Three Essays in Energy and Environmental Economics Dissertation Submitted in fulfillment of the requirements for the degree of doctor rerum politicarum (Dr. rer. pol.) by the Department of Law and Economics of the Technical University of Darmstadt by Moritz Tarach, M.Sc. (Place of birth: Hamburg) First supervisor: Prof. Dr. Jens Krüger Second supervisor: Prof. Dr. Michael Neugart Filing date: 29.05.2024 Date of defense: 05.11.2024 Place of publication: Darmstadt Year of the viva voce: 2024 D 17 Tarach, Moritz Three Essays in Energy and Environmental Economics Darmstadt, Technische Universität Darmstadt Year thesis published in TUprints: 2025 Date of defense: 05.11.2024 Published under CC BY 4.0 International https://creativecommons.org/licenses/ Acknowledgements This dissertation was written while I was research and teaching assistant at the Chair of Empirical Economics at the Technical University of Darmstadt, Germany. Without the support of many people, whom I sincerely thank in the following, the completion of this dissertation would not have been possible. First and foremost, I am deeply indebted to my supervisor, Prof. Dr. Jens Krüger for giving me the opportunity to pursue my doctoral thesis. Working with him has been a pleasure which I greatly appreciate. I want to thank him for his invaluable advice, constructive support, and guidance while writing this dissertation. I am thankful to him for sharing his academic experience with me, especially his knowledge in writing and publishing academic papers. Moreover, I would like to thank Prof. Dr. Michael Neugart for his review as my second supervisor. I would also like to thank Prof. Dr. Dirk Schiereck for chairing the exami- nation committee as well as the committee member Prof. Frank Pisch for their questions and insights shared during my defense. Furthermore, I thank my (former) colleagues from the Technical University of Darmstadt for the pleasant and cooperative working atmosphere. I am especially grateful to my colleagues from the Chair of Empirical Economics: Vanessa Belew, Dr. Jingwei Pan, Dr. Seulki Chung, Yannick Schmidt and Fahim Safi. I am also grateful to my colleagues from neighboring chairs, particularly from the chairs ’Technology and Innovation Management’ and ’Public Economics and Economic Policy’, for spending time together in a friendly and cheerful atmosphere during lunch breaks. Besides, I am thankful to project partners at the University of Kassel, Prof. Dr. Heike Wetzel and Larissa Fait, for their efforts in compiling the data that I use in Chapter 3 of this dissertation. Last but not least, I want to thank my friends and my family, especially my parents and my brother. Without their unwavering support and inspiration, during the years of writing this dissertation and before during my studies, the completion of this dissertation would not have been possible. iii Abstract This dissertation consists of three studies, each examining a different topic in the field of energy and environmental economics. The topics comprise: (i) estimating potentials for greenhouse gas emission reductions of economic sectors, (ii) forecasting the oil production of a region based on historical data from discoveries, and (iii) examining the determinants of electricity price fluctuations. Each of the studies uses a particular statistical method or mathematical model that is specifically adapted to the research question and the data set under investigation. The first study is a stochastic nonparametric efficiency analysis in which greenhouse gas emissions are included as bad outputs. For seven economic sectors and sixteen European countries, this study estimates greenhouse gas emission reduction potentials, i.e., the quantity of emissions that could potentially be reduced by improvements in productive efficiency. The standard DEA method is extended by a specific bootstrapping procedure used to implement a bias correction and to compute confidence intervals. The magnitudes of the emission reduction potentials are compared with the emission reduction targets for 2030 from the European Commission. The results show that improvements in productive efficiency are a quantitatively important element, potentially allowing for a substantial reduction of greenhouse gas emissions in the European Union. The second study presents a stochastic model for forecasting for an oil-producing region the amount of undiscovered oil, the future path of oil discovery and that of oil production. The model combines three submodels: (i) an empirically-founded production model at the level of individual oil fields, (ii) a successive sampling discovery model after Kaufman et al. (1975) for forecasting field sizes, and (iii) a stochastic birth process model for forecasting discovery dates. The model is estimated and evaluated for the oil-producing regions of Norway and the U.S. Gulf of Mexico (the latter further split into shallow- and deep-water parts). The results show that the predictions for oil discovery are somewhat too low compared to the actuals for Norway and for the shallow-water Gulf of Mexico, while for the deep-water Gulf of Mexico the predictions are too high. This is similarly reflected in the predictions for oil production. The third study is a multivariate wavelet analysis of the German wholesale electricity market, which examines the determinants of electricity price fluctuations using daily time series. The possible determinants are coal prices, gas prices, and the residual load (i.e., electricity consumption minus wind and solar generation). The multivariate wavelet method allows for a detailed examination of the relations between the time series in time- frequency space, while also taking into account the interdependencies among the different time series. The results show that the residual load is the key short-run determinant of electricity prices, while coal and gas prices are the key long-run determinants. Also, this study finds that the co-movement relation among the energy prices is time-varying, which is consistent with the findings of other studies (e.g., Sousa et al. (2014); Aguiar-Conraria et al. (2018)). iv Zusammenfassung Die vorliegende Dissertation beinhaltet drei Studien, die jeweils unterschiedliche Themen aus dem Forschungsfeld der Energie- und Umweltökonomie untersuchen. Die Forschungs- themen der Studien umfassen: (i) die Schätzung von Einsparpotentialen für Treibhaus- gasemissionen auf Sektorebene, (ii) die Prognose der Ölförderung einer Region auf Basis von historischen Daten zu Ölfunden, (iii) die Untersuchung der Bestimmungsfaktoren von Strompreisschwankungen. Jede der Studien nutzt dabei bestimmte statistische oder ma- thematische Methoden, welche speziell auf die Forschungsfrage und den zu untersuchenden Datensatz zugeschnitten sind. Die erste Studie ist eine stochastische, nichtparametrische Effizienzanalyse mit Treibh- ausgasemissionen als unerwünschte Outputs. Es werden für sieben Wirtschaftssektoren und sechstzehn Europäische Länder Einsparpotentiale für Treibhausgasemissionen ge- schätzt, d.h. die Emissionsmengen, die möglicherweise durch Produktivitätsverbesserun- gen eingespart werden könnten. Dafür wird die übliche DEA-Methode durch ein spezielles Bootstrapping-Verfahren ergänzt, um eine Bias-Korrektur durchzuführen und Konfiden- zintervalle zu ermitteln. Die geschätzten Einsparpotentiale für Treibhausgasemissionen werden mit den Emissionsreduktionszielen der Europäischen Kommission für 2030 ver- glichen. Der Vergleich zeigt, dass Produktivitätsverbesserungen ein quantitativ wichtiges Element darstellen, wodurch gegebenenfalls eine substanzielle Verringerung der Treibh- ausgasemissionen der Europäischen Union möglich ist. Die zweite Studie präsentiert ein stochastisches Modell, welches darauf abzielt, die unent- deckten Ölmengen sowie den Zeitpfad der Ölentdeckungen und der Ölproduktion für eine ölfördernde Region vorherzusagen. Das Modell kombiniert drei Submodelle: (i) ein empi- risch fundiertes Produktionsmodell für individuelle Ölfelder, (ii) ein „Successive Sampling Discovery Model“ nach Kaufman et al. (1975) zur Prognose der Feldgrößen, und (iii) ein stochastisches Modell vom Typ Poisson-Prozess zur Vorhersage der Entdeckungszeitpunk- te. Das Modell wird für die ölfördernden Regionen Norwegen und dem Golf von Mexiko (letztere weiter untergliedert in „Flachwasser-“ und „Tiefwasser-Region“) geschätzt und evaluiert. Die Ergebnisse zeigen, dass für Norwegen und für die „Flachwasser-Region“ des Golfs von Mexico die prognostizierten Ölentdeckungen etwas zu niedrig sind im Vergleich zu den tatsächlichen Ölentdeckungen, während für die Tiefwasser-Region des Golfs von Mexico die Prognosen zu hoch sind. Ähnliches spiegelt sich in den Prognosen für die Ölproduktion wider. Die dritte Studie ist eine multivariate Wavelet-Analyse des deutschen Großhandelsstrom- marktes, welche die Bestimmungsfaktoren von Strompreisfluktuationen anhand von tägli- chen Zeitreihen untersucht. Die möglichen Bestimmungsfaktoren sind Kohle- und Gasprei- se sowie die Residuallast (die gesamte Netzlast minus die Erzeugung aus Windkraft und Solarenergie). Die multivariate Wavelet-Methode erlaubt eine detaillierte Untersuchung der Beziehungen zwischen den Zeitreihen nach Zeit und Frequenz, wobei ebenso die Ab- hängigkeiten zwischen den verschiedenen Zeitreihen berücksichtigt werden. Die Ergebnisse zeigen, dass die Residuallast der wesentliche Bestimmungsfaktor über kürzere Perioden ist, während Kohle- und Gaspreise die wesentlichen Bestimmungsfaktoren über längere Perioden sind. Ebenso findet die Studie, dass der Zusammenhang zwischen den Energie- preisen zeitlich veränderlich ist, was mit Ergebnissen aus anderen Studien übereinstimmt (siehe z.B., Sousa et al. (2014); Aguiar-Conraria et al. (2018)). v Contents 1 Introduction 1 1.1 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Energy as a Factor of Production 6 2.1 The Macroeconomic Relations between Energy, GHG Emissions, and GDP 6 2.2 Historical Trends for GHG Emissions, Oil Production, and Renewable Energy 11 2.3 A Framework for Macroeconomic Production Functions with Energy and GHG Emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Greenhouse Gas Emission Reduction Potentials in Europe by Sector: A Bootstrap-Based Nonparametric Efficiency Analysis 16 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 Nonparametric Efficiency Measurement and Bootstrapping . . . . . . . . . 21 3.3.1 Technology Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3.2 Directional Distance Functions . . . . . . . . . . . . . . . . . . . . . 22 3.3.3 Variable Returns to Scale . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.4 Bootstrapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.1 Total Greenhouse Gas Emissions . . . . . . . . . . . . . . . . . . . 27 3.4.2 CO2 and other GHG (CH4 and N2O) Emissions . . . . . . . . . . . 29 3.4.3 Combined Direction with Output Enhancement . . . . . . . . . . . 31 3.4.4 Policy Recommendations . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4 Bottom-Up Aggregation of Field-Level Oil Production Profiles via a Successive Sampling Discovery Model and a Birth Process: An Appli- cation to the Gulf of Mexico and Norway 38 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2 Literature Review of Mathematical Modeling Approaches . . . . . . . . . . 41 4.3 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.1 Overview and Production Profiles . . . . . . . . . . . . . . . . . . . 45 4.3.2 Size-Biased Sampling Model . . . . . . . . . . . . . . . . . . . . . . 48 4.3.3 Models for the Discovery Times and Exploration Success . . . . . . 56 4.3.4 Combination, Distributional Properties, and an Asymptotic Ap- proximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 vi 4.4 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.5.1 Data Description and Pre-Analysis . . . . . . . . . . . . . . . . . . 70 4.5.2 Estimation Results for the Size-Biased Sampling Model . . . . . . . 