Effects of Unilateral Climate Policy on Terms of Trade, Capital Accumulation, and Welfare in a World Economy

Effects of Unilateral Climate Policy on Terms of
Trade, Capital Accumulation, and Welfare
in a World Economy



KARL FARMER
BIRGIT FRIEDL
ANDREAS RAINER


CESIFO WORKING PAPER NO. 2375
CATEGORY 8: RESOURCES AND ENVIRONMENT
AUGUST 2008

PRESENTED AT CESIFO VENICE SUMMER INSTITUTE 2008, WORKSHOP ON
‘EUROPE AND GLOBAL ENVIRONMENTAL ISSUES’

An electronic version of the paper may be downloaded
• from the SSRN website: www.SSRN.com
• from the RePEc website: www.RePEc.org
• from the CESifo website: www.CESifo-group.org/wp
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CESifo Working Paper No. 2375



Effects of Unilateral Climate Policy on Terms of
Trade, Capital Accumulation, and Welfare
in a World Economy


Abstract

We present a two-good, two-country overlapping generations model where emissions arise
from production and each country has a domestic emission permit system. When one country
unilaterally reduces her cap on emissions, her output available for domestic and foreign
consumption diminishes more than in the other country. With unchanged consumption
expenditure shares for both goods the terms of trade improve, while capital stocks decline in
the reducing and less strongly in the non-reducing country. The net welfare effect of
improving terms of trade and falling capital stocks is negative in both countries. However, if
the country which unilaterally reduces her emission permits is a net creditor to the world
economy, her own welfare loss remains below that of the non-reducing country.
JEL Code: F11, Q56, D91.
Keywords: capital accumulation, emission permits, terms of trade, overlapping generations,
welfare.

Karl Farmer
Birgit Friedl
Department of Economics
University of Graz
University of Graz
8010 Graz
Universitätsstrasse 15
Austria
Austria – 8010 Graz
birgit.friedl@uni-graz.at
karl.farmer@uni-graz.at
Andreas Rainer
University of Graz
Austria - 8010 Graz
andreas.rainer@uni-graz.at


We would like to thank Tetsuo Ono and Ronald Wendner for their comments on an earlier
version of this paper, and the Jubiläumsfonds der Oesterreichischen Nationalbank (project
No. 12290) for financial support. The views expressed in the paper do not imply an
endorsement by the funding agency. Moreover, we would like to thank for discussions and
inputs by conference participants of SURED 2008 in Ascona (Switzerland), EAERE 2008 in
Gothenborg (Sweden), ECOMOD 2008 in Berlin (Germany), and particularly Karsten
Neuhoff, Ray Riezman, and John Whalley for discussion during the CESifo Venice Summer
Institute workshop on “Europe and Global Environmental Issues” on San Servolo island
(Italy).

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1
Introduction
When both the Kyoto Protocol and the European Emissions Trading Scheme came into
force in 2005, there was considerable dispute concerning the different potential and real
impacts on trade relations between the European Union and non–participating competitor
countries (e.g., Grubb and Neuhoff, 2006; Van Asselt and Biermann, 2007). A cap on
emissions in the European Union induces domestic firms to reduce output and affects
the domestic trade balance which might lead to an improvement of the domestic terms
of trade.1 Moreover, the cap has a negative impact on domestic income which in turn
reduces domestic savings and hence domestic and foreign capital accumulation. This also
leads to adverse effects on domestic and foreign consumers’ welfare (Fischer and Fox,
2007; Kuik and Gerlagh, 2003). Thus, the burden of unilateral policy is shifted—at least
partly—from domestic consumers to consumers abroad (Babiker, 2005; Proost and Van
Regemorter, 2004). We will show in this paper for a world economy consisting of two
large economic areas, that the magnitude of this burden–shifting effect depends on the
external balance of the country implementing a unilateral climate policy.
The consequences for terms of trade, capital accumulation, and welfare have been dis-
cussed intensively for unilateral fiscal policy. Regarding the terms of trade effect, Frenkel
and Razin (1986) found in a two–period intertemporal equilibrium model that the effect
of unilateral fiscal expansion on domestic terms of trade depends on the external balance
(i.e., the net foreign asset position) of that country. In a model with endogenous capital
accumulation, Lipton and Sachs (1983) show that the impact on domestic and foreign
capital accumulation is unambiguously negative. The economic reason for this decline in
capital accumulation is that government debt implies an increase in the tax burden which
reduces both savings of younger households and the supply of loanable funds for private
capital accumulation (Zee, 1987). We will show that a qualitatively similar result can be
found for a more stringent unilateral environmental policy, in spite of a rising price of
emission permits.
1This terms of trade improvement can be interpreted as a sort of reversed “immiserizing growth” effect
`
a la Bhagwati (1958).
1

