Welfare Evaluation of Climate Change and Future Disasters

Academic Paper, 2016

24 Pages, Grade: 1,0



Table of Content

Table of Content


1. Introduction
1.1. Climate Change and Sustainable Development
1.2. Welfare Evaluation and Terminology

2. Review of Literature and Findings
2.1. Discount Rate
2.2. Predictions and Uncertainties

3. The Role of Uncertainty
3.1. Weitzman's Dismal Theorem
3.2. Validation and Criticism
3.3. State of Affairs and Non-probabilistic Models

4. Conclusion and Outlook


Reference List

Welfare Evaluation of Climate Change and future Disasters

Climate policy with regard to welfare optimization needs to focus on long-term development in the context of a sustainable future. Two prominent debates have been raised and sharply discussed. First, the long-term view has been highlighted by the appearance of the Stern review, which triggered a lively discussion on an adequate discount rate in the last decade. Second, the probability of the occurrence of severe disasters has been stressed. These considerations are mainly based on fat tails of a probability distribution, an issue initially raised by Weitzman. Based on structural uncertainties of input factors like climate sensitivity, society might experience an infinite high loss for low likelihood catastrophic disasters. His assumptions have been carefully scrutinized and revised in literature, which additionally provoked the question of applicability of traditional economic models. In addition, raising concerns are the potential tipping points that may lead to unpredictable impacts. A stringent policy has been suggested which can be mitigated over time while learning more about uncertainties through investigations. After a short review of traditional welfare evaluation of climate change will the paper turn its focus especially on uncertainty and reviews in this context the appropriateness of commonly used economic models for advising climate policy. Keywords: Climate Change - Welfare - Uncertainty - Disasters


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1. Introduction

1.1. Climate Change and Sustainable Development

Undoubtedly, the already perceptible climate change1 along with global warming, will affect our descendants. The degree of change and human contribution to it is still uncertain. The Economic World Forum admits that climate change bears the highest potential risk for the global economy in 2016 (Elliot, 2016; Cann, 2016), whereby even risks of political instability like terrorist attacks take a back seat. Since 2000, 6.506 natural disasters have occurred globally with 1.3 million people having died, 3.1 billion people being affected2 and damages of more than $1.8 trillion3. A disturbing fact is that an increasing trend of the total number of natural disasters since 1970 can be observed. (App. A.1-A.3). Additionally, it is striking, that particular rare but severe disasters have huge effects (Kellenberg & Mobarak, 2011). Still, predictions on impacts are complex if not impossible. Studies concerning potential temperature rise and economic costs vary very much among each other (Dumas, 2009).

With climate being a public good, climate change due to GHG emission can be regarded as an extreme case of externality that arouses worldwide and has effects globally (Stern, 2007). Both embody high degree of uncertainty for policy makers for whom to agree on an adaption path it becomes even more essential to rely on experts and models that maximize overall welfare4 concerning climate change damages. It is enormous complex by taking into account that consequences are mainly on the expenses of future generations. Since the Brundtland commission has agreed on a common definition of sustainability5 in 1987 the awareness of our responsibly for future generations has gained major public and political importance.

But how can politicians rely on models that are subject to great uncertainties? The way of how to treat uncertainties in standard economic models, especially, low-probability catastrophes, has motivated this paper. After an introduction of welfare evaluation, a literature review of discount rate and social cost of carbon (SCC) is provided, before dealing primarily with uncertainty and catastrophic disasters as well as their implications for further research.

