The Regional Economic Effects of a Reduction in Carbon Emissions

Anping Chen,
School of Economics,
Jinan University,
Guangzhou, 510632,
Guangdong Province,
China，
Nicolaas Groenewold,*
Economics Programme,
University of Western Australia
Crawley, WA 6009
Australia
andA. J. Hagger†
School of Economics and Finance,
University of Tasmania
Private Bag 85
Hobart, Tas 7001
Australia*Corresponding author; email: nic.groenewold@uwa.edu.au , phone: +61 (0)8 6488
3345, fax: +61 (0)8 6488 1016. We are grateful for comments received at seminars at
Curtin University, the University of Western Australia and the Ohio State University.
†

Alf Hagger died on the 29th October, 2010 at about the time the penultimate versionof this paper was completed.

1
The Regional Economic Effects of a Reduction in Carbon Emissions
Abstract:
Climate change has lead to policy to reduce CO2 emissions and it is likely that policy
will have differential regional impacts. While regional impacts will be politicallyimportant, very little analysis of them has been carried out. This paper contributes tothe analysis of this issue by building a small model involving two regions and weincorporate the right to emit CO2 as a factor of production with the level of permitted
emissions set by the national government. We argue that there is likely to be pressure
on governments to use other policies to offset the possible adverse regional economic
consequences of the pollution-reduction policy and also consider a range of suchpolicies. Using numerical simulation we find that a 10% reduction has relatively small
but regionally differentiated effects. Standard fiscal policies are generally ineffective
or counter-productive while labour market policies are more useful in offsetting theadverse effects. (150 words)
Key Words: carbon emission, regional effects, numerical modelling
JEL classifications: Q52, Q58, R12, R13

2
1. Introduction
There is considerable controversy about the existence, the nature, the causes
and the consequences of climate change; in particular, the relationship between
human activity, global warming and climate change is far from clear. Yet,
governments of many countries are beginning to pay more than lip-service to theimplementation of policy designed to limit the emission of greenhouse gases which
are claimed to be one of the main causes of global warming. The assumptions
underlying such policy may be characterised as: (i) climate change imposessignificant costs which are likely to grow; (ii) climate change is driven largely by
global warming; (iii) global warming, in turn, is caused by an increase in theconcentration of greenhouse gases in the atmosphere; and (iv) such gases are theresult of human activity.
Given this chain of reasoning, the policies being proposed are of the type thatwill limit the human activity which produces greenhouse gases of which carbon
dioxide, CO2, is the most commonly discussed. Two main alternative policies forachieving a reduction in CO2 emission have been proposed – a carbon tax and a “capand trade” scheme. The first of these is a common response to an external
diseconomy associated with production or consumption activity, the emission of CO2
in this case. It is to tax the externality so that its private and social costs are the same,
making for a socially optimal outcome (in the absence of other externalities). The
second policy involves a government decision on the maximum amount of CO2
emission to be allowed (perhaps as part of an international agreement) and the issue of
permits to pollute to this level. These permits are allocated to polluters in some

3
systematic fashion and are then freely traded in a market.1 No matter which scheme isimplemented, the price of goods which are pollution-intensive would be expected torise relative to other goods, thus shifting consumption from high- to low-polluting
production activity. The imposition of such a policy would be expected to havewidespread repercussions on the economy.
While popular discussion of climate change, global warming and the possible
policy responses to these developments is a recent phenomenon, the economic
analysis of the effects of pollution and the design of efficient policy has a long history
in the academic literature, much of it pre-dating the recent popular upsurge in interestin the area. Initial analysis tended to be partial equilibrium in nature, concentrating on
the market for the goods, the production of which is responsible for the emissions.
When pollution controls are widespread, there are likely to be economy-wide effects
of pollution abatement policies and general equilibrium analysis becomes more
appropriate as a tool of analysis. While the literature dealing with the general
economic effects of pollution and pollution-reduction policies is extensive, this is not
the case, however, for the analysis of the regional economic impacts of pollution or
pollution abatement measures. Yet, the costs of the implementation of emissionmitigation policies can reasonably be expected to affect different industries differently(after all, their purpose is to curb the activity of certain industries and to expand thatof others) and, to the extent that industry structure differs across regions, the initialcost of imposing the policies are likely to differ across regions, although adjustments
might well occur over time to spread the regional effects more evenly.
This is not to say that the regional effects have been neglected altogether,
however. A number of papers has contributed to the theoretical analysis of some of1

For an interesting recent paper discussing the relative merits of different forms of regulation in aregional context see Rose et al. (2009)

4
the issues at stake. An early paper in the area by Beladi and Frasca (1996) builds on aprevious one by Beladi and Rapp (1993) which was, in turn, based on the well-know
Harris-Todaro model of the dual developing economy (see Harris and Todaro, 1970).
While it is, strictly-speaking, a two-country model, it can be interpreted in a regional
context and analyses the regional employment, capital allocation and output effects ofpollution controls which have an initial impact which is regionally differentiated.
More recently, there has been a number of papers with models with regional
disaggregation which focus on the welfare effects of pollution-abatement policy andaddress questions about the design of policy needed to re-establish a Pareto-optimal
allocation of resources in the face of a pollution externality; examples are those by
Silva and Caplan (1997), Caplan and Silva (2005) and Hadjiyiannis et al. (2009). The
paper by Boucekkine and Germain (2009) adds endogenous growth to provide adynamic analysis of the problem in a two-region model which in previous papers has
been static. Finally, an interesting paper by Hosoe and Naito (2006) introduces thenotion of agglomeration into the static two-region model and focuses on the effects ofpollution (rather than pollution abatement policy) on urban structure including theinter-regional distribution of population.
The increasing complexity of these theoretical models, particularly whengrowth is introduced, makes clear analytical results increasingly difficult to derive.
Indeed, Hosoe and Naito use numerical simulations to derive some of theirconclusions. An extreme case of the use of numerical simulations is found in two
papers which use large-scale computable general equilibrium (CGE) models –Klepper and Peterson (2006) and Adams (2007), both of which use numerical solution
methods to analyse the general equilibrium effects of the imposition of pollution
control policy, the first for the European Union and the second for Australia. These5models both have structures which closely mimic the economic structure of theeconomy being analysed and are calibrated using data for those economies. Both areregionally disaggregated – the Klepper and Peterson application is for 16 European
countries while the model used by Adams distinguishes the eight Australian states andterritories. They both show substantial differences between the regional effects ofcentrally imposed policy; Adams, for example, generates regional output reductions
ranging from zero to 2.5% for a 21.1% reduction in emissions.
Our paper builds on the existing literature but differs from it in the following
ways. First, we recognise that in the current policy environment the need to limit
pollution is increasingly likely to be derived from obligations under international
agreements so that the immediate question and the focus of our paper is what theeconomic effects of the imposition of such limits will be, rather than the design ofwelfare-maximising policy instruments which has been an important question in past
papers.2 Thus we take the limit as exogenously given and analyse the effects of thepolicy on a range of economic variables including output, per capita output,
employment, unemployment, relative prices, consumption and welfare.
Second, we assume that, while the national rather than the regional
government has the obligation under international agreements to implement pollutioncontrol policies, both the national and the regional governments will be concerned
about the possible adverse regional consequences of such a policy. It is likely,
therefore, that the imposition of pollution-abatement measures will be accompanied
by further policies (such as regionally-differentiated expenditure boosts or labourmarket policies) designed to offset the expected adverse regional consequences of thepollution-reduction measures. Our paper extends the existing literature by2

For an interesting recent paper which assumes that the regional governments impose pollution limits
with a central government effecting transfers to achieve optimality, see Silva and Yamaguchi (2010).

6
considering not only the regional effects of imposition of emissions controls as such,
but also the effectiveness of a range such supplementary policies.
Third, given the questions we want to address, our model is distinct fromexisting ones. We use a simple two-region general equilibrium model which allows
for inter-regional migration in the long run and inter-regional capital mobility. We
incorporate pollution into the model by assuming that the right to pollute is a factor of
production in the manner of “environmental capital” of Hosoe and Naito (2006). We
assume that this factor is in fixed supply, its level being set by the national
government, that firms must purchase it like other factors and that it can besubstituted for other factors.
Fourth, the regional unemployment consequences of pollution-abatement
policy is a serious policy concern in many countries and to enable us to consider this
we incorporate equilibrium unemployment into the model using a union-firmbargaining structure to generate possible equilibrium deviations from full employment.
Finally, the model has an array of government policy instruments to allow us
to address questions about the effectiveness of possible regional and national
government policy responses to the imposition of limits to emissions.
While our model is small and incorporates many simplifications, it iscomplicated enough to be analytically intractable and we use it to analyse policy bylinearising it, calibrating it and simulating the effects of a variety of shocks. Thus,
strictly-speaking, it is a CGE model but one that is several orders of magnitude
smaller than traditional CGE models and, we argue, one in which the effects of shocks
are transparent. Moreover, while we use Australian data to calibrate the model, it
would be misleading to think of our analysis as an Australian application. For that the7model as it stands is too general and would require much greater detail about theactual structure of the Australian economy.
The structure of the rest of the paper is as follows. In the next section we set
out the model. In section three we discuss the linearisation and calibration of themodel and provide details of the simulations designed to assess the regional effects ofa pollution-reduction policy as well as policies that might be undertaken in order tooffset the adverse effects of the tightening of pollution controls. In section four wereport the results of these simulations and in section five we summarise our results
and draw conclusions.

2. The model
The model which we build has two regions, each with households, firms and aregional government. In addition to regional governments, there is also a national
government. The households and firms are optimisers. Governments at both levels
are treated as exogenous but subject to a budget constraint.
The firms in a region produce a single good which we assume to be different
to that produced in the other region. It is supplied, in the region in which it isproduced, to households and to the regional government as tax revenue. Households
consume some, trade some with households in the other region and give some up to
the national government as income tax. Governments costlessly transform the goodthey receive as tax revenue into a government good. The regional government
supplies the transformed good in equal amounts to households in its region free of
direct charge. It finances its expenditure by a payroll tax levied on firms located in its
region as well as its share of an income tax levied by the national government. The
national government provides output to households in both regions (possibly different

8amounts per capita) and finances this by its share of a tax levied at a uniform rate on
household incomes in both regions as well as revenue from the rental of emissions
permits to firms.
Output in each region is produced using four factors: land, labour, capital andthe right to emit CO2 (environmental capital). Land is region-specific and in fixed
supply. We assume that one unit of labour is supplied inelastically by eachhousehold and that households are employed only by firms in the region in which they
live, thus excluding the possibility of households’ living in one region and commuting
to work in the other. Regional population and labour force are therefore effectively
the same. We do allow inter-regional migration in the long run, however, and this is
one of several sources of inter-connectedness between the two regions. We follow theliterature in the area of fiscal federalism (see, e.g., Boadway and Flatters,1982, Myers,
1990, Petchey, 1995, Petchey and Shapiro, 2000, Groenewold, Hagger and Madden,
2003, Groenewold and Hagger, 2007) and assume migration to be costless and tooccur in response to inter-regional utility differentials.
Capital is owned by households and is mobile across regional boundaries inboth short and long runs. There is no capital accumulation in the model so that thecapital stock is given and we assume each household owns an equal share of thenational capital stock.3
The national government owns the stock of pollution permits which it rents tofirms nation-wide (just as households do the capital stock). In the case of both thecapital stock and the stock of permits, the inter-regional allocation is determined so as
to equalise the regional rental rates.

