Climate Policy with Heterogenous WTP
Luca Spinesi
University of Rome Tre
IAERE Fifth Annual Conference 16th -17th February 2017, Rome
University of Rome Tor Vergata, School of Economics
Luca Spinesi University of Rome Tre ()
Climate Policy with Heterogenous WTP
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Some Economic Consequences of Climate Change
The negative consequences of climate change are numerous and
wide-ranging and have signi…cant economic impacts (United Nations
Framework Convention on Climate Change, UNFCC, 2012; The Nature
Conservancy, 2013).
1
2
In absence of tight and strong clear actions taken to curb global carbon
emissions, climate change impacts could cost between 5% and 20% of
the annual global GDP (see, e.g., Hallegatte and Corfee-Morlot, 2011).
When projection of actual baseline growth and innovation is taken into
account, reduction, and then stabilization, of global carbon
concentrations could generate a cost in the year 2050 that range from
a 4% loss to a slight increase in GDP (IPCC).
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Climate Change Policies
Governments are undertaking international and domestic initiatives
aimed at reducing the impact of climate change.
(SIF15 and the Kyoto Protocol);
The American Clean Energy and Security Act (ACESA) of 2009 calls
for reducing US greenhouse gas (GHG) emissions by 17% below 2005
levels by 2020, and 83% by 2050;
Similar targets have been …xed by the EU and China (see Holdren,
2006; Popp, 2010).
Climate change policies span a range of mandatory approaches:
emission pricing in the form of carbon taxes and cap-and-trade system,
technology mandates, performance standards, hybrid approaches.
Considering the e¢ ciency of the whole tax system, the design of the
tax system matters from a cost-e¤ective point of view.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Which Policy?
While no option dominates the others, carbon tax or cap-and-trade
with auctioned allowances have found to be more e¤ective (Goulder,
2013):
when …scal interactions of climate policies with the whole …scal system
are taken into account, even if the tax-system is initially suboptimal;
when the scale of the tax-revenue requirement is not too great.
Exogenous emissions pricing has found to have some important
attractions over pure cap-and trade (Goulder and Shein, 2013):
prevent pricing volatility;
reduce expected policy errors in the face of uncertainties;
avoid potential wealth transfers to oil-exporting countries.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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/ 22
Empirical Analyses
The implementation of emission pricing (e.g., carbon tax) typically
come at a cost to individuals, like higher product prices and higher
taxes.
Are individuals willing to support them? Empirical analyses actually
focus on such an issue.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Empirical Analyses
It have been found that both preferences on climate issues and the
WTP to mitigate climate change are heterogeneously distributed
across individuals (see, e.g., Layton and Brown 2000; Hassett et al., 2009,
2010; Rausch et al., 2010; Wicker and Becken, 2013; Allo and Loureiro
2014; Dienes, 2015).
Heterogenous preferences are quite stable under di¤erent horizon time
of climate change mitigation intervention: 60 and 150 years (see, e.g.,
Layton and Brown 2000).
Consumers prefer mitigation to adaptation policy (Allo and Loureiro
2014).
Consumers prefer higher prices/taxes or a new tax instead of other
form of payments for mitigating climate change (Allo and Loureiro
2014).
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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/ 22
The Focus of the paper
A theoretical model with heterogenous WTP has not been developed
so far (this is not a paper on e¢ ciency of the tax system).
In the spirit of the empirical analyses above:
1
an easily implementable tax on polluting emissions is considered within
a theoretical model, with both clean and polluting products;
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
IAERE Fifth Annual Conference 16th -17 th Fe
/ 22
The Focus of the paper
A theoretical model with heterogenous WTP has not been developed
so far (this is not a paper on e¢ ciency of the tax system).
In the spirit of the empirical analyses above:
1
2
an easily implementable tax on polluting emissions is considered within
a theoretical model, with both clean and polluting products;
public’s WTP for climate policies, and asymmetric information on
individual’s WTP, are considered;
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
IAERE Fifth Annual Conference 16th -17 th Fe
/ 22
The Focus of the paper
A theoretical model with heterogenous WTP has not been developed
so far (this is not a paper on e¢ ciency of the tax system).
In the spirit of the empirical analyses above:
1
2
3
an easily implementable tax on polluting emissions is considered within
a theoretical model, with both clean and polluting products;
public’s WTP for climate policies, and asymmetric information on
individual’s WTP, are considered;
this paper also analyzes the e¤ects on the long run GDP growth rate
of the climate policy results within an endogenous R&D-driven growth
set-up.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
IAERE Fifth Annual Conference 16th -17 th Fe
/ 22
Population and Preferences
Let a continuum of households on the interval [0, 1] to exist.
The size of each household grows at a constant and exogenous rate
n > 0, so that population at any time t 0 is Nt = N0 e nt .
All households have intertemporal additive separable rational
continuous monotone preferences for a set β of dirty varieties (ω̃)
and a set α of clean varieties (ω).
Let qe,ω̃ be the quantity of polluting emissions for each unit of dirty
variety ω̃.