75 4.5.3 Simulation Results for the Overall Model . . . . . . . . . . . . . . . 79 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5 A Wavelet Analysis of the German Wholesale Electricity Market Using Daily Data 93 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3 Wavelet and Cross-Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . 96 5.3.1 Uni- and Bivariate Wavelet Tools . . . . . . . . . . . . . . . . . . . 97 5.3.2 Multivariate Wavelet Tools . . . . . . . . . . . . . . . . . . . . . . . 100 5.4 Time Series Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.5 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.5.1 Univariate Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . 104 5.5.2 Bivariate Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . 110 5.5.3 Multivariate Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . 114 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6 Conclusion 119 6.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 References 125 A Appendix to Chapter 3 142 B Formal Appendix to Chapter 4 147 B.1 Derivation of the Posterior Distribution from a Poisson prior . . . . . . . . 147 B.2 Numerical Computation of the General Gamma Density . . . . . . . . . . 149 B.3 Maximum Likelihood Estimation . . . . . . . . . . . . . . . . . . . . . . . 152 B.4 Proof of Proposition 4a and 4b . . . . . . . . . . . . . . . . . . . . . . . . 156 B.5 Further Derivations for the Size-Biased Sampling Model . . . . . . . . . . . 157 C Appendix to Chapter 4 162 D Appendix to Chapter 5 179 vii List of Figures 2.1 Global time-series relations, in total, 1971-2019 . . . . . . . . . . . . . . . 7 2.2 Global time-series relations, per capita, 1971-2019 . . . . . . . . . . . . . . 8 2.3 Cross-sectional relation between energy consumption and GDP in 2010-19 9 2.4 Cross-sectional relation between GHG emissions and GDP in 2010-19 . . . 10 2.5 GHG emissions of top 10 emitters and others, 1900-2022 . . . . . . . . . . 12 2.6 World (left panel) and US (right panel) liquid fuel production . . . . . . . 12 2.7 Crude oil production of top 18 oil-producing countries, 1971-2021 . . . . . 13 2.8 Renewable energy (RE) shares in primary energy consumption, 1990-2020 . 14 3.1 GHG emissions across sectors and countries . . . . . . . . . . . . . . . . . 21 3.2 Potential emission reduction of total GHG for the period 2008-2012 (upper panel) and the period 2012-2016 (lower panel), variant (a) . . . . . . . . . 28 3.3 Potential emission reduction of CO2 and other GHG for the period 2012- 2016, variant (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4 Potential emission reduction of CO2, CH4 and N2O for the period 2012- 2016, variant (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.5 Potential emission reduction of total GHG and output enhancement for the period 2012-2016, variant (d) . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.1 Four production profiles based on equation (4.2) and Table 4.1 . . . . . . . 47 4.2 Overall timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3 Transition-rate diagram for assumption 4a . . . . . . . . . . . . . . . . . . 58 4.4 Illustration of the estimation strategy for assumption 4a . . . . . . . . . . 59 4.5 Transition-rate diagram for assumption 4b . . . . . . . . . . . . . . . . . . 61 4.6 Plots of the ln(Size) distributions . . . . . . . . . . . . . . . . . . . . . . . 72 4.7 Simulation results illustration (scenario 2 of Figure 4.8 for GOM Flat) . . . 81 4.8 Simulation results for GOM Flat (t = 1962, ML-EST, assumption 4b) . . . 84 4.9 Simulation results for Norway (t = 1984, ML-EST, assumption 4b) . . . . . 85 4.10 Simulation results for GOM Deep (t = 2000, ML-EST, assumption 4b) . . 86 5.1 Comparison of proxy prices to monthly import prices . . . . . . . . . . . . 103 5.2 Univariate wavelet results . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.3 Wholesale electricity, natural gas, and hard coal prices in levels . . . . . . 106 5.4 Univariate wavelet results (cont’d) . . . . . . . . . . . . . . . . . . . . . . . 107 5.5 Fourier power spectra of the total load (day-to-day changes) and of a 7-day periodic dummy series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.6 Bivariate wavelet results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.7 Bivariate wavelet results (cont’d) . . . . . . . . . . . . . . . . . . . . . . . 112 viii 5.8 Multivariate wavelet results . . . . . . . . . . . . . . . . . . . . . . . . . . 115 C1 Actual oil (black) and gas (red) production for the three regions . . . . . . 163 C2 Discovery and exploration history - GOM Flat . . . . . . . . . . . . . . . . 163 C3 Discovery and exploration history - Norway . . . . . . . . . . . . . . . . . 164 C4 Discovery and exploration history - GOM Deep . . . . . . . . . . . . . . . 164 C5 Illustration of the depletion effect - GOM Flat . . . . . . . . . . . . . . . . 165 C6 Illustration of the depletion effect - Norway . . . . . . . . . . . . . . . . . . 166 C7 Illustration of the depletion effect - GOM Deep . . . . . . . . . . . . . . . 167 C8 Estimation results for GOM Flat (t =1962) . . . . . . . . . . . . . . . . . . 169 C9 Estimation results for Norway (t =1984) . . . . . . . . . . . . . . . . . . . 170 C10 Estimation results for GOM Deep (t =2000) . . . . . . . . . . . . . . . . . 171 C11 Estimation results for GOM Deep (t =2005) . . . . . . . . . . . . . . . . . 172 C12 Simulation results for GOM Flat (t = 1962, FIT-URR, assumption (4b)) . 173 C13 Simulation results for GOM Flat (t = 1962, FIT-URR, assumption (4a)) . 174 C14 Simulation results for Norway (t = 1984, FIT-URR, assumption (4b)) . . . 175 C15 Simulation results for Norway (t = 1984, FIT-URR, assumption (4a)) . . . 176 C16 Simulation results for GOM Deep (t = 2005, ML-EST, assumption (4b)) . 177 C17 Simulation results for GOM Deep (t = 2005, FIT-URR, assumption (4a)) . 178 D1 Univariate wavelet results for time series in levels . . . . . . . . . . . . . . 180 D2 Univariate wavelet results for time series in levels (cont’d) . . . . . . . . . 181 ix List of Tables 4.1 Summary statistics of standard production profiles from 725 oil fields ana- lyzed by IEA (2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2 Selected years for the empirical analysis . . . . . . . . . . . . . . . . . . . . 71 4.3 Summary of the ln(Size) distributions . . . . . . . . . . . . . . . . . . . . . 73 4.4 Results from regressing size and water depth on discovery rank . . . . . . . 74 4.5 Rank correlations (Spearman) between size, water depth and discovery date 74 4.6 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.7 Estimation results (cont’d) . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.8 Summary statistics for the simulation results . . . . . . . . . . . . . . . . . 83 5.1 Time series used in the wavelet analysis . . . . . . . . . . . . . . . . . . . . 101 5.2 Yearly total electricity load and electricity generation shares for Germany . 102 5.3 German VRE generation capacity, mean and variability of daily generation 110 A1 GHG emissions across sectors and countries . . . . . . . . . . . . . . . . . 142 A2 Potential emission reduction of total GHG for the period 2008-2012 (left columns) and period 2012-2016 (right columns), variant (a) . . . . . . . . . 143 A3 Potential emission reduction of CO2 and other GHG for the period 2012- 2016, variant (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 A4 Potential emission reduction of CO2, CH4 and N2O for the period 2012- 2016, variant (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 A5 Potential emission reduction of total GHG and output enhancement for the period 2012-2016, variant (d) . . . . . . . . . . . . . . . . . . . . . . . . . 146 B1 Exponential family form of the lognormal distribution . . . . . . . . . . . . 153 C1 Estimation results for â0 and b̂0 . . . . . . . . . . . . . . . . . . . . . . . . 168 D1 Results of unit-root tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 D2 German VRE and nuclear capacity, mean and variability of daily generation179 x 1 Introduction “Simply put, energy is the only truly universal currency, and nothing (from galactic rotations to ephemeral insect lives) can take place without its transformations” (Smil (2022), p. 21). Since the industrial revolution, there has been an unprecedented rise in human energy consumption across the various sectors of the economy, such as manufacturing, trans- portation, agriculture and housing, mainly in the form of fossil fuels (coal, oil, natural gas). As their combustion leads to CO2 emissions, this has triggered the problem of an- thropogenic global warming which is caused by CO2 and other greenhouse gas emissions (IPCC (2023)). From a resource point of view the above quote from Vaclav Smil qualifies energy as the “master resource” (Michaux (2021), p. 2; Martenson (2023), p. 125). If energy is the master resource, then oil in particular could be considered the “master” among the set of master resources due to its high energy density (both per unit volume and per unit mass), since it is easy to transport and store, and since it can fuel even the largest engines and vehicles (Hall et al. (2009), p. 35; Miller and Sorrell (2014), p. 2). The increased global access to energy has furthermore allowed the increasingly rapid exploitation of other mineral and ecosystem resources, also with consequential waste gen- eration, which has lead to the ongoing processes of resource depletion and environmen- tal degradation. Among others, these include biodiversity loss (i.e. species extinction), land-system impacts (e.g. deforestation, soil erosion), overfishing, depletion of some large aquifers, aerosol emissions, plastic pollution, and pollution by chemicals with eco-toxicities such as pesticides (see, for example, Steffen et al. (2015); Raugei (2023), p. 1). Although these processes operate primarily on the regional scale, there are interactions among these processes, and if the scope thereof transgresses certain boundaries this will turn into im- pacts at the global level (Steffen et al. (2015)). In this sense, Rockström et al. (2009) and Steffen et al. (2015) highlight the existence of multiple “planetary boundaries” that are better not exceeded in order to guarantee the stability of the current conditions prevailing on the Earth which can support human societies. A crucial paradigm of ecological economics is that economic analysis should be centered around the recognition that the economic system is a subsystem of the surrounding ecosys- tem or of the Earth system (Daly (2007), pp. 39, 41).1 The Earth system comprises the biosphere (i.e. the natural ecosystems), the “geosphere” (including the lithosphere where the soil and the deposits of minerals and fossil fuels reside), the hydrosphere (the oceans, ice sheets, etc.), and the atmosphere (Hagens and White (2021), p. 135). It is finite, non- growing, and materially closed (Daly (2007), pp. 9-10), though energetically it is open with a constant inflow of solar energy and an outflow of heat radiation. The Earth system supplies the necessary raw materials for economic production, absorbs waste flows, and delivers ecosystem services without which humans and other species could not survive (e.g. pollination, nutrient recycling, climate regulation). From the fact that the Earth system is finite and non-growing, the concept that there are biophysical limits to the size and scope of human economic activity and its growth 1The terminology “Earth system” is adopted from Steffen et al. (2015). Regarding the Earth as a integrated system that is akin to a complex organism is also the viewpoint behind the Gaia hypothesis (Lovelock and Margulis (1974)). 