A nold, Fabian; Ashou No i dous , Ami ; Theile, Philipp
A icle — Published Ve sion
En i onmen al Policy Ins umen s o In es men s in
Backs op Technologies Unde P esen Bias - An Applica ion
o he Building Sec o
En i onmen al and Resou ce Economics
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: A nold, Fabian; Ashou No i dous , Ami ; Theile, Philipp (2025) : En i onmen al
Policy Ins umen s o In es men s in Backs op Technologies Unde P esen Bias - An Applica ion
o he Building Sec o , En i onmen al and Resou ce Economics, ISSN 1573-1502, Sp inge
Ne he lands, Do d ech , Vol. 88, Iss. 4, pp. 1039-1070,
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Philipp Theile
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1 Ins i u e o Ene gy Economics a he Uni e si y o Cologne, Vogelsange S . 321a,
50827 Cologne, Ge many
En i onmen al Policy Ins umen s o In es men s in
Backs op Technologies Unde P esen Bias - An Applica ion
o he Building Sec o
FabianA nold1· Ami Ashou No i dous 1· PhilippTheile1
En i onmen al and Resou ce Economics
h ps://doi.o g/10.1007/s10640-025-00960-8
Abs ac
Go e nmen s wo ldwide ha e se a ge s o educe g eenhouse gas emissions om he
esiden ial sec o o ze o o close o ze o. Policy ins umen s, such as ca bon p icing o
subsidies, a e being discussed and implemen ed o achie e hese a ge s. I indi iduals
exhibi p esen bias, Heu el (2015) has shown ha op imal policies a ge ing in es men s
in ex e nali y-p oducing du able goods consis o wo componen s, one aimed a he ex-
e nali y and one aimed a he p esen bias. We gene alize Heu el’s heo e ical model by
de ining a la ge echnology se . This allows us o ep esen he dependence o uel p ices
and emission in ensi ies on echnologies used o include a ze o-emission backs op echnol-
ogy. We examine he implica ions o his model gene aliza ion, and we nume ically assess
he e ec in a s ylized case s udy o a ep esen a i e building in Ge many. We show ha
as long as social cos s o ca bon and he co esponding
CO2
p ice a e no high enough
o make he backs op echnology op imal, Heu el’s p oposi ion holds ha op imal policies
mus consis o wo componen s. Gene alizing Heu el’s p oposi ion, a single ins umen
can add ess p esen bias, i he social cos s o ca bon and he
CO2
p ice a e high enough.
While he le el o his single ins umen , i.e., a ax o subsidy, depends on he le el o
p esen bias, we ind ha he e exis s a ax-subsidy combina ion ha is op imal ega dless
o he le el o p esen bias.
Keywo ds P esen bias · Policy · Hea ing in es men s · Du able goods · Clima e
neu ali y
JEL Classi ica ion D15 · D62 · D91 · H23 · Q48 · Q58
1 3
F. A nold e al.
1 In oduc ion
1.1 Backg ound and Mo i a ion
Go e nmen s o many coun ies ha e se hemsel es clima e a ge s, i.e., emission educ ion
a ge s. These a ge s no longe aim a a me e pa ial educ ion o g eenhouse gas (GHG)
emissions, bu a he a a educ ion o GHG emissions o ze o o close o ze o. Mo e han
70 coun ies pledged o each ne -ze o emissions, including he coun ies o he Eu opean
Union, China, and he USA (Uni ed Na ions 2023). In es men s mus be s imula ed and
ca ied ou beyond e iciency imp o emen s o achie e hese goals. The e o e, in all sec o s
in es men s in ze o-emission echnologies, i.e., backs op echnologies, mus be made.1 A
backs op echnology is a p ocess o a echnology in which he use o an exhaus ible esou ce
can be comple ely a oided. In his pape , we de ine backs op echnology mo e na owly: as
a echnology ha does no emi
CO2
du ing ope a ion. We assume ha such a echnology
exis s a ini e cos .2
An example is he esiden ial building sec o : Global GHG emissions om building ope -
a ions, i.e., hea ing and ho wa e p o ision, ha e inc eased in ecen yea s. In 2021 global
di ec
CO2
emissions om building ope a ions accoun ed o a ound 8 % o global ene gy-
ela ed
CO2
emissions (IEA 2022). In he esiden ial building sec o , deca boniza ion needs
o be ca ied ou by p i a e households in es ing in new echnologies (e.g., hea ing sys ems
and e u bishmen ) and choosing hei indoo empe a u e le el. In his pape , he analysis is
applied o he esiden ial building sec o , al hough he esul s a e gene alizable.
The p ominen policy om classic economics o each he i s -bes ou come in he p es-
ence o an en i onmen al ex e nali y (i.e., he emi ed emissions) is o in oduce a p ice on
said ex e nali y (i.e., a ca bon o
CO2
p ice), in e nalizing he ex e nali y in o he decision-
making a ionale o he households, like he Pigou ian ax (Pigou 1920). Empi ical li -
e a u e sugges s ha indi iduals do no always beha e acco ding o classic a ional choice
heo y. Beha io al issues, such as ime-inconsis en discoun ing (e.g., p esen bias), could
p e en indi iduals om in es ing op imally in ime. Heu el (2015) has shown ha i con-
sume s expe ience p esen bias, a Pigou ian ax does no lead o wel a e op imal in es men
decisions o ex e nali y-p oducing du able goods. Ins ead, he op imal policy mix consis s
o an ins umen o co ec he ex e nali y and ano he one aiming a he p esen bias, con-
s i u ing an in e nali y. Besides ca bon axa ion o p icing, hese ins umen s can include
subsidies, axes based on e iciency, o manda es.
In his analysis, Heu el (2015) assumes ha consume s can in es in echnologies wi h
di e en e iciencies. Shee imp o emen o e iciencies in ex e nali y-p oducing du able
goods, howe e , canno educe ex e nali ies o ze o. Thus, by assump ion, no backs op
echnology exis s. The au ho inds ha he e is a wel a e-op imal amoun o ex e nali ies
(i.e., GHG emissions) co esponding o he Pigou ian ax a e, which ep esen s he mon-
e a y damage o he ex e nali y. The op imal le el balances he damage om he ex e nali y
wi h he u ili y de i ed om he ex e nali y-p oducing good. In con as , in many coun ies,
he decla ed poli ical a ge is o achie e ze o o close o ze o emissions.3 The implici
1 Al e na i ely o addi ionally, ha d- o-a oid emissions can be o se by na u al o echnical ca bon sinks.
2 Mo e de ails in sec ion 2.
3 In he ollowing, we abs ac om he possibili y o ca bon sinks o achie e ne -ze o a ge s and assume ha
he goal o he in es men s unde in es iga ion is o educe emissions o ze o.
1 3
En i onmen al Policy Ins umen s o In es men s in Backs op…
assump ion when applying a ze o-emission a ge is, ha he ma ginal damage om GHG
emissions is highe han co esponding ma ginal aba emen cos s, and co espondingly, he
op imal amoun o GHG emissions is ze o. Pu di e en ly, he policy make is in e es ed in
a ge -consis en
CO2
p icing and policy measu es a he han axing he ex e nali y a he
a e o social cos s o ca bon (Aldy e al. 2021).
Building on he wo k o Heu el (2015), his aises he ollowing ques ions. Fi s : How
can Heu el’s model be gene alized o accoun o he exis ence o ze o emission backs op
echnologies wi h ini e cos s? Second: Wha does his gene aliza ion imply o he main
p oposi ions o he model? Thi d: Wha a e op imal policies unde p esen bias o ex e -
nali y-p oducing du able goods i he op imal in es men decision is he in es men in he
backs op echnology?