3

This assumption considerably simplifies the likely response of the firm to the imposition of controls
such as the development of and substitution to more “pollution-efficient” capital. See Batabyal and
Nijkamp (2008) for an analysis of this process in a partial-equilibrium framework.

9
We model the labour market to allow for the possibility of unemployment ineach region. There are many ways in which this has been achieved in recent regional
literature: a fixed wage as in the multi-regional model of tax-competition by Ogawa etal. (2006) as well as in the two-region model of Fuerst and Huber (2006); an
efficiency-wage model as in Zenou (2006); job search as used by Epifani and Gancia(2005) in a model used to investigate spatial productivity differentials and by Moller
and Aldashev (2006) in their investigation of participation rates in East and West
Germany; or a union-based model used by Roemer (2006). We use a variant of thelast; we assume that in each region firms bargain with a union which representshouseholds. Bargaining is assumed to be restricted to wages and, once the wage has
been agreed upon, firms choose employment to maximise profits. There is no reason
why employment should equal the labour force in equilibrium so that, as required, themodel allows for equilibrium unemployment.
There are therefore several sources of interconnectedness between the regions– inter-regional migration, inter-regional capital flows, inter-regional flows ofpollution permits, inter-regional trade and the redistribution carried out by the national
government. We abstract from other possible inter-regional connections. So, we
assume that each regional government supplies the government good only tohouseholds living in its own region, thus abstracting from inter-regional spillover
effects in the provision of government goods. Further, we assume that each firm isowned by households in the region in which it is located so that there are no interregional profit flows.

2.1 Households

10Households derive utility from the consumption of the two privately-produced
goods as well as from a good supplied by regional and national governments.4 We
assume a representative household in each region and that the utility function for thishousehold is Cobb-Douglas and homogeneous of degree 1:5(1)

Vi = β i C1γi1i C2γi2 i Giδi ,

where

Vi =

utility of the representative household, region i,Cji =real private consumption of region j’s output per household in

i = 1, 2region i,

Gi =real government-provided consumption per household, region i.

βi , γji and δi are constants with:

βi > 0 ,i = 1, 2

0 < γji < 1,

j = 1, 2,

0 < δi < 1,

i = 1, 2

γ1i + γ2i + δi = 1

i = 1, 2.

i = 1, 2,

The representative household maximizes utility subject to a budget constraint
which requires combining quantities of the two goods. We compute real output by
deflating by the price of a composite good which has a price index:

PC = (P1)λ(P2)1-λwhere Pj is the price of good j ( j = 1, 2) and λ is the share of good 1 in total nominal
output.
The national government collects an income tax at a given rate TY which is thesame in both regions so that the household budget constraint in region i may be
written as:
4Note that pollution does not have adverse consequences for utility. To allow for this would
considerably complicate the model and, besides, it is likely that the direct welfare consequences ofpollution are not an important consideration in the type of short-run questions we analyse in this paper.
5
A list of the variables of the model is provided in Appendix 1.

11(1-TY)Ji = (P1 C1i +P2 C2i)/PC = P1-λC1i +P-λ C2i,

i= 1, 2where P has been used to denote the relative price P1/P2 and Ji denotes real householdincome in region i measured in terms of the composite good. Utility maximisation
subject to the household budget constraint gives the demand functions:
(2a)

C1i =

γ 1i
P λ −1 (1 − TY ) J i ,γ 1i + γ 2ii =1, 2,(2b)

C2 i =γ 2i
P λ (1 − TY ) J i ,γ 1i + γ 2ii =1, 2.

Households own a unit of labour each, they own the capital in the economy as awhole in equal shares and they own the firms in their region in equal shares.6 They
therefore receive wage income, capital income and profits. Some of the labour may
be unemployed in which case the household is paid unemployment benefits by theregional government. The household makes decisions on the basis of expected labour
income which is simply the sum of the wage, Wi, weighted by the employment rate,
1-Ui, and unemployment benefits, UBi, weighted by the unemployment rate, Ui.
Wages, unemployment benefits, profits and capital income are all measured in termsof units of output of the region in which they originate. Thus, the expression for theincome of the representative household measured in terms of the composite good is:(3a)J1 = P1-λ (ΠH1 +(1-U1)W1 + U1UB1+ RK1K1/N ) + P-λRK2K2/N,(3b)

J2 = P-λ (ΠH2 +(1-U2)W2 + U2UB2+ RK2K2/N ) + P1-λRK1K1/N,

where

ΠHi = real profit distribution per household, region i,
RKi= capital rental rate, region i, and6

We make the simplifying assumptions that only households in the region own the region’s firms (andso receive profit distributions) and that households supply labour only to firms in the region in which
they live. This helps to keep to a minimum the regional interrelationships and precludes commuting
between regions for employment purposes; see Corcoran et al.(2011) for a recent model of interregional commuting. We do not make similar assumptions about capital ownership since we willassume inter-regional capital mobility which requires the ability of households to shift their capital
freely from one region to the other.

12
Ki = capital stock region i.
Inter-regional migration is possible and we make the simplifying assumptionthat migration is costless and continues until utilities are equal across regions:(4)

V1 = V2
We also assume that capital is mobile across regions and that in equilibrium

the rates of return are equalised:(5)

RK1 = RK2.

2.2 Firms
We assume that there is a given number of firms in each region which,without loss of generality, we set equal to 1. Two goods are produced in the economy
and it is assumed that firms in each region are completely specialised so that firms inregion 1 produce good 1 and in region 2 firms produce good 2. Thus we can use i toindex both regions and goods. In each region, firms hire labour from households intheir own region and capital from households across the country and combine themwith the given supply of land to produce output.
In the process of production they emit pollution for which they must
purchase permits from the national government. There are various ways in whichemissions might be modelled. First, they might be included in the utility function toreflect the disutility of pollution. This would be particularly important for addressing
the question of the optimal level of pollution which would balance the benefits toutility of lower pollution against the extra production costs. 7 However, we do notdeal with this question, rather taking the level of permitted emissions as exogenous.
Besides, for the sort of policy environment which we have in mind, the benefits tohouseholds of lower CO2 emissions are likely to be much more diffused over both7

See Silva and Caplan (1997), Caplan and Silva (2005) and Banzhaf and Chupp (2010), for example.

13time and space that the extra costs. On the cost side, the literature has incorporated
pollution in two main alternative ways. The first is to assume that pollution produced
is linearly related to output – see, e.g., Hosoe and Naito (2006).8 The alternative,
more general approach which we also follow, is to treat pollution as a factor of
production; see Beladi and Rapp (1993), Beladi and Frasca (1996), Rosendahl (2008),
Hadjiyiannis et al. (2009) and Boucekkine and Germain (2009) for examples of thisapproach.
Production technology is assumed to be Cobb-Douglas with constant returns
to scale so that the production function for the representative firm in region i can be
written as:

Yi = Bi ( LANDi )(1−α Li −α Ei −α Ki ) ( Li ) Li ( Ei )α Ei ( K i )α Ki ,α

0 < α Li , α Ki , α Ei , (1 − α Li − α Ki − α Ei ) < 1
where

Bi = total factor productivity in region i,
Ki = the total capital in region i,
Li = total employment in region i, andEi = pollution emission permits, region i.

We can simplify by writing:Di = Bi ( LANDi )(1−αiL −α Ki −α Ei )so that the production function becomes:(6)

Yi = Di ( Li ) iL ( Ei )α Ei ( K i )α Ki ,α

0 < α Li , α Ki , α Ei , (1 − α Li − α Ki − α Ei ) < 1, i = 1, 2

Consider now firms’ behaviour. Profits (in terms of the firm’s own output) aredefined as:(7)8ΠFi = Yi – (1+TWi) WiLi – RKiKi – REiEi

j = 1, 2

An interesting recent variation is in Silva and Yamaguchi (2010) in which a separate energy good is
introduced which produces pollution 1:1.

14
where TWi is the payroll tax levied by the regional government on the wage bill inregion i and REi is the emission permit rental rate in region i. We allow for the
possibility that the emission permit rental rate differs across regions but will generally
assume it to be the same. Even though we have normalised the number of firms to be
1, we assume that each firm takes the wage, the payroll tax rate, the capital rental rate
and the emission permit rental rate as given when it maximises profits. Hence thechoice variables in each case are the level of employment, emissions and capital(which will also determine output via the production function).
he profit-maximising conditions are the usual marginal productivity conditions:(8a)

α LiYi = (1 + TWi )Wi Li ,i = 1, 2(8b)

α KiYi = RKi Ki ,i = 1, 2(8c)

α EiYi = REi Ei ,i = 1, 2

On the labour supply side, each household in each region is assumed toprovide one unit of labour inelastically to the firms in its own region so that labour
force and the number of households are equal.9 The wage is arrived at by a process ofbargaining between firms and unions after which firms choose employment to satisfy
the marginal productivity condition, equation (8a). We assume that the resulting levelof employment is always at most equal to the labour force and that generally there is(equilibrium) unemployment.

2.3 Wage Bargaining

9

We could, instead have proceeded along classical lines and assumed that households supply labour tomaximise utility after including leisure in the utility function. This would have been more complicatedand, more importantly, have been difficult to integrate with the union-bargaining model below which
we use to allow for the possibility of unemployment in the model. Our assumption, implies, of course,that leisure consequent upon unemployment has no utility benefits but this is a common feature of
wage-bargaining models.

