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Economic Growth and Air Pollution: Three Empirical Essays Based on Nonparametric Methods These presentee a la Faculte des sciences economiques Universite de Neuchatel Pour l’obtention du grade de docteur es science economiques Par Carlos Ordas Criado Acceptee sur proposition du jury de these: Prof. Jean-Marie Grether, Universite de Neuchatel, directeur de these. Prof. Jaime de Melo, Universite de Geneve, co-directeur de these Prof. Thanasis Stengos, University of Guelph Prof. Philippe Thalmann, Ecole Polytechnique Federale de Lausanne Prof. Milad Zarin-Nejadan, Universite de Neuchatel, president du jury Soutenue le 9 mars 2009
Neuchatel, 2009 . . Les propos et opinions exprimes dans ce document n’engagent que son auteur et en aucune maniere la Faculte des Sciences Economiques de l’Universite de Neuchatel. . English abstract Abstract: this dissertation includes 3 research papers, which explore empirically the link between the level of economic activity and air pollution at the macroeconomic level. A special emphasis is given to the application of recent tools developed in the nonparametric ? eld as they allow for a better control of potential misspeci? cation biases and they give more ? exibility to the underlying relationships.
Chapter 1 tests whether a sustainable link between per capita GDP levels and the environment exists for a variety of air pollutants’ emissions in a panel of 48 Spanish provinces over the period 1990-2002. Chapter 2 investigates how cross-country gaps in per capita CO2 emissions evolved over the 1960-2002 period for a panel of 166 world areas as well as for several country sub-groupings (rich/poor countries, speci? c geographic regions, economically integrated areas). An analysis of the dynamic of the cross-sectional distributions is conducted with robust scale and shape measures and formal shape and multimodality tests are applied.
The latter approach is contrasted with a stochastic convergence analysis a la Evans (1998). Chapter 3 makes use of a broad range of regression techniques to ? t a reduced form function, where growth rates in per capita CO2 emissions are explained with past pollution levels, past per capita GDP levels and per capita GDP growth rates. Panel models are estimated with standard linear and nonlinear least squares and these speci? cations are tested against their nonparametric counterpart. This framework also allows exploring beta-convergence in per capita emissions conditional on GDP as well as beta-convergence in GDP conditional on pollution.
Keywords: Air pollution, carbon dioxide emissions, Environmental Kuznets Curve, convergence, distributional dynamics, mixed nonparametric and semiparametric regressions, panel poolability test, unit roots. . Resume en francais Resume : cette these se compose de 3 recherches dont l’objectif est l’etude empirique du lien entre croissance economique et pollution atmospherique au niveau macroeconomique. Elle privilegie l’utilisation d’outils recents issus de l’analyse nonparametrique car ils permettent une meilleure prise en compte de biais de mauvaise speci? cation et introduisent plus de ? exibilite dans la forme fonctionnelle etudiee.
Le premier chapitre veri? e l’existence d’une relation soutenable entre le niveau de PIB par tete et l’environnement dans 48 provinces espagnoles pour di? erents polluants de l’air durant les annees 1990-2002. Le second chapitre s’interesse a l’evolution des di? erences de niveau d’emissions de CO2 par tete entre 1960 et 2002 dans 166 pays, ainsi que dans divers sous-ensembles de pays (riches/pauvres, appartenant a une meme zone geographique, membres d’une zone d’integration regionale. . . ). La dynamique des distributions transversales est etudiee a l’aide de mesures robustes d’echelle et de forme fonctionnelle.
Des tests d’egalite distributionnelle et de multi-modalite sont egalement appliques pour tester la stationnarite des densites et l’emergence de di? erents modes. Ces resultats sont compares a ceux obtenus a l’aide d’une analyse de convergence stochastique a la Evans (1998). Le dernier chapitre applique un large spectre de techniques de regressions a l’estimation d’une forme fonctionnelle reduite, dans laquelle la croissance des emissions de CO2 par tete est fonction du niveau passe d’emissions par tete, du niveau passe de PIB par tete et du taux de croissance du PIB par tete.
Des modeles de panel sont estimes par les moindres carres ordinaires et les moindres carres non-lineaires et ces speci? cations sont comparees a des modeles non-parametriques alternatifs. Ce cadre permet egalement d’explorer la notion de beta-convergence dans la pollution, conditionnelle au PIB, ainsi que la beta-convergence dans le PIB, conditionnelle a la pollution. Mots cles : Pollution atmospherique, emissions de CO2, Courbe de Kuznets Environnementale, convergence, dynamique distributionnelle, regressions non et semiparametrique melangees, test d’empilement de panel, racine unitaire. Acknowledgements
I would like to express my deepest gratitude to Prof. Jean-Marie Grether and Prof. Jaime de Melo who inspired me in the ? eld of economics and allowed me to undertake the present research under their supervision and ? nancial support. Many thanks for your trust, your encouragements in all aspects of my work, your critical feedbacks and the time spent reading the numerous drafts of my research papers, under tight time constraints sometimes. I am warmly grateful to Prof. Milad Zarin-Nejadan (University of Neuchatel) and to Prof. Thanasis Stengos (University of Guelph, Canada) for co-supervising my work as well as for their kindness.
Prof. Thalmann (University of Lausanne) has also accepted to provide his expertise to this work, which I am sincerely indebted. The Institute for Research in Economics from the University of Neuchatel (Irene) has been the memorable place where I have shared my joys, doubts, e? orts and my desk with stimulating colleagues, who have become friends. Thank you to Martine, Francoise and Kira for their help and smiles in all circumstances, and for making our institute feeling like a home. Mathieu, Johanne, Sonia, Gilles and Moez have very much contributed to make that time unforgettable, pushing me to ? d the right balance between work and refreshing breaks. My sincere acknowledgments also go to our IT scientists, Abdel, David and Florian, as well as to our library sta? , Denis, Sandra and Rene for always providing the quick and ? exible support needed in my task. I owe a great debt to my friend David Ardia, for the passionate talks on many technical aspects of my work, going from statistical/econometric issues to a variety of computational problematics (in the R and Latex environments in particular). His expertise has been a great asset.
I had the chance to spend a year of my PhD program visiting several Economic Departments in Canada (at the University of Guelph, the University of Toronto and the University of Calgary) under a grant kindly provided by the Swiss National Science Foundation. Thanks a million to the many people who made my visits possible and for having provided all the facilities for my researches. Least but not last, my family has always been by my side in this academic adventure. Thanks Dad, Javier and Ivan for being there when I was absorbed in my dissertation. Javier has been kind enough to revise the English drafts of my papers.