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Because of the international transmission of a unilateral fiscal expansion, welfare impacts
emerge domestically and abroad. Domestic intertemporal welfare is affected through
different channels, acting in opposite directions. In a one–commodity model, the welfare
effect of a unilateral fiscal expansion can be decomposed into a positive interest rate effect
and a negative lifetime net income (or wealth) effect (Persson, 1985). In a two–good, two–
country framework a third positive welfare impact is caused by a terms of trade effect,
leading to an ambiguous net welfare effect for Home and for Foreign (Ono and Shibata,
2005).2 In the dynamic context of our two–country model, we analyze the welfare effect
of unilateral climate policy by considering the opposing forces of all three effects and by
comparing the welfare effects at home and abroad. In this way, we are able to analyze the
burden–shifting hypothesis which was discussed above for a static world: in an integrated
world economy consisting of (two) large economic areas, a positive terms of trade effect
at home implies a negative one abroad.
We model a world economy consisting of two large industrialized countries, interconnected
through free trade in produced commodities and in bonds emitted by national govern-
ments. The model is based on Diamond’s (1965) overlapping generations economy with
productive capital and constitutes an extension of the closed economy model of Ono (2002)
towards a two–country setting. Pollution arises from production and is controlled by a
permit market in each country. There are two tradeable goods with perfect specialization
in each country. Following the set–up of the dynamic Heckscher–Ohlin models (see Chen,
1992; and more recently Ono and Shibata, 2005), we assume identical technologies and
preferences across countries. Regarding international trade, commodities and government
bonds are internationally mobile, labor and real capital are not. As a prerequisite for the
emergence of international trade, countries differ in their levels of public debt per capita
such that one country is a net creditor and the other one is a net debtor to the world
economy.
2In contrast, in a static closed economy model the only effect of a more stringent unilateral environ-
mental policy is a wealth effect (Hoel, 1991), while in a static open economy the only effect is the terms
of trade effect (Copeland and Taylor, 2005).
2

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To analyze the transitional dynamics and steady state effects of unilateral climate pol-
icy, the number of permits issued in Home is exogenously reduced. We disentangle the
consequences for the terms of trade, capital accumulation, and welfare, and show that
the magnitude of the domestic welfare effect and of the burden–shifting effect depends
on the country’s net foreign asset position. Our key finding is that if the country which
unilaterally reduces its emissions permits is a net creditor to the world economy, like the
European Union, the domestic welfare effect is smaller and the foreign welfare effect is
larger than if she were a net debtor like the United States.
This paper has five sections. The next section provides a description of the two–good, two–
country model with nationally tradable emission permits, and investigates the existence
and stability of steady state equilibria. In Section 3, the steady state and transitional
effects caused by a unilateral permit reduction, both on the terms of trade, and on domes-
tic and foreign capital accumulation are analyzed. We investigate the net welfare effect
of such a unilateral permit reduction in Section 4. Section 5 summarizes our results and
concludes.
2
The Basic Model
Consider an infinite–horizon world economy of two countries, Home H and Foreign F ,
which have the same population normalized to unity. Each country is composed of per-
fectly competitive firms and finitely lived consumers. Both countries have identical prefer-
ences and production technologies. They differ, however, in their levels of public debt per
capita, leading to diverging net foreign asset positions across countries. This assumption
is essential for the emergence of international trade in a large open economy framework.
There are two tradeable goods, x and y∗, and each country specializes in the production of
a unique good, which can be used for the purpose of consumption in both countries as well
as for investment.3 Both goods are produced by employing labor and capital, and both
3This assumption is a deviation of our model from the assumptions of the Heckscher–Ohlin model.
3

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cause a flow of pollution. Households save in terms of internationally immobile capital
and internationally mobile government bonds, where the supply of government bonds in
each country is constant over time (as in Diamond, 1965). Without loss of generality, the
rate of depreciation can be set at one, enabling investment of the current period to form
next period’s capital stock.
Regarding pollution and climate policy, we follow the established literature and focus on
producer emissions (Ono, 2002; Jouvet et al., 2005a,b). Due to the assumption of identical
technologies across countries (and sectors), the production of each good causes pollution.
In line with the empirical evidence of the European Emission Trading System (ETS),
we model country–specific emission trading systems where each country’s government
exogenously sets a cap on carbon emissions caused by domestic production.4
2.1
Production
Let the domestically produced good be x and the foreign–produced good be y⋆, both in per
capita terms (in the following, all foreign–country variables are denoted by a superscript
asterisk). Countries Home and Foreign are assumed to have the same Cobb–Douglas
constant–returns–to–scale production technology in per capita terms:
xt = M (kt)αK (pt)αP ,
y⋆ = M(k⋆)αK (p⋆)αP ,
t
t
t
where M denotes a productivity scalar, kt (k⋆) and p
) are respectively the capital–
t
t (p⋆
t
labor ratio and the pollution–labor ratio in H (F ).5
Our model can be regarded as an OLG analoguous to Obstfeld’s (1989) and Gosh’s (1992) two–good,
two–country ILA models.
4Alternatively, one could model a global emissions trading system, which would lead to equal permit
prices across countries. Another possibility would be to assume that goods consumed domestically (rather
than those produced) fall under the permit trading scheme.
5Ono (2002, 77) shows how, by rescaling parameters, a production function exhibiting constant re-
turns to scale with respect to labor and capital, and with emission intensity as a scaling factor, can be
4

