Physica A 414 (2014) 118–127

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Physica A

journal homepage: www.elsevier.com/locate/physa

Carbon financial markets: A time–frequency analysis of CO2pricesRita Sousa a,b,c, Luís Aguiar-Conraria d,e,∗, Maria Joana Soares d,f

a CENSE, Portugalb New University of Lisbon, Portugalc School of Economics and Management, University of Minho, Campus de Gualtar, 4710 - 057 Braga, Portugald NIPE, Portugale Department of Economics, University of Minho, Portugalf Department of Mathematics and Applications, University of Minho, Campus de Gualtar, 4710 - 057 Braga, Portugal

h i g h l i g h t s

• We characterize the interrelation of CO2 prices with energy.• We conclude that CO2 leads electricity variables in the time–frequency domain.• We do not find a significant relation between CO2 and gas.• We observe a high partial coherency between CO2 and electricity, with CO2 leading.• We observe a high partial coherency between CO2 and coal, with coal leading.

a r t i c l e i n f o

Article history:Received 2 February 2014Received in revised form 16 May 2014Available online 14 July 2014

Keywords:Carbon pricesFinancial marketsMultivariate wavelet analysis

a b s t r a c t

We characterize the interrelation of CO2 prices with energy prices (electricity, gas andcoal), andwith economic activity. Previous studies have relied on time-domain techniques,such as Vector Auto-Regressions. In this study, we use multivariate wavelet analysis,which operates in the time–frequency domain. Wavelet analysis provides convenienttools to distinguish relations at particular frequencies and at particular time horizons.Our empirical approach has the potential to identify relations getting stronger and thendisappearing over specific time intervals and frequencies. We are able to examine thecoherency of these variables and lead–lag relations at different frequencies for the timeperiods in focus.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

The European Union Emission Trading Scheme (EU ETS) is the largest carbon market in the world, covering about 45% ofgreenhouse gas emissions from the European Union. It is a regional compromise bywhich EU countries are bonded to a totalpre-set emissions for specific sectors,mainly power and other energy intensive industries. Under such scheme, the regulator,the European Commission, sets emission caps to be reached by the participants and enables them to trade emission permitsin order to achieve the established cap: it is a cap-and-trade scheme.

∗ Corresponding author. Tel.: +351 964108697.E-mail addresses: ritasousa@eeg.uminho.pt (R. Sousa), lfaguiar@eeg.uminho.pt, aguiarconraria@gmail.com (L. Aguiar-Conraria),

jsoares@math.uminho.pt (M.J. Soares).

http://dx.doi.org/10.1016/j.physa.2014.06.0580378-4371/© 2014 Elsevier B.V. All rights reserved.

R. Sousa et al. / Physica A 414 (2014) 118–127 119

Overall, the EU aims to reduce its emissions by 20% by 2020 compared to 1990, and by 40% by 2030. For this purpose theEU ETS contributeswith a 21% cut in emissions in 2020 compared to 2005, in the sectors covered by themarket. Although theEU ETS is the largest greenhouse gas (GHG) emission trading scheme in place, others exist in the USA, New Zealand, Japan,Australia, Canada, in three cities in China, amongst others. Carbon markets are a world accepted tool for climate changemitigation for they provide cost-efficient solutions. A few emission trading schemes more are under development.

The EU ETSwas the first carbonmarket to be implemented. The first phase took place between 2005 and 2007, the second,the Kyoto period, in 2008–2012, and the third, since 2013, will last until 2020. Despite meeting the emission reductiongoals, the functioning of the European carbon market has raised some concerns. The main issue relates to the evidence ofconsistently low prices following the sharp fall of 2007, in the result of an overallocation of permits, even without bankingof allowances allowed between phases. In this context, it is important to understand the origin of carbon prices and theirimpact on the prices of fossil fuels, whose combustion is the main emitter of CO2.

Initially, most of the research on carbon pricing used Granger causality methodology to find unidirectional relationsbetween pairs of variables, including carbon and energy prices [1,2]. More recently, Vector Auto-Regressive (VAR) studieswith multivariate analysis estimate impulse response functions that show the impact of innovations of a variable, namelycarbon [3–6]. Also, in complement, there are studies on carbon price volatility [7–10].