Thank you Joelle for your love, support and optimism. Carlos Ordas Criado . A la memoria de mi madre, Rosalia, a mi hermanito Ivan. . Contents Introduction 3 1 Temporal and Spatial Homogeneity in Air Pollutants Panel EKC Estimations. Two Nonparametric Tests Applied to Spanish Provinces. 7 1. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1. 2 Income-pollution relationship: from theory to empirics . . . . . . . . . . . 10 1. 3 The nonparametric approach . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 4 Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1. 5 Econometric analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1. 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1. 7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1. 7. 1 List of Spanish Provinces . . . . . . . . . . . . . . . . . . . . . . . 31 1. 7. 2 mth-order di? erencing estimator and optimal di? erencing weights . 31 1. 7. 3 Baltagi et al. (1996)’s nonparametric poolability test . . . . . . . . 32 2 Convergence-clubs in per capita CO2 emissions. Who’s converging, who’s diverging? 5 2. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2. 2 Empirical literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2. 2. 1 Convergence measures . . . . . . . . . . . . . . . . . . . . . . . . . 38 2. 2. 2 Convergence in carbon emissions . . . . . . . . . . . . . . . . . . . 40 Descriptive analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2. 3. 1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2. 3. 2 Historical trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2. 3. 3
Evolution of cross-section distributions . . . . . . . . . . . . . . . . 53 2. 3 2. 4 Time series analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2. 4. 1 Panel based tests for convergence . . . . . . . . . . . . . . . . . . . 70 2. 4. 2 Econometric results . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2. 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2. 6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 1 2 CONTENTS 3 Growth and convergence in air pollution. Evidence from a reduced form nonparametric approach. 99 3. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3. 2 Theoretical model 3. 3 Empirical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3. 3. 1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 3. 3. 2 Econometric methods . . . . . . . . . . . . . . . . . . . . . . . . . 114 3. 3. 3 Growth regressions . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 3. 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 3. 5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 General conclusion 135 List of Tables 141 List of Figures 143 Bibliography 145 Introduction While the environmental impacts of economic activity has become a major source of concern for policy makers, economists try to shed some light on the forces which shape the link between economic growth and pollution, both theoretically and empirically. This dissertation explores the latter side of the problematic at the macroeconomic level. It includes three applied essays which make use of recent econometric tools, mainly developed in the nonparametric ? ld, to examine the relationship between economic growth and air pollution both at the national level and in an international context. My ? rst essay investigates the link between the level of economic activity and air pollutants’ emissions, by focusing exclusively on per capita GDP and emissions levels. This simple bivariate model has generated a huge amount of interest in the empirical literature. Theoretically speaking, it may be seen as representing a reduced form function in which income in? uences technology, the scale and composition of output, and the demand for environmental quality. Changes in these factors in turn in? ence environmental pressure. This single equation implicitly assumes no feedback e? ect of environmental damages on the level of economic activity, it is static and it captures only instantaneous or short run e? ects of income on pollution. Indeed, the model is essentially descriptive and it does not provide any answer on whether the expected positive impact of a wealth increase on environmental quality is achieved by more stringent environmental policies or by autonomous structural and technological changes that are related to economic growth. Despite these limitations and di? culties in disentangling causal e? cts, this formulation tests ultimately the existence of a sustainable dynamics between economic growth and pollution, i. e. a steady increase in per capita income and in environmental quality. Among the many possible sustainable patterns, the U-inverted shape, also known as the Environmental Kuznets Curve (EKC henceforth), has been the most investigated and debated pattern. It posits an increasing pressure on natural resources at early stages of economic expansion which later stabilizes and ultimately declines as people get richer and the economy becomes more e? cient. This is the so called ‘EKC hypothesis’.
My ? rst paper proposes a strategy to check if the most common model used with panel data to test the EKC hypothesis provides consistent estimates of the income-pollution relationship for most of the individual countries/regions included in the panel. I employ nonparametric regressions to avoid a misspeci? cation bias when ? tting the data. Indeed, given the complexity of the income-pollution relationship, it is di? cult to specify a priori the correct function 3 4 Introduction which uncovers that link. Nonparametric methods let the data dictate the shape of the latter function by optimizing some ? criteria. With the help of a panel of 48 Spanish provinces on four air pollutants that covers the years 1990 to 2002, I explicitly show that EKC patterns can be found with non, semiparametric or cubic ? xed e? ects models even when the income-pollution pattern is decreasing, stabilized or even increasing over time for most of the provinces. I argue that the time and spatial homogeneity of the panel should be checked before making any inference on the shapes estimated with pooled or ? xed e? ects regressions. The U-inverted functions that I ? d in the Spanish dataset for all the pollutants appear to be consistent estimates of cross-sectional regressions for all the years of the panel. But these estimates do not depict time-series ? ts for the regions; they do not re? ect at all the income-pollution trends in the regions for the investigated period. The other two essays analyze whether carbon dioxide per capita emissions’ levels are converging across countries. We focus on pollution convergence (in air pollution per capita levels) for two essential reasons. First, among the many policy measures put forward to mitigate global warming in the post-Kyoto e? rt, a signi? cant number of proposals rely on per capita emissions targets. The supporters of that approach defend the fairness of this allocation scheme (‘each individual should have the same right to pollute’). This principle ignores speci? c structural characteristics of the countries and it is debatable whether or not it constitutes an e? cient approach. However, its operational simplicity and ability to set a ‘unifying principle that facilitates an international greenhouse warming agreement’ (Rose and Stevens, 1996, p. 2-3) between governments has attracted institutional support.
Finding convergence in per capita emissions worldwide or between groups of countries may thus be of particular interest in policy circles. Second, from a more theoretical perspective, several authors have amended standard macroeconomic growth models with pollution components and links have been established between income and pollution convergence. Investigating pollution growth with macroeconomic reduced form functions allow to analyze the relevance of these models, and to explore pollution growth and convergence at the same time within theoretically derived speci? cations. Di? rent tools exist to measure convergence in macroeconomic series. My second essay explores convergence in per capita CO2 emissions, at the world-wide level and also within di? erent subsets of countries, by focusing exclusively on the three main univariate convergence measures: sigma, stochastic and distributional convergence. My ? rst con- Introduction 5 tribution in that paper is to widely expand the number of countries used so far in the empirical literature on per capita carbon emissions’ convergence, in order to generate systematic groupings of countries, based on income, geographic and economic integration criteria.