1.2. Welfare Evaluation and Terminology

This chapter reviews relevant issues and assumptions of welfare evaluation and applied models. Welfare consists of economic indicators, e.g. GDP, as well as the social welfare function (SWF), which is a measure for aggregated individual utilities. It includes ranges of values like health and quality of life (Botzen & Bergh, 2014). Welfare evaluation of climate change implies to comprise inter-temporal parameter, to deal with risk and uncertainty and to find an appropriate approach to monetize or value economic and social impacts of damages. Risk, on the one hand, is “[...] the combination of the probability of an event and its negative consequences” (UNIDSR, 2007) and is thus, a probabilistic assumption referring either to the outcome or the appearance of a disaster as well as the probability to cross a threshold. Uncertainty, on the other hand, indicates a lack of information, either concerning the possible outcomes or their likelihood to appear which is meaningful large when dealing with the complexity of climate change (Weitzman, 2009). Another insecurity - even so not dealt with in this paper - is the compliance of countries to pursue obligations regarding energy-efficient use (Kunreuther, Heal, Allen, Edenhofer, Field & Yohe, 2013).

Economists mainly use Integrated Assessment Models (IAMs) that embody Cost-Benefit- Analysis (CBAs) that outweigh the expected costs and benefits of mitigation for greenhouse gas (GHG) so as to maximize net value of welfare and to provide application for an optimal abatement path to decision-makers (Yohe & Tol, 2007). The result is a social cost of carbon, an indicator for proper abatement cost to facilitate decision-making and policy approaches. Mainly, IAMs make use of the integrated utilitarian welfare function. It consists of a discount factor that embodies the discount rate, and the utility function including intra- and intergenerational consumption and constant relative risk aversion assumption (App. B.1). In addition to intergenerational equity and economic development it is decisive to deal with uncertainty when looking at welfare with regard to climate change. It is integrated into models in form of expected utility (Stern, 2007). Expected utility (App. B.2) is a product of the aggregation of utility of outcomes and probability of occurrence, which is used for decision-making under risk (Botzen & Bergh, 2014). The standard from presumes a risk aversion agent, and attaches probabilities for possible outcomes (Stern, 2007). Thus, uncertainties are dealt with in form of a probability distribution of outcomes that is calculated via Monte Carlo Simulations or by taking the mean. However, this is a severe restriction for uncertainties. For this reason IAMs based on probabilities are hardly debated in recent times, especially as impacts are rarely quantifiable. Weitzman (2009) claims that CBAs cannot be applied due to uncertainties of input factors.

An additional aspect is how to monetize welfare by including all direct and indirect impacts of climate change. To illustrate that at full length would require a specific paper. There exist an extensive discussion on how to define needs in a moral and ethical application (Gough, 2015). For instance, de Serres and Murtin (2011) review the measurements of welfare in more detail by focusing on GDP and life expectancy. Latter implies to be evaluated in monetary terms. Becker, Phillipson and Soares (2005) reinforced the value of statistical life and hence, health-related gains of mitigation policies, but dismiss other decisive externalities. For the purpose of this paper, the definition of IPCC on welfare is taken as base.

Another central issue - and for sake of completeness - of IAMs and global welfare is to specify inequalities and adapt appropriate weights in context of fairness. Individuals in richer countries have in general a higher income and can cope better to damages than poorer countries. To use the approach of willingness to pay and willingness to accept in context of environmental damage is with regard to unequal income distribution not just. Therefore, IAMs weight poorer region to a higher degree (Botzen & Bergh, 2014).

2. Review of Literature and Findings

2.1. Discount Rate

The publication of the Stern review (2007) heated up the discussion about adequate welfare frameworks for climate change. Well-know IAMs are PAGE used by Stern and DICE by Nordhaus. Their calculated SCC relies heavily on values of input factors like discount rates.

A prevailing discussion has been on the great disagreements among economists about an appropriated discount rate. The discount rate itself is divided into two components, namely the rate of pure time preference (5) and the wealth-based component (Ackerman, 2009: 36). The latter is a product of growth rate per capita (g) and marginal utility of consumption (q).

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Stern (2007) argued on a philosophical base that present and future generations are equally valuable and thus, sets delta to 0.1, which results from the probability of 0.1% that human will extinct until next period. By taking the mainly agreed growth rate (g = 1.3%, see App. A.4) and setting eta equal to 1 he receives a discount rate of 1.4% and thus, values the future generation greatly. He received many critics for his aggressive mitigation path.