We gene alize he analy ical model o Heu el (2015) o in es men s in ex e nali y-p o-
ducing du able goods unde p esen bias by allowing o a g ea e echnology space. In he
gene alized model, he in es men may be accompanied by he subs i u ion o he uel used,
o example, in he case o hea ing in es men s, swi ching om a gas hea ing sys em o an
elec ic hea pump. The in eg a ion o uel subs i u ion in o he in es men decision allows
us o depic he exis ence o a ze o emissions backs op echnology.
We i s examine he e ec o he model gene aliza ion on Heu el’s main p oposi ions,
assuming s ill ha he e is a wel a e-op imal inne solu ion, i.e., ha he backs op echnol-
ogy is no op imal. We hen discuss he implica ions o he si ua ion when he in es men
in he backs op echnology is op imal. This may be he case i he assumed damage o he
ex e nali y is high enough so ha he backs op echnology is wel a e-op imal, o due o
poli ically se ze o-emission a ge s. In a s ylized case s udy o a ep esen a i e building o
he Ge man building sec o , we assume a poli ically se ze o-emission a ge . We nume i-
cally es ima e eal-wo ld magni udes o he p esen bias e ec on hea ing- ela ed in es men
and u iliza ion decisions, emissions, policies, and associa ed deadweigh loss.
In ou analysis, we show ha as long as social damage o ca bon and he co esponding
CO2
p ice is no high enough o make he backs op echnology op imal, households in he
op imum will s ill emi
CO2
. In his case, Heu el’s p oposi ions hold ha o each he social
op imum, we need wo policy ins umen s, one o add ess he in e nali y and a second one
o add ess he ex e nali y. Gene alizing Heu el’s p oposi ions, i he social cos s o ca bon
and he co esponding
CO2
p ice a e high enough, a ma k-up on he
CO2
p ice can also
induce he social op imum. The e o e, p esen bias can be add essed by a ax o ano he
single ins umen when aiming a ze o emissions in he p esence o a ze o-emission back-
s op echnology. In nume ical simula ions o a ep esen a i e household in Ge many and
unde he assump ion o con inuous in es men choices, we quan i y he a ge -consis en
CO2
p ice o eaching ze o-emissions wi hou p esen bias a 192€/
CO2
. Applying his
a ge -consis en
CO2
p ice in he case o p esen bias leads o a wel a e loss. In he case o a
p esen -biased household, a highe
CO2
ax exis s ha eaches he a ge (in ou exempla y
building and an assumed p esen bias o 0.7: 235€/
CO2
including an in e nali y-ma k-up
o 43€/
CO2
). While he op imal ax a e and subsidy depend on he le el o p esen bias,
we ind ha he e exis s an op imal ax-subsidy combina ion ha is op imal ega dless o
he le el o p esen bias.
1 3
F. A nold e al.
1.2 Rela ed Li e a u e and Con ibu ion
E e since (S o z 1955) in oduced he idea o ime-inconsis en discoun ing wi h his heo y
o commi men , i has been ecognized ha consume s may de ia e om he assump ion o
exponen ial, hus ime-consis en , discoun ing.4 In line wi h ime-inconsis en discoun ing,
Laibson (1997) coined he concep o p esen bias, i.e., agen s’ p e e ence o immedia e
bene i s o e ad an ages in u u e pe iods beyond exponen ial discoun ing.5 To ep esen
his beha io , he li e a u e has in oduced and applied models o quasi-hype bolic discoun -
ing (Phelps and Pollak 1968; Laibson 1997; O’Donoghue and Rabin 1999).
One me ic o policy e alua ion is wel a e. Assuming ime-inconsis en p e e ences
implies ha p e e ences change o e ime, complica ing wel a e analysis. Economis s
p o ide se e al wel a e c i e ia o o e come his complica ion. The wo mos p ominen
c i e ia a e he Pa e o c i e ion, i.e., conside ing each pe iod’s pe spec i e in o e all u il-
i y, and he long- un c i e ion, i.e., e alua ing he " ue" u ili y om a long- un pe spec-
i e (O’Donoghue and Rabin 2015). O’Donoghue and Rabin (1999) a gue ha he Pa e o
c i e ion is oo s ong an assump ion when applied o in e empo al choice. O’Donoghue
and Rabin (2015) claim ha bo h app oaches, as well as o he hinkable wel a e c i e ia,
equen ly yield he same conclusions bu a gue o he usage o he long- un c i e ion.6 As
Heu el (2015) u ilizes he long- un c i e ion in his model, we will also apply i .
Applying he long- un c i e ion de ia es om s anda d social wel a e analysis, which
elies on e ealed p e e ences as in o ma ion abou he consume ’s ue u ili y. The pa e -
nalis ic assump ion ha he consume ’s choices do no op imize he wel a e is as c i ical
as i is con o e sial. Sain -Paul (2011) a gues ha axes le ied o inducing a pa icula
beha io migh only lead o consume s paying highe p ices ins ead o changing beha io ,
educing o e all wel a e. Acco ding o Whi man (2006), he jus i ica ions o policy in e -
en ions o add essing in e nali ies a e based on he idea o Pigou ian axa ion, igno ing
Coase’s heo em (Coase 1960). The heo em s a es ha ex e nali ies can be esol ed by
nego ia ion be ween indi idual pa ies when ansac ion cos s a e low. Since in e nali ies
consis o choices wi hin he indi idual, Whi man (2006) a gues ha Coase’s heo em is
be e sui ed o dealing wi h in e nali ies. The in o ma ion equi ed o ind he leas cos ly
op ion add essing he damage om ime-inconsis en discoun ing is only a ailable o he
indi idual. Mo eo e , K usell e al. (2002) a gues ha o ackle consume s’ ime-inconsis-
en p e e ences, only an in e en ion by a ime-consis en social planne is wel a e enhanc-
ing. Time-consis ency o social planne s could pa ly be achie ed by a oiding sho - e m
poli ical p essu e by es ablishing c edible ules and ins i u ions, en o cing commi men .
Examples o such ins i u ions a e independen cen al banks, iscal ules, and social secu i y
sys ems wi h au oma ic adjus men s based on demog aphic o economic changes.
We apply ou analysis o he case o households’ hea ing sys em in es men decisions.
The empi ical li e a u e ega ding beha io al biases in ene gy e iciency decision-making
4 F ede ick e al. (2002) includes a c i ical e iew o he his o y and models o ime discoun ing including
ime-consis en u ili y discoun ing models as well as ime p e e ences and (quasi-)hype bolic discoun ing
models.
5 See he e iews F ede ick e al. (2002) and DellaVigna (2009) o empi ical es ima es o p esen bias in
a ious ci cums ances and Imai e al. (2021) and Cheung e al. (2021) o ecen me a s udies o pape s
epo ing p esen bias es ima es.
6 Kang (2015) shows ha imp o emen s in he Pa e o c i e ion a e also wel a e-imp o ing om he long- un
pe spec i e.