Then recent exploratory methods are applied in the distributional as well as the stochastic convergence approach. The former analysis is essentially descriptive and relies on robust scale and shape indicators as well as distributional tests to evaluate changes in the cross-sectional distributions over time. The latter stochastic analysis is carried out essentially based on unit root tests combined with the concept of pair-wise convergence introduced by Evans (1998). Overall, signi? cant di? rences emerge in the cross-sectional distributions over time, mainly between those from the pre and post-70s oil shocks period, for the world as well as for di? erent groupings of countries. The distributional analysis provides little evidence of a strong polarization in national carbon series. Moreover, the evolution of the distributional patterns are di? cult to interpret in terms of conditional convergence. By contrast, the stochastic convergence analysis identi? es converging economies at the world-wide levels as well as for many country groupings.
Finally, the last essay employs the database on per capita CO2 emissions constructed in the second essay to explore growth and ? -convergence in carbon dioxide per capita emissions in a multivariate setting, i. e. with the help of the growth model with pollution of Alvarez et al. (2005). These authors derive in a simple way a reduced form function from a model a la Ramsey that allows to examine growth as well as ? -convergence in pollution, conditional on income levels and growth rates. Moreover, by simply reverting the correlation scheme and accounting for potential simultaneity bias with instrumental variables, I also explore growth and ? convergence in GDP, conditional on pollution levels and growth rates. The analysis is carried out in a panel framework, with a variety of regression techniques: ordinary least squares, nonlinear least squares, semi and nonparametric regressions. The original test equation is augmented with time and OECD dummies for the empirical treatment. A recent nonparametric speci? cation test is applied to check whether the functional constraints imposed by the theoretical model is supported by the data. I ? nd that parametric models are in general misspeci? d and that nonlinearities and interactions between the variables are better captured with non or semiparametric regressions. Fully nonparametric estimates, which involve discrete and continuous explanatory factors, show interesting interactions between the OECD status and the main explanatory continuous variables. They also indicate that convergence in per capita pollution levels across countries may happen between countries which experience increasing income dis- 6 Introduction parities. The structure of this dissertation is as follows. The three essays discussed n the above paragraphs are presented in chapters 1, 2 and 3 respectively. Special contributions to the essays are acknowledged after the conclusion of each chapter. Most Tables and Figures are included in the text but some additional information is provided in appendices located at the end of each chapter. The complete list of all Tables and Figures can be found at the end of the dissertation. We end the dissertation with a brief general conclusion, where we suggest further extensions. The bibliography includes all the papers cited along the three chapters.
Finally, most of the computations have been carried out in the R Development Core Team (2007) statistical environment. The code is available upon request. Chapter 1 Temporal and Spatial Homogeneity in Air Pollutants Panel EKC Estimations Two Nonparametric Tests Applied to Spanish Provinces Editorial note: A short version of this paper has been published in Environmental and Resource Economics 1 . Abstract: Although panel data have been used intensively by a wealth of studies investigating the GDP-pollution relationship, the poolability assumption used to model these data is almost never addressed.
This paper applies a strategy to test the poolability assumption with methods robust to functional misspeci? cation. Nonparametric poolability tests are performed to check the temporal and spatial homogeneity of the panel and their results are compared with the conventional F-tests for a balanced panel of 48 Spanish provinces on four air pollutant emissions (CH4 , CO, CO2 and NMVOC) over the 19902002 period. We show that temporal homogeneity may allow the pooling of the data and drive to well-de? ned nonparametric and parametric cross-sectional U-inverted shapes for all air pollutants.
However, the presence of spatial heterogeneity makes this shape compatible with di? erent time-series patterns in every province – mainly increasing or decreasing depending on the pollutant. These results highlight the extreme sensitivity of the income-pollution relationship to region-speci? c factors. JEL classi? cation: C14 ?? C23 ?? O40 ?? Q53 Keywords: Environmental Kuznets Curve, Air pollutants, Non/Semiparametric estimations, Poolability tests 1 See http://www. springerlink. com/content/f456761736487wt5/? p=f6f8f73015844ddfbd51f0b30921e0d2=0 7 8 Chapter 1.
Poolability in EKC panels 1. 1 Introduction In the last ? fteen years the relationship between economic growth and environmental quality has been one of the most investigated issues in the empirical literature. Air, water or land pollution, global warming or resources depletion are clearly related to human activities but the nature of that link remains highly controversial. The most famous example is probably the Environmental Kuznets Curve (EKC), which posits an U-inverted relationship between some measure of economic activity and environmental damage.
The existence of that hump-shaped pattern has been challenged by a plethora of empirical research, particularly for atmospheric pollutants. Two main caveats a? ect the empirical estimation of the income-pollution relationship. Firstly, economic theory suggests that the reduced form function postulated by the EKC hypothesis may not have a simple and unique functional shape. Secondly, even if a single function were to exist, it would be very sensitive to country or region speci? c factors, such as : factor endowments, sources of growth, di? rences in technology, social sensitivity to environmental damages, etc. These two characteristics have oriented the current empirical investigations on the income-pollution relationship in two directions: (i) parametric speci? cations have been replaced by nonparametric ? tting methods to avoid functional misspeci? cation; and (ii) controlling for heterogeneity in panel data has become a fundamental issue in obtaining unbiased estimates. The vast majority of EKC’s empirical papers use panel data structures (i. e. data on individual countries/regions observed over time).
These papers make use of all the data points to get estimates of a common functional form to all countries/regions up to some deterministic vertical shift speci? c to every country/region or year of the panel. These panel data models are referred to as ? xed e? ects and their estimates are said to be pooled because a unique function is assumed to hold for all countries or regions or years up to some intercept term. In most cases, and whether the functional form is parametrically speci? ed or not2 , no formal check of the homogeneity assumption is provided on the time (i. . stability of the cross-sectional regressions over time) and the spatial (i. e. equality of the time-series regressions across countries/regions) dimensions of the panel. Yet, 2 For parametric speci? cations, see among others Selden and Song (1994), Grossman and Krueger (1995), Holtz-Eakin and Selden (1995), Schmalensee et al. (1998), Heil and Selden (2001), De Groot et al. (2004) or Aldy (2005); for non- or semiparametric ones, see Taskin and Zaim (2000), Millimet et al. (2003), Bertinelli and Strobl (2005) or Azomahou et al. (2006). 1. 1.
