Climate change and psychological adaptation: A behavioral environmental economics approach

Climate change and psychological adaptation: A behavioral environmental economics approach

Accepted Manuscript Climate Change and Psychological Adaptation: A Behavioral Environmental Economics Approach Thomas Aronsson , Ronnie Schob ¨ PII: ...

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Accepted Manuscript

Climate Change and Psychological Adaptation: A Behavioral Environmental Economics Approach Thomas Aronsson , Ronnie Schob ¨ PII: DOI: Reference:

S2214-8043(18)30132-0 10.1016/j.socec.2018.03.005 JBEE 340

To appear in:

Journal of Behavioral and Experimental Economics

Received date: Revised date: Accepted date:

27 August 2017 8 January 2018 18 March 2018

Please cite this article as: Thomas Aronsson , Ronnie Schob ¨ , Climate Change and Psychological Adaptation: A Behavioral Environmental Economics Approach, Journal of Behavioral and Experimental Economics (2018), doi: 10.1016/j.socec.2018.03.005

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highlights  Economic models of environmental policy typically neglect psychological adaptation to changing life circumstances.  Our paper shows that psychological adaptation can play a crucial role in the design of an optimal, welfarist tax policy to internalize an intertemporal externality.  The paper also addresses some of the implications for tax policy of heterogeneity in peoples’ adaptation-ability

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Climate Change and Psychological Adaptation: A Behavioral Environmental Economics Approach**

Thomas Aronsson* and Ronnie Schöb+

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January 2018

Abstract

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Economic models of climate policy (or policies to combat other environmental problems) typically neglect psychological adaptation to changing life circumstances. People may adapt,

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to different degrees, to a deteriorated environment. The present paper addresses these issues in a model of optimal tax policy to combat climate change and discusses the consequences for optimal climate policies. Furthermore, from a normative-methodological point of view, we argue that psychological adaptation needs to be taken into account even by a pure welfarist policy maker, who aims at internalizing an intertemporal externality.

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Keywords: Behavioral environmental economics, climate change, intertemporal externalities, adaptation, taxation JEL Classification: D03, D61, D91, H21.

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The authors would like to thank two anonymous referees, David Granlund, and Daniel Nachtigall for helpful comments and suggestions. Aronsson would like to thank the Swedish Research Council (ref 421-2010-1420) for generous research grants. * Address: Department of Economics, Umeå School of Business and Economics, Umeå University, SE – 901 87 Umeå, Sweden. E-mail: [email protected] + Corresponding author: School of Business & Economics, Freie Universität Berlin, D–14195 Berlin, Germany. Tel. +49-30-83851240; E-mail: [email protected] 1

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1. Introduction One way to reduce the negative consequences of climate change is to adapt to new circumstances. Adaptation played an important role in the early policy discussions on climate change, but adaptation as a policy option was later fiercely opposed and the focus of climate policy shifted almost exclusively to curbing greenhouse gas emissions (Pielke et al. 2007).

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Taking adaptation into account was discredited as a “kind of laziness, an arrogant faith in our ability to react in time to save our skins” according to Al Gore (1992, p. 240).

Since then, at least, technological adaptation has gained in importance on the political agenda (see, e.g., OECD 2008, 2012, IPCC 2007, 2014), which is described as “the process of

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adjustment to actual or expected climate and its effects. In human systems, adaptation seeks to moderate or avoid harm or exploit beneficial opportunities. In some natural systems, human intervention may facilitate adjustment to expected climate and its effects.” (IPCC 2014, p. 5). According to the Stern Review (Stern 2007), political measures to facilitate or promote this (technological) adaptation is “crucial to deal with the unavoidable impacts of climate change

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to which the world is already committed”.

