International travelling and trade: further evidence for the case of Spanish wine based on fractional vector autoregressive specifications

Abstract

This article deals with the relationship between international travelling and trade. For this purpose we focus on a particular case study: the connection between the Spanish wine exports to Germany and the German travellers to Spain. Unlike previous studies we use a methodology based on fractional Vector AutoRegressive (VAR) models, which permits us to compute the impulse responses in a similar way as in the standard VAR case. The results show that the orders of integration of the two series are constrained between 0 and 1, being higher for the arrivals series than for the exports. The impulse response analysis reveals that an increase in travelling produces a positive initial impact on trade though it tends to disappear in the long run.

Acknowledgements

The authors L. A. Gil-Alana and C. Fischer gratefully acknowledges financial support from the Ministerio de Ciencia y Tecnologia (SEJ2005-07657, Spain) and H. Wilhelm Schaumann Stiftung, Hamburg, Germany, respectively. The authors are grateful for helpful comments from Alison Burrell on the first draft of this article. Comments of an anonymous referee are also gratefully acknowledged.

Notes

¹ Fischer and Gil-Alana (2007) showed that German travellers to Spain cause (in the Granger causality tests) exports of Spanish wines to Germany. We should expect a similar pattern for imports.

² The condition x_t = 0, t ≤ 0 is required for the Type II definition of fractional integration. For an alternative definition (Type I), see Marinucci and Robinson (1999).

³ Models with d ranging between −0.5 and 0 are short memory and have been addressed as anti-persistent by Mandelbrot (1977), because the spectral density function is dominated by high-frequency components.

⁴ See also Baillie (1996) for a complete review of I(d) processes. Other recent surveys are those of Doukhan et al. (2003), Robinson (2003) and Gil-Alana and Hualde (2009).

⁵ An I(0) vector process is defined as a covariance stationary process with spectral density matrix that is positive definite.

⁶ In another paper, Nielsen (2004) developed a likelihood approach in a fractionally integrated multivariate setting.

⁷ A full description of these methods is presented in Appendix 2.

⁸ Alternative identification strategies also involving restrictions on the long-run behaviour of the series are given in King et al. (1991). Other possibilities include restrictions on the sign and/or shape of the impulse responses (Faust, 1998); via heteroskedasticity (Rigobon, 2003); or the use of high-frequency data (Faust et al., 2004).

⁹ See Gil-Alana and Robinson (2001) and Gil-Alana (2002, 2005) for descriptions of seasonal fractional models.

¹⁰ The Bloomfield (1973) model is a nonparametric approach of modelling the I(0) disturbances that produces autocorrelations decaying exponential as in the AR(MA) case.

¹¹ Note that a nondiagonal matrix in Equation 20 would lead to the analysis of fractional cointegration, which is an area of research that has received increasing attention in recent years. (See Gil-Alana and Hualde, 2009, for a review.)

¹² Similar results were obtained when using higher VAR orders for the disturbance term.

¹³ Standard F-tests were conducted in the VAR(1) specification and we could not reject the null hypothesis of no serial correlation. A likelihood ratio test also produced evidence for the VAR(1) against the VAR(2) model.

¹⁴ Furthermore, and following the recommendations in Sims (1981) (see, also Lutkepohl and Breitung, 1997) we also checked whether the results were robust to the ordering of the variables. Altering the order of the variables the results for the impulse responses were practically identical to those reported in Fig. 4.

¹⁵ The confidence intervals here were obtained based on the asymptotic theory for multivariate fractional processes. (See, Nielsen, 2004.)