Introduction 9 this assumption is crucial to get robust and unbiased estimates. Moreover, among the few authors who have tackled this issue3 for di? erent kinds of environmental damage, con? icting results have been reached for CO2 emissions data. Dijkgraaf and Vollebergh (2005), for the 24 OECD countries, overwhelmingly reject the hypothesis of homogeneous income-pollution relationship between regions/countries made in the ? xed-e? ects panel data models commonly used in the literature. Pooled estimates are consequently rejected. Azomahou et al. 2006) reach the opposite conclusion when checking the temporal poolability on a much larger panel of 100 countries with a poolability test robust to functional misspeci? cation. This discrepancy may be attributed to the di? erent procedures used; but it also raises a more fundamental question: to what extent is temporal homogeneity compatible with spatial heterogeneity? This research contributes to the recent empirical literature on the EKC curve by testing for the ? rst time the adequacy of the homogeneity assumption on both the temporal and the spatial dimensions with nonparametric tests robust to functional misspeci? ation. Following Azomahou et al. (2006), we make use of Baltagi et al. (1996)’s nonparametric poolability test to check the temporal homogeneity of a panel on anthropogenic emissions of four air pollutants (CH4 , CO, CO2 and NMVOC) for the Spanish provinces over the 1990-2002 period. These pollutants are particularly interesting as they display di? erent growth aggregate patterns over the investigated period. Furthermore, we apply the simple procedures of Yatchew (2003) to check the equality of non- and semiparametric estimations of the income-emissions relationship (IER) at the regional level.
This allows us to verify the spatial homogeneity hypothesis with a method robust to functional misspeci? cation. We compare the results provided by the standard F-tests procedures applied to the quadratic and cubic models to our nonparametric tests. We are able to con? rm the existence of robust and stable cross-sectional EKCs over time for most of the air pollutants investigated. However, this does not mean that every province displays the same IER for a given pollutant; for all of them, we ? nd that the spatial homogeneity hypothesis is overwhelmingly rejected.
We show explicitly that stable cross-sectional EKCs are perfectly compatible with either increasing or decreasing emissions in most of the regions depending on the pollutant. Consequently, pooled EKC estimates are compatible with all kinds of IERs at the most aggregated level. These results con? rm the warnings made by de Bruyn et al. (1998) regarding the interpretation of the EKC shapes found with pooled panel data 3 See List and Gallet (1999), Koop and Tole (1999), Dijkgraaf and Vollebergh (2005) or Aldy (2005) or Azomahou et al. (2006) 10 Chapter 1. Poolability in EKC panels models.
The structure of this paper is as follows. Section 1. 2 o? ers a brief survey of the main theoretical determinants of the income-pollution relationship. It includes a review of empirical literature focused on CO2 -IER encapsulating the main econometric issues which are linked to EKC estimates for other pollutants. The main ? ndings for IER estimations on air pollutants with panel data at low level of geographical aggregation are also provided. Section 1. 3 presents the econometric strategy. The Spanish data are described in Section 1. 4 and Section 1. 5 shows the econometric results. We present our conclusions in Section 1. . 1. 2 Income-pollution relationship: from theory to empirics Most of the empirical studies4 investigating the relationship between the level of economic activity and some pollution indicator have faced two main issues: de? ning the functional shape to be estimated; and getting robust estimates despite the short time series available. Theoretical background. As Copeland and Taylor (2003) point out, in the absence of change in the structure and technology of the economy, increasing economic activity would result in an equiproportionate growth in pollution or other environmental impacts.
This ‘scale’ e? ect suggests a monotonically increasing relationship between real GDP and pollution and makes economic growth and sustainable development two con? icting goals. However, economic growth generates technological progress; polluting inputs are used more e? ciently in the production process or through abatment technologies. If the ‘technical’ e? ect is strong enough to o? set the scale e? ect, economic growth is compatible with less pollution and the link may become locally decreasing.
Three other mechanisms also lead to changes in the output composition of countries: unbalanced growth processes of production factors; biased technological progress between industries or variations in relative world prices. These specialisation patterns between unequally pollution-intensive sectors are usually referred to as ‘composition’ e? ects. The sources-of-growth explanation of the 4 See Brock and Taylor (2004a) for an empirical and theoretical review of the literature on the relationship between economic growth and the environment or Stern (2003) for the EKC literature. . 2. Income-pollution relationship: from theory to empirics 11 EKC shape relies on that particular argument. If economic growth is ? rst induced by accumulation of a production factor (capital) used relatively more intensively in a polluting sector but then shifts toward accumulation of a factor (labor or human capital) more intensively used in a less or non polluting sector, a straightforward application of Rybczinsky’s theorem leads pollution to follow the same path as the production of the polluting good, an U-inverted pattern.
A similar argument can be used to explain why capital abundant economies (rich countries) are expected to pollute more than labor-abundant ones (poor countries). All these supply side arguments have two major implications. Firstly, economic growth may not require any environmental policy measure to be compatible with a more e? cient use of polluting inputs or natural resources. Secondly, as Copeland and Taylor (2003, Ch. 3. 1) indicate, we can have a stable relationship between pollution and technology and primary factors, and between income and these same variables, without having a simple and stable relationship between ollution and income. In plain words, the same level of income may be linked to di? erent levels of pollution, depending on the factor which generated this income level. From a social point of view, the willingness to tolerate the inconveniences of pollution in order to increase income plays a major role in determining the strength of policy responses to environmental damages. Consequently a pure scale e? ect generated by neutral growth could be overcome by environmental policy measures if, at some level of income, the relative willingness to pay for pollution reduction exceeds the relative growth in income5 .
The income-pollution relationship is also sensitive to the way pollution is measured (i. e. in levels, per capita or intensity terms), as well as to the level of spatial aggregation of the data. In this paper, we focus on per capita levels of pollution as it represents the most common speci? cation of the dependent variable in the IER literature on air pollutants. Empirical estimations. Given the variety of theoretical foundations, no single functional form can be advocated a priori to link indicators of environmental degradation with measures of economic activity.
As the income-pollution relationship is a reduced form function, all the underlying forces which determine its shape for a particular geographical area are subsumed, i. e. they remain unexplained. The early empirical IER literature has addressed the functional uncertainty by retaining three main parametric ? exible speci? cations: quadratic and cubic functions which capture nonlinearities and spline linear 5 This is usually referred to as an income elasticity of marginal damage greater than one in the literature. 12 Chapter 1. Poolability in EKC panels functions which gauge thresholds e? cts. More recently, researchers have turned to nonparametric and semiparametric regressions which leave the functional form unspeci? ed and avoid the risk of choosing an inadequate parametric function. Moreover, the lack of long time series on pollutants at the country level has made authors favour cross-country/region panel data. The absence of a range of explanatory variables which consistently capture the di? erences between countries may lead to biased estimates. This heterogeneity issue has been neglected in most of the parametric and nonparametric analysis of IER panels.