15
We assume, then, that the wage in region i is determined by a process ofnegotiation between employers and trade unions. The union’s bargaining aim is topush the wage bill as high as possible relative to the figure they believe workers could
obtain elsewhere in the region if the bargaining process breaks down. In pursuing thisaim, however, they are constrained by the bargaining aim of the employers which is topreserve profits. We formalise this set of assumptions, following Layard et al. (1991),
by supposing that, for the representative firm in region i, the bargained wage is theoutcome of the following optimisation problem:max Ωi = (ΠFi ) ((Wi - Ai ) Li )ωi
{Wi }

,

0< ωi <1subject to (6), (7) and (8a) where Ai is the income workers expect to be able to obtainelsewhere in region i if an agreement is not reached and ωi is a parameter
representing union strength in the bargaining process in region i. We assume that in
the bargaining process (and so in the solution to the maximisation problem), the firm
and the union both ignore the general economic implications of their stance; inparticular, the firm takes output and employment as given in assessing the effect ofwage changes on its profit and the union takes the alternative wage, Ai, as given.
W assume that Ai depends on both the expected wage in the rest of the region(WEi) as well as unemployment benefits (UBi):
Ai = (1-Ui)WEi + UiUBi
where (1-Ui) is taken as the probability of employment elsewhere and Ui theprobability of unemployment, should the bargaining process break down. In
equilibrium the expected wage elsewhere and the actual wage are the same. Under
these assumptions, the first-order condition for the bargaining problem can be written
as:

16
(9)

Ui (Wi-UBi) (1+TWi) = ωi (ΠFi/Li), i = 1,2,

Thus, the higher is union power, as measured by ωi, the lower is profit per employee
and the higher is the excess of the wage over the level of unemployment benefits,ceteris paribus.

2.4 Governments
There are two levels of government, a national government and two regional
governments. The national government levies a tax on household income at aconstant rate across the country, the revenue from which it shares with the regional
governments. We allow the tax shares to differ across regions although in mostfederal systems they would be the same. The national government also receives theincome from firms for the rental of emissions permits. The national government’s
revenue is therefore:
TY[(1-θ1)J1N1 + (1-θ2)J2N2] + P1-λRE1E1 + P-λRE2E2
where we denote the share of income tax going to region i’s government by θi and wehave measured revenue in terms of the composite good (noting that income, Ji, isalready in terms of the composite good).
On the expenditure side of its budget, the national government converts its
revenue into a government consumption good at the rate of one unit of theconsumption good per unit of the composite good. It provides this good to theresidents of both regions on an equal per capita basis within each region although the
per capita amount may differ across regions. Denoting the government consumption
good per capita supplied by the national government in region i by GNi, we can write
the national government’s budget constraint as:(10)

TY[(1-θ1)J1N1 + (1-θ2)J2N2] + P1-λRE1E1 + P-λRE2E2 = N1GN1 + N2GN2.

17
where we have assumed that the government good is private in the rival sense.
Each of the regional governments also has its own tax, viz., a payroll tax
which is levied on the region’s wage bill. Regional governments receive payroll tax
in the form of output produced in their region and use part of the revenue to pay
unemployment benefits, converting the remainder into the government consumption
good in the same way that the national government does. Regional governments also
convert their share of the national income tax to the government consumption good.
The budget constraint for the regional governments can be written as:(11a) P1-λ[TW1W1(1-U1) – U1UB1]+ θ1TYJ1 = GR1, and(11b) P-λ[TW2W2(1-U2) – U2UB2]+ θ2TYJ2 = GR2, .
where we use GRi to denote the government good provided to residents of region i by
their regional government and both sides of the constraint are in per capita terms.

2.5 Definitions and closure
There remains a number of definitions and market-clearing conditions whichclose the model. We first define the unemployment rate:(12)

Ui = 1 – Li/Ni ,i = 1, 2

Next, the relationship between Gi and its components is given by:(13)

Gi = GRi + GNi,

i = 1, 2

There is a given national population, N:(14)

N1 + N2 = N,a given national capital stock, K:(15)

K1 + K2 = K,

and a given stock of emission permits:

18
(16)

E1 + E2 = E.

Firms are assumed to distribute all their profits to households in their own region inequal per capita amounts:10(17)

ΠFi = NiΠHi,

i = 1, 2Finally, regions must “balance their budgets”, i.e. there must be balanced trade:(18)

N1C21 = N2 P C12.
To summarise, the model consists of the 35 equations, (1) to (18) in 49

variables: Vi, Cji, Gi, GRi, P, Ji, ΠHi, Wi, REi, Di, Yi, Li, Ki, RKi Ni, ΠFi, TY, TWi, GNi, θi,
N, K, Ui, UBi, Ei, E, of which 13 are exogenous: Di, θi, N, K, E, two of (GRi, UBi TWi)for each i=1,2 and two of (GN1, TY, GN2), so that there are 36 endogenous variables:
Vi, Cji, Gi, P, Ji, ΠHi, Wi, REi, Yi, Li, Ki, RKi Ni, ΠFi, Ui, UBi, Ei, one of (GRi, UBi TWi)for each i=1,2 and one of (GN1, TY, GN2). This leaves us one equation short which ismade up by the condition that the emissions permit rental rate is equal across regions.

2.6 Short-run and long-run versions of the model
In the simulations to be reported below we distinguish between short-run andlong-run versions of the model. The distinction is very simple: we define the short
run as the stretch of time before inter-regional migration begins to respond to a gap
between V1 and V2. In terms of the model, this simply involves suspending equations(4) and (14) and making N1 and N2 exogenous in the simulation. The long run is used
to refer to the simulation results using the model as set out above.

3. Linearisation, calibration and simulation of the model

10

Note that firms do not pay a land rental so that profits include a return to land.

19
The model which we have set out in the previous section is non-linear and toocomplex to solve algebraically. We therefore solve it numerically and do so in linear
form, converting each equation to proportional changes. The linearised model is given
in Appendix 2.
The linearised model is solved numerically. To accomplish this there is alarge number of parameters which need to be replaced with numerical values before
the effects of a shock can be simulated. The parameters are of two kinds. The first
are the parameters of the utility and production functions and the second are shares
which arise during the lineariseation procedure. Using all the definitions andconstraints in the model to ensure the numerical version of the model satisfies them,
we are able to reduce the data required for calibration to the following: Ci, GRi, GNi,
Li, Wi, Ni, REiEi, RKiKi, UBi(Ni-Li) and transfers from the national government to theregional governments. The data used are for Australia for the period 2004-2008 andare reported in Appendix 3.11 Australia has 6 states, data for which were used for theregions. We carry out preliminary simulations (choosing each state in turn as region 1
and the rest of the country as region 2) to identify the state which is most severely
affected by the reduction in permits and call this region 1, the high-polluting region,and the remainder of the country region 2.
Most of the data were straightforward national accounting data but there weresome exceptions where strong assumptions needed to be made to enable us tocompute the parameters. First, inter-regional trade data are not available for Australia
so that Ci could not be split up into its components Cji. On the basis of anecdotal

11

To reiterate a point made earlier, we note that using Australian data to calibrate the model does notmake this an Australian application. This is in contrast to large CGE models which have a moreelaborate structure which is specifically designed to mimic the actual economy from which the data arederived.

20
evidence, we assumed that interstate trade is approximately 20% of output and used
this assumption to split up C1, then splitting up C2 to ensure a balance of trade.
The payments to capital and for emissions permits were more problematical.
There are no data on capital stock or capital income for the states so that a roughvalue for the capital stock was estimated by accumulating published data on grossfixed capital formation for the longest period available ( from 1985(3)) and assuming
a common real rate of return of 5%. Capital income was then calculated bymultiplying the capital stock by a rate of return of 5%. While this is undoubtedly avery rough guess, it should be pointed out that these data are used only in shares sothat it is the relativities between the regions rather than the absolute figures which areused in the model.
Payments for emissions permits were even more problematical since they do
not exist at present and we could not, therefore, use actual data to calibrate therelevant production function parameters. We proceeded by using data in the Garnaut
Climate Change Review (Garnaut, 2008) from which we gained information thatcurrent Australian emissions of CO2 of 650MtCO2-equivalent would cost $15,600m
per annum at an estimated carbon price of $24 per tonne. These estimates were notdisaggregated by state but in one of the background papers, Economic ModellingTechnical Paper No.7, the likely effect of a 10% reduction in emissions on Gross
State Product (GSP) was estimated and we used the ratios of these state-level effects
to total to allocate the $15,600m across the states. The overall cost is very modest –1.3% of annual GDP for 2008-09 and when we ran initial simulations, the effects of a
10% reduction in carbon emission permits resulted in only small effects on real
economic variables. However, the simulated effects were comparable in magnitude tothose projected by Garnaut and simulated by Adams (2007) and our parameter values

21
are similar to other estimates such as those in Keilbach (1995). An alternative
approach would have been to calibrate the production function parameters to ensurethat our model generated an output effect of the magnitude reported in the Garnaut
background paper but this would have given us similar results. We are reasonably
confident, therefore, that we got the order of magnitude of the resulting production
function parameters right.
Finally, in this section we set out the simulations which we chose to throw
light on the two issues identified in the introductory section of the paper: “what are
the general regional economic effects of a reduction in emissions permits?” and “willpolicies which regional governments and/or the national government might
implement to offset possible adverse regional economic effects of the reduction inpermits be effective?”
The simulations we carry out can be collected into two groups. First we
simply look at the effects of the reduction in emissions permits on the regions witheach of the states as region 1 in turn (and region 2 comprising the rest of the country),making for six simulations. We call this the “base case”. We find widespread adverse
effects of the reduction in permits on economic variables such as output,
unemployment and welfare. Given political pressures in the face of unpopular antipollution policy, it is likely that either regional governments or the national
government or both will undertake policy to attempt to offset its effects by changing
standard policy instruments at their disposal. In the second group of simulations we
examine the effectiveness of a number of such policies – increases in government
expenditure (by both levels of government) and a reduction in unemployment benefits
designed to reduce equilibrium unemployment. We report these simulations only for
one state as region 1, choosing as region 1 the state which our base case simulations

22
show to be the most severely affected by the original policy (which turns out to be
Queensland, QLD).
In particular the simulations we have run are the following.
1. The effect of a unit reduction in emissions permits. The results for thissimulation are reported for each state as region 1 in turn with the remainder ofthe country being region 2.
2. The effects of a unit reduction in emissions permits together with regional
government increase in expenditure (balanced by an increase in regional
payroll taxes). We compute two simulations, one where only region 1 (themore seriously affected region) responds by increasing expenditure and theother where the second region also increases expenditure (perhaps in “reaction
to” region 1’s response). The results in this case are reported only for QLD asregion 1.
3. The effects of a unit reduction in emissions permits together with regional
government unemployment-benefit reductions. In contrast to the policy insimulation 2 which might be termed a “Keynesian” response to unemployment,
this is a classical response designed to increase the cost of unemployment andso reduce its incidence. The results are reported only with QLD as region 1
and, again, two cases are reported – the first where only region 1 responds andthe second where region 2 also reacts, perhaps in response to region 1’s policy
action.
4. The effects of a unit reduction in emissions permits together with national
government increases in expenditure. The results are reported only with QLD
as region 1 and, in this simulation too, two cases are reported – the first where

23
only expenditure in region 1 is increased and second where the national
government also raises expenditure in region 2.

