Straight to Journal Publications, Other Publications, and Book Draft on Environmental Economics.

  Current Working Papers  

Short Abstracts:

Full Abstracts:

1   Climate Economics

1.1 ACE – Analytic Climate Economy. (Forthcoming in AEJ: Ecomic Policy)

Short: The Analytic Climate Economy (ACE) closes a gap between complex numeric integrated assessment models used in policy advising and stylized models built for analytic insight. It connects a general production system relying on a variety of energy sectors to a climate system explicitly tracking carbon emissions, greenhouse effect, and temperature dynamics. The paper discusses how model components and calibration assumptions affect the optimal carbon taxes and shows that different reasonable calibrations can lead to vastly different optimal taxes. (collapse) Full Abstract: The paper derives the optimal carbon tax from a comprehensive integrated assessment model (IAM) in closed form. The model links IAM components and parametric assumptions directly to their policy impacts. Novel to analytic IAMs are the explicit temperature dynamics, a general economy, energy sectors including capital, various degrees of substitutability across energy sources, aspects of capital persistence, and objective functions including CES preferences and population weighting. In particular, I discuss the distinct roles of carbon and temperature dynamics in determining the optimal tax level. The analytic non-linear temperature model is at the forefront of the models used in policy advising. A distinction between consumption and investment sectors plays an important role for model calibration. I use the see-through model to quantify and discuss various aspects of IAM calibrations. ACE opens the door to tractable forward-looking stochastic modeling and dynamic strategic interactions in complex IAMs, explored in accompanying work. Full Abstract

1.2 Uncertainty in the Analytic Climate Economy.

Short: The paper analyzes the optimal carbon tax under uncertainty about carbon dynamics, temperature response, and climate damages. Building on the Analytic Climate Economy (ACE), I derive a general stochastic solution for an arbitrary degree of Arrow-Pratt risk aversion, which I disentangle from the base model's intertemporal elasticity of substitution (Epstein-Zin preferences). Temperature dyanmics as opposed to carbon dynamics becomes the crucial driver of the risk premium and the stochastic model is even more senstivity to time preference than the deterministic model. (collapse) Full Abstract: The paper derives the optimal carbon tax from a comprehensive integrated assessment model (IAM) in closed form. The solution links IAM components and parametric assumptions directly to their policy impacts. It facilitates stochastic analysis and highlights the interaction between elements that compound the optimal tax. Uncertainty makes IAMs even more sensitive to the discount rate and its composition. Using a recent survey’s median estimate for pure time preference, the endogenous climate uncertainty almost triples the optimal tax. Full Abstract

1.3 Pricing Climate Risk. With Svenn Jensen.

Short: We derive a general formula for the risk premium on the optimal carbon price in response to the large uncertainties surrounding the climate's sensitivity to antropogenic emissions. The formula expands simple precautionary savings analysis to more complex economic interactions, and it trains economic intuition about policy response to uncertainty. (collapse) Full Abstract: Anthropogenic greenhouse gas emissions are changing the energy balance of our planet. Various climatic feedbacks make the resulting warming over the next decades and centuries highly uncertain. We derive a general analytic formula for the “risk premium” on the resulting climate policy. It clarifies the distinct roles of risk aversion, prudence, characteristics of the damage formulation, and future policy response. More generally, the formula expands simple precautionary savings analysis to more complex economic interactions, and it trains economic intuition about policy making under uncertainty. The formula relies on approximations. We compare the results to the optimal policy in a recursive stochastic dynamic programming implementation of DICE. Our analytic formula implies only small errors, clarifies the relative importance of the different risk channels and structural assumptions, and allows researchers to derive estimates of uncertainty’s policy impact from deterministic models. Full Abstract