Moreover, when it has been investigated, the F-tests used were not robust to functional misspeci? cation. Consequently, the estimated IER appears to be highly sensitive to the pollutant or environmental damage considered, to changes in the sample composition (size or/and time periods considered) and to di? erences in econometric speci? cations. The case of air pollutants is suggestive, particularly the one for CO2 emissions. Many authors make use of di? erent versions of the database from the Carbon Dioxide Information Analysis Center (CDIAC) to test the EKC hypothesis with a panel of world countries.
Holtz-Eakin and Selden (1995) (HES95), Heil and Selden (2001) (HS01) and Schmalensee et al. (1998) (SSJ98) use similar countries’ panel data sets including over 120 countries and covering roughly 40 years6 ; they estimate time- and country-? xed e? ects quadratic functions (HES95 and HE01) and a spline-regression model with the same ? xed e? ects (SSJ98). HES95 and HE01 ? nd U-inverted shapes with very di? erent turning points, ranging from US$35,000 to several millions depending on whether per capita income and emissions are measured in levels or in logarithms. SSJ98 get a within sample maximum of US$10,000 with a 10-segment regression.
A nonparametric pooled regression is used by Taskin and Zaim (2000) to investigate the link between a CO2 environmental e? ciency index and GDP per capita for 52 countries over 1975-1990. Their results point towards a third order polynomial speci? cation. A semiparametric version of the time- and country? xed e? ects models used by HES95, HS01, and SSJ98 is estimated by Bertinelli and Strobl (2005) for a panel7 of 122 countries over the 1950-1990 period. They ? nd that the pooled regression are monotonically increasing. Recently, Dijkgraaf and Vollebergh (2005) and Azomahou et al. 2006) tackle the fundamental assumption of poolability for CO2 -IER panels in parametric or nonparametric 6 HES95, HE01 and SSJ98 make use of respectively 130, 135 and 141 countries and the time span is 1951-1986, 1951-1992 and 1950-1990. 7 In that case, the data come from the World Resource Institute. 1. 2. Income-pollution relationship: from theory to empirics 13 frameworks respectively. Focusing on the sample of 24 OECD countries mainly responsible for the U-inverted shape found in HES95, HS01 and SSJ98, Dijkgraaf and Vollebergh (2005) compare directly di? erent versions of ? xed-e? cts models to country-speci? c timeseries regressions (with and without trends) and conclude that less than half (11) of the OECD countries display the U-inverted shape depicted by the pooled ? xed-e? ects estimates. Azomahou et al. (2006) check the structural stability of the per capita IER with a nonparametric poolability test for a panel of 100 countries over the 1960-1996 period. They conclude that there is a stable cross-sectional relationship through time which allows the pooling of the data. The pooled country-? xed e? ects nonparametric regression displays a monotonically increasing pattern.
In addition, nonparametric estimates are shown to be preferred to parametric ones. Some authors have carried IER estimates with panels at low level of spatial aggregation. List and Gallet (1999) use state levels of SO2 and NOx emissions for the US spanning from 1929 to 1994. They estimate IERs with per capita data and a linear trend. The state-? xed e? ects models produce global EKCs for all states; quadratic and cubic state-speci? c regressions also yield a majority of respectively 79% and 98% hump-shaped functions for SO2 emissions and a rough 80% EKCs for NOx with both speci? cations. However, the vast majority of the state-speci? turning points fall outside the con? dence interval for the peak produced by the ? xed-e? ects models. With the same data, Millimet et al. (2003) compare pooled time- and individual-? xed e? ects cubic models and spline regressions with time- and state-? xed e? ects semiparametric speci? cations8 . They show that while the EKC obtained for per capita NOx emissions is robust to the estimation strategy, the functional forms for SO2 vary substantially. However, the null hypothesis of equality between the spline or cubic models and the partial linear models is rejected for both pollutants.
These authors also compute speci? c semiparametric estimates for selected US states9 and they conclude that the EKC shape remains robust at the state level for NOx , but the results for SO2 are mixed. De Groot et al. (2004) utilise a panel dataset on Chinese provinces covering the period 1982-1997. They investigate the IER for wastewater, waste gas (aggregate emissions of CO2 , NOx and SO2 ) and solid waste from the industrial sector with the pooled region-? xed e? ects model. They contrast the results obtained when expressing the dependent variable in levels, per capita and intensity terms. The linear trend from state-? xed e? ects cubic models of List and Gallet (1999) are here replaced by time-? xed e? ects. 9 The time-? xed e? ects are replaced by state-speci? c linear time trends. 14 Chapter 1. Poolability in EKC panels The relationship is shown as being monotonically decreasing for wastewater regardless of the dependent variable, increasing (respectively decreasing) for waste gas with the explained variable in levels or per capita (respectively intensity) terms and very versatile for solid waste depending on the dependent variable used.
More recently, Aldy (2005) tests the EKC hypothesis for production as well as consumption-based per capita CO2 emissions in the US at the state level. The author globally validates the EKC shape with the stateand year-? xed e? ects quadratic models as well as with the spline regressions. He provides evidence of signi? cant di? erent peaks for both CO2 series. When state-speci? c quadratic models are ? tted, the equality of the estimated functions and EKC peaks between states is rejected despite the fact that the vast majority of the states does depict EKC-type relationships.
