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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- 1.
Note the R package ‘fGarch’ requires to install Rmetrics. See https://www.rmetrics.org/.
- 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.
This basic relationship will be explained in more details in the next sections of this chapter.
- 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.
Note that the dataset for this study is not provided in this chapter.
- 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.
See Chap. 4 for a description of the basic VAR model.
- 8.
Note that PCA can also be used for the correlation matrix ρ r of r.
- 9.
The data for this chapter is not available for download.
- 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.
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.
Hence, this result is conform to the relationship between carbon markets and the macroeconomy based on purely theoretical grounds.
- 13.
Note this data is not available for download for this chapter.
- 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.
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.
Loosely speaking, a time series is said to be ‘chaotic’ if it follows a nonlinear deterministic process, but looks random.
- 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.
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.
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.
See also Bradley and Jansen (2004, [17]) for an application of STAR models to stock returns and industrial production.
- 21.
Note that the transition variable s t must be part of the lags of these variables if it is not a trend.
- 22.
Note this task may also be performed by looking at the information criteria, or at the residual sum of squares.
- 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.
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.
The (−1) term into parentheses means that the variable is lagged one period.
- 26.
Note for the transition variable EUAFUTRET(−1), the STAR model has not been estimated owing to near singularity of the moment matrix.
- 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.
NA stands for ‘Not Available’ when the test encounters a matrix inversion problem. df stands for degree of freedom.
- 29.
Standard errors are in parentheses. ∗∗∗, ∗∗, ∗ denote respectively statistical significance at the 1%, 5% and 10% levels.
- 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.
References
Alberola E, Chevallier J, Cheze B (2008) Price drivers and structural breaks in European carbon prices 2005-07. Energy Policy 36:787–797
Alberola E, Chevallier J, Cheze B (2008) The EU emissions trading scheme: the effects of industrial production and CO2 emissions on European carbon prices. Int Econ 116:93–125
Alberola E, Chevallier J, Cheze B (2009) Emissions compliances and carbon prices under the EU ETS: a country specific analysis of industrial sectors. J Policy Model 31:446–462
Bailey W, Chan KC (1993) Macroeconomic influences and the variability of the commodity futures basis. J Finance 48:555–573
Basci E, Caner M (2005) Are real exchange rates nonlinear or nonstationary? Evidence from a new threshold unit root test. Stud Nonlinear Dyn Econom 9:1–19
Brock W, Dechert WD, Scheinkman JA (1987) A test for independence based on the correlation dimension. Working paper, Department of Economics, University of Wisconsin, Madison, USA
Brock WA, Hsieh DA, LeBaron B (1991) Nonlinear dynamics, chaos, and instability: statistical theory and economic evidence. MIT Press, Cambridge
Brock WA, Dechert WD, Scheinkman JA, LeBaron B (1996) A test for independence based on the correlation dimension. Econom Rev 15:197–235
Benz E, Trück S (2009) Modeling the price dynamics of CO2 emission allowances. Energy Econ 31:4–15
Bera AK, Higgins ML (1993) ARCH models: properties, estimation and testing. J Econ Surv 7:305–366
Bernanke B, Boivin J, Eliasz P (2005) Measuring monetary policy: a factor augmented vector autoregressive (FAVAR) approach. Q J Econ 120:387–422
Bessembinder H, Chan KC (1992) Time-varying risk premia and forecastable returns in futures markets. J Financ Econ 32:169–193
