Adaptation, Mitigation and Trade
Addressing the Economic Effects of Climate Change
Alain-Désiré Nimubona and Horatiu A. Rus1
Abstract
Given a common objective such as welfare maximization and the constraints shaped by
climate change, the choice of the efficient quantities of mitigation, adaptation and openness
are linked. Thus, optimal policy-making processes should consider these elements simultaneously. The paper explores the interaction between nationally based carbon mitigation policies
implemented through instruments such as carbon taxes - in essence a global public good and domestic adaptation efforts - which can be seen as a global private good, in a small open
economy. Heterogeneous domestic economies with their own carbon tax and adaptation spending are linked to the world economy via international trade. In a general equilibrium model
of international trade where climate change affects production possibilities, the paper first
investigates the role played by climate change adaptability and vulnerability parameters in determining comparative advantage and the pattern of specialization. Then the effect of opening
to international trade on a country’s pollution level is analyzed. Subsequent sections introduce
cross-sector heterogeneity in the effects of climate change and extend the basic framework to
multiple countries, factors and goods.
JEL: Q25, Q54, F18
Keywords: climate change, adaptation, mitigation, carbon taxes, international trade.
1
Department of Economics, University of Waterloo, 200 University Drive, Waterloo, ON, Canada
N2L 3G1 (animubon@uwaterloo.ca, hrus@uwaterloo.ca)
2
This is a PRELIMINARY AND INCOMPLETE VERSION. Please do not cite without permission.
Preprint submitted to CREE Annual Meeting 2014, University of Saskatchewan
September 27, 2014
1. Introduction
The relationship between greenhouse gas emissions mitigation policies that price
carbon and ultimately aim to curb emissions (such as pollution taxes, cap-and-trade
mechanisms or command and control policies), adaptation to the effects of climate
change, and international trade has not received sufficient attention in the literature.
Given a common objective, such as welfare maximization, and the constraints shaped
by climate change, the choice of the efficient quantities of mitigation, adaptation and
openness are linked. Thus, optimal policy-making processes should consider these elements simultaneously. While there exist substantial and rapidly growing sub-literatures
on each of these components separately, as well as on trade and the environment more
generally, this trilateral interaction has only recently begun to attract attention. Moreover, as further detailed below, the few existing contributions do not have the same
scope as the present undertaking. The premise of this paper is that acknowledging the
interactions between the effort to reduce the carbon footprint of the domestic industry,
the (potentially different sectoral) costs of adaptation to climate change, and the role
played by international trade in determining the level of domestic production in various sectors of the economy offers an important novel perspective in the current search
for new viable economic policy approaches to these issues. Nationally optimal climate
change mitigation and adaptation regimes interconnected via international trade could
result in lower costs of multilateral cooperation. A secondary goal of the paper then
is to contribute to deepening our understanding of the nature of the global collective
action hurdles preventing international cooperation in tackling the challenges presented
by climate change.
Compounding the domestic heterogeneity across industries with respect to climate
vulnerability and GHG-emissions mitigation, there also exist important differences in the
cost of both abatement and adaptation internationally. In addition to the well-known
1
differences in the average cost of reducing carbon emissions, some countries’ economies
are projected to suffer massive losses as climate change impacts materialize, with others
being neutral and yet others perhaps even benefitting marginally from the effects of
global warming. These heterogeneities need to be accounted for when designing both
national environmental policies as well as blueprints for long-term international collective
action on climate change. An integrated mitigation-adaptation-trade framework has
the potential to provide new insights applicable both to individual countries economic
policymaking, as well as to international efforts for cooperation.
The issue of the optimal mix of adaptation to versus mitigation of climate change is
not sufficiently well studied to date. Most of the existing studies introduce adaptation
into a computable general equilibrium (CGE) model of the economy and of climate, aiming to derive implications for the optimal climate change policy. Integrated assessment
models (IAMs) such as De Bruin et al. (2009b) who consider 13 regions and selected
countries, or De Bruin et al. (2009a) who also look at various sectors, have provided
initial calibration results with respect to projected costs induced by climate change.
Stephan and Schenker (2012) consider the spillover effects of climate-induced costs which
are transmitted via international trade and conclude that even in low-exposure, highadaptability regions, the share of such costs due to international exchanges is substantial.
In our paper we look at international trade as a potential implicit adaptation channel,
thus also having cost-reducing effects. While the results of these existing models are
important from a policy perspective, they shed insufficient light on the economic drivers
of various results. Complementary theoretical as well as empirical work is needed in
order to achieve a better understanding of the issues and the way economic policy interactions play out. These are not only critical for designing better domestic environmental
policies, but also for understanding the prospects for international cooperation on the
issue of climate change in general.
2
A small but growing literature looks at the trade-off between the carbon policy or
mitigation of greenhouse gas generation and adaptation to changing temperatures and
some of their implications for global concerted action. In a framework without international trade, Farnham and Kennedy (2010) show that the availability of adaptation
to climate change can have deleterious effects on countries which are less able to adapt,
thus increasing their incentives to seek an international cooperative solution. Antweiler
(2010) uses an optimal control model also without trade to analyze the optimal policy mix between mitigation and adaptation and finds that the latter appears to carry
more weight in a framework where emissions are heterogeneous across countries. Buob
