Integrated Assessment Models (IAMs) are created to model the cause and effect chain of climate change as completely as possible. In such modelseconomic growth is linked to the amount of emissions associated with production, which is then linked to the level of climate change, which results in final (economic) impacts associated with climate change. Though IAMs have evolved and improved significantly since their inception in the early 1990s, they still are lacking in several respects. There appear to bethree main issues regarding the IAM’s that ought to be addressed (Tol and Fankhauser (1998); Dowlatabadi (1995); Kelly and Kolstad (1999); Ackerman et al. (2009); Schneider (1997)). Firstly, quantifying/estimating the impacts of climate change remains a challenging issue. In the IAM literature to date impacts have been aggregated (across sectors of the economy and regions of the world), in the interest of model simplicity. Increased computational capabilities have, however, rendered such considerations less relevant. Secondly, IAMs apply unbounded utility functions, more from reasons of convenience than from any fundamental principles, and the most commonly used functional form, the Power (or Constant Relative Risk Aversion (CRRA), under uncertainty ) turns out to be unsuited for the task at hand.
Finally, uncertainty is pervasive in the climate change problem, including in the climatic system (from the link between increases in GHG’s and its impact on climate –the famous "climate sensitivity" parameter-and the oceanic uptake of carbon, among others), in the economic system (a variety of parameters and the damage and utility functions) and in areas where these systems interact (induced learning, mitigation, adaptation etc.). The handling of such uncertainty in the IAM’s has been known to be lacking in many respects (Morgan and Dowlatabadi (1996); Peterson (2006); van Asselt and Rotmans (2002); Weitzman (2009)) (see below for more details).
In this paper we address the last two of these issues. Our IAM (ADDICE2013) is based on the AD-DICE09 model, an extension of DICE2007 allowing for explicit adaptation decisions (see De Bruin et al. (2009) for a description of AD-DICE09). The AD-DICE2013 model has the advantage of having three policy (control) variables, namely mitigation, reactive adaptation and proactive adaptation. Adaptation, in our context, refers to social and economic changes which limit the amount of damage associated with a certain level of climate change. Proactive adaptation involves long term investments, which take place in expectation anticipation of climate change whereas reactive adaptation takes place in reaction to actual observed climate change. These modifications are intended to mollify many of the significant drawbacks in the IAM’s identified in the recent literature.
The model, thus modified, is then used to obtain a fuller understanding of three aspects, in particular: how sensitive is the social cost of carbon to uncertainties? Are mitigation decisions substantially impacted by uncertainty in key parameters? And, what are the impacts on adaptation, under uncertainty in key parameters? In what follows we will discuss how we deal with these two issues within our modeling framework and elaborate on the importance of these issues.
In IAMs, welfare is represented by utility in the form of a power function of consumption per capita, which in combination with heavy-tailed distributions leading to very low values of consumption, can imply infinite expected utility and infinite marginal expected utility, which is the conceptual crux of Weitzman’s "Dismal Theorem" to essentially deterministic IAM’s (such as DICE). Essentially, this form of the utility function is a convenient, but not essential, one for these applications.
In this context, Ikefuji et al. (2011) (and Millner (2011), in the context of a more analytical model) indicate that once the convenience of the CRRA form of utility if discarded, and a utility function which is bounded is used, heavy tailed distributional assumptions can easily be handled. They provide an alternative utility function ("Burr utility"), which at typically observed consumption levels behaves like the CRRA function whereas in more extreme (low) utility levels, behaves like the exponential function. In this paper we adopt this so-called Burr utility function (which is of the Hyperbolic Relative Risk Aversion (HRRA) family) instead of the more common CRRA form.
Uncertainty within IAMs can result from different sources, namely measurement errors, variability, model structure and aggregation (Katz (2002)). There are two ways of conceptualizing these uncertainties: the mostly physical science based approach of viewing these as intrinsically not a part of the decision making process, allowing one to “draw” the presumptive unknown parameters from known (or estimated) distributions, and averaging the resultant paths from many different draws. This is known as the "montecarlo" approach (also the ex-ante approach) and is the most popular way of introducing uncertainty into IAM’s.