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Besides technological adaptation, the ability of psychological reactions to changing life circumstances may also be crucial for the way mankind will cope with climate change. These

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reactions encompass “appraisals of situations, affective responses, cognitive analysis and reframing, disengagement, defensive responses, and emotion regulation” (Reser and Swim

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2011, p. 278).1 Psychological adapation may neither be complete nor inevitable, may occur at different paces, and may differ considerably among individuals (see Frederick and

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Loewenstein 1999, Diener, Lucas, and Scollon 2006, Lucas 2007, Lyubormirsky 2011) but nevertheless plays an important part in the determination of subjective well-being (Luhmann et al. 2012).

With respect to psychological adaptation to environmental circumstances there is, so far, only indirect evidence. Levinson (2013) finds that fluctuations of the current day’s air quality affect happiness while changes in the local annual average do not. This is interpretable as

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Evolutionary explanations for the emergence of hedonic adaptation are elaborated by Robson (2002), Rayo and Becker (2007), and Perez-Truglia (2012). 2

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habituation to the public good air quality over time. Schkade and Kahneman (1998) asked people to rate their own life satisfaction and the life satisfaction of someone similar in another region. Climate-related questions were typically more important for someone living in the other region than for someone living in the own region, suggesting that the climate problem is more important in evaluating some imaginary situation than actual well-being. We interpret

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this result to mean that people do not account for their ability to adapt when conceiving themselves in another situation while adapting to their actual own circumstances. A novel approach to analyzing psychological adaptation is made by Baylis (2015), who uses Twitter tweets to measure temperature-dependent hedonic states, defined as a one-dimensional measure of mood. His results suggest a weaker reaction to temperature change in areas with

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more extreme climate. He interpret these findings “as suggestive evidence in favor of incomplete adaptation to warmer temperatures, a careful consideration in modeling the potential adaptive capability of individuals to higher temperatures “ (Baylis 2015, p 32). Part of this adaptation may be explained by more wide-spread use of air-conditioning in hot

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regions and by sorting. But psychological adaptation is also likely to affect hedonic states over time.

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The psychological aspects of adapting and coping with climate change were emphasized in a comprehensive report by the American Psychological Association Task Force on the

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Interface between Psychology and Global Climate Change (2010):

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“Adapting to and coping with climate change is an ongoing and ever-changing process that involves many intrapsychic processes that influence reactions to and preparations for adverse impacts of climate change, including chronic events and disasters. Psychological processes include sense making; causal and responsibility attributions for adverse climate change impacts; appraisals of impacts, resources, and possible coping responses; affective responses; and motivational processes related to needs for security, stability, coherence, and control.” American Psychological Association Task Force on the Interface between Psychology and Global Climate Change 2010, p. 7)

In this paper, we address the policy implications of psychological adaptation in an intertemporal context with externalities. By including psychological adaptation to climate change in an economic model, we want to contribute to the economics literature in two ways. 3

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First, the paper makes a normative-methodological contribution by showing that psychological adaptation may be an important determinant of optimal tax policy. Thereby, it contradicts the standard argument that adaptation, i.e., habituation, does not have to be considered in optimal taxation analysis (Becker and Murphy 1988). In an intertemporal framework, the decisions the government make today must be based on the best available

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information about both today’s cost of mitigation and tomorrow’s cost of coping with the consequences of today’s decisions. Thus, future costs should not be assessed in the way we perceive them today, but must be based on our knowledge about how psychological adaptation will affect the way in which they are perceived by future generations.

Second, the paper illustrates how the incorporation of psychological adaptation may

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influence an optimal corrective tax policy. In an intertemporal cost-benefit analysis we have to weigh the cost of today’s measure to combat global warming against the cost borne by future generations resulting from climate change. If we ignore psychological adaptation, we may over-estimate the welfare cost of future environmental damage. Taking account of

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psychological adaptation will thus modify the optimal Pigouvian tax. Analytically, the degree by which people can adapt to changing environmental circumstances plays a somewhat

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similar qualitative role for optimal tax policy as the physical depreciation rate of CO2 in the atmosphere.