1 3
En i onmen al Policy Ins umen s o In es men s in Backs op…
is limi ed (Gillingham e al. 2009). Schleich e al. (2019) in es iga ed he ole o p esen
bias and o he beha io al aspec s in adop ing ene gy-e icien echnologies wi hin di e en
coun ies in he Eu opean Union. They p o ide e idence o he signi icance o p esen
bias in educing in es men s in ene gy-e icien appliances and building e o i ing. We h-
schul e and Löschel (2021) ind ha p esen bias inc eases powe consump ion. The e o e,
as households unde alue ene gy cos s, p ice-based policies migh ail o educe household
ene gy consump ion. Fu he mo e, in he speci ic case o in es men in household appli-
ances in India, Fue s and Singh (2018) ind ha p esen bias becomes mo e signi ican he
la ge he pu chase objec in es iga ed. This inding is ele an o ou wo k, as hea ing sys-
em eplacemen ep esen s a pa icula ly la ge in es men decision o households. O e all,
he e is no ye a comp ehensi e empi ical iew on he e ec o p esen bias on hea ing
sys em in es men s. We accoun o his lack o es ima es by conside ing a ange o p esen
bias ac o s in ou nume ical simula ion.
This pape ocuses on he consequence o p esen bias in agen s’ decision-making on
policies o deca boniza ion. The model om Heu el (2015) cons i u es he basis o ou
analysis. A de ailed desc ip ion o he model o analyzing op imal policy ins umen s o
ex e nali y-p oducing du able goods unde p esen bias can be ound in Sec ion 2.1. Heu el
(2015) conside s a echnology space wi h e iciency and in es men cos s as dimensions. We
expand his space by allowing echnologies o di e in emission in ensi y and uel p ice. As
we will see, his gene aliza ion enables us o discuss he subjec o ze o-emission backs op
echnologies. O he esea che s ha e also add essed he ques ion o how o design policy
wi h ex e nali ies and in e nali ies such as p esen bias (Alco e al. 2012; Allco and Sun-
s ein 2015). Allco and Suns ein (2015) discuss p inciples o egula ing in e nali ies in he
ield o ene gy. They ind ha in e nali ies such as p esen bias can jus i y go e nmen in e -
en ion, gi en ha " ue p e e ences" o indi iduals can be iden i ied in con as o e ealed
p e e ences. Alco e al. (2012) ind ha when households unde alue long- e m ene gy
cos s in hei in es men decisions o du able goods, an ex e nali y ax such as a GHG ax
yields a double di idend, since i also add esses he in e nali y. They also ind, ha op imal
policy mixes add essing bo h ex e nali ies and in e nali ies depend on unknown in o ma ion
abou le els o in e nali ies, p i a e o households. Ou esul s de ia e om his inding due
o he p esence o a ze o-emission backs op echnology. Since Heu el (2015), ecen wo k
has deepened he unde s anding o p esen bias in economic policy design and wel a e anal-
ysis (D ugeon and Wigniolle 2021; Ko sogiannis and Schwage 2022; Kang 2022; Ba -Gill
and Hayashi 2021; Lades e al. 2021; Chan and Globus-Ha is 2023). Ba -Gill and Hayashi
(2021) discuss he in es men decisions o du able goods by p esen -biased agen s. In con-
as o ou wo k, hey ocus on he e ec o pu chase inancing. They ind coun e ailing
e ec s o p esen bias on he aluing o he bene i s o an in es men and he cos s o inanc-
ing said in es men and de i e ecommenda ions o c edi egula ion. Since hey discuss
gene al du able goods, hey do no conside he emission ex e nali ies om using ene gy
echnologies. Lades e al. (2021) examine in es men s om p esen -biased households in
ene gy e iciency echnologies. They illus a e pa icula ly how adminis a i e bu den can
educe hese in es men s. Simila o ou wo k, hey apply a heo e ical model and a simu-
la ion wi h exempla y building da a. Chan and Globus-Ha is (2023) discuss incen i iza-
ion o ene gy-e icien appliances such as ai condi ione s and e ige a o s. They ind ha
e iciency incen i es on hei own such as subsidies do no di ec ly add ess ex e nali ies
and hus dis o consume decision-making. They show ha unde ce ain ci cums ances,
1 3
F. A nold e al.
e iciency subsides may lead o mo e ene gy use o e all due o he ebound e ec . As we
will see, ou key poin o depa u e om Heu el (2015), Lades e al. (2021), and Chan and
Globus-Ha is (2023) is ha we conside policies eaching ze o emissions combined wi h
he a ailabili y o a backs op echnology.
While he e is li e a u e on policies in he con ex o p esen bias, o he bes o ou
knowledge, he e is no li e a u e add essing he subjec o policies o ex e nali y-p oducing
du able goods aiming a ze o emissions. In he p esen wo k, we aim o close his gap by (i)
gene alizing he model om Heu el o mo e complex echnologies also di e ing in emis-
sion in ensi y and uel p ice o be able o accoun o ze o emission backs op echnologies,
(ii) analyzing he consequences o he exis ence o an op imal backs op echnology, and (iii)
illus a ing he consequence o such policies in he esiden ial building sec o nume ically.
2 Analy ical Model
In his Sec ion, we i s desc ibe he ep esen a i e agen model o in es men s in ex e -
nali y-p oducing du able goods unde p esen bias om Heu el (2015). Then we gene alize
he model and apply i o he building sec o . By de ining a la ge echnology se , we a e
able o ep esen echnologies unning on di e en uels and hus ze o emission backs op
echnologies. Based on he gene alized model, we discuss wo di e en cases: Fi s , he case
ha he backs op echnology is no op imal. Second, he case ha he backs op echnology
is he op imal echnology choice.
2.1 A Rep esen a i e Agen Model o In es men s in Ex e nali y-p oducing
Du able Goods Unde P esen Bias
Heu el (2015) desc ibes he in es men and ope a ion p oblem o ex e nali y-p oducing
du able goods unde p esen bias in a ep esen a i e agen model. We p esen he model
based on nomencla u e o esiden ial hea ing. The in es men decision is made in he ini-
ial pe iod (
=0
) and he good las s T pe iods. In each pe iod a e he in es men (
=1
h ough
=T
), he household decides on he ope a ing in ensi y o he good: he gene a ed
hea o indoo empe a u e.
The model is de ined by he household’s p oblem and he social planne ’s p oblem. In
he household’s p oblem, u u e u ili y and cos s a e discoun ed using quasi-hype bolic dis-
coun ing. Quasi-hype bolic discoun ing is a me hod o modeling he beha io o house-
holds who expe ience p esen bias, i.e., p e e immedia e payo s and unde alue u u e
cos s and payo s.7 To his end, wo discoun ac o s a e in oduced.
δ
is called he “long-
un” discoun ac o , and
β
ep esen s he “p esen bias”. I a household expe iences p esen
bias, hen
β<1
.
The p esen -biased household pe spec i e is con as ed wi h he social planne ’s p ob-
lem. P esen bias is a beha io al anomaly ha a social planne does no expe ience due o
ully a ional beha io . One way o sol e he social planne ’s op imiza ion p oblem is o
di ec ly apply he long- un c i e ion while dis ega ding he household’s p esen bias, i.e.,
se ing
β=1
. The app oach assumes ha he household’s u ili y maximiza ion de ia es
7 Technically speaking, p esen -biased households discoun u ili y and cos s in he nea u u e a a highe
implici discoun a e han in he dis an u u e (Laibson 1997).
1 3
En i onmen al Policy Ins umen s o In es men s in Backs op…
om op imal wel a e e en om he household’s pe spec i e. Thus, he household "makes a
mis ake" and does no op imize i s " ue u ili y".8
In he ini ial pe iod, he household chooses he hea ing sys em’s a io o uel inpu and
gene a ed hea , he so-called e o coe icien ph ( uel pe hea ), ep esen ing he in es -
men decision o he du able good. In he subsequen pe iods, he hea gene a ed in each
pe iod
h
( ) is chosen, which ansla es in o indoo empe a u e.