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In each country and each period, the long–lived government sets an emissions cap and
assigns corresponding emission permits to the production sector, where the total number
of emission permits is denoted by S in Home and by S⋆ in Foreign. Following the specifi-
cation of the permit market in Ono (2002), emission permits are distributed free of charge
to the firms. If a firm’s emissions exceed its allowance, then it buys emission permits in
the market, while for the opposite case it sells excess permits.
In each period, firms in Home (and analogously for Foreign) choose k and p to maximize
profit πt:
πt = xt − qtkt − wt + et (S − pt) ,
where qt (q⋆) is the rental price of capital, w
) is the wage rate, and e
) is the
t
t (w⋆
t
t (e⋆
t
permit price in Home (Foreign). As described above, emission permits are traded in a
perfectly competitive market. Since, moreover, firms rent capital and employ labor in
perfect factor markets, the optimality conditions for maximizing profits in each period
are given by:
x
q
t
t = αK M (kt)αK −1 (pt)αP = αK
,
(1)
kt
wt = (1 − αK − αP ) M (kt)αK (pt)αP = (1 − αK − αP ) xt,
(2)
x
e
t
t = αP M (kt)αK (pt)αP −1 = αP
,
(3)
pt
y⋆
q⋆ = α
)αK−1 (p⋆)αP = α
t ,
(1⋆)
t
K M (k⋆
t
t
K k⋆t
w⋆ = (1 − α
)αK (p⋆)αP = (1 − α
,
(2⋆)
t
K − αP ) M (k⋆
t
t
K − αP ) y⋆
t
y⋆
e⋆ = α
)αK (p⋆)αP −1 = α
t .
(3⋆)
t
P M (k⋆
t
t
P p⋆t
Profit maximization implies that the firm’s revenues net of the payments to production
factors give a profit equal to the initial endowment of permits, etS. This profit is collected
by the government and reimbursed to the young households.6
transformed into a three–factor constant returns to scale production function with labor, capital and
pollution as inputs.
6In essence, this particular modeling of the permit system guarantees that the subsidy is non–
distortionary and that permits are not “grandfathered”.
5

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2.2
Consumption
Each country is inhabited by identical consumers and each generation lives for two pe-
riods, one working and one retirement period. In Home, the representative consumer’s
intertemporal utility depends on consumption during the working period, composed of
the consumption goods of both countries, x1 and y1, and consumption during the retire-
t
t
ment period, x2
and y2 , and similarly for Foreign. For simplicity, the representative
t+1
t+1
households of countries H and F are assumed to have identical preferences across goods
(0 < ζ < 1) and over time (0 < β < 1) and are represented by a log–linear intertemporal
utility function:
Ut = ζ ln x1 + (1 − ζ) ln y1 + β ζ ln x2
t
t
t+1 + (1 − ζ ) ln y2
t+1 ,
(4)
U⋆ = ζ ln x⋆,1 + (1 − ζ) ln y⋆,1 + β ζ ln x⋆,2 + (1 − ζ) ln y⋆,2 .
(4⋆)
t
t
t
t+1
t+1
In maximizing intertemporal utility the young household in Home is constrained by a
budget constraint in each period of life. When young, wage income wt, net of a lump–
sum tax τt imposed by the national government, is spent on consumption of the Home
and the Foreign good, with ht denoting the terms of trade of Home (units of Foreign good
per unit of Home good). Furthermore, for transferring income to their retirement period,
young households save in terms of domestic capital kt+1 and in terms of bonds of Home
bH and of Foreign b⋆,H
t+1
t+1 . From saving, the old household gains interest income, where it+1
and i⋆t+1 denote the interest rates in Home and Foreign. When old, the household spends
interest income and capital on consumption, again for the Home and Foreign good (x2t+1
and y2t+1, respectively). Thus, the first period budget constraint is given by:
1
x1 +
y1 + s
t
h t
t = wt − τt,
(5)
t
where savings are defined as
st ≡ kt+1 + bH + (1/h
.
(6)
t+1
t) b⋆,H
t+1
After taking account of the no–arbitrage condition of the asset market in Home (1 + it =
qt, ∀t), the second period budget constraint is given by:
1
1
x2
y2
b⋆,H
t+1 + h
t+1 = (1 + it+1) kt+1 + bH
t+1
+ 1 + i⋆t+1
t+1 .
(7)
t+1
ht+1
6