and Stephan (2011) analyze a non-cooperative game with mitigation and adaptation
as perfect substitutes where countries’ responses to climate change depend on their
income: rich countries mitigate and adapt, while poor countries mitigate only. This
counterintuitive finding is obtained under particular assumptions about the interaction
between mitigation and adaptation and in the absence of international trade. Stephan
and Schenker (2012) look at the effect of international trade of both spreading the costs
of climate change and allowing specific regions to adapt to it and derive a motive for
developed countries to help finance adaptation in developing countries.
Unlike most of the existing papers on climate change, including Copeland and Taylor
(2005), Thurunen-Red and Woodland (2004) or Keen and Kotsogiannis (2014), Kotsogiannis and Woodland (2013) adopt a notion of climate change that does not impact
the utility of consumers directly, but rather it affects the factors of production endowments. There are strong indications from the Stern Report to the impact assessment
literature that most losses due to climate change will be due to damages to production
sectors.1 In an analytical general equilibrium framework with climate change policies
and international trade, they provide a characterization of the equilibrium and suggest
1
See Stern (2007), Parry et al. (2007), among others.
3
conditions for Pareto-improving environmental policy reform. Their work focuses on the
optimal reform of carbon policies and does not consider adaptation.
Several issues have remained unaddressed or unresolved in the received literature.
While mitigation and adaptation are often treated as policy substitutes (if more mitigation is undertaken in the present, less adaptation may be required in the future, see
e.g. Barrett (2008)), there are documented instances in which the two policies may be
complementary (for instance when mitigation increases the effectiveness of adaptation,
like in Perry et al (2001)), or neutral from the point of view of individual countries.
Moreover, there are important domestic and global asymmetries with respect to mitigation and adaptation. While an efficient pollution policy raises the cost of emissions
for all polluters across industries, the costs of adaptation are likely to be borne disproportionately by some sectors of the economy. Activities such as agriculture, forestry,
fisheries, transportation and tourism are more ‘climate sensitive than, for instance, general consumer goods manufacturing or telecommunications. Due to this asymmetry, the
incentive structures necessary for adaptation and mitigation are also different. While a
private industry may not require that centralized policies are in place in order to make
investments in an adaptation strategy, which may or may not include re-specialization
and trade, the implementation of mitigation efforts typically require a mandatory policy
instrument that prices the carbon content of emissions.
This paper aims to contribute to this developing literature by analyzing the interplay between climate change mitigation via pollution policy, costly adaptation policies,
and the domestic production mix determined by international trade. We adopt the general framework provided in Kotsogiannis and Woodland (2013) and develop a general
equilibrium model of international trade with carbon taxes and adaptation, where the
impact of climate change is manifested via a (potentially differential) reduction in the
effective endowments of factors of production. The effect of climate change vulnerability
4
and adaptability on countries’ comparative advantage is analyzed. The paper exploits
three types of heterogeneity within, as well as among countries, with respect to: the
cost of emissions mitigation, the cost of adaptation to the effects of climate change,
and the degree of involvement in international exchanges. The latter is interpreted as
a vent for industrial re-alignment based on true relative costs, which include mitigation and adaptation expenses. The model acknowledges that different economies (and
different industries within national economies) are characterized by different marginal
costs with respect to pollution abatement in general and to greenhouse gas emissions
reduction in particular. On the other hand, the adaptation efforts necessary to alleviate
the consequences of climate change impact different countries (and different sectors) in
a non-uniform manner and act to alter the relative cost of production in these locations.
This then further ties into the pattern and composition of international trade, as an
important determinant of a country’s welfare. A more open economy allows for the
minimization of the total mitigation and adaptation costs by specializing in areas in
which these are relatively low, and this also results in smaller global costs.
This optimal re-shuffling of economic activity is, however contingent not only on
efficient national environmental policies and openness to trade, but also on the internalization of the inter-sectoral and international adaptation externalities. In the absence
of these conditions, second-best scenarios can lead to several counter-intuitive conclusions. On the one hand, an open economy can use the international prices signals to
re-adjust its production mix according to its respective mitigation and adaptation costs,
and thus reduce the costs of internalization. At the same time, however, opening up to
trade does not allow domestic producers to pass the same share of the climate change
policies cost onto their domestic consumers, with potentially detrimental implications
for the equilibrium stringency of such policies. On the other hand, a relatively closed
economy is necessarily more diversified in production, thus not able to use the costs of
5
mitigation and adaptation to climate change as drivers of industrial specialization in
the least-relative cost sectors. Furthermore, the net cost of mitigation and adaptation,
and the benefit of specializing in certain economic activities are important determinants
of countries willingness to participate in International Environmental Agreements, and
ultimately in their success.
To preview the main results, potential comparative advantage depends on the country’s vulnerability to climate change, as well as on its mitigation and adaptation costs in
a complex way. The production factors effects of climate change will generally increase
goods prices when the degree of adaptability to climate change is significantly low. Also,
a higher stock of the global pollutant would result in higher prices when the degree of
vulnerability of the factors of production to climate change is high enough and when
the degree of adaptability is very low. However, for moderate degrees of adaptability,