U(h )
, whe e
U′>0
and
U′′ <0
, desc ibes he u ili y om gene a ed hea in mone a y e ms. The cos s pe kWh o
uel a e calcula ed as he sum o he ime-dependen uel cos (
p
) and a ax pe kWh o uel
(
τ
). This uel ax, he eina e e e ed o as ca bon ax, is in ended o pu a p ice on he GHG
emissions. When choosing a le el o ph, he household aces in es men cos s o c( ph). I
is assumed ha
c′<0
, meaning ha less e icien goods (hea ing sys ems) a e less expen-
si e, and
c′′ >0
. The household’s p oblem is hus desc ibed in Equa ion (1):
max
ph,
{
h
}
T
=1
−c( ph)+β·
[
T
∑
=1
δ ·
[
U(h )−[p +τ ]· ph ·h
]]
(1)
The social planne ’s p oblem is cha ac e ized by including he ex e nali y o uel con-
sump ion. The ex e nal damage om uel consump ion, i.e., damage om GHG emissions,
depends on
h
, he kWh o uel used in each pe iod , imes ph, he uel used o p oducing
he hea . The damage is deno ed as
d(h · ph)
, whe e
d(0) = 0
,
d′>0
and
d′′ =0
. The
co esponding social planne ’s p oblem, using he long- un c i e ion o discoun ing and
including ex e nal damages, is desc ibed in Equa ion (2):
max
ph,
{
h
}
T
=1
−c( ph)+
T
∑
=1
δ ·[U(h )−p · ph ·h −d(h · ph)] (2)
2.2 Model Gene aliza ion
In he model desc ibed in he p e ious sec ion, consume s in es in one echnology and
can decide on i s e iciency. By assump ion, no backs op echnology exis s because e i-
ciency imp o emen s canno educe ex e nali ies o ze o, and uel cos di e ences be ween
echnologies used a e neglec ed. We ex end he echnology se by allowing echnologies
unning on di e en uels. The e o e he in es men decision a ec s uel cos s and GHG
emissions pe uni o gene a ed hea . This enables us o analyze how op imal in es men
decisions depend on uel cos a ios and o include a ze o emission backs op echnology. An
example o a ze o emission backs op echnology in he building sec o would be he swi ch
o enewably gene a ed hea om sola he mal ene gy o o elec ic hea ing powe ed by
enewably gene a ed elec ici y.
8 Al e na i e wel a e c i e ia in he case o ime-inconsis en discoun ing include he Pa e ian app oach (e.g.
Bha acha ya and Lakdawalla (2004)), o he "dic a o ship o he p esen " app oach discussed in G ube and
Köszegi (2004) o Laibson (1997), which p io i izes he p e e ences o he cu en sel o e he p e e ences
o all u u e sel es. Analogous o he app oach in Heu el’s basic model and ollowing he a gumen s o
O’Donoghue and Rabin (1999), we apply he long- un c i e ion.
1 3
F. A nold e al.
By allowing echnologies o a y in uel p ice and emission in ensi y (down o ze o),
we ex end he echnology se and gene alize he model. In his gene alized model, he uel
p ice
p ( ph)
and he
CO2
ac o o he hea ing sys em ep ( ph) a e ep esen ed as unc-
ions o he e o coe icien ph.9 The unc ional o m o
p ( ph)
is ambiguous: i is con-
cei able ha he change o a mo e e icien hea ing sys em, e.g., om a gas boile o an
elec ic hea pump, is accompanied by dec easing uel p ices, in € pe
kWh uel
, bu also
ha he uel p ice inc eases, i , o example, elec ici y is mo e expensi e han gas.10 We
inco po a e a backs op echnology wi h ini e cos s
phBS
by assuming ha he emission
unc ion ep ( ph) equals ze o o all
ph <= phBS
, and
ep ′>0
o
ph >= phBS
.
This means ha when in es ing in he educ ion o ph, ep ( ph) dec eases linea ly un il he
backs op echnology
phBS
is eached, whe e emission in ensi y is ze o. Fu he in es -
men s in educing ph canno u he educe he emission in ensi y.
The household’s p oblem, including quasi-hype bolic discoun ing as de ined in Sec ion
2.1, is hus desc ibed as ollows11:
max
ph,
{
h
}
T
=1
−c( ph)+β·
[
T
∑
=1
δ ·
[
U(h )−[p ( ph)+ep ( ph)·τ ]· ph ·h
]]
(3)
The household’s p oblem di e s om Heu el (2015), since he in es men decision ph
depends on
p
and he newly in oduced
CO2
ac o ep . This yields i s -o de condi ions
o ph and each
h
. Assume ha he e exis s a unique in e io solu ion.12 The solu ions o
he household’s p oblem a e called
ph∗
and
h∗
.
−c
′(
ph
∗)
−β·
T
∑
=1
δ ·h∗
·[p ( ph∗)+ep ( ph∗)·τ ]
−β·
T
∑
=1
δ ·h∗
·
[
[p′
( ph∗)+ep ′( ph∗)·τ ]· ph∗
]=0
(4)
U′(
h
∗
)−[
p
(
ph
∗)+
ep
(
ph
∗)
τ
]·
ph
∗=0
,
∀
(5)
In Eq. 4, conside ing he nega i e sign, he i s e m
−c′( ph∗)
is posi i e. The e m ep e-
sen s he bene i o a ma ginal inc ease in ph. Since
c′>0
, i is cheape o choose a sys em
wi h highe ph and hence, lowe e iciency. Simila o Heu el (2015), he i s sum ep e-
sen s he discoun ed cos o a ma ginal inc ease in ph due o he dec ease in e iciency: he
u ili y in each u u e pe iod dec eases as hea ing cos s inc ease. The second sum adds he
changes in uel p ices
p′
( ph)
and changes in emission cos s
ep ′( ph)·τ
. While
ep ′
is
9 We model he choice o ph, he in es men cos s, he change in uel p ice, and
CO2
ac o as con inuous.
This se es he heo e ical ac abili y o he model.
10 By including
p ( ph)
as a con inuous unc ion we do no conside explici ly he case o a backs op-
echnology wi hou uel cos s (
p ( ph)
equals ze o o all
ph <= phBS
). An example o ha could be
sel -su iciency using sola ene gy. The esul s o ou analysis apply o ha case as well.
11 Appendix A shows he isocos cu es o he household’s decision p oblem o illus a ion.
12 I is assumed ha
lim
h →
0
U′(h
)=∞
o ensu e a unique in e io solu ion.