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The corresponding budget constraints for the Foreign consumer are:
htx⋆,1 + y⋆,1 + s⋆ = w⋆ − τ ⋆,
(5⋆)
t
t
t
t
t
s⋆ ≡ k⋆
t
t+1 + b⋆,F
t+1 + htbF
t+1.
(6⋆)
ht+1x⋆,2 + y⋆,2 = 1 + i⋆
k⋆
+ b⋆,F
+ h
.
(7⋆)
t+1
t+1
t+1
t+1
t+1
t+1 (1 + it+1) bF
t+1
2.3
Intertemporal Equilibrium Dynamics
Using market equilibrium conditions for each period, we examine the intertemporal equi-
librium dynamics of this world economy. Since government bonds are perfectly mobile
across Home and Foreign, the real interest parity condition holds across both countries
h
1 + i⋆
t
= (1 + i
t+1
h
t+1) .
(8)
t+1
Considering the two national no–arbitrage conditions of asset markets (1+it = qt, 1+i⋆ =
t
q⋆, ∀t) and the firms’ first order conditions (1) and (1⋆) in (8), the equation of motion of
t
the terms of trade follows
α
k⋆
K −1 (S⋆)αP
h
t+1
t+1 = ht
.
(9)
(kt+1)αK−1 (S)αP
Market clearing for Home and Foreign bonds demands
b = bH + bF ,
b⋆ = b⋆,H + b⋆,F ,
∀t,
(10)
t
t
t
t
where total bonds issued are, due to the assumption of a “constant stock” budget policy,
time–stationary and denoted by b in Home and by b⋆ in Foreign.
Utility maximizing domestic savings are given by st = σ (wt − τt) , σ ≡ β/(1 + β), and
foreign optimal savings by s⋆ = σ (w⋆ − τ ⋆). Clearing of the world asset market requires
t
t
t
the supply of savings to be equal to the demand for savings (from (6), (6⋆), and (10)):
1
1
st +
s⋆ = k
k⋆
+ b⋆ ,
∀t.
(11)
h t
t+1 + b +
t+1
t
ht
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This equation thus relates the terms of trade movements to capital accumulation and to
the levels of domestic and foreign debt. Defining the net foreign asset positions of Home
and Foreign as
φt+1 ≡ kt+1 + b − st,
φ⋆
,
(12)
t+1 ≡ k⋆
t+1 + b⋆ − s⋆
t
(11) can be rewritten as:
k⋆
+ b⋆ − s⋆
φ⋆
h
t+1
t
t+1
t = −
≡ −
,
∀t.
(13)
kt+1 + b − st
φt+1
Since ht > 0, either φt+1 < 0 and consequently φ⋆
> 0, i.e. Home is a net creditor
t+1
to the world economy and Foreign a net debtor, or vice versa if φt+1 > 0 and φ⋆
< 0.
t+1
According to (13), terms of trade movements are determined by changes in the relative
capital account positions of Home and Foreign. For instance, if Home is initially a net
creditor, increasing terms of trade are the consequence of Home becoming a stronger net
creditor to the world economy (and consequently Foreign a stronger net debtor).
To derive the combined product market clearing condition, we start by stating the budget
constraints of Home’s and Foreign’s government:
τt + etS = itb,
τ ⋆ + e⋆S⋆ = i⋆b⋆.
(14)
t
t
t
Reformulating the first period budget constraint for st (s⋆), substituting for taxes from
t
(14), for the optimal consumption quantities and for the firm’s first order conditions (1)–
(3), acknowledging the no–arbitrage condition for the domestic asset market, and clearing
of permit markets (pt = S, p⋆ = S⋆, ∀t), yields an expression for s
) which depends
t
t (s⋆
t
only on kt (k⋆) and exogenously given parameters. By inserting these expressions into
t
the international asset market clearing condition (11), we obtain the second equation of
motion:
htkt+1 + k⋆
)αK − b⋆ (σ i⋆ + 1) ,
(15)
t+1 = ht [σ0 (kt)αK − b (σ it + 1)] + σ⋆
0 (k⋆
t
t
where σ0 ≡ (1 − αK) σMSαP and σ⋆0 ≡ (1 − αK) σM (S⋆)αP .
Clearing of Home’s product market requires that domestic supply balances with domestic
demand and exports (x⋆,1 + x⋆,2):
t
t
xt = x1 + x2 + k
+ x⋆,2,
∀t,
(16)
t
t
t+1 + x⋆,1
t
t
8

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