1.4 Smart Cap. With Larry Karp.

Short: We introduce a “smart” cap and trade system that eliminates the welfare costs of asymmetric information (“uncertainty”). The cap endogenously responds to technology or macroeconomic shocks based on observed trading prices. We explain why optimal carbon prices have to respond much more sensitivitly to emission fluctuations than suggested by the slope of the social cost of carbon. (collapse) Full Abstract: We introduce a “smart” cap and trade system that eliminates the welfare costs of asymmetric information (“uncertainty”). This cap responds endogenously to technology or macroeconomic shocks, relying on the market price of certificates to aggregate information. It allows policy makers to modify existing institutions to achieve more efficient emission reductions. The paper also shows that the efficient carbon price is more sensitive to technological innovations than usually assumed. The lasting impact and slow diffusion of these innovations typically make the optimal carbon price a much steeper function of emissions than suggested by the social cost of carbon. Full Abstract

1.5 Prices Versus Quantities Reassessed. With Larry Karp.

Short: The paper discusses the welfare costs of tax versus cap and trade-based regulation of greenhouse gases. We explain why the favoring of taxes based on Weitzman's (1974) “Prices versus quantities” argument is misleading. Persistence of greenhouse gases and technological innovations favor cap and trade. (collapse) Full Abstract: “Prices versus quantities” (Weitzman 1974), a hugely influential paper, is widely cited (and taught) in current debates about the best policy to reduce greenhouse gas emissions. The paper’s criterion for ranking policies suggests that technological uncertainty favors taxes over cap and trade. Weitzman models a flow pollutant, but greenhouse gases are persistent. The present paper derives the ranking criterion for stock pollutants. Innovations’ persistence and their gradual diffusion both favor the use of cap and trade. Numerical results show that the case for cap and trade as a means of reducing greenhouse gas emissions is stronger than widely believed. Full Abstract

1.6 SolACE - Solar Geoengineering in an Analytic Climate Economy. With Felix Meier.

Short: We discuss optimal and strategic sulfur-based geoengeneering in a quantitative analytic integrated assessment model of climate change. In the strategic setting, two active regions play a dynanmic game targeting different temperatures based on heterogenous characteristics. (collapse) Full Abstract: “Prices versus quantities” (Weitzman 1974), a hugely influential paper, is widely cited (and taught) in current debates about the best policy to reduce greenhouse gas emissions. The paper’s criterion for ranking policies suggests that technological uncertainty favors taxes over cap and trade. Weitzman models a flow pollutant, but greenhouse gases are persistent. The present paper derives the ranking criterion for stock pollutants. Innovations’ persistence and their gradual diffusion both favor the use of cap and trade. Numerical results show that the case for cap and trade as a means of reducing greenhouse gas emissions is stronger than widely believed. Full Abstract

Current projects with conference presentations:

1.7 IAMs and CO2 Emissions – An Analytic Discussion

Short: The paper discusses the core drivers of carbon dioxide emissions in a variety of integrated assessment models of climate change (IAMs), including an almost exact analytic solution of DICE's emissions and a careful discussion of emissions in Golosov et al. (2014) and Traeger's (2018) more complex IAMs. (collapse) Full Abstract: The paper presents an analytic discussion of the core drivers of CO2 emissions in several integrated assessment models of climate change (IAMs). I derive an approximate analytic solution for emissions in the widespread DICE model (conditional on the SCC). I compare its emission dynamics to the model of Golosov et al. (2014), whose numeric emission simulation and results I analyzed in detail. Finally, I analyze emissions in the Analytic Climate Economy (ACE) model (Traeger 2018), which relies on a variety of energy sectors that rely on capital, labor, and primary energy sources whose substitutability can differ across sectors and over time. Full Abstract