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We proceed as follows. In Section 2 we develop a simple intertemporal model that focuses

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exclusively on the impact psychological adaptation has for the disutility of climate change. Thus, many important aspects of global climate change such as changes of the world’s

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ecosystem that can have severe impacts on the agricultural production or the risk of catastrophic changes (see, e.g., Stern 2007, Weitzman 2009) are left out. This allows us to illustrate the differential effect the incorporation of psychological adaptation can have on intertermporal cost-benefit considerations and optimal intertemporal tax policies to fight the consequences of climate change, which is the topic of Section 3. Heterogeneity in the degree to which people adapt will be considered in Section 4. Section 5 concludes.

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2. The model This section presents a simple model of a closed economy with stock pollution where production today leads to environmental damage in the future. We consider a case where pollution has a direct negative effect on individual utility. Individuals are assumed to adapt to the environmental damage through a habit-formation process. The three agent types are

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consumers, firms, and a policy maker, which are characterized below. Individuals and firms

We develop an overlapping generations (OLG) model where each individual lives for two periods. An individual of generation t is young in period t and old in period t+1, and enjoys

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utility from his/her consumption when young, ct , leisure when young, zt , and consumption when old, xt 1 . The individual also derives disutility from pollution, where et denotes the stock of pollution in period t. Without loss of generality, we simplify the notations below by normalizing the number of individuals in each generation to one. The instantaneous utility

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function faced by a young and old individual, respectively, of generation t is given by (1a)

uto1  u o ( xt 1 , et 1   et )  q( xt 1 )   (et 1   et ) ,

(1b)

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uty  u y (ct , zt , et   et 1 )  ct  h( zt )  (et   et 1 ) ,

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where super-scripts y and o refer to “young” and “old”, respectively, and sub-script t to time period. In equation (1b), the dependence of utility on leisure has been suppressed, since the

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individual is assumed to be retired when old. The parameter  indicates the degree of adaptation to the environmental damage. We can think of et   et 1  t and et 1   et  t 1

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as “adaptation-adjusted” measures of the environmental damage in period t and t+1, respectively, to be further discussed below. The functions h() and q() are increasing in their respective arguments and strictly concave, i.e., hz ()  0 , hzz ()  0 , qx ()  0 , and qxx ()  0 , while  () is decreasing and strictly concave such that   ()  0 and   ()  0 , where a single sub-script denotes first order derivative and a double sub-script second order derivative.2 The utility of zero environmental damage is normalized to zero, i.e.,  (0)  0 . Adding a decreasing and strictly concave utility of pollution function,  () , to the other parts of the utility function, as we have done, is qualitatively equivalent to subtracting an increasing and strictly convex cost function (as is done in some other studies). 5 2

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The functional form assumptions in equations (1a) and (1b) are analytically convenient by allowing us to abstract from environmental feedback effects and income effects; yet, neither additive separability nor quasi-linearity is essential for the qualitative insights.3 Note that the young generation adopts the “adaptation-adjusted” environmental damage of the old generation.4

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We adopt Loewenstein, O’Donoghue, and Rabin’s (2003) idea of internal habit formation such that last period’s stock of pollution serves as a reference measure (”habit stock”) with which the current stock is compared. Adaptation abilities may be quite different among people but we postpone the discussion about heterogeneity among individuals in terms of adaptation to Section 4. For the time being, we stick to the simplified case of uniform

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adaptation behavior for the sake of the argument. The uniform degree of adaptation  is assumed to be in the interval [0,1] whereby   1 means full adaptation (or habituation).5 Based on equations (1a) and (1b), the life-time utility function of an individual of generation t can then be written as

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Ut  uty  uto1 ,

(2)

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in which  represents the utility discount factor, i.e.,   1/ (1   ) where  denotes the

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utility discount rate. The life-time budget constraint becomes

wt lt  bt  st  ct ,

(3a)

st (1  rt 1 )  xt 1 ,

(3b)

