Asymmetric adjustment and nonlinear dynamics in real exchange rates

International Journal of Finance and Economics

Volumn 10, Issue 1, 2005, Pages 15-39

  Leon, Hyginus ^a   Najarian, Serineh ^b  

^a INTERNATIONAL MONETARY FUND   (United States)

^b HERTFORD COLLEGE   (United Kingdom)

Author keywords

Asymmetry; Nonlinearities; Real exchange rates

Indexed keywords

NONLINEARITY; PURCHASING POWER PARITY; REAL EXCHANGE RATE;

EID: 14344255370     PISSN: 10769307     EISSN: None     Source Type: Journal    
DOI: 10.1002/ijfe.257     Document Type: Article

References (118)

1. Nonlinearities in exchange rates can also occur because of: (i) heterogeneity in agents' expectations, given different investment horizons, risk profiles and institutional constraints (Brock and Holmes, 1998; DeGrauwe and Grimaldi, 2002; Kilian and Taylor, 2002); and (ii) local-to-currency pricing (LCP), under which producers selling abroad are assumed to set prices in the currency of consumers rather than their own (Feenstra and Kendall 1997; Haskel and Wolf, 2001).
2. The original idea dates back to Eli Heckscher (1916) and Gustav Cassel (1922).
3. Recent surveys of foreign exchange intervention include Sarno and Taylor (2001) and Humpage OF (2003). While there is no conclusive consensus on the overall effectiveness of official intervention, more recent studies (e.g. Fatum and Hutchinson, 2003) demonstrate a high-frequency relationship between foreign market intervention and both the level and change of exchange rates.
4. See also Coakley and Fuertes (2001), who employ a symmetric model to examine market segmentation in Europe.
5. Other nonlinear models exist in the literature. For example, Nicholls and Quinn (1982) discuss random coefficient autoregressive models (RCAR) processes; Granger and Joyeux (1980) introduce fractionally integrated processes, ARFIMA (0,d,0); and Kim (2000) develops a test of whether a process shifts from a stationary to a nonstationary series. We do not consider these models in this paper.
6. Kapetanios and Shin (2002) also propose a direct unit root test designed to have power against globally stationary three-regime self-exciting TAR processes. Their approach differs from that of Caner and Hansen who apply the threshold nonlinearity explicitly to all parameters and use the difference of the series as the transition variable. Neither model explicitly allows for a time-varying threshold.
7. Dahl and González-Rivera (2003) propose new tests that are free of unidentified nuisance parameters under the null of linearity, robust to the specification of the variance-covariance function of the random field, and appear to have superior performance in detecting bilinear, neural network and smooth transition autoregressive specifications.
8. We use the same countries in Dutta and Leon (2002), except for South Africa, which did not satisfy this geographical breakdown.
9. The Caner and Hansen design does not allow for time-varying thresholds. We are unaware of a general asymptotic theory for time-varying thresholds; however, our use of the bootstrap lessens the dependence on an asymptotic theory.
10. Sarno et al. (2002), using a similar approach, caution that there may be a cost to over-fitting a TAR model, because the power of Hansen's linearity test was found to be higher the lower the lag length of the TAR.
11. If the true process is stationary, the bootstrap distribution converges in probability to the correct asymptotic distribution. For unit root cases, the asymptotic distribution is discontinuous in the parameters at the boundary where ρ = 0 and is not consistent for the correct sampling distribution. Thus, the constrained bootstrap, which ensures that the bootstrap distribution will not be inconsistent for the correct sampling distribution, is first-order asymptotically correct under the null if the true process is a unit root, but incorrect if the true process is stationary.
12. 2}].
13. t = 1 (Lundbergh S, et al., 2003). Allowing for asymmetric speeds of transition between the outer and the middle regimes generates the time-varying BSTR model.
14. These models have been widely used since Hamilton's (1989) application of Markov-switching models to characterize fluctuations in the growth rate of US GDP.
15. Each iteration of the EM algorithm has two steps: (1) the expectation step estimates the unobserved states by their smoothed probabilities; and (2) the maximization step generates estimates of the parameter vector using the smoothed probabilities from the expectation step.
16. We use real effective exchange rates to focus on competitiveness and to avoid issues relating to the choice of numeraire currency (see O'Connell, 1998; Coakley and Fuertes, 2000). Further, because the real effective exchange rate is a weighted average of real bilateral exchange rates and averaging is more likely to generate stationarity, our results can be interpreted as conservative with respect to a finding of nonstationarity.
17. Following the IMF's World Economic Outlook (WEO) classification, the advanced countries are G7: Canada, France, Germany, Italy, Japan, United Kingdom, United States and Other: Australia, Belgium, Israel, Korea, New Zealand, Spain. The developing countries are Asia India, Indonesia, Malaysia, Philippines, Thailand and Western Hemisphere (WH): Argentina, Brazil, Chile, Colombia, Costa Rica, Mexico, Paraguay, Uruguay.
18. Nonnormality in financial data has implications for asset pricing, portfolio choice, value at risk and option valuation (see Jondeau and Rockinger, 2003). For example, nonnormality will affect the usefulness of forecasts if normality is assumed in generating these forecasts, and skewness in preferences of investors may affect the extent of portfolio diversification.
19. max. While runs with d = 2, 3 were less satisfactory, we also think d = 1 is more easily interpretable in our modelling context.
20. See Coakley et al. (2003) who propose an algorithm with low computational burden but accurate grid search.
21. While the results for the subregions are similar to Leon H, and Najarian S. (2002), overall averages differ in some instances, reflecting the influence of the countries that were included in that study but not included here.
22. We also calculated constrained bootstrap Wald statistics for the Lin vs. TAR. These indicated that if the DGP is a simple unit root process and we tested for linearity (stationary) against TAR, then for some countries we would falsely accept the null too frequently.
23. The terms resulting from a second-order expansion do not allow discrimination among the nonlinear alternatives.
24. 0 : π = 0. Few countries' data supported the TVBSTAR.
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26. L = γH = γz.ast; the BSTAR transition function closely approximates the second-order LSTAR model, especially for large values of slope parameter (γ).
27. The detailed test results are available on request.
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