the effect of vulnerability is reversed: a high degree of vulnerability results in a negative price effect of climate change. In general, while a state of autarky conditions the
domestic economy to incur potentially massive welfare losses by having to produce in
sectors of activity which are highly affected by the climate, openness to trade allows it to
specialize and potentially reduce such costs. When marginal adaptation and mitigation
costs are allowed to vary across sectors, these effects persist and are more pronounced.
The rest of the paper is organized as follows. The following section sets out the
general equilibrium model of international trade with climate change affecting the effective factor endowments. After the autarkic case with country-specific adaptability and
vulnerability to climate change is described, the paper goes on to introduce the case of
the small open economy involved in international trade. The following section extends
the benchmark model by allowing sector-specific climate change impact parameters, and
the last section concludes.
6
2. Some Empirical Motivation
In order to inform and further motivate our theoretical study, we have assembled
a panel dataset including all countries for the period 1960 to 2013 and information
regarding economic size, carbon emissions, carbon dioxide intensity of production, international trade openness, membership in international environmental agreements, as
well as climate-related natural disaster experience, climate vulnerability and carbon
policies. Appendix A provides a detailed list of variables and data sources and Table 1
contains the main summary statistics. Table 2 includes six different models illustrating
the relationship between a carbon policy dummy and GDP per capita, trade openness,
CO2 intensity of GDP and climate change vulnerability and readiness indicators, as
well as interaction terms between trade openness and carbon intensity and vulnerability
measures. The coefficients have the expected signs: while the carbon intensity of production is shown to decrease the likelihood that a country would adopt climate policies
(opposition to climate measures) and the vulnerability measures and GDP per capita
is generally increasing it (demand for climate measures), what is interesting is that the
interaction terms involving the degree of international trade integration are generally significant. Thus, given a certain degree of openness, a higher projected impact of climate
change leads to an increased likelihood that some carbon price policy is adopted. Table
3 shows how a country’s membership in various international environmental agreements
depends on some of the same controls, and again the signs are generally what would be
expected.
3. The Model and Some Preliminaries
We consider a standard competitive general equilibrium model of international trade,
which we modify to account for the presence of global pollution and adaptation to
the effects of pollution. In each of the two countries indexed by j = 1, 2 there are a
7
representative consumer and a private sector that produces two tradable commodities, x
and y. The production of x, the dirty good is always more polluting than the production
of y, the clean good. We assume that x can be sold at price p and y is the numeraire
good. We denote by τ j the trade tax or subsidy for x in country j. The domestic price
of x in country j therefore corresponds to pj = p + τ j .
We assume that the two countries have different factor endowments: producers in
each country j have access to factor endowments v j to produce x and y. The emissions
generated in country j by the production of x, which we denote by z j , are subject
to an exogenous pollution tax, which is country-specific and denoted by θj . Global
P
emissions are given by Z = j z j . We follow Kotsogiannis and Woodland (2013) in
considering Z as the steady state of climate, also equivalent - by a proper normalization
- to its economic impact. Therefore, climate change is exogenous with respect to an
individual country’s policy decisions. Also as in Kotsogiannis and Woodland (2013)
and unlike many other papers in the literature who assume climate change directly
impacts consumers’ utility, we adopt the view that the climate state or global pollution
primarily affects production possibilities of each of the two countries through its negative
impact on their effective factor endowments, according to v j (Z, aj ).2 In this function, aj
denotes the level of adaptation chosen by country j. We assume that v j = αj aj − β j Z,
which implies that each country j can reduce the negative impact of global pollution
on its factor endowments by undertaking adaptation efforts. Parameters αj > 0 and
β j > 0 represent the country-specific degrees of adaptability and vulnerability to global
pollution, respectively. This allows for climate change to have different impacts on factor
endowments in different countries, which concurs with most of the available evidence
2
Significant evidence points to effects of climate change that primarily refer to infrastructure,
agricultural yields and natural disasters.
8
to date. Moreover, the returns from adaptation efforts also differ by country.3 For
concreteness, the cost of adaptation in country j is assumed to be given by C (aj ) = γ j aj ,
where γ j is the marginal cost of adaptation in country j, which is taken to be exogenous
and again, country-specific.
3.1. Adaptation and Mitigation under Autarky
We first characterize the equilibrium in country j under autarky, to be used as a
benchmark. The revenue function for country j is defined by:
r j pj , θj , γ j , v j (Z, aj ) = max pj xj + y j − θj z j − γ j aj : f j xj , y j , z j , v j (Z, aj ) ≤ 0 ,
(1)
where f j (.) is the implicit production possibility frontier in country j. Making use of the
envelope property, the net output level xj , the emissions level z j and the adaptation level
aj , are respectively given by the following partial derivatives of the revenue function:
rpj pj , θj , γ j , v j (Z, aj ) = xj ,
(2)
rθj pj , θj , γ j , v j (Z, aj ) = −z j ,
rγj pj , θj , γ j , v j (Z, aj ) = −aj .
(3)
(4)
The expenditure function of the representative consumer is given by:
ej pj , uj = minxj ,yj pj xj + y j : U j xj , y j ≥ uj ,
(5)
where U j (xj , y j ) is the utility from consuming commodities x and y. Notice that, as
pointed out above, we differ from most of the extant literature in assuming that the
utility function does not depend on the level of global pollution. By the Shephard’s
lemma, the gradient vector ejp (pj , uj ) provides the demands for x.
3
One could further assume that these climate change impacts and/or adaptation returns are factor-
specific.
9
Thus, the equilibrium under autarky in country j is characterized by the following
set of conditions:
ej pj , uj = r j pj , θj , γ j , v j (Z, aj ) + θj z j + γ j aj ,
(6)
ejp pj , uj = rpj pj , θj , γ j , v j (Z, aj ) ,
X j
