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Econometric Analysis of Carbon Markets

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Abstract

This chapter is dedicated to the connection between carbon prices and macroeconomic risk factors, besides the other determinants linked to energy and institutional variables studied in previous chapters. Several variables from the stock and bond markets are first studied, along with their influence on the carbon market. Second, macroeconomic, financial and commodity indicators are introduced by the means of factor models. Third, the relationship between carbon prices and industrial production is investigated based on nonlinearity tests, self-exciting threshold autoregressive models, smooth transition autoregressive models and Markov regime-switching models. Overall, the results show that carbon allowances form a very specific market among energy commodities, and that the interactions with the macroeconomy differ depending on several parameters.

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Notes

  1. 1.

    Note the R package ‘fGarch’ requires to install Rmetrics. See https://www.rmetrics.org/.

  2. 2.

    The spot carbon price series is not studied here due to the banking restrictions implemented between Phases I and II of the EU ETS (see Chap. 2 on this topic).

  3. 3.

    This basic relationship will be explained in more details in the next sections of this chapter.

  4. 4.

    For example, wood and heating oil are typically more sensitive to the business cycle than gold and silver, which exhibit little variation with the stock markets (and may be considered as safe havens in periods of market turbulence).

  5. 5.

    Note that the dataset for this study is not provided in this chapter.

  6. 6.

    Compared to gold and silver for instance, industrials do not incur any storage cost for carbon allowances (see Chap. 5 for more details).

  7. 7.

    See Chap. 4 for a description of the basic VAR model.

  8. 8.

    Note that PCA can also be used for the correlation matrix ρ r of r.

  9. 9.

    The data for this chapter is not available for download.

  10. 10.

    See Chevallier (2011, [27]) for the description of the time series which have been gathered in a large database to represent the broad economic environment.

  11. 11.

    Standard initial conditions can be found in Koop (2003, [52]). This numerical approach is easier to implement than Markov Chain Monte Carlo Methods (MCMC). Note also that the PCA provides a solution only to the factor equation, without taking into account the dynamics of the factors (see Stock and Watson (2005, [67]).

  12. 12.

    Hence, this result is conform to the relationship between carbon markets and the macroeconomy based on purely theoretical grounds.

  13. 13.

    Note this data is not available for download for this chapter.

  14. 14.

    Std. Dev. is the standard deviation. JB stands for the Jarque Bera test. LB stands for the Ljung-Box test, whose p-values have been computed with a number of 20 lags (the values found are qualitatively similar with 10 or 15 lags). The same comments apply for the Engle ARCH test.

  15. 15.

    For the ADF and PP tests, the null hypothesis is EU27PRODINDRET (EUAFUTRET) has a unit root (where EU27PRODINDRET (EUAFUTRET) stands for the EU27 Seasonally Adjusted Industrial Production Index in Logreturn form (the EUA Futures Price in Logreturn form)). For the ADF test, a lag length of 1 (0) is specified based on the Schwarz Information Criterion. For the PP test, a Bartlett kernel of bandwith 5 (1) is specified using the Newey-West procedure. For both tests, Model 1 (without trend nor intercept) is chosen. Test critical values at the 5% level are based on MacKinnon (1996). For the KPSS, the null hypothesis is EU27PRODINDRET (EUAFUTRET) is stationary. A Bartlett kernel of bandwidth 5 (3) is specified using the Newey-West procedure. Asymptotic critical values at the 5% level are based on KPSS (1992). Model 2 (with intercept) (Model 3 (with intercept and deterministic trend)) is chosen.

  16. 16.

    Loosely speaking, a time series is said to be ‘chaotic’ if it follows a nonlinear deterministic process, but looks random.

  17. 17.

    This restriction is necessary because if the true model is linear, the threshold parameter is undefined, in which case an unrestricted search may result in the threshold estimator being close to the minimum or maximum data values, making the large-sample approximation ineffective (Cryer and Chan (2008, [30])).

  18. 18.

    Note that repeating the test with a=0.1 and b=0.9 yields identical results. This comment applies in the remainder of the chapter.

  19. 19.

    The discontinuity of the thresholds is replaced by a smooth transition function (typically the logistic or exponential functions, see Van Dijk et al. (2002, [79]) for an exhaustive review of STAR models).

  20. 20.

    See also Bradley and Jansen (2004, [17]) for an application of STAR models to stock returns and industrial production.

  21. 21.

    Note that the transition variable s t must be part of the lags of these variables if it is not a trend.

  22. 22.

    Note this task may also be performed by looking at the information criteria, or at the residual sum of squares.

  23. 23.

    Note also that in order to make γ scale-free, it is divided by \(\hat{\sigma}_{s}^{K}\), the Kth power of the sample standard deviation of the transition variable.

  24. 24.

    Note that the traditional ARCH LM test for the presence of heteroskedasticity and the Jarque-Bera test for normality may also be developed for STAR models.

  25. 25.

    The (−1) term into parentheses means that the variable is lagged one period.

  26. 26.

    Note for the transition variable EUAFUTRET(−1), the STAR model has not been estimated owing to near singularity of the moment matrix.

  27. 27.

    Note that the estimate of γ (the slope parameter) is not significant. Its large standard deviation estimate reflects the numerical difficulties in estimating γ accurately when it is large, and the transition function is thus close to a step function (for a more detailed discussion of this phenomenon, see for example Granger and Teräsvirta (1993, [47]) or Teräsvirta [69, 70]).

  28. 28.

    NA stands for ‘Not Available’ when the test encounters a matrix inversion problem. df stands for degree of freedom.

  29. 29.

    Standard errors are in parentheses. ∗∗∗, ∗∗, ∗ denote respectively statistical significance at the 1%, 5% and 10% levels.

  30. 30.

    The regime (smoothed) probability at time t is the probability that state t will operate at t, conditional on information available up to t−1 (conditional on all information in the sample). Regime 1 is ‘expansion’. Regime 2 is ‘contraction’. NBER business cycles reference dates are represented by gray vertical lines.

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  1. CGEMP/LEDa Department of Economics, University Paris Dauphine, Place du Marechal de Lattre de Tassigny, 75016, Paris, France

    Dr. Julien Chevallier

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Chevallier, J. (2012). Link with the Macroeconomy. In: Econometric Analysis of Carbon Markets. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2412-9_3

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