Since the data span over a long time period, Aldy (2005) also controls for common stochastic trends in the time-series and concludes that only about 20% of the state-speci? c relationships were cointegrated10 . 1. 3 The nonparametric approach The previous EKC literature has not tested the appropriateness of the homogeneity assumption on both the cross-section and the time dimensions of panel data sets in a nonparametric framework. This section proposes a simple strategy to ? ll this gap. Let us de? ne a very general functional relationship between one pollutant and an income indicator in a panel framework: it = git (yit ) + oit with i = 1, . . . , N ; t = 1, . . . , T (1. 1) where pit represents per capita emissions for some pollutant in state i at time t, yit and git () are respectively the per capita income and an unspeci? ed heterogeneous function 2 for state i and time t and oit is an iid(0, ?? ) error term. As reported by Vollebergh et al. 2005, equation (1. 1) cannot be identi? ed without further restrictions, since for each (i,t) combination one single observation (yit , pit ) is available. Following Hsiao’s F-test strategy (2003, Ch. ) for the parametric case, we can identify git () by imposing some general homogeneity assumptions on the cross-sectional and time dimensions. We can assume that git () is constant over time but varies across states, thus git () = gi (). Alternatively, 10 This result con? rms the concerns raised by Perman and Stern (2003). 1. 3. The nonparametric approach 15 we can make the assumption that git () is constant across states but varies over time, thus git () = gt (). Therefore, two tests can be formulated : H0 : gi (yit ) = gj (yit ), ? i, ? j H1 : gi (yit ) = gj (yit ), for some i = j H0 : gt (yit ) = gs (yit ), ? s, ? t ? H1 : gt (yit ) = gs (yit ), for some t = s ? H0 is the individual or spatial homogeneity hypothesis and H0 is the temporal homo? geneity hypothesis. Given that H0 is assumed to hold when testing H0 (and vice-versa), ? accepting either H0 or H0 yield to the same pooled regression pit = g(yit ) + oit . A number of procedures exist for testing equality of nonparametric regressions functions. Yatchew (2003) suggests a simple nonparametric test which compares the weighted sum of the residual variance of every individual nonparametric regressions (i. the unrestricted residual variance s2 ) with the residual variance of the nonparametric pooled estimate (i. e unr the restricted residual variance s2 ). res ? Under H0 or H0 , the pooled estimates (? N P pool ) at some per capita income level y0 pit can be computed by the Nadaraya-Watson estimator: g(y0 ) = ? wit (y0 )pit = i,t NT yit ? y0 1 K( ? )pit NT yit ? y0 1 K( ? ) (1. 2) where K() is a kernel function and ? is the bandwidth. We estimate the pooled nonparametric11 regression by using a cross-validation12 bandwidth and a gaussian kernel and we calculate its residual variance (s2 ) by simply averaging the sum of squared residuals. es ? Under H1 (H1 ), there exist Q = T cross-sectional (Q = N time-series) distinct non11 Equation (1. 2) shows explicitly the intuition behind nonparametric regressions. The estimated conditional mean at the local point y0 , E(pit |y0 ) = g(y0 ), is a weighted average of all N T pit ? values of the panel, with weights inversly proportional to the distance between each of the N T yit observations of the independent variable and the local value y0 . The kernel function K() is a density-shaped function which de? nes the weights while the ? erm simply determines how many of the N T yit points are included in the neighborhood of y0 to compute the local conditional mean. The larger the bandwidth ? , the closer each local conditional mean to the unconditional mean and the smoother the estimate. 12 In large samples, selecting ? through cross-validation is the same as computing the bandwidth that minimizes the integrated mean-squared error. This method balances optimally the bias and the variance of the estimate. 16 Chapter 1. Poolability in EKC panels parametric regressions. Let q = 1, ?? ?? ?? , Q be the q th subpopulation of size nq = N (nq =
T ). The weighted sum of unrestricted residual variances (s2 ) can be computed by makunr ing use of mth order di? erencing estimators13 . Yatchew (2003, Ch. 4) shows that if we make use of the optimal bandwidth for pooled estimates, optimal di? erencing weights in 2 s2 and under the classical assumptions that the errors are iid(0,?? ) and independent unr ? between and within subpopulations, H0 and H0 can be tested with the following statistic: 1 V = (mn) 2 (s2 ? s2 ) D unr res ? N (0, 1) > s2 unr (1. 3) where: m is the order of di? erencing, ? ?Q = N and n = T if we test H 0 nq , q = 1, . . . , Q and where n = NT = ?Q = T and n = N if we test H ? , q=1 q 0 Q s2 = res s2 = unr s2 f,q dif 1 n N T (pit ? pN P pool )2 , ?it i=1 t=1 Q nq 2 , s n dif f,q q=1 1 = nq nq ? m r=1 (d0 pq,r + d1 pq,r+1 + d2 pq,r+2 + ?? ?? ?? + dm pq,r+m)2 , m d0 , d1 , d2 , ?? ?? ?? , dm are di? erencing weights that satisfy m d2 = 1. k dk = 0, k=0 k=0 ? This test14 is one-sided, so we do not accept H0 (or H0 ) at the 95% con? dence level if the empirical V is greater than 1. 645. An important advantage of this test procedure is that it can easily be modi? ed to check di? rent kinds of null hypotheses. If the poolability ? assumption (H0 or H0 ) is accepted, we can verify the pertinence of conditioning E(pit ) on 13 Note that the data must be previously reordered so that within each subpopulation the (yq,1 , pq,1 ), (yq,2 , pq,2 ), ?? ?? ?? , (yq,nq , pq,nq ) observations are in increasing order relative to the y’s. 14 When the residuals are heteroscedastic with unknown covariance matrix ? , the denominator in equation (1. 3) can be replaced, without modifying the asymptotic properties of the V statistic, 1 1? 1? by ? = m ( n o? o? + ?? ?? ?? + n o? o? m ), where o is the vector of the pooled nonparametric regression ? ? ? residuals and the subscript ? i stands for the lag order of o. Note also that, under the null ? hypothesis, s2 in equation (1. 3) can be replaced by s2 because both estimators of the residual res unr variance are consistent, see Yatchew (2003, p. 64). 1. 3. The nonparametric approach 17 yit by replacing in equation (1. 3) pN P pool by E(pit ) in s2 and s2 by s2 f , where s2 f ? it unr res dif dif is simply the residual variance di? erencing estimator applied to the pit data as a whole.
The same idea can be followed to compare parametric and nonparametric speci? cations15 . Given the strong independence assumption imposed on the residuals, we also tested ? H0 by computing the Baltagi et al. (1996) J statistic16 , which allows the error term to have an arbitrary form of serial correlation and/or conditional heteroscedasticity on the time dimension or to include individual e? ects. As for the V statistic, the J statistic follows a N(0,1) distribution and the test is one-sided. Panel structures rarely display enough homogeneity to allow estimations under H0 or ?
H0 . Therefore, the vast majority of the IER literature attempts to capture the time and spatial nonhomogeneities by assuming isomorphic functions through time and individuals up to some vertical deterministic shifts or intercept term (the so-called ‘? xed e? ects’). This makes git () becomes a semiparametric speci? cation of the form git () = ? it + z(yit ). Taking it further, the latter model becomes fully parametric by imposing z(xit ) = K k k=1 ? k xit . Consequently, the ? xed-e? ects assumption transforms equation (1. 1) into the following two standard ? xed-e? ects models: 1. 4a) pit = ? it + z(yit ) + ? it K Pit = ? 0it + k=1 k ?k yit + ? it , k = 1, ?? ?? ?? , K (1. 4b) where the intercepts ? it and ? 0it in equations (1. 4a) and (1. 4b) are linear nonstochastic ? xed e? ects which gauge unobserved state-speci? c factors that a? ects the di? erences in per capita emissions as well as time-speci? c factors which capture macroeconomic e? ects, changes in environmental legislation, etc; z(yit ) and 15 K k k=1 ? k xit respectively in models Ibid. The null hypothesis that a known parametric regression function estimated by Least Squares h(yit , ?