rθ pj , θj , γ j , v j (Z, aj ) = −Z.
(7)
(8)
j
Condition (6) represents the budget constraint in country j. It states that the total
expenditure must be financed by income from production, pollution tax revenues, as
well as factor income from adaptation activities. Equation (7), in turn, corresponds
to the market clearing conditions for commodity x in country j, in the absence of
international trade. Finally, equation (8) ensures that global emissions are equal to the
sum of emissions generated by all countries.
Let us first analyze the determinants of the change in emissions and adaptation
levels. The change in the emissions generated in country j can be obtained by totally
differentiating (3) as follows:
j
j
j
j
dz j = −rθp
dpj − rθθ
dθj − rθγ
dγ j − rθv
αj daj − β j dZ ,
(9)
j
j
j
j
where rθp
, rθθ
, rθγ
, and rθv
indicate the respective effects on emissions of a change in
the equilibrium price of x, the emission tax, the marginal cost of adaptation, and the
effective factor endowments. In turn, the change in the level of adaptation is derived
from the total differentiation of (4):
j
daj = 1 + rγv
αj
−1
j
j
j
j
rγv
β j dZ − rγp
dpj − rγθ
dθj − rγγ
dγ j ,
(10)
j
j
j
j
where rγv
, rγp
, rγθ
, and rγγ
represent the effects on the level of adaptation of a change
in the effective factor endowments, the price of x, the emission tax, and the marginal
10
cost of adaptation. Substituting (10) into (9), we get the following:
j
j
j
j
dz j = −rθp
dpj − rθθ
dθj − rθγ
dγ j + rθv
β j dZ
−1 j j
j
j
j
j
j
− rθv
αj 1 + rγv
αj
rγv β dZ − rγp
dpj − rγθ
dθj − rγγ
dγ j . (11)
Solving (11) for dpj , we get the following expression of the change in autarky prices:
h
−1 i j
j
j
j
dpj = A−1 Bβ j dZ − A−1 dz j − A−1 rθθ
− rθv
αj 1 + rγv
αj
rγθ dθ
i
h
j
j
j
j −1 j
−1
rθγ − rθv α 1 + rγv α
rγγ dγ j , (12)
−A
i
i
h
h
j
j
j
j
j
j
j −1 j
j
j
j −1 j
rγv .
where A = rθp − rθv α 1 + rγv α
rγp and B = rθv − rθv α 1 + rγv α
Given that θ and γ are exogenous by assumption, (dθj = 0 and dγ j = 0), the comparative statics results of the equilibrium autarky prices with respect to the climate
state or global pollution is as follows:
j
dpj
dz j
j
−1
j
−1 dz
−1
Bβ −
.
= A Bβ − A
=A
dZ
dZ
dZ
The expression for
dpj
dZ
(13)
suggests that climate change has two distinct effects on the
autarky price of x. The first one corresponds to the direct effect of climate change
on the price via its impact on factor endowments and the origin of the emissions that
contributed to climate change does not matter in this respect. The second effect is
indirect and it relates to the impact of climate change on the equilibrium emissions
generated in country j. Given that vZ < 0 and rpv > 0 by assumption, we can conclude
that
dz j
dZ
< 0, i.e. a worsening (improvement) of the climate state leads to less (more)
pollution generation in a specific sector in country j. The only way climate change can
affect production under autarky is through its deleterious effect on factor endowments.
Turning to analyze the signs of expressions A and B, we can state the following
intermediate result:
Lemma 1. The sign of A depends on the level of adaptability αj as follows:
11
(i) A < 0 if αj > − rj1 ;
γv
j
rθp
j
j j
θp rγv −rθv rγp
(ii) A ≷ 0 if α < − rj1 and αj ≷ − rj
j
γv
.
j
j
Proof: The sign of A depends on the signs of rθp
and rθv
, which respectively corre-
spond to the negative of the change in emissions due to the change in price and factor
j
j
endowments, as well as the signs of rγp
, and rγv
, which respectively correspond to the
negative of the change in adaptation level due to the change in price and factor enj
j
j
dowments. From our assumptions, we can show that rθp
< 0, rγp
> 0, rθv
< 0, and
j
rγv
< 0. It directly follows that A < 0 if αj > − rj1 . When αj < − rj1 , A ≷ 0
γv
γv
j
j
j
j
j −1 j
if rθp ≷ rθv α 1 + rγv α
rγp . After some simplifications, the last condition is also
j
rθp
equivalent to αj ≷ − rj
j
j j
θp rγv −rθv rγp
. Condition (i) in the above lemma is equivalent to ajv αj > 1, while the two conditions
−1
in (ii) are equivalent to ajv αj < 1 and αj ≷ zpj zpj ajv − zvj ajp . These conditions show
that the sign of A depends on the marginal value of the factors of production in terms
of adaptation to climate change. We have A < 0 (A > 0) when the marginal value
of factors of production in terms of adaptation is higher (lower) than unity. For a
wide range of cases / parameter values, A < 0 if the level of adaptability of factors of
production αj is either too high (i.e. when αj > − rj1 ) or too low (i.e. when αj < − rj1
γv
j
and α < − rj
j
rθp
j
j j
θp rγv −rθv rγp
and αj > − rj
j
rθp
j
j j
θp rγv −rθv rγp
γv
). For moderate degrees of adaptability (i.e. when α < − rj1
j
γv
), however, we have A > 0.
Lemma 2. The sign of B depends on the level of adaptability αj as follows: B ≷ 0 if
αj ≷ − rj1 .
γv
j
j
1 + rγv
αj
Proof: After some simplifications, B can be re-written as follows: B = rθv
−1
j
j
From our assumptions, we have rθv
< 0, αj > 0, and rγv
< 0. It directly follows that
B ≷ 0 if αj ≷ − rj1 . γv
The conditions in Lemma 2 are also equivalent to ajv αj ≶ 1. These conditions show
12
.
that the sign of the elements of B also depends on the marginal value of the factors of
production in terms of adaptation to climate change. They suggest that B > 0(< 0)
when the marginal value of factors of production in terms of adaptation is lower (higher)
than unity. Therefore, B is negative if the level of adaptability of factors of production
is too low (i.e. αj < − rj1 ). When the degree of adaptability is too high (i.e. when
γv
αj > − rj1 ), B is positive.
γv
From Lemma 1, Lemma 2, and (13), we have the following proposition, which summarizes the effect of climate change on the equilibrium price under autarky.
Proposition 1. The impact of climate change on the equilibrium price under autarky
is as follows:
dpj
dZ
(i)
> 0 if the degree of adaptability αj is too low such that αj < − rj1 and αj <
γv
j
rθp
− rj
j
j
j j
θp rγv −rθv rγp
dpj
dZ
(ii)
, while the degree of vulnerability βj is too high such that Bβ −
γv
dp
dZ
dp
dZ
dz j
dp
dZ
dZ
,
j
rθp
j
j j
θp rγv −rθv rγp
,
j
rθp
j
j j
θp rγv −rθv rγp
,
> 0;
γv
dz j
dZ
> 0;
< 0 if αj is low but not too low such that αj < − rj1 and αj > − rj
γv
while the degree of vulnerability βj is too high such that Bβ j −
(v)
j
rθp
j
j j
θp rγv −rθv rγp
< 0 if both αj and β j are both too low such that αj < − rj1 , αj < − rj
and Bβ j −
(iv)
< 0;
> 0 if αj is low but not too low such that αj < − rj1 and αj > − rj
while the degree of vulnerability βj is too low such that Bβ j −
(iii)
dz j
dZ
dz j
dZ
< 0, and ;
< 0 if αj is too high such that αj > − rj1 .
γv
Proof: The impact of climate change on the equilibrium price under autarky depends
on the signs of A and B (as described in Lemma 1 and Lemma 2) and is generally ambiguous, i.e.
dp
dZ
> 0 or
dp
dZ
< 0. The following specific two cases always result in
13
dp
dZ
> 0:



αj < − rj1


γv


rj
(i) αj < − j j θp j j
rθp rγv −rθv rγp





Bβ j − dz j < 0
dZ
,
which imply that A < 0 and B < 0; this is generally the case when the degree of adaptability is too low while the degree of vulnerability is too high.



αj < − rj1


γv


rj
(ii) αj > − j j θp j j
rθp rγv −rθv rγp





Bβ j − dz j > 0
dZ
,
in which case A > 0 and B < 0; this corresponds to the case where the degree of
adaptability is low but not too low, while the degree of vulnerability is also low.
In turn, we will have
dp
dZ
< 0 if:



αj < − rj1


γv


rj
(i) αj < − j j θp j j
rθp rγv −rθv rγp





Bβ j − dz j > 0
dZ
,
which imply that A < 0 and B < 0; this is generally the case when both thes degrees of
adaptability and vulnerability are too low.



αj < − rj1


γv


rj
j
(ii) α > − j j θp j j
rθp rγv −rθv rγp




 j dz j

Bβ − dZ < 0
,
in which case A > 0 and B < 0; this corresponds to the case where the degree of
adaptability is low, but not too low while the degree of vulnerability is high.
14
(iii) αj > − rj1 in which case A < 0 and B > 0; this last situation corresponds to the
γv
case where the degree of adaptability is too high. Proposition 1 above shows how adaptability and vulnerability to climate change mediate the impact of climate change on equilibrium prices under autarky. It confirms that
climate change will generally increase (decrease) commodity prices when the degree of
adaptability to climate change is significantly low (high). The role of the vulnerability
parameter is not straightforward. Our results suggest that the worsening of climate
would result in higher (lower) prices when the degree of vulnerability of factors of production to climate change is high (low) enough if the degree of adaptability is very low.
However, for moderate degrees of adaptability, the effect of vulnerability is reversed: a
high (low) degree of vulnerability results in a negative (positive) price effect of climate
change.
Totally differentiating (6), we have:
ejp dpj + eju duj = rpj dpj + rθj dθj + rγj dγ j − rvj β j dZ + rvj αj daj + θj dz j + z j dθj + γ j daj + aj dγ j ,
where eju = 1 by an appropriate choice of units. Given (7) and our assumption that θ
and γ are endogenous, the above expression can be re-written as follows:
duj = −rvj β j dZ + θj dz j + rvj αj + γ j daj .
(14)
Substituting (10) into (14), we get the following expression of the welfare effect of climate
change:
duj
dpj
dz j
= C + θj
−D
,
(15)
dZ
dZ
dZ
h
i
−1 j
−1 j
j
j
where C = (rvj αj + γ j ) 1 + rγv
αj
rγv − rvj β j and D = (rvj αj + γ j ) 1 + rγv
αj
rγp .
Equation (15) says that climate change has direct and indirect effects on social welfare
in each country j. The direct effect is captured by C, and the indirect effects stem from
15
the change in own emissions, and the change in the equilibrium price of x following
climate change.
In what follows, we analyze how the degrees of vulnerability and adaptability to
global pollution for a country can affect the impact of global pollution on welfare. Let
us first analyze the signs of expressions C and D.
Lemma 3. The sign of C depends on the level of adaptability αj as follows: C ≷ 0 if
αj ≷ − rj1 .
γv
j
Proof: From our assumptions, we have αj > 0, rvj > 0, γ j > 0, rγv
< 0, and β j > 0.
It directly follows that C < 0 if αj < − rj1 . This proves part of Lemma 3. To prove the
γv
remaining part, let us analyze the sign of C when αj > − rj1 . After some simplifications,
γv
we can show that C ≷ 0 if
j
γ j rγv
≶
rvj .
Since
j
γ j rγv
<
rvj
by assumption, we can conclude
that C > 0 whenever αj > − rj1 . γv
Lemma 4. The sign of D depends on the level of adaptability αj as follows: D ≷ 0 if
αj ≶ − rj1 .
γv
j
j
Proof: From our assumptions, we have αj > 0, rvj > 0, γ j > 0, rγv
< 0, and rγp
> 0.
It directly follows that D ≷ 0 if αj ≶ − rj1 . γv
We can now use the above results to analyze the impact of climate change on social
welfare.
Proposition 2. The impact of climate change on the welfare of country j under autarky
is as follows:
(i)
(ii)
duj
dZ
duj
dZ
< 0 if
≷ 0 if
dpj
dZ
dpj
dZ
> 0;
< 0.
Proof: Using Proposition 1, Lemma 3, Lemma 4, and (15), we can show that
16
duj
dZ
<0
in the following cases:
which imply that
dpj
dZ



αj < − rj1


γv


rj
(i) αj < − j j θp j j
rθp rγv −rθv rγp





Bβ j − dz j < 0
dZ
,
> 0, C < 0, and D > 0; this is generally the case when the degree
of adaptability αj is too low while the degree of vulnerability is too high.
which imply that
dpj
dZ



αj < − rj1


γv


rj
(ii) αj > − j j θp j j
rθp rγv −rθv rγp





Bβ j − dz j > 0
dZ
,
> 0, C < 0, and D > 0; this corresponds to the case where the
degree of adaptability is low but not too low, while the degree of vulnerability is also low.
which imply that
dpj
dZ



αj < − rj1


γv


rj
(iii) αj < − j j θp j j
rθp rγv −rθv rγp





Bβ j − dz j > 0
dZ
,
< 0, C < 0, and D > 0; this is generally the case when both
the degrees of adaptability and vulnerability are too low, and it will likely occur when
j
D dp
≅ 0.
dZ
which imply that
dpj
dZ



αj < − rj1


γv


rj
(iv) αj > − j j θp j j
rθp rγv −rθv rγp





Bβ j − dz j < 0
dZ
,
< 0, C < 0, and D > 0; this corresponds to the case where the
17
degree of adaptability is low but not too low, while the degree of vulnerability is too
j
≅ 0.
high, and it will likely occur when D dp
dZ
(v) αj > − rj1 , which implies that
γv
dpj
dZ
< 0, C > 0, and D < 0; this corresponds to the
case where the degree of adaptability is too high, and it will likely occur when C ≅ 0.
In turn, we can have
which imply that
dpj
dZ
duj
dZ
> 0 if:



αj < − rj1


γv


rj
(i) αj < − j j θp j j
rθp rγv −rθv rγp





Bβ j − dz j > 0
dZ
,
< 0, C < 0, and D > 0; this is generally the case when both the
degrees of adaptability and vulnerability are too low, and it will likely occur when D
and/or
dpj
dZ
are significantly high.
which imply that
dpj
dZ