1 becomes evident (Meadows et al. (1972); Daly (2007)). These pertain to the limited capacity “of the ecosystem to absorb wastes and replenish raw materials in order to sustain the economy [and the population]” (Daly (2007), p. 9). To give an example, the waste stream of CO2 emissions could in principle be absorbed by biomass production (i.e. CO2 uptake in plant mass and topsoil), but the rate at which this can happen is limited (though it can be influenced by human efforts, e.g. via afforestation and farming practices). With regard to nonrenewable resources use, the issue of limits or sustainability is more difficult to define. For example, one can extend the definition of limited capacity from above by saying that nonrenewable resources should not be extracted at rates that “exceed the rate of development of renewable substitutes” (Daly (2007), p. 14). One can extend this definition to allow for the substitution with other nonrenewable substitutes (which then, of course, should be available in quantities so that their extraction rate does not violate the same definition of limited capacity). Since global primary energy consumption in 2022 was still to 82% based on fossil fuels (Energy Institute (2023), p. 9), this means that, as of now, global civilization is largely a fossil-fuel based civilization. In fact, this is in part related to the four materials that are most indispensable for modern society, which Smil (2022, p. 77) refers to as the “four pillars of modern civilization: cement, steel, plastics, and ammonia”. The large-scale production of these materials is crucially dependent on fossil fuels as an energy source or as a petrochemical feedstock. The process of iron ore smelting is fueled by coking coal and natural gas, cement production involves coal or heavy fuel oil, plastics are largely made from oil and natural gas, and ammonia is synthesized from natural gas that is also used as the energy source for the synthesis. In total, the global production of these four materials is responsible for 17% of global primary energy supply, and a quarter of the CO2 emissions from fossil fuels (Smil (2022), p. 78). This dependence on fossil fuels for many production processes shows that an important research topic is the study of greenhouse gas (GHG) emission reduction potentials that could arise by improving the productive efficiency of firms, and therefore, of economic sectors. Chapter 3 of this thesis deals with this topic by examining efficiency-related GHG emission reduction potentials by sector (e.g. manufacturing, power generation) for a sample of European countries. Reconsidering the above paragraph where I have referred to energy and oil in particular as the “master resource”, it is hard to imagine the current world without oil. Aside from being used to produce plastics, oil is currently essential for powering heavy transportation, including heavy machinery in agriculture and mining. It is vital for transportation also in other ways: synthetic rubber for tires is made from oil (or natural gas),2 and the asphalt pavement of roads contains bitumen, a viscous residue from oil distillation.3 Since oil has provided 31.6% of global primary energy in 2022 (Energy Institute (2023), p. 9), and considering the nonrenewable nature of this fossil resource, this makes it important to study the future prospects of oil availability. Chapter 4 of this thesis considers this topic by formulating a predictive model for oil production, which is then applied to the oil-producing regions of Norway and the U.S. Gulf of Mexico. Both the resource depletion issue and the issue of global warming highlight the importance 2See https://www.britannica.com/science/rubber-chemical-compound 3See https://www.britannica.com/science/bitumen 2 of developing and deploying substitutes for fossil fuel use. The renewable energy flows harnessed by solar panels and wind turbines, hydropower plants, and biomass use are widely regarded as substitutes for fossil fuels, and a massive expansion of these renewable technologies is planned by many of the world’s nations. Alternative candidates could be the latest generation nuclear power reactors and geothermal power generation. Since these energy technologies produce mainly electricity (except for biomass), if they are to substitute for the fossil energy that is used in non-electric sectors, their expansion would require the further electrification of the other sectors, by which the electricity sector would further rise in importance. The analyses presented in Chapters 3 and 4 necessarily employ a long-run perspective since efficiency-related emission reduction potentials require time to be realized and since oil discovery and depletion are per se lengthy processes. Chapter 5 of this thesis con- siders, among other things, the energy mix of German electricity generation. This is now approached from a short-run perspective by examining how the electricity price is dynamically influenced by the electricity mix and fuel prices. In particular, this study of electricity price formation deals with a situation where electricity is generated from a mix of fossil and renewable energy sources, and where the renewable generation capacity is subject to a steady expansion. The German electricity market is well suited for this because Germany is currently a forerunner where large investments into renewable energy expansion have been made. In 2022, 40% of the total electricity demand was provided by wind and solar, 11% by hydropower and biomass, while 34% was provided by coal and 8% by gas (data obtained from the Bundesnetzagentur). In Chapter 5, therefore, I examine for the German electricity market with a suitable method the relative importance of the “periodic oscillations” in renewable energy generation versus those in fossil energy prices for explaining the “periodic oscillations” in daily wholesale electricity prices. 1.1 Outline of the Thesis The doctoral thesis is structured as follows. Chapter 2 starts with an empirical exami- nation of the global macroeconomic relationships between primary energy consumption, GHG emissions, and GDP. Afterwards, historical trends of GHG emissions, oil production, and renewable energy generation shares are briefly explored. The chapter is concluded by briefly sketching a framework for macroeconomic production functions with energy as an input and GHG emissions as an undesirable output. Chapter 3 presents a stochastic nonparametric efficiency analysis in which the emission of greenhouse gases are taken into account as bad outputs. The chapter reports point estimates and confidence intervals for GHG emission reduction potentials for 7 sectors (comprising the largest GHG emitting sectors) in a sample of 16 large European countries. In addition to GHG emissions, the variables used in the efficiency analysis are gross value added as the good output and the conventional labor and capital measures as inputs. The nonparametric approach of the efficiency analysis employs directional distance functions (DDF) to find the maximum possible reduction of the bad outputs which is feasible within a convex technology set that envelopes the input-output combinations of the sample countries. The first variant obtains in this way estimates of the reduction potentials for a single GHG aggregate, computed as the sum of CO2, CH4 and N2O emissions. In other variants the reduction potentials for splits of the different greenhouse gases are examined as well. In a further variant the combination of GHG emission reduction and 3 output enhancement is examined. In these cases where the inefficiency is assessed in the direction of multiple bad outputs or of a combination of bad and good outputs, the direction vector of the DDF is determined endogenously with the inefficiency. Since the nonparametric efficiency analysis provides only point estimates that are also biased, which is a peculiarity that generally arises for frontier function estimation, the computations are extended by a specifically designed bootstrapping procedure to compute confidence intervals and correct the bias. Thus, the main results of Chapter 3 are bias-corrected GHG emission reduction potentials with confidence intervals. In the final sections of Chapter 3, some policy implications of the analysis are discussed and the magnitudes of the emission reduction potentials are put into perspective by comparison with the emission reduction targets for 2030 as set by the European Commission (see EU (2020)). Chapter 4 presents a stochastic model for oil production in a region with empirical appli- cations to oil production in Norway and the U.S. part of the Gulf of Mexico. The chapter starts with a literature review of previous mathematical approaches for modeling oil pro- duction in a region, such as those based on fitting suitable curves (e.g. bell-shaped) to regional production time series, often called “top-down” models. The chapter then formu- lates in great detail a stochastic “bottom-up” model for the regional rate of oil production that combines three mathematical submodels. The first one is an empirically-derived field- level production model, where it is assumed that each individual oil field follows a certain deterministic production profile over time, which can vary by field size (i.e. the amount of recoverable oil). The second model is based on certain axioms about how the discovery of new fields proceeds. The main axiom postulates that the fields are not discovered as a random sample but instead via a successive sampling scheme where field size is the key determinant of the discovery order, henceforth called size-biased sampling. The third model is about the dates of “when” the new fields are discovered. Here I use the stochastic process model referred to as a pure birth process. I also introduce time-varying behavior into this model for the discovery times by using extrapolations of certain temporal trend functions, which either pertain to the pace of exploration well drilling or directly to the pace of new field discoveries. A large part of the methods section of Chapter 4 covers the statistical estimation procedure for the size-biased sampling model in detail. The estimation allows to infer from a sample of oil fields (or rather their sizes) a predictive distribution for the undiscovered resource potential (i.e. the remaining amount of oil that “is still out there” in the undiscovered fields). The methods section then proceeds with the pure birth process model for the discovery times, after which the overall properties of the combined model for regional oil production are summarized, and expectations regarding the dynamics of the model are discussed. The empirical part of Chapter 4 first reports the parameter estimates of the size-biased sampling model jointly with the resulting estimates of undiscovered resources. These are then compared to the estimates that are published by the respective official agencies for the regions. The final subsection presents the main results of the chapter, namely the projections of regional oil production (and discovery) for each year beyond the time period that was used to estimate the parameters. These projections are conditional on certain scenarios for future exploration well drilling or for the future pace of new field discoveries. The projections comprise a whole predictive distribution that is shown as a mean forecast with an associated quantile range. Chapter 5 presents a conditional wavelet analysis that examines the relation between German wholesale electricity prices and a few possible determinants, using daily data from 2015-2023. These determinants are the total electricity demand, wind and solar electricity generation, the residual load (i.e. total demand minus wind and solar generation), and 4 proxy price series for the import prices of hard coal and natural gas. The chapter starts with a brief review of related literature and continues with the methodology of wavelet and cross-wavelet analysis, where also the novel multivariate wavelet methods (partial and multiple wavelet coherence) which are applied in this chapter are explained. After a brief data description, the empirical