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where l denotes the hours of work, defined by a time endowment (normalized to one) less the

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time spent on leisure, i.e., l  1  z , while w denotes the wage rate, s saving, and r the

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We also abstract from adaptation in consumption and leisure. The qualitative differential effects of adaptation to environmental damage do not depend on whether rational consumers adapt in other dimensions. 4 A possible generalization would be to allow the parameter  to differ between generations (or vary over time). Yet, such an extension leads to few qualitative insights beyond those discussed below, which motivates us to focus on the simpler case with a constant . 5 To give an idea about the magnitude of , consider the following example. According to Sackett and Torrance (1978) healthy people evaluate one additional life year as a dialysis patient as being equivalent of living 0.39 additional years as a healthy person, while patients who actually suffer from dialysis evaluate one additional year of their current life as equivalent of living 0.56 additional healthy years. Assuming that healthy people completely disregard adaptation while actual dialysis patients make the judgment after having adapted, the actual loss in quality-adjusted life years is 28% lower due to adaptation. 6

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interest rate. The variable b is a lump-sum transfer paid to each young consumer, which equals the tax revenue raised through environmental taxation (see below).6 An individual of generation t chooses lt and st to maximize the life-time utility given by equation (2) subject to the life-time budget constraint presented in equations (3). Thereby, each individual is perfectly rational and is fully aware of the degree by which he/she will

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adapt to changing environmental circumstances. Furthermore, each individual is assumed to behave as an atomistic agent, treating factor prices, the lump-sum transfer, and the stock of pollution as exogenous. The first order conditions for work hours and saving then become

uty,c wt  uty, z  0 ,

(4b)

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uty,c  uto1, x [1  rt 1 ]  0 ,

(4a)

in which the second sub-script denotes partial derivative, i.e., uty,c  uty / ct , uty,z  uty / zt and uto1,x  uto1 / xt 1 .

The homogenous consumption good is produced by identical and competitive firms under

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constant returns to scale, and the number of such firms is normalized to one for notational convenience. The objective function of the representative firm in period t is written as (5a)

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F (lt , kt ) 1   t   wt lt  rt kt ,

where F () denotes the production function, k the capital stock, and  t an output tax levied

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on the firm in period t. The firm then obeys the first order conditions

Ft ,l 1   t   wt and Ft ,k 1   t   rt ,

(5b)

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where Ft ,l  F (lt , kt ) / lt and Ft ,k  F (lt , kt ) / kt .

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Accumulation of pollution We assume that pollution is a state variable, which accumulates as follows:

et  t F (lt , kt )  (1   )et 1 .

(6)

The parameter  represents physical depreciation of the stock of pollution, which in the case of greenhouse gases may be close to zero. The additions to the stock of pollution in the atmosphere are assumed to be proportional to output, where the factor of proportionality t is 6

Since we are solely concerned with efficiency aspects of environmental policy, it is not important for the results whether the tax revenue is returned to the young or old age-group; the same tax policy implications of adaptation as those presented below would follow if the tax revenue is used as a lump-sum payment to the old. 7

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fixed within each period although it may vary over time. Such a setting encompasses special cases such as the switch from dirty (   0 ) to clean (   0 ) technologies as time passes. The policy maker Our concern is to characterize an optimal tax policy that fully internalizes the intertemporal environmental externality and analyze how this policy is influenced by adaptation to the

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environmental damage. Therefore, we follow convention in the literature on optimal taxation in dynamic economies with externalities in assuming that the policy maker takes the utility of all future generations into account through a social welfare function. To simplify the calculations, we consider a utilitarian social welfare function given by the discounted sum of

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life-time utilities over all generations7

W   U t t .