αj < − rj1


γv


rj
(ii) αj > − j j θp j j
rθp rγv −rθv rγp





Bβ j − dz j < 0
dZ
,
< 0, C < 0, and D > 0; this corresponds to the case where the
degree of adaptability is low but not too low, while the degree of vulnerability is too
high, and it will likely occur when D and/or
(iii) αj > − rj1 , which implies that
γv
dpj
dZ
dpj
dZ
are significantly high.
< 0, C > 0, and D < 0; this corresponds to
the case where the degree of adaptability is too high, and it will likely occur when C is
significantly high. Proposition 2 confirms that climate change will always have a negative impact on
social welfare, except when its price effect is negative. The likelihood of this negative
effect of climate change also increases as the level of adaptability of factors of production
18
decreases. In contrast, when the level of adaptability increases it is possible that social
welfare could increase. Compared to the degree of adaptability, the level of vulnerability
to climate change seems to have a lower effect on social welfare. In particular, social
welfare can increase following climate change when the degree of vulnerability is very
high, provided that the level of adaptability is also high enough.
4. Impact of Climate Change in the Presence of International Trade
We now turn to the case where international trade is allowed. First, we complete
the model described in the above section by defining the net expenditure function in
country j as follows:
S j p + τ j , θj , γ j , v j (Z, aj ) = ej p + τ j , uj − r j p + τ j , θj , γ j , v j (Z, aj ) .
(16)
The partial derivatives of (16) with respect to p, the world price of x, and θ, the emission
tax, respectively give the following functions of the compensated import of x, which we
denote as mj , and the emission level z j in country j:
mj p + τ j , θj , γ j , v j (Z, aj ) = Spj p + τ j , θj , γ j , v j (Z, aj )
= ejp p + τ j , uj − rpj p + τ j , θj , γ j , v j (Z, aj ) , (17)
z j p + τ j , θj , γ j , v j (Z, aj ) = Sθj p + τ j , θj , γ j , v j (Z, aj ) = −rθj p + τ j , θj , γ j , v j (Z, aj ) .
(18)
We can now express the equilibrium conditions in country j as follows:
ej p + τ j , uj = r j p + τ j , θj , γ j , v j (Z, aj ) + θj z j + γ j aj + τ j mj , j = 1, 2,
X
j
X
j
(19)
Spj p + τ j , θj , γ j , v j (Z, aj ) = 0,
(20)
rθj p + τ j , θj , γ j , v j (Z, aj ) = −Z.
(21)
19
Condition (19) is the new budget constraint for country j. It states that the total expenditure in country j, ej (.) must be financed by income from production, r(.), plus tax
revenues, factor income from adaptation activities, as well as tariff revenues. Equation
(20) corresponds to the world market equilibrium conditions for commodity x. Finally,
equation (21) sets global emissions equal to the sum of emissions generated by the two
countries.
The changes in the emissions and adaptation activities in country j are now given
by the following expressions, respectively:
j
j
j
j
j
αj daj − β j dZ ,
dz j = −rθp
dp − rθp
dτ j − rθθ
dθj − rθγ
dγ j − rθv
j
αj
daj = 1 + rγv
−1
j
j
j
j
j
rγv
β j dZ − rγp
dp − rγp
dτ j − rγθ
dθj − rγγ
dγ j .
(22)
(23)
Substituting (23) into (22), we get :
h
h
−1 j i
−1 j i j
j
j
j
j
j
j
dz j = − rθp
− rθv
αj 1 + rγv
αj
rγp dp − rθp
− rθv
αj 1 + rγv
αj
rγp dτ
h
−1 i j h j
−1 j i j
j
j
j
j
− rθθ
− rθv
αj 1 + rγv
αj
rγθ dθ − rθγ − rθv αj 1 + rγv
αj
rγγ dγ
h
−1 j i j
j
j
j
+ rθv
− rθv
αj 1 + rγv
αj
rγv β dZ, (24)
Given that θ, τ and γ are exogenous by assumption, we have dθj = 0, dτ j = 0, and
dγ j = 0. Moreover, if we assume that the two countries in our model are price-takers,
we know that dp = 0. Therefore, (24) can be simplified to yield the following expression
of the impact of climate change on country j’s own emissions: :
h
−1 j i j
dz j
j
j
j
= rθv
− rθv
αj 1 + rγv
αj
rγv β .
dZ
(25)
The following proposition summarizes the effect of adaptation and vulnerability on
the impact of climate change on country j’s own emissions:
Proposition 3. With international trade, the impact of climate change on country j’s
own emissions is as follows:
20
(i)
(ii)
dz j
dZ
dz j
dZ
< 0 if αj < − rj1 ;
γv
> 0 if α > − rj1 .
j
γv
j
j
Proof: From our assumptions, we have αj > 0, rθv
< 0, rγv
< 0, and β j > 0. It
directly follows that
dz j
dZ
< 0 if αj < − rj1 . This proves (i) of Proposition 3. To prove
γv
(ii), let us analyze the sign of
show that
dz j
dZ
always have
≷ 0 if
dz j
dZ
j
rθv
dz j
dZ
≶ 0. Since
when αj > − rj1 . After some simplifications, we can
γv
j
rθv
< 0 by assumption, we can conclude that we will
> 0 if αj > − rj1 . γv
Proposition 3 shows how the degree of adaptability influences the response of the
emissions level in a specific country to mitigation efforts in the rest of the world. The
more effective the adaptation activities in a country, the less likely will this country
be to free-ride on other countries’ mitigation efforts. For example, if the rest of the
world participates in an agreement to reduce pollution, emissions in country j will tend
to decrease (increase) when the degree of adaptability to climate change is high (low).
This result is in line with that of Benchekroun et al. (2011) who show in a different
context that more effective adaptation reduces the incentive of individual countries to
free-ride on international environmental agreements. From (25), it is also direct to see
that the degree of vulnerability amplifies the net effect of climate change on country j’s
emissions level.
Total differentiation of (19) gives:
ejp dp + ejp dτ j + eju duj = rpj dp + rpj dτ j + rθj dθj + rγj dγ j − rvj β j dZ
+ rvj αj daj + θj dz j + z j dθj + γ j daj + aj dγ j + τ j dmj + mj dτ j , (26)
where, from (17),
j
j
j
j
j
j
dp − rpp
dτ j − rpθ
dθj − rpγ
dγ + β j rpv
dZ − αj rpv
daj .
dmj = ejpp dp + ejpp dτ j + ejpu duj − rpp
Given (17) and our assumption that θ, γ, and τ are endogenous, (26) can also be written
21
as follows:
j
eju − τ j ejpu duj = τ j mjp − mj dp + β j τ j rpv
− rvj dZ
j
j
+ θj dz j + rvj αj + γ j − τ j αj rpv
da .
Assuming price taking countries, we have dp = 0, and the above expression becomes
j
j
j
eju − τ j ejpu duj = β j τ j rpv
− rvj dZ + θj dz j + rvj αj + γ j − τ j αj rpv
da .
(27)
Substituting (23) into (27) and after some simplifications, we get the following expression
of the welfare effect of climate change:
−1 dz j
duj
= H + θj eju − τ j ejpu
,
(28)
dZ
dZ
−1 h j j
−1 j i j
j
j
where H = eju − τ j ejpu
τ rpv − rvj + αj rvj − τ j rpv
+ γ j 1 + rγv
αj
rγv β .
Lemma 5. The sign of H depends on the level of adaptability αj and the cost of adaptation γ j as follows:
(i) H < 0 if αj < − rj1
γv
(ii) H ≷ 0 if α > − rj1 and γ j ≷
j
γv
j
rvj −τ j rpv
.
j
rγv
j
Proof: From our assumptions, we have eju > 0, τ j > 0, ejpu > 0, rpv
> 0, rvj > 0,
j
αj > 0, γ j > 0, rγv
< 0, and β j > 0. By homogeneity of the expenditure and revenue
j
functions in the price of good x, we can show that eju − τ j ejpu > 0 and rvj − τ j rpv
> 0.
It therefore follows that H < 0 if αj < − rj1 . This proves (i) of Lemma 5. To prove
γv
j
1
(ii), we sign H when α > − rj . After some simplifications, we can show that H ≷ 0 if
γv
j
1
j
α > − rj and γ ≷
γv
j
rvj −τ j rpv
.
j
rγv
We are now ready to analyze formally the welfare effect of climate change in the
presence of international trade.
Proposition 4. In a world with international trade, the impact of climate change on
social welfare in a specific country j is as follows:
22
duj
dZ
(i)
> 0 if both the degree of adaptability and the cost of adaptation are high enough
such that αj > − rj1 and γ j >
γv
duj
dZ
(ii)
≷ 0 if the degree of adaptability or the cost of adaptation is too low, i.e. αj <
− rj1 or γ j <
γv
j
rvj −τ j rpv
;
j
rγv
j
rvj −τ j rpv
.
j
rγv
Proof: From Proposition 3, Lemma 5, and (15), we can show that
duj
dZ
> 0 in the
following cases:
(i)αj < −
which implies that
1
j ,
rγv
dz j
dZ
< 0 and H < 0; this is generally the case when the degree of
adaptability αj is too low, and it will likely occur if θj is significantly high or eju − τ j ejpu
is low enough.
(ii)
which imply that
dz j
dZ