results section first considers each time series separately via univariate wavelet analysis. Then, the bivariate wavelet analysis examines the co- movement relations between the electricity price and the possible price determinants in time-frequency space, where the frequency dimension corresponds to cycles with period lengths ranging from 2 days to 2-4 years. The bivariate results are presented graphically via wavelet coherence plots jointly with an indication of the statistical significance of the coherence, which is computed from simulations of independent surrogate series. Also derived from the bivariate analysis are phase difference plots that allow to assess the lag- lead relation between the pair of series and how this relation changes over time. Finally, the analysis in Chapter 5 goes beyond the usual bivariate wavelet analysis by computing also partial and multiple wavelet coherences. The partial wavelet coherence allows to analyze in time-frequency space the relation between the electricity price and the quantity series (e.g. the residual load series) after elimination of the potentially distorting influence of the price series (i.e. coal and gas prices), and vice versa. Besides, the multiple wavelet coherence allows to quantify the explanatory power that the quantity and price series jointly have for the electricity price across the time-frequency space. In the final part of Chapter 5, I summarize the insights gained from the wavelet analysis regarding the question of which of the possible electricity price determinants are most important at which frequency, and how this has changed during 2015-2023. Chapter 6 briefly reviews the key insights gained from the analyses in Chapters 3 - 5, and based on these insights, possible avenues for future research are outlined. 5 2 Energy as a Factor of Production To motivate the studies in Chapters 3 - 5 which deal with GHG emissions, energy (oil) supply and energy (electricity) prices, sect. 2.1 starts with a descriptive examination of the macroeconomic dependence on energy consumption by studying the relations between energy, GDP, and GHG emissions for the economies of the world. Sect. 2.2 proceeds with a further data description of historical trends for GHG emissions, oil production, and renewable energy generation shares. Finally, sect. 2.3 offers a brief sketch of a macroeconomic production function in which the previously established central role of energy and associated GHG emissions can be accounted for explicitly. 2.1 The Macroeconomic Relations between Energy, GHG Emis- sions, and GDP The data used in this section are GDP and population data from the Penn World Table 10.01,4 primary energy consumption data published by the OECD (called “primary energy supply” on their website),5 and GHG emission data published by the Potsdam Institute for Climate Impact Research (PIK).6 The PIK emission time series are officially called the PRIMAP-hist national historical emissions (version 2.1) time series, and the sources and methods used for the construction of this dataset are described in detail by Gütschow et al. (2016; 2019). The GHG emission series include all Kyoto gases (excluding land use, land use change and forestry, LULUCF) and are expressed in tons of CO2 equivalents. Figure 2.1 shows the bivariate relationships for each pair of the three time series (primary energy consumption, GDP, GHG emissions). The time series are computed as sums over the 110 countries for which data during the period 1971-2019 is available, comprising most of the major economies. On the left-hand side the series are depicted in levels. A linear fit is added as a red line, for which the linear regressions are reported above the panels. On the right-hand side the series are plotted as year-to-year percentage changes and as functions of time. The linear regressions of the red-colored series on the black-colored series are reported above the panels. In Figure 2.2, analogous plots are shown when the series are expressed in per capita terms. The upper row in Figure 2.1 shows how global energy consumption and GDP have in- creased over the past 50 years in perfect lockstep. The upper-left panel suggest an almost one-to-one co-movement relation between global GDP and global energy consumption. In order to remove the trend in the time series to avoid spurious correlation between the two nonstationary series, the relation is studied on the right using year-to-year changes. The high correlation is evident and the correlation coefficient amounts to √ 0.6 ≈ 0.77. The upper-right panel also shows that there were two recessions in terms of global GDP which followed or co-occurred with a decline energy consumption: the first one was in 1981 following a decline in energy consumption in 1979-81 after the second oil crisis, the second one was in 2008 after the 2007–08 financial crisis, which co-occurred with a tiny decline of global energy consumption in 2008. 4The data are accessible at https://www.rug.nl/ggdc/productivity/pwt/ 5The data are accessible at https://data.oecd.org/energy.htm 6The data are accessible at https://www.climatewatchdata.org/ 6 Figure 2.1: Global time-series relations, in total, 1971-2019 l l lll l l l lllll l l l l l l l l l l l l l ll l l l l l l l l l ll l l l l lll l l l 20 40 60 80 100 120 6 0 8 0 1 0 0 1 2 0 1 4 0 GDP (trillion US$ of 2017) P ri m a ry e n e rg y c o n s u m p ti o n ( P e ta − W h ) 1971 1983 1991 1998 2009 2019 y = 39 + 0.98x, R 2 = 0.984, T = 49 (0.018) Year Y e a rl y c h a n g e i n % 0 2 4 6 8 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5 2 0 1 0 2 0 1 5 Primary energy GDP y = −0.12 + 0.63x, R 2 = 0.6, T = 48 (0.08) l l lll l l l l l l ll l l l l l ll ll l l l l ll l ll l l l l l l l l l l l l lll l l l 20 40 60 80 100 120 2 0 2 5 3 0 3 5 4 0 GDP (trillion US$ of 2017) G H G e m is s io n s ( G ig a − to n s ) 1971 1983 1991 1998 2009 2019 y = 14 + 0.27x, R 2 = 0.991, T = 49 (0.004) Year Y e a rl y c h a n g e i n % − 2 0 2 4 6 8 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5 2 0 1 0 2 0 1 5 GHG emisions GDP y = −0.77 + 0.69x, R 2 = 0.63, T = 48 (0.08) l l lll l l l l l l ll l l l l l ll ll l l l l ll l ll l l l l l l l l l l l l lll l ll 60 80 100 120 140 2 0 2 5 3 0 3 5 4 0 Primary energy consumption (Peta−Wh) G H G e m is s io n s ( G ig a − to n s ) 1971 1983 1991 1998 2009 2019 y = 4 + 0.27x, R 2 = 0.995, T = 49 (0.003) Year Y e a rl y c h a n g e i n % − 2 0 2 4 6 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5 2 0 1 0 2 0 1 5 GHG emissions Primary energy y = −0.38 + 0.97x, R 2 = 0.83, T = 48 (0.06) Source: OECD energy data, PIK historical GHG emission data, Penn World Table 10.01. Note: World totals are computed from 110 countries, comprising all major economies. The equations above the panels on the right show the results from regressing the red time series on the black time series. 7 Figure 2.2: Global time-series relations, per capita, 1971-2019 l l l l l l l l l l l l l l ll l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l ll 6 8 10 12 14 16 1 5 1 6 1 7 1 8 1 9 2 0 2 1 GDP (per capita, 1000 US$ of 2017) P ri m a ry e n e rg y c o n s u m p ti o n ( p e r c a p it a , M W h ) 1971 1983 1991 1998 2009 2019 y = 12 + 0.55x, R 2 = 0.976, T = 49 (0.012) Year Y e a rl y c h a n g e i n % − 2 0 2 4 6 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5 2 0 1 0 2 0 1 5 Primary energy GDP y = −0.66 + 0.62x, R 2 = 0.61, T = 48 (0.07) l l l l l l l l l l l l l ll l l l l l l l l l l ll l l l l l l l l l l l l l l ll l l l l l l 6 8 10 12 14 16 5 .0 5 .2 5 .4 5 .6 5 .8 6 .0 6 .2 GDP (per capita, 1000 US$ of 2017) G H G e m is s io n s ( p e r c a p it a , to n s ) 1971 1983 1991 1998 2009 2019 y = 5 + 0.1x, R 2 = 0.67, T = 49 (0.01) Year Y e a rl y c h a n g e i n % − 4 − 2 0 2 4 6 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5 2 0 1 0 2 0 1 5 GHG emissions GDP y = −1.26 + 0.7x, R 2 = 0.63, T = 48 (0.08) l l l l l l l l l l l l l ll l l l l l l l l l l ll l l l l l l l l l ll l l ll ll l l l l l 15 16 17 18 19 20 21 5 .0 5 .2 5 .4 5 .6 5 .8 6 .0 6 .2 Primary energy consumption (per capita, MWh) G H G e m is s io n s ( p e r c a p it a , to n s ) 1971 1983 1991 1998 2009 2019 y = 2 + 0.19x, R 2 = 0.738, T = 49 (0.016) Year Y e a rl y c h a n g e i n % − 4 − 2 0 2 4 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5 2 0 1 0 2 0 1 5 GHG emissions Primary energy y = −0.44 + 1.01x, R 2 = 0.84, T = 48 (0.06) Source: OECD energy data, PIK historical GHG emission data, Penn World Table 10.01. Note: World totals are computed from 110 countries, comprising all major economies. The equations above the panels on the right show the results from regressing the red time series on the black time series. 8 Figure 2.3: Cross-sectional relation between energy consumption and GDP in 2010-19 l l l l l l l l l l l l l l l l l l l l l ll l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l GDP (per capita, 1000 US$ of 2017) P ri m a ry e n e rg y c o n s u m p ti o n ( p e r c a p it a , M W h ) CHN USA QAT KWT IRN TTO RUS DEU NOR HKG IRL ISL CAN AUS MLT PAN GBR IND LKA BGD YEM ZWE NER COD NGA BHR 1 0 1 0 0 1 10 100 y = 1.88 x 0.83 , R 2 = 0.86, n = 135 (0.03) l l l l l l l l l l l l l l l l l l l l l ll lll l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l 0 20 40 60 80 0 2 0 4 0 6 0 8 0 1 0 0 GDP (per capita, 1000 US$ of 2017) P ri m a ry e n e rg y c o n s u m p ti o n ( p e r c a p it a , M W h ) LUXUSA CHN SAU KWT BHR IRN RUS DEU JPN DNK NORSGP HKG CHEIRL CAN AUS MLT PAN GBR IND ARE FIN SWE KOR TKM LKA BRN y = −0.3 + 1.37 x + −0.0048 x 2 , R 2 = 0.74, n = 135 (0.17) (0.0024) Source: OECD energy data, Penn World Table 10.01. Note: The variables are taken as medians over 2010-2019. ISO alpha-3 country codes are shown for selected countries. Trinidad and Tobago (TTO), Qatar (QAT) and Iceland (ISL) (not shown in the right panel) are not used to compute the regressions in both panels as they are clearly outliers. The upper row in Figure 2.2 shows that the relations between per capita energy consump- tion and GDP exhibit correlations of the same high magnitude. From the upper-right panel showing the short-run relationship one can see that per capita GDP has declined in 1974 after a decline in per capita energy consumption in 1973-74 (the years of the first oil crisis), and also in 2014 jointly with a decline in per capita energy consumption in 2014-15. This brief descriptive analysis suggests that the direction of causation between energy and GDP goes in both ways, as there were clearly recessions that were preceded by a decline in energy consumption, but there were also recessions where the decline in energy consumption occurred only in the same year or afterwards. Moreover, the bottom row of Figure 2.1 shows a very close association between GHG emissions and primary energy consumption, which according to Figure 2.2, however, is less close when expressed in per capita terms. In particular, the bottom-left panel of Figure 2.2 reveals that the emission intensity of energy consumption has substantially declined after the second oil crisis, but then has increased back again during the 1990s and 2000s. In Figure 2.3, the relation between per capita energy consumption and GDP is analyzed from a cross-sectional perspective. For a global cross-section of 135 countries, where the variables are taken as the medians over 2010-19, the left panel shows the results from regressing energy consumption on GDP on a double-logarithmic scale, while the right panel shows the results for a quadratic specification. Figure 2.4 shows the same kind of plots and regressions where GHG emissions are used instead of energy consumption. Note that in the left panels the axes have a log-scale. The regression on the left in Figure 2.3 shows that the power function Energy/capita = 1.88(GDP/capita)0.83 fits the macroeconomic data well. As noticed by West (2017) and by Hagens and White (2021, p. 198), such a power law