4. The results
In this section we report the results of the simulations set out in the previous
section, beginning with the effects simply of the imposition of a reduction inemissions limits (the “base case”) and then going on to combine this with a number ofpolicies which governments might be expected to implement to offset the adverse
regional economic effects of the pollution limitations.

4.1 The base caseWe begin with the base case in which we shock the national stock ofemissions permits by -1%. The effects on the main variables for both regions in the
short run and the long run are reported in Table 1 with each of the six states being
taken as region 1 in turn.
[Table 1 about here]

Consider first the case where NSW is region 1, starting with the short-run
effects. The immediate effect of the restriction on the availability of carbon permits is
to push the emission rental rate up in each region and firms, in response, reduce theuse of carbon permits in each region; the reduction in region 2 is greater than that inregion 1 since region 2 has a higher emissions level in the data base which transforms
into a higher coefficient of the right to pollute factor in the production function.12
Since emissions permits are treated as a normal factor of production, the fall in the useof permits is accompanied, other things held constant, by a fall in output in both

12

Indeed, each state except QLD has a share in total emissions lower than its output share.

24
regions, larger in region 2 than in region 1. The change in relative outputs also results
in a fall in the price of output in region 1 relative to that in region 2, i.e., a fall in P. In
this sense the effects are what would be anticipated on the basis of standard partial
equilibrium analysis: within the fall in national output, there has been a re-allocationof output from the high- to the low-pollution region/industry and a rise in the relative
price of the high-pollution output.
There are further repercussions when we take the rest of the economy into
account. The fall in the use of permits reduces the marginal products of both otherfactors, labour and capital, both of which reduce the firms’ demand for these factors.
The fall in the demand for labour reduces employment and increases unemployment
and weakens labour’s position in the bargaining process and so leads to a fall in thebargained wage. This reduction in the wage is exacerbated by the fall in profits whichstrengthens the firms’ resolve to resist wage pressure.
The fall in the demand for capital reduces the return to capital sufficiently toclear the national market for a given capital stock. Since the demand for capital falls
by more in region 2 (being harder-hit by the reduction in pollution permits) than it
does in region 1, inter-regional capital mobility results in capital moving from region
2 to region 1.
Finally, the fall in wages, profits and capital income and the rise in
unemployment all serve to reduce household incomes and so the consumption of both
goods. Not surprisingly, welfare is reduced in both regions.
Thus the signs of the effects of the abatement policy are therefore easily
explained in terms of the model structure. The reduction in the availability of permits
reduces aggregate output but also shifts output from the more heavily-polluting region
to less-heavily polluting one. Moreover, regional governments are right to be25
concerned about the adverse consequences: output, output per capita, employment,
wages and welfare all fall and the unemployment rate rise. As expected, the moreheavily-polluting region is worse affected.
Nevertheless, the magnitudes of the repercussions are small, surprisingly so,
perhaps. Thus a 10% reduction in emissions (which is a figure commonly cited inpublic debate in Australia and elsewhere) causes a fall in output of only around 0.2%
in each region and an increase in the unemployment rate of about 0.01 percentage
points; even for QLD which is hardest hit, the increase in the unemployment rate is
only about twice this magnitude. Yet, as already mentioned in our discussion ofcalibration, these are magnitudes similar to those reported by Garnaut (2008) andAdams (2007). Garnaut projects output losses of about 0.1 percentage points for a
10% reduction in emissions and Adams predicts a fall in output of about 1.3% for a
21.1% reduction in emissions as a result of the imposition of an emissions-trading
scheme. Thus, in the short run, the effects on output, unemployment and welfare areadverse but small and differ across regions.
In the long run, households move between regions in response to welfare
differences. Since utility of the representative household in region 2 falls by morethan it does in region 1 in the short run, people move from region 2 to region 1. Thisputs further downward pressure on the wage in region 1 and increases employment
but not by enough to absorb all the new labour market entrants; the level of output
rises but by less than the population so that, in the transition to the long run, output
per capita falls. The opposite happens in region 2 – as people move out, output andemployment fall but by less than population so that output per capita rises and theunemployment rate falls (relative to the short run). The relative price of region 2’s
output falls further. Finally, welfare improves in region 2 but worsens in region 1.

26
Thus, in the long run internal migration results in some equalisation of the effects
across the two regions – output per capita and unemployment effects are broughtcloser together and welfare effects are equalised (by assumption).
These results are more or less the same whichever state is chosen as region 1
with the exception of QLD. This state is the only one to be harder hit by the policy
than average so that the relative regional effects are reversed when QLD is chosen as
region 1. We presume, therefore, that the QLD government is most likely to use
policy or advocate that the national government implement policy to offset theadverse regional consequences (even though these turn out to be small). Further
simulations will focus on the case of QLD as region 1.

4.2 The effects of offsetting government policy: an increase in regional government
expenditure
The next group of simulations are ones in which we combine the emissions
reduction with policy intended to offset the adverse effects on output andunemployment. Naturally, such policies may be undertaken by governments
independently of the imposition of pollution controls but, in practice, are likely to be
combined with the latter since there is considerable political sensitivity to the possible
adverse economic consequences of a reduction in emissions permits and therefore
pressure on both national and regional governments to ensure that adverse effects on
output, employment, unemployment, incomes and so on are minimised. Such policy
may, therefore, be undertaken either by the regional government(s) or the national
government since both will be under pressure to “do something”. The first of these isreported in this sub-section and the results are given in Table 2 in which weinvestigate the case where the offsetting policy is an increase in expenditure by the27
regional government. The first set of results in Table 2 simply repeat the base case for
QLD as region 1, taken from Table 1, with the second set of results adding an increasein GR in region 1 (the worse affected region) and the third set assuming that bothregions attempt to offset the fall in output and increase in unemployment by an
expenditure boosts.
When only region 1’s government increases its expenditure the results are as
follows. Compared to the base case (no policy reaction), the fall in output is now
larger for region 1 and smaller for region 2 with a consequently greater increase in
unemployment for region 1 and a marginally larger increase in region 2. This
unemployment effect reflects a larger fall in employment in region 1 than when theregional government did nothing, the reason for which is the rise in the payroll tax
needed to balance the regional government’s budget – this reduces both wages andemployment considerably in region 1 and marginally in region 2. Thus region 1’s
response to the reduction in emission permits seems to have been counter-productive– the fall in output (and output per capita) is greater and the rise in the unemployment
rate is higher compared to the case where the government did nothing. Even region 2
seems to have been fared slightly worse as a result of the reaction of the other region’s
government. Despite this perverse effect, however, welfare in region 1 has been
improved due to the direct effect of the expenditure boost on utility, while that inregion 2 has worsened slightly. Thus, in the short run at least, the government ofregion 1 has been able to improve the lot of its citizens at the expense of that of thoseliving in region 2.13

13

It is, of course the case that the government of region 1 could have undertaken an increase in
expenditure financed by a payroll tax in the absence of the national government’s reducing emissions
permits and could, thereby, have improved the welfare of its representative citizen. This simply
reflects the fact that for the particular parameterisation we use, government expenditure is not optimal(in the welfare-maximising sense). However, we would argue that, in practice, it is difficult forgovernments to assess the optimality of their expenditure levels and, moreover, that the national

28
The reversal of the relative welfare effects causes households to migrate fromregion 2 to region 1 in the long run. This substantially offsets the short-run fall in
output in region 1 but still leaves output per capita lower and the unemployment rate
higher. The effect on region 2 is the opposite – output falls further but output percapita rises and the unemployment rate falls. Welfare falls in region 1 but rises inregion 2. In the long run, the adverse welfare consequences of the reduction inemissions permits are effectively unchanged by the policy reaction of the governmentof region 1.
In summary, the results of region 1’s government’s expenditure boost areperverse for output, output per capita and the unemployment rate but “inadvertently”
beneficial for welfare (with small costs for region 2) in the short run. In the long run,however, region 1’s policy is completely counter-productive – output per capita falls
by more and the unemployment rate rises by more than they would have done in theabsence of the policy and welfare is largely unaffected.
Consider now what happens if the governments of both regions react to theemissions-permits cut by increasing expenditure by the same proportion, comparing
the result to those when only region 1’s government reacts. In the short run the fall in
output and per capita output is smaller in region 1 but larger in region 2, while the risein the unemployment rate is greater for both regions, considerably so for region 2.
Thus, from the point of view of per capita output and unemployment, the decision byregion 2 to increase its expenditure given that region 1 has “already” done this seems
counterproductive. However, from a welfare point of view, the decision by region 2’s
government to join the fray has a small benefit although at considerable cost to region
1’s citizens.
government’s imposing a pollution-control policy is an occasion for an expansionary fiscal policy
whether it is optimal or not but simply in response to the need to “do something” to offset the(imagined) effects of the pollution policy.

29
In the long run there is migration from region 1 to region 2, boosting output inregion 2 but not by as much as population so that output per capita is lower, and theunemployment rate higher than it would otherwise have been. In the long run welfare
is lower in both regions than it would have been had neither regional government
reacted or had region 1 alone reacted.
In summary, if a regional government reacts to the loss of output andemployment by increasing expenditure, the results are counter-productive – output percapita is lower and the unemployment rate is higher than in the absence of theexpenditure increase. In the short run there is a welfare benefit to the citizens of theregion in which the government acts but this disappears in the long run.