Berndt E, Hall B, Hall R, Hausman J (1974) Estimation and inference in nonlinear structural models. Ann Econ Soc Meas 3:653–665
Bollerslev T (1986) Generalized autoregressive conditional heteroskedasticity. J Econom 31:307–327
Bollerslev T, Chou RY, Kroner KF (1992) ARCH modeling in finance: a review of the theory and empirical evidence. J Econom 52:5–59
Bollerslev T, Engle RF, Nelson DB (1994) ARCH models. Handb Econom 4:2959–3038
Bradley MD, Jansen DW (2004) Forecasting with a nonlinear dynamic model of stock returns and industrial production. Int J Forecast 20:321–342
Caballero R, Farhi E, Gourinchas P (2008) Financial crash, commodity prices and global imbalances. Brookings Pap Econ Act 2:1–55
Cai J (1994) A Markov model of unconditional variance in ARCH. J Bus Econ Stat 12:309–316
Caner M, Hansen BE (2001) Threshold autoregression with a unit root. Econometrica 69:1555–1596
Chan KS (1991) Percentage points of likelihood ratio tests for threshold autoregression. J R Stat Soc B 53:691–696
Chan KS (1993) Consistency and limiting distribution of the least squares estimator of a continuous autoregressive model. Ann Stat 21:520–533
Chan KS, Tong H (1985) On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations. Adv Appl Probab 17:666–678
Chan KS, Tong H (1986) On estimating thresholds in autoregressive models. J Time Ser Anal 7:179–190
Chan KS, Tsay RS (1998) Limiting properties of the conditional least squares estimator of a continuous TAR model. Biometrika 85:413–426
Chevallier J (2009) Carbon futures and macroeconomic risk factors: a view from the EU ETS. Energy Econ 31:614–625
Chevallier J (2011) Macroeconomics, finance, commodities: interactions with carbon markets in a data-rich model. Econ Model 28:557–567
Chevallier J (2011) Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models. Econ Model (forthcoming). doi:10.1016/j.econmod.2011.08.003
Chevallier J (2011) A model of carbon price interactions with macroeconomic and energy dynamics. Energy Econ (forthcoming). doi:10.1016/j.eneco.2011.07.012
Cryer JD, Chan KS (2008) Time series analysis with applications in R, 2nd edn. Springer texts in statistics. Springer, New York
Deschamps PJ (2008) Comparing smooth transition and Markov-switching autoregressive models of US unemployment. J Appl Econom 23:435–462
Ding Z, Granger CWJ, Engle RF (1993) A long memory property of stock market returns and a new model. J Empir Finance 1:83–106
Dufrenot G, Mignon V (2002) Recent developments in nonlinear cointegration with applications to macroeconomics and finance. Springer, New York
Ellerman AD, Buchner BK (2008) Over-allocation or abatement? A preliminary analysis of the EU ETS based on the 2005-06 emissions data. Environ Resour Econ 41:267–287
Engle RF (1982) Autoregressive conditional heteroskedasticity with estimates of variance of United Kingdom inflation. Econometrica 50:987–1008
Engle RF (2001) GARCH 101: the use of ARCH/GARCH models in applied econometrics. J Econ Perspect 15:157–168
Engle RF (2003) Risk and volatility: econometric models and financial practice. Nobel Lecture, December 2003
Engle RF, Lilien DM, Robins RP (1987) Estimating time varying risk premia in the term structure: the ARCH-M model. Econometrica 55:391–408
Engle RF, Patton AJ (2001) What good is a volatility model? Quant Finance 1:237–245
Fama EF, French KR (1987) Dividend yields and expected stock returns. J Financ Econ 22:3–25
Fama EF, French KR (1989) Business conditions and expected returns on stocks and bonds. J Financ Econ 25:23–49
Fama EF, French KR (1992) The cross-section of expected stock returns. J Finance 47:427–465
Fama EF, French KR (1993) Common risk factors in the returns on stocks and bonds. J Financ Econ 33:3–56
Fleming J, Ostdiek B (1999) The impact of energy derivatives on the crude oil market. Energy Econ 21:135–167
Franses PH, Van Dijk D (2003) Nonlinear time series models in empirical finance, 2nd edn. Cambridge University Press, Cambridge
Godfrey L (1988) Misspecification tests in econometrics. Cambridge University Press, Cambridge
