Laté A Lawson
email: l.lawson@unistra.fr

Roberto Martino

Phu Nguyen-Van

Environmental convergence and environmental Kuznets curve: A unified empirical framework

Keywords: Environmental Kuznets curve, environmental convergence, CO2 emissions, regressor endogeneity, semiparametric panel data model

Existing studies disjointly addressed the environmental convergence and environmental Kuznets curve hypotheses, though these research lines are theoretically interconnected. This paper proposes a unified empirical methodology to simultaneously investigate both hypotheses, relying on a semiparametric dynamic panel data model that accounts for regressor endogeneity. The approach, when applied to CO2 emissions in 106 countries, suggests that there is no global level evidence supporting the environmental Kuznets hypothesis, while a convergence process is taking place. Our results imply that current international agreements have not been sufficiently binding to globally curb CO2 emissions, especially in high-income countries, as aimed by Sustainable Development Goals.

Introduction

This paper proposes a unified framework bridging two lines of empirical literature in environmental and ecological economics: the environmental convergence (EC) and the environmental Kuznets curve (EKC) hypotheses. The EKC argument states that environmental degradation increases with income until a turning point after which it decreases, depicting an inverted U-shaped curve as in Figure 1. EC occurs if countries with low emissions of pollutants per capita increase their level of emissions, while the opposite applies to high emissions countries, leading to a catch-up in pollutants emissions per capita. Indeed, the EKC hypothesis holds if the richest (and most polluting) countries reduce their emissions. As long as this is true, the process of economic growth undertaken by poorer and developing countries will get their level of emissions per capita closer to that of developed economies. This is also what a convergence process implies [START_REF] Strazicich | Are CO 2 emission levels converging among industrial countries?[END_REF][START_REF] Nguyen-Van | Distribution dynamics of CO 2 emissions[END_REF]. 1 Thus, the two lines of research are theoretically related and are worth a unified empirical treatment.

Though the interconnection between these two topics, existing empirical studies so far discuss the EKC and EC hypotheses in separate frameworks. This has been the case, among others, in the studies by [START_REF] Galeotti | Reassessing the environmental Kuznets curve for CO 2 emissions: A robustness exercise[END_REF], [START_REF] Nasr | Is there an environmental Kuznets curve for South Africa? A co-summability approach using a century of data[END_REF] and [START_REF] Apergis | Environmental Kuznets curves: New evidence on both panel and country-level CO 2 emissions[END_REF] for the EKC analysis and in [START_REF] Mohammadi | Cross-country convergence in energy and electricity consumption, 1971-2007[END_REF] and [START_REF] Criado | Convergence in per capita CO 2 emissions: A robust distributional approach[END_REF] for EC. From a policy perspective, evidence of EC together with an EKC relationship would have two consequences. Firstly, it may ensure sustainability of the economic growth process. Secondly, it would make global agreements targeting the reduction of pollutants or greenhouse gas (GHG) emissions politically feasible, as developing countries would be encouraged to accept a cap on their emissions without fearing serious consequences for economic growth [START_REF] Romero-Ávila | Convergence in carbon dioxide emissions among industrialised countries revisited[END_REF].

Our paper's contribution to the existing literature is twofold. Firstly, it introduces a novel and robust unified empirical framework, a semiparametric dynamic panel data model, relating the EKC argument to EC. Secondly, it relies on the latter unified framework to simultaneously investigate (i) whether the current growth process is sustainable and (ii) whether the existing global agreements are sufficiently efficient in reducing GHG emissions. This paper, therefore, brings together economic and policy discussions from two empirical strands into a unified framework which accounts for misspecification biases related to functional form and/or regressor endogeneity.

It must be highlighted that the scope of the application to CO 2 emissions data in this paper is neither to investigate their determinants nor to determine the ceteris paribus impact of income on CO 2 emissions. 2 Our concern is rather the provision of a robust long-run relationship between GHG emissions and income together with the assessment of the existence of an EC process with our data. By doing so, we will be able to discuss whether a sustainable growth process is in place, whether (groups of) economies are converging in terms of CO 2 emissions and which levels of emissions the economies are actually converging to.

The paper proceeds as follows. Section 2 overviews the related literature. Section 3 presents the data and investigates distribution dynamics of CO 2 emissions per capita, following the approach originally proposed by [START_REF] Quah | Twin peaks: Growth and convergence in models of distribution dynamics[END_REF]. Section 4 describes the econometric specification. In Section 5 we present the results for the semiparametric specification, as well as for several parametric estimators. In Section 6 we distinguish between OECD and non-OECD economies and we perform some robustness checks within the traditional parametric estimators and compare them with the semiparametric specifications. Section 7 concludes the analysis.

Linking the EKC and the EC hypotheses

Theoretically, the EKC relationship between environmental degradation and income per capita (Figure 1) is triggered by three mechanisms [START_REF] Panayotou | Empirical tests and policy analysis of environmental degradation at different stages of economic development[END_REF][START_REF] Stern | The Rise and Fall of the Environmental Kuznets Curve[END_REF]. Firstly, the composition of output determines the environmental impact of economic activities. Hence, economies mostly specialized in agricultural production or tertiary activities pollute less than economies relying mostly on manufacturing production. It follows that the EKC is strictly linked to the transition from a manufacturing to a service-based economy, since the tertiarization of the economy favours changes in the input mix which becomes less environmentally damaging [START_REF] Marsiglio | The environmental Kuznets curve and the structural change hypothesis[END_REF]. Secondly, technological advance may promote the adoption of the above mentioned changes in the input mix, as well as the diffusion of less polluting techniques of production, favouring energy efficiency [START_REF] Stern | The Rise and Fall of the Environmental Kuznets Curve[END_REF][START_REF] Turner | Energy efficiency, rebound effects and the environmental Kuznets curve[END_REF]. Finally, changes in individual preferences together with regulation and enforcement contribute to increasing supply and demand for environmentally-friendly goods and services. EC, theoretically, implies that environmental degradation (in per capita) occurs faster in pre-industrial economies than in post-industrial economies, leading to a catch-up phenomenon among countries. Regarding CO 2 emissions, several mechanisms engender EC. Primarily, while international agreements (Kyoto Protocol) establish emission goals for high-income economies, no commitments exist for developing countries. Furthermore, as noted by [START_REF] Requate | Dynamic incentives by environmental policy instruments-a survey[END_REF] and [START_REF] Vine | Energy savings certificates: A market-based tool for reducing greenhouse gas emissions[END_REF], economic instruments such price-based (carbon taxes) and rights-based measures drive reduction of emissions in industrialized countries. In addition to tertiarization of the economy and technological advance, these mechanisms, while slowing down environmental degradation in high-income countries, favour growing CO 2 emissions in low-income countries [START_REF] Payne | The convergence of carbon dioxide emissions: A survey of the empirical literature[END_REF].

Relating the EKC and EC hypotheses, the only existing theoretical study we have identified is the work by [START_REF] Brock | The green Solow model[END_REF]. These authors proposed a 'green Solow model' where the EKC appears as a by-product of the convergence process to a sustainable growth path. Their model predicts a conditional convergence of pollutant emissions, similarly to the concept of conditional income convergence. [START_REF] Brock | The green Solow model[END_REF] made the observation that the mechanisms leading to income growth and convergence are also at the origin of the EKC and the EC. This is particularly relevant when international agreement and economic instruments are sufficiently strong enough to flatten and then significantly curb down CO 2 emissions in high-income countries. Thus, even in case where substantial decreases in emissions (a notable downward trend) do not occur in high income countries as depicted by Figure 1, EC (a catch-up) remains possible as long as industrialized countries decelerate environmental degradation, while pre-industrial countries do not. Therefore, based on this discussion, we can make the conjecture that the existence of an EKC can imply (conditional) environmental convergence, similarly to the case of income convergence. However, the reverse would not be true, i.e. the existence of (conditional) EC is not sufficient to ensure the emergence of an EKC relationship as illustrated by Figure 2. Our study proposes a novel empirical approach (which will be detailed below) to test this conjecture, which has never been tested so far.

Environmental Kuznets curve

Environmental convergence

Environmental convergence

Environmental Kuznets curve

No environmental Kuznets curve

if rich countries reduce their emissions per capita sufficiently enough to a sustainable growth path [START_REF] Brock | The green Solow model[END_REF] otherwise Investigating the EKC hypothesis traces back to the nineties. Following the leading studies by World Bank (1992), [START_REF] Shafik | Economic growth and environmental quality: Time series and cross section evidence[END_REF], Grossman andKrueger (1993, 1995) and [START_REF] Panayotou | Empirical tests and policy analysis of environmental degradation at different stages of economic development[END_REF], among others, empirical analyses of the EKC hypothesis abound in the literature. 4 Various environmental degradation indicators have been examined: emissions or concentrations of pollutants (CO, CO 2 , SO 2 , NO x among others), deforestation rate, water quality, etc. The standard approach adopts a parametric specification in which the environmental indicator (in per capita) is regressed on income per capita as a linear, quadratic and also cubic function. Results vary according to the environmental indicator and the data sample under analysis. For instance, Suri and Chapman (1998) used parametric panel models finding that the relationship between energy consumption and income displays an increasing pattern with turning point outside the data sample. Richmond and Kaufmann (2006a,b), by using parametric specifications for panel data, found little evidence of an EKC for energy consumption which increases with income at a decreasing rate. The study of Özokcu and Özdemir (2017), based on panel data estimation, did not give any empirical support to the EKC, neither for OECD countries nor for a sample of 52 emerging countries observed over the period 1980-2010.

