Regime-switching models for exchange rates

Abstract

This study provides evidence of periodically collapsing bubbles in the British pound to US dollar exchange rate in the post-1973 period. We develop two- and three-state regime-switching (RS) models that relate the expected exchange rate return to the bubble size and to an additional explanatory variable. Specifically, we consider six alternative explanatory variables that have been proposed in the literature as early warning indicators of a currency crisis. Our findings suggest that the RS models are, in general, more accurate than the Random Walk model in terms of both statistical and especially economic evaluation criteria for exchange rate forecasts. Our three-state RS model outperforms the two-state models and among the variables considered in our analysis, the short-term interest rate is the optimal variable, closely followed by imports. Results are more promising for one-month predictions and are qualitatively robust over sample spans. However, various robustness checks based on other exchange rates show that the optimal bubble measures and optimal predictors critically depend on the exchange rate.

Keywords:

• bubbles
• exchange rates
• regime switching
• forecasting

JEL Classification:

• F3
• G1
• C3

Acknowledgements

We would like to thank two anonymous referees, the editor and an associate editor of the journal for their useful comments and suggestions that greatly improved the paper.

Notes

1. For a literature review on the monetary approach, see Neely and Sarno (2002).

2. Panel regression techniques in conjunction with long-run relationships have shown some potential usefulness (Mark and Sul 2001).

3. See also Bollen, Gray, and Whaley (2000) and Chen and Lee (2006).

4. See also van Norden and Schaller (1993), Schaller and van Norden (1997, 1999) and van Norden and Vigfusson (1998).

5. The term ‘bubble’ is employed in the text to denote the deviation from fundamentals.

6. Details on bubble calculations and fundamental-based models are given in Section 3.

7. For a more detailed description of the model, see Rapach and Wohar (2002) and references therein.

8. For notational simplicity, we drop the superscript i=A, B, C, D for the four bubble measures

9. van Norden (1996) includes an additional term, in the probability equation, while Brooks and Katsaris (2005) employ the absolute value of the bubble, .

10. The subscripts c₀, c₁ refer to the constant and slope coefficient of the collapse state. Similarly, s₀, s₁ refer to the survival state and q₀, q₁ refer to the coefficients associated with the probability of collapse, q_t.

11. See also Evans (1991).

12. For an elaborate discussion on this issue, see Brooks and Katsaris (2005).

13. The derivation of the likelihood function is given in Appendix 1.

14. The calculation of the smoothed (ex post) probabilities is given in Appendix 2.

15. The following IFS codes are employed: nominal exchange rate: xx..AE.ZF…; price levels: xx64… ZF…; output levels (y-o-y growth rate): xx66… ZF…; short-term interest rate: xx60B..ZF…; long-term interest rate: xx60C… ZF…; international reserves: xx.1D.DZF…; exports: xx72..CZF… and imports: xx73..CZF…, xx refers to the country code, which is 112 for UK and 111 for US. The M3 monetary aggregate is sourced from the OECD Main Economic Indicators.

16. The explanatory variables do not enter Model 1, so Model 1 is estimated just once for each bubble measure.

17. The results for the other bubble measures and models are not reported for brevity but are available from the authors upon request.

18. Instead of using the asymptotic chi-squared distribution, we can apply Monte Carlo simulations (following the approach of Cheung and Erlandsson 2005) to obtain the empirical distribution of the LR statistic. We do not follow this approach because our goal is to examine the forecasting performance of all three RS models and thus model selection is not important in our analysis.

19. The (full-sample) estimated value of c is about , while the estimate of σ is about 0.04.

20. See Marcellino, Stock, and Watson (2006) for additional details.

21. Appendix 3 provides a detailed description of the Clark and West methodology.

22. This is based on unreported results from Monte Carlo simulations (Clark and West 2007).

23. We employ the three-month Eurosterling and Eurodollar deposit rate for the domestic and foreign interest rate, respectively. The series are available from the Bank of England database.

24. Details on the forecasting scheme are given in Section 5.1.