To simplify exposition, the quantity of polluting emissions is
homogeneous across dirty varieties, and it is normalized to one, i.e.,
qe,ω̃ = 1.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Willingness to Pay
Heterogeneous WTP of individuals is represented through a
real-valued random variable η 2 [0, 1], which is the share of a green
tax rate τ an individual is willing to pay.
Each household is then indexed by its WTP η.
Higher η indicates stronger WTP for each unit of dirty variety.
WTP η is distributed across households according to any continuous
0
cdf Φ (η ): Φ (0) = 0, Φ (1) = 1, Φ ( ) > 0.
WTP η is assumed to be independently distributed across households.
The individual WTP η can be of private information, and its cdf is
common knowledge.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Tax on polluting emissions
Let τ q be a tax (value) on polluting emissions qe,ω̃ for each unit of
product.
Tax τ q can be expressed as a homogeneous tax rate τ for each dirty
variety.
The price of a dirty variety ω̃ gross of the green tax rate τ is
pω̃,η = pn,ω̃ (1 + ητ ),
pn,ω̃ is the price net of the green tax rate.
This speci…cation allows actual empirical evidence to be matched:
consumers respond di¤erently to a tax-change and to a tax-inclusive
price change (Li et al. 2014, Bajo-Buenestado 2016).
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Individual Demand with WTP and tax
Optimal consumption choice allows the demand of dirty variety ω̃ of
a household with any WTP η 2 [0, 1] to be obtained: qη ( ) Υω̃,η ,
qη ( ) is any continuous decreasing function of its price;
0 if pω̃ > p̄ω̃,η
Υω̃,η is an indicator function: Υω̃,η =
1 if pω̃ p̄ω̃,η
p̄ ω̃,η is the maximum price an individual is willing to pay for the dirty
variety ω̃.
The demand of an individual η is a continuous function of the price
level up to p̄ω̃,η , then it falls to zero for any price pω̃,η > p̄ω̃,η , i.e.,
qη ( ) Υω̃,η =
0 if pn,ω̃ (1 + ητ ) > p̄ω̃,η
qη ( ) if pn,ω̃ (1 + ητ ) p̄ω̃,η
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Aggregate Demand
As the demand for any variety ω̃ is a continuous function of price up
to p̄ω̃,η , and because a continuum of WTP η 2 [0, 1] exists in the
population,
The demand function a …rm producing variety ω̃ faces is a continuous
function of price up to pω̃ = p̄ω̃,1 (where η = 1 is used).
Aggregate demand for any variety ω̃ is
N
Z 1
0
qη ( ) d Φ (η ) = N q̃ ( ) .
Aggregate demand of any clean variety ω is
Nq ( ) d ω = Nq ( )
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Manufacturing
Manufacturing …rms produce any variety ω̃ 2 β and ω 2 α under a
CRS technology by means of labor and energy.
A …rm in any variety ω̃ and ω has a constant unit cost function
cd (w , pd ) φ and cc (w , pc ) ι respectively,
w is the wage of workers, labor is the numeraire, so that w = 1,
pd and pc are the prices of energy obtained from dirty and clean
energy sources respectively.
The cost function here adopted allows for any degree of
substitution between labour and energy, i.e., the unit cost function
can be obtained from a CES production function.
Assumption: strictly positive pro…t ‡ows of a …rm producing any
variety.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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/ 22
The Firm’s problem
When the WTP of each individual is a priori unknown by …rms, while
the cdf is common knowledge, a dirty …rm solves the following
maximization problem
8
9
=
R1<
Max 0 pω̃,n (qω̃ ) (1 + ητ ) qω̃ φ [1 + (1 η ) τ c ] qω̃ pω̃,n (qω̃ ) ητqω̃ d
q
:|
{z
} |
{z
};
GROSS PROFIT FLOW
TAX BURDEN
The maximization problem reduces to
Max pn (qω̃ ) qω̃
q |
φ [1 + (1
{z
η̂ ) τ c ] qω̃
}
NET PROFIT FLOW
where η̂ =
R1
0
ηd Φ (η ).
Solution: pω̃,n = λφ [1 + (1
η̂ ) τ c ], λ mark-up.
pω̃ = pω̃,n (1 + η̂τ ): price gross of the green tax rate.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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/ 22
Tighter green tax rate
Instantaneous pro…t ‡ows, gross of the green tax, of the …rm in
variety ω̃ are:
π (ω̃, t ) = pω̃ q (pω̃ )
cd [q (pω̃ )]
0.
The marginal change in the pro…t ‡ows in any variety ω̃ 2 β when
τ " is:
∂pω̃
∂π (ω̃, t )
=
q (pω̃ ) [1
∂τ
∂τ
jεj]
mcd
∂q (pω̃ )
,
∂pω̃
p ω̃
> 0, jεj is the (gross) price elasticity of demand, and
where ∂∂τ
mcd > 0 is the marginal cost of production.