One of the major opponents is Nordhaus (2009) who recommends delta to be at least 1.5%, as this would reflect the observable behavior more realistically. In general he favors much more a market-based approach by referring to interest rates. Dasgusta (2007) on the other hand, agrees on Sterns calculation for delta but critics the assumption on parameter eta as it Welfare evaluation of climate change and future disasters describes the well-being of human which is based on inequalities and risks, hence, requires a more ethical consideration. Standard assumption relies on economic growth, which would imply future generations to be richer than today's generation. Adopting a higher eta (of 2 to 4) leads to a higher discount rate. Still, the future growth rate is an uncertain parameter as well. After all, the use of different discount rates lead to different results in the discounted utilitarian welfare function. Nordhaus calculated in DICE with an initial higher discount rate a SCC of $35 for the first period, thus a lower GHG reduction path, whereas Stern, using PAGE and a lower discount rate, supports a SCC of $350 (Ackerman, 2009).

Up to now, there exist no consensus of a discount rate, however, it is a crucial and influential input factor of IAMs. Pindyck (2013) states that due to the uncertainty and arbitrariness of input factors IAMs are not as reliable and the results mainly reflect the modelers opinion.

2.2. Predictions and Uncertainties

Within the debate on an adequate climate policy, evaluating welfare of climate change is composed of a range of uncertainties. It concerns the illustrated discount factor, possible future natural disasters, responsiveness of temperature to an increasing GHG concentration as well as estimating damages and abatement costs ex ante (Botzen & Bergh, 2014; Weitzman, 2011b). Expected damages as well as the probability of occurrence of catastrophes increase likewise with a temperature rise (Ackerman, 2009, App. A.7). Scientist agree on a high probability of climate sensitivity6 of 2-3°C above preindustrial7 level, but even a low probability of 5°C increase cannot but ruled out (App. A.5 & A.6). At preindustrial level carbon dioxide accumulated to 280 ppm, nowadays we are crossing the level of 400 ppm and keep on emitting 2 ppm each year. The world might well reach 700 ppm by 2100, keeping BAU, if emitters would not pursue decisive reduction (Wagner & Weitzman, 2015).

The even more severe question is how these impacts come at public expense. The term catastrophic outcome is mainly used by economist referring to great temperature increase that is accompanied by high impacts not only in economic but also in human welfare terms (Pindyck, 2013). When considering feedback loops and thresholds of tipping points it might not be warrantable to take a quasi-linear approach for calculating damages. Due to deep uncertainty there exist no definite prediction whether GDP would decline by 10%8 or even by up to 30% (App. A.7). In the context of average economic growth of 3% per year (App. A.4), the generation in 100 years will still be better off. However, this becomes more challenging if climate change does not affect output level but output rates (Wagner & Weitzman, 2015). Bear (2007) endorses holding temperature constant at an even lower degree than 3°C. Even a low temperature rise of 2°C causes enormous effects in terms of melting on the Greenland ice sheet. He states that the lower bound of stabilization of Stern is not robust and concludes that the review is unable to provide quantifiable data concerning risks of catastrophic events.

Concluding, uncertainty about input factors, like discount rate, used in IAMs are no deniable. Next chapter picks up the debate and spreads the topic to catastrophic outcomes.

3. The Role of Uncertainty

3.1. Weitzman's Dismal Theorem

Weitzman (2009, 2011a, 2011b) made a decisive breakthrough concerning uncertainty as he steers away the attention from the debate for a suitable discount rate and rather puts emphasis on high-impact catastrophes caused by climate change that might predominate.