relation is quite similar to a well-known scaling law that applies 9 Figure 2.4: Cross-sectional relation between GHG emissions and GDP in 2010-19 l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l GDP (per capita, 1000 US$ of 2017) G H G e m is s io n s ( p e r c a p it a , to n s ) CHN USA QAT KWT IRN TTO RUS DEUNOR HKG IRLISL MLT PAN GBR IND LKA BGD YEM ZWE NER COD NGA BRN 1 1 0 1 10 100 y = 0.77 x 0.72 , R 2 = 0.79, n = 136 (0.03) l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 0 20 40 60 80 0 5 1 0 1 5 2 0 2 5 3 0 3 5 GDP (per capita, 1000 US$ of 2017) G H G e m is s io n s ( p e r c a p it a , to n s ) LUX USA CHN SAU KWTBHR IRN RUS DEUJPN DNK NOR SGP BRN HKG CHE IRL ISL AUS MLT PAN GBR IND SWE KOR TKM LKA y = 0.9 + 0.37 x + −0.0019 x 2 , R 2 = 0.59, n = 136 (0.06) (8e−04) Source: PIK historical GHG emission data, Penn World Table 10.01. Note: The variables are taken as medians over 2010-2019. ISO alpha-3 country codes are shown for selected countries. Trinidad and Tobago (TTO) and Qatar (QAT) (not shown in the right panel) are not used to compute the regressions in both panels as they are clearly outliers. to biological organisms, namely Kleiber’s law. This refers to the empirical relationship between the metabolic rate and the mass of animals, which is found to be well-described by a power function with an exponent of 0.75 (West (2017); Thommen et al. (2019)). In the environmental economics literature, quadratic or cubic functional forms have been employed for the relationship between environmental pollution and GDP, specifically in the literature that studies the so-called Environmental Kuznets Curve (EKC). The EKC refers to an inverse-U-shaped relation between a measure of economic development or output on the x-axis and an environmentally relevant variable on the y-axis. The concept was first studied by Grossman and Krueger (1991; 1995) and Panayotou (1993) with respect to air pollution such as SO2 emissions, but there were also early studies using CO2 emissions (e.g. Holtz-Eakin and Selden (1995)). In the following decades a long list of studies has been published on this topic, as recently surveyed by Shahbaz and Sinha (2019). Some of the papers also examine an EKC with energy consumption as the environmental variable, for example Richmond and Kaufmann (2006). From the right panels in Figures 2.3-2.4 it is possible to assess whether the relations between energy consumption / GHG emissions and GDP follows an EKC. Figure 2.3 shows that, although the quadratic term is statistically significant, the resulting curve is not inversely U-shaped since the hypothetical turning point for GDP per capita lies far outside the sample range (at about 143,000 US$ per capita). The picture for GHG emissions in Figure 2.4 is similar, as expected because both variables are strongly tied due to the CO2 emissions from fossil fuels. The hypothetical turning point is here comparatively lower at about 97,000 US$ per capita. Since this point is still quite outside of the sample range, I conclude that there is also no EKC for GHG emissions and GDP. In sum, Figures 2.1-2.4 elucidate the very strong connection between energy consump- tion / GHG emissions and GDP both from a global time-series perspective and from a 10 country-level cross-sectional perspective. This result is not very surprising from a physical understanding of the role of energy for economic production, i.e. from the point of view of thermodynamics (as expressed for example in the introductory quote to Chapter 1 from Vaclav Smil). As also stated by Ayres and Warr (2009, p. xviii): “In contrast to the neoclassical economic model, the real economic system depends on physical material and energy inputs, as well as labour and capital. The real economic system can be viewed as a complex process that converts raw materials (and energy) into useful materials and final services. Evidently materials and energy do play a central role in this model of economic growth.” Besides, Hall et al. (2001, p. 663) point out that “the two laws [of thermodynamics] say that nothing happens in the world without energy conversion and entropy production, with the consequence that every process of biotic and industrial pro- duction requires the input of energy”. In particular, the second law of thermodynamics implies that “the valuable part of energy (exergy) is transformed into useless heat at the temperature of the environment (anergy), and usually matter is dissipated, too. This results in pollution and, eventually, exhaustion of the higher grade resources of fossil fuels and raw materials” (Hall et al. (2001), p. 664). One of the first economists who stressed the importance of taking into account the relation between the laws of thermodynamics and the economic process was Nicholas Georgescu-Roegen (1971). Among others, these scientists have criticized the prevalent (macro-)economic doctrine where the important role of energy is largely ignored. As Smil (2022, p. 21) states: “Given all of these readily verifiable realities, it is hard to understand why modern economics, that body of explana- tions and precepts whose practitioners exercise more influence on public policy than any other experts, has largely ignored energy”. 2.2 Historical Trends for GHG Emissions, Oil Production, and Renewable Energy In this section, further historical time series on GHG emissions, oil production, and re- newable energy shares are depicted and briefly analyzed. Figure 2.5 depicts the GHG emissions (measured in tons of CO2 equivalents) during the time period 1900-2022 for the 10 countries that are the largest emitters as of 2022. As the gray line the figure also shows the aggregate emissions of the remaining countries. To allow for comparison with the sample of 16 European countries examined in Chapter 3, I also added a dashed black line that shows their total GHG emissions. First, one can see that the GHG emissions of the sample from Chapter 3 and of India have been converging so that both are of the same magnitude in 2022. The figure also illustrates the proportions of the GHG emissions of the two largest economies, the United States and China, versus those of “Others”. Particularly noteworthy is the unprecedented rise in the GHG emissions of China after 2000. On the other hand, while the Chinese population is more than four times as large as the US population, the Chinese GHG emissions were only about twice as large as the US emissions in 2022. Figure 2.6 shows the monthly production of liquid fuels for the world (left panel) and for the US only (right panel), obtained from the US Energy Information Administration (EIA). The blue area represents crude oil production and the lightest orange represents natural gas liquids (NGL) production.7 The NGL category includes the hydrocarbon 7The other orange areas pertain to refinery or processing gain and fuel ethanol production, for defini- 11 Figure 2.5: GHG emissions of top 10 emitters and others, 1900-2022 1900 1920 1940 1960 1980 2000 2020 0 5 1 0 1 5 Year G H G e m is s io n s ( G ig a − to n s ) Others CHN USA Sample as in Chap. 3 IND RUS JPN IDN BRA IRN MEX DEU Source: PIK historical GHG emission data Figure 2.6: World (left panel) and US (right panel) liquid fuel production Ju l 1 9 9 3 Ja n 1 9 9 5 Ju l 1 9 9 6 Ja n 1 9 9 8 Ju l 1 9 9 9 Ja n 2 0 0 1 Ju l 2 0 0 2 Ja n 2 0 0 4 Ju l 2 0 0 5 Ja n 2 0 0 7 Ju l 2 0 0 8 Ja n 2 0 1 0 Ju l 2 0 1 1 Ja n 2 0 1 3 Ju l 2 0 1 4 Ja n 2 0 1 6 Ju l 2 0 1 7 Ja n 2 0 1 9 Ju l 2 0 2 0 Ja n 2 0 2 2 Ju l 2 0 2 3 6 0 7 0 8 0 9 0 1 0 0 M ill io n b a rr e ls / d a y NGL (natural gas liquids) Other (mainly fuel ethanol) Refinery gain Crude oil 84.6 82.5 102.3 102.4 5 1 0 1 5 2 0 2 5 3 0 P e rc e n t N G L Pct NGL Ju n 1 9 9 7 D e c 1 9 9 8 Ju n 2 0 0 0 D e c 2 0 0 1 Ju n 2 0 0 3 D e c 2 0 0 4 Ju n 2 0 0 6 D e c 2 0 0 7 Ju n 2 0 0 9 D e c 2 0 1 0 Ju n 2 0 1 2 D e c 2 0 1 3 Ju n 2 0 1 5 D e c 2 0 1 6 Ju n 2 0 1 8 D e c 2 0 1 9 Ju n 2 0 2 1 D e c 2 0 2 2 0 5 1 0 1 5 2 0 M ill io n b a rr e ls / d a y Oxygenates NGL Fuel ethanol Refinery gain Crude oil 13 13.3 20.3 22.5 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 P e rc e n t N G L Pct NGL Source: Energy Information Administration (EIA). Own illustration, inspired by similar charts from Art Berman, Labyrinth Consulting Services, Inc. 12 F ig u re 2. 7: C ru d e oi l p ro d u ct io n of to p 18 oi l- p ro d u ci n g co u nt ri es , 19 71 -2 02 1 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 2 0 1 0 2 0 2 0 024681012 Million barrels / day S A U R U S U S A 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 2 0 1 0 2 0 2 0 0123456 Million barrels / day IR N C H N V E N 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 2 0 1 0 2 0 2 0 01234 Million barrels / day M E X A R E IR Q 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 2 0 1 0 2 0 2 0 01234 Million barrels / day C A N K W T N O R 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 2 0 1 0 2 0 2 0 0.00.51.01.52.02.53.0 Million barrels / day N G A B R A G B R 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 2 0 1 0 2 0 2 0 0.00.51.01.52.02.5 Million barrels / day L B Y A G O K A Z S ou rc e: O E C D en er gy d at a on cr u d e oi l p ro d u ct io n 13 Figure 2.8: Renewable energy (RE) shares in primary energy consumption, 1990-2020 1990 1995 2000 2005 2010 2015 2020 0 5 1 0 1 5 Including solid biofuels R E s h a re i n % o f p ri m a ry e n e rg y World G20 G7 EU28 OECD 1990 1995 2000 2005 2010 2015 2020 0 5 1 0 1 5 Excluding solid biofuels R E s h a re i n % o f p ri m a ry e n e rg y World G20 G7 EU28 OECD Source: OECD energy data on renewable energy. molecules ethane, propane, butane, and pentane. The shorter molecules (ethane, propane) are rarely used for transportation but rather for petrochemicals or heating and have a considerably lower energy content than crude oil. Ethane occupies the largest share of NGL production and is almost exclusively used to make plastics.8 The left panel of Figure 2.6 shows that the recovery of world liquid fuel production after the onset of the COVID crisis has to a larger extent come from NGLs than from crude oil. In fact, global crude oil production so far has not recovered to the peak production that occurred in November 2018, which was more than one year before the beginning of the COVID crisis. Of course, this may still be the aftereffects of the COVID crisis combined with a lagged recovery for crude oil in a capital-intensive industry, but this recent trend highlights the importance of examining the prospects of future crude oil availability. To provide a country-level resolution, Figure 2.7 shows the yearly crude oil production time series for 18 of the largest oil-producing countries over the period 1971-2021, obtained from the OECD website.9 Finally, Figure 2.8 shows the shares of renewable energy in primary energy consumption for several country groups, obtained from the OECD website.10 One can see a shift of the curves when comparing the left panel (with solid biofuels) to the right panel (without solid biofuels), but the rates of increase after 2005-2010 are similar in both panels, showing that this recent increase has come from the new renewables (solar, wind, non-solid biofuels) or hydropower. Still, when excluding solid biofuels, the renewable energy shares in 2020 amounted only to 6.3% for the world and to 9.8% for the EU-28. Overall the EU countries show the fastest rise of the renewable energy share. tions see https://www.eia.gov/tools/glossary 8See https://www.eia.gov/todayinenergy/detail.php?id=5930 9See ’crude oil production’ at https://data.oecd.org/energy.htm 10See ’renewable energy’ at https://data.oecd.org/energy.htm 14 2.3 A Framework for Macroeconomic Production Functions with Energy and GHG Emissions To conclude this chapter, what follows is a brief sketch of a framework for macroeconomic production functions in which the central role of energy consumption and of associated GHG