The Antonios Kalatzis

Martin Buber

Faraway, So Close: Skepticism, subjective Idealism and the Problem of Shine in Hegel' s Science of Logic

published or not. The documents may come

At first, the chapter on Essence and Shine in Hegel's Science of Logic appears to be just another, or more specifically, the second subchapter of the Doctrine of Essence; an intermediate point between the opening of the Doctrine of Essence and one of its core chapters, the one on Reflection. Yet, at a closer look, this seems to be anything but the case.

As we will see, Hegel's purpose in this chapter is not merely to give an account of the logical content and the relation between Essence and Shine, but to substantiate the claim that the logical structure he is dealing with here is the fundamental logical structure on the basis of which both, ancient skepticism and transcendental/subjective idealism operate. [START_REF] Hegel | Encyclopedia of the Philosophical Sciences in Basic Outline[END_REF] Hence, what we encounter in this specific chapter is not only an account of some isolated and limited set of logical contents, i.e. the logical contents of Essence and Shine, but Hegel's attempt to account for and, ultimately, to refute two of the most significant trends in the history of philosophy, [START_REF] Hackenesch | Die Logik der Andersheit[END_REF] i.e. skepticism and subjective idealism. What I will try to do is divided in three parts. First, I will show why, according to [START_REF] Hegel | Encyclopedia of the Philosophical Sciences in Basic Outline[END_REF] Along with skepticism and transcendental Idealism Hegel adds the philosophies of Leibniz and Fichte, but I will leave this aspect aside. [START_REF] Hackenesch | Die Logik der Andersheit[END_REF] For the centrality of the refutation of the skeptical claims throughout Hegel's work see Forster 1989, pp. 99 ff. 2 Hegel, skepticism and subjective idealism share the same onto-logical commitments; second, I will provide an account of Hegel's critical exposition of the logical content of Essence and Shine, as depicted in the Science of Logic and in the recently published volumes of the Vorlesungen über die Logik from the critical edition of Hegel's works. Finally, I will show in what sense both skepticism and transcendental/subjective idealism are variations, according to Hegel, of one and the same logic, the logic of Shine, and how this logic proves to be aporetic -and replaced by another more consistent and adequate set of concepts.

Skepticism and subjective idealism

To begin with, let us start with the core-sentence of the subchapter, the meaning of which I will unravel gradually. Immediately after the introductory account of the categories of Essence and of Shine Hegel makes the following remark: Shine, the "phenomenon" of skepticism, and also the "appearance" of idealism, is thus this immediacy which is not a something nor a thing -in general, not an indifferent being that would exist apart from its determinateness and connection with the subject. Skepticism did not permit itself to say "It is," and the more recent idealism did not permit itself to regard cognitions as a knowledge of the thing-in-itself. The shine of the former was supposed absolutely not to have the foundation of a being: the thing-in-itself was not supposed to enter into these cognitions. (SL, pp. 342-343) What we encounter in this passage is, thus, the aforementioned identification between the logical content of Shine, the "phenomenon" of skepticism, and the "appearance" of (subjective) idealism. Skepticism and subjective idealism respectively reject the claim that knowledge can be objective, i.e. that it can grasp or refer to being or to things-in-themselves as such. This is because both skepticism and subjective idealism share the same assumption, namely that positioning things into a relationship, or, in Hegelese, in "determinateness" is a subjective act, i.e. an act that stems from the subject of knowledge, but that actually is external to the nature of the object of knowledge as such. 3 Moreover, it is this act that makes impossible the claim for objective knowledge on the basis of a second premise. According to this second premise, which is intrinsically connected to the claim that human knowledge cannot achieve objectivity in its effort to grasp things (-inthemselves) or beings, is that these things or beings are primordially "indifferent" and external to any given relation. 4 In short, according to Hegel, both skepticism and transcendental/subjective Idealism discard the claim for objectivity on the basis of the assumption that things exist before entering any relations and that true knowledge should be able to grasp things as such, before any relation to each other (cf. GW 26,1, p. 127). Because discursive knowledge can only know things through their relation, it cannot be considered as objective. In a word, relatedness in ontology means relativism in epistemology. 5 Thus, Hegel's account of skepticism in his Lectures on the History of Philosophy appears to be in complete accordance to the connection between Shine and skepticism in the Science of Logic. In the Lectures we read:

Skepticism consummated the assumption regarding the subjectivity of all knowledge. Furthermore, it replaced the term being by the term shine in all knowledge. Skepticism is the ultimate peak [of the philosophical stance that takes all knowledge to be relative -A.K.]: the form of being and the knowledge of being are destroyed completely. Skepticism is philosophy, but a philosophy that either is able or willing to become a system. (TW 19, p. 358, my translation) The same applies to the critical philosophy of subjective idealism which declares only immediateness as the measure for ultimately objective knowledge, and on the basis of this assumption it declares knowledge of entities that belong to a relation, and, thus, all knowledge as untrue and the knowable entities themselves as appearances.

Hence, there would only be two things that could claim to achieve objective truth.

First, the mere, and thus, immediate, identity of the transcendental I, as the subject of knowledge:

The acquaintances with things, gathered from experience, do not measure up to this identity utterly devoid of determinateness, since they are in any case findings of a determinate content. Insofar as such an unconditioned object is taken to be the absolute and the true object of reason (as the idea), acquaintances with things gathered from experience are as a result declared to be the untrue, to be appearances. (EPS, p. 89, § 45) And, secondly, the equally unmediated and immediate object of knowledge, which rests beyond all relations, i.e. beyond all discursivity:

The thing-in-itself (and under thing, spirit, God are also included) expresses the object insofar as one abstracts from everything that it is for consciousness, i.e. from all determinations of sensation as well as from all determinate thoughts of it. (EPS, p. 89, § 44) In a word, Hegel's ultimate account of skepticism and subjective idealism is that they take as measure of truth entities that per definitionem cannot be truly grasped. 6

Essence and Shine

Now I would like to move from Hegel's account and identification of skepticism and transcendental/subjective idealism to the concrete reconstruction of the subchapter on Essence and Shine in the Science of Logic. The aim is not only the clarification of this part of the book, but at the same time the depiction of the common logical structure of skepticism and transcendental/subjective idealism and, to a greater degree, the means through which Hegel thinks he can refute the claims and the epistemological limitations encountered in these philosophical trends.

We must keep in mind that according to Hegel's account both skepticism's and transcendental/subjective idealism's claim regarding the subjectivity or relativity of all knowledge is based on the assumption that objective knowledge should refer to -ontologically possible or/and actual -immediate objects, i.e. to objects that can and should be conceived independently of any relation. In other words, in objects which are identical with or related only to themselves.

In particular, the two first sets of conceptual contents that we encounter in the chapter of the Doctrine of Essence entitled Shine (SL, pp. 341-353) are: a) the Essential and the Unessential and b) Essence and Shine (cf. SL, p. 342). Since the second set is only a contentual development of the first set, I shall begin with the first. 7 In what exactly does the logical content of its concepts consist? Let us begin from the logical content of the Essential:

If, therefore, the absolute was at first determined as being, now it is determined as essence. Cognition cannot in general stop at the manifold of existence; but neither can it stop at being, pure being; immediately one is forced to the reflection that this pure being, this negation of everything finite, presupposes a recollection and a movement which has distilled immediate existence into pure being. Being thus comes to be determined as essence, as a being in which everything determined and finite is negated. So it is simple unity, void of determination [.] (SL, pp. 337-338) Essence or the Essential is, thus, clearly defined as the "simple unity", or identity, that is "void of determination".

On the other hand, Shine, we read, is the exact opposite of Essence. It is the development of the logical content of the "Unessential" (SL, p. 314). It is "an independent side vis-à-vis essence" (SL, pp. 343). Or more specifically, since Essence refers to a mere unity, identity or negativity -the terms in this context mean the same for Hegel -Shine refers to what is conceptually excluded from Essence. Shine refers to being or to immediacy as such.

Furthermore, since the whole Doctrine of Being was the negative proof for the ontological impossibility of any immediate content or entity, the conceptual content of Shine has the peculiar status of being part of the logical discourse, but as something non-existent -as

Shine:

Since the unessential no longer has a being, what is left to it of otherness is only the pure moment of non-existence; shine is this immediate non-existence, a non-existence in the determinateness of being, so that it has existence only with reference to another, in its nonexistence; it is the non-self-subsistent which exists only in its negation. (SL, pp. 342) 8 From these two definitions we learn three things, which mark the shift from the Doctrine of Being to the Doctine of Essense, i.e. the shift from a whole set of problems -and of logical contents -to another 9 . What we first learn is that on every level of the logical climax of the Doctrine of Essence we will encounter couples of logical contents, where one of them will be a variation of identity, mediation or unity -in our case represented from the logical content of Essence -whereas the other one will stand for difference, immediacy or disunity -in our case the logical content of Shine. 10 Furthermore, we learn that because of the radical critique of all sorts of logical immediacy, which took place in the Doctrine of Being, any immediate logical content has to be considered as non-being, whereas all logical contents referring to unity, mediation and/or identity as being. This is the reason why Essence is here considered as being, whereas Shine as a mere phaneomenon or as illusory being or as shine.