LS ) is similar to some pooled pure nonparametric alternative f (yit ) can checked by replacing pN P pool by pLS in s2 and applying s2 f to pit in equation (1. 3). ?it ?it res dif 16 This statistic must be computed ensuring that some speci? c conditions on arbitrary parameters are satis? ed, cf. Baltagi et al. (1996, p. 349, condition C3). Note that the asymptotic properties of the J statistic relies on convergence properties of the residuals and not on di? erences between sum of squares of the pooled and unpooled nonparametric regressions. We would like to thank P. Nguyen Van for providing the Gauss code that we adapted to R. . 4. 1 to compute this test. All errors are my own. 18 Chapter 1. Poolability in EKC panels (1. 4a) and (1. 4b) are the unrestricted and restricted17 common functional forms to each year as well as to each state of the panel; ? it and ? it are stochastic error terms, both 2 2 assumed iid over t and i and of mean 0 and constant variance (?? and ?? ). Model (1. 4a) is a partial linear model which can be consistently estimated in three ways: (i) by Robinson (1988)’s double residuals as in Millimet et al. (2003), Bertinelli and Strobl (2005) or Nguyen Van and Azomahou (2007); (ii) by di? rencing as in Yatchew (2003, Ch. 4. 5); or (iii) by replacing z() by a consistent nonparametric estimate (some spline smoother of order r ) and minimizing a penalised residual sum of squares. The latter method has been preferred because of its operational simplicity in R’s statistical environment18 . Equation (1. 3) can be applied in the spirit of a speci? cation test to assess if the semiparametric model consistently captures the temporal or spatial heterogeneity. When the partial linear regression (1. 4a) is not rejected, the pertinence of including its linear term ? t can be tested with a slightly modi? ed version of the V-stat procedure, which is equivalent19 to the standard linear restrictions test R? = r. 17 The polynomial function is usually limited to K=3 when checking the EKC hypothesis. When the coe? cient of its linear component is positive and signi? cant, the coe? cient of the quadratic component is negative and signi? cant and the slope of the cubic component is nonsigni? cant, the EKC hypothesis is validated. 18 This procedure consist in minimizing n min ?,r,? i=1 (yi ? Xi ? ? ? (Zi ? z, r))2 + ? zmax [??? (z)]2 dx, zmin where ? ) is a rth -order polynomial function and the integrated term is a roughness penalty. The gam function in the mgcv package proposes a consistent procedure to ? t Generalized Additive Models that can be used to estimate semiparametric speci? cations. See Wood (2006) for further details. 19 Yatchew (2003, p. 179) shows that n(s2 ? s2 ) D 2 unr ? ? ? (R? ? r)? (R?? R? )(R? ? r) = 2 res ? ? rank(R) > 1 sunr (1 + 2m ) where the right-hand side ratio correspond to the modi? ed V-stat. This equality is directly linked to the di? erencing estimation method for the semiparametric model. Following Yatchew (2003, Ch. . 5), we can rewrite the SP model (1. 4a) in matrix notation as p = F ? + z(y) + ?. The nonlinear component z(y) can be removed by di? erencing, i. e. Dp = DF ? + Dz(y) + D? ? DF ? + D? , where D is a (n x n) di? erencing matrix. The OLS estimator of ? is therefore given by ? ols = [(DF )? (DF )]? 1 (DF )? Dp. With these notations at hand, the components of the modi? ed ? 1 1 V-stat can be de? ned as s2 = n (Dp ? DF ? ols )? (Dp ? DF ? ols )), s2 = n (Dp)? (Dp) and D is ? ? unr res the di? erencing matrix of order m computed with optimal weights. Note that the p’s can then be purged from its parametric e? cts (p ? F ? ols ) and a standard nonparametric method can be ? 1. 4. Data description 19 Finally, model (1. 4b) is the standard parametric model used to check the EKC hypothesis. Most authors control for ? xed e? ects by applying the F-test that involves the sum of squared residuals from the pooled (SSRp ) and within (SSRw ) versions of model (1. 4b). However, they omit a comparison of these magnitudes with the unrestricted20 sum of squared residuals (SSRu ). We apply in section 1. 5 the full F-test strategy on the spatial and time dimension. 1. 4 Data description
Our database is a balanced panel of 48 Spanish provinces over the 1990-2002 period. The series come from two di? erent sources. Spanish provinces’ statistics for population and GDP, in constant 1996 USD and adjusted to PPP, are taken from Herrero et al. (2004). We focus on 48 provinces21 whose air pollutant emissions are included in the inventory provided by Spain to the Convention on Long-Range Transboundary Air Pollution (CLRTAP). The annual emissions data on atmospheric pollutants have been supplied to us by the Spanish Ministry of the Environment and are extracted from the European Corinair 1990 inventory22 .
These data contain the anthropogenic and natural emissions of eight pollutants, split at the most aggregated level into eleven source groups23 . To be consistent with our purpose, we excluded the natural emissions category and considered only the anthropogenic ones. The pollutants included in the Corinair 1990 inventory are methane (CH4 ), carbon monoxyde (CO) and dioxyde (CO2 ), nitrous oxide (N2 O), ammonia (NH3 ), non-methanic volatile organic compounds (NMVOC), nitrogen (NOX ) and sulphur oxydes (SOX ). In order to keep our analysis manageable, we focus on four of them, CH4 , CO2 , CO and NMVOC, which present very di? rent evolution patterns at the aggregate level. The ? rst two (CH4 , CO2 ) are greenhouse gases for which Spain has commited, under the Kyoto applied to get the estimated nonlinear portion of the semiparametric model (? (x)). z 20 This term is contructed from either the cross-sectional parametric regressions for all years or the time-series parametric regressions for all regions/countries, see Hsiao (2003, Ch. 2). 21 See Appendix 1. 7. Spain comprises 50 provinces. We excluded the overseas provinces of Las Palmas and Tenerife. 22 Note that Roca et al. (2001) used the same database at the national level for di? rent periods in a parametric context. 23 These eleven categories are the ? rst level of the Selected Nomenclature for Air Pollution (SNAP) and can be further divided into 57 sub-sectors, which include 277 detailed activities. 20 Chapter 1. Poolability in EKC panels Protocol, not to increase emissions by more than 15% over the 1990 level by 2012. CO is a poisonous gas and NMVOC is a ground level ozone precursor. In 1990, three main sectors were the source for the majority of emissions: power generation (SNAP-group 1) for CO2 ; road transport (SNAP-group 7) for CO and NMVOC; and agriculture (SNAP-group 10) for CH4 .