In addition, based on a spatial and panel GMM analysis, [START_REF] Wang | Spatiotemporal variations of energy-related CO 2 emissions in China and its influencing factors: An empirical analysis based on provincial panel data[END_REF]; [START_REF] Wang | Spatial economic dependency in the Environmental Kuznets Curve of carbon dioxide: The case of China[END_REF] found no support for an EKC for CO 2 emissions in Chinese provinces and regions for the period 1995-2013. The panel data study performed by del Pablo-Romero and De Jesús (2016) did not either support the EKC hypothesis for 22 countries in Latin America and the Caribbean for the period 1990-2011. On the contrary, [START_REF] Apergis | Testing environmental Kuznets curve hypothesis in Asian countries[END_REF] applying a parametric GMM model to a panel data of 14 Asian countries found evidence of an EKC for CO2 emissions, similarly to [START_REF] Sarkodie | A review on environmental Kuznets curve hypothesis using bibliometric and meta-analysis[END_REF] on the sample of 17 African countries observed between 1971 and 2013.

It is to observe that existing parametric models are based on relatively restricted assumptions. [START_REF] Dijkgraaf | A test for parameter homogeneity in CO 2 panel EKC estimations[END_REF] cast doubt on the EKC results based on parametric panel data models by pointing out the weakness of the parameters' homogeneity assumption underlying these models. Similar results are obtained by [START_REF] Hettige | Industrial pollution in economic development: The environmental Kuznets curve revisited[END_REF], [START_REF] Heil | Carbon emissions and economic development: Future trajectories based on historical experience[END_REF] and [START_REF] Bertinelli | The environmental Kuznets curve semi-parametrically revisited[END_REF] for different indicators, while evidence of an inverted U-shaped relationship was obtained by [START_REF] Shafik | Economic development and environmental quality: An econometric analysis[END_REF] and [START_REF] Schmalensee | World carbon dioxide emissions: 1950-2050[END_REF], etc. More recently, semi and non-parametric techniques have been implemented to investigate the validity of the EKC hypothesis. The advantage of such an approach is that semi and non-parametric estimations do not require the specification of an ad hoc functional form. However, even in such a case, empirical results are still not univocal and vary with the sample and the indicator used. For instance, Nguyen- [START_REF] Nguyen-Van | Energy consumption and income: A semiparametric panel data analysis[END_REF] found no evidence of an EKC for energy consumption using semiparametric techniques applied on a panel of countries, while a similar result was obtained by [START_REF] Nasr | Is there an environmental Kuznets curve for South Africa? A co-summability approach using a century of data[END_REF] for South Africa, a carbon-intensive and non oil-producing developing country. Differently, [START_REF] Sephton | Further evidence of an environmental Kuznets curve in Spain[END_REF] and [START_REF] Apergis | Environmental Kuznets curves: New evidence on both panel and country-level CO 2 emissions[END_REF] provided empirical support for the EKC hypothesis in the case of Spain and for 12 countries respectively. 5Recently, [START_REF] Shahbaz | The CO2-growth nexus revisited: A nonparametric analysis for the G7 economies over nearly two centuries[END_REF] revisited the CO 2 emissions-income nexus for G7 countries by combining non-parametric and time series techniques. Using historical data covering the period 1820-2015, the authors showed evidence of EKC for almost every country in the G7, except Japan. Moreover, mixed results appear in the studies by [START_REF] Sarkodie | A review on environmental Kuznets curve hypothesis using bibliometric and meta-analysis[END_REF]; [START_REF] Ansari | Environmental Kuznets curve revisited: An analysis using ecological and material footprint[END_REF]; [START_REF] Kacprzyk | Shining a new light on the environmental Kuznets curve for CO2 emissions[END_REF] and [START_REF] Altıntaş | Is the environmental Kuznets curve in Europe related to the per-capita ecological footprint or CO2 emissions?[END_REF]. While the meta-analysis by [START_REF] Sarkodie | A review on environmental Kuznets curve hypothesis using bibliometric and meta-analysis[END_REF] leads to blurred conclusions regarding the existence of an EKC, it is noted that differences in time span, econometric specifications, estimation methods and in indicators justify the results' disparity. Thus, [START_REF] Kacprzyk | Shining a new light on the environmental Kuznets curve for CO2 emissions[END_REF] and [START_REF] Altıntaş | Is the environmental Kuznets curve in Europe related to the per-capita ecological footprint or CO2 emissions?[END_REF], respectively using data samples on 161 countries observed between 1992-2012 and 14 countries (observed between 1991-2014), find results indicating that EKC also depends on environmental and development indicators.

In conclusion, it is to observe that independently on environmental indicators, econometric specification and data sample, existing studies overlooked the interconnection between EKC and EC.

The EC literature

Environmental convergence has been a prolific subject of empirical studies following methodologies used in the economic growth literature. Hence, the topic has been investigated in terms of β-convergence using cross-sectional analysis (as in [START_REF] Strazicich | Are CO 2 emission levels converging among industrial countries?[END_REF], [START_REF] Mohammadi | Cross-country convergence in energy and electricity consumption, 1971-2007[END_REF] and [START_REF] Brock | The green Solow model[END_REF], among others), panel data models (see, e.g., [START_REF] Nguyen-Van | Distribution dynamics of CO 2 emissions[END_REF], [START_REF] Miketa | Energy productivity across developed and developing countries in 10 manufacturing sectors: Patterns of growth and convergence[END_REF], [START_REF] Mulder | Sectoral energy-and labour-productivity convergence[END_REF], [START_REF] Panopoulou | Club convergence in carbon dioxide emissions[END_REF], Criado et al. (2011[START_REF] Camarero | Eco-efficiency and convergence in OECD countries[END_REF]), distribution dynamics techniques (for instance, in Nguyen- [START_REF] Nguyen-Van | Distribution dynamics of CO 2 emissions[END_REF], [START_REF] Aldy | Per capita carbon dioxide emissions: Convergence or divergence?[END_REF], [START_REF] Criado | Convergence in per capita CO 2 emissions: A robust distributional approach[END_REF], Criado et al. (2011), [START_REF] Bassetti | CO 2 emissions and income dynamics: What does the global evidence tell us?[END_REF]), or time series approach (e.g., [START_REF] Strazicich | Are CO 2 emission levels converging among industrial countries?[END_REF]. 6However, less attention has been devoted to the link between the EKC hypothesis and EC, in particular accounting for the implications described above. Even though in some cases the standard EKC equation has been transformed in a dynamic setting by adding lagged emissions among the regressors there is no explicit argument relative to convergence. This has been done mainly to justify a persistent behaviour in emissions. This is the case for example of [START_REF] Agras | A dynamic approach to the environmental Kuznets curve hypothesis[END_REF]; [START_REF] Lee | Does one size fit all? A reexamination of the environmental Kuznets curve using the dynamic panel data approach[END_REF]; [START_REF] Bernard | Environmental Kuznets curve: Tipping points, uncertainty and weak identification[END_REF], in which no reference to the EC was made.7 Theoretically, some specific models for EC in an EKC framework were given by [START_REF] Bulte | Regulatory federalism and the distribution of air pollutant emissions[END_REF] and [START_REF] Brock | The green Solow model[END_REF], which build on the Solow model assuming that pollution occurs as a by-product of economic activity and it can be reduced through abatement efforts. In a slightly different vein, Criado et al. (2011) adopted a a Ramsey-Cass-Koopmans model without referring to the EKC hypothesis to provide theoretical support and empirical evidence for EC. Such a theoretical background and the lack of an empirical strategy clearly addressing together convergence and the EKC motivate the present study.