emissions, as consistent with the conclusions from sect. 2.1, is explicitly taken into account. Specifically, I consider a function that maps the three inputs capital (K), labor (L), and energy consumption (E) into the economic output such as GDP (Y ), jointly with a second production function for GHG emissions (U) as a by-product from producing the economic output. Besides, energy consumption is further subdivided into fossil fuel energy (Ef ) and energy from other sources (Eo), where E = Ef + Eo. The general framework thus looks as follows: Y = F ( KA Y K , LA Y L , (Ef + Eo)A Y E ) , U = G ( K/A U K , L/A U L , Ef/A U E ) , (2.1) where also the partial derivatives of the functions F and G with respect to each argument are nonnegative. The function F contains as parameters the augmentation indices of capital (A Y K ), labor (A Y L ), and energy (A Y E ) which can be interpreted as reflecting changes in technology or efficiency that improve the capability of the respective inputs to produce GDP. For the function G, the parameters A U K , A U L , and A U E are analogous augmentation indices that reduce the GHG emissions per input use. To give an example, an increase in A U E (lowering GHG emissions per fossil energy consumption) could occur due to the substitution of coal with gas (since gas contains less carbon per unit of energy), due to reduced leakage of methane emissions at gas or oil production sites, or due to the application of carbon capture and storage (CCS). The next chapter now continues with an environmental efficiency analysis of 7 main GHG emitting sectors in 16 European countries, from which GHG emission reduction potentials are estimated for the sectors and countries. While the analysis does not explicitly include energy consumption, an implicit estimation of the functional relation (or rather of the efficient frontier) between the other variables (GHG emissions, economic output, labor and capital) is conducted by using a nonparameteric efficiency analysis approach. 15 3 Greenhouse Gas Emission Reduction Potentials in Europe by Sector: A Bootstrap-Based Nonpara- metric Efficiency Analysis11 3.1 Introduction The reduction of greenhouse gas (GHG) emissions on a global level is the key measure to counteract the detrimental effects of climate change and global warming. Other ap- proaches to limit global warming, like carbon removal or geoengineering approaches are either infeasible or extremely risky (see Nordhaus (2019, p. 1998) for a clear statement). This is largely undisputed in the economic literature (see the survey articles by Myhre et al. (2001), Aldy et al. (2010), Hsiang and Kopp (2018) and Tol (2018), among others) and is the basis for several international agreements. The most prominent agreements are the Kyoto Protocol of 1997 and the Paris Agreement on climate change of 2015 to reduce GHG emissions to reach the 2°C target, meaning the stabilization of the increase in temperature at “well below 2°C above pre-industrial levels”.12 The European Union (EU) as a key actor in this area has achieved an agreement among its member countries to reduce GHG emissions by 40% until 2030, 60% until 2040 and 80% until 2050, compared to the levels of 1990 (EU (2011), p. 3). Recently these targets have been tightened to reduce GHG emissions by 55% until 2030, 80% percent until 2040 and to reach climate neutrality by 2050, also accounting for the effects of carbon removal technologies, land use change and forestation (see EU (2020) and especially figure 1 therein). Efforts to improve the productive efficiency of sectors could be a potentially important building block of an emission reduction strategy. Therefore it is important to know to which extent GHG emissions could be reduced by achieving productive efficiency while holding the economic inputs and outputs constant. In our companion paper Krüger and Tarach (2020) we applied nonparametric methods of efficiency analysis in the presence of undesirable outputs derived from a variant of data envelopment analysis (DEA) to give an account of the potential reductions of GHG by country and sector for the period 2008- 2016. The main finding is that efficiency improvements can contribute considerably to emission reduction, albeit the extent to which the measured potentials could be realized in practice remains open. However, the measurement approach used in the companion paper is purely deterministic and prone to biases. Furthermore, no account of the estimation uncertainty is provided there. In this paper we pick-up these issues by combining the nonparametric efficiency mea- surement approach with a specifically designed bootstrapping procedure to achieve a bias correction and to compute confidence intervals for assessing estimation uncertainty. To our knowledge this is the first time that a nonparametric approach combined with stochas- tic elements is applied in an environmental efficiency measurement context. We report estimates of aggregate emission reduction potentials for 16 major EU countries and 7 main 11This chapter is joint work with Jens Krüger and is published in Environmental and Resource Eco- nomics, see Krüger and Tarach (2022). 12This 2°C target is defined in Article 2 of the Paris Agreement jointly with the plea to pursue an even tighter target of 1.5°C, see https://newsroom.unfccc.int/process-and-meetings/the-paris-agreement/the- paris-agreement. 16 sectors of the private economy. As emissions we consider a broad GHG aggregate as well as splits to single GHG (CO2, CH4 and N2O). The results show that the bias correction leads to larger emission reductions compared to the “raw” measures from our compan- ion paper which are based on the purely deterministic approach. We can show that the potentials for emission reduction are concentrated in certain countries and sectors. In addition, we find that the estimation uncertainty is substantial in these cases. In contrast to much of the literature on eco-efficiency which is also concerned with emission reduction on a macroeconomic level or major sectors we assess the contribution of potential efficiency improvements to the EU reduction targets by expressing them as potential reductions measured in physical units, i.e. CO2 equivalents (CO2e). The usual habit in the literature (see Camarero et al. (2014), Färe et al. (2004), Korhonen and Luptacik (2004), Kortelainen (2008), Kuosmanen and Kortelainen (2005), Rashidi and Farzipoor Saen (2015), Zaim and Taskin (2000), Zhou and Ang (2008) and Zofío and Prieto (2001), among others) is to focus on relative measures instead. More closely related to our analysis are studies such as Domazlicky and Weber (2004) and Krautzberger and Wetzel (2012) which are also based on a methodological setting employing directional distance functions and are also confined to specific industries. The exposition in this paper starts with a description of the data and the country-sector coverage in section 3.2. This is followed by the description of the nonparametric method- ology we use to obtain our estimates of emission reduction potentials in section 3.3. In this section, the implementation of the bootstrapping approach as well as the computa- tion of the bias-corrected measures and the confidence intervals are also outlined. Section 3.4 contains the discussion of the results from several specifications of the undesirable outputs. The specifications comprise a single total GHG aggregate as well as splits to CO2, CH4 and N2O. We also discuss the results of a variant where possible enhancements of the economic output are permitted in addition to the emission reductions. Policy rec- ommendations are provided at the end of the section. The final section 3.5 concludes with an evaluation of the contribution of the emission reduction by efficiency improvements to the EU emission reduction targets and discusses the feasibility of the potential reductions measured. 3.2 Data Description The data required for the efficiency analysis comprise the inputs, the good (desirable) outputs and the bad (undesirable) outputs, i.e. the emissions of greenhouse gases. In the subsequent measurement of inefficiency and the potential emission reduction derived from the inefficiency measure we always include the two conventional inputs labor and capital as well as value added as the single economic output. The emissions as undesirable outputs are used in different forms. As the description of the methods will show, the inefficiency is measured as the potentially reachable enhancement of the good output and/or the potentially reachable reduction of the emissions. The economic data, meaning the inputs and the good (desirable) output are taken from the EU-KLEMS database. The November 2019 release we use is described by Stehrer et al. (2019) and can be obtained from https://euklems.eu. Labor input is measured in total hours worked by employees (comprising self-employed persons and expressed in full-time equivalents). Capital input is quantified by the real fixed capital stock (at constant 2010 prices). The output variable 17 is gross value added (also at constant 2010 prices).13 Using this variable is associated with a much more comprehensive data coverage compared to the alternative of using a gross output measure with materials and energy as additional input variables.14 The emissions data to quantify the bad (undesirable) outputs15 are taken from two sources.16 As greenhouse gas (GHG) emissions, we focus on the three main greenhouse gases (GHGs) which are emitted by anthropogenic sources, namely carbon dioxide (CO2), methane (CH4) and nitrous oxide (N2O). The global warming potentials usually differ for each GHG, but they can be converted to CO2 equivalents (abbreviated CO2e and measured in tons, kilotons or megatons). CO2 emissions are retrieved from the World Input Output Database (WIOD) described in Timmer et al. (2015) and can be down- loaded from http://www.wiod.org. The data for CH4 and N2O emissions are retrieved from the Eurostat Air Emission Accounts (AEA).17 In the AEA database, CH4 and N2O emissions are already expressed in tons of CO2e and so we obtain our measure of total GHG emissions by simply adding them to the CO2 emissions from the WIOD. There are further GHGs which are of minor quantitative importance and therefore neglected.18 All three major GHGs have specific anthropogenic sources. CO2 emissions stem primarily from burning fossil fuels (coal, oil and natural gas), but also from industrial processes such as the manufacturing of cement. In addition, CO2 is emitted from land use, land use change and forestry (LULUCF). Although its global warming potential per ton is less than that of CH4 or N2O, CO2 is quantitatively the most important GHG. In 2010 CO2 emissions (without LULUCF) accounted for 82% of total GHG emitted by the EU (Debelke and Vis (2015), p. 96). CH4 has an atmospheric lifetime of 12 years, meaning that on average it stays in the atmosphere for only 12 years before it is broken down into CO2 and water (Hsiang and Kopp (2018), p. 12). It has a global warming potential of 25 CO2e (meaning one ton of CH4 has the global warming potential of 25 tons of CO2, Eurostat (2015), p. 105). The two major anthropogenic sources of CH4 emissions are industrial livestock farming and the exploitation of fossil fuels. Natural gas (largely consisting of CH4) may be leaking when recovered from gas or oil fields or during transport and storage. CH4 is also contained in coal beds (coal mine methane), especially in deeper coal beds and coals with higher carbon content (i.e. hard coal), and may similarly leak during coal mining (Kholod et al. (2020)). In the EU, CH4 emissions already declined between 1990-2010 by 32% (Debelke and Vis (2015), p. 96). N2O is a very potent GHG with the same global warming potential as 298 tons of CO2 (Eurostat (2015), p. 105) during an atmospheric lifetime of 116 ± 9 years (Tian et al. 13We always mean the good (desirable) economic output when we simply refer to the output in the following. 