“At high enough greenhouse gas (GHG) concentrations, climate change might conceivably cause catastrophic damages with small but nonnegligible probabilities. Other things being equal, this should lower the discount rate used to evaluate mitigation-investment decisions and raise the social cost of carbon (SCC).” (Weitzman, 2014: 544)

He raises concern over a CBA that depends on expected discounted utility function, which depends mainly on the modelers themselves. He argues that structural uncertainties in the fat tails of PDFs9 have thus far not been taken into account and make calculation of CBAs even non-feasible. Hence, he questions the applicability of CBA grounded on expected utility with uncertainties and stresses, that economy is unable to provide predictable data concerning the accompanied losses for a climate disaster and science is pervaded by profound uncertainty. His model, the dismal theorem (DT), is based on fat-tailed10 probability distributions, which turns one's attention to unexpected disasters, which is indispensable according to him. Thereby, he refers to Bayesian statistics and states that fat tails cannot be neglected especially not in the context of structural11 uncertainty concerning climate sensitivity (App. A.5 & A.6). He refers to the probability of having climate sensitivity values higher than 4,5°C as he claims that the previous used coefficient for climate sensitivity (S1) is dubiously or at least not significant enough. He avers that it lacks a component that indicates a certain feedback loop Welfare evaluation of climate change and future disasters of anthropocentrically injected GHG, exemplary artic permafrost or hydrates of methane in offshore deposits, which will aggravate global warming drastically while temperatures rises. Therefore, he adds in his model the above-mentioned heat-induced feedbacks loops to climate sensitivity (S2). There exists a 5% (1%) probability that global warming might accompanied by mean temperature rise of 10°C (20°C), using S2. These undisputed possibilities of temperature increase would lead in many ways to destructive consequences. Hence, it reinforces the exigency to discount present expected utility.

He refers to a two period model that is based on strictly positive relative risk aversion (u > 1). Marginal utility of consumption MU(C) is multiplied with the probability of an outcome P(C). The probability function of the consumption growth rate is a normalized function with a known location parameter and an uncertain scale parameter, the generalized climate sensitivity. As argued above, there exists uncertainty in the parameter of the distribution for future consumption. If the occurrence of a catastrophic outcome lets C become low (tend to zero), then in the fat tails the probability P does not diminish rapidly enough to keep in line with our risk aversion and drastically rise of MU, so that standard economic tools cannot be applied as expected utility becomes minus infinity. Society would expect an infinite high loss as the marginal utility becomes positive infinity and unbounded (or utility negative infinitely). Weitzman applies conditional marginal utility and uses the stochastic discount factor that states the willingness to give one unit of consumption (marginal willingness to pay) for a sure unit in future consumption. DT states that society would give up an infinite amount of today's consumption, or in other words, have an infinite rate of willingness to pay to prevent potential future climate catastrophes. This holds under the assumption of a CRRA utility function being greater than one. Weitzman refers by the mean of zero consumption to the value of statistical life. However, this assumption has been criticized as being non-realistic (Nordhaus, 2011). Weitzman provides five empirical argumentations for deep structural uncertainties. Firstly, the already mentioned difference in past and present GHG concentration. Secondly, also already debated, the existence of great unknown in equilibrium climate sensitivity. Third argument stresses the self-amplification of GHG and the feedback loops that are mainly omitted in models. Then, he refers to the non-robustness of damage functions for outcomes of extreme temperature. In the end, he reflects the insecurity concerning discounting the future when dealing with disastrous events.

Main statement of Weitzman's analysis is that DT indicates expected loss of catastrophes to be indefinitely. This implies stringent reduction of exogenous GHG emission and more cautious when advising climate policies. Thereby, he presumes risk-averted decision-makers.

Precisely, he favors insurances and preparation for worst-case outcomes instead of agreeing and modeling mean prediction. Research should consider filling in the information gap concerning uncertainties, and create emergency plans for fat tail scenarios. He endorses a generalized precautionary approach12 for disastrous climate events according to which policy should not wait for available scientific data. It promotes to reduce preventive damages or any harm for environment and social health in advance. In a broader context does precautionary principle aim to avoid irreversibility, however, this could also lead to overinvestment (Botzen & Bergh, 2014). The implementation at international political level is relative complex. Iverson and Perrings (2011) deal more precisely with implementation tools.

Concluding, DT states that disastrous outcomes have enormous impacts on future welfare and outweigh any discussion of discount rate and expected damages, accompanied with an increase in SCC. Weitzman claims that general CBAs do not consider structural uncertainty of a catastrophic climate event that is non-negligible. Hence, he assumes that CBAs only have limited application for policy and provide not reliable estimates for SCC. They are able to mislead decision makers, and we rather need an insurance to safeguard catastrophic events.