Im recent literature, researchers have been considering, in addition to CO 2 emissions, environmental indicators such emissions and energy intensities as well as eco-efficiency index in addressing EC. Among others, this has been the case in the study by [START_REF] Camarero | Eco-efficiency and convergence in OECD countries[END_REF]; [START_REF] Zhao | Province-level convergence of China's carbon dioxide emissions[END_REF]; [START_REF] Apergis | Per capita carbon dioxide emissions across US states by sector and fossil fuel source: Evidence from club convergence tests[END_REF] and [START_REF] Yu | Convergence of per capita carbon emissions in the Yangtze River Economic Belt, China[END_REF]. Relying on eco-efficiency indicators (obtained by data envelopment), [START_REF] Camarero | Eco-efficiency and convergence in OECD countries[END_REF] assess EC to find results suggesting the existence of 4 convergence clubs across OECD countries. Comparable results appear in the study by [START_REF] Barassi | Fractional integration versus structural change: Testing the convergence of co2 emissions[END_REF] for 28 OECD countries (stochastic convergence), and by [START_REF] Zhao | Province-level convergence of China's carbon dioxide emissions[END_REF] and [START_REF] Apergis | Per capita carbon dioxide emissions across US states by sector and fossil fuel source: Evidence from club convergence tests[END_REF] respectively in 30 Chinese provinces and 50 US States. Finally, considering CO 2 and energy intensity in value-added, Fernández-Amador et al. ( 2019) and [START_REF] Apergis | Carbon Dioxide Emissions Intensity Convergence: Evidence From Central American Countries[END_REF] also investigate the EC hypothesis. The primer, using a conditional β-approach on the sample of 66 countries and 12 regions provide evidence supporting (slower) global convergence in addition to country-specific conditional convergence. The latter on a sample of 6 Central America countries mainly conclude for the existence of 2 convergence clubs.

Overall, contrary to EKC studies where depending on samples, model specifications and estimation procedures, discordant results are observed, it is to note that studies on EC seem less divergent, whether the framework is β, σ or stochastic convergence. Nevertheless, as mentioned above, existing studies so far lack of a framework linking EKC to EC.

In what follows, we propose a unique framework to concurrently assess the occurrence of both the EKC hypothesis and EC, using CO 2 emissions as an illustrative application, since it is a major greenhouse gas and closely linked to energy consumption and economic activity. The estimation relies on the panel data model proposed by [START_REF] Li | Semiparametric estimation of partially linear panel data models[END_REF], [START_REF] Baltagi | On instrumental variable estimation of semiparametric dynamic panel data models[END_REF] and [START_REF] Li | Nonparametric Econometrics: Theory and Practice[END_REF]. This approach has two interesting aspects. Firstly, it allows for a dynamic structure capturing some habits or persistence behaviour in CO 2 emissions, since emissions cuts might take time. Indeed, the literature has shown that adoption of energy-saving technologies is costly and that diffusion of these technologies is a lengthy process [START_REF] Jaffe | The energy paradox and the diffusion of conservation technology[END_REF][START_REF] Mulder | Explaining slow diffusion of energy-saving technologies: A vintage model with returns to diversity and learning-by-using[END_REF]. Moreover, and most important for our purposes, such a dynamic setting can be used to test for convergence, following the panel solution provided by [START_REF] Islam | Growth empirics: A panel data approach[END_REF] in the spirit of a theoretical framework in line with [START_REF] Bulte | Regulatory federalism and the distribution of air pollutant emissions[END_REF] and [START_REF] Brock | The green Solow model[END_REF]. Secondly, our model includes a non-parametric function of income which allows us to avoid possible misspecified functional forms that might affect parametric EKC studies [START_REF] Azomahou | Economic development and CO 2 emissions: A nonparametric panel approach[END_REF][START_REF] Bertinelli | The environmental Kuznets curve semi-parametrically revisited[END_REF].

Data and distribution dynamics

Data

We use CO 2 emissions per capita (in kiloton of oil equivalent), drawn from the World Development Indicators. This corresponds to carbon dioxide emissions stemming from the burning of fossil fuels and the manufacture of cement. CO 2 emissions are then strictly linked to production and economic activity in general. GDP per capita (outputside real GDP) is instead drawn from the Penn World Table 9.0 and expressed in PPP of $2011. The sample includes 106 countries which greatly differ in GDP per capita, over the period 1970-2015. We also focus the analysis on two subsamples consisting of 21 OECD and 85 non OECD economies to assess potential heterogeneities between developed and developing countries. Table 1 reports the descriptive statistics. The high value of the standard deviation for both GDP and CO 2 emissions per capita is indicative of the heterogeneity of the sample. The very high maximum value for GDP per capita corresponds to Saudi Arabia in 1973. Similar high values are also observed for Bahrain, especially in the seventies. The highest value of CO 2 emissions per capita corresponds to Bahamas, in which consumption of liquid fuels more than doubled in the seventies for then reverting to the previous trend in the eighties. Overall, higher levels of CO 2 per capita are observed in the oil countries included in the sample (Bahrain and Saudi Arabia) and also in Luxembourg and the United States. Complementary to Table 1, Figure 3 reports the kernel density estimates. Values are standardized with respect to the mean. The distribution of CO 2 and GDP per capita is reported for the waves 1975, 1995 and 2015 and the pattern is similar in both cases. The proportion of countries at the bottom of the distribution is decreasing over time, while the mass increases in the interval [1,3] favouring a bimodal distribution in the case of GDP per capita. This implies that the average levels of GDP and CO 2 are increasing over time, underlying that CO 2 is a by-product of economic activity.

Distribution dynamics

Convergence analysis in growth econometrics is usually done by either estimating a convergence equation using cross-sectional data, panel data, or time series. However, the estimation results provide information regarding the average behaviour in the sample and no relevant insights are given with respect to relative performances of the entire sample distribution. Hence, the analysis of distribution dynamics is a complementary tool providing a complete picture of CO 2 emissions [START_REF] Quah | Twin peaks: Growth and convergence in models of distribution dynamics[END_REF][START_REF] Quah | Empirics for growth and distribution: Stratification, polarization, and convergence clubs[END_REF]. In particular, we study the evolution of the distribution of CO 2 emissions assuming that the process determining its dynamics is time-invariant and first-order [START_REF] Johnson | A nonparametric analysis of income convergence across the US states[END_REF][START_REF] Johnson | A continuous state space approach to 'convergence by parts[END_REF], so that the distribution prevailing at time t + τ is given by:

φ t+τ (y) = +∝ 0 f τ (y|x)φ t (x)dx (1)
where x and y are relative CO 2 emissions per capita (i.e standardized with mean value) at time t and t + τ , respectively. Function φ t (x) corresponds to the distribution of emissions at time t. Finally, f τ (y|x) is the conditional density that informs about transition dynamics within the distribution during the period considered, mapping the position of each country at time t and t + τ .8 Figure 4 plots f τ (y|x), for which τ = 5, hence considering data for 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010 and 2015. 9 Observations that did not change their relative position from t to t + τ lie on the 45 degrees line. Observations below the 45 degrees line improved their relative position along the period (i.e. relative emissions increase in t + τ conditionally to information in t), while observations above fell behind (i.e. relative emissions decrease in t + τ )). The density contours and the dotted line (which is the median curve) plotted in Figure 4 show that observations of the distribution are stable over time, notably for observations between the range 0.5-1.5. The observed peak for values close to 0 is below the 45 degrees line, indicating an improvement of their relative positions in the distribution. Overall, the picture shows a convergence pattern for low-emitting countries towards higher emission values whereas the relative positions of high-emitting countries remain stable over time.

Higher levels of CO 2 emissions are usually observed in high-income countries, because of the output structure largely relying on fossil energy use. Simultaneously, these countries are the most engaged in policies to reduce the environmental impact of economic activity and to exploit alternative energy sources. Taking into account this heterogeneity related to high-income countries, we perform the above analysis for the subsample of 21 OECD countries. Figure 5 plots the resulting conditional density. The contours indicate that, contrary to the full sample, distribution dynamics are characterized by higher mobility. Two main peaks can be detected. One of them between 0.5 and 1 below the 45 degrees line, suggesting an increase in emissions for low-emitting countries. Another peak in the upper tail around 2 of the distribution is mostly located above the 45 degrees line, suggesting a reduction of emissions for high-emitting countries. Hence, this suggests a bi-polarization process among OECD countries, but with a convergence for the whole OECD countries. Such evidence is consistent with findings for industrial countries reported by Nguyen- [START_REF] Nguyen-Van | Distribution dynamics of CO 2 emissions[END_REF] and [START_REF] Strazicich | Are CO 2 emission levels converging among industrial countries?[END_REF].