14This alternative would also increase the dimensionality of the input-output space which is a crucial issue for nonparametric analyses in general. 15We subsequently refer to emissions when we mean the bad (undesirable) outputs. 16These data bases are used instead of the Emissions Database for Global Atmospheric Research (EDGAR) because of their conformability to an economic sector classification and their coverage of more recent periods. 17These data can be accessed at https://ec.europa.eu/eurostat/web/products-datasets/- /env_ac_ainah_r2. 18Further anthropogenic GHGs are sulphur hexafloriode, hydrofluorcarbons and perfluorcarbons, which are not included in our measure of total GHG emissions. They made up only 2% of total GHG emissions in the EU-28 in 2010 (Debelke and Vis (2015), p. 96), slightly rising to about 2.5% in 2018 (EEA data). 18 (2020)). In addition, N2O has a depleting effect on the stratospheric ozone layer. The major anthropogenic source of N2O is the agricultural sector, in particular the large-scale use of nitrogen fertilizers. According to Tian et al. (2020) agricultural emissions accounted for about 70% of anthropogenic N2O emissions globally in 2007-16. Other comparatively smaller anthropogenic sources include the fossil fuel and chemical industry. In contrast to rising or stagnant N2O emissions in most other countries globally, European emissions from agriculture declined by 21% between 1990-2010 (Tian et al. (2020), p. 254), which the authors attribute to European agricultural policies favoring more efficient fertilizer use. Besides, non-agricultural N2O emissions in the EU were reduced even more strongly during that period, mainly due to improved abatement technologies in the chemical industry (Tian et al. (2020), pp. 253-255). Assessing the data coverage in the database we are able to achieve an almost complete coverage for 16 countries and 7 sectors during the period 2008-2016 on a classification of sectors (industries) according to NACE Rev. 2 (equivalent to ISIC Rev. 4). The countries covered comprise (with World Bank country codes in parentheses): Austria (AUT) Germany (DEU) Poland (POL) Belgium (BEL) Greece (GRC) Slovakia (SVK) Czech Republic (CZE) Ireland (IRL) Spain (ESP) Denmark (DNK) Italy (ITA) Sweden (SWE) Finland (FIN) Netherlands (NLD) United Kingdom (GBR) France (FRA) The sectors covered are: A Agriculture, Forestry and Fishing B Mining and Quarrying C Manufacturing D Electricity, Gas, Steam and Air Conditioning Supply E Water Supply Sewerage, Waste Management and Remediation Activities F Construction G Wholesale and Retail Trade; Repair of Motor Vehicles and Motorcycles H Transportation and Storage The emissions data in the AEA database are only available for a sector combining the sectors D and E. So we had to aggregate the economic input-output data of the sectors D and E to a combined sector, henceforth named DE. Cross checking assures that the sums of the values of the sectors D and E are very close to the values of the combined sector DE which is also available in the EU-KLEMS data.19 Since the sector D is considerably larger than E in most countries we refer to the combined sector DE frequently as “energy” or as “energy and water” in the subsequent discussion. We exclude Estland, Lithuania, Luxembourg and Slovenia from our analysis despite full data coverage. The reason is that these are very small countries and Luxembourg is merely a large city rather than a country. Including those small countries can severely bias the entire efficiency analysis when they determine parts of the frontier function and overstate the potential emission reductions. Growiec (2012) provides further discussion 19An exception are two capital stock values of Belgium in 2008 and 2009 where the sums of the values of the sectors D and E deviate from those of the combined sector DE by 18 and 5 percent, respectively. Here we use the time series of the sum of the single sectors which looks more plausible than the time series of the combined sector. In the case of Spain only data for the combined sector are available and therefore these data are used directly. 19 of this issue. In some of these countries we also suspect recording errors in the data for some sectors (e.g. zero emissions in sector G in Slovenia). The value added and capital stock data are directly expressed in Euro for the major- ity of the countries (appropriately deflated with base year 2010). In the case of the non-Euro countries Czech Republic, Denmark, Poland, Sweden and the United Kingdom these variables are expressed in the respective national currencies. To convert the data to a common currency we use purchasing power parities (PPPs) from the OECD Na- tional Accounts Statistics (OECD (2020)). While exchange rates only convert currencies, PPPs also take account of different price levels of the countries. This is important since price levels tend to be systematically higher in high-income countries than in low-income countries. Using exchange rates would therefore overstate the values of the variables in the case of high-income countries and understate them in low-income countries. Instead, PPPs convert expenditures to a common price level. This is also important for countries with a common currency (as the Euro) which also can have rather different national price levels.20 We split these data in two five-year subperiods t1 = 2008-2012 and t2 = 2012-2016 and take medians over these subperiods for the subsequent empirical analysis. This eliminates the effects of single or even two outlying observations and makes the efficiency analysis more robust. The way of taking medians to robustify the analysis is in our view preferable to the alternative of outlier detection by methods such as those proposed by Wilson (1993) and subsequent outlier elimination. This procedure also solves the problem with two missing values in sector C of Ireland.21 Thus, when we refer to the first and second subperiod in the following we always mean the medians of the inputs and outputs (including emissions) over the indicated five-year intervals. The aggregate GHG emissions over all countries and sectors are 3341 mt of CO2e in the first subperiod, declining to 3070 mt in the second subperiod. Figure 3.1 shows stacked barplots of the three GHG emission variables for both subperiods (the corresponding data are reported in Table A1 in the appendix). The left-hand side of each plot depicts the bars for the sectors, followed by the bars of the countries on the right-hand side (separated by the thick vertical line). This kind of plot gives a succinct summary of the distribution of the aggregate emissions over sectors and countries jointly with an indication of the distribution of the different GHGs (CO2, CH4 and N2O in mt of CO2e). More descriptive information on the data is discussed in the companion paper of Krüger and Tarach (2020). From Figure 3.1 we immediately see that the sectors C and DE are most emission intensive, while A and H also contribute considerably, and the remaining sectors (B, F and G) are of minor importance. CO2 is the quantitatively most important emission category in all sectors except A where CH4 and N2O emissions are dominating. CO2 is the main emission category in all countries, including those with large aggregate emissions (Germany, Spain, France, the United Kingdom, Italy and Poland), although the contribution of CH4 and N2O is also visible here. While the overall quantity declines from the first to the second 20PPPs are also central for the construction of comparable national accounts provided in the Penn World Table (see Feenstra et al. (2015)). 21In the case of Ireland the capital stock values for the final years 2015 and 2016 are missing in sector C. Since the preceding values 2012-2014 show a rising trend (and capital is an accumulating stock variable) we can safely suppose that the missing values are larger than the value in 2014. Then taking the 5- year median over the subperiod 2012-2016 will result in just the value of 2014 irrespective of the exact magnitudes of the missing values. 20 Figure 3.1: GHG emissions across sectors and countries N2O CH4 CO2 0 200 400 600 800 1000 1200 A B C DE F G H AUT BEL CZE DEU DNK ESP FIN FRA GBR GRC ITA IRL NLD POL SVK SWE GHG Emissions (in mt of CO2e) 2008 − 2012 N2O CH4 CO2 0 200 400 600 800 1000 1200 A B C DE F G H AUT BEL CZE DEU DNK ESP FIN FRA GBR GRC ITA IRL NLD POL SVK SWE 2012 − 2016 subperiod, the distribution of the emissions across sectors and countries is rather similar in both subperiods. 3.3 Nonparametric Efficiency Measurement and Bootstrapping For the estimation of the potential emission reductions we apply nonparametric methods of efficiency analysis. These methods are an extension of data envelopment analysis (DEA), developed by Charnes et al. (1978) and Banker et al. (1984). The specific modification we rely on is based on the device of the directional distance function (DDF), introduced by Chambers et al. (1996) and extended to an environmental context by Chung et al. (1997). This approach allows to measure inefficiency as the distance to a piece-wise linear frontier function along a mix of possible reduction of inputs and enhancement of some outputs (the good, desirable outputs), while other outputs (the bad, undesirable outputs) are supposed to be reduced (see Färe and Grosskopf (2004)). This property of reducing outputs allows to incorporate undesirable outputs like GHG emissions in a consistent way (Zhou et al. (2008b)). Like in DEA, here also no price information is required and no functional form assumptions about the underlying technology (e.g. a production function) need to be imposed. These are major advantages of the nonparametric approach. 3.3.1 Technology Set The nonparametric approach of efficiency analysis is based on the concept of an abstract technology set, comprising the feasible input-output combinations. It can be stated as 21 T = {(x,y,u) ∈ R m+s+r + : x ≥ 0 can produce (y,u) ≥ 0}, (3.1) where x denotes the m-vector of the input quantities, y the s-vector of the quantities of the good (desirable) outputs and u the r-vector of the quantities of the bad (undesirable) outputs.22 Since we are dealing with sectors within countries it is suitable to suppose that each sector operates with a different technology set.23 To impose some structure on the technology set it is supposed to be closed, bounded and convex (Färe and Primont (1995)). Furthermore, it is supposed that standard axioms such as strong disposability of the inputs and the good outputs are satisfied. Two additional axioms are required in the context of an environmental efficiency analysis to incorporate the special role of undesirable outputs in a consistent way. The first is null-jointness, meaning that it is not possible to produce positive quantities of the good outputs without generating emissions (i.e. if (x,y,u) ∈ T and u = 0 then y = 0). The second is weak disposability stating that proportional reductions of emissions are always feasible as long as the good outputs are reduced by the same proportion (i.e. if (x,y,u) ∈ T then (x, αy, αu) ∈ T for α ∈ [0, 1]). For more detailed discussions of these axioms see Färe and Grosskopf (2004), Färe et al. (2005) and Zhou et al. (2008a).24 3.3.2 Directional Distance Functions The directional distance function (DDF) is defined on the technology set T as proposed by Chambers et al. (1996) and extended to the incorporation of undesirable outputs by Chung et al. (1997). It is a generalization of the Shephard (1970) distance function to the case of non-proportional changes of the inputs and outputs and can be formally stated as DDF (x,y,u; gx, gy, gu) = sup{δ ≥ 0 : (x− δgx,y + δgy,u− δgu) ∈ T }. (3.2) Herein, the inefficiency measure δ expresses the distance of a particular input-output com- bination (x,y,u) towards the boundary of the technology set along a particular direction gx ≥ 0, gy ≥ 0, gu ≥ 0. This measure is equal to zero if the input-output combination is a point on the boundary (is on the frontier function) and it is larger than zero if the input-output combination is below the boundary (is below the frontier function). In the following we mostly impose the restriction gx = 0 and gy = 0, meaning that the inefficiency is measured exclusively as the extent of possible reduction of the bad outputs. In our application the entities under investigation are sectors in different countries. On such a high level of aggregation it is appropriate to assume that no reduction of input usage is intended. Since we are mainly interested in measuring the maximum potential 22In the subsequent discussion of the results we will frequently simply refer to the outputs when we mean the good outputs and to the emissions when we mean the bad outputs. 