The 34 reference contexts in paper Christopher F. Baum, Mustafa Caglayan, John Barkoulas (1998) “Nonlinear Adjustment to Purchasing Power Parity in the post-Bretton Woods Era” / RePEc:boc:bocoec:404

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    like transaction costs, taxation, subsidies, actual or threatened trade restrictions, the existence o fnontraded goods, imper fect competition, foreign exchange market interventions, and the differential composition of market baskets and price indices across countries, one may expect PPP to be valid only in the long-run. Empirical studies over long periods have supported long-run PPP
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    (Diebold et al. (1991), Taylor (1996), Michael et al. (1997)).
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    However, results are mixed when the recent Boating-rate period is examined. Using standard unit-root tests, Corbae and Ouliaris (1988), Meese and Rogoff (1988), Edison and Fisher (1991), and Grilli and Kaminsky (1991) cannot reject the unit-root null hypothesis for real exchange rates in the managed-Boat regime.
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    Empirical studies over long periods have supported long-run PPP (Diebold et al. (1991), Taylor (1996), Michael et al. (1997)). However, results are mixed when the recent Boating-rate period is examined. Using standard unit-root tests, Corbae and Ouliaris (1988),
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    Meese and Rogoff (1988), Edison and Fisher (1991), and Grilli and Kaminsky (1991)
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    cannot reject the unit-root null hypothesis for real exchange rates in the managed-Boat regime. In contrast, Pedroni (1995), Frankel and Rose (1996), Lothian (1997), Oh (1996), Wu (1996), and Papell and Theodoridis (1998) 1nd strong evidence of mean reversion in real exchange rates by implementing panel data variants o fstandard unit-root tests.
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    Using standard unit-root tests, Corbae and Ouliaris (1988), Meese and Rogoff (1988), Edison and Fisher (1991), and Grilli and Kaminsky (1991) cannot reject the unit-root null hypothesis for real exchange rates in the managed-Boat regime. In contrast,
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    Pedroni (1995), Frankel and Rose (1996), Lothian (1997), Oh (1996), Wu (1996), and Papell and Theodoridis (1998)
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    1nd strong evidence of mean reversion in real exchange rates by implementing panel data variants o fstandard unit-root tests.However, OFConnell (1998a) strongly disputes these mean-reversion 1ndings in real exchange rates as they fail to control for cross-sectional dependence in the data.
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    In contrast, Pedroni (1995), Frankel and Rose (1996), Lothian (1997), Oh (1996), Wu (1996), and Papell and Theodoridis (1998) 1nd strong evidence of mean reversion in real exchange rates by implementing panel data variants o fstandard unit-root tests.However,
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    OFConnell (1998a)
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    strongly disputes these mean-reversion 1ndings in real exchange rates as they fail to control for cross-sectional dependence in the data. Additional evidence against reversion to PPP based on a panel o freal exchange 3 4 1 Relative PPP, which is implied by absolute PPP, states that the growth rate in the nominal exchange rate equals the differential between the growth rates in home and foreig
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    Additional evidence against reversion to PPP based on a panel o freal exchange 3 4 1 Relative PPP, which is implied by absolute PPP, states that the growth rate in the nominal exchange rate equals the differential between the growth rates in home and foreign price indices. See
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    Rogoff (1996) and Froot and Rogoff (1995)
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    for a review of the literature on PPP. Employing an alternative multivariate unit-root test where the null hypothesis is nonstationarity o fat least one o f the series under consideration, Taylor and Sarno (1998) 1nd strong support for mean reversion in a panel of CPI-based U.
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    See Rogoff (1996) and Froot and Rogoff (1995) for a review of the literature on PPP. Employing an alternative multivariate unit-root test where the null hypothesis is nonstationarity o fat least one o f the series under consideration,
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    Taylor and Sarno (1998)
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    1nd strong support for mean reversion in a panel of CPI-based U.S. dollar exchange rates o fthe G5 countries. However, their evidence is not supportive o fmean reversion for GNP deBator- and PPICbased real exchange rates for the same panel of countries.