1 3
En i onmen al Policy Ins umen s o In es men s in Backs op…
eal hea demand (Me esacke 2021; Loga e al. 2012). To accoun o his o e p edic-
ion, we assume an adap a ion ac o o 0.8 o ou ep esen a i e building, based on Loga
e al. (2012) and IWU (2016). The choice o his ac o is consis en wi h he esul s o
Me esacke (2021), who es ima es lowe adap a ion ac o s, bu does no ake in o accoun
domes ic ho wa e gene a ion. The hea demand in ou model h [kWh] is hen app oxima ed
as a linea unc ion, depending on he chosen empe a u e T [
◦
C]:
h
=0.8·147.1m2·
(
11.61 kWh
m2
·◦
C·T−19.85 kWh
m2
)
(12)
To e alua e a con inuous in es men choice o households, we es ima e unc ions o in es -
men cos s,
CO2
emissions, and uel p ices based on eal da a (Danish Ene gy Agency 2021;
Picke e al. 2022; BAFA 2021). The hea ing echnologies include oil and gas condens-
ing boile s wi h and wi hou sola he mal suppo and an ai -sou ce hea pump. As in he
heo e ical model, he unc ions a e o mula ed conce ning he hea ing echnology’s ene gy
in ensi y le el ph. We assume a sys em li e ime and an assessmen pe iod o 20 yea s. Table
1 shows he esul ing echnology unc ions.22 I should be no ed ha uel p ices inco po a e
consume axes, including alue-added ax, as well as elec ici y and gas axes. Addi ionally,
elec ici y p ices include he cos s o emission ce i ica es de i ed om he Eu opean Emis-
sion T ading Sys em. When in e p e ing he nume ical esul s, one should keep in mind ha
hese in icacies in oduce dis o ions in op imal policy ins umen s and deadweigh loss.23
3.2 Resul s
3.2.1 Con inuous Model
F om he nega i e g adien o he uel p ice in Table 1 ollows ha
p′( ph)<0
. Conside -
ing P oposi ion 2 om Sec . 2,
p′( ph)<0
means ha a
CO2
p ice (o a subsidy) has o
22 Appendix C.3 p esen s he unde lying da a and he compu a ion o he echnology unc ions.
23 One dis o ion, o example, is ha since he elec ici y sec o in Ge many has no been ully deca bonised,
elec ici y p ices oday do no e lec he p ice o ze o-emission elec ici y. These could be highe , and he
esul s would change acco dingly.
Table 1 Es ima ed con inuous unc ions o in es men cos s,
CO2
emissions, and a iable cos s
Uni Func ion Da a
In es men
cos s
€
c( ph)=14,100e−1.019· ph
Fi ed unc ion illus a ed in he
le plo in Figu e 10. Unde lying
ph da a om column 3 and cos s
om columns 4 and 5 in Table 3.
CO2
emissions kg/kWh
ep ( ph)=−0.110 + 0.358 · ph
Fi ed unc ion illus a ed in he
middle plo in Figu e 10. Unde ly-
ing ph da a om column 3 in
Table 3 and emissions de i ed
om column 3 o Table 4.
Fuel p ice € /kWh
p( ph)=0.394 −0.331 · ph
Fi ed unc ion illus a ed in he
igh plo in Figu e 10. Unde lying
ph da a om column 3 in Table 3
and p ices de i ed om column 2
o Table 4.
1 3
F. A nold e al.
a leas o se he dec ease o he hea ing sys em’s a iable uel p ice induced by inc eas-
ing ph. Fo such a
CO2
p ice, p esen bias leads o unde -in es men and, consequen ly,
unde -consump ion o he mal ene gy. The nume ical esul s eplica e his inding on he
ela ionship be ween p esen bias, in es men , and consump ion choices as illus a ed in
Fig. 2. In case o no p esen bias,
β=1.0
, he e is no in es men up o a
CO2
p ice o
137€/
CO2
. The chosen indoo empe a u e a his p ice is 17.8°C. Wi h an inc easing
CO2
p ice, he in es men s in lowe ph inc ease. As hea ing cos s dec ease, he indoo em-
pe a u e inc eases, which is commonly e e ed o as he ebound e ec . A a
CO2
p ice
o 192€/
CO2
, he household in es s in ze o-emission hea ing echnology and eaches he
co esponding indoo empe a u e o 18.2°C. As desc ibed in Sec . 3.1.1, we in e p e his
ca bon ax a e
τneu
as he implied emission damage o e alua e social wel a e and con-
sequen ly deadweigh loss. In he p esence o p esen bias, he household in es s less and
chooses a lowe indoo empe a u e.
Figu e 3 shows ha he o al
CO2
emissions o e he 20 yea s o hea ing sys em li e ime
ollow he household’s in es men and consump ion choices. As discussed in Sec . 2.3.1,
he in es men in lowe ph impac s emissions mo e han dec easing indoo empe a u e.
In case o
β=0.7
, emissions dec ease om 81
CO2
o 75
CO2
o a
CO2
p ice inc ease
Fig. 3 To al emissions and deadweigh loss o e he hea ing sys em’s li e ime o 20 yea s depending on
he
CO2
p ice o p esen biases o 1.0, 0.9, 0.8, and 0.7
Fig. 2 The chosen ph and indoo empe a u e le els depending on he
CO2
p ice o p esen biases o
1.0, 0.9, 0.8, and 0.7
1 3
En i onmen al Policy Ins umen s o In es men s in Backs op…
om 0€/
CO2
o 157€/
CO2
, due o he dec ease in empe a u e. The emission decline u ns
mo e signi ican once he in es men s in lowe ph s a a 158€/
CO2
. A an emission p ice
o 235€/
CO2
, he household in es s in he ze o-emission echnology so ha o al
CO2
emissions a e 0.
The deadweigh loss o e he hea ing sys em’s li e ime o 20 yea s is illus a ed in Fig. 3.
I is based on he wo-s ep p ocedu e desc ibed in Sec . 3.1.1 and ollows he chosen ph
le el. The deadweigh loss cons i u es he di e ence o he case o an in es men in he
ze o-emission echnology in in es men cos s, hea ing cos s, gained u ili y om indoo em-
pe a u e, and emission damage. Whe eby he emission damage is calcula ed applying he
minimal a ge -consis en ca bon ax a e inducing in es men s sui able o ze o-emission
goals. The esul ing deadweigh loss is mainly d i en by he emission damage educed by
bene i s h ough lowe in es men and hea ing cos s. Wi hou a
CO2
p ice, he household
in es s in he op ion wi h he highes ph, leading o a deadweigh loss abo e 3,000€ due o
he emissions. Wi h an inc easing
CO2
p ice, he indoo empe a u e i s dec eases sligh y
and wi h i consequen ly he emissions. Once he household in es s in lowe ph, he dead-
weigh loss dec eases con exly. Wi hou p esen bias, he ca bon ax a e
τneu
o 192€/
CO2
is su icien o incen i ize in es men in he ze o-emission echnology. As P oposi ion 2 in
Sec . 2.3.1 sugges s, p esen bias leads o a deadweigh loss caused by unde -in es men
and, consequen ly, unde -consump ion. Fo
β=0.9
,
β=0.8
and
β=0.7
he deadweigh
loss a
τneu
is 58€ , 252€ , and 613€ , espec i ely. The loss esul s om he p esen bias
in e nali y as he
τneu
add esses he emission ex e nali y. In Sec . 2.3.2, we a gue ha unde
a ze o-emission a ge egime, a ma k-up on op o he
CO2
p ice which add esses he
ex e nali y can add ess he in e nali y and each he ze o-emission echnology. The equi ed
ma k-ups in he case s udy o
β=0.9
,
β=0.8
and
β=0.7
a e 11€/
CO2
, 25€/
CO2
, and
43€/
CO2
, espec i ely.