4.3 The effects of offsetting government policy: a cut in unemployment benefits
The next regional government policy reaction we consider is a cut in
unemployment benefits which a government might do in the hope of reducing theunemployment consequences of the cut in emissions permits imposed by the national
government. As explained in the previous section, we might consider this a“classical” rather than a “Keynesian” response to the emergence of unemployment.
We again assume that the endogenous variable in the regional government’s budget
constraint is the payroll tax rate. The results for this simulation are reported in Table
3 where we have again repeated the effects of an emissions permits cut in the first twocolumns of results and then those for the case where only region 1’s government
reacts, followed by the case where region 2’s government also reacts.
[Table 3 about here]

When only regions 1’s government changes the level of unemployment
benefits, the “immediate” short run effect is on the labour market and on the

30bargaining process in region 1 in particular. The wage rate still falls as a result of theemissions cut but by less than in the absence of offsetting policy and employment
actually rises instead of falling. The fall in emissions permits and the rise inemployment act in opposite directions on output and, given the relative shock sizes(and, of course, the model parameters) the overall effect in this simulation is to reduce
output but by less than in the base case. Output per capita also falls by less. Under
the dual effects of the fall in unemployment benefits and the fall in payroll taxes
needed to balance the budget, the unemployment rate actually falls. Finally, welfare
still falls but by less than it would have had the regional government not responded by
cutting unemployment benefits. Thus, the decision of the regional government to cut
unemployment benefits in response to the national government’s reduction inemissions permits is beneficial in all dimensions (per capita output, employment,
unemployment and welfare). It is not without cost to region 2, however. In particular,
the boost to region 1’s output partially reverses the relative price change generated by
the emissions reduction policy with the result that region 2’s output falls by more andunemployment rises by more. Despite this, region 2 is also made slightly less worseoff because the relative price effect allows residents of both regions to increase theirconsumption of region 1’s output relative to the base case.
In the long run, the utility gap opened up in favour of region 2 induces
migration from region 1 to region 2 although the size of the migration flow is smaller
than it would have been in the absence of region 1’s policy response. There is also a
capital flow from region 1 to region 2 in response to changes in the relative rates ofreturn but, again, smaller than in the base case. These combine to make for a boost in
employment and output in region 2 relative to region 1 although the per capita output
magnitudes move in the opposite direction. Finally, welfare in both regions falls by31less than it did in the base case so that the policy response by region 1’s government
makes the residents of both regions better-off in the long run.
The final two columns in Table 3 show the effects when region 2’s
government also reacts by reducing its unemployment benefits (matched by a payroll
tax cut). In the short run employment now increases in both regions (with theincrease in region 1 being similar in magnitude to that which occurred when only
region 1 reacted) but a larger outflow of capital from region 1 (due to enhanced
marginal product of capital in region 2) leaves output in region 1 smaller (although
not compared to the base case). In both regions the unemployment rate now falls.
Finally, the welfare loss in region 1 is now smaller than it was when only region 1
acted while region 2 is actually better-off than in the initial equilibrium. Thus, in the
short run, there are clear benefits to region 2 of its government also reacting to theimposition of a reduction in emissions permits and this benefit is at no appreciable
cost to region 1.
In the long run the welfare gap in favour of region 2 attracts migrants fromregion 1 which further boosts employment in region 2 and more than offsets the shortrun employment gains in region 1. The consequence is that unemployment falls
further in region 2 but rises slightly in region 1 relative to the short run. Output
follows the same pattern with that in region 1 falling and in region 2 expanding
relative to the short run. Finally, despite these favourable developments, there is stilla welfare loss in both regions relative to the initial equilibrium although this reduction
is considerably smaller than when neither regional government or only one regional
government reacts to the reduction in emissions permits. There are, therefore, distinct
benefits to each of the regions of both regional governments responding to thenational government’s pollution reduction policy by reducing unemployment benefits.

32This is in contrast to the ineffectiveness of a traditional fiscal response of a taxfinanced increase in government expenditure.

4.4 The effects of offsetting government policy: an increase in national government
expenditure
The final case in this second group of simulations is where the national
government increases its expenditure (financed from income tax) at the same time thatit imposes the cut in pollution permits. It seems likely that there will be pressure frommany quarters, including regional governments, for the national government to “dosomething about” the feared adverse consequences of it pollution-abatement policy.
In Table 4 we explore two possible reactions: a rise in national government
expenditure in region 1 and a rise in expenditure in both regions. In both cases weassume that the national government balances its budget by adjusting income taxes.
[Table 4 about here]

Consider first the case where the national government increases expenditure
only in region1, the region expected to be hit hardest by the reduction in emissions
permits. The consequence is that output and output per capita still fall in both regions
but by less in each case than when the government does not engage in an offsetting
expenditure increase. Similarly, the fall in employment and wages are less than in thebase case so that unemployment rates are lower than they would have been in theabsence of the national government’s action. The reason for this favourable output
effect is that the national government increases income tax to maintain a balanced
budget and since this revenue is shared with the regional governments, the latter areable to reduce payroll taxes which boost employment and wages. This effect operates
in both regions. Profits still fall in both regions because of the tightening of pollution

33
controls and so the income change, though positive, is smaller than the increase inincome tax so that consumption of both goods falls. Welfare therefore falls in region
2 but rises in region 1 because of the direct effect on utility of the national
government’s increase in expenditure.
In the long run the differential welfare effects cause households to migratefrom region 2 to region 1, reinforcing the favourable short-run output effects in region
1 but offsetting them in region 2. The resulting output increase in region 1 isinsufficient to absorb the extra labour so that the unemployment rate rises in the longrun in region 1 while it falls for the opposite reason in region 2. In the long run thenational government’s policy has made little difference to welfare – it still falls inboth regions although by slightly less than it did in the base case.
Although there will be pressure for the national government to act in theregion most affected by the emissions reduction, it is likely that in the interests offairness, the government will act in both regions and the second set of results in Table
4 shows the economic effects of the national government’s increasing expenditure by
the same proportion in both regions. The immediate result is, not surprisingly, a muchlarger increase in income tax needed to balance its budget (in our data base region 2 isabout four times the size or region 1) and, consequently given the tax-sharing
assumptions, a much larger cut in payroll tax is possible in both regions. This has theeffect of increasing employment in both regions, thus offsetting the negative effects
on output of the reduction in allowable pollution. The main difference to the previous
case, where expenditure was increased only in region 1, is that the households inregion 2 now also benefit from the direct utility effects of the increase in expenditure.
Indeed, the incomes tax increase is so much greater now, that region 1 actually suffersa welfare loss, although not as large as in the base case.

34
The short-run welfare effects now mean that there is migration from region 1
to region 2 which reinforces the output increase in region 2 and reduces output inregion 1, although per capita magnitudes move in the opposite direction. In the longrun the unemployment rate falls and welfare falls in both regions but the latter by lessthan in the base case. Thus both from an unemployment and a welfare perspective,
the policy is worthwhile in that it benefits both regions relative to the base case

5. Conclusions
This paper has investigated some of the regional economic consequences of
the imposition by the national government of a policy to reduce carbon emissions.
We did this in the context of a small two-region model in which we modelled
pollution by assuming that firms have to rent permits to pollute from the national
government and these permits are treated like a factor in the production function.
We argued that governments (both regional and national) would likely facepressure to undertake additional policy to offset the feared adverse effects of the
reduction in pollution permits and so also assessed the effects of a number of possible
policies which might be undertaken by either regional governments or the national
government to curb the possible adverse impacts of the tightening of pollution
controls on regional output, unemployment and welfare. The various questions wereanalysed using a series of numerical simulations of the model.
Broadly, the simulation results show that the economic effects of a substantial
reduction in emissions are adverse but small. Secondly, we show that some policies
designed to reduce the negative regional economic impacts of the cut in emissions
permits are ineffective, some are counter-productive and others are effective. Thus, ingeneral, policies which involve increasing government expenditure in the regions

35(either by the regional governments of by the national government) have relatively
small effects or are even counter-productive. On the other hand, a reduction in
unemployment benefits financed by a payroll tax cut can offsets the adverse welfare
effects of the national government’s pollution-abatement policy. This is especially sowhen the offsetting policy is implemented in both regions rather than being
concentrated in the worse-affected region.

36
References
Adams, P. D. (2007), “Insurance against Catastrophic Climate Change: How Much
Will an Emissions Trading Scheme Cost Australia?”, Australian Economic
Review, 40, pp.432-452.
Banzhaf, H. S. and B. A. Chupp (2010), “Heterogeneous Harm vs. Spatial Spillovers:
Environmental Federalism and US Air Pollution”, NBER Working Paper
15666.
Batabyal,A. A. and P. Nijkamp (2008), “The Impact of Innovation on a Polluting
Firm's Regulation Driven Decision to Upgrade Its Capital Stock”,
International Regional Science Review, 31, pp. 389-403.
Beladi, H. and R. Frasca (1996), “Regional Pollution and Multinational Firms”,
Ecological Economics¸ 17, pp. 117-125.
Beladi, H. and J. Rapp (1993), “Urban Unemployment and the Backward Incidence of
Pollution Control”, Annals of Regional Science, 27, pp.153-163.
Boadway, R. and F. Flatters (1982), ‘Efficiency and Equalisation Payments in a
Federal System of Government: A Synthesis and Extension of Recent Results’,
Canadian Journal of Economics, 15, 613-633.
Boucekkine, R. and M. Germain (2009), “The Burden Sharing of Pollution
Abatement Costs in Multi-Regional Open Economies”, The B. E. Journal of
Macroeconomics, 9, Article 21, pp. 1-32.
Caplan, A. J. and E. C. D. Silva (2005), “An Efficient Mechanism to Control
Correlated Externalities: Redistributive Transfers and the Coexistence ofRegional and Global Pollution Permit Markets”, Journal of Environmental
Economics and Management, 49, pp. 68-82.
Corcoran, J, A. T. Murray and R. J. Stimson (2011), “Spatially Disaggregating
Employment Growth Estimates”, International Regional Science Review, 34,
pp. 138-156.
Epifani, P. and G. A. Gancia (2005), “Trade, Migration and Regional
Unemployment”, Regional Science and Urban Economics,, 35, 625-644.
Fuerst, C. and B. Huber (2006), “Can Regional Policy in a Federation Improve
Efficiency?”, Journal of Public Economics, 90, 499-511.
Garnaut, R. (2008) The Garnaut Climate Change Review: Final Report, Cambridge
University Press, Port Melbourne, Victoria, Australia.