We follow the previously referred studies and consider CO2 prices interrelation with energy prices (gas, coal andelectricity), and with economic activity index. These are the critical variables for carbon market actors. However, in thisstudy we use multivariate wavelet analysis, to see how carbon prices behave at different frequencies and how this behaviorchanges over time. With data for the second and third EU ETS phases until today, the compulsory periods, our purpose inthis paper is to identify relations getting stronger and then disappearing over specific time intervals and frequencies. Withthis approach, we are able to examine the coherency of these variables and lead–lag relations at different frequencies forthe time period in focus.

The results we obtain are of particular relevance to market regulators, States and also emitting companies, because weprovide a perception of the annual relationships between decision variables. This is different from the previous causalityand impulse-response analysis, usually more pertinent for financial market players.

In the next section, we briefly describe the wavelet analysis tools. Section 3 describes our dataset. Section 4 presentsresults and Section 5 concludes.

2. Wavelet analysis

Applications of the ContinuousWavelet Transform (CWT) to economics started to grow in the end of 2000s.1 For example,Aguiar-Conraria et al. [16] analyze the effects of the monetary policy in some macroeconomic variables, Baubeau andCazelles [17] look into French economic cycles, Rua andNunes [18] consider stockmarket returns, Aguiar-Conraria et al. [19]analyze the relation between the yield curve and the macroeconomy, Fernández-Macho [20] studies the Eurozone stockmarkets, and Kristoufek [21] tests the fractal market hypothesis during the last financial crisis.

Naturally, other authors, before us, have relied on wavelets to analyze the energy markets or the relation betweenenergy prices and other financial or macroeconomic variables. Actually, one can argue that wavelet analysis is particularlywell suited for this purpose. Energy price dynamics is nonstationary and so it is important to use methods that donot require stationarity. Moreover, there is evidence showing that several energy markets display consistent nonlineardependencies [22]. Based on their analysis, the authors call for nonlinear methods to analyze the impact of oil shocks.Wavelet analysis is one such method. Aguiar-Conraria and Soares [23], Naccache [24], Jammazi [25] and Tiwari et al. [26]have already relied onwavelets to study the evolution of oil prices, and Aloui and Hkiri [27], used the same tools to study theGulf Corporation Council stock markets. Interestingly, Vacha and Barunik [28] look to other energy commodities and findinteresting dynamics of correlations between crude and heating oil, gasoline and natural gas. Vacha et al. [29] rely on thewavelet coherence methodology to relate biofuels to several commodities (such as gasoline, diesel, corn, and rapeseed oil).To the best of our knowledge, specifically about carbonmarkets, there is no previouswork performed in the time–frequencydomain.

One common feature to all the above cited papers is that they rely on uni and bivariate wavelet analysis. So far,multivariate wavelet analysis has never been applied to economic data. This is an important shortcoming, becausewhen theassociation between two series is to be assessed, it is often important to account for the interaction with the other series. Toestimate the interdependence, in the time–frequency domain, between two variables after eliminating the effect of othervariables, we will rely on the concept of partial wavelet coherency and partial phase-difference.2

This section is necessarily brief. If interested in a detailed technical overview the reader can check Ref. [30]. We start byintroducing some standard wavelet tools: (1) the wavelet power spectrum, which describes the evolution of the varianceof a time-series at the different frequencies, with periods of large variance associated with periods of large power at the

1 Applications of the discrete wavelet transform to economic data started 10 years earlier. See, e.g. Refs. [11–14] for some early applications and Ref. [15]for a recent one.2 Fernández-Macho [20] also proposes new statistical tools to determine the overall correlation for the whole multivariate set on a scale-by-scale basis.

