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Rational speculative bubbles and duration dependence in exchange rates: an analysis of five currencies

2006; Chapman and Hall London; Volume: 16; Issue: 3 Linguagem: Inglês

10.1080/09603100500378997

1466-4305

Benjamas Jirasakuldech, Riza Emekter, Peter Went,

Global Financial Crisis and Policies

Abstract We investigate the presence of rational speculative bubbles in the exchange rates of the British pound, the Canadian dollar, the Danish krone, the Japanese yen and the South African rand against the US dollar. The unit root test shows that the exchange rates and fundamental variables – money supply, income and interest rates – are integrated of order one, indicating no rational speculative bubbles. Further, the cointegration test indicates evidence of a long-run relationship between the exchange rate series and the fundamental variables, corroborating that no speculative bubble is present. The results of the non-parametric duration dependence test suggest that rational expectations bubbles do not affect these exchange rates. Acknowledgements The authors would like to thank the participants at the FMA International 2005, an anonymous referee, and the editors for their helpful comments and suggestions that greatly improved our study. All remaining errors are ours. Notes 1 A rational expectations bubble occurs when investors realize that traded assets are overvalued, but investors are still not willing to close out their positions. Investors believe that potential higher positive excess returns will compensate them for the increased risks that the continuing price appreciation ends, or the bubble collapses. 2 Examples of parametric tests include variance ratio tests (e.g., Tauchen and Pittis, Citation1983; Kalyvitis and Pittis, Citation1994; Guimaraes-Filho, Citation1999; and Chang, Citation2004), volatility tests (e.g., Liu and He, Citation1991; Alexander, Citation1995; Chang, Citation2004; and Karras et al., Citation2005), and forward-looking techniques (e.g., Elwood et al., Citation1999; Puri et al., Citation2002). While these tests do not require a prior specification of the underlying exchange rate determination process, the very nature of unit root and cointegration tests do (e.g., Woo, Citation1987; MacDonald and Taylor, Citation1994; van Norden, Citation1996; Lajaunie and Naka, Citation1997; Oh, Citation1999; Francis et al., Citation2001; Chowdhury, Citation2004; Davrakadis, Citation2005; Frommel et al., Citation2005). Most studies fail to offer conclusive evidence for the existence of bubbles. 3 Bierens (Citation1997) developed a non-parametric cointegration tests that Coakley and Fuertes (Citation2001) and Davrakadis (Citation2005) applied on the determination of long-run exchange rate relationships. 4 The duration dependence test has been used widely to test for rational speculative bubbles in various asset markets (e.g., Zuehlke, Citation1987; McQueen and Thorley, Citation1994; Chan et al., Citation1998; Lavin and Zorn, Citation2001; Harman and Zuehlke, Citation2004). 5 Several studies use this relationship (e.g., MacDonald and Taylor, Citation1989 and Citation1994; and Kearney and MacDonald, Citation1990; Cheng, Citation1999; Francis et al., Citation2001; Tawadros, Citation2001; Groen, Citation2002; and Rapach and Wohar, Citation2002). 6 The asterisk denotes foreign, or non-US variables. 7 The reduced form derives from the following relationships: (1) (m − p) t = β yt − α it , determines the monetary equilibrium condition for the US; (2) (m* − p*) t = β yt * − α it *, is the monetary equilibrium condition for the foreign country; (3) , is the uncovered interest rate parity; and (4) st = (p − p*) t , is purchasing power parity. All values are natural logarithms. 8 The ADF model is . The PP model is . 9 This approach assumes efficient foreign exchange markets populated by a large number of risk neutral agents, who trade without incurring any transaction costs. The expectations of all agents are rational. 10 For full derivation of this equation, see McQueen and Thorley (Citation1994). 11 The yields are three-months government bill yields, except for Japan, where we used corresponding money market yields. 12 The money supply and industrial production series are seasonally adjusted. 13 The lag length l = 14 in the ADF and PP unit root tests is the highest significant lag order from either autocorrelation function or the partial autocorrelation function of the first differenced series. Both unit root tests are performed under the assumptions of a constant mean and no trend and a constant mean with trend. 14 The PP unit root tests reject the null hypothesis of a unit root for model with constant mean and trend in mean for Denmark's industrial production and interest rate, for South Africa's money supply and industrial production, and for UK's money supply. These results are consistent with those reported by Black and McMillan (Citation2004) for the Canadian dollar, Brotish Pound and Japanese yen. 15 The lag lengths for the VAR were chosen based on the lag exclusion test and Akaike's Information Criterion. 16 Under the null hypothesis of ‘no bubble’, the hazard rate should be constant, or β = 0. Under its alternative hypothesis, or the ‘existence of a bubble’, the hazard rate is negative, or β < 0 only for runs of positive returns, but not for runs of negative returns, because by definition, the bubble must grow. 17 In analysing equity markets, a bubble cannot be negative since stock prices, by construct, cannot be negative. Similarly, it would take a considerable stretch of the imagination to conjure non-positive exchange rates.