From the above condition it follows that
∂π (ω̃, t )
∂τ
0 () pω̃
mcd
= Free monopolistic price
1 j1εj
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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The Firm’s problem
From above
∆ΠG = ∆ΠN + ∆TR > 0
if ∆ΠN
0, no rebate needed.
if ∆ΠN < 0, rebate needed and feasible: ∆ΠN + ∆TR > 0
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
IAERE Fifth Annual Conference 16th -17 th Fe
/ 22
Policy Results 1: Partial Equilibrium
A tighter tax rate on polluting emissions that increases the price
charged by …rms using polluting energy sources does not reduces
pro…t ‡ows of these …rms.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Policy Results 1: Partial Equilibrium
A tighter tax rate on polluting emissions that increases the price
charged by …rms using polluting energy sources does not reduces
pro…t ‡ows of these …rms.
This result matches and explains acutal empirical evidence: supply
response of dirty producers
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
IAERE Fifth Annual Conference 16th -17 th Fe
/ 22
Policy Results 1: Partial Equilibrium
A tighter tax rate on polluting emissions that increases the price
charged by …rms using polluting energy sources does not reduces
pro…t ‡ows of these …rms.
This result matches and explains acutal empirical evidence: supply
response of dirty producers
Considering electricity power generation in the US, the …rms’reaction
to a higher carbon tax primarily is a reduction in output, primarily at
older plants, rather than changing emission rates (Holland 2010).
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Policy Results 2: General Equilibrium
When consumers have love for variety preferences, a higher tax on
polluting emissions increases both the relative market size and relative
pro…t ‡ows of clean to dirty varieties.
When disaggregate data on …rms and industries are considered, the
elasticity of substitution between products is greater than one in the
US (Anderson and Van Wincoop 2004, Imbs and Mejean 2009).
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
IAERE Fifth Annual Conference 16th -17 th Fe
/ 22
Policy Results 2: General Equilibrium
When consumers have love for variety preferences, a higher tax on
polluting emissions increases both the relative market size and relative
pro…t ‡ows of clean to dirty varieties.
When disaggregate data on …rms and industries are considered, the
elasticity of substitution between products is greater than one in the
US (Anderson and Van Wincoop 2004, Imbs and Mejean 2009).
This result matches and explains acutal empirical evidence: demand
response to tax chages:
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
IAERE Fifth Annual Conference 16th -17 th Fe
/ 22
Policy Results 2: General Equilibrium
When consumers have love for variety preferences, a higher tax on
polluting emissions increases both the relative market size and relative
pro…t ‡ows of clean to dirty varieties.
When disaggregate data on …rms and industries are considered, the
elasticity of substitution between products is greater than one in the
US (Anderson and Van Wincoop 2004, Imbs and Mejean 2009).
This result matches and explains acutal empirical evidence: demand
response to tax chages:
strong and robust evidence that gasoline tax changes are associated
with larger changes in gasoline consumption and vehicle choices in the
US (Li et al 2014).
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Robustness and Extensions
Endogenous R-D can be considered in the model set-up, various
approaches in describing the R&D sector can be used:
Schumpeterian R&D: innovation improves either the quality or the
production process of existing products (G-H 1991, A-H 1992); variety
proliferation R&D: innovation creates new varieties of products (Romer
1990, G-H 1991); R&D conducted in perfectly competitive markets
(B-L 2002); Directed Technological change (Acemoglu 2002).
An upstream energy sector with both clean and dirty energy sources
can be accounted for (Lin and Wagner, 2007, Atewamba and Nkuiya
2017).
Endogenous human capital accumulation (educational choices) and
then unskilled/skilled labor can be accounted for.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Policy implications for long-run growth
Policy results imply relatively stronger innovation incentives in clean
varieties:
" ∆π (ω, t ) > ∆π (ω̃, t ) =) ∆I (ω, t ) > ∆I (ω̃, t ) =) I "
Stronger innovation incentives generate higher per capita GDP
growth rate.
When endogenous educational choices are accounted for, policy
results 1 and 2 imply stronger human capital accumulation.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
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Policy implications for welfare
Welfare analysis in the market economy, no social planner.
To get welfare analysis a speci…c functional form for utility is needed
in this case.
Considering a quality ladder model with endogenous educational
choices (D-S 1999):
an optimal tax rate can be pinned down: it is the tax rate which
maximizes human capital accumulation;
major drawbacks: higher skill premium and inequality between skilled
and unskilled workers;
higher skill premium does not imply lower unskilled wage.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
IAERE Fifth Annual Conference 16th -17 th Fe
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Conclusions
An easily implementable green tax scheme is indicated in a general
theoretical framework for preferences and production of dirty and
clean products.
In the spirit of empirical analyses heterogeneous public’s WTP is
accounted for.
Tighter climate change policy does not hurt economic performance of
…rms producing with polluting energy, while positively a¤ects …rms
using clean energy.
These policy results spur aggregate innovation and per capita GDP
growth rate of an economy.
With some more speci…c functional assumptions, a tighter green tax
rate improves well-being of individuals.
Results do not account for the reduced negative environmental
externality and climate damages.
Luca Spinesi University of Rome Tre (Department
Climate
of Economics,
Policy withUniversity
Heterogenous
of Rome
WTP
Tre)
IAERE Fifth Annual Conference 16th -17 th Fe
/ 22