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    However, their evidence is not supportive o fmean reversion for GNP deBator- and PPICbased real exchange rates for the same panel of countries. Taylor and Sarno also point to a number o fpit falls when using panel unit-root tests. See Higgins and Zakra jsek (1999) for evidence contrary to that of OFConnellFs. 2 3 4 2 rates is reported in
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    Engel et al. (1997). Papell (1997) and Liu and Maddala (1996)
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    also 1nd that evidence o fmean reversion in panels o freal exchange rates is very sensitive to the groups o fcountries considered. Recently, an alternative explanation bases the persistence o fmanaged-Boat deviations from parity on the presence of market frictions that impede commodity trade.
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    Papell (1997) and Liu and Maddala (1996) also 1nd that evidence o fmean reversion in panels o freal exchange rates is very sensitive to the groups o fcountries considered. Recently, an alternative explanation bases the persistence o fmanaged-Boat deviations from parity on the presence of market frictions that impede commodity trade.
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    Dumas (1992),
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    Uppal (1993), Sercu et al. (1995), and Coleman (1995) develop equilibrium models o freal exchange rate determination which take into account transactions costs and show that adjustment o freal exchange rates toward PPP is necessarily a nonlinear process.
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    Papell (1997) and Liu and Maddala (1996) also 1nd that evidence o fmean reversion in panels o freal exchange rates is very sensitive to the groups o fcountries considered. Recently, an alternative explanation bases the persistence o fmanaged-Boat deviations from parity on the presence of market frictions that impede commodity trade. Dumas (1992), Uppal (1993),
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    Sercu et al. (1995), and Coleman (1995)
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    develop equilibrium models o freal exchange rate determination which take into account transactions costs and show that adjustment o freal exchange rates toward PPP is necessarily a nonlinear process.
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    In this dynamic equilibrium framework, deviations from PPP follow a nonlinear stochastic process that is mean-reverting. In an initial test o fthe hypothesis o fthe analytic work o fPPP adjustment process based on market frictions,
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    Michael et al. (1997)
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    apply an exponential smooth transition autoregression (ESTAR) model to two data setsCa two-century span o fannual data and a monthly sample o finterwar observationsCand 1nd strong support for the nonlinear representation.
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    o fthe hypothesis o fthe analytic work o fPPP adjustment process based on market frictions, Michael et al. (1997) apply an exponential smooth transition autoregression (ESTAR) model to two data setsCa two-century span o fannual data and a monthly sample o finterwar observationsCand 1nd strong support for the nonlinear representation. Subsequently, using threshold autoregression modelling,
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    Obstfeld and Taylor (1997) and OFConnell and Wei (1997)
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    report additional evidence o fnonlinear price adjustment induced by the presence o ftransaction costs. However, OFConnell (1998b), utilizing an equilibrium threshold autoregression (TAR) model to post-Bretton Woods real exchange rates in a panel framework, 1nds little support to a market-frictions 5 6 7 8 5 6 7 8 A summary o fstylized facts regarding real exchange rate behavior in th
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    Subsequently, using threshold autoregression modelling, Obstfeld and Taylor (1997) and OFConnell and Wei (1997) report additional evidence o fnonlinear price adjustment induced by the presence o ftransaction costs. However,
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    OFConnell (1998b),
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    utilizing an equilibrium threshold autoregression (TAR) model to post-Bretton Woods real exchange rates in a panel framework, 1nds little support to a market-frictions 5 6 7 8 5 6 7 8 A summary o fstylized facts regarding real exchange rate behavior in the post-Bretton Woods era is presented in Lothian (1998).
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    However, OFConnell (1998b), utilizing an equilibrium threshold autoregression (TAR) model to post-Bretton Woods real exchange rates in a panel framework, 1nds little support to a market-frictions 5 6 7 8 5 6 7 8 A summary o fstylized facts regarding real exchange rate behavior in the post-Bretton Woods era is presented in
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    Lothian (1998).