Acco ding o P oposi ion 3 in Sec . 2.3.1, a subsidy is an al e na i e o a ma k-up on he
ca bon ax. I he subsidy is high enough o induce in es men s in hea pumps, no
CO2
p ice
is needed since subsequen hea ing does no emi
CO2
. Consequen ly, a nega i e ela ion-
ship exis s be ween he wo policies. All policy combina ions ha lead o he social op imum
a e illus a ed in Fig. 4. The unc ion’s slope desc ibing he ela ionship be ween policies
depends on he le el o p esen bias and is lowe o a high p esen bias. The slope di e -
ences o igina e om he di e ing imes a which subsidies and
CO2
p ices a ec he house-
hold. P esen bias hinde s households om ully conside ing he
CO2
p ice in hei op imal
choice p oblem. Subsidies ake e ec di ec ly a he ime o he in es men . The highe he
le el o p esen bias, he mo e he
CO2
p ice mus inc ease o educe he equi ed subsidy.
A a
CO2
p ice o 89€/ and a subsidy o 8,000€ , he e is an in e sec ion o he unc-
ions o he di e en le els o p esen biases. Thus, a his combina ion o
CO2
p ice and
subsidy, he equi ed policy o he social op imum is independen o he le el o p esen
bias. The policy combina ion’s
CO2
p ice c ea es pa i y be ween he a iable cos s o all
echnology op ions. In o he wo ds, he a iable cos s become independen o he chosen
ph. We iden i y his in e sec ion in P oposi ion 2 in Sec . 2.3.1 by s a ing ha p esen bias
leads o unde -in es men and, consequen ly, unde -consump ion as long as o al u u e dis-
coun ed hea ing cos s, including uel and emission cos s, o a ma ginal inc ease in ph a e
g ea e o equal o ze o. I his is no he case, i.e., less e icien hea ing sys ems ha e lowe
u u e hea ing cos s, p esen bias will lead o o e -in es men . A he in e sec ion be ween
bo h cases, when u u e discoun ed hea ing cos s a e equal o all ph, he in es men cos s
1 3
F. A nold e al.
de e mine he in es men choice. As p esen bias a ec s he household’s weigh ing be ween
ma ginal changes in in es men cos s and ma ginal changes in o al u u e discoun ed cos s,
i does no a ec he household’s decision o equal u u e discoun ed cos s. 89€ / is he
CO2
p ice, which o se s he di e ences in he uel cos s. In his case, he subsidy mus com-
pensa e households o he di e ence in in es men cos s be ween
CO2
-emi ing and ze o-
emission echnologies. This subsidy is 8,000€ . As a esul , he policy mix a he in e sec ion
o he unc ions is op imal, independen o he le el o p esen bias.24
The u ili y unc ion o households is a c i ical assump ion. As shown in Appendix C.1,
we iden i y di e en alua ion le els o indoo empe a u e. Figu e 5 shows he ph le el
and chosen indoo empe a u e o e
CO2
p ice o h ee di e en alua ion ac o s gi en a
24 The alues o he op imal policy mix depend on he assump ions ed in o he model, like uel p ices, hea ing
e iciencies, and he u ili y unc ion.
Fig. 5 The chosen ph and indoo empe a u e le els depending on he
CO2
p ice o alua ion ac o s o
15€/
∆T2
, 25€/
∆T2
, and 35€/
∆T2
Fig. 4 Combina ions o
CO2
p ice and subsidy ha lead o he social op imum o p esen biases o 1.0,
0.9, 0.8, and 0.7
1 3
En i onmen al Policy Ins umen s o In es men s in Backs op…
p esen -bias o
β=0.8
. A highe alua ion ac o implies a lowe necessa y
CO2
p ice o
incen i ize in es men s in ph. In he case o a low alua ion ac o , he household eac s
i s wi h dec easing indoo empe a u e, as his yields lowe u ili y loss compa ed o he
addi ional cos s o in es ing, as is shown in he igh pa o Fig. 5. As soon as in es men s in
mo e e icien echnologies a e p o i able, e iciency inc eases, and he household inc eases
he indoo empe a u e un il he ins alla ion o he ze o-emission backs op echnology.
The
CO2
emissions and deadweigh losses o e he hea ing sys em’s li e ime o 20 yea s
illus a ed in Fig. 6 show a sligh decline un il he s a o in es men s in lowe ph ollowed
by a con ex decline un il he in es men in o he ze o-emission echnology. Be o e in es -
men s in mo e e icien echnologies s a , he deadweigh loss is he highes o he high
alua ion ac o since he unde -consump ion o indoo empe a u e weighs he mos . The
same logic also applies o why households wi h a high alua ion ac o s a in es ing in
mo e e icien hea ing sys ems a lowe
CO2
p ices han households wi h lowe alua ion
ac o s. As a highe le el o in es men s dec eases he deadweigh loss no only h ough
inc eased e iciency bu also h ough educed uel cos s, hey exhibi a quad a ic e ec on
he deadweigh loss. Thus, he decline in wel a e is less signi ican o lowe alua ion
households, which s ill eac by dec easing indoo empe a u e.
3.2.2 Disc e e Model
So a , he p esen ed heo e ical and nume ical esul s assume con inuous echnology
op ions so ha all ph le els a e easible be ween he ze o-emission and he leas e icien
op ion. In eali y, he e is only a limi ed se o hea ing echnologies. Figu e 7 illus a es he
household’s in es men and consump ion choices, gi en a disc e e echnology se , including
an oil condensing boile , a gas condensing boile , bo h boile combined wi h sola he mal,
and an ai - o-wa e hea pump. We de ine he se o echnologies as he a ailable ph le els
om Sec . 3.1 and choose he cos and emission le els acco ding o he unc ions om he
con inuous model (see Appendix C.3).
Fo each p esen bias le el, he e a e ou b eak-e en
CO2
p ices ha lead o a echnol-
ogy swi ch. In case o no p esen bias, i.e.,
β=1.0
, he household in es s in he highes ph
o 1.09, i.e., he oil condensing boile , un il a
CO2
p ice o 139€/
CO2
. Fo highe p ices,
he household chooses a ph o 1.02, i.e., he gas condensing boile . The b eak-e en poin s
Fig. 6 To al emissions and he deadweigh loss o e he hea ing sys em’s li e ime o 20 yea s depending
on he
CO2
p ice o alua ion ac o s o 15€ /
∆T2
, 25€ /
∆T2
, and 35€ /
∆T2
and a p esen bias o 0.8
1 3
F. A nold e al.
o in es ing in he oil condensing boile combined wi h sola he mal and he gas condens-
ing boile combined wi h sola he mal a e a 145€/
CO2
and 150€/
CO2
espec i ely. A a
CO2
p ice o 170€/
CO2
, he household in es s in he hea pump. Thus, in he disc e e case
170€/
CO2
is he ca bon ax a e
τneu
ha induces in es men in he ze o-emission ech-
nology. The
τneu
is lowe in he disc e e case han in he con inuous case because he
CO2
p ice only has o c ea e a b eak-e en be ween he gas condensing boile wi h sola he mal
and he hea pump, and no be ween an in ini esimal less e icien hea ing echnology and
he ze o-emission backs op echnology. Analogously o he con inuous case, p esen bias
leads o unde -in es men and unde -consump ion.