Still, given the radical critique of all sorts of immediacy, and their demonstration as non-being, Hegel's insistence to re-introduce or to maintain a logical content that stands for immediacy begs the question. In other words, it is anything but clear that in the beginning of the Doctrine of Essence we continue to encounter logical contents, such as the Unessential or Shine that are characterized as "Leftovers of Being" (SL, p. 345; see also p. 342). These logical contents, even if declared as non-being or as aporetic persist in the logical discourse of the Doctrine of Essence. 11 Why is Hegel actually re-introducing logical contents that have proven to be aporetical in the preceding Doctrine of Being and, even more puzzling, in the ambivalent status of non-being?

The answer to this question is actually the third fundamental element that we get to know about the whole Doctrine of Essence and about the status of all logical contents that it entails. By the same token, it is as well the solution, as we are about to see, to the problematic relation between Essence and Shine and to the shift to the next, less aporetic logical constellation of Reflection. -We must not forget, the reappearance of immediate being as shine or as non-being is a part of the argument for the explication of the logical inconsistency of the logical set of Essence and Shine and of the need for the introduction of a new, less problematic set of conceptual contents. Along with this, we should bear in mind that in Hegel's understanding Essence and Shine do not exemplify just an individual onto-logical problem, but that the eventual demonstration of their aporetic logical character amounts to the explication of the common aporias and of the implicit fallacious premise, on the basis of which skepticism and transcendental/subjective idealism operate and declare all knowledge as relative.

This third element, now, consists in the broadening of the way that immediacy is understood by Hegel. In other words, the logical breakthrough of the Doctrine of Being, fest das Wesen, und das Unwesentliche ist auf der andern Seite, es ist auch, es bezieht sich auf sich: es gibt freilich Unwesentliches aber es ist um das wahrhafte Seyn zu thun, nicht um solches schlechtes Seyn: Das Wesen ist Insichseyn, Identität mit sich, durch Negation der Negation überhaupt, das Wesen ist also Bewegung, Prozeß, es ist das Scheinen in sich selbst, der Schein ist Unterschiedenes, zunächst Seyendes aber herabgesetzt zu einem Ideellen." (GW 23,2, p. 747). 11 As Michael Theunissen puts it: "An die Stelle des Scheins der Vorgegebenheit tritt, kurz und abkürzend gesagt, die Vorgegebenheit des Scheins." (Theunissen 1980, p. 337).

which conditions all further logical development, and, thus, the Doctrine of Essence as a whole, is that immediacy does not just refer to logical contents that explicitly stand for immediacy, difference, and independence. "Immediacy" refers to all logical contents that are in fact immediate insofar they do not refer explicitly to their opposite logical content. This means that logical contents that stand for identity, unity, and/or mediation are also immediate if their logical content does not explicitly entail its logical counterpart. In one word, mediation isolated from immediacy is immediate as well.

In the case of the logical set of Essence and Shine this means that the logical content of Essence would be itself something immediate and, thus, a non-being, if it would not refer explicitly to its opposite, to Shine. So it is only now that we can understand why Hegel speaks about and operates with "Leftovers of Being", i.e. with logical contents that stand for immediacy, even if immediacy along with all its variations has been shown to be aporetic, or non-being. In other words, the logical content of Essence refers necessarily in an expliciteven if still problematic (see Kalatzis (forthcoming) -b) -way to its opposite, and this is the reason why immediacy or Shine cannot be abandoned once and for all. The logical content of Essence, which consists in identity, mediation and/or unity makes sense, according to Hegel, only in reference to its opposite, i.e. to Shine which stands for difference, immediacy and disunity.

An Essence without its Shine, to put it bluntly, would not be an Essence at all; and conversely we cannot speak about Shine or about phenomena without operating with a concept of being, i.e. without the concept of an actually existing Essence. Furthermore, the critique of immediacy and of self-subsisting difference in the Doctrine of Being did not aim at the dismissal of all difference, immediacy and/or disunity, but only at the ones that are articulated independently of any identity, mediation and/or unity. In a word: Essence is Shine and Shine is Essence, because they belong necessarily in one logical context, outside of which they would be deprived of meaning -and of being.

Moreover, if we would actually try to think Essence independently of Shine and vice versa, then we would arrive at Hegel's dialectical paradox (see EPS, pp. 128-133, § § 81-82): both of them would show themselves to be the opposite of what their original logical content was. Essence -deprived of its reference to something immediate or different -would show itself to be immediate and different to the conceptual content that stands explicitly for difference itself.

Conversely, the conceptual content of the Unessential or of Shine, even if examined independently from its opposite, Essence, refers explicitly to its opposite; to something that is not Shine, but Being; to something, whose conceptual content consists in identity, mediation and unity: to Essence. Hence, even if the original conceptual content of Shine appeared to be solely the conceptual content of difference, immediacy and disunity, when we try to actually think of as an isolated and self-standing logical content, it shows itself, by means of its negative reference to its opposite, to function as a conceptual unifier, 12 which brings unity to logical contents. But this would mean that it would no longer correspond to its original logical content, but to the logical content that only Essence was supposed to have in the first place. 13 Thus, in order to avoid this paradox of logical instability, we will have to think Essence and Shine not as independent conceptual contents, but as mutually constitutive parts of a broader logical content, of Reflection. Consequently, Essence and Shine show themselves to be -in this specific sense -one and the same logical content, i.e. they are parts of one and the same unity of meaning:

The determinateness that shine is in essence is, therefore, infinite determinateness; it is only the negative which coincides with itself and hence a determinateness that, as determinateness, is self-subsistence and not determined. -Contrariwise, the selfsubsistence, as self-referring immediacy, equally is just determinateness and moment, negativity solely referring to itself. -This negativity which is identical with immediacy, and thus the immediacy which is identical with negativity, is essence. Shine is, therefore, essence itself, but essence in a determinateness, in such a way, however, that the determinateness is only a moment, and the essence is the shining of itself within itself. (SL, p. 345) 14

The speculative solution

Now, the proof that Essence and Shine (or Identity and Difference, Mediation and Immediacy and/or Unity and Disunity) can only be conceived in their explicit, immanent and primordial 12 By conceptual unifier I mean a concept, the content of which refers to another conceptual content in a necessary way and, consequently, unifies itself with it. In this context unification does not mean identification but necessary reference. 13 Cf. "Das Mittelbare ist ein Gesetztes" (GW 23,1, p. 92) and "Die momente des reinen Scheinens sind die der allgemeinen abstracten Denkbestimmungen, die isoliert genommen werden vom Verstande, und so sind die gedanken Cathegorien des abstracten verstandes. In so fern sie momente des wesens sind, gelten sie als die allgemeinen wesentlichen Denkbestimmungen, und grund gesetze des Denkens, die aber das Gegentheil und falsch sind, weil sie nur die Momente des Scheinens ausser ihrer Wahrheit nehmen, welche sie sind unwahr durch die Isolirung" (GW 23,2, p. 612). 14 Cf. "Man scheidet das Wesentliche vom Unwesentlichen, das Wesen bezieht sich auf das Sein überhaupt, das unwesentliche ist das äußerliche, das wohl ist, aber das nicht wesentlich ist. Dem Wesen ist das Unwesentliche nicht unwesentlich es ist nur durch seine negative Beziehung auf das Sein. Es ist in sich, also ist es gegen ein anderes. Dem Wesen ist der Schein wesentlich" (GW 23,2, p. 498).

unity 15 has some far-reaching implications: it uncovers the common false premise upon which both skepticism and transcendental/subjective idealism operated, and based their rejection of the possibility of objective knowledge. 16 As we have seen, both skepticism and transcendental/subjective idealism postulated that true knowledge should only be knowledge of immediate things, i.e. of things cognized independently of any relation. Thus, since all discursive knowledge is knowledge of things in and/or through relations, they thought themselves justified to discard all knowledge as relative or as subjective knowledge.

The unfounded presupposition of this claim, though, consists in the assumption that unity and self-subsistence (or mediation and immediacy) are onto-logically possible as separated. But the impossibility of this claim is what we have just encountered in the dialectic of Shine. Essence and Shine cannot be thought as independent of each other. Unity or Identity or Mediation cannot be isolated from Disunity, Difference and Immediacy.

Thus, the claim of skepticism and of transcendental/subjective idealism regarding the relativism and subjectivity of all knowledge is based on a premise that shows itself to be aporetic. Most importantly, the explication of the falsity of this premise opens the ground for a knowledge that is objective: it is not only that discursive knowledge is a knowledge through relations, but that the eventual object of knowledge is as well an object that can exist only within relations. 17 Hegel's solution consists, hence, in the shift of our understanding regarding the manifoldness of reality and the alleged subjective cognitive act of its unification. For Hegel, this unification of the manifold is not an external and, thus, a subjective act, but rather what exists from the very beginning. Being as such has to be grasped as the unity of the Essence and its Shine, as an implicit unity that is waiting 18 to be grasped and made explicit 19 .