120 R. Sousa et al. / Physica A 414 (2014) 118–127

different scales, (2) the cross-wavelet power of two time-series, which describes the local covariance between the time-series, and the wavelet coherency, which can be interpreted as a localized correlation coefficient in the time–frequencyspace, and (3) the phase, which can be viewed as the position in the cycle of the time-series as a function of frequency, andthe phase-difference, which gives us information on the delay, or synchronization, between oscillations of the two time-series. The previous tools are standard, however they are important, because they will help us to describe the concepts ofpartial and multiple wavelet coherency and partial phase-difference, which are analogous to their bivariate counterparts,after controlling for the effects of other variables.

2.1. The wavelet

For most of the applications, a wavelet ψ is a well localized function, both in the time domain and in the frequencydomain, with zero mean, i.e.

∞

−∞ψ(t)dt = 0. This means that the function ψ has to wiggle up and down the t-axis, i.e. it

must behave like a wave.The specificwaveletwe use is selected from the so-calledMorlet wavelet family, first introduced in Ref. [31] and is defined

by:

ψ(t) = π−14 ei6te−

t22 . (1)

TheMorlet wavelet has an important property: it has optimal joint time–frequency concentration. The Heisenberg principlesays that one cannot be simultaneously precise in the time and the frequency domain. Theoretically, the time–frequencyresolution of the continuous wavelet transform is bounded by the so called Heisenberg box. The area of the Heisenberg box,which describes the trade-off relationship between time and frequency, is minimizedwith the choice of theMorlet wavelet.Another important characteristic is that it implies a very simple inverse relation between scale and frequency, allowing usto use the terms interchangeably.

2.1.1. The continuous wavelet transformStarting with amother waveletψ , a familyψτ ,s of ‘‘wavelet daughters’’ can be obtained by simply scaling and translating

ψ:

ψτ ,s(t) :=1

√|s|ψ

t − τ

s

, s, τ ∈ R, s = 0, (2)

where s is a scaling or dilation factor that controls the width of the wavelet.Given a time-series x(t), its continuous wavelet transform (CWT) with respect to the wavelet ψ is a function of two

variables,Wx (τ , s), obtained by ‘‘comparing’’ xwith a whole family of wavelet daughters:

Wx (τ , s) =

∞

−∞

x(t)1

√|s|ψ

t − τ

s

dt, (3)

where the bar denotes complex conjugation.

2.2. Univariate tools

2.2.1. The wavelet power and the wavelet phaseIn analogy with the terminology used in the Fourier case, the (local)wavelet power spectrum (sometimes called scalogram

or wavelet periodogram) is defined as

(WPS)x(τ , s) = |Wx(τ , s)|2 . (4)

This gives us a measure of the variance distribution of the time-series in the time-scale (time–frequency) plane.When the wavelet ψ(t) is chosen as a complex-valued function, as in our case, the wavelet transform Wx(τ , s) is also

complex-valued and can be separated into its real part, ℜ(Wx), and imaginary part, ℑ(Wx), or in its amplitude, |Wx(τ , s)|,and phase, φx(τ , s) : Wx(τ , s) = |Wx(τ , s)| eiφx(τ ,s). Recall that the phase-angle φx(τ , s) of the complex number Wx(τ , s)can be obtained from the formula: tan(φx(τ , s)) =

ℑ(Wx(τ ,s))ℜ(Wx(τ ,s))

, using the information on the signs of ℜ(Wx) and ℑ(Wx) todetermine to which quadrant the angle belongs to.

2.3. Bivariate tools

In many applications, one is interested in detecting and quantifying relationships between two non-stationarytime series. The concepts of cross-wavelet power, cross-wavelet coherency and wavelet phase-difference are naturalgeneralizations of the basic wavelet analysis tools that enable us to deal with the time–frequency dependencies betweentwo time-series.

R. Sousa et al. / Physica A 414 (2014) 118–127 121

The cross-wavelet transform of two time-series, x(t) and y(t), is defined as

Wxy (τ , s) = Wx (τ , s)Wy (τ , s) , (5)

whereWx andWy are the wavelet transforms of x and y, respectively. We also define the cross-wavelet power, asWxy(τ , s)

.For simplicity, in the next formulae we will omit (τ , s). The cross-wavelet power of two time-series depicts the localcovariance between the series at each time and frequency. Therefore, cross-wavelet power gives us a quantified indicationof the similarity of power between two time-series.