(7a)

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Thereby, the policy maker has full information about the individual ability to adapt. By assuming that the capital stock in period t equals the savings in period t1, and then using

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equations (3) and (5a) together with the condition for public sector budget balance, i.e.,

bt   t F (lt , kt ) , the resource constraint for the economy as a whole is given as follows:

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F (lt , kt )  ct  xt  kt 1  kt for all t,

(8)

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meaning that output in any period is used for private consumption and net investment. The resource allocation preferred by the policy maker can be derived by choosing ct , lt ,

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xt , kt , and et for all t to maximize the social welfare function given in equation (7a) subject to the resource constraint and accumulation equation for the stock of pollution given by

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equation (8) and (6), respectively. The Lagrangean can then be written as

L  W    t  F (lt , kt )  kt  ct  xt  kt 1    t et  t F (lt , kt )  (1   )et 1  . t

(9)

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The Lagrange multipliers,  and  , are interpretable as present value shadow prices of physical capital and pollution. The allocation for generation t preferred by the policy maker is

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In the context of climate change, which is a global environmental problem, the most natural interpretation of our policy maker would be in terms of a global social planner who strives at internalizing the externality at the global level. This approach is justified here, since our purpose is to examine how adaptation to environmental damage modifies an optimal Pigouvian tax policy. A corresponding interpretation in terms of national policy makers would follow naturally in case of more local environmental problems. 8

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represented by the social first order conditions for ct , lt , xt 1 , kt 1 , and et , which can be written as (10a)

uty,z t   t Ft ,l  t t Ft ,l  0 ,

(10b)

uto1, x t 1   t 1  0 ,

(10c)

 t   t 1 (1  Ft 1,k )  t 1t 1Ft 1,k  0 ,

(10d)

uty,t  uto,t  t   uty1,t 1  uto1,t 1  t 1  t  t 1 (1   )  0 ,

(10e)

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uty,c t   t  0 ,

where we have used the short notation t  et   et 1 for the adaptation-adjusted measure of

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environmental damage affecting individuals in period t.

3. Optimal tax policy

We analyze the optimal environmental tax policy for any period t. The optimal environmental tax on output can be derived by combining the first order conditions for the firm with the

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social first order conditions for consumption and work hours attached to the young of generation t given in equations (10a) and (10b). In general, the optimal marginal output tax

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can be characterized as follows (the proof is delegated to the Appendix):

t  t  tt t  t (1   )t t for all t. t 

(11)

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t 

The intuition is straightforward. The variable t (1   )t represents the current value shadow

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price of the stock pollution in period t, which is equal to the sum of the marginal willingness to pay over all future generations to avoid pollution, measured in units of private consumption

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in period t (having uty,c  1 ). The value of the marginal externality generated through production in period t is equal to t (1   )t times the marginal effect of output on emission,

t . Equation (11) thus represents a first-best Pigouvian tax on the intertemporal externality.8

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Since the production sector is characterized by constant returns to scale, an alternative way of implementing the first best optimum (as perceived by the utilitarian government described above) would be to use income taxation. Marginal labor income taxes and marginal capital income taxes are then implemented to decrease the hours of work and saving, respectively, with the same implication as the output tax described here. 9

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Let us start by analyzing the standard case without adaptation, which serves as a reference case for the analysis to follow. By solving the difference equation (10e) under the assumption that   0 and then using equation (11), we obtain the following result: Observation

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(benchmark

policy).

Without

any adaptation to

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environmental damage, i.e., if   0 , we have s 0

ts

 uto s ,t  s t  s (1   ) s



 2 e (et  s ) (1   )  0 t s

s 0

such that t  0 implies  t  0 for all t.

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t   uty s ,

(12)

Without any adaptation, the shadow price t equals the negative of the standard discounted

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sum of marginal utilities of pollution measured over all future generations, times the remaining part of this marginal unit of pollution (1   ) in the periods following period t. Accordingly, the government implements a standard Pigouvian tax in all periods in which

t  0 .