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    Instead o fassuming instantaneous trade, Coleman considers the case in which time elapses when goods are shipped between markets. Goldberg et al. (1997) derive a nonlinear Gmean reverting elastic random walk toward a stochastic PPP rateH and 1nd that the mean-reversion process is not linear for some countries.
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    (TAR) model to post-Bretton Woods real exchange rates in a panel framework, 1nds little support to a market-frictions 5 6 7 8 5 6 7 8 A summary o fstylized facts regarding real exchange rate behavior in the post-Bretton Woods era is presented in Lothian (1998). Instead o fassuming instantaneous trade, Coleman considers the case in which time elapses when goods are shipped between markets.
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    Goldberg et al. (1997)
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    derive a nonlinear Gmean reverting elastic random walk toward a stochastic PPP rateH and 1nd that the mean-reversion process is not linear for some countries. Obstfeld and Taylor detect Iband reversionF for price differentials of disaggregated as well as aggregated CPIs for thirty-two city and country locations during the 1980-1985 period.
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    First, we estimate the deviations series from PPP using cointegration analysis, rather than imposing the strict PPPcointegrating vector in calculating real exchange rates. Strong PPP might not hold due to differential composition o fprice indices across countries
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    (Patel (1990)),
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    differential productivity shocks (Fisher and Park (1991)), and measurement errors in prices as a result o faggregation and index construction (Taylor (1988), Cheung and Lai (1993)). This latter rationale is very compelling, since available price indices are likely to be Bawed approximations to the theoretical constructs underlying PPP.
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    First, we estimate the deviations series from PPP using cointegration analysis, rather than imposing the strict PPPcointegrating vector in calculating real exchange rates. Strong PPP might not hold due to differential composition o fprice indices across countries (Patel (1990)), differential productivity shocks
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    (Fisher and Park (1991)), and
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    measurement errors in prices as a result o faggregation and index construction (Taylor (1988), Cheung and Lai (1993)). This latter rationale is very compelling, since available price indices are likely to be Bawed approximations to the theoretical constructs underlying PPP.
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    Strong PPP might not hold due to differential composition o fprice indices across countries (Patel (1990)), differential productivity shocks (Fisher and Park (1991)), and measurement errors in prices as a result o faggregation and index construction
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    (Taylor (1988),
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    Cheung and Lai (1993)). This latter rationale is very compelling, since available price indices are likely to be Bawed approximations to the theoretical constructs underlying PPP. These analytical justi1cations which explain why the cointegrating vector between nominal exchange rates and prices may vary greatly across countries have received strong empirical support.
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    These analytical justi1cations which explain why the cointegrating vector between nominal exchange rates and prices may vary greatly across countries have received strong empirical support. The data in several studies (e.g.
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    Pedroni (1997) and Li (1999))
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    strongly reject the symmetry and proportionality restrictions required for strict PPP. As a second contribution, we employ the ESTAR framework to analyze the dynamic behavior of deviations from PPP, which may be advantageous relative to the standard TAR framework in which regime changes occur abruptly.
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    Consistent with Teräsvirta (1994), i fan aggregated process is observed, which is the case with our data set here, regime changes may be smooth rather than discrete as long as heterogeneous economic agents do not act simultaneously (which is unlikely) even i fthey individually make dichotomous decisions. Additionally, in the analytics by
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    Dumas (1992) and
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    others, the adjustment process to parity is smooth rather than discrete. We apply the ESTAR methodology to a sample o fpost-Bretton Woods monthly data for a broad set of U.S. trading partners: seventeen countriesF CPI-based measures and eleven countriesF WPI-based measures.