Granger CWJ, Teräsvirta T (1993) Modelling nonlinear economic relationships. Oxford University Press, Oxford
Hamilton JD (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57:357–384
Hamilton JD (2008) Regime-switching models. In: Durlauf SN, Blume LE (eds) The new Palgrave dictionary of economics, 2nd edn. Palgrave Macmillan, Basingstoke, pp 1–15
Hamilton JD, Susmel R (1994) Autoregressive conditional heteroskedasticity and changes in regime. J Econom 64:307–333
Keenan DM (1985) A Tukey nonadditivity-type test for time series nonlinearity. Biometrika 72:39–44
Koop G (2003) Bayesian econometrics. Wiley, New York
Li WK, Ling S, McAleer M (2002) Recent theoretical results for time series models with GARCH errors. J Econ Surv 16:245–269
Ludvigson SC, Ng S (2007) The empirical risk-return tradeoff: a factor analysis approach. J Financ Econ 83:171–222
Ludvigson SC, Ng S (2009) Macro factors in bond risk premia. Rev Financ Stud 22:5027–5067
Lütkepohl H, Krätzig M (2004) Applied time series econometrics. Cambridge University Press, Cambridge
Luukkonen R, Saikkonen P, Teräsvirta T (1988) Testing linearity against smooth transition autoregressive models. Biometrika 75:491–499
Nelson DB (1991) Conditional heteroskedasticity in asset returns: a new approach. Econometrica 59:347–370
Paolella MS, Taschini L (2008) An econometric analysis of emission allowance prices. J Bank Finance 32:2022–2032
Pippenger MK, Goering GE (1993) A note on the empirical power of unit root tests under threshold processes. Oxf Bull Econ Stat 55:473–481
Pippenger MK, Goering GE (2000) Additional results on the power of unit root and cointegration tests under threshold processes. Appl Econ Lett 7:641–644
Ploberger W, Kramer W (1992) The CUSUM test with OLS residuals. Econometrica 60:271–285
Sadorsky P (2002) Time-varying risk premiums in petroleum futures prices. Energy Econ 24:539–556
Sadorsky P (2006) Modeling and forecasting petroleum futures volatility. Energy Econ 28:467–488
Stock J, Watson M (2002) Forecasting using principal components from a large number of predictors. J Am Stat Assoc 97:1167–1179
Stock J, Watson M (2002) Macroeconomic forecasting using diffusion indexes. J Bus Econ Stat 20:147–162
Stock J, Watson M (2005) Implications of dynamic factor models for VAR analysis. NBER working paper 11467, USA
Tang K, Xiong W (2009) Index investing and the financialization of commodities. Working Paper, Princeton University, Princeton
Teräsvirta T (1994) Specification, estimation, and evaluation of smooth transition autoregressive models. J Am Stat Assoc 89:208–218
Teräsvirta T (1998) Modeling economic relationships with smooth transition regressions. In: Ullah A, Giles D (eds) Handbook of applied economic statistics. Dekker, New York, pp 229–246
Teräsvirta T (2004) Smooth transition regression modelling. In: Lütkepohl H, Krätzig M (eds) Applied time series econometrics. Cambridge University Press, Cambridge
Teräsvirta T, Anderson HM (1992) Characterizing nonlinearities in business cycles using smooth transition autoregressive models. J Appl Econom 7:S119–S136
Tong H (1978) On a threshold model. In: Chen CH (ed) Pattern recognition and signal processing. Sijthoff and Noordhoff, Amsterdam, pp 101–141
Tong H (1983) Threshold models in non-linear time series analysis. Springer, New York
Tong H (1990) Non-linear time series: a dynamical system approach. Clarendon Press, Oxford
Tong H, Lim KS (1980) Threshold autoregression, limit cycles and cyclical data (with discussion). J R Stat Soc B 42:245–292
Tsay RS (1986) Nonlinearity test for time series. Biometrika 73:461–466
Tsay RS (2010) Analysis of financial time series, 3rd edn. Wiley, New York
Van Dijk D, Teräsvirta T, Franses PH (2002) Smooth transition autoregressive models—a survey of recent developments. Econom Rev 21:1–47
Zakoian JM (1994) Threshold heteroskedastic models. J Econ Dyn Control 18:931–955
Zagaglia P (2010) Macroeconomic factors and oil futures prices: a data-rich model. Energy Econ 32:409–417
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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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