The econometric model

To complete the previous distribution analysis, we propose a framework to study the nexus between income and an environmental indicator. The latter corresponds to CO 2 emissions for our illustrative application. Following the definition of (income) convergence in the panel data framework proposed by [START_REF] Islam | Growth empirics: A panel data approach[END_REF], we can model convergence for environmental indicator y (or CO 2 emissions per capita) as follows:

y it = αy i,t-1 + ζ it (2)
where y it is the log of CO 2 emissions per capita of country i (i = 1, ..., N ) at period t (t = 1, ..., T ). The equation allows capturing the local dynamics toward the steady-state. More generally, it accounts for adjustment dynamics of emissions over time: if α is less than 1, pollutants in time t + 1 are a smaller proportion of the level in t. It should be noted that, in equation ( 2), α = exp -λτ , where λ and τ respectively indicate the rate of convergence and the time span. The former measures how fast emissions are converging to their steady-state or, more generally, how fast the gap between countries is being closed. 10 The smaller α, the larger the rate of convergence λ. When an estimation of α is available, we can use the delta method to recover λ [START_REF] Islam | What have we learnt from the convergence debate[END_REF]. The time span between t and t + 1 may be fixed to a period of several years. Following [START_REF] Islam | Growth empirics: A panel data approach[END_REF] we opt for 5 years time intervals in order to avoid short-term disturbances or business cycle fluctuations which are likely present in shorter periods. Hence, as in the previous analysis about distribution dynamics, the data used in the regressions below correspond to 1970, 1975, ..., 2015. Regarding, the CO 2 emissions-GDP nexus (EKC literature), existing studies usually assume the following parametric specification for an environmental indicator y and income z (in logs) y it = Z it β + η it , often relying on a quadratic form in income

Z it β = β 0 + β 1 z it + β 2 z 2 it .
Our methodological novelty involves gathering these two analytical perspectives into a single-equation specification which allows for investigating both the EKC and the EC hypotheses:11

y it = αy i,t-1 + Z it β + ε it .
(3)

We assume that the data are independent across the i index. It is also assumed that the residuals in model ( 3) are given by ε it = µ i + u it where µ i represents the country-specific effect and u it the standard error term. Moreover, our analysis is based on the case of large N and fixed T . It should be noted that this model can be estimated by using divers approaches: random effects (GLS estimator), fixed effects (within estimator), instrumental variables (IV). However, the presence of the lagged dependent variable y i,t-1 implies a correlation between it and the regression residuals, which makes the RE-GLS and the FE-within estimators inconsistent and then justifies the use of the IV estimator. 12Recent studies underline the possible misspecification regarding the parametric form of the EKC [START_REF] Azomahou | Economic development and CO 2 emissions: A nonparametric panel approach[END_REF][START_REF] Bertinelli | The environmental Kuznets curve semi-parametrically revisited[END_REF]. Taking this into account, we replace the parametric function Z it β by a non-parametric form g(z it ) which does not require any ad-doc functional form. The resulting specification is the semiparametric dynamic panel data model (4).

y it = αy i,t-1 + g(z it ) + ε it (4) with ε it = µ i + u it .
The model includes the situation where µ i are considered as random effects. The case of fixed effects µ i is interesting but much more complex to handle. 13 Moreover, the model covers the case E(u it | z is ) = 0 ∀s ≤ t, which is much more general than the assumption E(u it | z is ) = 0 ∀s, t usually adopted in existing parametric settings. Estimation of model in (4) can be performed following the methods developed by [START_REF] Li | Semiparametric estimation of partially linear panel data models[END_REF], [START_REF] Baltagi | On instrumental variable estimation of semiparametric dynamic panel data models[END_REF] and [START_REF] Li | Nonparametric Econometrics: Theory and Practice[END_REF]. These authors proposed two instrumental variable solutions for estimating α, which also allow for the assumption that the residuals ε it are serially correlated. Following this procedure, we firstly eliminate g(z it ) as in [START_REF] Robinson | Root-N -consistent semiparametric regression[END_REF] by taking the expectation of (4) conditional on z it and then by subtracting it from (4). This yields: [START_REF] Li | Semiparametric estimation of partially linear panel data models[END_REF] and [START_REF] Baltagi | On instrumental variable estimation of semiparametric dynamic panel data models[END_REF], assuming there exists q ≥ 1 instrumental variables w it which are correlated with y i,t-1 and uncorrelated with ξ it , the instrumental variable estimators are given by:

y it -E(y it |z it ) = α [y i,t-1 -E(y i,t-1 |z it )] + [ε it -E(ε it |z it )] ≡ αv it + ξ it (5) where v it ≡ y i,t-1 -E(y i,t-1 |z it ) and ξ it ≡ ε it -E(ε it |z it ). If we use E(ε it |z it ) = 0, then ξ it = ε it . Following
αIV O = (v ww v) -1 v ww (y -ψ) (6) αIV G = (v Σ -1 w(w Σ -1 w) -1 w Σ -1 v) -1 v Σ -1 w(w Σ -1 w) -1 w Σ -1 (y -E(y it |z it )) (7)
where ψ it ≡ E(y it |z it ). Note that estimator (6) is computed using OLS while estimator (7) relies on GLS using w it as an instrument. Moreover, the IVO estimator requires w it to be weakly exogenous, while the IVG requires strong exogeneity of the instrument and conditional homoskedasticity of the residuals.

Li and Stengos (1996) used w it = z i,t-1 as an IV for v it = y i,t-1 -E(y i,t-1 |z it ) because z i,t-1 is uncorrelated with ξ it and it is possibly correlated with v it . However, [START_REF] Baltagi | On instrumental variable estimation of semiparametric dynamic panel data models[END_REF] showed that in some cases E(v it z i,t-1 ) = 0 so that w it = z i,t-1 is uncorrelated with v it .14 To avoid this possibility, they proposed to use w it = E(y i,t-1 |z i,t-1 ), instead of z i,t-1 , as an instrument for v it . This is the approach we follow. It should be noted that these conditional expectations in estimations are replaced by the non-parametric (kernel) estimators, i.e. ŵit = N,T it K(z it )y i,t-1 / N,T it K(z it ) where K(.) is the kernel function. In addition, we use bootstrap procedures to get consistent estimates of standard errors. When an estimator of α is available, g can be non-parametrically estimated by applying the kernel regression to equation (3

): ĝ(z it ) = E [y it -αy i,t-1 | z it ]. 15
A further piece of information concerns the appropriateness of the functional form. Indeed, it may be interesting to test whether the parametric functional form is a good approximation. Therefore, we apply the procedure developed by [START_REF] Henderson | Nonparametric estimation and testing of fixed effects panel data models[END_REF] to test the parametric dynamic panel data model in (3) against the semiparametric dynamic panel data model in (4). The test statistic is given by:

I N = 1 N T N i T t αy i,t-1 + Z it β -αy i,t-1 -ĝ(z it ) 2 (8)
where α and β denote the consistent estimators based on model (3) and α and ĝ are consistent estimators based on (4). The H 0 hypothesis corresponds to the parametric model (3), while the alternative H 1 is the semiparametric specification (4). Note that I N converges to zero in probability under the null and it converges to a positive constant under the alternative. However, the asymptotic distribution of I N is unknown. Therefore, [START_REF] Henderson | Nonparametric estimation and testing of fixed effects panel data models[END_REF] employed a bootstrap procedure to generate an empirical distribution for I N which approximates its finite sample null distribution. Hence, our inference is done by calculating such an empirical distribution.16

6. Estimation results

Specification tests

At a first step, we compare various parametric models (Hausman test). Tests results are reported in Table E1. Overall, the random effect estimator is rejected in favour of a FE specification. Also, the IV estimator (which takes the endogeneity of y i,t-1 into account) outperforms the FE within estimator.17

At a second step, though the semiparametric models have the advantage of imposing no ad-hoc parametric functional form, their results could be compared to those of a parametric specification. In what follows, we perform further specification tests (using the [START_REF] Henderson | Nonparametric estimation and testing of fixed effects panel data models[END_REF]) comparing the semiparametric counterpart among then and also to the IV estimator , in order to find the most reasonable approximation to the data. Applying the test of [START_REF] Henderson | Nonparametric estimation and testing of fixed effects panel data models[END_REF], we compare the IV parametric model to both the IVO and IVG semiparametric models, the null hypothesis being that the IV estimator is preferred. The test statistics for the whole sample case are respectively 6.233 and 6.140 for the IVO and IVG alternatives. Compared to the semiparametric models, the test results reject the IV estimator. Replicating the test for the OECD and non-OECD subsamples provides very comparable results. Hence, both the IVO and the IVG appear to be good fits for our data. In conclusion, though the parametric IV method seems suitable in estimating the quadratic model, it is outperformed by the semiparametric dynamic panel data framework introduced by this paper, thanks to its generality. From a methodological perspective, our approach helps be more confident about assumptions on regressor endogeneity and misspecified functional forms. Finally, our discussions about convergence in CO 2 emissions and existence of an EKC-relationship between GDP and CO 2 emissions per capita will rely on the outcomes of the IVO and IVG estimators.

Estimation results

We start by reporting the two semiparametric estimators for model (4), using w it = E(y i,t-1 | z i,t-1 ) as instrument for v it . Table 3 displays the results of the IVO and IVG estimators.18 Globally, our results suggest convergence in CO 2 emissions per capita, given the estimated parameter for α lower than 1 and statistically significant for both the IVO and the IVG models. Comparable results of an overall EC appear, among others, in the recent studies by [START_REF] Runar | Convergence in carbon dioxide emissions and the role of growth and institutions: A parametric and non-parametric analysis[END_REF] and [START_REF] Rios | Convergence in CO2 emissions: A spatial economic analysis with crosscountry interactions[END_REF] respectively for a sample 124 and 141 countries observed over relatively long periods. Note. * * * p < 0.01, * * p < 0.05, * p < 0.1. Bootstrapped standard errors in parenthesis. The implied λ is calculated by the delta method. N = 106 countries and T = 10 five-years periods).