15 On Hegel's dialectical argument, which I call the argument of logical instability, which should lead the acceptance that contradictory logical contents are not self standing but only parts of a broader logical content, which consists in their explicit unity see EPS, p. 286, § 214. 16 See also Winfield 2012, pp. 159-160. 17 Of course, this argument stands if one, as Hegel does, presupposes the identity of thought and reality. 18 The term "waiting" is not to be understood in a metaphorical way. Hegel's understanding of reality consists in a double teleological scheme, epistemological and ontological. According to this scheme reality is predetermined to be grasped, and the human intellect predetermined to grasp it. 19 For a critical reading of Hegel's argument see Theunissen 1980, pp. 377-382. Despite its thoroughness and subtlety, it seems that Theunissen fails to discern and account for Hegel's systematic use of the scheme of implicit and explicit logical relations. Furthermore, it appears that Theunissen does not distinguish in his reading between negation as privation and negation as differentiation.

Manifoldness is not an external given, but just the other, necessary side of unity 20 . To put it differently, relations are not states independent to beings that determine them in an external way, as skepticism and transcendental/subjective idealism believe to be the case. On the contrary, beings (or "things") can only be beings within a relation. 21 Hence, the shift that allows the overcoming of skepticism and the shift from the transcendental/subjective to the objective idealism is to think the relation of beings as self-relation, or as one, primordially unified object of knowledge. In Hegel's words:

But at the same time skepticism allowed a manifold of determinations for its shine, or rather the latter turned out to have the full richness of the world for its content. Likewise for the appearance of idealism: it encompassed the full range of these manifold determinacies. So, the shine of skepticism and the appearance of idealism do immediately have a manifold of determination. This content, therefore, might well have no being as foundation, no thing or thing-in-itself; for itself, it remains as it is; it is simply transposed from being into shine, so that the latter has within itself those manifold determinacies that exist immediately, each an other to the other. The shine is thus itself something immediately determined. It can have this or that content; but whatever content it has, it has not posited it but possesses it immediately. Idealism, whether Leibnizian, Kantian, Fichtean, or in any other form, has not gone further than skepticism in this: it has not advanced beyond being as determinateness. (SL, p. 343) 22 Seen from this perspective, skepticism with its skeptical method (see TW 19, pp. 359-360), and transcendental/ subjective idealism (see GW 21, p. 40), with its re-discovery of the antinomies of pure reason are to be positioned in the pre-history of speculative philosophy; as philosophies that pointed to the elements that should be overcome, so that objective knowledge can be attained.

Of course, when inspected more closely, both skepticism and transcendental/subjective idealism could object that they are being measured on a philosophical measure external to them, and from a philosophical standpoint that they would never adopt. Furthermore, they could claim that it is not them that operate with unfounded assumptions, but speculative philosophy itself. Both of these topics, though, would equally require not one, but a series of 20 Cf. "der Schein ist dem Wesen wesentlich", quoted in Theunissen 1980, p. 352. Michael Theunissen is also right when he writes: "Aber die Auflösung des Scheins des daseinsmäßigen Unmittelbarkeit welche die Idealisten und Skeptizisten, damit ihren geheimen Positivismus verratend, dem Schein andichten, soll die »wahre« Unmittelbarkeit dieses Scheins zutage fördern. Was ist daran »wahr«? Daß er ist." (Theunissen 1980, p. 346) 21 As Richard D. Winfield puts it: "Essence is in virtue of reflecting itself, being through what it posits." (Winfield 2012, p. 161) 22 For a concise account of Hegel's argumentative strategy against skepticism (and, ultimately, subjective idealism) see Forster 1989, pp. 171-180.

For the proximity of skepticism and subjective Idealism in Hegel's Jena period seeVieweg 1999, pp. 171-177.

For this controversy see also Horstmann 1984.

As Richard D. Winfield puts it: "Although the sphere of being may have relinquished its own form of immediacy, it still retains determinacy, whose content is simply given to the process that mediates it. The residual givenness of content of what is posited is exhibited in how being gets treated when relegated to a realm of "appearance" or mere "phenomena" by ancient skepticism or Kantian transcendental idealism. Although being now counts as merely relative to our experience or to some concealed ground, it does not lose any of its manifold character but simply forfeits its independent being"(Winfield 2014, pp. 38-39; see also p. 44). For the way that epistemological relativism fits to the overall agenda of the skeptic seeVieweg 2007, pp. 28 ff.

For Hegel's critical account of the Kantian -but not exclusively Kantian -conception of truth see SL, pp. 507-525.

 7 In concrete, Essence is a developed form of the Essential and Shine constitutes a developed form of the Unessential.

See alsoHackenesch 1987, pp. 213-214.

For the three different accounts of concepts and the three different models of dialectic ("passing over into other", "shining in the opposite" and "development") that correspond to the three books of the Science of Logic see EPS, p. 302, § 240 and Kalatzis (forthcoming) -a.

Cf. "Vom Wesen unterscheiden wir das Unwesentliche. Das Seyende überhaupt, aber 2tens hält der Verstand

different articles.


Elena Stolyarova
email: elena.stolyarova@chaireeconomieduclimat.org

Keywords: CO 2 emissions, Panel Data Analysis, Economic Growth, Hierarchical Clustering on Principal Components. Carbon Dioxide Emissions, economic growth and energy mix: empirical evidence from 93 countries

This paper provides an empirical analysis of CO2 emissions and economic growth, based on a panel dataset covering 93 countries over the period 1960-2008, and examines the challenge of country selection for homogenous and appropriates groups. Foremost, we have proposed a no parametric hierarchic clustering approach, based on 17 criteria and used the Hierarchical Clustering on Principal Components (HCPC). The results of the clustering indicate the optimal partition of 93 countries into 7 groups, each with its own characteristics. The unit root and cointegration tests show that the long-run relationship does not exist for any clusters and the nature of stationary is different between and into the groups. This result indicates the short-run relationship between CO2 emissions and its determinants. Dynamic Panel Data and WITHIN models were estimated to explain the growth rate of per capita CO2 emissions. It's found that the growth rate of per capita CO2 emissions depends positively on the growth rate of per capita GDP and negatively on the growth rate of energy mix.

Introduction

Between 1960 and 2008, emissions of CO2 from fuel combustion have tripled and the main actors have changed. In 1960 the contribution of emissions by China was around 9%, 1% for India and 10% for rest of the world. By 2008, their contribution was 24%, 5% and 23% respectively, and China becomes the largest emitter in the world. This growth is the results of 210% increase on energy consumption, much of which was met by a 370% increase in electricity generation. The share of electricity's emissions in the total emissions of CO2 was between 18% and 78% in 2008 (WDI, 2012). The variation between the countries can be explained by many determinants among which are the level of income and the energy mix.

Most previous studies of CO2 -Income relationship aim either to verify and estimate the Environmental Kuznets Curve (EKC) hypothesis of economic inequity or to describe the long-run equilibrium relationship between GHG emissions and energy consumption, or GDP, or other. The EKC bases on hypothesis of U-inverted relationship between income level of country and level of GHG emissions. In low income countries energy use and GHG emissions increase as income increases. As income levels increase, societies have the awareness and means to implement costly environmental schemes, leading to reductions in emissions. So the level of emissions decreases from a certain level of income. The first application of Kuznets Curve to environmental studies is done by Grossman and Krueger (1991, 1993, 1995) [START_REF] Grossman | Economic growth and the enironment[END_REF], who were followed by Holtz-Eakin (1995) [START_REF] Holtz-Eakin | Stoking the fires? CO2 emissions and economic growth[END_REF], or more recently by [START_REF] Perman | Evidence from panel unit root and cointegration tests that the environmental Kuznets curve does not exist[END_REF] [START_REF] Perman | Evidence from panel unit root and cointegration tests that the environmental Kuznets curve does not exist[END_REF], McKitrick and Strazicich (2005) [START_REF] Mckitrick | Stationarity of global per capita carbon dioxide emissions: implication for global warming scenario[END_REF], Aldy (2006) [START_REF] Aldi | Per capita carbon dioxide emissions: convergence or divergence?[END_REF] and [START_REF] Dinda | Environmental Kuznets Curve hypothesis: a survey[END_REF] [START_REF] Dinda | Environmental Kuznets Curve hypothesis: a survey[END_REF]. The results of these studies are controversial about EKC's hypothesis, giving opposite conclusions.