The second approach consists of modeling uncertainty as not being resolved all at once; rather, uncertainty is an intrinsic part of the decision making process, and each period’s decision must be made prior to realization of uncertain aspects (parameters) of the model. In this framework, labeled as the "ex-post" approach, then, a variety of interesting and new concepts arise (including learning, risk aversion, the value of information etc.). Yet, these models are inherently difficult to solve, and pose problems in interpretation and simulation (in large dimensions of the state space).
Understanding, quantifying and incorporating these uncertainties is a major challenge for Integrated Assessment modelers. As IAMs are often used to advice policies, it is crucial that the effects of uncertainty on Integrated Assessment modeling results are better understood. In this paper we attempt to provide better understanding of how uncertainty affects optimal mitigation and adaptation policies prescribed by the AD-DICE model.
We use a modified ex-ante approach to uncertainty, following Pizer (1999). Unlike the usual montecarlo approach, wherein the resultant path of variables of interest are averaged to obtain the "mean" outcome across different states, we work in a "contingent utility" framework. In our setting, (say) 1000 "states of the world" (uncertain parameters) are drawn from (know or estimated) distributions, with each state having a specified (usually equal) probability. The policy maker then maximizes the objective function, which is a weighted (by state probability) sum of utility in each state, and chooses his control variables. Thus, the optimization is ex-post, given the known range of uncertain outcomes (and can be seen as a mild form of preference aggregation across states). Pizer (1999) shows that this approach to uncertainty is more natural and makes a substantive difference to the model outcomes, when compared with the traditional ex-ante approach.
In contrast to much of the existing literature, which focuses on a very few key parameters, we focus on 10 parameters identified as relevant within an IAM framework. Also departing from much of current literature, we move away from the ubiquitous normal distribution for many parameters, and allow for a range of more plausible distributions, including those with skew and/or heavier tails.
While many of these questions have been addressed in the past, the contribution of this paper is in analyzing these questions in a richer framework. Closest to our analysis is Nordhaus (2008), who performs a simulation of the impact of uncertainty regarding key parameters; this suffers from several drawbacks, including the very limited nature of the simulation activity, the type of distributions used, and the simplifications in the model being simulated. Somewhat related the extent of the simulations is Ackerman et al. (2010), who perform a more extensive set of simulations, focused however on two key parameters, damages and climate sensitivity, in an attempt at simulating "catastrophe" in an IAM (they use the PAGE model, somewhat different in structure from DICE). In both of these analyses, however, the basic structure is very similar,and uses the CRRA utility function. Ikefuji et al. (2011), who propose the use of the Burr utility, on the other hand, work with DICE; yet they do not perform a thorough simulation exercise and use a simplified version of DICE. Pizer (1999) uses a much simpler model, with analytically derived optimal policy approximation, and with damage estimates which are rather dated. None of these models include adaptation explicitly, as ours does, and none (except Pizer (1999)) uses the contingent utility approach.
On the other hand, the analysis in Cai et al. (2012) is similar, in spirit, to ours; theirs is an ex-post uncertainty approach, and is a full dynamic stochastic optimization model. The model however is very similar to DICE in using the CRRA form of utility and in not modeling adaptation. The different roles of adaptation and mitigation will play under uncertainty is an interesting topic of research. Though the effect of uncertainty on mitigation has been studied in the past, studies concerning adaptation are virtually non-existent. The role of uncertainty on adaptation policies has not been studied, outside a rather simple framework with one uncertain parameter (Felgenhauer and De Bruin (2009)). Prior analytical work (e.g. Ingham et al. (2007)) finds that uncertainty leads to increased adaptation and reduced mitigation, which is something our model can shed light on.
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