In particular, α is equal to 0.769 in the case of the IVO estimator and 0.903 in the case of the IVG estimator, leading to a convergence rate ( λ) of 5.3% and 2.0%, respectively. Compared to the IVG, the IVO seems to overestimate the convergence speed (or equivalently, the IVG underestimates the convergence rate, compared to the IVO). However, the latter is overestimated the most by the parametric IV model among all the parametric and semiparametric models considered. 19 Note that the convergence obtained here must be interpreted in terms of steady-state convergence within the conditional convergence framework of equation (4), i.e. convergence towards country-specific steady states as emphasized by [START_REF] Islam | What have we learnt from the convergence debate[END_REF]. 20Concerning the CO 2 emissions and GDP per capita nexus, Figure 6 displays the function g(z it ) resulting from the two semiparametric estimators. An increasing relationship is observed along the whole range of income, despite a short decreasing path at the lower tail. A similar increasing pattern has been recently observed in the contribution by [START_REF] Nasr | Is there an environmental Kuznets curve for South Africa? A co-summability approach using a century of data[END_REF], del Pablo-Romero and De Jesús (2016) and [START_REF] Sarkodie | The invisible hand and EKC hypothesis: What are the drivers of environmental degradation and pollution in Africa?[END_REF] with environmental indicators such as CO 2 , energy use and ecological footprint. Overall, this indicates that CO 2 emissions per capita keep rising, not only in low-and middle-income countries but also at higher levels of GDP per capita, i.e. in the very upper tail of the distribution. This contrasts with the EKC hypothesis predicting a reduction of emissions for high-income levels. The shape of g(.) is much similar for both the IVO and the IVG estimators, the former having a steeper slope. We observe that the slope of both curves becomes steeper for levels of log-income higher than 10, which is exactly the opposite feature of an EKC. Globally, relying on no ad-hoc specification of the emissions-income relationship, the semiparametric analysis for the 106 developing and developed countries does not support the EKC hypothesis. Regarding EC, our results show evidence of convergence in CO 2 emissions per capita. Combined with the distribution analysis in Section 3, we can conclude that this convergence is rather towards higher emissions levels. The result confirms the conjecture according to which the existence of an EKC can imply the EC but the reverse is not true. It remains to check the robustness of our findings. Such an exercise can be performed by using data subsamples on OECD and non-OECD countries. The next Section is devoted to that.

Subsample analysis

Subsample analysis: OECD versus non-OECD countries

As outlined in the Introduction, the theoretical EKC argument implies that we should observe a negative relationship between pollutant emissions and income in high-income economies. Therefore, replicating the above estimates for a subsample of OECD countries should provide evidence of either an EKC relationship or, at least, a deceleration of CO 2 emissions for high-income levels. In addition, we should simultaneously find evidence of a convergence process as long as we consider a group of high income countries with similar structure of production, implementing relatively environmentally-friendly technologies and in which interventions targeting environmental degradation are in the policy agenda. Some empirical results support this view, for instance [START_REF] Galeotti | Reassessing the environmental Kuznets curve for CO 2 emissions: A robustness exercise[END_REF], which reports evidence of an inverted U-shaped relationship for OECD countries, while an increasing curve is found for non-OECD economies. Indeed, countries belonging to the OECD group are more likely to present the mechanisms triggering the EKC, as discussed above. We firstly estimate the semiparametric and parametric models for the subsample of the OECD economies. Then, we compare the results with those obtained for non-OECD countries. The results for the 21 OECD countries are reported in Table 4. Semiparametric estimates for α in the first two columns indicate that OECD countries are converging in terms of CO 2 emissions per capita. The rate of convergence is about 3.6% in the IVO analysis, while it is 1.1% in the IVG case and both are statistically significant. Though the IV model is outperformed by the semiparametric models (IVO and IVG), Table 4 reports the output of the IV estimation for comparison purposes. ) in the IVO as well as in IVG case. Since the confidence bands for both estimators are quite large, we conclude that no empirical support for the EKC argument can be claimed. Overall, our results for OECD countries do not support the EKC argument. Moreover, the estimations above and distribution dynamics analysis in Figure 5 indicate that environmental convergence is in place in terms of both convergence toward the country's steady-state and relative emissions for OECD countries.

OECD countries

Non-OECD countries

The results of the semiparametric analysis in Table 5 (first two columns) suggest EC among non-OECD countries, since α is lower than 1 for both IVO and IVG estimators, corresponding to significant convergence rates of 6.2% and 2.6%. Similar conclusions can be drawn from the parametric IV estimator which however overestimates the convergence rate (12.4%). Thus, independently of the estimations procedure, EC is also noticeable among non-OECD countries.

Regarding EKC, similarly to the full sample case, we do not find empirical support for the EKC hypothesis. Both the semiparametric curves g(z), as displayed in Figure 8, are increasing along the whole income range. Overall, our results for non-OECD countries are very similar to those obtained for the full sample, supporting EC while disproving the EKC hypothesis. Finally, while increasing patterns between income per capita and CO 2 emissions appear in non-OECD countries, a flat relationship is observed in OECD countries. Regarding EC, both sub-sample show evidence of EC with a (significantly) higher convergence rate in non-OECD countries. Hence, this OECD versus non-OECD analysis confirms the results obtained using the full sample, namely EC in the presence of an EKC.

Subsample analysis: High-income versus low-income countries

In a further step of testing the sensitivity of our outcomes to income level and economic structure, we assess EC and EKC decoupling high-income countries (HIC) from low-income countries (LIC). 21 The results of this additional step (reported in Table 6 and Figure 9) are largely coherent with the ones previously observed for the full sample. More concretely, our IVO and IVG estimators show a significant estimate for α, implying a statistically significant convergence rate in both HIC and LIC. Regarding EKC, our results display overall increasing patterns. As noted above, the evidence of EC concurrently with the non-existence of an EKC is not surprising, since the downward part of the EKC relationship is observable only if HIC sufficiently curb down their emissions levels. Note. * p<0.1; * * p<0.05; * * * p<0.01. Bootstrap (semiparametric) and robust (parametric) standard errors in parenthesis. We used the median value of GDP to decouple high from low-income countries.

Globally, the results of our analysis for the full sample and the subsamples can be summarized as follows. Firstly, even though we consider a sample large enough to satisfy the structural conditions likely to trigger the EKC effects, we find no evidence of an inverted U-shaped relationship between CO 2 emissions and income, when considering the most preferred estimators (IVO and IVG). The estimations reveal an increasing pattern for the whole income range and no reversion occurs in the upper tail. This implies that the EKC argument fails because rich economies did not sufficiently reduce their emissions. Such a pattern is confirmed by considering sub-samples such as HIC, LIC and even in the OECD countries.

High-income countries

Low-income countries Secondly, the evidence of EC (supported by the distribution analysis and by both parametric and semiparametric specifications) can be linked to the failure of the EKC argument. Indeed, the relationship between CO 2 emissions and income together with the conditional densities in Section 2 clearly show that emissions are converging towards high levels of emissions, although the convergence speed is quite low (its estimated range is 3.6%-6.2% based on the IVO estimator and 1.1%-2.6% based on the IVG one). Rich countries, in particular OECD countries, are not remarkably reducing their emissions yet.22 Concretely, the observed emissions convergence process does not appear as a result of an environmentally friendly change in economic activity, but rather as a catching-up phenomenon resulting from economic performances in lowincome countries.

Discussions

The semiparametric dynamic panel data model Noting that the mechanisms leading to EC are the same that favour EKC, this paper introduces a unified framework to simultaneously assess EC and EKC. Contrary to existing literature, where tests of the EC hypothesis ignore EKC (and vice versa), our paper fills this gap by proposing to link these two arguments. Certainly, a (parametric) IV methodology can help estimate regression models together testing EC and EKC. Nevertheless, the IV method, still based on parametric specifications upon the data, would probably be outperformed by more flexible specifications. Moreover, the IV method can be misleading, when testing nonlinear relationships such as the EKC hypotheses. This is exactly why our proposed semiparametric dynamic panel data model (with IVO and IVG estimators) seems to be the most satisfactory approach to address EKC and EC within this unified framework.

EC in the absence of an EKC

Applying the unified empirical framework to EC and EKC, we obtain results supporting the EC hypothesis while questioning the existence of EKC, whether considering the full sample or subsamples (HIC, LIC and of OECD and non-OECD countries). Overall, our results strengthen conclusions of existing empirical studies on EC, which report an ongoing catching-up process among countries in terms of CO 2 emissions per capita. This would also suggest that international agreements, environmental conservation effort and economic instruments have contributed to slow down emissions per capita in industrialized countries, enabling a global (conditional) convergence process.

The indications of decelerating environmental degradation with per capita income, also observable in HIC and LIC, proceed together with the absence of an EKC for CO 2 emissions. This evidence of EC in the absence of an EKC has two major implications. Firstly, despite raising question on the sustainable nature of ongoing development process, these results remain encouraging as a flatten EKC-relationship is still noticeable in OECD countries. Secondly, although they successfully contribute to decelerating pollutant emissions, international agreements and economic mechanisms remain insufficiently strong and binding enough to substantially curb down CO 2 emissions per capita in high-income countries. Hence, larger efforts are still needed, especially in HIC, to achieve a sustainable development process.