Studies of long-run equilibrium relationships, which are often complementary to the EKC studies, focus on long-run causal relationships between several variables affecting the level of emissions or energy consumption. Energy consumption and economic growth are commonly the focus. For example, [START_REF] Ang | CO2 emissions, energy consumption and output in France[END_REF] [START_REF] Ang | CO2 emissions, energy consumption and output in France[END_REF] proposed a Vector Error Correction Model for France, Narayan and Smith (2008) [START_REF] Narayan | Energy consumption and GDP in G7 countries: new evidence from panel cointegration with structural breaks[END_REF] studied the Energy Consumption-Economic growth nexus for the G7 countries. [START_REF] Mehara | Energy consumption and economic growth: the case of oil exporting countries[END_REF] [START_REF] Mehara | Energy consumption and economic growth: the case of oil exporting countries[END_REF] investigated the same relationship in the case of oil producing countries. Finally, Halicioglu's (2009) *10+ studied on the Turkish long-run elasticity between energy consumption and economic growth. There has been relatively little work published on the relationship between GDP and emissions growth, but some examples can be done. Dinda and Coondoo (2006) [START_REF] Dinda | Income and emission: a panel data-based cointagration analysis[END_REF] performed cointegration analysis between per capita CO2 emissions and per capita GDP on a panel of 88 countries and conclude that a long-run relationship exists between the variables. Lee and Lee (2009) [START_REF] Lee | Income and CO2 emissions: evidence from panel unit root and cointegration tests[END_REF] applied a different methodology -the more efficient panel unit root test (SURADF) and concluded differently: in several regions, the long-run relationship does not exist. Marrero (2010) [START_REF] Marrero | Greenhouse gases emissions, growth and energy mix in Europe[END_REF] proposed a dynamic panel data model that combines the EKC hypothesis for nexus GHG emissions-Income and energy mix for EU27. He concludes that European countries converge on per capita GHG emissions while EKC hypothesis are rejected. [START_REF] Hossain | Panel estimation for CO2 emissions, energy consumption, economic growth, trade opnness and urbanization of newly industrialized countries[END_REF] [START_REF] Hossain | Panel estimation for CO2 emissions, energy consumption, economic growth, trade opnness and urbanization of newly industrialized countries[END_REF] examined the short-run and long-run relationship between per capita CO2 emissions, energy consumption, per capita GDP, trade openness and urbanization for NIC countries, and found that the long-run elasticity is higher than short-run elasticity.

The econometric approach, which is usually used to estimate the relationship between GHG emissions and economic growth, as well as to test EKC hypothesis, has been criticized in academic literature on many points. [START_REF] Dijkgraaf | A test of parameter homogeneity in CO2 Panel EKC estimation[END_REF] [START_REF] Dijkgraaf | A test of parameter homogeneity in CO2 Panel EKC estimation[END_REF] tried to verify the assumption of the same emissions-income elasticity across countries (regions) and time. It is a strong assumption that is in generally difficult to observe. The authors found that the turning point is different for each OECD country and that a slight change in the model leads to a significant change in the estimated parameters. [START_REF] Aslanidis | Environmental Kuznets Curves for carbon emissions: a critical survey[END_REF] [START_REF] Aslanidis | Environmental Kuznets Curves for carbon emissions: a critical survey[END_REF] proposes a critical survey of the econometric techniques used to estimate EKC hypothesis. These techniques refer to baseline model, homogeneity across countries, fallacious test of unit root and cointegration, spurious regressions and spatial dependence. M. [START_REF] Wagner | The carbon Kuznets curve: a cloudy picture emitted by bad econometrics?[END_REF] [START_REF] Wagner | The carbon Kuznets curve: a cloudy picture emitted by bad econometrics?[END_REF] also criticizes econometric approach used to estimate EKC. He focuses on studying the problems of non-linear transformation and unit root tests. These critics led us to leave the model with EKC hypothesis and to find a solution of weakness Panel Data Model. Some studies attempt to refine the models by assembling the countries in homogeneous groups. The most popular techniques of building the sub-panel are based on group selection, according to either one qualitative or quantitative variable. [START_REF] Sharma | Determinants of carbon dioxide emissions: empirical evidence from 69 countries[END_REF] [START_REF] Sharma | Determinants of carbon dioxide emissions: empirical evidence from 69 countries[END_REF] groups 69 countries using income level. [START_REF] Niu | Economic growth, energy conservation and emissions reduction: a comparative analysis based on panel data for 8 Asian-Pacific countries[END_REF] [START_REF] Niu | Economic growth, energy conservation and emissions reduction: a comparative analysis based on panel data for 8 Asian-Pacific countries[END_REF], [START_REF] Dinda | Income and emission: a panel data-based cointagration analysis[END_REF] [START_REF] Dinda | Income and emission: a panel data-based cointagration analysis[END_REF], [START_REF] Lee | Income and CO2 emissions: evidence from panel unit root and cointegration tests[END_REF] [START_REF] Lee | Income and CO2 emissions: evidence from panel unit root and cointegration tests[END_REF] and [START_REF] Narayan | Carbone dioxide emissions and economic growth: panel data evidence from developing countries[END_REF] [START_REF] Narayan | Carbone dioxide emissions and economic growth: panel data evidence from developing countries[END_REF] assemble the countries by region. [START_REF] Wang | Modeling the nonlinear relationship between CO2 emissions from oil and economic growth[END_REF] [START_REF] Wang | Modeling the nonlinear relationship between CO2 emissions from oil and economic growth[END_REF] analyses the relationship between CO2 emissions from oil and economic growth by pooling according to economic growth regime. Some studies focus on groups of economic union or with the same level of economic development -for example, Hossain (2011) [START_REF] Hossain | Panel estimation for CO2 emissions, energy consumption, economic growth, trade opnness and urbanization of newly industrialized countries[END_REF] for Newly Industrialized Countries, Pao (2010) [START_REF] Pao | CO2 emissions, energy consumption and economic growth in BRIC countries[END_REF] for BRIC, [START_REF] Lee | Energy-income causality in OECD countries revisited: the key role of capital stock[END_REF] [START_REF] Lee | Energy-income causality in OECD countries revisited: the key role of capital stock[END_REF] for OECD countries. Mehrara (2007) [START_REF] Mehara | Energy consumption and economic growth: the case of oil exporting countries[END_REF] works on a panel of 11 oil exporting countries.

However, groupings by country can make some problems for panel data analysis approach. Panel analysis is used to enhance econometric estimations and to obtain more robust results thanks to their two-dimensional data: time and individual. Full or partial homogeneity in parameters is necessary to estimate the model and so the appropriate selection of individuals to compose a panel is very important. Grouping based only on the region division or on the economic level could recover inadequate and lead to a very imprecise estimation of parameters, as well as weakening the power of the tests. In a case of panel data analysis of GHG's determinants, several factors must be considered other than mentioned above, like reserves of fossil fuel, energy mix, size of country, energy and environmental policies, level of production, level of trade and many other. The countries with the same level of economic development may have different relationship between emissions and economic growth for many reasons. For example, small island countries generate electricity from oil, because this solution is the least expensive, and so they have high level of emissions per capita. Some developing countries can have more Renewable Energy Sources (RES) than developed countries and so they have a lower emissions level. Energy mix can be different and depends on domestic resource endowments.

The purpose of this paper is twofold: first, to investigate the short-run nexus between CO2 emissions, income and energy mix, and second, to propose homogeneous groups of countries in order to obtain a more efficient model. To confirm the choice of a short-run model, we are use cointegration analysis to demonstrate the absence of cointegration between CO2 emissions and income. We propose a WITHIN model with an evolving mix of alternative and nuclear energy use.

The rest of this paper is organized as follows: Section 1 offers some reflections on the question on the issue of choice determinants. Section 2 provides a brief survey of studies on countries' homogeneity. The data and some descriptive statistics are presented in section 3. Section 4 presents the methodology and the results of clustering to make groups of homogenous countries. Section 5 describes the econometric approach for modeling the short-run relationship between CO2 emissions, economic growth and energy mix, and the results of model specification tests. Section 6 presents the model and its results. At least, section 7 concludes with final remarks.

Determinants of CO 2 emissions

Carbon Dioxide emissions have two principal sources. The largest source is the combustion of fossil fuels, such as natural gas, crude oil and coal. The second source is from industrial processes that emit CO2 as a result of a chemical reaction. In both cases, CO2 emissions -energy consumption nexus is mainly chemical and physical. But the relationship fluctuates according to the types of combustion, means of production and energy generation, energy efficiency etc. This suggests that the two relationships CO2 emissions-GDP and Energy consumption-GDP do not necessarily have the same elasticity or follow the same trend over time, in which case energy consumption can only partially explain the variation of CO2 emissions. Additionally if energy consumption and CO2 emissions are coupled in a linear relationship, we cannot use these variables in the same model for reasons of collinearity.

The literature on the relationship between energy consumption and economic growth is rich in examples of application and provides a unanimous conclusion on the existence of the relationship between energy consumption and economic growth. By contrast, the literature on the emissionseconomic growth nexus is scarce. [START_REF] Dinda | Environmental Kuznets Curve hypothesis: a survey[END_REF]Coondoo (2004, 2006) [START_REF] Dinda | Environmental Kuznets Curve hypothesis: a survey[END_REF], [START_REF] Dinda | Income and emission: a panel data-based cointagration analysis[END_REF] study a panel of 88 countries grouped by region to examine the long-run nexus between per capita CO2 emissions and per capita GDP by using IPS panel root test and Engel-Granger methodology of cointegration. The results show that series have a same order of integration and that a long-run relationship exists for Africa, Central America and Europe. [START_REF] Lee | Income and CO2 emissions: evidence from panel unit root and cointegration tests[END_REF] [START_REF] Lee | Income and CO2 emissions: evidence from panel unit root and cointegration tests[END_REF] devote their paper to study the order of integration of per capita CO2 emissions and per capita GDP, using SURADF unit root test, to consider the presence of cross-country correlation in the data. They conclude that two variables don't have the same order of integration and so the long-run relationship between emissions and income does not exist. Naryan and Naryan (2010) [START_REF] Narayan | Carbone dioxide emissions and economic growth: panel data evidence from developing countries[END_REF] examined the EKC hypothesis for 43 developing countries and estimated long-run and short-run elasticity between emissions and income, taking into account the problems of collinearity between income and income-squared, which is usually used as EKC model specification. This is not the first time that model specification and variable selection are criticized for example, see Perman and Stern (2004) [START_REF] Perman | Evidence from panel unit root and cointegration tests that the environmental Kuznets curve does not exist[END_REF]. More recently, [START_REF] Sharma | Determinants of carbon dioxide emissions: empirical evidence from 69 countries[END_REF] [START_REF] Sharma | Determinants of carbon dioxide emissions: empirical evidence from 69 countries[END_REF] propose a short-run multivariate model that considers trade openness, urbanization, per capita electric power consumption and per capita total primary energy consumption, all in addition to per capita CO2 emissions and per capita GDP. The author concludes that for all countries, except for those with high income, only per capita GDP and urbanization are determinant for CO2 emissions. But the author uses both GDP and energy consumption as CO2 emissions' determinants. This may distort the results.