1.8 Self-Enforcing Agreements. With Hiroaki Sakamoto.

Short: We suggest a new equilibrium concept for coalition-formation games with externalities and voluntary participation. It connects free-riding constraints with belief formation and ideas related to von Neumann-Morgenstern stability. Compared to much of the literature on international environmental agreeemnts, our concept predicts larger coalitions that are more sensitive to the number of players. (collapse) Full Abstract: We consider a coalition-formation game with externalities in which participation is voluntary and non-binding. We assume that players (countries) form beliefs over possible long-term outcomes of the game. These beliefs have to be consistent with common free-riding constraints as well as farsighted expectation formation relating to von Neumann-Morgenstern stability. We obtain a simple equilibrium concept that permits a general characterization of the emerging coalitions. An application to examples in the literature on international environmental agreements predicts larger coalition sizes that grow with number of countries, contrasing sharply with the typical results in this literature that coalitions are small and independent of the number of players. Full Abstract

1.9 Pricing an Unknown Climate. With Svenn Jensen.

Short: Anthropogenic greenhouse gas emissions trigger many feedbacks with unknown warming implications. Given these uncertainties are insufficiently described by simple likelihoods, we integrate ambiguity and (rational) ambiguity aversion into DICE-based integrated assessment model of climate change to evaluate the implications of ambiguity for optimal climate policy. (collapse) Full Abstract: Anthropogenic greenhouse gas emissions are changing the energy balance of our planet. A multitude of climatic feedbacks make the resulting surface warming over the next decades and centuries highly uncertain. The likelihood of vastly differing global warming scenarios is not reliably quantifiable. Decision theory distinguishes between known, quantifiable risks and situations of deep uncertainty, or ambiguity. A fully rational decision maker can respond differently to ambiguity and to risk, and real-world decision makers frequently do. We show how aversion to ambiguity affects optimal climate policy in an integrated assessment of climate change. We derive an analytic social cost of carbon formula for an ambiguity averse decision maker in a generic integrated assessment model. We quantify the impact of smooth ambiguity aversion for a stochastic dynamic programming implementation of DICE with ambiguity under different damage assumptions. Full Abstract

2  Risk, Uncertainty, Decision Theory (and not Climate)

2.1 Characterizing and Comparing Intrinsic Risk Attitude

Short: The paper introduces a new measure of risk aversion in a multidimensional world and carefully elaborates risk comparisons across individuals. (collapse) Full Abstract: The paper introduces a new notion of risk aversion. It relies on intertemporal choice to distinguish intrinsic aversion to risk from deterministic preference characteristics such as taste or satiation. Its measures are independent of the good under observation, commodity prices, and liquidity constraints. The paper develops a new way of comparing risk attitude across individuals. Full Abstract

2.2 Once Upon a Time Preference - How Rationality and Risk Aversion Change the Rationale for Discounting       Slides of earlier version: Intertemporal Risk Aversion, Stationarity and Discounting

Short: A comprehensive risk attitude eliminates pure time preference from the discounted expected utility model. Rational agents give more weight to the future the more they know about the consequences of their current actions. (collapse) Full Abstract: The paper develops an axiomatic framework for rational decision making. The von Neumann-Morgenstern axioms give rise to a richer risk attitude than that captured in the standard discounted expected utility model. I derive three models that permit a more comprehensive risk evaluation. These preference representations differ regarding the consistency requirements that are imposed in the evaluation of uncertain scenarios. Imposing all rationality constraints jointly eliminates pure time preference from economic evaluation. The resulting preference representation still gives reduced weight to expected future utility when uncertainty increases over time. The more we know about the future welfare consequences of our (in) actions, the more weight they receive. If uncertainty is endogenous to the decision process, the new rationale for discounting will yield quite different policy implications than the discounted expected utility model based on pure time preference. Full Abstract

2.3 Subjective Risk, Confidence, and Ambiguity     (Slides)

Short: How should we evaluate our uncertain future once we realize that there are different types of uncertainty? The classical von Neumann-Morgenstern then imply a rational and normatively justified form of ambiguity attitude neglected in the standard model. (collapse) Full Abstract: The paper extends a dynamic version of the classical von Neumann-Morgenstern setting to incorporate a degree of confidence in (or subjectivity of) probabilistic beliefs. It provides a simple axiomatic characterization of a new preference representation that addresses ambiguity from a straight forward perspective, employing only basic tools from risk analysis. Conceptually, the paper renders the concept of smooth ambiguity aversion more precise and extends it to a more general notion of aversion to the subjectivity of belief. The representation maintains the normatively desirable axioms of the standard setting including the von Neumann-Morgenstern axioms and time consistency. Full Abstract