Implication for environmental policy

Our main results suggesting an ongoing EC in the absence of EKC has some implications for environmental policy. Firstly, they encourage HIC to further work toward a transition from fossil energies to less polluting energies, in order to achieve the Sustainable Development Goals (SDG), a low-carbon development. The energy transition will cause substantial decreases in pollutant emissions and favour the emergence of an EKC. This policy implication also applies to OECD countries. Although the relation CO 2 emissions-income show a relatively flat behaviour, a significant reduction in emissions is still very feasible in OECD countries, as theoretically suggested by Figure 1. Secondly, our results invite LIC and middle-income countries to promote investments in green and renewable energies supply as well as in energy-efficient technologies. Contrary to the HIC, these actions may ensure in LIC an economic transition to post-industrial stages with low-carbon levels and relatively low environmental impacts.

Concluding remarks

This paper aims to merge empirical literature on environmental convergence and Kuznets curve hypothesis, arguing that the two perspectives are genuinely related. It, therefore, proposes a unified empirical framework simultaneously testing EC and EKC, relying on a semiparametric dynamic panel data model which also accounts for regressor endogeneity.

Applying the so-called unified empirical framework to a panel data sample of 106 countries observed between 1970 to 2015 delivers very insightful outcomes on the CO 2 emissions and income nexus. Globally, our results, mainly based on an instrumental variable estimator for semiparametric dynamic panel model, do not support the existence of an inverted U-shaped relationship between CO 2 emissions and GDP per capita. On the opposite, an increasing path is observed (although the relation flattens for lower high-income levels). Our results, which are robust across both subsamples of OECD versus non-OECD countries, and LIC versus HIC, provide clear evidence of convergence in CO 2 emissions. This convergence can be reconciled with the absence of an EKC relationship as economies converge towards their steady states with high levels of CO 2 emissions.

Consequently, we can state that although their promising impacts on the reduction of emissions (notably in rich countries), international efforts and agreements, aiming to reduce the global environmental impact of economic activities, need to be intensified in order to invert the increasing relationship between economic growth and greenhouse CO 2 emissions. Such conclusions are relevant especially because they also hold for OECD countries. Indeed, the overall relationship between CO 2 emissions and income remains increasing (although it slightly flattens at high-income levels), despite existing international agreements, the tertiarization of output structure, technological advance, economic incentives for environmentally-friendly technologies of production. From a policy point of view, such evidence weakens the ability of rich economies and international institutions to effectively implement pro-environmental policies in developing countries and raises serious concerns about the sustainability of the current development process.

The present study can be extended and replicated in various ways, for instance by applying the analysis using different environmental indicators. It may be of interest to further augment the main specification to investigate the role of determinants of CO 2 emissions and other environmental indicators. In particular, two kinds of factors could deserve special attention: technological advance and policy measures. This is left to future research.

Appendices

A. Countries included in the study We apply here the standard parametric estimations to the model in equation (3). In particular, we firstly compute the RE and the FE estimators. Because of the potential endogeneity of the lagged dependent variable y i,t-1 , both the RE and the FE estimators would be inconsistent. We, therefore, also perform an instrumental variables estimation for model (3) using w it as instrument. The results of these estimators are reported in Table E2.23 The first two columns report the results of the RE and the FE estimators, respectively. In both cases, α, the estimated coefficient for y i,t-1 is less than 1 and significant, implying convergence rates of 8% and 3% respectively. Regarding the relationship between emissions and income, both the RE and the FE estimators support a quadratic form even though the turning point is outside the sample. Therefore no confirmation of the EKC argument is provided for the data sample. The third column reports results for the IV estimator. In this case the estimate parameter of y i,t-1 is lower than those obtained for both the parametric (RE and FE) and semiparametric (IVO and GVO) estimators. It is indeed equal to 0.523, corresponding to a convergence rate of 13%. Moreover, the results support a quadratic relationship with, however, a turning point outside of the sample. Similarly to the semiparametric analysis presented above, Figure E1 displays the relationship between CO 2 emissions per capita and GDP per capita for the RE, FE and IV estimators. As indicated above, the curves do not show any evidence supporting the EKC hypothesis for the considered data sample.

C. Decoupling EC from EKC analysis

E.2. Results of the FE, RE and IV estimators

F. Decoupling high and low-income countries

  3

Figure 1 .

 1 Figure 1. Illustration of an EKC relationship between pollutants emissions and income

Figure 2 .

 2 Figure 2. Illustration of the occurrence of an EKC together with an EC

  Note. Carbon dioxide and Real GDP per capita (PPP, $2011). The sample includes 1060 observations (N = 106 countries and T = 10 five-years periods).

Figure 3 .

 3 Figure 3. Distribution of CO2 and GDP per capita.

Figure 4 .

 4 Figure 4. Conditional distribution of relative CO2 emissions per capita, where the dotted curve corresponds to the median value.

Figure 5 .

 5 Figure 5. Conditional distribution of relative CO2 emissions per capita in OECD countries, where the dotted curve corresponds to the median value.

Figure 6 .

 6 Figure 6. Semiparametric estimation of the relationship between CO2 emissions and income. The black curves represent the IVO and IVG estimates. The grey curves correspond to the bootstrap 95% confidence intervals.

Figure 7 .

 7 Figure 7. Semiparametric estimation of the relationship between CO2 emissions and income for the OECD subsample. The black curves represent the IVO and IVG estimates. The grey curves correspond to the bootstrap 95% confidence intervals

Figure 7

 7 Figure7plots the estimation of the relationship between emissions per capita and GDP per capita (g(z)) in the IVO as well as in IVG case. Since the confidence bands for both estimators are quite large, we conclude that no empirical support for the EKC argument can be claimed. Overall, our results for OECD countries do not support the EKC argument. Moreover, the estimations above and distribution dynamics analysis in Figure5indicate that environmental convergence is in place in

Figure 8 .

 8 Figure 8. Semiparametric estimation of the relationship between CO2 emissions and income for the non-OECD subsample. The black curves represent the IVO and IVG estimates. The grey curves correspond to the bootstrap 95% confidence intervals

Figure 9 .

 9 Figure 9. Semi-parametric estimation of the relationship between CO2 emissions and income.

  China/2005-16, Pollution emi. efficiency multivariate intermed. model Different distances from EKC Notes: * LAC and AF respectively stand for Latin American and Caribbean and Africa.

  001 * * * OECD versus non-OECD H 0 rejected H 0 rejected Note. * * * p < 0.01, * * p < 0.05, * p < 0.1. See Tables4 and 5for results of the different estimations used to perform the test. The null-hypothesis H 0 is: λoecd = λnon-oecd . The test-statistic is given by Z = λoecd -λnon.oecd

Figure E1 .

 E1 Figure E1. Parametric estimation of the relationship between CO2 emissions and income (both in per capita).

  Figure F1. Semi-parametric estimation of the relationship between CO2 emissions and income.High income countries (non-OECD sample)Low income countries (non-OECD sample)

Table 1 .

 1 Descriptive statistics

	Variables	Observation	Mean	St. Dev.	Min	Max
	GDP per capita	1060	9200.614	11251.730	215.396	89805.750
	CO 2 emissions	1060	4.017	5.513	.011	40.444

  Table 2 summarizes these test results.

Table 2 .

 2 Results of the Henderson et al. (2008) test, parametric IV versus semiparametric IVO and IVG.

	Sample	IV versus Semiparametric IVO IV versus Semiparametric IVG
	Full sample	6.233 * * * , IV rejected	6.140 * * * , IV rejected
	OECD countries	2.020 * * , IV rejected	2.384 * * , IV rejected
	Non-OECD countries 2.163 * * , IV rejected	2.129

* * , IV rejected Note. * * * p < 0.01, * * p < 0.05, * p < 0.1. See Tables

3, 4

and 5 for results of the different estimators.

Table 3 .

 3 Semiparametric estimations

		IVO		IVG		IV
	Coefficient	Estimate (Std. Err.) Estimate (Std. Err.) Estimate (Std. Err.)
	lag CO 2 per capita, α	.769 * * *	(.030)	.903 * * *	(.025)	.523 * * *	(.067)
	log GDP per capita, β 1	-		-		1.245 * * *	(.180)
	Squared log GDP per capita, β 2	-		-		-.058 * * *	(.010)
	Intercept	-		-		-
	Implied λ	.053 * * *	(.002)	.020 * * *	(.001)	.130 * * *	(.026)

Table 4 .

 4 Semiparametric estimations for OECD countries p<0.1; * * p<0.05; * * * p<0.01. Bootstrap (semiparametric) and robust (parametric) standard errors in parenthesis. The implied λ is calculated by the delta method. The sample includes 210 observations (N = 21 countries and T = 10 five-years periods).

