t-i_t^* = E_t s_{t+1}-s_t + \rho \), and \(E_t s_{t+1}-s_t = (s_{t+1}-s_t)+\varepsilon _t\), where \(\rho \) is the risk premium of holding risky foreign asset. By some manipulations, we can get

    $$\begin{aligned}&r_t -r_t^*=\rho +\gamma t +\varepsilon _t. \end{aligned}$$
    (13)

    If \(\rho =0\) and \(\gamma =0\), then Eq. (12) is equivalent to Eq. (8) with zero mean and is consistent with the RIP hypothesis. If \(\rho \ne 0\) and \(\gamma =0\), then Eq. (12) is satisfied with the RIP hypothesis with the nonzero risk premium. Equation (12) shows that if the real exchange rate appreciates at \(\gamma \)% over time and a nonzero risk premium, i.e., \(\rho \ne 0\) and \(\gamma \ne 0\), then the real interest rate differential is not a zero mean-reverting process, but is a trend stationary process. Hence, it is called the RIP in the presence of trend real exchange rate appreciation/depreciation described by Arghyrou et al. (2009).

  7. The exponential function (15) assumes symmetry in the rise and fall of the real interest rate differential around a transition mid-point. Sollis (2005) relaxed this assumption by making use of a switching version of the exponential function as follows.

    $$\begin{aligned} SE_t(\gamma _1, \gamma _2, \tau )=(1-\exp \{-I_t \gamma _1^2[t-\tau T]^{2}- (1-I_t)\gamma _2^2[t-\tau T]^{2}\}), \end{aligned}$$
    (21)

    where \(I_t=1\) if \(t-\tau T \le 0\) and 0 otherwise. We also consider this switching exponential function and redo all estimation and test. The statistics are labeled the \(ae_{\alpha }\) and \(ae_{\alpha \beta }\) corresponding to the Sollis-AA and Sollis-CC models, respectively.

  8. Readers are also referred to Phylaktis (1999, p. 268), Liu and Hsu (2006, p. 670–673), and Gulcu and Yildirim (2019, p. 672) for a brief overview of the financial liberalization in Asian countries.

  9. We omit the results of descriptive statistic of the \({\text {rid}}\) to save space. This table is available from the authors upon request.

  10. We also apply the Kwiatkowski et al. (1992, thereafter KPSS) test to ascertain the order of integration of the real interest rate differential. The ADF test assumes the null hypothesis of a unit root against the alternative of stationary process. In contrast, the KPSS procedure tests for the null hypothesis of level stationary (\(\eta _{\mu }\)) or trend stationary (\(\eta _{\tau }\)) against the alternative of a unit root. In this sense, the KPSS principles involve different maintained hypothesis from the ADF unit root test. We report the results in the fifth and sixth columns of Table 2. The results suggest that the level stationary (\(\eta _{\mu }\)) or trend stationary (\(\eta _{\tau }\)) can be rejected at the 5% significance level for all of the real interest rate differentials. Based on the KPSS test, no evidence is found in support of the RIP hypothesis.

  11. We consider two breaks at most in testing for the unit root null because, as noted by Prodan (2008), it is quite difficult to properly estimate the number and the magnitudes of multiple breaks, particularly when the breaks are of opposite sign. Moreover, the power of the test decreases significantly when the number of breaks is above two.

  12. The \(F_{\mu }(\hat{k})\) statistic is to test for the null hypothesis of linearity.

  13. We code all of the tests of Papell and Pordan (2006) and obtain critical values for the empirical size via Monte Carlo simulations by using the WinRats software.

  14. To save space, we do not show the graphs of estimated trend of the unrestricted, restricted one-break and two-break models of Papell and Pordan (2006) for the other countries. These graphs are available from the authors upon request.

  15. We owe this suggestion to an anonymous referee.

  16. As noted in Enders and Lee (2012a, p. 196), an important feature of the Fourier unit root is that ‘it is not necessary to assume that the number of breaks or the break dates are known a priori. Hence, instead of selecting specific break dates, the number of breaks, and the form of the breaks, the specification problem is transformed into incorporating the appropriate frequency components into the estimating equation.’ Likewise, the Sollis (2005) unit root test uses the exponential smooth transition function to characterize the temporary breaks of a series.

  17. We thank an anonymous referee for raising this suggestion to us.

  18. Remember that this restriction is required for the RIP hypothesis to hold because the coefficients on the breaks are of equal and opposite sign.

  19. Our simulation results echo Becker et al. (2004), and a structural change can be captured by the relatively low-frequency component of a series since breaks shift the spectral density function toward zero.

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Acknowledgements

We would like to thank the editor, Professor Robert M. Kunst and an anonymous referee of this journal for helpful comments and suggestions. The authors report no potential conflict of interest. The usual disclaimer applies.

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Authors and Affiliations

  1. Department of International Economics and Trade, School of Economics, Jinan University, Guangzhou, China

    Zixiong Xie

  2. Department of International Business, Tunghai University, No. 1727, Sec.4, Taiwan Boulevard, Xitun District, Taichung, 407224, Taiwan, ROC

    Shyh-Wei Chen

  3. Department of International Business, Tamkang University, New Taipei City, 251301, Taiwan, ROC

    An-Chi Wu

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Xie, Z., Chen, SW. & Wu, AC. Real interest rate parity in the Pacific Rim countries: new empirical evidence. Empir Econ 64, 1471–1515 (2023). https://doi.org/10.1007/s00181-022-02282-w

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