In analogywith the concept of coherency used in Fourier analysis, given x(t) and y(t) one can define their complexwaveletcoherency, ϱxy, by:

ϱxy =SWxy

S (Wxx) S

Wyy

1/2 , (6)

where S denotes a smoothing operator in both time and scale.The absolute value of ϱxy is the wavelet coherency, denoted by Rxy, i.e.: Rxy =

ϱxy.With a complex-valued wavelet, we can compute the phase of the wavelet transform of each series and thus obtain

information about the possible delays of the oscillations of the two series as a function of time and scale (frequency), bycomputing the phase difference. The phase difference can be computed from the cross-wavelet transform, by using theformula

tanφx,y =ℑ

Wxy

ℜ

Wxy

, (7)

with information on the signs of each part to completely determine the value of φxy ∈] − π, π]. A phase-difference of zeroindicates that the time series move together at the specified frequency; if φxy ∈ (0, π2 ), then the series move in phase, butthe time-series x leads y; if φxy ∈ (−π

2 , 0), then it is y that is leading; a phase-difference ofπ (or−π ) indicates an anti-phaserelation; if φxy ∈ (π2 , π), then y is leading; time-series x is leading if φxy ∈ (−π,−π

2 ).

2.4. Multivariate tools

In this paper, we apply the concepts of multiple and partial coherency from Fourier spectral analysis to the context ofwavelet time–frequency analysis—see Ref. [30].Wewill display the formulae for the case of three variables. Formore generalcases, the reader is referred to the appendix of the aforementioned paper.

Given three series x, y, z, the complex partial wavelet coherency of x and y, after controlling for z, is given by the formula

ϱxy .z =ϱxy − ϱxzϱyz

(1 − R2xz)(1 − R2

yz). (8)

Naturally, we define the partial wavelet coherency, Rxy .z , as the absolute value of ϱxy .z .Having defined the complex partial wavelet coherency ϱxy .z between the series x and the series y, after removing the

influence of z, we define the partial phase-difference of x over y, given z, as the angle of ϱxy .z . We will denote this phase-difference by φxy .z .

2.5. Statistical significance

There are some theoretical distributions that could be used for significance testing for the wavelet power spectrum—e.g.Ref. [32] concluded that the wavelet power spectrum of an AR(0) or AR(1) process is reasonably well approximated by achi-squared distribution. Ge [33], Cohen and Walden [34] and Sheppard et al. [35] have some important theoretical resultson significance testing for the wavelet coherency. To our knowledge, no work has been done on significance testing for thepartial coherency.3

All our significance tests are obtained using surrogates. To perform significance tests of wavelet measures, we fit anARMAmodel to the series and construct new samples by drawing errors from a Gaussian distribution with a variance equalto that of the estimated error terms. For each time-series (or set of time-series) we perform the exercise 2000 times, andthen extract the critical values at 5% and 10% significance.

Related to the phase-difference, there are no good statistical tests. This is so because it is very difficult to define thenull hypothesis. In fact, Ge [33] argues that one should not use significance tests for the phase-difference. Instead, oneshould complement its analysis by inspecting coherency, and only focus on phase-differences corresponding to statisticallysignificant coherencies.

3 However, the method of Sheppard et al. [35] may probably be extended for this case.

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3. Our data

The European Union Emissions Trading System is the first and the largest international system for trading greenhousegas emission allowances. The time length of this study is 2008–2013, representing EU ETS Phase II (2008/2012) and one yearof Phase III (2013–2020). As CO2 variable we used the European Union Allowance (EUA) spot price, the unit of the EU ETS,referring to the emission of one tonne of CO2 equivalent. Data for CO2 was available from 2008/02/26 up to 2012/11/01,from Bluenext, the most important EUA spot market in volumes. Prices from 2012/11/02 until 2013/11/12 were collectedfrom SendeCO2.