37
Groenewold, N. and A.J. Hagger (2007), “The Effects of Fiscal Equalisation in a
Model with Endogenous Regional Governments: An Analysis in a TwoRegion Numerical Model”, Annals of Regional Science, 41, 353-374
Groenewold, N., Hagger, A. J. and Madden, J. R. (2003), ‘Interregional Transfers: A
Political-Economy CGE Approach’, Papers in Regional Science, 82, 535-554.
Hadjiyiannis, C., P. Hatzipanayotou and M. S. Michael (2009), “Public Pollution
Abatement, Regional Capital Mobility, and Tax Competition”, Southern
Economic Journal, 75, pp. 703-719.
Harris, J. R. and M. Todaro (1970), “Migration, Unemployment and Development: A
Two-Sector Analysis”, American Economic Review, 60, 126-142.
Hosoe, M. and T. Naito (2006), “Trans-Boundary Pollution Transmission andRegional Agglomeration Effects”, Papers in Regional Science, 83, pp. 99-119
Keilbach, M.(1995), “Estimation of the Value of the Marginal Product of Emission ina Country Where Emissions Output is Regulated – An Empirical Study”,
Environmental and Resource Economics, 5, 305-319.
Klepper, G. and S. Peterson (2006), “Emissions Trading, CDM, JI, and More: The
Climate Strategy of the EU”, The Energy Journal, 27, pp. 1-26.
Layard, R., S. Nickell and R. Jackman (1991), Unemployment: Macroeconomic
Performance and the Labour Market, Oxford University Press.
Moller, J. and A. Aldashev (2006), “Interregional Differences in Labor Market
Participation”, Jahrbuch fur Regionalwissenscahft, 26, 25-50.
Myers, G. M. (1990) ‘Optimality, Free Mobility and the Regional Authority in a
Federation’, Journal of Public Economics, 43, 107-121.
Ogawa, H., Y. Sato and T. Tamai (2006), “A Note on Unemployment and Capital Tax
Competition”, Journal of Urban Economics, 60, 350-356.
Petchey, J. (1995), ‘Resource Rents, Cost Differences and Fiscal Equalization’,
Economic Record, 71, 343-353.
Petchey, J. and Shapiro, P. (2000), ‘The Efficiency of State Taxes on Mobile Labour
Income’, Economic Record, 76, 285-296.
Roemer, J.E. (2006), “The Global Welfare Economics of Immigration”, Social Choice
Welfare, 27-311-325.
Rose, A., D. Wei, J. Wennberg and T. Peterson, (2009), “Climate Change Policy
Formation in Michigan: The Case for Integrated Regional Policies”,
International Regional Science Review, 32, p. 445-465.

38
Rosendahl, K. E. (2008), “Incentives and Prices in an Emissions Trading Scheme with
Updating”, Journal of Environmental Economics and Management, 56, 69-82.
Silva, E. C. D. and A. J. Caplan (1997), “Transboundary Pollution Control in Federal
Systems”, Journal of Environmental Economics and Management, 34, pp.
173-186.
Silva, E. C. D. and C. Yamaguchi (2010), “Interregional Competition, Spillovers andAttachment in a Federation”, Journal of Urban Economics, 67, 219-225.
Zenou, Y, (2006), “Efficiency Wages and Unemployment in Cities: The Case of High
Relocation Costs”, Regional Science and Urban Economics, 36, 49-71.

39
Table 1 Base Case: Effects of a Reduction in Carbon Emission (e=-1)
Var

Region 1 = NSW Region 1 = VIC Region 1 = QLD Region 1 = SA Region 1 = WA Region 1 = TAS
SR

LR

SR

LR

SR

LR

SR

LR

SR

LR

SR

LR

v1
v2

-0.0205 -0.0226 -0.0188 -0.0226 -0.0398 -0.0226 -0.0102 -0.0226 -0.0162 -0.0228 -0.0211 -0.0226-0.0237 -0.0226 -0.0239 -0.0226 -0.0182 -0.0226 -0.0236 -0.0226 -0.0235 -0.0228 -0.0226 -0.0226

c11-0.0247 -0.0251 -0.0224 -0.0230 -0.0593 -0.0591 -0.0092 -0.0143 -0.0186 -0.0147 -0.0291 -0.0298

c21-0.0315 -0.0435 -0.0314 -0.0528 -0.0217 0.0894 -0.0307 -0.0914 -0.0305 -0.0883 -0.0291 -0.0367

c12-0.0247 -0.0129 -0.0224 -0.0015 -0.0593 -0.1705 -0.0092 0.0468 -0.0186 0.0426 -0.0291 -0.0223

c22-0.0315 -0.0313 -0.0314 -0.0312 -0.0217 -0.0220 -0.0307 -0.0303 -0.0305 -0.0310 -0.0291 -0.0291

j1
j2-0.0230 -0.0310 -0.0230 -0.0390 -0.0230 0.0661 -0.0230 -0.0796 -0.0230 -0.0742 -0.0230 -0.0304-0.0230 -0.0189 -0.0230 -0.0174 -0.0230 -0.0454 -0.0230 -0.0186 -0.0230 -0.0168 -0.0230 -0.0228

πh1-0.0184 -0.0196 -0.0160 -0.0183 -0.0526 -0.0427 -0.0019 -0.0121 -0.0123 -0.0139 -0.0210 -0.0222

πh2-0.0248 -0.0243 -0.0249 -0.0240 -0.0152 -0.0179 -0.0242 -0.0233 -0.0239 -0.0239 -0.0226 -0.0226

w1-0.0187 -0.0218 -0.0165 -0.0227 -0.0533 -0.0200 -0.0034 -0.0304 -0.0126 -0.0266 -0.0235 -0.0272

w2-0.0255 -0.0239 -0.0255 -0.0232 -0.0157 -0.0240 -0.0247 -0.0226 -0.0246 -0.0231 -0.0232 -0.0231

l1
l2-0.0006 0.0075 -0.0005 0.0153 -0.0016 -0.0890 -0.0001 0.0552 -0.0003 0.0506 -0.0011 0.0061-0.0008 -0.0048 -0.0008 -0.0062 -0.0005 0.0223 -0.0007 -0.0053 -0.0008 -0.0069 -0.0007 -0.0009

k1

0.0044 0.0116 0.0068 0.0208 -0.0297 -0.1081 0.0208 0.0678 0.0098 0.0563 0.0016 0.0078

k2-0.0020 -0.0053 -0.0021 -0.0065 0.0077 0.0281 -0.0014 -0.0045 -0.0019 -0.0110 0.0000 -0.0001

rk1-0.0228 -0.0230 -0.0227 -0.0230 -0.0229 -0.0230 -0.0228 -0.0234 -0.0220 -0.0190 -0.0226 -0.0226

rk2-0.0228 -0.0230 -0.0227 -0.0230 -0.0229 -0.0230 -0.0228 -0.0234 -0.0220 -0.0190 -0.0226 -0.0226

e1
e2-0.9955 -0.9881 -0.9929 -0.9780 -1.0227 -1.0828 -0.9782 -0.9291 -0.9892 -0.9380 -0.9984 -0.9922-1.0019 -1.0050 -1.0017 -1.0054 -0.9854 -0.9466 -1.0004 -1.0014 -1.0009 -1.0053 -1.0000 -1.0002

re1

0.9771 0.9767 0.9769 0.9758 0.9702 0.9518 0.9763 0.9735 0.9770 0.9753 0.9774 0.9774

re2

0.9771 0.9767 0.9769 0.9758 0.9702 0.9518 0.9763 0.9735 0.9770 0.9753 0.9774 0.9774

y1-0.0184 -0.0114 -0.0160 -0.0022 -0.0526 -0.1310 -0.0019 0.0443 -0.0123 0.0373 -0.0210 -0.0148

y2-0.0248 -0.0283 -0.0249 -0.0296 -0.0152 0.0052 -0.0242 -0.0280 -0.0239 -0.0300 -0.0226 -0.0228

n1

0.0000 0.0081 0.0000 0.0161 0.0000 -0.0884 0.0000 0.0564 0.0000 0.0512 0.0000 0.0074

n20.0000 -0.0040 0.0000 -0.0055 0.0000 0.0231 0.0000 -0.0047 0.0000 -0.0061 0.0000 -0.0002
y1-n1 -0.0184 -0.0195 -0.016 -0.0183 -0.0526 -0.0426 -0.0019 -0.0121 -0.0123 -0.0139 -0.021 -0.0222
y2-n2 -0.0248 -0.0243 -0.0249 -0.0241 -0.0152 -0.0179 -0.0242 -0.0233 -0.0239 -0.0239 -0.0226 -0.0226
πf1-0.0184 -0.0114 -0.0160 -0.0022 -0.0526 -0.1310 -0.0019 0.0443 -0.0123 0.0373 -0.0210 -0.0148

πf2-0.0248 -0.0283 -0.0249 -0.0296 -0.0152 0.0052 -0.0242 -0.0280 -0.0239 -0.0300 -0.0226 -0.0228

p-0.0068 -0.0184 -0.0090 -0.0297 0.0376 0.1485 -0.0215 -0.0771 -0.0119 -0.0736 0.0000 -0.0068

u1
u2

0.0104 0.0122 0.0101 0.0138 0.0354 0.0133 0.0025 0.0220 0.0070 0.0148 0.0175 0.0203
0.0161 0.0151 0.0154 0.0140 0.0093 0.0142 0.0147 0.0135 0.0150 0.0142 0.0140 0.0139

tw1

0.0100 0.0327 0.0106 0.0536 0.0228 -0.2084 0.0119 0.1421 0.0070 0.1591 0.0199 0.0353

tw2

0.0145 0.0039 0.0138 -0.0015 0.0105 0.0703 0.0131 0.0000 0.0139 0.0001 0.0128 0.0123

ty

0.0322 0.0322 0.0322 0.0326 0.0322 0.0325 0.0322 0.0328 0.0322 0.0307 0.0322 0.0323

e-1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000
Notes: The symbols in the first column are the proportional changes of their upper-case counterparts;
thus, for example, v1 is the proportional change in V1. NWS, VIC, QLD, SA, WA and TAS are
Australian states New South Wales, Victoria, Queensland, South Australia, Western Australia andTasmania respectively. SR and LR are abbreviations of “short run” and “long run”. Since yj and nj arelog differences of output and population respectively, yj-nj is the log difference of output per capita.