Note that, according to this inventory, nature rarely accounts for more than 5% of global emissions in Spain, except for NMCOV where it represents a roughly stable 45% share between 1990 and 2002. Figure 1. 1: Spanish GDP, emissions and population. Period 1990-2002. 140 Evolution of the GDP, emissions & population in Spain. Period 1990? 2002 x / o + o Population GDP (in US$96 cst ppa) CH4 CO CO2 NMVOC o o x 100 Index (100=1990) 120 x x + x o / o + / x o x / + x o + / x x x x o o o x o x o / + o + + + + + + / + / + / / / 80 / / / 1990 1992 1994 1996 1998 2000 2002 Years
Source: Spanish Ministry of Environment (MMA) for air pollutants and Herrero et al. (2004) for GDP and population. Figure 1 shows the evolution of aggregate anthropogenic Spanish emissions for the retained air pollutants. This ? gure also shows the changes of the Spanish population and 1. 4. Data description 21 GDP over the sample period. CO2 emissions clearly follow the exponential upward trend of GDP, while CH4 emissions grow along a fairly linear path since 1990. NMVOC and CO emissions have been declining at di? erent rates over the period, 8. 3% and 29. 2% respectively. Table 1. presents some descriptive statistics on per capita emissions and real GDP for the whole panel. We can observe that the mean of the variables is always higher than the median, suggesting the presence of extreme values at the right tail of the data distributions. The standard deviation remains close to, or below, the median for most of the variables except for CO2 . A more accurate picture of the variability of the panel on its temporal and spatial dimensions is given by a one-way analysis of variance. Table 1. 1: Descriptive statistics. Provincial GDP, Spain. Period 1990-2002.
Variables Median Mean Std. dev. CH4 48. 4 68. 50 53. 6 CO 98. 3 107. 6 49. 4 CO2 6146. 7 8818. 3 9071. 3 NMVOC 47. 2 57. 8 31. 0 GDP 1. 5 1. 6 0. 4 Obs. 624 emissions and population in Min. 7. 3 17. 8 836. 0 13. 5 0. 9 Max 263. 0 317. 8 68013. 4 158. 1 2. 7 Note: All ? gures are per capita. Spanish provinces anthropogenic air pollutant emissions are in kg and real GDP in 10’000 USD1990 corrected by PPP. Table 1. 2 summarizes the data inter- and intra-variation for provinces and years. Variation here is predominantly ‘between’ provinces, ranging from 80. 9% for per capita GDP to 98. % for NMVOC per capita emissions, while it is higher ‘within’ than ‘between’ years and it varies from 84. 5% for GDP per capita to 99. 6% for NMVOC per capita emissions. Note that an ANOVA analysis (F-tests) always reject strongly the equality of the regional means for all the variables while the equality of the temporal means is accepted for per capita CH4 , CO2 and NMVOC emissions. These results indicate that between-region variation is a major source of variation in our panel. 22 Chapter 1. Poolability in EKC panels Table 1. 2: One-way analysis of variance. Provincial GDP, emissions and population in Spain. Period 1990-2002. 2 2 2 2 Variables ?tot ?b,i ?w,i ?b,t ?w,t ? ? CH4 2865. 9 (100%) 96. 0% 4. 0% 1. 4% 98. 6% ? ? ? CO 2442. 6 (100%) 90. 7% 9. 3% 5. 2% ? 94. 8% CO2 82. 3 (100%) ? 96. 1% ? 3. 9% 1. 2% 98. 8% NMVOC 963. 1 (100%) ? 98. 5% ? 1. 5% 0. 4% 99. 6% ? ? ? GDP 14182 (100%) 80. 9% 19. 1% 15. 5% ? 84. 5% Note: *: signi? cant at the 5% level. All ? gures are in per capita terms. CH4 , CO, and NMVOC are in kg, CO2 in tonnes and GDP in USD90 and PPP-corrected. Total, between and within variances are given by 2 2 2 ?tot , ? b , ? w . The ratios of the mean squares are F-distributed with (47;576) and (12;611) degrees of freedom respectively.
The corresponding critical F-values are 1. 384 and 1. 768. 1. 5 Econometric analysis Nonparametric regressions are usually investigated through graphical devices. For each pollutant, Figure 2 compares the nonparametric pooled regression with nonparametric time-series regressions for each province; it roughly checks the equality of the IER between regions, i. e. the spatial homogeneity hypothesis. Figure 3 compares, for each pollutant, the pooled regression with nonparametric cross-sectional regressions for selected years and aims at investigating the structural stability of the relationship through time, i. . the time homogeneity hypothesis. In all graphs, the nonparametric pooled regression is surrounded by the 95% uniform con? dence band24 suggested by Yatchew (2003, p. 36). It contrasts graphically the equality between di? erent pooled nonparametric and parametric functions by controlling whether the parametric shape falls within the whole con? dence band. Spatial heterogeneity. It is clear from a visual inspection of the four panels in Figure 2 that the pooled model with a single constant should be rejected as almost none of the region-speci? c regressions lie within the 95% con? dence band.
The existence of a common function for every province up to a vertical shift is neither strongly supported. Table 1. 3 reports the results of the statistical tests described in section 1. 3. In lines 1 and 2 we can see the V-tests strongly reject the H0 hypothesis for all pollutants as well as the semiparametric speci? cation. Consequently, the pooled nonparametric and partial linear 24 This interval is more interesting than the pointwise one as 95% of the estimated con? dence intervals contain the entire true function. 1. 5. Econometric analysis 23 Figure 1. 2: Spatial heterogeneity. Time series GDP-emissions ? s for Spanish provinces. Period 1990-2002. CO/capita 300 250 CH4/capita 200 0 50 50 100 150 emissions (kg/capita) 200 150 100 emissions (kg/capita) Pooled regression +/? 95% UCI States regressions 250 Pooled regression +/? 95% UCI States regressions 1. 0 1. 5 2. 0 2. 5 1. 0 1. 5 2. 0 CO2/capita 2. 5 GDP/capita (10’000 USD) NMVOC/capita 70 GDP/capita (10’000 USD) 150 Pooled regression +/? 95% UCI States regressions 0 10 50 100 emissions (kg/capita) 40 30 20 emissions (t/capita) 50 60 Pooled regression +/? 95% UCI States regressions 1. 0 1. 5 2. 0 GDP/capita (10’000 USD) 2. 5 1. 0 1. 5 2. 0 2. 5