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In the more general case that allows for adaptation, the shadow price of environmental quality is given by 

s 0



 



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t   uty s ,

ts

 uto s ,t  s   uty s 1,t  s 1  uto s 1,t  s 1  t  s (1   ) s 

 2   (et  s   et  s 1 )    (et  s 1   et  s ) (1   )

.

(13)

s

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t s

s 0

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In equation (13), uty,t  uto,t    (et   et 1 ) denotes the marginal utility of pollution faced by any (young or old) individual living in period t, which now depends on the adaptation-

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adjusted measure of pollution,   et   et 1 . Since we assume a quasi-linear utility function, we can interpret   (et   et 1 )t as the marginal willingness to pay by any such consumer to avoid pollution in period t, ceteris paribus. The second component in the square bracket on the right hand side, i.e., the expression proportional to  , is due to the fact that increased pollution today affects the marginal utility of pollution in the future. With adaptation,   (0,1] , this component reduces the shadow price of pollution and, therefore, most likely the optimal level of the corrective policy measure. 10

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To see this more clearly, let us consider how a small increase in the degree of adaptation starting from the benchmark case   0 affects the optimal corrective tax. Differentiating equation (13) with respect to  and evaluating the resulting derivative at   0 , we obtain

t 

 0 for all t if  0

et  1 for all t. 

(14)

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The proof is delegated to the Appendix. Using equations (11) and (14), we obtain Proposition 1. A small increase in the degree of adaptation, starting at no adaptation, lowers the optimal marginal tax on output in period t, i.e.,

 t 

 0,  0

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if (14) is satisfied and t  0 .

Note that (14) provides a sufficient (but not necessary) condition for a negative relationship between the shadow price of environmental quality and the degree of adaptation, since the derivative of t with respect to  (evaluated at the point where   0 ) can clearly be

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negative even if et /   1 for all t. The requirement et /   1 ensures that the direct negative effect of  on the marginal willingness to pay to avoid pollution is not offset by a

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corresponding indirect effect through increased pollution. To further elaborate on how psychological adaptation affects the optimal tax over time,

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consider an environmental steady state in which the stock of pollution in the atmosphere is

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constant over time at some level e . Equation (13) reduces to read

t  2  (e   e )

1  1





t s

(1   ) s .

(15)

s 0

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In an environmental steady state, adaptation matters in two respects. The term   (e   e ) indicates that psychological adaption decreases the marginal willingness to pay to avoid pollution, ceteris paribus, although the stock of pollution remains constant. The multiplier (1     ) / (1   ) is interpretable as a weight that adaptation attaches to the marginal utility

of pollution in the shadow price formula. For   0 , this weight is equal to one. Therefore,

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adaptation decreases the weight attached to the marginal utility of pollution below unity.9 The extreme case of full adaptation then implies the following Pigouvian tax policy: Proposition 2. Suppose that the stock of pollution is constant over time. With full adaptation such that   1 , the Pigouvian tax takes the form

for all t, where

t  

2 t

t

 1

t ,



  (0) t  s (1   ) s s 0

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t 

is the current marginal value of pollution in equilibrium where   0 , i.e., the conventional Pigouvian tax formula for period t evaluated at   1 .

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To interpret Proposition 2, we note first that Weitzman (2010) discusses the properties of damage functions in the context of climate change, i.e., the disutility and marginal disutility of pollution, and presents a utility function where the marginal utility of environmental damage is zero when the environmental damage (measured as temperature change) is zero. In terms of

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our model, where adaptation is present, the analogous property would be   ()  0 if

  e   e  0 . In this case Proposition 2 implies that  t  0 for all t. If the stock of

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pollution is constant, full adaptation means that a welfarist policy maker refrains from taxing pollution since full adaptation implies that the marginal disutility of pollution approaches

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zero. In this case, pollution taxes are only used along the transitional path but not in a stationary equilibrium. For instance, if the stock of pollution increases at a decreasing rate