Greenhouse gas emissions considered in the European carbon market come from fossil fuels burning. More than 11000power stations, industrial plants and airlines, in Europe, operate under GHG emission limits. Hence, energy markets havean expected importance in the variations of CO2 prices. We included prices for natural gas, coal and electricity in Europe asenergy variables. For all of them, one month future contract was selected. This choice is in line with the established notionthat energy future prices lead spot prices essentially due to the difficulty of storage and consequent ease of shorting.

Regarding natural gas prices, we used The Intercontinental Exchange Futures (The ICE) data. Originally in £/therm, thedata was transformed to Euros/MMBTU for compatibility with other variables and better perception. As for coal, one monthfuture prices were also retrieved from The ICE database. Coal prices are cost, insurance and freight (CIF) with deliveryin Amsterdam, Rotterdam and Antwerp (ARA). They were originally in USD/tcoal and were converted to EUR/tcoal. Forelectricity, the Phelix baseload prices were retrieved from the European Energy Exchange (EEX), in Euros/MWh. The Phelixprices regard the German/Austrian market area. They were selected as representatives of the European base electricityprices, because Germany is the largest electricity producer in Europe, which, combined with Austria, reached 680 TWh ofgenerated electricity in 2011. Also, correlation levels between Phelix data and other electricity prices (tested for France andUK) range from 0.87 to 0.95. Therefore, variations presented through Phelix prices should appropriately represent variationsin other European electricity prices.

Noting that industries included in the EU ETS are energy intensive, and thus their production levels are highly associatedwith general economic growth, we considered necessary the inclusion of a variable which mirrored economic activity.This is in line with several previous authors in the subject [36,37,1,38]. For this purpose we considered FTSEurofirst 300Index (E3X.L), available at YahooFinance. It is a capitalization-weighted price tradable index measuring the performance ofEurope’s largest 300 companies.

4. Data analysis

The daily price returns of the several variables are depicted in Fig. 1, on the left-hand side panel, together with theirwavelet power spectrum, on the right-hand side. The wavelet power indicates, for each moment of time, the intensity ofthe variance of the time-series for each frequency of cyclical oscillations. This provides a first assessment of the behavior ofeach variable in the time–frequency domain.

Looking at Fig. 1, it is interesting to note that themarket for CO2 ismuch less volatile than the othermarkets. Additionally,the periods of high volatility do not coincide. While markets for gas, electricity, coal and FTSE exhibit high levels of volatilityuntil 2010, especially at 4 months frequencies (and also at longer run cycles, such as cycles with a periodicity of 20months),volatility in the CO2 market is only apparent after 2012 and, especially, during 2013, at very high frequencies. Based on thewavelet power spectra it is difficult to discern any interrelations between these markets.

As we said before, we use daily price returns for each variable of interest. While the price levels seem to follow a unitroot, the daily returns exhibit no unit root, both according the traditional ADF and KPSS unit root tests, or a more robustwavelet based unit root test [39].

We performed two more tests. First, for every variable, with the exception of the daily returns of CO2, we tested andrejected the null of no serial correlation using amulti-scale test for serial correlation proposed by Gençay and D. Signori [40].Then we estimated Hurst coefficients and found them very close to zero. This means that while the daily returns showsome linear dependency they do not show any discernible long-range dependency.We also estimated an ARMAmodel withGARCH errors, to deal with the linear dependency and time evolving variance, as several others have done with financialdata. However, even after doing so, the hypothesis that the standardized residuals follow a white noise is severely rejected.We tested this latter hypothesis using the BDS statistic [41] and the null was rejected in every single case. This suggests thatsome non-linearities are robust to this traditional modeling and provides one more reason to rely on wavelet analysis.

In Fig. 2, we estimate the coherency between CO2 and the other variables. It is interesting to note that before 2010,at longer run frequencies (corresponding to cycles of periodicity between 8 and 20 months), we observe a statisticallysignificant coherency. Looking at the phase-difference, and focusing in particular in the 8–20 frequency band,4 we observevery stable lead–lag relationships. The phase-difference between CO2 and the energy variables is typically between 0 andπ/2, indicating that the variables are in phase (positive correlation), with CO2 leading. The phase-difference between CO2

4 It is difficult to attach any meaning to the phase-difference in regions where coherency is not statistically significant. Therefore, we refrain frominterpreting the phase-differences at the shorter run frequencies.