To solve this problem, we need that the energy variable which is related to CO2 emissions, does not depend on per capita GDP and explains energy consumption or mix. Alternative and nuclear energy use in % of total energy use (ANEU) is a good specification which meets the requirements. First, ANEU reflects all sectors, including the power sector. Second, an increase of this variable explains the decrease of level per capita CO2 emissions. And finally our tests show that ANEU is not correlated with GDP per capita.

Countries' homogeneity in econometric studies

Several authors have studied the problem of homogeneity. [START_REF] Burnside | Production function regressions, returns to scale and externalities[END_REF] [START_REF] Burnside | Production function regressions, returns to scale and externalities[END_REF] analyzed a panel of US manufacturing industries and concluded that production function is not homogenous for all industries. [START_REF] Baltagi | Pooled estimators vs. their heterogeneous countreparts in context of dynamic demand for gasoline[END_REF] [START_REF] Baltagi | Pooled estimators vs. their heterogeneous countreparts in context of dynamic demand for gasoline[END_REF] studied the determinants of gasoline demand in OECD countries and rejected the hypothesis of coefficients' homogeneity. Furthermore, Baltagi, Griffin and Xiong (2000) [START_REF] Baltagi | To pool or not to pool: homogeneous versus heterogeneous estimators applied to cigaretter demand[END_REF], as well as [START_REF] Baltagi | Comparaison of forecast performance for homogeneous, heterogeneous and shrinkage estimators. Some empirical evidence from US electricity and natural gas consumption[END_REF] [START_REF] Baltagi | Comparaison of forecast performance for homogeneous, heterogeneous and shrinkage estimators. Some empirical evidence from US electricity and natural gas consumption[END_REF] emphasize the degeneration of results when observation number is large. In case of misspecification of the countries' group, not only the estimations are wrong, but all tests are not consistent. Number of solution has been proposed to cluster the countries in homogeneous groups for Panel Data Analysis. [START_REF] Durlauf | Multiple regimes and cross-country growth behaviour[END_REF] [START_REF] Durlauf | Multiple regimes and cross-country growth behaviour[END_REF] suggest to detail individuals to groups, using regression tree analysis. Information criterion method was proposed by [START_REF] Kapetanious | Cluster Analysis of Panel Datasets using non-standard optimisation of Information Criteria[END_REF] [START_REF] Kapetanious | Cluster Analysis of Panel Datasets using non-standard optimisation of Information Criteria[END_REF]. This method is based on a concept of hierarchical clustering, and leaves the individual estimates. But such a practice is questionable due to a small number of observations. V. Sarafidis and N. Weber (2009) [START_REF] Sarafidis | To pool or not to pool: a partially heterogeneous alternative[END_REF] proposed a method based on the principle of partitional clustering, which can circle the problem of small number observations. They use hill-climbing algorithm which tries to find a best partition in predetermined number of group. The algorithm is based on minimization of total residuals sum of squares (RSS) obtained for each cluster partition's estimation. But in case of atypical initial partition, the results may conduct to wrong class partition. Moreover this method is only based on model estimation and is sensible to model specification.

In our paper, we propose hierarchical clustering on principal components (HCPC) which presents some advantages. The HCPC does not need any econometric modeling, it uses the resemblances and differences among the individuals from multivariable criteria. It can be applied in a case of non-linear relationship between the series, and does not depend on the number of observations1 . We can also consider the additional data set of variables, which can explain the different income-emission elasticity between the countries, and at the same time, does not affect the relationship between per capita emissions, per capita GDP and percent of alternative and nuclear energy use. In addition to the variables already used, we use the following variables to groups the countries: the level of CO 2 emission and GDP, country's population, percentage of different sources used to produce electricity, contribution of power and industrial sectors in CO 2 emissions, production of fossil fuel (oil, natural gas and coal), as well as geographical criterion. To solve the nonlinear relationships problem, and eliminate disparities between variables, all quantitative series are transformed to qualitative data set. We consider that qualitative variables are insensitive to the time, so that only last year is considered to perform the classification. For example: if the country does not produce the oil at the moment, it will not become the largest producer next year.

Data presentation and descriptive statistics

We used annual unbalanced panel data covering the period from 1960 to 2008 for 93 countries. The data of CO 2 emissions (Mt) was obtained from the Climate Analysis Indicators Tool (CAIT); the data of GDP (in $ at 2000 prices), population and percentage of alternative and nuclear energy use (ANEU) from the World Development Indicators (WDI) of the World Bank. We also used an additional dataset which allowed us to perform hierarchical clustering. Electricity production from oil, coal, RES, nuclear, natural gas and hydraulic resources ( in percent of total electricity production); contribution of power and industrial sectors in total CO 2 emissions (in percent of total CO 2 emissions) are provided from the WDI. The production of oil (Mt), coal (Mt) and natural gas (Mteo) derives from BP statistical review of world energy. The level of per capita GDP varies from 72 to 61374 $ per capita across the time. The mean per capita GDP is highest for: United Arab Emirates, Switzerland, Qatar, Luxembourg and Japan. In 2008, the five richest countries were Luxembourg (55.8)2 , Norway (41.4), Japan (40.2, United States (38.3) and Switzerland (38.2). Nigeria has the lowest level of per capita GDP in 2008 (0.5).

The description of panel countries composition is given in

The mean of % of alternative and nuclear energy use varies from 0% to 82.9%. 11 countries of our dataset do not use any clean energy. Iceland (82%), Sweden (45%), France (45%), Norway (40%) and Switzerland (39%) present the best average performance in 2008. The additional data set is present in Table 2. We take CO 2 emissions, GDP and population to consider economic and geographical scale of countries. The percentage of electricity production from different sources allows us to take into account countries' electricity mix. CO 2 emissions from electricity and industrial sectors give an overview of sectorial contribution in CO 2 emissions. Oil, natural gas and coal productions have a double effect on emissions. First the production of fossil fuels is polluting itself, secondly, the energy mix depends on fossil fuel endowments. Finally geographical variable describes advantages and facilities between the countries in same region.

Classification

The Principal Component Methods are usually used to transform the data in a new set of variables (principal components) done by eigenvalue decomposition before applying the hierarchical clustering. The procedure depends on the type of variable and on how they relate to each other. In the case of quantitative variable and linear relationship between the variable, Principal Component Analysis (PCA) is used. Multiple Correspondence Analysis (MCA) is applied for categorical variables and based on χ 2 distance. It is possible to perform principal component method for mixed data. One of the solutions was given by Hill and Smith (1976) [START_REF] Hill | à ajouter[END_REF].

We chose to transform a data from quantitative to categorical variable and apply MCA procedure for many reasons. First, several variables have outliers: they may not be ignored and cannot be used without distorting the results of clustering. For example, the biggest countries (China, USA, Canada, Russia, India etc.) have a very high level of population, income, CO 2 emissions and they extract a lot of fossil fuel. After transformation on principal components variables and PCA application, they will have very high coordinates and will be far from center of mass, as well as far from other countries. As a result, HCPC based on PCA application rank atypical countries at least and they will have their own cluster. Secondly, some variables are not linearly associated as the percentage of nuclear and RES power production, or as the natural resource endowment does not depend on the level of GDP. Finally, the regional partition is important: economic ties between the countries, access to the same resources and infrastructure, etc.

To perform the HCPC, we use R package for multivariate analysis (FactoMineR) developed by Lê, Josse and Husson (2010) [START_REF] Husson | Principal component methods -hierarchical clusteringandpartitional clustering: why would we need to choose for visualizing data?[END_REF]. The clustering procedure is based on Ward's criterion which allows us to choose the pair of clustering to merge at each step by minimizing the growth of within inertia, i.e. minimization of the reduction of between inertia. Optimal number of cluster can be chosen by comparison with the level of total inertia. In general the optimal number of cluster is two or three, but in our case we need a finest class composition in a range of 5-10 clusters.