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such that et  et 1  et 1  et  0 for all t along the transitional path, and if  is time-invariant (i.e., t    0 for all t), the marginal pollution tax is positive (yet decreasing) along this

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path, while it becomes equal to zero once the steady state is reached. On the other hand, if   (0)  0 there will still be a motive for corrective taxation in a

stationary equilibrium. The marginal willingness to pay for decreased environmental damage,

  , must then be evaluated at the point where the effective damage ( e   e ) is zero.  t 9

Sensitization, whereby the individuals become more sensitive to the environmental damage, would have effects opposite those discussed here by scaling up the marginal disutility of pollution as well as the Pigouvian tax. The model can easily be extended to cover sensitization by allowing  to be negative. With respect to some negative environmental externalities, people may become more sensitive over time, e.g. with respect to permanent noise exposure (see Frederick and Loewenstein 1999). 12

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denotes the discounted sum of the marginal willingness to pay to avoid pollution over all future generations and may be interpreted as the conventional Pigouvian tax formula for period t evaluated at   1 . Full adaptation changes the conventional Pigouvian tax formula as  t must be multiplied by an adjustment factor,  / (1   )  0 , in order to reach the correct level of Pigouvian taxation. The positive adjustment factor may seem surprising at first

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thought, as one might expect full adaptation to eliminate the utility loss of the damage, thus also eliminating the need for corrective policy. However, although full adaptation means that the current utility loss of increased pollution will be equal to the undiscounted utility gain caused by adaptation in the next period, the next period’s utility gain is discounted to present value, meaning that full adaptation does not fully compensate for the current marginal damage

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of pollution. To exemplify, if   0.03 the actual Pigouvian tax in any period t,  t , would correspond to roughly 2.9 per cent of the level implied by  t . Therefore, in the steady state a high degree of adaptation to pollution may contribute in two ways to a reduction in the

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corrective tax. 4. Heterogeneity in the ability to adapt

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Psychological research suggests that variables such as personality traits explain heterogeneity in the ability to adapt (for further references, see Luhmann et al. 2012). The results by Albouy

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et al. (2013), who analyze U.S. households’ preferences over local climates, show that preferences vary by location due to sorting or adaptation, indicating the potential importance

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of heterogeneity in adaptation with respect to future climate change. We analyze this case by assuming that only a share of the population 0    1 is able to adapt, i.e.,   0 , while the

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share 1  is not able to adapt, i.e.,   0 . If people face the same preferences but only differ in the degree of adaptation, the

welfarist model with a utilitarian policy maker will lead to a modified cost-benefit analysis compared to above. The social welfare function can then be written as

W   U ta t  (1   )U tn t , t

(7b)

t

where super-script a refers to adapters and n to non-adapters. To focus on heterogeneity with respect to adaptation, we assume that the individuals are identical in all other respects. The 13

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resource constraint and accumulation equation for environmental damage take the same form as above. Since we assume that individuals have the same preferences, and that the utility function is separable in the environmental damage, the social first order conditions for consumption and work hours do not differ between adapters and non-adapters. Therefore, the social first order conditions for ct , lt , xt 1 and kt 1 will remain as in equations (10a)-(10d),

 uty,,a  uto,,a  t   uty,1,a   uto,1,a  t

t 1

t



t 1

t 1

 t  t 1 (1   )  0.

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whereas the social first order condition for et changes to read

  (1   ) uty,,n  uto,,n  t t   t  .

(17)

With equation (17) at our disposal, the following result immediately follows from equation (11) (see the Appendix):

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Proposition 3. If only a fraction  of the population adapts to the pollution, a welfarist government implements the first best through the following tax policy

t 

t t



t   t   uty,sa,  uto,as , s 0

t s

t s



   u

y ,a t  s 1, t  s 1



 uto,as 1,t s1   s (1   ) s 

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 t (1   ) uty,sn,t s  uto,ns ,t s  s (1   ) s s 0



(18)

 2 t   s (1   ) s     (et  s   et  s 1 )    (et  s 1   et  s )  (1   )  (et  s ) .