2.4 Discounting and Confidence

Short: Does ambiguity or a lack of confidence in our forecast increase or decrease the weight on future consumption? How should we discount the future when confidence in our forecasts falls in futurity? (collapse) Full Abstract: The paper analyzes the social discount rate under uncertainty, employing a representation that enriches probabilistic descriptions of the world by a degree of confidence. Special cases of the model comprise discounting under smooth ambiguity aversion and under a disentanglement of risk aversion and aversion to intertemporal substitution. I characterize the general class of preferences for which uncertainty reduces the discount rate. I also characterize the class of preferences that lower the discount rate compared to the standard model. I derive a particular parametric discounting formula under the assumptions of isoelastic preferences and normal growth rates. Apart from the usual characteristics, the rate depends on a measure of confidence into future growth estimates and a measure of aversion to the lack of confidence. Full Abstract

Peer Reviewed Publications:

Lemoine, D. and C.P. Traeger (2016), Ambiguous Tipping Points. Jounral of Economic Behaviour & Organization 132B: 5-18.

We analyze the policy implications of aversion to Knightian uncertainty (or ambiguity) about the possibility of tipping points. We identify the channels analytically and evaluate the policy impact in a stochastic integrated assessment model.

Lemoine, D. and C.P. Traeger (2016), Economics of Tipping the Climate Dominoes, Nature Climate Change 6:514-20.

We analyze optimal climate change mitigation and the cost of delaying policy in the presence of three interacting climate tipping points ("domino effect") with unknown thresholds in a stochastic integrated assessment model.

Crost, B. and C.P. Traeger (2014), Optimal CO2 Mitigation under Damage Risk Valuation, Nature Climate Change 4: 631–636, Review in News & Views.

Future economic damages from climate change are highly uncertain. Using a stochastic integrated assessment model based on DICE-2007 (see 4-Stated DICE), we show how this damage uncertainty affects the optimal carbon tax, emission path, and temperature trajectory. Whereas uncertainty over the damage coefficient reduces the carbon tax, uncertainty over the damage exponent increases the optimal carbon tax more significantly. We show that the optimal carbon tax approximately doubles when using the Epstein-Zin-Weil preferences which better calibrate the model to observed asset pricing premia.  Note: The article circulated originally under the title "Risk and Aversion in Assessing Climate Policy".

Traeger, C. (2014), A 4-stated DICE: Quantitatively Addressing Uncertainty Effects in Climate Change, Environmental and Resource Economics 59: 1-37.

The paper introduces a state reduced, recursive dynamic programming implementation of the wide-spread DICE integrated assessment model of climate change. By simplifying the climate system's representation, the model cuts DICE's state variables into half, moderating the curse of dimensionality in dynamic programming. In comparison to the AOGCMs emulated by MAGICC, the simplified climate system performs just as well as the climate module of the original DICE 2007 and DICE 2013 models. The paper also addresses numeric accuaracy and choice of basis functions. It introduces a numerically convenient normalization and solves the infinite time horizon problem at an arbitrary time step.

Traeger, C.P. (2014), On Option Values in Environmental and Resource Economics, Resource and Energy Economics 37: 242-252.

Global warming, alterations of ecosystems, and sunk investments imply irreversible changes with uncertain future costs and benefits. The Arrow-Fisher-Hanemann-Henry quasi-option value and the Dixit-Pindyck option value both measure how irreversibility and uncertainty change the value of preserving an ecosystem or postponing an investment. This paper derives the precise relation between the two option values and shows how either of them alters the common net present value decision rule.