The class composition and their characteristics are present in Table 3. The geographical countries' distribution in groups is shown in Figure 1. The countries are distributed in 7 clusters according to 17 criteria. The electricity mix and geographical criteria characterize most clusters, as well as fossil fuel endowments. Only cluster 1 is specified by the economic size of countries (very high level of CO 2 emissions and GDP). The cluster 4 is characterized exclusively by medium level of nuclear and RES electricity production. It may be noted that the EU countries are shared out among four classes: rich countries in Western Europe with a lot of clean energy; countries from Eastern Europe with high level of coal power source; the countries with a balance electricity mix and finally United Kingdom belongs to the same cluster as USA, China, Russia etc. This result is interesting because it gives an unusual distribution which has never been applied. In the next section we will verify if our classification allows having groups of homogeneous countries.

Econometric approach

In the case of insufficient data observations and the presence of many same individuals, the panel data analysis is the most appropriate method to estimate econometric models, thanks to its double temporal and individual dimensions. Assembling several individuals leads to enhance an econometric model. To confirm the validity of the final model, it's necessary to apply different tests. First, we need to know if grouping individuals makes sense. In the case of group's misspecification, the rest of the tests and the econometric model can lead us to the wrong conclusion. So, begin with test parameters' homogeneity seems important. After that, the unit root and cointegration tests should be performed to determine the nature of stationary and justify the choice of a short-term model.

Finally the dynamic regression model is estimated to understand the connection between the series.

To Pool or not to pool?

Panel Analysis is based on hypothesis of coefficients' partial homogeneity for selected groups of individuals. But two extreme cases exist: Either the relationship between studied variables is different for each individual, or the individuals are perfectly homogenous. In the first case panel analysis makes no sense and the individual models should be estimated. In the other case, a simple pooling model is enough. We take an interest in the test procedure proposed by [START_REF] Hsiao | Analysis of Panel data[END_REF] Where each equation assumes a relationship between the rate of per capita CO 2 emissions (CO2n,t) and the rate of per capita GDP (GDPn,t), observed for an individual n at the time t 5 . In the model (1) α is an intercept and γ is an invariant elasticity between emissions and income. In the model ( 2) αn describes time-invariant individual fixed effects and βt describes individual-invariant time fixed effect, γ represents an invariant elasticity between emissions and income. Finally, the model (3) presents N equations for each country where αn country intercept, di -nine time dummies and γn -N slopes own for each country. The error term is denoted by εn,t. Variables are represented by growth rates to make them stationary in the possible presence of the unit root. The first equation presents a perfect homogeneity of parameters. The equation ( 2) -presents partial homogeneity with the elasticity γ identical for each individual, and finally equation ( 3) presents full heterogeneity of the parameters. Foremost, we test perfect homogeneity of parameters (1) against at least one of the parameter which is not common for individuals. In the event of rejection of parameter's perfect homogeneity, the test of partial homogeneity (2) is performed. If partial homogeneity is rejected again, panel data analysis cannot be applied and the models for each individual should be estimated; otherwise the grouping of individuals is correct and panel analysis could be performed. In this case, it is possible to realize a third test to confirm the first one, which verifies the homogeneity of parameters outside the own constant terms assumed for each individuals.

The Table 3 summarizes the results of three tests. The first test allows us to conclude that null hypothesis of perfect homogeneity is rejected for clusters 1, 2, 3, 4 and 7. For cluster 5 and 6 (African and Middle East countries, producers of fossils fuels) the first test suggests that the pooled model is appropriate. The results of a partial homogeneity test suggests that elasticity between the rate of per capita CO 2 emissions and the rate of per capita GDP is the same for all countries, except cluster 1 which represents the largest countries like US, Canada, China etc. For cluster 2 (Western countries with high level of per capita GDP) and 7 (South American countries with a lot of hydraulic power) the null hypothesis of partial homogeneity is not rejected at 1% level. The third test reinforces the choice of a partial homogeneity model with country and time fixed effects, because the results of the third test suggest that time and country fixed effects are not homogeneous. We conclude that panel data analysis can be applied for all clusters and the results of estimations and tests will not be biased, except for the first cluster.

Panel unit roots test

In most cases, the time series data have a non-stationary nature. Several tests of unit roots exist for panel data. We can refer to the test of Levin-Lin-Chu (2002) [START_REF] Levin | Unit root tests in panel data: asymptotic and finite-simple properties[END_REF], which bases on the assumption of a common level of integration for all individuals. The weakness of this test lies in the formulation of the test hypotheses: all series have unit root against all series are stationary. Maddala and Wu (1999) [START_REF] Maddala | A comparative study of unit root test with Panel Data and a new simple test[END_REF] have proposed the test with heterogeneous specifications of unit root whith an individual unit root process. A similar test was proposed by Im, Persan and Schin (2003) [START_REF] Im | Testing for unit roots in heterogeneous panels[END_REF]. Meanwhile, [START_REF] Hadri | Testing for unit roots in heterogeneous panel data[END_REF] [START_REF] Hadri | Testing for unit roots in heterogeneous panel data[END_REF] suggested a test with opposite hypotheses: stationary of panel data against a presence of unit root. We have chosen to apply IPS test to check the order of integration of study series. The authors specify a separate regression for each cross section:

∆𝑦 𝑖,𝑡 = 𝛼 * 𝑦 𝑖,𝑡 + 𝛽 𝑖𝑗 * ∆𝑦 𝑖𝑡 -𝑗 𝑝 𝑖 𝑗 =1
+ 𝑋′ 𝑖𝑡 * 𝛿 + 𝜖 𝑖𝑡 With hypothesis:

𝐻 0 : 𝛼 𝑖 = 0, ∀ 𝑖 𝐻 1 𝛼 𝑖 = 0, ∀ 𝑖 = 1, … , 𝑁 1 𝛼 𝑖 < 0, ∀ 𝑖 = 𝑁 1 + 1, 𝑁 1 + 2, … , 𝑁
Where presence of unit root is tested against some cross-section have a unit root. The authors propose two statistics: Z-bar with expected value and variance of asymptotic distribution and W-bar with stronger statistical power, especially for a small number of observations and residuals' autocorrelation. They also emphasize that the results of the test without trend are more powerful.

To perform this test we apply logarithmic transformation for per capita CO 2 emissions, per capita GDP and % of alternative and nuclear energy use. The results are given in Table 4.

Per capita CO 2 emissions with logarithmic filter have a unit root for cluster 1, 5 and 7, either with both trend-intercept or only with an intercept model, whereas cluster 2, 3 and 4 have opposite test's conclusions. For these groups, null hypothesis of unit root are not rejected in the case of a model with trend, and are rejected in the case of a model with only an intercept. This means that several cross-sections do not have a unit root. In the case of per capita GDP cluster 1, 5, 6 and 7 have a unit root. For cluster 2 and 4 the null hypothesis is rejected in test with intercept, for cluster 3 in the case of a test whit trend and intercept. Our results join the conclusions of Lee and Lee (2009) [START_REF] Lee | Income and CO2 emissions: evidence from panel unit root and cointegration tests[END_REF]: per capita CO 2 emissions and per capita GDP is stationary for a part of the countries. Only clusters 1, 5 and 7 have a same order of integration for emissions and income and so they may have a long-run relationship between emissions and GDP.

The variable ANEU is not stationary for cluster 3, 4 and 6. This result is interesting: ANEU is measured in percentage and we might have expected stationary of the variable for all clusters. But countries from these groups have to make progress to improve the carbon intensity and to use more clean energy sources. For class 2, the null hypothesis of unit root is rejected; it is probably due to their very high level of electricity production from clean sources. For France, Sweden, Switzerland, Norway and Iceland, electricity production from fossil fuel does not exceed 10 percent. Considering that it is more difficult to use alternative energy for other than electricity sector, the value of ANEU does not increase. The null hypothesis is also rejected for class 5 because of the absence of alternative energy use or a very low value of ANEU. Members of this cluster are fossil fuel producers and low GDP per capita. At the moment they are not interested in improving their performances. For cluster 1 the null hypothesis of unit root in ANEU is rejected in the case of a test without trend, but only India's ANEU is stationary, while for Russia and United Kingdom, ANEU has a trend. So we can conclude that the results from the test with trend and intercept are most probable.

In conclusion, we can tell that the long-run relationship is possible only for cluster 1, between per capita CO 2 emissions, per capita GDP and % of alternative and nuclear energy use. For other clusters, three data series do not have the same order of integration. The cointegration is possible between per capita CO 2 emissions and per capita GDP for cluster 1, 5 and 7.

Panel cointegration test

If we have established that the order of integration is similar for all series and greater than 0, it is possible to test the long-run relationship among the variables. Several non-stationary variables with the same order of integration are cointegrated if their linear combination is stationary, i.e. I(0) processes. This means that the random shocks are just a short-run deviation from long-run equilibrium and the series did not drift away from each other across the time. The notion of cointegration was introduced by Granger in 1981, followed by Engel, Johansen and Phillips contributions. Pedroni (1995Pedroni ( , 1997) ) proposed a be-directional panel conitegration test and in 1999, 2004 [START_REF] Pedroni | Panel cointegration. Asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis[END_REF] an extension to test the relation of cointegration for more than two variables. He proposed seven statistics to test the existence of long-run equilibrium: four statistics based on within-dimension and three other based on between-dimension. Other tests exist: a bivariate conitegration test, with hypothesis of homogenous vectors of cointegration was proposed by [START_REF] Kao | International R&D spillovers: an application of estimation and inference in panel cointegration[END_REF] [START_REF] Kao | International R&D spillovers: an application of estimation and inference in panel cointegration[END_REF] or several extensions of Johansen test to apply on panel data were proposed by Larsson and all (2001), Groen and Kleibergen (2003), Breitung (2005). If the cointegration test indicates that the long-run relationship exists between the series, the error correction models (ECM) should be applied. The ECM model enables to capture the deviation from long-run equilibrium and the speed of return in case of a deviation. Otherwise the relationship between the series will be estimated by using variables in first difference.