40
Table 2 Effects of an Increase in Regional Government Expendituree = -1e = -1 and gr1 =1
e = -1 and gr1=1, gr2=1
SR
LR
SR
LR
SR
LR
v1
-0.0398-0.0226-0.0157-0.0225-0.0432-0.0276v2-0.0182-0.0226-0.0243-0.0225-0.0236-0.0276c11-0.0593-0.0591-0.2715-0.2716-0.2669-0.2668c21-0.02170.0894-0.0191-0.0630-0.2158-0.1150c12-0.0593-0.1705-0.2715-0.2276-0.2669-0.3679c22-0.0217-0.0220-0.0191-0.0190-0.2158-0.2161g1
0.00000.00000.6716
0.6716
0.6716
0.6716g2
0.00000.00000.00000.00000.65650.6565j1-0.0230
0.0661-0.0593-0.0945-0.1882-0.1073j2-0.0230-0.0454-0.0593-0.0505-0.1882-0.2085πh1-0.0526-0.0427-0.0589-0.0628-0.0578-0.0488πh2-0.0152-0.0179-0.0149-0.0139-0.0201-0.0226
w1-0.0533-0.0200-0.2976-0.3108-0.3096-0.2794w2-0.0157-0.0240-0.0216-0.0183-0.2613-0.2688l1-0.0016-0.0890-0.0091
0.0254-0.0095-0.0888l2-0.0005
0.0223-0.0007-0.0097-0.0079
0.0128k1-0.0297-0.1081-0.0349-0.0039-0.0299-0.1011k2
0.00770.02810.00910.00100.00780.0263
rk1-0.0229-0.0230-0.0240-0.0240-0.0279-0.0280rk2-0.0229-0.0230-0.0240-0.0240-0.0279-0.0280e1-1.0227-1.0828-1.0267-1.0030-1.0229-1.0774e2-0.9854-0.9466-0.9828-0.9981-0.9852-0.9501
re1
0.97020.95180.96780.97510.9651
0.9484re2
0.97020.95180.96780.97510.9651
0.9484y1-0.0526-0.1310-0.0589-0.0279-0.0578-0.1290y2-0.0152
0.0052-0.0149-0.0230-0.0201-0.0017n10.0000-0.0884
0.00000.03490.0000-0.0802n2
0.00000.02310.0000-0.0091
0.00000.0209y1-n1-0.0526-0.0426-0.0589-0.0628-0.0578-0.0488y2-n2-0.0152-0.0179-0.0149-0.0139-0.0201-0.0226
πf1-0.0526-0.1310-0.0589-0.0279-0.0578-0.1290πf2-0.0152
0.0052-0.0149-0.0230-0.0201-0.0017p
0.03760.14850.25240.2086
0.05110.1518u1
0.03540.01330.19750.20630.20550.1854u2
0.00930.01420.01280.01090.15450.1590tw1
0.0228-0.20842.34632.43762.47352.2636tw2
0.01050.07030.07570.05212.57372.6280ty
0.03220.03250.05250.0524
0.1984
0.1986e-1.0000-1.0000-1.0000-1.0000-1.0000-1.0000
Notes: The symbols in the first column is the proportional changes of their upper-case counterparts;
thus, for example, v1 is the proportional change in V1. SR and LR are abbreviations of “short run” and“long run”. Since yj and nj are log differences of output and population respectively, yj-nj is the log
difference of output per capita.
VariableTable 3 Effects of a Reduction in Unemployment Benefits
Variable

Base Case, e = -1

e = -1, ub1=-1

e= =-1, ub1=-1,ub2=-1

SR

LR

SR

LR

SR

LR

v1
v2

-0.0398-0.0182-0.0226-0.0226-0.0227-0.0174-0.0185-0.0185-0.01930.0024-0.0020-0.0020c11-0.0593-0.0591-0.0314-0.0313-0.0325-0.0324c21-0.02170.0894-0.02200.00520.00490.1163c12-0.0593-0.1705-0.0314-0.0585-0.0325-0.1442c22-0.0217-0.0220-0.0220-0.02210.00490.0045j1
j2-0.0230-0.0230

0.0661-0.0454-0.0188-0.0188

0.0029-0.0243-0.0020-0.00200.0874-0.0245πh1-0.0526-0.0427-0.0259-0.0235-0.0319-0.0220πh2-0.0152-0.0179-0.0167-0.0173

0.00550.0027w1-0.0533-0.0200-0.0265-0.0184-0.03200.0014w2-0.0157-0.0240-0.0171-0.01910.0054-0.0029l1
l2-0.0016-0.0005-0.08900.02230.0298-0.0005

0.00850.00510.02960.0306-0.0580
0.0535k1-0.0297-0.1081-0.0073-0.0265-0.0297-0.1083k2

0.00770.02810.00190.00690.00770.0282

rk1-0.0229-0.0230-0.0186-0.0186-0.0023-0.0023

rk2-0.0229-0.0230-0.0186-0.0186-0.0023-0.0023e1
e2-1.0227-0.9854-1.0828-0.9466-1.0056-0.9964-1.0203-0.9869-1.0227-0.9854-1.0830-0.9465

re1

0.97020.95180.97970.97520.99080.9724re2

0.97020.95180.97970.97520.99080.9724y1-0.0526-0.1310-0.0259-0.0450-0.0319-0.1106y2-0.0152

0.0052-0.0167-0.01170.00550.0259n1

0.0000-0.0884

0.0000-0.02160.0000-0.0887n2
y1-n1

0.0000-0.0526

0.0231-0.04260.0000-0.0259

0.0056-0.02340.0000-0.03190.0231-0.0219y2-n2-0.0152-0.0179-0.0167-0.0173

0.00550.0028πf1-0.0526-0.1310-0.0259-0.0450-0.0319-0.1106

πf2-0.0152

0.0052-0.0167-0.01170.00550.0259p0.03760.14850.00940.03650.03740.1487u1
u2

0.03540.00930.01330.0142-0.64610.0101-0.6515
0.0113-0.6425-0.5945-0.6647-0.5896ub1

0.00000.0000-1.0000-1.0000-1.0000-1.0000

ub2

0.00000.00000.00000.0000-1.0000-1.0000

tw1

0.0228-0.2084-0.2760-0.3325-0.2798-0.5118

tw2

0.01050.07030.00990.0246-0.3153-0.2553ty
0.03220.03250.02640.02640.00280.0031e-1.0000-1.0000-1.0000-1.0000-1.0000-1.0000
Notes: The symbols in the first column is the proportional changes of their upper-case counterparts;
thus, for example, v1 is the proportional change in V1. SR and LR are abbreviations of “short run” and“long run”. Since yj and nj are log differences of output and population respectively, yj-nj is the log
difference of output per capita.

Table 4 Effects of a National Government Expenditure Increase
Variable

Base Case, e = -1LRSR
-0.0398-0.0226-0.0182-0.0226-0.0593-0.0591-0.02170.0894-0.0593-0.1705-0.0217-0.02200.00000.00000.00000.0000-0.0230
0.0661-0.0230-0.0454-0.0526-0.0427-0.0152-0.0179-0.0533-0.0200-0.0157-0.0240-0.0016-0.0890-0.0005
0.0223-0.0297-0.10810.00770.0281-0.0229-0.0230-0.0229-0.0230-1.0227-1.0828-0.9854-0.9466
0.97020.95180.97020.9518-0.0526-0.1310-0.0152
0.00520.0000-0.0884
0.00000.0231e = -1, gn1=1SRLR
0.0223-0.0211-0.0322-0.0211-0.0766-0.0770-0.0396-0.3195-0.0766
0.2037-0.0396-0.0388
0.32840.32840.00000.00000.0055-0.21890.0055
0.0618-0.0517-0.0767-0.0143-0.0074-0.0107-0.0946
0.02700.0479-0.00030.21970.0008-0.0566-0.02970.16780.0077-0.0436-0.0220-0.0219-0.0220-0.0219-1.0227-0.8714-0.9853-1.0829
0.97101.0174
0.97101.0174-0.05170.1460-0.0143-0.0655
0.00000.22260.0000-0.0581e = -1,gn1=1,gn2=1SRLR-0.0340-0.0182-0.0141-0.0182-0.1492-0.1490-0.1149-0.0126-0.1492-0.2516-0.1149-0.1152
0.32840.32840.3436
0.3436
0.12450.20650.12450.1039-0.0481-0.0390-0.0107-0.0132
0.1677
0.19840.20550.19790.0051-0.0753
0.00630.0273-0.0297-0.10190.00770.0265-0.0184-0.0185-0.0184-0.0185-1.0227-1.0781-0.9853-0.94970.97470.95770.97470.9577-0.0481-0.1204-0.01070.00800.0000-0.08140.00000.0212

v1
v2
c11
c21
c12
c22
g1
g2
j1
j2
πh1
πh2
w1
w2
l1
l2
k1
k2
rk1
rk2
e1
e2
re1
re2
y1
y2
n1
n2
y1-n1
-0.0526-0.0426-0.0517-0.0766-0.0481-0.039y2-n2-0.0152-0.0179-0.0143-0.0074-0.0107-0.0132-0.0526-0.1310-0.05170.1460-0.0481-0.1204
πf1-0.0152
0.0052-0.0143-0.0655-0.01070.0080πf2
0.03760.14850.0370-0.24250.03430.1364p0.03540.01330.0071
0.0628-0.1113-0.1317
u10.00930.0142-0.0160-0.0283-0.1215-0.1170
u2
0.0228-0.2084-0.3853
0.1973-2.0919-2.3049
tw1
0.01050.0703-0.4351-0.5859-2.2983-2.2432
tw2
0.03220.03250.27530.27471.29191.2921ty-1.0000-1.0000-1.0000-1.0000-1.0000-1.0000e
Notes: The symbols in the first column is the proportional changes of their upper-case counterparts;
thus, for example, v1 is the proportional change in V1. SR and LR are abbreviations of “short run” and“long run”. Since yj and nj are log differences of output and population respectively, yj-nj is the log
difference of output per capita.

43
Appendix 1: A list of variables
Vi = utility of the representative household, region i,
C1i = real private consumption of good 1 per household, region i,C2i = real private consumption of good 2 per household, region i,
Gi = real government-provided consumption per household, region i,
GRi = amount of regional government provided per household, region i,
GNi = amount of national government provided good per household, region i,
P = price of good 2 in terms of good 1,
Ji = real household income in region i,ΠHi = real profit distribution per household, region i,
Wi = real wage per worker, region i,
REi = emission permit rental rate, region i,
Di = productivity parameter, region i,
Yi = output of the representative firm, region i,
Li = employment, in region i,
Ki = capital, region i,
RKi =capital rental rate,
Ni =workforce (= population), region i,ΠFi = real profit per firm, region i,
TY = income tax,
TWi= payroll tax, region I,
θi = share of national income tax to region i
N = national population.
K = national capital
Ui = unemployment rate, region i,
UBi= real unemployment benefits per unemployed person, region i,
Ei = pollution emission, region i
E = national pollution emission