		IVO		IVG		IV
	Coefficient	Estimate (Std. Err.) Estimate (Std. Err.) Estimate (Std. Err.)
	lag CO 2 per capita, α	.835 * * *	(.124)	.949 * * *	(.067)	.526 * * *	(.103)
	log GDP per capita, β 1	-		-		3.202 * * *	(.878)
	Squared log GDP per capita, β 2	-		-		-.165 * * *	(.043)
	Intercept	-		-		-
	Implied λ	.036 * * *	(.007)	.011 * * *	(.004)	.128 * * *	(.039)
	Number of observations	210		210		210
	Adjusted R 2					.740
	F -statistic					284.915 * * *
	Note.

*

Table 5 .

 5 Semiparametric estimations for non-OECD countries

		IVO		IVG		IV
	Coefficient	Estimate (Std. Err.) Estimate (Std. Err.) Estimate (Std. Err.)
	lag CO 2 per capita, α	.733 * * *	(.047)	.877 * * *	(.038)	.537 * * *	(.076)
	log GDP per capita, β 1	-		-		.429 * * *	(.130)
	Squared log GDP per capita, β 2	-		-		-.032 * * *	(.012)
	Intercept	-		-		-
	Implied λ	.032 * * *	(.004)	.026 * * *	(.003)	.124 * * *	(.028)
	Number of observations	850		850		850
	Adjusted R 2					.653
	F -statistic					493.465 * * *
	Note.

* p<0.1; * * p<0.05; * * * p<0.01. Bootstrap (semiparametric) and robust (parametric) standard errors in parenthesis. The implied λ is calculated by the delta method. The sample includes 210 observations (N = 21 countries and T = 10 five-years periods).

Table 6 .

 6 Results for high and low-income countries (Full Sample)

	Full sample	High income countries	Low income countries
		IVO	IVG	IV	IVO	IVG	IV
	lag CO 2 per capita, α	.677 * * * (.027)	.871 * * * (.042)	.483 * * * (.085)	.752 * * * (.019)	.861 * * * (.020)	.546 * * * (.104)
	log GDP per capita, β 1			2.684 * * * (.514)			.789 * * * (.332)
	Sq. log GDP per capita, β 2			-.133 * * * (.026)			-.031 (.021)
	Implied λ	.078 * * * (.002)	.027 * * * (.004)	.145 * * * (.035)	.057 * * * (.001)	.030 * * * (.001)	.121 * * * (.038)
	Number of observations	530	530	530	530	530	530
	Number of countries	53	53	53	53	53	53
	Adjusted R 2			.676			.633
	F -statistic			631.801 * * *			374.466 * * *

Table A1 .

 A1 List of countries

	Countries included
	Angola	Albania	Argentina	Australia *	Austria *
	Burundi	Belgium *	Benin	Burkina Faso Bulgaria
	Bahrain	Bahamas	Belize	Bolivia	Brazil
	Barbados	Bhutan	Canada *	China	Cote d'Ivoire
	Congo, Dem. Rep.	Congo, Rep.of Colombia	Comoros	Cape Verde
	Costa Rica	Cyprus	Djibouti	Dominica	Denmark *
	Dominican Republic Egypt	Spain *	Ethiopia	Fiji
	France *	Gabon	United Kingdom *	Ghana	Guinea
	Gambia	Guinea-Bissau Equatorial Guinea Greece *	Grenada
	Guatemala	Honduras	Hungary	Indonesia	Iran
	Iraq	Iceland *	Israel *	Italy *	Jamaica
	Jordan	Japan *	Kenya	Cambodia	St. Kitts & Nevis
	Korea, Rep. *	Lebanon	Liberia	St. Lucia	Luxembourg *
	Madagascar	Mali	Malta	Mongolia	Mauritania
	Mauritius	Malawi	Malaysia	Niger	Nigeria
	Netherlands *	Nepal	New Zealand *	Panama	Peru
	Philippines	Poland *	Portugal *	Paraguay	Romania
	Rwanda	Saudi Arabia	Senegal	Singapore	Sierra Leone
	El Salvador	Suriname	Sweden *	Swaziland	Syria
	Togo	Thailand	Trinidad & Tobago Tunisia	Turkey
	Uganda	United States * Venezuela	South Africa Zambia
	Zimbabwe
	Note: OECD countries are starred.
	B. Summary tables of the literature on EC and EKC hypothesis

Table B1 .

 B1 Review of selected studies on the EKC hypothesis

Table B2 .

 B2 Review of selected studies on EC

	Authors, year Countries/period Environmental indicators Model/Method Results	Strazicich and List (2003) 100 countries/60-1997 CO 2 emissions β conv./stochastic convergence Evidence of stoch. convergence	Nguyen-Van (2005) 100 countries/66-1996 CO 2 emissions β conv./distributional dynamics conv. in 26 industrialized countries	Aldy (2005) 111 countries/60-2000 CO 2 emissions σ conv./distributional dynamics conv. in OECD countries	Panopoulou and Pantelidis (2009) 128 countries/60-2003 CO 2 emissions Method of club convergence Existence of 2 conv. clubs	Brock and Taylor (2010) 173 countries/60-1998 CO 2 emissions β conv./distributional dynamics Evidence of β conv.	Criado and Grether (2011) 166 countries/60-2002 CO 2 emissions Distributional dynamics Mixte conv. dynamics	Criado et al. (2011) 25 Europ. countries/80-2005 SOX and NOX Theory and non-parametric method Support convergence	Li and Lin (2013) 110 countries/71-2008 CO 2 emissions Absolute adn condi. β conv. Mixte, β conv. within income class.	Camarero et al. (2013) 22 OECD countries/80-2008 Eco-efficiency, CO 2 em. Method of club convergence Mixte, 4 convergence clubs	Solarin (2014) 39 AF countries/60-2010 CO 2 emissions Absoluteβ and stoch. conv. Mixte, Stoch. conv. in 31 AF countries	Zhao et al. (2015) 30 provinces, China/95-2011 CO 2 em. intensity Cond. β conv (spatial dyn. panel) Cond. β conv. across provinces	Acaravci and Erdogan (2016) 7 regions/60-2011 CO 2 emissions Stoch. conv. (unit root) Stoch. conv. with structural breaks	Runar et al. (2017) 124 countries/1885-2010 CO 2 emissions Cond. β conv. Evidence of conv. for entire sample	Apergis and Payne (2017) 50 US States/97-2013 CO 2 intensity Abs. β conv., σ and stoch. conv. Mixte. Evidence of Abs. β, σ conv.	Barassi et al. (2018) 28 OECD countries/50-2013 CO 2 emissions Stoch. conv.(fractional integration) Weak evidence of Stoch. conv.	Spatial conv., spillovers effect Rios and Gianmoena (2018) 141 countries/70-2014 CO 2 emissions Cond. β conv., spatial conv. clubs	Evidence of β, σ conv. No stoch. Yu et al. (2019) 74 cities, China/05-2015 CO 2 intensity Cond. β conv., σ and stoch. conv.	Slower global conv. Country cond. conv. Fernández-Amador et al. (2019) 66 countries, 12 regions/97-2014 CO 2 em. intensity Cond. β conv (Bayesian model)	Mixte. 2 Conv. clubs for CA countries Apergis et al. (2020) 6 CA countries/71-2014 2 em. Energy intensity Club convergence, CO	Notes: * CA, and AF respectively stand for Central America and Africa.

Table C1 .

 C1 Decoupling EC from EKC analysis (IV estimations) p<0.1; * * p<0.05; * * * p<0.01. Robust standard errors in parenthesis.

	Full sample	EC	EKC
	lag CO 2 per capita, α	.873 * * * (.039)	log GDP per capita, β 1	1.929 * * * (.232)
	Implied λ	.027 * * * (.009)	Squared log GDP per capita, β 2	-.084 * * * (.014)
	Number of observations	1060		1060
	Adjusted R 2	.618		.208
	F -statistic	511.108 * * *		357.652 * * *
	Note.

*

Table C2 .

 C2 Decoupling EC from EKC analysis (IV estimations)

	OECD sample	EC	EKC
	lag CO 2 per capita, α	.471 * * * (.071)	log GDP per capita, β 1	7.011 * * * (.738)
	Implied λ	.151 * * * (.030)	Squared log GDP per capita, β 2	-.351 * * * (.038)
	Number of observations	210		210
	Adjusted R 2	.714		.296
	F -statistic	43.750 * * *		100.898 * * *
	Note.

* p<0.1; * * p<0.05; * * * p<0.01. Robust standard errors in parenthesis.

Table C3 .

 C3 Decoupling EC from EKC analysis (IV estimations)

	Non-OECD sample	EC	EKC
	lag CO 2 per capita, α	.931 * * * (.044)	log GDP per capita, β 1	1.388 * * * (.291)
	Implied λ	.014(.09)	Squared log GDP per capita, β 2	-.049 * * * (.017)
	Number of observations
	Adjusted R 2	.612		.224
	F -statistic	444.488 * * *		306.745 * * *
	Note.

* p<0.1; * * p<0.05; * * * p<0.01. Robust standard errors in parenthesis.