In our paper we use Pedroni test of cointegration with null hypothesis of the absence of cointegration against the presence of cointegration. In the case of our dataset, we apply the test of cointegration on cluster 1 to determine the presence or the absence of the long-run equilibrium between per capita CO 2 emissions, per capita GDP and ANEU, as well as for clusters 1, 5 and 7 between per capita CO 2 emissions and per capita GDP. All variables are expressed in natural logarithms, so in case of variables in first dereference, the parameters represent the elasticity. As shown in Table 5, the null hypothesis of no cointegration is not rejected for cluster 1 and 7. This means that the long-run relationship between the variables does not exist. For cluster 5 only 1 of 7 tests (group ADF) rejects the null hypothesis at 1% in model with trend and intercept and 2 of 7 tests for the model with intercept (Panel ADF at 10% and Group ADF at 5%). It is not enough to conclude that the long-run nexus between per capita CO 2 emissions and per capita GDP exists. For all clusters and 93 countries, the long-run equilibrium does not exist between per capita GDP, per capita CO2 emissions and ANEU. Only short-run model may be estimated.

Model presentation and results

The results of unit root tests show us that a part of variable is stationary for some clusters, as well as the nature of variable stationary into the cluster is not similar for all countries. To remedy the no stationary of some variables and estimate a similar model for all clusters, we apply the first difference for all variables expressed in the natural logarithm. This is equivalent to take a growth rate of variables that is easily interpretable. We suppose that the growth rate of per capita CO 2 emissions is affected by its lag growth rate of GDP per capita (in level and with lag), also the evolution of the percentage of clean energy use (ANEU). To estimate the relationship between per capita CO 2 emissions, per capita GDP and ANEU, we propose the following model: 𝑔𝐶𝑂2 𝑛,𝑡 = 𝛼 𝑛 + 𝛽 𝑡 + 𝛾 1 * 𝑔𝐶𝑂2 𝑛,𝑡-1 + 𝛾 2 * 𝑔𝐺𝐷𝑃 𝑛 ,𝑡 + 𝛾 3 * 𝑔𝐺𝐷𝑃 𝑛 ,𝑡-1 + 𝛾 4 * 𝑔𝐴𝑁𝐸𝑈 𝑛,𝑡 + 𝜖 𝑛,𝑡 Where gCO2 n,t is a growth rate of per capita CO 2 emissions, gGDP n,t is a growth rate of per capita GDP and gANEU n,t is a growth rate of percentage of alternative and nuclear energy use. The elasticity between gCO2 and regressors are represented by γ. The unobserved differences between the countries into the class are captured by α (country time-invariant fixed effect) and can explain the unobserved factors such as social and local policy aspects. The time dummies β enables us to take into account temporal effects as economics and politics crises. The choice of taking time dummy variables has been motivated by an asymmetric link between growth rates of per capita emissions and per capita GDP, especially in the case of a negative growth rate of GDP. For example, during the last financial crisis, the CO 2 emissions decreased much faster than GDP. Nevertheless, the difference between growth rate of CO 2 emissions and GDP is less strong. To estimate the model, we use two econometric techniques: Within estimation with country and time fixed effects and System GMM estimator, which is a more efficient estimation in the presence of dependant variable with a lag. These two estimations will indicate good or bad model specification. In case of non significant parameter, we will remove unnecessary variables from a model. The result of WITHIN and SYS-GMM estimation are given in Tables 6 and7. We can observe that the two models give approximately same results, except for the parameter of gCO2t-1. The Within model indicates a negative relation between the growth rate of per capita CO 2 emissions at time T and T-1 for 6 clusters, while SYS-GMM estimator suggests that the relation is positive, except for cluster 3. Moreover the SYS-GMM method indicates that the relation is significant only for cluster 5 at 1% and for cluster 1 at 10%. First, we can only take into account the SYS-GMM results because WITHIN estimator is severely biased. Secondly, as mentioned in section 5.1, the cluster 1 is composed of heterogeneous countries and so, it may give wrong estimations. Under these conditions, the nexus between per capita CO 2 emissions and its lag exists only for cluster 5.

The elasticity associated with the growth rate of per capita GDP is significantly higher than zero and under one, for all clusters and both WITHIN and SYS-GMM estimations. The growth rate of GDP with a lag is significantly different from zero for clusters 2 and 3 in WITHIN model, and only for cluster 3 in SYS-GMM model. The elasticity between growth rate of per capita CO 2 emissions and growth rate of ANEU is significant for 5 clusters in WITHIN model and for clusters 1, 2, 4 and 7 for SYS-GMM model. The negative sign of ANEU's parameter suggests that the increase of clean energy use enables to reduce the per capita CO 2 emissions. The results of these two estimations approaches show that the relationship between per capita CO 2 emissions and its determinants is unique for each cluster, as well as the main determinants are different. We remove non-significant variables and estimate once again the model for seven clusters. We do not need any more to use SYS-GMM estimator because the growth rate of per capita CO 2 emissions does not depend on its lag, except for cluster 5. The Table 8 summarizes the results of the final model estimation. The elasticity associated with the rate of per capita GDP is positive and less than 1 for all clusters. The value of the GDP elasticity is higher for countries from Western Europe, who use a lot of clean energy (cluster 2). The elasticity from cluster 1 and 3 has approximately the same value, but in the case of cluster 3 (Eastern Europe countries, no fossil fuel producers, electricity production from coal) per capita emissions depend also on the lag of per capita GDP. The smallest value of CO 2 -Income elasticity is given for cluster 4 (0.34) and for cluster 5 (0.38). Though the value of elasticity is almost equal for the two groups, we cannot conclude that countries from these clusters have a same relation between CO 2 emissions and GDP. The growth rate of per capita emissions is affected by the percentage of clean energy use for cluster 4, while the dependant variable is affected by lag of CO 2 emissions for cluster 5. However, we can notice that CO 2 -Income elasticity decreases according to the country's level of economic development. The elasticity for South American countries is between countries from clusters 1, 2, 3, on one side and from clusters 5, 6 on the other side.

The second determinant of CO 2 growth rate is the variation of clean energy use. The ANEU is affected negatively by the growth rate of per capita emissions for clusters 1, 2, 3, 4 and 7 and not related for clusters 5 and 6 because both groups do not have clean energy or a very little percentage. Moreover, the CO 2 -ANEU elasticity depends on energy mix and percentage of clean energy. Among the 5 groups, for which CO 2 -ANEU relationship exists, the value of elasticity is more important for cluster 4 (-0.11) and 7 (-0.13). If we rank countries according to their level of clean energy use, we observe that cluster 2 presents the best performance and cluster 7 the worse. But the second group has a low elasticity compared to cluster 7. This observation suggests the existence of U-inverted evolution of elasticity or decreasing returns to scale and that this relationship does not depend on the level of economic development. Countries have to make progress in clean energy with a low cost, it would reduce the per capita emissions more significantly compared to countries with high level of ANEU. However ANEU has a low effect on growth rate of emissions. For example if ANEU increases by 10%, the growth rate of per capita CO 2 emissions decreases by 1.1%. This observation suggests that clean energy have very little impact on emissions.

Conclusions

This paper examined the relationship between per capita CO2 emissions, per capita GDP and energy mix. We also proposed the classification methodology to solve the problem of parameters' heterogeneity. To do so, the unbalanced panel data set, covering 93 countries, and the time period from 1960 to 2008, were used. Foremost, we proposed no parametric hierarchic clustering approach, based on 17 criteria and used the Hierarchical Clustering on Principal Components (HCPC). The results of the clustering indicate the optimal partition of 93 countries into 7 groups, each with its own characteristics. The region affiliation and the level of economic development do not determine single-handedly class partition for 5 of 7 groups. Moreover, these two criteria do not determine cluster 1 (biggest countries) and cluster 4 (countries with middle level of nuclear energy and RES). This suggests that grouping the countries by region or/and by level of economic development is insufficient. The Europe Union countries are usually examined together or with two sub-panels (Western and Eastern European countries), but our results imply to split EU27 into four. The clustering results were confirmed by the test of partial homogeneity of parameters which indicates that the Panel Data Analysis is applicable for all groups, except cluster 1.

The unit root and cointegration tests showed that a long-run relationship does not exist for any clusters and the nature of stationary is different between and into the groups. The static and dynamic estimations demonstrate that the main determinants of growth rate of per capita CO2 emissions are the growth rate of per capita GDP and the percentage of alternative and nuclear energy use (ANEU), if the level is significantly different from zero. The per capita CO2 emissions depends neither on its lag nor on the lag of per capita GDP, it increases with the growth of per capita GDP and decreases with the growth of ANEU. It's found that the CO2-Income short-run elasticity is between 0.3 and 0.79 according to the groups. We also have found that the CO2-ANEU short-run elasticity depends on clean energy level. For the groups of countries with the best performance, the elasticity is equal to -0.03, while for countries with a low level of ANEU, the elasticity is -0.11 and -0.13.