23Here we also include conventional inputs as labor and capital. Related papers such as Picazo-Tadeo et al. (2012) measure eco-efficiency scores by directional distance functions without using inputs. 24An alternative to this approach is the so-called by-production approach proposed by Murty et al. (2012) which relies on the availability of abatement options (and requires appropriate data). This ap- proach models the technology set as the intersection of two parts to be estimated separately. One part is related to the production of the good outputs and the other part is related to the production of the bad outputs. This setting avoids the assumptions of weak disposability and null-jointness. Further discussion and critique is provided by Dakpo et al. (2016). 22 emission reductions, we also exclude the possibility of output enhancement for most of the analysis. In one variant we only impose gx = 0 so that the output enhancement would also be possible. The data required for the computation of the DDF pertain to n countries in a particular sector. The analysis is performed for each sector separately, so that an additional index to distinguish sectors is not necessary. The data for the m inputs are contained in the m × n matrix X with the ith column xi comprising the input quantities of country i (i = 1, ..., n). Likewise, the data for the s good outputs are contained in the s× n matrix Y and the data for the r bad outputs are contained in the r × n matrix U , with the ith columns yi and ui comprising the observations pertaining to country i for the good and bad outputs, respectively. In (3.2) the direction vectors gy and gu are not specified. A frequent choice in applications is to make the directions proportional to the variables yi and ui which serves to let the inefficiency measure be invariant to units of measurement (see e.g. Chung et al. (1997) and Färe et al. (2007)). Since this is restrictive it would be beneficial to compute the directions endogenously. Hampf and Krüger (2015) propose one possibility to endogenize the direction in an environmental efficiency setting and Färe et al. (2013) provide a re- lated proposal to compute endogenous directions in the case of a slacks-based inefficiency measure. As pointed out by Chen and Delmas (2012), these proposals have the additional advantage of avoiding the problem of dominated (weakly-efficient) reference points on the frontier function. We follow Hampf and Krüger (2015) and propose the following optimization problem to endogenize the computation of the direction vector max δ,αy ,αu,λ δ s.t. xi ≥ Xλ yi + δαy � yi ≤ Y λ ui − δαu � ui = Uλ 1 ′αy + 1 ′αu = 1 λ,αy,αu ≥ 0 (3.3) where ’�’ denotes the direct (Hadamard) product. Herein, λ is a n-vector containing the weight factors to determine the reference point on the frontier function. The direction weights αy and αu are computed jointly with δ and λ with the objective of maximizing the distance towards the frontier function. The identification of δ is permitted by the additional constraint 1 ′αy + 1 ′αu = 1. In this specification the direction vectors are proportional to yi and ui which lets the inefficiency measure be invariant to the units of measurement. The optimization problem (3.3) is nonlinear and therefore difficult so solve. This is caused by δ and αy or αu arising multiplicatively. By defining γy = δαy and γu = δαu the problem can be transformed to a well-behaved linear programming problem max γy ,γu,λ 1 ′γy + 1 ′γu s.t. xi ≥ Xλ yi + γy � yi ≤ Y λ ui − γu � ui = Uλ λ,γy,γu ≥ 0 (3.4) 23 Taking the constraint 1′αy+1 ′αu = 1 from (3.3) into account we easily see that the value of the objective function 1 ′γy + 1 ′γu = δ · (1′αy + 1 ′αu) is equal to δ as before. Program (3.4) can be easily solved by the ordinary simplex algorithm.25 The solution values for δ, αy and αu can be backed out from the solutions for γy and γu by δ = 1 ′γy +1 ′γu as well as αy = γy/δ and αu = γu/δ. For a particular country i the solution values are denoted δi, αyi, αui, γyi, γui and λi (i = 1, ..., n).26 With these solution values we can compute the efficient input-output combination on the frontier function with the coordinates x̂i = Xλi, ŷi = Y λi and ûi = Uλi. The potential reductions of the r bad outputs for country i in the sector under consideration can be computed as ui − ûi = γui � ui = δiαui � ui. We see that the potential emission reductions depend on the magnitude of the inefficiency measure δi as well as on the optimized direction vector αui of country i. The total emission reduction potential of country i is the sum over all emission categories RPi = 1 ′(ui − ûi) with 1 denoting a conformable vector of ones and the prime denoting transposition. The sum can, of course, only be validly computed if the emission variables are denominated in a common unit of measurement. This is indeed the case in our application where greenhouse gas emission are expressed in CO2 equivalents. To report the results later on we further aggregate the potential emission reductions across countries and sectors. Potential output enhancement can likewise be computed as ŷi − yi = γyi � yi = δiαyi � yi for the case where we do not impose γyi = 0 or αyi = 0 a priori. 3.3.3 Variable Returns to Scale All above stated optimization problems compute the inefficiency measures under the as- sumption of constant returns to scale (CRS). In a cross-country sectoral setting with countries of rather different size and with a rather different sectoral structure CRS seems to be an overly restrictive assumption. So it would be beneficial to get rid of this rather unrealistic assumption and to measure inefficiency under variable returns to scale (VRS). In nonparametric approaches of efficiency measurement VRS is usually induced by adding the constraint 1 ′λ = 1 to the optimization problems. In the case of environmental effi- ciency analysis this would violate the weak disposability property. Zhou et al. (2008a) show how to induce VRS in a way which is consistent with weak disposability. This implementation again leads to a linear programming problem max β,γy ,γu,ζ 1 ′γu + 1 ′γu s.t. βxi ≥ Xζ yi + γy � yi ≤ Y ζ ui − γu � ui = Uζ 1 ′ζ = β 1 ≥ β ≥ 0 , ζ,γy,γu ≥ 0 (3.5) with an additional parameter β which is bounded in [0, 1]. Details can be found in Zhou et al. (2008a). As before, we obtain the solution values for γu which allow to back out 25For the computation of the solutions in this paper the R-package “lpSolve” is used. 26In the case of the efficient countries (with δ = 0) the solution for αy and αu is indeterminate. Clearly, there exists no direction towards the frontier function if an observation already stays on the frontier function. 24 δ = 1 ′γy + 1 ′γu, αy = γy/δ and αu = γu/δ and to compute the emission reduction potentials. This problem can again be easily solved by the simplex algorithm. Here also, the solution values are denoted δi, αyi, αui, γyi, γui and λi for a particular country i (i = 1, ..., n). We stick to the VRS assumption throughout this paper. 3.3.4 Bootstrapping The inefficiency measures and the derived reduction potentials are estimates from a data sample which are subject to measurement error and therefore stochastic in nature. Fron- tier function estimation is associated with a further peculiarity. Specifically, the empirical implementation of the linear programming problems (3.4) or (3.5) is based on the ob- served input-output combinations in the data. This lets the empirically estimated fron- tier function provide a closer envelopment of the data than the true (unobserved) frontier function. As a consequence, the empirically determined technology set T̂DDF underlying the empirical analysis is a subset of the true technology set T , i.e. T̂DDF ⊆ T . This leads to downward-biased estimates of the inefficiency measures and the emission reduction potentials. This bias can be substantial and bootstrapping provides a practical way to achieve a correction (see Simar and Wilson (2008, 2011)). We resort to a bootstrapping approach to compute bias-corrected estimates of the re- duction potentials and to establish confidence intervals for these measures. The specific approach pursued here is analogous to the procedure proposed by Simar and Wilson (1998) adapted to the setting of directional distance functions. Compared to the double- bootstrap algorithm of Simar et al. (2012) the chosen approach is more transparent and easier to communicate. The approach of Simar et al. (2012) uses a complicated orthog- onal transformation of the data and two smoothing loops which requires the selection of two critical bandwidth parameters instead of one. This bandwidth choice is particularly problematic in small-sample situations. Moreover, the algorithm seems not to be adapted to the inclusion of bad outputs since the direction vector pertaining to the outputs is restricted to be non-negative. The smoothed bootstrap algorithm adapted from Simar and Wilson (1998) to the DDF setting starts with some preparatory steps. First, the DDF and the optimal directions are computed from the original data by solving (3.5) to obtain δ̂i as well as the optimal directions αyi and αui for all i = 1, ..., n. The directions are computed once and kept fixed during the whole procedure. Furthermore, the bandwidth parameter h for the smoothing is chosen as described in Simar and Wilson (2011) where also some R code is provided. The main part of the bootstrapping algorithm cycles B times through the following steps: • A bootstrap resample is obtained by first drawing with replacement from D = {δ̂1, ..., δ̂n,−δ̂1, ...,−δ̂n} which implements a boundary reflection about zero. The result of this step is denoted δ̃i (i = 1, ..., n). • The smoothing step is performed by adding h · εi to each draw, where the εi are independent standard normal draws, thus obtaining δ̃i + h · εi and finally returning δ∗i = ∣∣∣δ̄ + (δ̃i + h · εi − δ̄)/ √ 1 + h2/σ̃2 δ ∣∣∣ for all i = 1, ..., n where δ̄ and σ̃2 δ denote the sample mean and variance of δ̃i (i = 1, ..., n), respectively. 25 • These resampled inefficiencies are used to construct the bootstrap resample of the reference points by setting x∗ i = xi, y∗ i = yi + (δ̂i − δ∗i )αyi � yi, u ∗ i = ui − (δ̂i − δ∗i )αui � ui for all i = 1, ..., n. By that operation the observation (yi,ui) is first projected on the frontier (by +δ̂i) and then randomly away from the frontier (by −δ∗i ) along the fixed direction (αyi � yi and −αui � ui). The resulting bootstrap resample consists of X∗ = (x∗ 1, ...,x ∗ n), Y ∗ = (y∗ 1, ...,y ∗ n) and U ∗ = (u∗ 1, ...,u ∗ n). • The efficiency measures are computed by solving (keeping the directions fixed) max β,δ,ζ δ s.t. βxi ≥ X∗ζ yi + δαyi � yi ≤ Y ∗ζ ui − δαui � ui = U ∗ζ 1 ′ζ = β β ≥ 0 , ζ ≥ 0 (3.6) for each i = 1, ..., n, where xi, yi and ui constitute the original observation for country i and X∗, Y ∗ and U ∗ are taken from the preceding step. The results are the bootstrap inefficiency measures δ̂∗i for all i = 1, ..., n. From the bootstrap inefficiency measures the emission reduction potentials ∆û∗ i