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    Section 4 concludes with a summary o fthe evidence. 2.1 2 Nonlinear Adjustment toward PPP The ESTAR model of deviations from PPP In a framework of dynamic equilibrium in spatially separated markets,
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    Dumas (1992),
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    Uppal (1993), Sercu et al. (1995), and Coleman (1995) show that the presence o ftransaction costs in international trade implies that deviations from PPP converge to parity in a 5 nonlinear fashion. Transaction costs create a band of inaction within which international price differentials are not arbitraged away; only price differentials exceeding transaction costs (outside the band) are pro1table
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    Section 4 concludes with a summary o fthe evidence. 2.1 2 Nonlinear Adjustment toward PPP The ESTAR model of deviations from PPP In a framework of dynamic equilibrium in spatially separated markets, Dumas (1992), Uppal (1993),
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    Sercu et al. (1995), and Coleman (1995)
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    show that the presence o ftransaction costs in international trade implies that deviations from PPP converge to parity in a 5 nonlinear fashion. Transaction costs create a band of inaction within which international price differentials are not arbitraged away; only price differentials exceeding transaction costs (outside the band) are pro1table to arbitrage.
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    Therefore, in equilibrium under rational expectations the real exchange rate can deviate from its parity value of unity. In this framework, the real exchange rate exhibits mean reversion for large deviations from PPP, but Gspends most of the time away from parity...H
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    (Dumas (1992),
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    p.154). To model the behavior o fthe real exchange rate in this nonlinear context, we must specify a structure which may be considered a generalization of the standard linear model and which may be estimated from the available data.
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    Also, as long as heterogeneous economic agents (who individually make dichotomous decisions) do not act simultaneously, regime changes at an aggregated level may be smooth rather than discrete. These considerations led
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    Michael et al. (1997) to
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    apply a particular form of the Ismooth transitionF threshold autoregressive (STAR) model. In the STAR framework, the 1xed thresholds o fa standard threshold autoregressive (TAR) model are replaced with a smooth function, which need only be continuous and non-decreasing (Tong (1993), p. 108).
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    These considerations led Michael et al. (1997) to apply a particular form of the Ismooth transitionF threshold autoregressive (STAR) model. In the STAR framework, the 1xed thresholds o fa standard threshold autoregressive (TAR) model are replaced with a smooth function, which need only be continuous and non-decreasing
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    (Tong (1993),
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    p. 108). The need for symmetry in the response to positive and negative deviations from PPP leads to the exponential STAR, or ESTAR model described by Teräsvirta (1994). The ESTAR model can be viewed as a generalization o fthe double-threshold TAR model.
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    It is particularly attractive in the present context, as the strength o fthe equilibrating force is increasing in the (absolute) magnitude of the degree of disequilibrium, in line with predictions from the analytics of Dumas and others. Their framework, in which G...longrun behavior is very different from short-run behavior...H
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    (Dumas (1992),
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    p. 171), is poorly approximated by the constant speed o fadjustment o fthe linear cointegration framework, compared to the Bexible nature of the ESTAR approach. In this context, the ESTAR model will be more suitable than the TAR framework in analyzing the dynamic behavior o fthe deviations from PPP.
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    modelFs estimate o fthe impact o fthe lagged levelwill be inconsistent due to misspeci1cation (essentially, the omitted variables in the bracketed portion o fIn the ESTAR model, the coefficientwill govern the adjustment process for small deviations from PPP, whereas when deviations are sizable, and Fapproaches unity, thecoefficient becomes more and more important. The 8 t y .\r \r () o f
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    Granger and Teräsvirta (1993,
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    p.124). The scaling speeds the convergence and improves the stability o fthe nonlinear least squares estimation algorithm and makes it possible to compare estimates o facross equations. (+) \r\r \r \r quantitymust be negative to ensure global stability and mean reversion in the IouterF regime.
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    InternationalFinancialStatistics 3.2 Tests for cointegration t ()ttt (111) ε S,P,P ,, The validity o fthe PPP hypothesis as a long-run equilibrium concept requires that in (5) be a stationary process, that is, the system variablesshould form a cointegrated system
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    (Engle and Granger (1987)).
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    The strict (absolute) version o fPPP requires that the cointegrating vector be, imposing the joint restrictions of symmetryand proportionality. However, as discussed above, these restrictions may not be consistent with the empirical evidence due to measurement errors in prices, differential composition o fprice indices across countries, and differential productivity shocks.