αj > − j1
r
γv

γ j >
j
rvj −τ j rpv
j
rγv
,
> 0 and H > 0; this corresponds to the case where both the degree
of adaptability and the cost of adaptation are too high.


αj > − j1
rγv
(iii)
,
j
j

γ j < rv −τj j rpv
r
γv
which imply that
dz j
dZ
> 0 and H < 0; this corresponds to the case where the degree
of adaptability is high while the cost of adaptation are low, and it will likely occur if
H ≅ 0.
In turn, we can have
duj
dZ
< 0 if:
(i)αj < −
which implies that
dz j
dZ
1
j ,
rγv
< 0 and H < 0; this is generally the case when the degree of
adaptability αj is too low, and it will likely occur if θj is significantly low or eju − τ j ejpu
23
is high enough.
(ii)
which imply that
dz j
dZ


αj > − j1
r
γv

γ j <
j
rvj −τ j rpv
j
rγv
,
> 0 and H < 0; this corresponds to the case where the degree of
adaptability is high while the cost of adaptation are low, and it will likely occur if H is
significantly high. Proposition 4 shows that both the cost of adaptation and the degree of adaptation
matter in the welfare analysis of climate change when international trade is allowed. It
suggests that climate change will generally have a negative welfare effect, except when
both the degree of adaptation and the cost of adaptation are high enough or when
environmental regulation is stringent enough.
5. Conclusion
This paper offers a novel perspective in the current search for viable economic policy
approaches to tackling climate change. It focuses on the interactions between greenhouse
gas mitigation policies that aim to curb emissions, adaptation to the effects of climate
change, and international trade.
The theoretical study in the first part of the paper exploits the types of heterogeneity
within as well as among countries, with respect to the cost of emissions mitigation, the
cost of adaptation to the effects of climate change, and the degree of their involvement in
international exchanges. We show that potential comparative advantage depends on the
country’s vulnerability to climate change, as well as on its mitigation and adaptation
costs in a complex way. In fact, the production factor effects of climate change will
generally increase commodity prices when the degree of adaptability to climate change
is significantly low. Also, a higher stock of the global pollutant would result in higher
24
prices when the degree of vulnerability of factors of production to climate change is high
enough when the degree of adaptability is very low. However, for moderate degrees of
adaptability, the effect of vulnerability is reversed: a high degree of vulnerability results
in a negative price effect of climate change. In general, while an autarky state conditions
the domestic economy to incur potentially massive welfare losses by having to produce in
sectors of activity which are highly affected by the climate, openness to trade allows it to
specialize and potentially reduce such costs. When marginal adaptation and mitigation
costs are allowed to vary across sectors, these effects persist and are more pronounced.
The second part of the paper crucially put selected predictions derived from the formal
model to the test.
25
Appendix A.
Data Sources and Variables:
1. GAIN Index from Global Adaption Institute:4
GAIN = an overall measure of a country’s vulnerability to climate-related hazards
and its readiness to adapt to the challenges posed by climate change and other global
forces.
GAINrdns = the readiness index seeks to measure the ability of a country to successfully absorb additional private sector investment resources and apply them effectively
toward increasing resiliency to climate change and other global challenges. 14 indicators
are used to measure three categories of readiness:economic, socialandgovernance
2. DARA Climate Vulnerability Monitor:5
All indicators are time-invariant.
DARACC2010 = Total effects of climate change for 2010: scale 5-1 represents Acute,
Severe, High, Moderate and Low.
DARACC2030 = Total effects of climate change, projected for 2030: scale 5-1 represents Acute, Severe, High, Moderate and Low
3.
EM-DAT the International Disaster database from the Centre for
Research on the Epidemiology of Disasters:6
Only climate-related disasters have been kept.
total affected = Total population affected by the disaster during the year
total damage = Total damage caused by the disasters during the year (in US $)
