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IMF Research Department and National Bank of New Zealand, respectively. The authors thank Peter Clark, Geoffrey Kingston, Sam Ouliaris, Kenneth Rogoff, Miguel Savastano, Peter Wickham and seminar participants at the International Monetary Fund, the Sixth Australian Macroeconomics Workshop (University of Adelaide) and New Zealand Exchange Rate Workshop (Victoria University of Wellington) for their comments and suggestions. The views expressed are those of the authors, and do not necessarily represent those of the International Monetary Fund or the National Bank of New Zealand.
Abuaf and Jorion (1990) use data on bilateral real exchange rates between the United States and several industrial countries during the 20th Century, and find average half-lives of a little over 3 years. Frankel (1986) and Lothian and Taylor (1996) use two centuries of annual data on the pound-dollar real exchange rate in calculating half-lives of about 5 years. Wu (1996) and Papell (1997) use panel data methods on quarterly post-Bretton Woods data to derive half-lives of between two to three years.
The version of PPP with the longest pedigree is that of relative PPP, which states that the exchange rate will be proportional to the ratio of money price levels (including traded and nontraded goods) between countries, that is to the relative purchasing power of national currencies (see Wickham (1993)). For recent surveys on PPP and exchange rate economics, see Isard (1995) and Froot and Rogoff (1995).
The results of the recent burst of activity in the conduct of univariate tests of PPP have been characterized by Taylor (2000) as either in the “whittling down half-lives” camp (such as Frankel and Rose (1996) and Wu (1996)) or the “whittling up half-lives” camp (such as Papell (1997), O’Connell (1998) and Engel (2000)). The latest wave in this research is supportive of the latter camp, which cast doubt on the stationarity of international relative prices.
While this bias is certainly present in standard (least squares) estimation of the unit root model, panel-data methods (such as those applied by Wu (1996), Papell (1997) and Taylor and Sarno (1998)), which pool cross-country information, will also be subject to the near unit root bias that lowers the estimated rate of reversion to parity (see Cermeno (1999)).
Point and interval estimates of the half-life of shocks to economic time series have also been used by Cashin, Liang and McDermott (2000) in modeling the persistence of shocks to world commodity prices. Earlier, Stock (1991) considered point and asymptotic confidence intervals for the largest autoregressive root in a time series.
Time trends are sometimes included in tests of PPP in an attempt to control for the Balassa-Samuelson effect, where the failure of PPP to hold can be due to differential rates of productivity growth in the tradable and nontradable sectors.
Other sources of bias in estimation of unit root regressions have been examined in the large literature on PPP, which will not be examined in this paper. These include: large size biases in univariate tests for long-run PPP, due to a significant unit root component in the relative price of nontraded goods (Engel (2000)), and in multivariate tests for long-run PPP due to a failure to control for cross-sectional correlation (O’Connell (1998)); and sample-selection bias of the countries analyzed, which biases the results toward understating the general relevance of parity reversion (Cheung and Lai (2000a)).
The unbiased model selection procedure based on the median-unbiased estimate of the AR(1) model is an exact test, as are its associated confidence intervals. However, the unbiased model selection procedure based on the median-unbiased estimate of the AR(p) model is an approximate test, as are its associated confidence intervals. This is because the distribution of
Both the Dickey-Fuller and Phillips-Perron median-unbiased measures of persistence and associated confidence intervals can be compared with their least squares counterparts, where the least squares point and interval estimates will (given they are functions of a downwardly-biased α) tend to understate the actual amount of persistence in shocks to economic time series (see Sections III.A and III.B).
Wij can be interpreted as the sum over all markets of a gauge of the degree of competition between producers of country i and j, divided by the sum over all markets of a gauge of the degree of competition between producers of country i and all other producers.
The 22 countries (and IFS country numbers) are: Australia (193), Austria (122), Belgium (124), Canada (156), Denmark (128), Euro Area (163), Finland (172), France (132), Germany (134), Iceland (176), Ireland (178), Italy (136), Japan (158), Netherlands (138), New Zealand (196), Norway (142), Portugal (182), Spain (184), Sweden (144), Switzerland (146), and United Kingdom (112), United States (111). A decline (depreciation) in a country’s REER index indicates a rise in its international competitiveness (defined as the relative price of domestic tradable goods in terms of foreign tradables). For a detailed explanation and critique of how the Fund’s REER indices are constructed, see Zanello and Desruelle (1997) and Wickham (1993).
These half-life results are comparable to those obtained by Cheung and Lai (2000b) using least squares estimation on monthly bilateral (post-Bretton Woods) dollar real exchange rates, which calculated an average half-life of 3.3 years.
Starting with the maximum lag, first-differences of the logarithm of the REER (qt) were sequentially removed from the AR model until the last lag was statistically significant (at the 5 percent level). At that point all lag lengths smaller than or equal to p-1 are included in the AR(p) regression of equation (2).
Consistent with Papell (1997), we find that accounting for serial correlation in the disturbances weakens the evidence against a null hypothesis of a unit root in the real exchange rate series, as the point estimates of the autoregressive parameter are typically lower in the AR(p) case than for the AR(1) regression.
Median-unbiased estimates (and confidence intervals) of the half-life of a shock (for T=253 observations (1979:1-2000:1)) were determined using quantile functions of
Our results for the median-unbiased Dickey-Fuller regression are similar to those of Andrews (1993), who calculated point and interval estimates of the half-life of monthly bilateral dollar real exchange rates for several industrial countries over the period 1973 to 1988. He found that, using least squares, the half life of PPP deviations for each real exchange rate was finite, with an average half life of about 31 months. However, using the median-unbiased procedure (for an AR(1) model) only three of the eight real exchange rates had finite half-lives of PPP deviations, with an average half life of about 60 months. The remaining five exhibited permanent parity deviations. Similarly, while all of Andrews’ median-unbiased lower bounds of the 90 percent confidence interval were less than 24 months (as is the case for the majority of countries in the present study), the upper bounds were all infinite (as is the case in this study).
Murray and Papell (2000) follow Andrews and Chen (1994) in calculating median-unbiased estimates of half-lives for bilateral dollar real exchange rates. They find that the median half-life is about 3 years, but with confidence intervals that are typically so large that the point estimates of half-lives from ADF regressions provide virtually no information regarding the size of the half-lives.
Interestingly, the broad pattern found in the biased least squares estimates of half-lives of parity reversion (reported in Tables 1-3) is also found for the median-unbiased estimates of half-lives of parity reversion (reported in Tables 4-6), with the estimation method which controls for serial correlation and heteroscedasticity (the PP regression) yielding the smallest half lives.