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    However, as discussed above, these restrictions may not be consistent with the empirical evidence due to measurement errors in prices, differential composition o fprice indices across countries, and differential productivity shocks. The PPP relationship in (5) is estimated using the Johansen method
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    (Johansen (1988), Johansen and Juselius (1990)),
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    a reduced rank regression technique.The Johansen 11 1212 (=)(==1) ---13 13 All system variables have been tested for the presence of a unit root using the Augmented Dickey-Fuller and method employs a VAR framework which incorporates both the short- and long-run dynamics o fthe system.
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    This is especially true for CPI-based real exchange rates for Germany, Denmark, Norway, and Finland and WPI-based real exchange rates for Japan and Greece, for which no evidence o flinear cointegration was found. p, , 16 17 15 Some authors (e.g.
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    Papell and Theodoridis (1998))
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    argue that the strengthening o fthe evidence in support of long-run PPP for extended samples is only found when using panel methods but not univariate methods. These studies however impose the symmetry and proportionality restrictions in constructing the deviations series from parity: restrictions clearly rejected by the data.
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    Additionally, a comparison o fthe values o fthe transition parameter obtained here with those reported F F, ()=0) ()=1) ˆ 180 H--F,. -,-, :+=0(1263)=9168 ˆˆ The hypothesisresults in anwith a marginal signi1cance level o f0.002. However, the evidence for Norway should be interpreted with caution, as none of the crucial coefficients (and are individually statistically signi1cant. ˆ) 15 in
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    Michael et al. (1997)
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    suggests that the persistence o fdeviations from parity is much stronger in the post-Bretton Woods era than in the interwar period (the 1920s) or in the two-century span 1802-1992 included in their study. 19 3.5 Generalized impulse response functions To obtain further insights into the dynamic structure of real exchange rates, we perform impulse response function analysis to evaluate the propagat
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    Unlike a linear model, impulse response functions for a nonlinear model are characterized by dependence on initial conditions (history or path dependence) and the size and sign o fthe innovation (shock dependence. or asymmetry). Following
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    Koop et al. (1996),
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    the impulse response function can be expressed as the difference between two conditional 1rst-moment pro1les: (6) |-| --1+1+1 1 Xttthtttht X tt ()=[][] GI h,- ,ω EX - ,ω EX ω GIX h -tω t whereis the generalized impulse response function of a variable,is the forecasting horizon,is the perturbation to the process at time ,is the conditioning information set at time(reBecting the history o
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    We produce impulse response functions by estimatingcorresponding to a representative (average) history or initial conditions vector. Setting the conditioning vector to ensures that the vector o finitial conditions G...lies near the center o fthe data where the conditional density is most precisely estimatedH
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    (Gallant et al., (1993),
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    p. 887). The conditional forecasts are simulated realizations obtained by iterating the 1 [] [] E E 0 =[] ωEω -11 tt 20 19 This section was included at the suggestion o fan anonymous re feree. 20 11 An alternative strategy of estimating generalized impulse response functions for a nonlinear model involves esti[]tt-Eωω. matingfor each historyand then average the obtained sequences over all possi
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    involves esti[]tt-Eωω. matingfor each historyand then average the obtained sequences over all possible drawings fromGiven nonlinearities, the impulse response functions derived by these alternative strategies are not expected to be the same. 16 time series model, randomly drawing with replacement from the estimated residuals of the model, and then averaging over the number o frandom draws (see
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    Koop et al.(1996)
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    for a detailed description of this methodology). For our real exchange rate series, we derive impulse response functions by settingmonths and averaging the conditional forecast for each forecasting horizon over 5,000 draws.
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    Evidence from generalized impulse response functions also supports the presence o fnonlinearities. This evidence o fnonlinear adjustment to parity is in contrast to the negative evidence obtained by
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    OFConnell (1998b)
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    for panels o freal exchange rates in a TAR framework. Although the unit-root hypothesis may be rejected for a number of the PPP deviations series, a shock to these series dies out very slowly. Future research may focus on the factors that distinguish those countries whose deviations from long-run PPP are characterized by nonlinear behavior, as well as those related to this unusually slow speed o
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