The o al
CO2
emissions o e he hea ing sys em’s li e ime o 20 yea s in Fig. 8 mi o
he s ep unc ion o ph. The e is a nea ly linea dec ease in
CO2
emissions ollowing he
household’s empe a u e dec eases and a mo e signi ican s ep whene e he
CO2
p ice
causes a swi ch be ween wo hea ing echnologies. A he ca bon ax a e
τneu
, he e a e ze o
CO2
emissions in case o no p esen bias. The unde -in es men , due o p esen bias, leads
o
CO2
emissions inc eases. These inc eases a e o p esen biases o
β=0.9
,
β=0.8
, and
β=0.7
, 49
CO2
, 49
CO2
, and 54
CO2
. This s ep is signi ican ly highe han in he con-
inuous case as he nex a ailable echnology is a gas condensing boile wi h sola he mal
Fig. 8 The o al emissions and deadweigh loss o e he hea ing sys em’s li e ime o 20 yea s in case o
disc e e echnology op ions depending on he
CO2
p ice o p esen biases o 1.0, 0.9, 0.8, and 0.7
Fig. 7 The chosen ph and indoo empe a u e le els in case o disc e e echnology op ions depending on
he
CO2
p ice o p esen biases o 1.0, 0.9, 0.8, and 0.7
1 3
En i onmen al Policy Ins umen s o In es men s in Backs op…
compa ed o a echnology wi h in ini esimal highe emission in ensi y. A ma k-up on he
CO2
p ice can add ess he in e nali y and incen i ize in es men in he hea pump as s a ed
in Sec . 2.3.2. Fo
β=0.9
,
β=0.8
, and
β=0.7
, he ma k-up is 10€/
CO2
, 21€/
CO2
,
and 36€/
CO2
, espec i ely. Following he wo-s ep p ocedu e desc ibed in Sec . 3.1.1, he
implied damage om
CO2
emissions
τneu
is lowe han in he con inuous case, na u ally
esul ing in a lowe o al le el o deadweigh loss. The deadweigh loss due o p esen bias
om unde -in es men and unde -consump ion is 101€ o a p esen bias o
β=0.7
. The
household chooses he oil condensing boile wi h sola he mal ins ead o a hea pump. Fo
p esen biases o
β=0.9
and
β=0.8
he household chooses a gas condensing boile wi h
sola he mal, which leads o neglec able deadweigh loss since
τneu
is de ined as he neces-
sa ily implied damage o b eak-e en be ween he wo hea ing echnologies.
4 Discussion
In ou s ylized model, we ind ha single-ins umen policies can be wel a e op imal and a -
ge -consis en e en i he household is p esen biased. We implici ly assume ha all house-
holds, hei alua ion ac o s, and hei le el o p esen bias a e homogeneous. Accoun ing
o household he e ogenei y, howe e , implica ions o policy ins umen s can di e , espe-
cially in dis ibu ional e ec s.
Acco ding o ou analysis, he lowe he alua ion o hea , he highe he
CO2
p ice mus
be o induce in es men in he ze o-emission backs op echnology. Assuming he policy-
make in oduces a
CO2
p ice su icien o incen i izing in es men in o he ze o-emission
backs op echnology o a household wi h an a e age alua ion ac o , low- alua ion house-
holds would no in es in he ze o-emission echnology. Ins ead, hey would pay he
CO2
p ice and hea less, while high- alua ion households in es in he ze o-emission backs op
echnology. Simila ly, i ins ead o a
CO2
p ice, he policymake se s a a ge -consis en
subsidy o a e age households, low- alua ion households will no in es su icien ly. Fo
households wi h highe alua ions, howe e , he subsidy is no only su icien bu oo high:
hey ecei e mo e money om he s a e han would ha e been necessa y o s imula e he
in es men . The empi ical li e a u e sugges s ha high-income households ha e a highe
alua ion o he mal ene gy han low-income households (Cayla e al. 2011; Me esacke
2021). This would imply ha a single, uni o m subsidy, which aims o each households
wi h low alua ion ac o s as well, a o s high-income households.
Households also show he e ogenei y wi h espec o hei le el o p esen bias. Assume
he policymake se s a
CO2
p ice ha is a ge -consis en o households wi h a e age p es-
en bias. As shown in Sec . 3.2.1, households wi h s onge p esen bias (
β<¯
β
) would
unde in es and pay he
CO2
p ice in u u e pe iods, hea ing less han op imal. Li e a u e
es ima ions o he co ela ion be ween income and he p esen bias le el ange be ween no
co ela ion and a nega i e co ela ion, sugges ing ha low-income households expe ience
highe le els o p esen bias (Meie and Sp enge 2010; Can and E dem 2013; Filippini
e al. 2021).
Based on he abo e, i migh he e o e make sense o he policy make o se a
CO2
p ice
ha is a ge -consis en o households wi h he highes p esen bias o ha e a a ge con-
sis en
CO2
p ice o all households. Howe e , he e is ano he eal-wo ld issue which ou
s ylized model does no conside . In eali y, in es men dis o ions exis , hinde ing house-
1 3
F. A nold e al.
holds om in es ing. Possible dis o ions and, hus, obs acles o in es men include budge
cons ain s, lack o access o capi al, echnological o egional ci cums ances, o spli incen-
i es be ween landlo ds and enan s. In cases whe e households canno in es , o he wise
a ge -consis en
CO2
p ices may lead o high cos s. And hese cos inc ease wi h he heigh
o he chosen p ice. Subsidies can help o o e come budge cons ain s and lack o access o
capi al. Suppose a subsidy is in oduced as a single ins umen . In ha case, he e is no p ice
signal o a leas pa ially in e nalize he ex e nali ies o households ha canno in es and
whose hea ing is s ill associa ed wi h GHG ex e nali ies.
Acco ding o he Tinbe gen ule Tinbe gen (1952), each poli ical goal needs an own
poli ical measu e. Fo ins ance, income e ec s o ce ain poli ical in e en ions can be
add essed mo e e icien ly and mo e consis en ly by non-linea income axa ion. None he-
less, he dis o iona y e ec s and he in es men ba ie s discussed abo e could pa ly be
add essed by a ge ed subsidies o non-linea axes on ene gy consump ion. Ta ge ed sub-
sidies may incen i ize ce ain households o in es in ze o-emission hea ing echnologies,
ei he o he wise being unable o in es o ha ing oo low o a alua ion o hea . Nonlinea
axa ion may alle ia e bu dens o lowe income households, in he case ha he
CO2
p ice
does no lead o he in es men in o ze o-emission echnologies and hea ing s ill p oduces
emissions. Bo h hese op ions a e di icul o implemen and need obus empi ical e idence,
which we he e o e do no u he elabo a e on.
We show in Sec . 3.2.1 ha an op imal policy combina ion o a
CO2
p ice and subsidy
exis s ha can accoun o di e en (unknown) le els o p esen bias.
The policy ins umen s also di e ega dless o households’ he e ogenei y. In he case o
a singula implemen a ion o a
CO2
p ice o bans on GHG emi ing echnologies, he house-
holds bea he ull cos s. Wi h (supplemen a y) subsidies, by con as , he s a e pays (pa
o ) he cos s. The la e may make sense om a social jus ice poin o iew o o inc ease
accep ance among he popula ion.
Ou assump ion ha he e is a backs op echnology a ini e cos s a ailable may be o e
simpli ied when conside ing eal-wo ld applica ions. E en wi hin one sec o , he cos s o
backs op echnologies can a y be ween households and in ime (Acemoglu e al. 2012).
The di e ences migh become e en mo e p onounced when compa ing ac oss sec o s, such
as hea ing and a ia ion. Policy mechanisms mus accoun o he ac ha a uni o m c oss-
sec o al
CO2
p ice could incen i ize backs op echnology adop ion in one sec o while lea -
ing i uneconomical in ano he . Fo example, while a
CO2
p ice alone migh su ice o d i e
adop ion in one sec o , ano he sec o may equi e addi ional, a ge ed echnology-speci ic
in es men subsidies o achie e simila ou comes.