R. Sousa et al. / Physica A 414 (2014) 118–127 123

Fig. 1. (a) Plot of the daily rate of return of each time-series. (b) The wavelet power spectrum. The black/gray contour designates the 5%/10% significancelevel. The cone of influence, which indicates the region affected by edge effects, is shown with a black line. The color code for power ranges from blue (lowpower) to red (high power). The white lines show the maxima of the undulations of the wavelet power spectrum. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)

and FTSE is very close to zero, indicating an almost simultaneous relationship. If anything, the phase difference is slightlynegative, suggesting that the leading variable is FTSE.

The relations described in the previous paragraph should not be taken as much more than descriptive statistics. Infact, when more than two series are given and the association between two of them is to be assessed, it is important toaccount for the interaction with the other series, otherwise one risks of incurring an omitted variable bias. To estimate the

124 R. Sousa et al. / Physica A 414 (2014) 118–127

Fig. 2. On the left—wavelet coherency. The black/gray black contour designates the 5%/10% significance level. The color code for coherency ranges fromblue (low coherency—close to zero) to red (high coherency—close to one). On the right—phase-differences between CO2 and another variable. Top: 2–8frequency band. Bottom: 8–20 frequency band. (For interpretation of the references to color in this figure legend, the reader is referred to the web versionof this article.)

interdependence, in the time–frequency domain, between two variables after eliminating the effect of other variables, werely on the concepts of partial coherency and partial phase-difference, described in the previous section.

Note that so far, much of our analysis could, conceivably, be done using multiscale entropy. Multiscale entropy can beused to measure the complexity of a time series at different scales, and is, thus, a function of scale. In a similar manner,cross-multiscale entropy can be used as a measure of asynchrony between two series at different scales. To have a time-scale measure, we would need to localize the function in time. Martina et al. [42] use a sliding window to localize multiscaleentropy in time. In principle, a similar procedure could be applied to two series, computing the cross-multiscale entropy ofthe two windowed series. However, as far as we are aware of, this was never done in the literature.

In Fig. 3,wehave the partial coherency betweenCO2 and each of the other variables, after controlling for all the others. It isnot obvious how to usemultiscale entropy to do something that could be comparedwith ‘‘partialwavelet coherency’’ results,i.e. how to control the influence of other series when comparing two series, which is one major concern of this paper.

Comparing Fig. 3 with Fig. 2, we see that the results change somewhat and that not considering the partial coherencywould lead us to erroneous conclusions. First, the relation between CO2 and gas is almost nonexistent, once we control forthe other variables. The other two variables that reflect energy markets exhibit quite different dynamics.

R. Sousa et al. / Physica A 414 (2014) 118–127 125

Fig. 3. On the left—partial wavelet coherency. The black/gray contour designates the 5%/10% significance level. The color code for coherency ranges fromblue (low coherency—close to zero) to red (high coherency—close to one). On the right—partial phase-differences between CO2 and the other variable. Top:2–8 frequency band. Bottom: 8–20 frequency band. (For interpretation of the references to color in this figure legend, the reader is referred to the webversion of this article.)

On the one hand, the region of (statistically significant) high partial coherency between CO2 and Electricity is situated inthe 8–20 frequency band and is observable across most of the sample. For that frequency range, the partial phase-differenceis consistently between 0 and π/2, which shows that the series move in-phase, with CO2 leading.

On the other hand, partial coherency between CO2 and coal is stronger after 2011, especially after 2012. It is alsointeresting to note that this relation is also clearly visible at higher frequencies. Moreover, the partial phase-difference isvery close to π at the lower frequency band and it switches between −π and π at higher frequencies. This shows that thevariables are almost perfectly out-of-phase and that, if anything, coal is the leading variable along the 8–20 frequency band.