D. Results of comparing convergence rate λ between OECD and non-OECD countries

Table D1 .

 D1 Results of comparing convergence rate λ between OECD and non-OECD countries

Table E1 .

 E1 Results of the Hausmantest. | y i,t-1 , z it ) = 0 RE rejected FE vs IV E(u it | y i,t-1 ) = 0 FE rejectedNote. The second column describes the restriction under the H 0 . The last column describes the conclusions of the test. See TableC2for further results.

	Estimators	Hypothesis	Result
	RE vs FE	E(µ i

Table E2 .

 E2 Parametric regressionsNote. * p<0.1; * * p<0.05; * * * p<0.01. See Table5for further comments.

	Coefficient	RE	FE	IV-FE
	lag CO 2 per capita, α	.866 * * * (.011)	.674 * * * (.020)	.523 * * * (.067)
	log GDP per capita, β 1	.707 * * * (.102)	1.048 * * * (.154)	1.245 * * * (.180)
	Squared log GDP per capita, β 2	-.033 * * * (.006)	-.050 * * * (.009)	-.058 * * * (.010)
	Intercept	-3.448 * * * (.440)	-	-
	Implied λ	.029 * * * (.003)	.079 * * * (.006)	.130 * * * (.026)
	Number of observations	1060	1060	954
	Adjusted R 2	.968	.661	.649
	F -statistic	9695.065 * * *	656.643 * * *	844.618 * * *

Table F1 .

 F1 Results for high and low-income OECD countriesNote. * p<0.1; * * p<0.05; * * * p<0.01. Bootstrap (semiparametric) and robust (parametric) standard errors in parenthesis.

	OECD sample	High income countries	Low income countries
		IVO	IVG	IV	IVO	IVG	IV
	lag CO 2 per capita, α	.924 * * * (.096)	.991 * * * (.051)	.066 (.474)	1.016 * * * (.082)	1.058 * * * (.224)	.604 * * * (.111)
	log GDP per capita, β 1			2.393 (2.644)			2.444 * * * (.847)
	Sq. log GDP per capita, β 2			-.131 (.131)			-.127 * * * (.042)
	Implied λ	.016 * * * (.004)	.002(.002)	.544 (1.435)	-.003(.003)	-.011(.009)	.101 * * * (.037)
	Number of observations	110	110	110	100	100	100
	Number of countries	11	11	11	10	10	10
	Adjusted R 2			.335			.806
	F -statistic			53.556 * * *			224.547 * * *

Table F2 .

 F2 Results for high and low-income non-OECD countries per capita, α .648 * * * (.052) .876 * * * (.044) .522 * * * (.101) .763 * * * (.046) .878 * * * (.032) .543 * * * (.114) log GDP per capita, β 1 1.661 * * * (.579) .788 * * (.393) Sq. log GDP per capita, β 2 -.076 * * * (.030) -.031 (.026) Implied λ .086 * * * (.005) .026 * * * (.004) .130 * * * (.039) .054 * * * (.003) .026 * * * (.002) .122 * * * (.042)

	Non-OECD sample		High income countries		Low income countries
		IVO	IVG	IV	IVO	IVG	IV
	lag CO 2 Number of observations	430	430	430	420	420	420
	Number of countries	43	43	43	42	42	42
	Adjusted R 2			.659			.649
	F -statistic			467.168

* * * 308.938 * * *

This perspective, however, has some critics.[START_REF] Arrow | Economic growth, carrying capacity, and the environment[END_REF] and[START_REF] Stern | Economic growth and environmental degradation: The environmental Kuznets curve and sustainable development[END_REF] noted that the process is mainly driven by the reallocation of polluting economic activities from developed to developing countries, while[START_REF] Dasgupta | Confronting the environmental Kuznets curve[END_REF] noted that the argument does not apply to every pollutant.

This review does not cover studies on Granger causality between energy and growth, as our paper is about a different topic.

See Stern (2004),[START_REF] Azomahou | Economic development and CO 2 emissions: A nonparametric panel approach[END_REF],[START_REF] Kijima | Economic models for the environmental Kuznets curve: A survey[END_REF] and[START_REF] Bo | A literature survey on environmental Kuznets curve[END_REF] for a more detailed review on non-parametric EKC studies. As the purpose of our paper is not to systematically review the EKC literature, we only report some existing papers to motivate our approach. Other papers can be found in previous issues of journals in the field, like Ecological Indicators, Energy Economics and Renewable and Sustainable Energy Reviews, which can give more insights on parametric and non-parametric investigations on the EKC hypothesis using panel or time series data on various environmental indicators.

See Pettersson et al. (2014) for a survey on environmental convergence studies.

For example,[START_REF] Lee | Does one size fit all? A reexamination of the environmental Kuznets curve using the dynamic panel data approach[END_REF] estimate the convergence equation in levels rather than in logs which would be required to keep consistency with a standard convergence model (see[START_REF] Islam | What have we learnt from the convergence debate[END_REF]).

The conditional density represents the continuous analogue of the transition matrix. See[START_REF] Johnson | A nonparametric analysis of income convergence across the US states[END_REF][START_REF] Johnson | A continuous state space approach to 'convergence by parts[END_REF] and Nguyen-[START_REF] Nguyen-Van | Distribution dynamics of CO 2 emissions[END_REF] for estimation details.

Results obtained with τ =

are very similar.

[START_REF] Islam | What have we learnt from the convergence debate[END_REF] remarked the tension between the neoclassical and the general interpretation of the convergence parameters α and λ. This tension arises whenever additional regressors other than the lagged dependent variable are considered. In such a case, if the neoclassical derivation of equation (2) is considered, convergence towards each economy's steady-state and the reduction of cross-countries gaps do not longer coincide.

As stated, the scope of this study is to investigate the long-run relation between CO 2 emission and GDP. It does not investigate the determinants of CO 2 emissions, nor determine the ceteris paribus effect of GDP.

The parametric model can be also estimated using the GMM estimators developed by[START_REF] Arellano | Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations[END_REF],[START_REF] Arellano | Another look at the instrumental variable estimation of error-components models[END_REF] and[START_REF] Blundell | Initial conditions and moment restrictions in dynamic panel data models[END_REF], which work under the assumption that y i,t-1 and z it are weakly exogenous (or predetermined), i.e.E(u it | y i,t-1-s ) = E(u it | z is ) = 0, ∀s ≤ t.GMM estimates are reported in Appendix B. They however provide mixed results.

This issue would deserve to be studied in a further work.

See Baltagi and Li (2002) for more details.

The analysis would account for series nonstationarity if the time dimension T was high. In the empirical application as performed below, as we focus on the long-run relationship between variables by using observations corresponding to five-years periods (thus T = 10) in order to eliminate business cycle effects, our estimation is then less concerned by this issue. There exist very numerous EKC studies based on time series. For more details on them, one can refer to, e.g.,[START_REF] Bölük | The renewable energy, growth and environmental Kuznets curve in Turkey: An ARDL approach[END_REF], Ben[START_REF] Jebli | Testing environmental Kuznets curve hypothesis: The role of renewable and non-renewable energy consumption and trade in OECD countries[END_REF]), Ben Youssef et al. (2016),Apergis et al. (2017),[START_REF] Liu | The impact of renewable energy and agriculture on carbon dioxide emissions: Investigating the environmental Kuznets curve in four selected Asian countries[END_REF][START_REF] Zoundi | CO2 emissions, renewable energy and the environmental Kuznets curve: A panel cointegration approach[END_REF], to name just a few.

The bootstrap procedure generates R new samples of y * it , according to the parametric model. Then, both models (3) and (4) are estimated R times and the respective coefficients are obtained. For further details see[START_REF] Henderson | Nonparametric estimation and testing of fixed effects panel data models[END_REF].

See Appendix C for more details on the test results and the RE and FE estimations.

Results of IV estimates are reported in Table3for comparison purposes. We thank an anonymous reviewer for this suggestion.

Other parametric estimators except the IV (i.e. RE, FE, GMM) give results of comparable magnitude. See also Appendices B and C for more details.

We also dissociate the EKC and EC analysis and observed results very comparable to those of tre IV estimator (see TablesC1, C2 and C3). We thank an anonymous reviewer for this suggestion.

We rely on sample median value of income per capita to dissociate HIC and LIC.

Recalling again[START_REF] Islam | What have we learnt from the convergence debate[END_REF] argument on the interpretation of a conditional convergence equation, we may state that countries are converging towards their own steady-states which do not need to coincide each other. Results in Section 2 are consistent with this interpretation

All the parametric models are estimated allowing for individual effects. Including time effects does not change the results for the RE GLS, FE within, and IV estimators as they are not statistically significant.

Acknowledgements: We are grateful to Michael Hübler, Stefan Stoeckl, and participants at the EAERE 2016 (Zurich, Switzerland), the AFSE 2016 (Nancy, France), the ISEM 2019 (Salzburg, Austria), and several seminars for their useful comments and suggestions. The usual caveat applies.