Fu he mo e, go e nmen s hemsel es could po en ially be p esen biased, which could
a ec he e ec i eness o measu es o co ec in e nali ies. These aspec s o go e nmen
we e excluded in his s udy, which assumed a social planne wi h a comple e long- e m
o ien a ion. Howe e , elec ed o icials a e o en unde p essu e o implemen sho - e m
solu ions such as empo a y ax cu s o spending inc eases be o e elec ions, complica ing
he design o policies o long- e m wel a e imp o emen s. As men ioned in he li e a u e
e iew, one app oach o add essing go e nmen s own po en ial p esen bias is o es ablish
ins i u ions like independen cen al banks, iscal ules o au oma ically adjus ing spending
o social secu i y sys ems and o he a eas o go e nmen . Cen al banks, o example, o en
ope a e unde ules designed o ake a long- e m iew. While hese ules a e no in allible
1 3
En i onmen al Policy Ins umen s o In es men s in Backs op…
and may some imes be b oken, hey p o ide a amewo k ha can help mi iga e he sho -
e m poli ical p essu es p e alen in poli ical decision-making.
Gi en he he e ogenei y o households and hei po en ial in es men cons ain s, as well
as he possible desi abili y o dis ibu ing cos s be ween households and he s a e, he e
a e a gumen s in a o o combining axes (o bans) wi h subsidies. By dis inguishing
he e ec s o policies on in es men and u iliza ion decisions, ou analysis can suppo a
nuanced discussion o app op ia e policy mixes.
5 Conclusion
The p esen pape examines he impac o p esen bias on op imal en i onmen al policies
aimed a achie ing ze o emissions. The s udy gene alizes Heu el’s model o policy design
o ex e nali y-p oducing du able goods when in e nali ies a e p esen . Besides inc easing
e iciency, in es men s in a new hea ing sys em may subs i u e he uel used. Accoun ing o
his subs i u ion adds he dimensions o uel p ice and emission in ensi y o ou echnology
space. The gene aliza ion allows us o include a backs op echnology wi h ini e cos and
analyze policy choices ha each ze o emissions.
This wo k con ibu es o he scien i ic li e a u e in h ee ways. Fi s , we gene alize Heu-
el’s model by allowing echnologies o di e in uel p ice and emission in ensi y. Second,
we in oduce a model amewo k o de eloping a ge -consis en en i onmen al policies
gi en a backs op echnology. I can se e as one elemen wi hin a oolbox o wel a e analy-
sis gi en poli ical a ge s beyond ex e nali y p icing. Thi d, we apply he model amewo k
o he case o deca boniza ion in he Ge man hea ing sec o o p i a e households unde
p esen bias and de i e nume ical magni udes o he p esen bias e ec s.
We ind ha , gene alizing Heu el’s p oposi ions, one ins umen can be su icien o
add ess bo h ex e nali y and in e nali y. S ill, a combina ion o subsidies and axes can be
ad an ageous, as we show ha he e exis s a ax-subsidy combina ion ha is op imal ega d-
less o he p esen bias le el. This inding can be applied o compa able in es men deci-
sions in ex e nali y (GHG emission) p oducing du able goods, such as p i a e mobili y
in es men s. The exis ence o he op imal policy mix is pa icula ly ele an because he
le el o p esen bias is p i a e in o ma ion unknown o he policymake and he e ogeneous
among households. Policymake s could a oid dis ibu ional e ec s by u ilizing he p esen
bias agnos ic op imal policy mix. The e a e u he a gumen s suppo ing policy mixes ha
all sho in ou s ylized model, including he e ogenei y in he alua ion o hea ing, in es -
men dis o ions, and he cos s’ dis ibu ion be ween households and he s a e.
Based on ou analysis, he e emains oom o u he esea ch. In con as o ou g een-
ield analysis wi h cons an p ices, in eali y, households al eady own hea ing sys ems, and
he hea ing sys em s ock’s age s uc u e is he e ogeneous. The e o e, households a e aced
no only wi h he ques ion o which echnology o in es in, bu also whe he i is wo h
in es ing in a new hea ing sys em ea ly on be o e he exis ing one b eaks down. This aises
ques ions abou he iming o policy ins umen s, e.g., conce ning he in e dependencies o
p ice pa hs o
CO2
axes o uel p ices o e ime. He e, as well, he ques ion a ises as o
wha cons i u es a ge -consis en policy ins umen s. The issue could p o e complica ed, as
i is di icul o de e mine unde which ci cums ances ea ly hea ing sys ems eplacemen is
equi ed o achie e clima e a ge s. Fu he , we discussed he ole o household he e ogene-
1 3
F. A nold e al.
i y in ou indings quali a i ely. Households di e in hei le el o p esen bias, hei cu en
hea ing sys ems, and hei inancial capabili ies. A mo e de ailed examina ion o hese p op-
e ies could, in addi ion o heo e ical analyses, e.g., conce ning op imal policy mixes ac oss
households, also quan i y e ec s a he le el o he en i e Ge man building s ock.
Appendix A: Isocos Cu es
Figu e 9 illus a es he isocos cu es o he household’s decision p oblem. Fo illus a i e
pu pose, he plo s a e based on he da a o he nume ical example, al hough he plo s shall
only p o ide an in ui ion abou he p ope ies o he household’s decision con ex . The cos s
consis o he in es men cos s, uel cos s, and he chosen ph. Mo eo e , emission axes o
subsidies would a ec he cos s. The indi e ence cu es would be ho izon al lines, since
he household’s u ili y depends solely on he hea . In he le illus a ion o Fig. 9, he e
a e he basic isocos cu es. The da ke he colo , he highe he cos s. Wi hou any policy
in e en ion, highe ph can p o ide hea a lowe cos s, as he isocos cu es a e con ex in
ph. Emission axes and subsidies can u n he cou se o he isocos cu es so ha hey a e
dec easing wi h ph, and lowe phs can p o ide hea a lowe cos s.
Wi hou any policy in e en ion, o all empe a u e le els, highe phs a e he op ion
wi h he lowes cos . The isocos cu es show a s eepe inc ease owa ds high phs so ha
he e is in any case a high ph al e na i e o each empe a u e le el. In oducing an emis-
sion ax, dec eases he slope o he isocos cu es a he end o highe phs, he e addi ional
cos o paying he emission ax a e added o he o al cos s. Wi h ha , he slope a lowe ph
is highe so ha o all empe a u e le els a lowe ph cons i u es he echnology wi h he
lowes cos s. Analogously, a subsidy depending on he ph dec eases he slope o he isocos
cu es a high ph. In con as o he case o emission axes, he e ec does no scale wi h
he chosen empe a u e le el, so ha o high empe a u e le els he shape emains simila
o he case wi hou subsidy, as he ela i e impac is lowe . A low- empe a u e le els, he
impac o he subsidy, howe e , is highe . The household can ake he subsidy p o i om
he highe e iciency and each highe empe a u e le els, o wai e he subsidy and emain
on lowe empe a u e le els.
Fig. 9 Illus a ion o he isocos cu es o he household’s decision p oblem. The da ke he colo , he
highe he cos s. The le plo shows he isocos cu es o he o iginal p oblem, he middle he isocos s
unde an emission ax a e, and he plo o he igh he isocos s gi en a echnology subsidy. The plo s a e
based on he inpu s o he nume ical case s udy
1 3
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