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s 0

Proposition 3 implies that the formula for the externality correcting pollution tax becomes a

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linear combination of the formulas for adapters and non-adapters. For any given resource allocation (which means a given path for the stock of pollution), a higher share of adapters

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implies a lower optimal pollution tax. Lowering the pollution tax in response to adaptation makes the non-adapters worse off. As long as at least some people adapt to the environmental

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damage, therefore, the application of the conventional tax formula in Observation 1 (which assumes away adaptation completely) typically leads to excessive taxation. 5. Discussion Climate policy hardly addresses psychological adaptation processes and thus cannot claim to provide reliable cost-benefit estimates for climate change. Information about these processes are needed in order to improve intertemporal efforts to minimize the social cost of global warming. Here, further research on psychological adaptation promises high returns. 14

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Our results suggest that adaptation might be very important for welfare analysis, even when economic agents are fully rational. This is in contrast to the view that adaptation provides no justification for policy makers to intervene when individuals have rational expectations about their adaptation abilities (e.g., Aronsson and Schöb 2017). In the presence of intertemporal externalities, psychological adaptation to environmental damage need to be

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considered in the policy maker’s intertemporal decision problem. A normative requirement of intertemporal welfare functions should thus be that today’s decision must be based on the cost of today’s measure to combat global warming and the actual cost borne by future generations resulting from climate change, depend on the future generations’ ability to psychologically adapt.

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Our study focuses solely on economic efficiency. However, heterogeneity in the ability to adapt is also relevant from the perspective of intergenerational redistribution. Early in the debate about climate change, Schelling (1992) suggested that highly developed, richer societies are less vulnerable to climate change as they have the financial and human capital,

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the knowledge and the appropriate technologies for an optimal reaction to climate change while poor societies lack the capability to cope. If technological adaptation is positively

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correlated with psychological adaptation, this so-called “Schelling-conjecture” (Anthoff and Tol 2012) carries over to the case of psychological adaptation. A purely efficiency-oriented

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policy that gives equal weight to all individuals may harm the non-adapters and thus lead to

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an intertemporal redistribution of welfare from future non-adapters to the current producing generation. Therefore, if heterogeneity in the ability to adapt is not perfectly correlated with

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income, there is an additional dimension of redistribution to be explored in future research. Appendix

Derivation of equation (11): Combining equations (10a) and (10b) gives 

 t  Ft ,l  

uty, z    t t Ft ,l . ut1,c 

(A1)

Use the individual first order condition for work hours, wt  uty, z / ut1,c  0 , and the firm’s first order condition for labor input, (1   t ) Ft ,l  wt , we obtain Ft ,l  uty, z / ut1,c   t Ft ,l . Substituting into equation (A1) gives equation (11). 15

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Derivation of (14): Differentiating equation (13) with respect to  , and evaluating the resulting derivative at the point where   0 , implies

t 

 0

  e  2    (et  s ) 1  t  s   s 

      (et  s 1 )   

(A2)

where   (et  s )  0 and   (et  s )  0 for all s. A sufficient condition for the right hand side

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of equation (A2) to be negative is et  s /   1 for all s. Proof of Proposition 3: Solve equation (17) forwards to derive 

t    uty,sa,  uto,as , ts

s 0

ts

   u

y ,a t  s 1, t  s 1



  (1   ) uty,sa,t  s  uto,as ,t  s t  s (1   ) s s 0





 uto,as 1,t  s 1  t  s (1   ) s 

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 2    (et  s   et  s 1 )    (et  s 1   et  s )  (1   ) s 0



ts

(A3)

s

 2 (1   )   (et  s ) t  s (1   ) s s 0

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Substituting into equation (11) gives equation (18). References

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