The last crucial point to add here is that the relevance for dismal theorem would require empirical studies for extreme end tails, which however are rarely observable and experienced.

3.2. Validation and Criticism

Weitzman triggered the debate of fat tails and questions whether the traditionally used welfare function in terms of CBAs and expected utility are adequate for climate change. Tail events having low probabilities, cannot be ruled out, as the prominent example of the financial world crisis 2007/08 shows. Nordhaus (2011) provided further illustrations for deviations of normal distributions. Considering the fall of U.S. stock price on October 19, 1987 by 23% that had a standard deviation of 1% during that time. Similarly, the U.S. housing market where prices fall drastically in 2006 after a steady rise over fifty years, or the drop in oil price in 1973. These incidents are indeed surprising and all these distributions had rather fat tails.

Weitzman also referred to the insufficient historical or empirical data to predict generalized climate sensitivity accordingly, which lead to the constraint to apply a sample of observation, including uncertainties. This is clearly not restricted only to climate sensitivity. Just recently, the news published an article stating, “Sea level rise from ocean warming underestimated, scientists say” (Guardian News, 2016). It reinforces the fact of deviations in out predictions.


1 Here defined according to IPCC: “Climate change refers to any change in climate over time, whether due to natural variability or as a result of human activity” (IPCC-AR4b, 2007, Glossary). Another way to look at climate change would be to regard only human-induced climate change caused by GHG emissions.

2 “People requiring immediate assistance during a period of emergency, i.e. requiring basic survival needs such as food, water, shelter, sanitation and immediate medical assistance“ (EM-DAT, 2015, Glossary).

3 Based on EM-DAT database: http://www.emdat.be/advanced_search/index.html.

4 “An economic term used to describe the state of well-being of humans on an individual or collective basis. The constituents of well-being are commonly considered to include materials to satisfy basic needs, freedom and choice, health, good social relations, and security“ (IPCC-AR4b, 2007, Glossary).

5 “[...] development that meets the needs of the present without compromising the ability of future generations to meet their own needs” (WCED, 1987: 43).

6 Climate sensitivity is the “equilibrium temperature rise that would occur for a doubling of CO2 concentration above pre-industrial levels” (IPCC-AR4a Glossary, 2007) and a key macro-indicator.

7 “the term ‘pre-industrial' refers, somewhat arbitrarily, to the period before 1750” (IPCC-AR4b Glossary, 2007).

8 10% of global GDP nowadays equal approximately $7 trillion (Wagner & Weitzman, 2015: 61).

9 “A probability density function is a function that indicates the relative chances of occurrence of different outcomes of a variable. The function integrates to unity over the domain for which it is defined and has the property that the integral over a sub-domain equals the probability that the outcome of the variable lies within that sub-domain.“ (IPCC AR4b Glossary, 2007)

10 If a PDF implies that “its moment generating function is infinite - that is, the tails probabilities approaches 0 more slowly than exponentially” (Weitzman, 2009: 2).

11 Parameters are uncertain concerning the distribution of future consumption (Millner, 2013: 312).

12 Precautionary principle applies “if an action or policy has a risk of causing harm to the public or to the environment, then a lack of full scientific certainty is not a reason for postponing cost-effective measures to prevent environmental degradation and the burden of proof that it is not harmful falls on those taking the action” (Botzen & Bergh, 2014: 22).

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Welfare Evaluation of Climate Change and Future Disasters
University of Paderborn
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Welfare, Climate Change, future disasters, disasters, climate policy, sustainable development, discount rate, uncertainties, weizman, dismal theorem, non-probabilistic, carbon dioxide, cost-benefit, social cost of carbon, nordhaus, evaluation
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Anonymous, 2016, Welfare Evaluation of Climate Change and Future Disasters, Munich, GRIN Verlag, https://www.grin.com/document/909629


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