Finally, the partial coherency between CO2 and economic activity, measured by FTSE, is particularly strong between late2011 and early 2013, especially for cycles with periodicities slightly above 8 months. In this time–frequency range, thepartial phase-difference is between −π/2 and 0, suggesting that the variables are in-phase, with CO2 lagging FTSE.

5. Conclusions

In this paper we observed several situations relating carbon prices to energy prices that are consistent with a growingmaturity of the European carbon market. We found evidence that, in cycles between 8 and 20 months, CO2 and electricity

126 R. Sousa et al. / Physica A 414 (2014) 118–127

variables are correlated, with CO2 leading, contributing to the accomplishment of the main objective of the market, whichis to penalize emissions from fossil fuels.

Surprisingly we do not find a significant relation between CO2 and gas in the time-cycles referred. Instead, we observeda high partial coherency between CO2 and electricity, with CO2 leading, and between CO2 and coal, with coal leading. Thisresult suggests that carbon pricing is having effects in the final good, electricity, instead of on primary fuels, gas and coal. Itseems that power suppliers are passing on the emission cost of using coal in their generation mix to the consumers throughthe electricity price. This is consistent with a low price demand elasticity of this good.

We also find higher volatility in carbon prices only after 2012, which may relate to the political uncertainties over thethird phase of the market, starting in 2013. At the same time, we observe that the carbon price follows the economy trends,in line with previous studies.

Information on carbon prices causes and effects is of major relevance to polluters and regulators of the carbon market.In this cap-and-trade system, prices are a signal that guide the polluting companies’ investments towards the use of cleanerfuels and energy efficiency. With the development of the EU market and higher liquidity levels, the consideration of thecarbon price on polluters’ production decisions should increasingly be transmitted to their products prices. Prices are alsoessential data for regulators to study and analyze the market operation and efficiency. Recently, Europe proposed a newpolicy framework for climate and energy, for 2030, where a reform of the EU ETS is presented. It is the regulator reactionto low carbon price levels, consequence of an overallocation of permits. It includes the establishment of a market stabilityreserve and an automatic adjustment of the allowances available in each allocation auction. The proposal refers that, startingin 2021, 12% of the total allowances in year x-2, shall be placed in the reserve. With the results presented, namely the in-phase relations of CO2 with electricity prices around a 12 months cycle, CO2 leading, and of the economy with CO2, in thesame frequency band, with the economy leading, regulators should consider that the intended effects of the carbon marketare present, even if only in longer cycles. Also, results show us that there is no evidence that penalizing CO2 emissionsdepleted economic activity in the time frame considered, controlling for final and primary energy variables. When therelation between carbon and the economy is significant, from mid-2011 almost until the end of our sample data, bothvariables move in phase, with the economy leading. In short, in our data frame, carbon prices are related with energy prices,and they follow the economy tendencies.

Knowing this, we propose that the market stability reserve percentage (currently 12%), should be reviewed yearly or,at least, every two years, to account for the effects observed of carbon price in the electricity price, of coal and carbonrelation, and finally, of the economy in the carbon price. It should not have an effect in the overall economic level variations.Recalling that the reserve amount is calculated using the allowances number from two years before, it is relevant to repeatthis analysis closer to 2019, and observe if new results are consistent with the ones presented in this study. Shorter cyclemeasures applied to the carbon market, such as the cancelation of a limited number of privately owned auctions shouldnot have a significant effect in energy prices. Only structural, long-term measures, such as a retirement of a number ofallowances or early revision of the linear reduction factor should matter.

To conclude, the idea that carbon prices are capturing coal price information and reflecting it in electricity prices, allowsus to say that the EU ETS is reaching stability, operating towards the right goal.

Acknowledgments

This work was partially supported by FEDER funds through ‘‘Programa Operacional Factores de Competitividade -COMPETE’’ and by Portuguese national funds through ‘‘FCT - Fundação para a Ciência e Tecnologia’’: project FCOMP-01-0124-FEDER-037268 (PEst-C/EGE/UI3182/2013).

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