The present study is innovative in two aspects. Foremost, the problem of panel heterogeneity was solved by using the Hierarchical Clustering on Principal Components and the additional dataset, which aim was to rank countries according to 17 criteria as electricity mix, region, fossils fuel endowments, size of country, contribution of electric and industrial sectors on CO 2 emissions etc. Secondly, we used the evolution of alternative and nuclear energy use as energy mix.

Figure 1 :

 1 Figure 1 : Geographical distribution of country's sample

Table 1 .

 1 Annex A and descriptive statistics for principal data set are given in The 93 countries of our data set cover 97% of worldwide CO 2 emissions. The five countries with the highest mean per capita emission over time are: Luxembourg (33.36), Qatar (30.47), Kuwait (25.04), United Arab Emirates (24.26) and United States (19.57). In 2008, a per capita CO 2 emission was the highest in the Qatar (30.47) and the lowest in the Sudan (0.2). The highest level of per capita CO 2 emissions over time was in Luxembourg in 1961 (55.55) and in Qatar in 2005 (55.30).

Table 1 : Summary of basic statistics

 1

		CO 2 per capita GDP per capita	ANEU (in %)
	Mean	6.55	8078	7.36
	Median	5.05	3666	2.44
	Maximum	55.54	61374	82.86
	Minimum	0.05	72	0
	Std. Dev.	7.05	9609	11.8
	Observation	4540	3664	3472
	Cross	93	93	93
	sections

Table 2 : Description of additional data set

 2

	Variable	Description

  [START_REF] Hsiao | Analysis of Panel data[END_REF], which is simple; apply in the case of a model with fixed effects. He suggests 3 consecutive tests. Foremost he tests under null hypothesis perfect homogeneity of parameters against full heterogeneity. After that, he tests under null hypothesis partial homogeneity of parameters (constant slopes and different intercepts for each country) against full heterogeneity. And finally partial homogeneity is tested against perfect homogeneity of parameters. The test's statistics follow Fisher's distribution. A slight modification is necessary to take into account time fixed effects. Given that the number of observations equals the number of time dummy, we cannot estimate for each country the model with 49 time fixed effects for hypothesis of full heterogeneity. Nine dummies are introduced to circle this problem. They represent the first and the second oil crises, Asian financial crisis and the last global financial crisis. We propose three models: 𝐶𝑂2 𝑛,𝑡 = 𝛼 + 𝛾 * 𝐺𝐷𝑃 𝑛 ,𝑡 + 𝜀 𝑛,𝑡 (1) 𝐶𝑂2 𝑛,𝑡 = 𝛼 𝑛 + 𝛽 𝑡 + 𝛾 * 𝐺𝐷𝑃 𝑛 ,𝑡 + 𝜀 𝑛,𝑡[START_REF] Holtz-Eakin | Stoking the fires? CO2 emissions and economic growth[END_REF]

	𝐶𝑂2 𝑛,𝑡 = 𝛼 𝑛 +	9 𝑖=1	𝑑 𝑖

+ 𝛾 𝑛 * 𝐺𝐷𝑃 𝑛 ,𝑡 + 𝜀 𝑛,𝑡

Table 3 : Results of homogeneity tests, F statistic

 3

	Cluster	Pooled	a	Partial	b	Pooled	c
	Class 1	7.56***	8.12***	1.93***
	Class 2	7.43***	2.31**	3.66***
	Class 3	2.44***	0		2.91***
	Class 4	7.37***	0		2.59***
	Class 5	0		0		1.36***
	Class 6	1.08		0		3.35***
	Class 7	4.42***	2.06**	1.34**
	Note:
	a -H 0 : α, β, γ are invariant against at least one of parameter depending on time or country
	b -H 0: model with time and country fixed effects against full heterogeneity of parameters
	c -H 0 : α and γ is invariant under condition invariant slope against partial homogeneity
	d -***, ** and * indicate statistical H 0 rejection at 1%, 5% or 10% level respectively

Table 4 : Panel IPS test for per capita CO2 emissions, per capita GDP and ANEU

 4

	W -bar	Log CO 2 per capita	Log GDP per capita	Log ANEU (in %)
		Trend,	Intercept	Trend,	Intercept	Trend,	Intercept
		intercept		intercept		intercept
	Class 1	-1.14	-0.23	-0.06	3.39	0.11	-2.36***
	Class 2	-1.50*	-6.08***	-0.06	-4.28***	-6.08***	-4.32***
	Class 3	0.14	-4.39***	-12.9***	0.21	-0.45	-2.25
	Class 4	-0.43	-4.21***	-0.14	-2.38***	-0.01	-0.68
	Class 5	0.08	2.31	-0.04	2.10	-2.99***	-4.49***
	Class 6	-3.74***	-3.88***	0.22	0.02	-1.97**	0.34
	Class 7	0.99	-0.33	1.78	2.11	-0.33	-3.66***
	Note:
	***, ** and * indicate statistical H 0 rejection at 1%, 5% or 10% level respectively

Table 5 : Results of cointegration test Model with trend and intercept

 5

		Cluster 1 (a) Cluster 1 (b) Cluster 5 (b)	Cluster 7 (b)
	Panel v-statistic	-0.11	0.61	-0.78	-0.82
	Panel rho-statistic	0.46	0.45	0.57	0.31
	Panel PP-statistic	-0.37	-0.48	0.18	-0.17
	Panel ADF-statistic	-0.51	0.03	-0.33	-0.19
	Group rho-statistic	1.38	0.8	1.62	1.51
	Group PP-statistic	-1.18	-1.24	-0.39	0.96
	Group ADF-statistic	0.34	-1.01	-2.3***	1.2
		Model with intercept
		Cluster 1 (a) Cluster 1 (b) Cluster 5 (b)	Cluster 7 (b)
	Panel v-statistic	0.18	0.31	-1.08	-0.43
	Panel rho-statistic	0.64	-0.74	-0.74	-0.26
	Panel PP-statistic	0.25	-1.29	-1	-0.65
	Panel ADF-statistic	0.28	-0.91	-1.28*	-0.49
	Group rho-statistic	1.4	0.34	0.64	0.09
	Group PP-statistic	0.56	-0.88	-0.78	-0.54
	Group ADF-statistic	0.49	-0.78	-2.01**	-0.25
	Note:
	***, ** and * indicate statistical H 0 rejection at 1%, 5% or 10% level respectively
	(a) test of cointegration between per capita CO2 emissions, per capita GDP and ANEU
	(b) test of cointegration between per capita CO2 emissions and per capita GDP

Table 6 : The estimation results using WITHIN approach

 6

		Class 1	Class 2	Class 3	Class 4	Class 5	Class 6	Class 7
	gCO2t-1	0.08**	-0.14***	-0.1**	-0.02	-0.14***	-0.05	-0.01
	gGDP	0.72***	0.73***	0.34***	0.41***	0.42***	0.58***	0.61***
	gGDPt-1	-0.06	0.31***	0.5***	-0.11	0.11	-0.1	0.05
	gANEU	-0.08**	-0.03***	-0.02***	-0.11***	-0.01	0.01*	-0.13***
	R²	0.61	0.41	0.61	0.59	0.16	0.62	0.48

Table 7 : The estimation results using SYS-GMM approach

 7

		Class 1	Class 2	Class 3	Class 4	Class 5	Class 6	Class 7
	gCO2t-1	0.11*	0.07	-0.09	0.12	-0.26***	0.08	0.05
	gGDP	0.73***	0.68***	0.28***	0.55***	0.41***	0.52**	0.59***
	gGDPt-1	0.16	0.38	0.78***	-0.08	0.22	-0.12	0.09
	gANEU	-0.073***	-0.4***	-0.027	-0.12***	-0.0009	0.018	-0.13***
	AB AR(1)	-6.6***	-6.05***	-	-3.32***	-	-	-2.59***
	AB AR(2)	1.18	0.24	-	0.01	-	0.11	0.38

Table 8 :

 8

		Final models
		Class 1	Class 2	Class 3	Class 4	Class 5	Class 6	Class 7
		(Within)	(Within)	(Within)	(Within)	(SYS-GMM)	(Within)	(Within)
	gCO2t-1	-	-	-	-	-0.23***	-	-
	gGDP	0.72***	0.79***	0.34***	0.38***	0.30***	0.52***	0.62***
	gGDPt-1	-	-	0.44***	-	-	-	-
	gANEU	-0.08***	-0.03***	-0.025***	-0.11***	-	-	-0.13***
	R²	0.6	0.39	0.61	0.57		0.34	0.48

Under the assumption that membership in a group does not change over time

In k$ per capita

We do not interesting in percentage of alternative and nuclear energy use because null value for some countries and we suppose that the main determinant of per capita CO2 emissions is per capita GDP.

Annex A

Table 9 : Country set and associate code Country Code Country Code Country Code Country Code Country Code Algeria

Peru, Colombia 3 The members of EU ETS in bold italic 4 Renewable Energy Sources