Jensen, S. and C.P. Traeger (2014), Optimal Climate Change Mitigation under Long-Term Growth Uncertainty: Stochastic Integrated Assessment and Analytic Findings, European Economic Review 69(C): 104-125.

Economic growth over the coming centuries is a major determinant of today’s optimal greenhouse gas mitigation policy. At the same time, long-run economic growth is highly uncertain. This paper evaluates optimal mitigation policy under long-term growth uncertainty in a stochastic integrated assessment model of climate change. We explain the mechanisms driving optimal mitigation under deterministic growth and uncertain technological progress in the discounted expected utility model as well as in the more comprehensive Epstein-Zin-Weil framework.

Traeger, C.P. (2014), Why Uncertainty Matters - Discounting under Intertemporal Risk Aversion and Ambiguity, Economic Theory 56(3): 627-664.

In the standard economic model, uncertainty has a negligible effect on the valuation of future project payoffs because of an implicit assumption of risk neutrality. I show that this picture changes dramatically under comprehensive risk and uncertainty attitude (intertemporal risk aversion, ambiguity). The paper also shows the importance of considering the correlation between project payoffs (e.g. greenhouse gas mitigation) and economic baseline growth in these settings.

Lemoine, D. and C.P. Traeger (2014), Watch Your Step: Optimal Policy in a Tipping Climate, American Economic Journal: Economic Policy 6(1): 1–31.

In an integrated assessment of climate change, we explicitly capture two alternative tipping points in the climate system affecting climate sensitivity and the carbon cycle, respectively. We derive the optimal climate policy accounting for endogenous welfare consequences of tipping and anticipated Bayesian learning.

Traeger, C.P. (2013), Discounting Under Uncertainty: Disentangling the Weitzman and the Gollier Effect , Journal of Environmental Economics and Management 66(3): 573–582.

The Weitzman-Gollier puzzle: The seemingly same argument justifies falling and increasing discount rates in the face of uncertainty. The paper shows: These rates mean different things and are created by different channels through which risk affects evaluation. Both make long-term payoffs more attractive.

Crost, B. and C.P. Traeger (2013), Optimal Climate Policy: Uncertainty versus Monte-Carlo, Economic Letters 120(3): 552–558..

We show that both size and sign can differ between the optimal climate policy under undertainty and the approximate policies obtained from individually optimizing and averaging Monte-Carlo runs.

Schneider, M., C. Traeger, and R. Winkler (2012), Trading off Generations: Equity, Discounting, and Climate Change, European Economic Review 56: 1621-1644.

Climate change affects future generations. We develop a new continuous time overlapping generations (OLG) model with deterministic life-time, population growth, and technological progress. We analyze observational equivalences between the OLG and infinitely-lived agent economies. We employ the model to identify short-comings in the equity trade-off in Stern's normative approach to discounting, and to critically discuss implicit assumptions in Nordhaus positive, calibration-based approach to discounting.

Traeger, C. (2011), Sustainability, Limited Substitutability and Non-constant Social Discount Rates, Journal of Environmental Economics and Management 62: 215–228.

The paper explores limited substitutability in welfare between environmental and produced goods. Limited substitutability affects magnitude and term structure of optimal social discount rates. Translating the notions of weak and strong sustainability into the degree of substitutability, I show that a strong notion of sustainability results in lower weights given to long-run service and consumption streams than a weak notion of sustainability.

Traeger, C. (2009), Recent Developments in the Intertemporal Modeling of Uncertainty, Annual Review of Resource Economics 1:261-285.

Time and uncertainty constitute essential ingredients to many of the most challenging resource problems. This review discusses models and concepts that aim at disentangling time and risk attitude and discusses resource economic applications. If also briefly reviews a generalization of risk attitude to situations where uncertainty is not captured by unique probability measures.