disas duration = Total duration of the disasters during the year (in days)
4
5
See http : //index.gain.org/about/methodology
See http : //daraint.org/climate − vulnerability − monitor/climate − vulnerability − monitor −
2012/data/
6
See http : //www.emdat.be/criteria − and − def inition
26
4. World Bank:7
GDPcap = GDP per capita
tradeopen = Trade (% of GDP)
CO2ems = total CO2 emissions (kt)
CO2perGDP = CO2 emissions divided by GDP
carbontax national = dummy variable indicating the existence of a national carbon
tax
carbonpolicydum = dummy variable indicating the existence of either regional/national
carbon emissions trading schemes or regional/national carbon tax systems
!"#$"%&'(
!
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34&5!
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AC9&9?AD5&<C=E!
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%&5F=E?E&<C=E&>!
"GHI!
"GHI5AE9!
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%&5F=E'=>C%3AD8!
67,'45"#$!
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()*+!
/-,)2!
/**-*!
,-+*!
,-+*!
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,-+*!
))(1!
/-,)2!
,((,!
-*,+!
!
((-+!
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/-,)2!
/-,)2!
)0)1!
+'",(
-./0(1'20(
!
!
+*,-./0/! /,/+/.--!
/()+.1!
/1.1)+-0!
1)(+(*.0! ,-*+-+2!
,/+/21(!!!!! /.++4;*0!
---,++.,! /),)--2!
!
!
/1.//,0/! -/.-2+1+!
0-.0+0-1! 20.)//+)!
.**0+0)2!!!!! .*)0,(,)!
10.)2+/)!!!!!! //.+1-0!
.1,12-*+!!!!! ./-20(2(!
!
!
,.112-2)!!!!! /.-(-)00!
-./)20)-!!!!! /.+-)/22!
/.)-2+))!!!!! ,.0/1(1+!
.*,0/**-! ./+,-)/0!
/.+24:*+!!!!! ,.**4:*+!
+$,(
!
-1.-+01(!
/(+*!
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*!
*!
!
*!
.-*))*,(!
*!
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.//,000!
!
/!
/!
*!
*!
:0.)*4:*)!
+"3(
!
/)+,2,.(!
,*/-!
-.,,4;*0!
-.2,4;*)!
2.*-4;*0!
!
-12!
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!
1!
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Table 1: Summary Statistics
7
See http : //data.worldbank.org/data − catalog/world − development − indicators
27
EQUATION
VARIABLES
Model
(1)
(2)
CO2policy CO2policy
Panel logit Panel logit
(3)
CO2policy
Panel logit
(4)
CO2policy
Panel logit
(5)
CO2policy
logit
(6)
CO2policy
Panel logit
GDPcap
0.00014
(0.00011)
0.39***
(0.14)
-1.57e+07
(1.82e+07)
-405,660*
(217,988)
-0.00032*
(0.00020)
0.70
(0.62)
-1.86e+08**
(7.77e+07)
0.00024**
(0.00011)
-0.22
(0.17)
-3.56e+07***
(8.98e+06)
0.000032***
(7.8e-06)
-0.0093***
(0.0031)
-4.27e+06***
(511,699)
0.00070***
(0.000061)
-0.019
(0.024)
0.36**
(0.16)
0
(0)
0.0098***
(0.0025)
-2.95***
(0.45)
tradeopen
CO2perGDP
tradeopen*CO2perGDP
GAIN
0.00050***
(0.000086)
-1.25**
(0.64)
-0.64
(0.73)
0.019**
(0.0088)
tradeopen*GAIN
GAINrdns
90.3
(132)
-0.67
(0.81)
tradeopen*GAINrdns
tradeopen*DARACC2030
DARACC2030
0
(0)
DARACC2010
tradeopen*DARACC2010
Constant
Observations
Number of countrycode2
1300
33
491
435
1300
29
29
33
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Table 2: Carbon Policy, Trade and Climate Change Vulnerability
28
2.91***
(0.65)
6659
-28.5***
(4.12)
0.080***
(0.015)
-1.57
(6.06)
7138
178
EQUATION
VARIABLES
Model
(1)
IEtreaties
Panel OLS
(FE)
(2)
IEtreaties
Panel OLS
(FE)
(3)
IEtreaties
Panel OLS
(FE)
(4)
IEtreaties
Panel OLS
(FE)
(5)
IEtreaties
Panel OLS
(FE)
(6)
IEtreaties
Panel OLS
(FE)
GDPcap
0.00017***
(4.2e-06)
0.022***
(0.0013)
1.5e-06***
(1.6e-07)
1.16***
(0.25)
0.00018***
(0.000011)
0.045***
(0.0028)
4.7e-07**
(2.0e-07)
2.15***
(0.51)
0.018***
(0.0017)
0.00015***
(0.000011)
0.044***
(0.0027)
0.00012***
(4.3e-06)
0.021***
(0.0012)
0.00012***
(4.7e-06)
0.021***
(0.0012)
0.00012***
(4.7e-06)
0.021***
(0.0012)
-348,076***
(19,667)
1.37***
(0.31)
-353,584***
(19,712)
-355,497***
(19,727)
0.74**
(0.35)
0.86***
(0.21)
0.61***
(0.097)
8096
0.314
217
tradeopen
CO2ems
OECD
disas_duration
CO2perGDP
1.68***
(0.49)
0.017***
(0.0017)
-709,739***
(71,381)
carbontax_national
carbonpolicydum
Constant
-0.39***
(0.10)
-0.49**
(0.20)
0.66***
(0.23)
0.57***
(0.097)
1.05***
(0.18)
0.62***
(0.097)
Observations
R-squared
Countries
6820
0.321
186
1919
0.376
165
1919
0.407
165
8096
0.312
217
8096
0.314
217
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Table 3: Membership in International Environmental Agreements and Trade
29
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