Appendix I: Derivation portfolio compositions (8) and (9)
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Monetary and Economic Policy Department, De Nederlandsche Bank, PO Box 98, 1000 AB Amsterdam, The Netherlands, and European 1 Department, IMF, Washington, DC. We would like to thank Tamim Bayoumi, Peter van Bergeijk, Carlo Cottarelli, Tarhan Feyzioglu, Aerdt Houben, Lex Hoogduin, Malcolm Knight, Zenon Kontolemis, Erik Lundback, Donogh McDonald, Kevin Ross, Nikola Spatafora, Elmer Sterken, Job Swank, Peter Vlaar, and various participants at the 1998 Annual Conferences of the Royal Economic Society and the European Economic Association for useful comments on an earlier version of the paper. Henk van Kerkhoff provided expert research assistance. Nonetheless, the usual disclaimer applies.
This does not apply to the anchor country in an asymmetric, fixed but adjustable exchange rate regime like Bretton-Woods or the Exchange Rate Mechanism (ERM) of the European Monetary System (De Grauwe, 1994).
Recent studies involving long-term rates are Kasman and Pigott (1988), Howe and Pigott (1991), Pigott (1993), Throop (1994), Fell (1996), Kirchgässner and Wolters (1996), Fase and Vlaar (1998), and Meredith and Chinn (1998).
Deviations from covered interest parity appear to be somewhat larger among long-term assets than among short-term assets, but for the major currencies the differences remain fairly limited (Popper, 1993; Fletcher and Taylor, 1996).
We used monthly data on so-called benchmark bonds, obtained from BIS. It is important that the properties of these bond contracts are identical (so that they differ only in currency of denomination), and benchmark bonds come closest to this ideal. Differences are however likely to remain, for example stemming from variations in the degree of liquidity of underlying markets as well as differences in tax treatment, payment of coupons, and in the method by which the contracts are sold (Holmes and Wu, 1997).
The methodology which has been adopted to classify a major swing in the bond market is similar to that used by the NBER to date business cycles. Peaks and troughs were identified using a 12-month moving window. A ‘bull’ market is defined as at least 6 consecutive months of declining bond yields and a ‘bear’ market is defined in the opposite way.
This hiccup is not identified in Table 1, as the number of consecutive months with unidirectional movements was limited to 5 instead of the required 6 (see previous note).
In this respect, Browne and Tease (1992) find little tendency for long-term interest rates to vary systematically with the business cycle.
We also investigated more general (G)ARCH processes, but additional ARMA terms were generally insignificant and, hence, did not materially affect the estimated parameter of the risk premium either.
Ideally, one should use the expected PPP rate at maturity as the anchor guiding exchange rate expectations under PPP. The difference between the expected PPP rate k years ahead,
The two-step procedure is as follows. First, by minimizing the sum of squares of the second differences a monthly series is interpolated, ensuring smoothness whilst preserving the movement of the original series. Subsequently, monthly observations on PPP are constructed as the fitted values of a regression of the smoothly interpolated monthly series on the quotient of monthly movements in the CPI between the United States and the foreign country.
The fact that our PPP-based measure of expected depreciation is measured with error (see footnote 11) would in itself tend to bias downward its coefficient.
Switzerland has often been referred to as an ‘interest rate island’, owing to the stylized facts that real interest rates have been lower in Switzerland than in most other industrialized countries and that Swiss interest rates seem to be decoupled from world interest rates to a greater extent than in other countries. These features may relate to an excess of national savings over investment for many years, that has resulted in a persistent current account surplus and the largest ratio of net foreign assets to GDP in the world (Mauro, 1995). Also the role of the Swiss franc as a ‘safe haven’ currency could have played a role in explaining the results for Switzerland.
This standardization, common in the evaluation of (G)ARCH models, implies dividing the residuals from the model estimated in Table 2 by their conditional standard deviation, and ensures that the residuals are identically and independently distributed, with zero mean and unit variance. The critical values for the residuals-based test for cointegration depend on the number of I (1) variables (in this case, three) in the cointegrating regression (Engle and Granger, 1987, and Engle and Yoo, 1987).
For the sake of parsimonity the diagnostics have been omitted from Table 3. In general, most diagnostics were clearly supportive of the risk-adjusted UIP specification (13) across the decades, except (again) for the presence of excess kurtosis in France and Switzerland during the 1980s and Japan during the 1990s.
The results for Japan may have been adversely affected because our method of gauging exchange rate expectations from current PPP rates does not take account of trends in PPP, such as the long-run upward trend that Japan has witnessed (see also footnote 11). There is also evidence that equilibrium exchange rates can be influenced by trends in overseas net assets, which may also have been potentially important for Japan.
UnfortunateIy, the backward-looking specification of the time-varying risk premium in our model (13) is unable to directly pick up the type of contemporaneous risk-premium shocks that contaminate short-horizon tests of UIP.
Using REH-based expected rates of depreciation over the period 1973-88, Meredith and Chinn (1998) also report quite strong support for UIP at the ten-year horizon. Owing to the ‘inverse’ specification of the UIP-relation, the absence of a time-varying risk premium, and the use of quarterly instead of monthly data, caution has to be exercised when comparing results. Meredith and Chinn (1998) report β-parameters that are either insignificantly different from one (Canada, France, and Germany), or at least significantly positive but smaller than one (Italy, Japan, and the United Kingdom). Translated to an inverse specification such as (13), however, the latter estimates would imply that changes in exchange rate expectations will be reflected in adjustments to interest rate differentials in a more-than-one-for-one fashion.