Book Draft:

Karp, L. and C. Traeger (2021, draft), Dynamic Methods in Environmental and Resource Economics.

The book discusses discrete and continuous time dynamic methods in the context of environmental economic appications. In particular, we cover dynamic programming (discrete, continuous, stochastic, numeric), the Maximum principle, non-convex dynamic systems, learning, time inconsistency, and general risk and ambiguity attitude. The book aims at graduate students and researchers in the field.

Other Publications:

Karp, L. and C. Traeger (2013), Discounting, In: Shogren, J.F., (ed.) Encyclopedia of Energy, Natural Resource, and Environmental Economics, volume 2, pp. 286-292 Amsterdam: Elsevier.

We introduce the basic theory of discounting, including a discussion of normative versus positive discounting, risk, uncertainty, and catastrophes, limited substitutability of environmental goods, hyperbolic discounting, and overlapping generations.

Traeger, C., G. Perino, K. Pittel, T. Requate, A. Schmitt (2019), The Flexcap – An Innovative CO2 Pricing Method for Germany, ifo DICE Report, ISSN 2511-7823, ifo Institut, München, Vol. 18, Iss. 01, pp. 42-48.

We discuss a practical implementation of the smart cap, which connects the advantages of cap and trade and price regulation, tailored to the German policy reform.

Generalized Cost-Benefit-Analysis and Social Discounting with Intertemporally Dependent Preferences. Paper Draft from 2009 with Larry Karp.

Short: We derive the social discount rate in the context of intertemporally dependent preferences. Contains the proof underlying Dietz Venman's The endowment effect, discounting and the environment (collapse) Full Abstract: We derive a general framework for cost-benefit analysis and social discounting with intertemporally dependent preferences. Here, the marginal contribution of an additional unit of consumption in some period depends on what is consumed in the other periods. We use a simple model of history dependent preferences to analyze how habit formation affects the social rate of discount. Getting used to good life before a potential decline in growth as well as getting used to bad life during a decline in growth both affect social discount rates, not only during the time of the growth rate change but also before and after. Full Abstract

PhD Thesis (Doktorarbeit):

Theoretical aspects of long-term evaluation in environmental economics

The dissertation addresses the evaluation of long-term trade-offs between economic activity and its environmental repercussions. It concentrates on social discount rates, i.e. the weight given to the long versus the short run, and the treatment of uncertainty. The results render contributions to the fields of environmental economics and decision theory. From an applied view, they directly affect sustainability and cost benefit analysis. The first part of my thesis is dedicated to the relation between the notions of strong and weak sustainability and the time behavior of social discount rates. The second part introduces a new concept of risk aversion, which captures the willingness to undergo preventive action. The concept also provides a way to define a simple risk measure in a mutli commodity setting. It relates aspect of standard risk aversion and intertemporal substitutability. The third part of the dissertation derives several generalized evaluation rules, based on axioms concerning the timing of uncertainty resolution, uncertainty attitude, stationarity and time consistency. In particular I give a simple axiomatization that forces the rate of pure time preference to zero. A decision maker who subscribes to these axioms only discounts for reasons of uncertainty, but not for reasons of impatience.

Master Thesis (German): Freedom of choice and the structure of intertemporal decision-making      The thesis investigates how freedom of choice can be integrated into economic welfare analysis. The first part examines existing static axiomatizations of freedom of choice and fleshes out their implicit normative assumptions and shortcomings. It concludes that a meaningful measure of freedom must necessarily account for individual valuation of choice alternatives and the similarity of alternatives. The second part of my thesis analyzes the temporal structure in confining and evaluating opportunity sets. It establishes a relation between evaluation of opportunity sets in terms of freedom and preference for flexibility. I explain how, in a dynamic framework with uncertainty about future preferences, the two criteria to be considered in static axiomatizations (preference valuation of alternatives and similarity judgement) merge. The last part of the thesis elaborates the consequences of these insights for the informational basis of a comprehensive welfare analysis.