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Oil price shocks and stock markets: testing for non-linearity

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Abstract

This paper formally tests for non-linearity in the relationship between real oil prices and real stock returns for Canada, Germany, the UK, and the US, and also assesses whether there are significant differences in the impact of oil price shocks on the stock markets studied. The findings provide evidence of non-linearity when windows with a fixed number of observations are considered. The non-linear specification that seems to do the best job of summarizing such non-linearity is the scaled specification, which considers not just whether oil prices increase or decline (and by how much) but also the environment in which the movements take place, highlighting more specifically the importance of controlling for the time-varying conditional variability of oil price shocks. An oil shock in a stable price environment is likely to have larger consequences on stock returns than one in a volatile price environment. Moreover, we find negative responses of real stock returns to oil price shocks for all countries. These responses are generally statistically similar between the North American countries considered, and between the European countries studied, although statistically different between the two groups of countries.

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Notes

  1. See Hamilton (1983), Gisser and Goodwin (1986), Mork (1989), Hamilton (1996), Hooker (1996), and Hamilton (2003), among others, for the US; and Burbidge and Harrison (1984), Mork et al. (1994), Jiménez-Rodríguez and Sánchez (2005), Kilian (2008), and Jiménez-Rodríguez and Sánchez (2009) for countries different from the US.

  2. See, for example, Davis and Haltinwager (2001), Edelstein and Kilian (2007), and Edelstein and Kilian (2009).

  3. See Bohi (1989), Lee and Ni (2002), Herrera (2007), Jiménez-Rodríguez (2008), and Jiménez-Rodríguez (2011).

  4. See Huang et al. (1996) for a nice explanation.

  5. Bernanke (1983) and Pindyck (1991) argue that changes in energy prices create uncertainty about future economic conditions, which give rise to firms to postpone investment decision (see also, for example, Henriques and Sadorsky 2008; Yoon and Ratti 2011).

  6. See footnote 1.

  7. See, for example, Bernanke et al. 1997.

  8. See Maghyereh (2004), Basher and Sadorsky (2006), Nandha and Hammoudeh (2007), Apergis and Miller (2009), Jawadi et al. (2010) among others, for evidence for other different countries.

  9. In the related literature, there are only a very few authors who have tested for the existence of a non-linear relationship between oil prices and stock returns (Ciner 2001, who uses the Hiemstra and Jones 1994, non-linear Granger test; and Reboredo 2010, who applies the six non-linear tests employed by Ashley and Patterson 2006: Brock et al. 1996; Engle 1982; McLeod and Li 1983; Tsay 1986; Hinich and Patterson 1995, and Hinich 1996). The tests used in this paper (i.e., Hamilton 2001 and also Dahl and González-Rivera 2003) have the main advantage of being flexible parametric tests in the sense that they do not force a particular functional form on the regression model under the alternative hypothesis.

  10. This way of measuring oil prices allows us to have a common shock to all countries. However, it is important to be aware that the actual impact of the oil shock would be modified in countries other than the US by changes in the bilateral exchange rate.

  11. Dahl (1999) finds that this test performs well in finite samples and that, in general, it has good size and power properties when it is compared to some of the most popular and powerful non-linearity tests in the literature (see, for instance, Ramsey’s Reset test, Ramsey 1969; Tsay’s test, Tsay 1986; the V23 test, Terasvirta et al. 1993; the neural network test, White 1989, and Lee et al. 1993).

  12. Hamilton’s (2001) approach considers the function \(\mu (\cdot )\) itself as being the outcome of a random field. He uses the generalization of the finite-differenced Brownian motion.

  13. An Appendix with the estimates for the linear specification and the four non-linear specifications (discussed below) is available from the authors upon request.

  14. For clarification purpose, shocks are identified through a standard Choleski decomposition, imposing the following order of innovations: real oil price changes (or its non-linear transformations) and real stock returns. This ordering is consistent with that used in the related literature (see, for instance, Park and Ratti 2008; Bjornland 2009).

  15. Dahl and González-Rivera (2003) show that their non-linearity tests have better power properties than the popular Tsay’s test (Tsay 1986).

    Table 2 Non-linearity test
    Full size table

  16. According to Dahl and González-Rivera (2003), the \(\lambda -tests\) have a better size than the g-test. This could explain the results of \(g_\mathrm{OP}^{A}\) statistic observed for Canada in Table 3.

  17. To ensure comparability across specifications, Table 7 scales the estimated effects as follows: for the scaled specification, they are divided by the sample mean of the standard deviation (i.e., 3.81); for the net and net3 specifications, they are divided by the ratio between the standard deviation of the growth rate of real oil prices and the NOPI/NOPI3 (i.e., 1.55).

  18. Similar results are found when the Akaike Information Criterion is used.

  19. Hamilton (2003) also finds that the transformation proposed by Lee et al. (1995) seems to do the best job of summarizing the non-linearity in the relationship between oil price changes and GDP growth.

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Acknowledgments

I thank the editor, Robert Kunst, and two anonymous referees for their helpful comments and suggestions. I acknowledge support from the Ministerio de Economía y Competitividad under Research Grant ECO2012-38860-C02-01.

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  1. Department of Economics, University of Salamanca, Campus Miguel de Unamuno, 37007 , Salamanca, Spain

    Rebeca Jiménez-Rodríguez

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Jiménez-Rodríguez, R. Oil price shocks and stock markets: testing for non-linearity. Empir Econ 48, 1079–1102 (2015). https://doi.org/10.1007/s00181-014-0832-8

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