43

44
Appendix 2: The linearised version of the model
The model is linearised in terms of proportional differences by taking
logarithms and differentials of each equation. The linearised form of equations (1) to(18) are as follows, with the linearised form having the same number as the original
equation but being distinguished by a prime.
The linearised utility function is:
i = 1, 2(1’) vi = γ 1i c1i + γ 2i c2i + δ i gi
where lower-case letters represent the proportional changes (log differential) of their
upper-case counterparts.
The linearised consumption demand functions are:i = 1, 2(2a’) c1i = (λ − 1) p − σ TY tY + ji
i = 1, 2(2b’) c2i = λ p − σ TY tY + ji
where σTY =TY/(1-TY).
The linearised definitions of real household income are:(3a’) j1 = σ J ΠH 1[(1 − λ ) p + σ ΠH ΠH 1π h1 + σ ΠHW 1 ( w1 − σ U 1u1 ) + σ ΠHUB1 (u1 + ub1 )+ σ ΠHK 1 (rK 1 + k1 − n)] + σ JK 2 (−λ p + rK 2 + k2 − n)P1-λ [ΠH1 + (1- U1 )W1 + U1UB1 + RK 1 K1 / N ]
,
J1
Π H1
,
σ ΠH Π H 1 =[Π H1 + (1- U1 )W1 + U1UB1 + RK 1 K1 / N ]W1 (1- U1 )σ ΠHW 1 =,[Π H1 + (1- U1 )W1 + U1UB1 + RK 1 K1 / N ]U1UB1σ ΠHUB1 =,[ΠH1 + (1- U1 )W1 + U1UB1 + RK 1 K1 / N ]where σ J ΠH 1 =RK 1 K1 / N
U1P − λ RK 2 K 2 / Nσ ΠHK 1 =, σU1 =, σ JK 2 =,1 − U1[ΠH1 + (1- U1 )W1 + U1UB1 + RK 1 K1 / N ]J1and(3b’) j2 = σ J ΠH 2 [−λ p + σ ΠH ΠH 2π h2 + σ ΠHW 2 ( w2 − σ U 2u2 ) + σ ΠHUB 2 (u2 + ub2 )+ σ ΠHK 2 (rK 2 + k2 − n)] + σ JK 1 ((1 − λ ) p + rK 1 + k1 − n)P - λ [ΠH 2 + (1- U 2 )W2 + U 2UB2 + RK 2 K 2 / N ]
,
J2
ΠH 2
,
σ ΠH Π H 2 =[ΠH 2 + (1- U 2 )W2 + U 2UB2 + RK 2 K 2 / N ]W2 (1- U 2 )σ ΠHW 2 =,[ΠH 2 + (1- U 2 )W2 + U 2UB2 + RK 2 K 2 / N ]U 2UB2σ ΠHUB 2 =,[Π H 2 + (1- U 2 )W2 + U 2UB2 + RK 2 K 2 / N ]RK 2 K 2 / NU2σ ΠHK 2 =, σU 2 =,[Π H 2 + (1- U 2 )W2 + U 2UB2 + RK 2 K 2 / N ]1−U2

where σ J ΠH 2 =P1−λ RK 1 K1 / N
J2The linearised migration equilibrium condition corresponding to equation (4) is:σ JK 1 =4445(4’) v1 = v2 .
The capital allocation equilibrium condition is:(5’) rK1 = rK2
The linearised production functions are:(6’) yi = di + α Ei ei + α Li li + α Ki ki
i = 1, 2.
The linearised profit definitions, rewritten as output equations, are given by:(7’) yi = σ Y ΠFiπ fi + σ YWi (σ TWi tWi + wi + li ) + σ YKi (rKi + ki ) + σ YEi (rEi + ei )i = 1, 2
ΠFi(1 + TWi )Wi Li
T
R K
R E
where σ Y ΠFi =, σ YWi =, σ TWi = Wi , σ YKi = Ki i , σ YEi = Ei i .
1 + TWiYi
Yi
Yi
Yi
The profit-maximisation conditions in linear form are:(8a’)
yi = σ TWi tWi + wi + li ,i = 1, 2
i = 1, 2(8b’) yi = rKi + ki ,i = 1, 2(8c’) yi = rEi + ei ,The linear version of the wage-bargaining equilibrium condition is:(9’)
σ twi twi + li + ui + σ WBWi wi − σ WBUBi ubi = ωi * +π fi ,i = 1, 2Wi
UBi
where σ WBWi =, σ WBUBi =, and ωi* is the proportional change in ω.
Wi − UBi
Wi − UBi
The national government’s budget constraint is linearised as:(10’) σ RVTY [tY + σ JJ 1 (−σ θ 1θ1 * + n1 + j1 ) + σ JJ 2 (−σ θ 2θ 2 * + n2 + j2 )]+σ RVE1[(1 − λ ) p + rE1 + e1 ] + σ RVE 2 [−λ p + rE 2 + e2 ] = σ EXGF 1 (n1 + gn1 ) + σ EXGF 2 (n2 + gn2 )TY [(1 − θ1 ) N1 J1 + (1 − θ 2 ) N 2 J 2 ]where σ RVTY =TY [(1 − θ1 ) N1 J1 + (1 − θ 2 ) N 2 J 2 ] + P1−λ RE1 E1 + P − λ RE 2 E2
(1 − θ1 ) N1 J1(1 − θ 2 ) N 2 J 2, σ JJ 2 =σ JJ 1 =,(1 − θ1 ) N1 J1 + (1 − θ 2 ) N 2 J 2(1 − θ1 ) N1 J1 + (1 − θ 2 ) N 2 J 2σ RVE1 =P1−λ RE1 E1
TY [(1 − θ1 ) N1 J1 + (1 − θ 2 ) N 2 J 2 ] + P1−λ RE1 E1 + P − λ RE 2 E2

P − λ RE 2 E2TY [(1 − θ1 ) N1 J1 + (1 − θ 2 ) N 2 J 2 ] + P1−λ RE1 E1 + P − λ RE 2 E2
θN1GN1
N 2GN 2σ EXGF 1 =, σ EXGF 2 =, σ θ i = i , θi* = dθi/θi.
1 − θiN1GN1 + N 2GN 2
N1GN1 + N 2GN 2
Region 1’s government budget constraint in linear form is given by:(11a’) σ RVTW 1[(1 − λ ) p + σ TWTW 1 (tW 1 + w1 − σ U 1u1 ) − σ TWUB1 (u1 + ub1 )]+σ RV 1TY (θ1 * +tY + j1 ) = gr1 ,σ RVE 2 =P1−λ [TW 1W1 (1 − U1 ) − U1UB1 ]TW 1W1 (1 − U1 ), σ TWTW 1 =,1− λP [TW 1W1 (1 − U1 ) − U1UB1 ] + θ1TY J1
TW 1W1 (1 − U1 ) − U1UB1
U1UB1
θ1TY J1
σ TWUB1 =, σ RV 1TY = 1−λ.
TW 1W1 (1 − U1 ) − U1UB1
P [TW 1W1 (1 − U1 ) − U1UB1 ] + θ1TY J1Similarly, for region 2’s government budget constraint we have:(11b’) σ RVTW 2 [−λ p + σ TWTW 2 (tW 2 + w2 − σ U 2u2 ) − σ TWUB 2 (u2 + ub2 )]+σ RV 2TY (θ 2 * +tY + j2 ) = gr2 ,where σ RVTW 1 =45

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P − λ [TW 2W2 (1 − U 2 ) − U 2UB2 ]where σ RVTW 2 = − λ,P [TW 2W2 (1 − U 2 ) − U 2UB2 ] + θ 2TY J 2
TW 2W2 (1 − U 2 )σ TWTW 2 =,TW 2W2 (1 − U 2 ) − U 2UB2U 2UB2
θ 2TY J 2
σ TWUB 2 =σ RV 2TY = − λ.
TW 2W2 (1 − U 2 ) − U 2UB2
P [TW 2W2 (1 − U 2 ) − U 2UB2 ] + θ 2TY J 2
The definition of the unemployment rate is linearised as:(12’) ui = (1/ σ Ui )(ni − li ) ,i = 1, 2
The definition of Gi is linearised as:(13’) gi = σ GGRi gri + σ GGFi gni
i = 1, 2GRi
GN i
where σ GGRi =, σ GGFi =Gi
GiThe national employment constraint results in the following linearised condition:(14’) σ N 1n1 + σ N 2 n2 = n
where σ N 1 = N1 / N , σ N 2 = N 2 / N .
The national capital constraint is linearised as:(15’) σ K 1k1 + σ K 2 k2 = k
where σ K 1 = K1 / K , σ K 2 = K 2 / K
The linearised form of the national emissions permits constraint is:(16’) σ E1e1 + σ E 2 e2 = ewhere σ E1 = E1 / E , σ E 2 = E2 / E
The profit distribution condition can be linearised to give:(17’) π fi = ni + π hi ,i = 1, 2
The final equation of the model is the balance of trade condition which, in linear form,is:(18’) n1 + c21 = n2 + p + c12

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Appendix 3: Data-Base
RegionC($m) LW ($m) GN($m) GR($m) L ( ‘000) N ( ‘000) RkK($m) REE($m)

UB(N-L)($m) TR($m)

Region 1 NSW 196376.0 149557.3 18545.4 35108.2

3286.53460.6 50031.8

4690.02836.7 23423.2

Region 2 ROC 361787.4 280734.7 36333.6 71171.0

6667.1

6993.7 110763.6 11232.0

5323.0 43980.8

Nation558163.4 430292.0 54879.0 106279.2

9953.6 10454.3 160795.4 15922.0

8159.7 67404.0

Region 1 Vic

144591.6 109211.7 14830.2 26446.0

2542.82676.5 38373.6

3120.02178.9 17107.8

Region 2 ROC 413571.8 321080.3 40048.8 79833.2

7410.97777.9 122421.9 12802.0

5980.9 50296.3

Nation558163.4 430292.0 54879.0 106279.2

9953.6 10454.3 160795.4 15922.0

8159.7 67404.0

Region 1 Qld

107950.4 84478.3 10591.8 21656.6

2068.02163.3 33185.9

6240.01553.7 13232.8

Region 2 ROC 450213.0 345813.7 44287.2 84622.6

7885.78291.0 127609.5

9682.06606.0 54171.2

Nation558163.4 430292.0 54879.0 106279.2

9953.6 10454.3 160795.4 15922.0

8159.7 67404.0

Region 1 SA

41331.6 29415.9

8612.2757.3

798.5 10076.2

673.3

Region 2 ROC 516831.8 400876.1 50442.8 97667.0

9196.49655.8 150719.3 15610.0

7486.4 62796.4

Nation558163.4 430292.0 54879.0 106279.2

9953.6 10454.3 160795.4 15922.0

8159.7 67404.0

Region 1 WA

56082.8 49053.5

4949.0 11486.4

1074.61117.3 26359.6

696.3

Region 2 ROC 502080.6 381238.5 49930.0 94792.8

8879.09337.0 134435.9 14674.0

7463.4 59714.9

Nation558163.4 430292.0 54879.0 106279.2

9953.6 10454.3 160795.4 15922.0

8159.7 67404.0

Region 1 Tas

11831.0

224.5

220.8

8575.24436.21526.42969.8238.1

2768.5312.0

1248.0312.04607.77689.11343.5

Region 2 ROC 546332.4 421716.8 53352.6 103309.4

9729.1 10216.3 158027.0 15610.0

7939.0 66060.5

Nation9953.6 10454.3 160795.4 15922.0

8159.7 67404.0

558163.4 430292.0 54879.0 106279.2

Notes: Data for Ci, Li, LWi N, NG, GRi UB and TR are from ABS times series averaged over the period
2004 – 2008. Capital income RkK is calculated by multiplying the capital stock by a rate of return of
5%. Payment for emissions permits are estimated from Garnaut (2008).

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