P.S.P.
2
/10-2-96
I I I
ENCUENTRO
DE
ECONOMIA
PUBLICA
Depa amen o
de Teo ía Económica y Economía Polí ica
Uni e sidad
de
Se illa
Se illa
9, 10 de
eb e o
de 1995
PONENCIA
The o igin p incipie and he
wel a e
gains om
indi ec ax
ha moniza ion.
Miguel Ángel LÓPEZ GARCÍA
Depa amen o
de Economía Aplicada.
Uni e sidad
Au ónoma de
Ba celona.
In oduc ion
The
li e a u e dealing
wi h
he coo dina ion o economic policies among coun ies o
g oups
o coun ies in an in eg a ed wo ld
s ands
ou as one o he mos p ominen
de elopmen s o he las ew yea s. Al hough no he only one, a clea applica ion o he esul s
eme ging om his li e a u e is associa ed
wi h
he ax app oxima ion e o s
ha
ha e been
ca ied
ou
in
he Eu opean
Union,
and, wi hou any
doub ,
he abo e-men ioned de elopmen
canno be unde s ood wi hou a e e ence o
hese
eal wo ld e en s. One o he issues mos
ac i ely
esea ched has p obably been
ha
o indi ec axa ion, s imula ed by he Eu opean
Comission
p oposals aimed a ha monizing
alué
added
axes and
excises.
In pa icula , some
ques ions ela ed o ax compe i ion ha e been analyzed
in
di e en con ex s
[Min z
and
Tulkens
(1986),
de C omb ugghe and Tulkens
(1990),
Sinn
(1990),
Lockwood
(1993),
Kanbu and
Keen
(1993)]
as
well
as he wel a e e ec s o indi ec ax ha moniza ion policies
[Keen
(1987,1989.a,1989.b),
Tu unen-Red and Woodland
(1991),
Keen
and
Lahi i
(1993)].
The
amewo k o he analysis o he impac o ha monizing e o ms has been he
des ina ion
p incipie,
i.e., he p incipie
ha
in e na ionally aded commodi ies a e axed a he
a es o (and he e enue acc ues o) he coun y in
which
inal
consump ion akes place. The
al e na i e o he des ina ion p incipie is he o igin, o sou ce, p incipie, unde
which
commodi ies en e ing in ema ional
ade
a e axed a he a es p e ailing in he coun y whe e
hey a e p oduced ( his being he one
which
collec s he e enue). Al hough he des ina ion
p incipie
has been he cen al idea go e ning he ha monizing e o s o indi ec axa ion
ha
ha e been ca ied ou by he Eu opean
Comission,
he aboli ion o
bo de
con ols has ende ed
i
unsus ainable. The de ini i e sys em, o be enac ed a he s a o 1997, main ains he
des ina ion sys em o ansac ions be ween i ms bu c oss-bo de pu chases by
indi iduáis
will
be axed on an o igin basis,
hus
appea ing as a mixed sys em.
The
pu pose
o his
pape
is o es ablish a pa allelism be ween he analyses in
Keen
(1987,1989.a)
e e ed o indi ec ax ha moniza ion when axes a e le ied acco ding o he
des ina ion p incipie and i s coun e pa when axes a e imposed on an o igin basis.
Using
a
simple wo-coun y model o in ema ional
ade
i is a gued
ha
indi ec ax ha moniza ion
unde he o igin p incipie, conside ed as a mo emen o domes ic axes owa ds an
app op ia ely designed "a e age" ax s uc u e, is po en ially Pa e o
imp o ing,
in he sense
ha
he wel a e o a gi en coun y can be inc eased p o ided
ha
he
o he
coun y's wel a e is kep
unchanged
wi h
he aid o an in ema ional ans e . In he same
ein,
i is shown
ha
i he
ini ial
posi ion is a Nash equilib ium,
he e
a e si ua ions unde
which
he abo e-men ioned
1
e o m
may
gené a e
an ac ual Pa e o imp o emen , so
ha
bo h coun ies imp o e hei wel a e
wi hou any need o a compensa ing in ema ional ans e .
As
s a ed abo e, he de ini i e sys em
will
be a
mixed
one, so
ha
he
pu é
o igin case is
no he mos ealis ic amewo k om a policy poin o
iew.
Howe e , i may be use ul in
yielding
indica ions
ha ,
coupled
wi h
he esul s
ha
ha e been ob ained unde he des ina ion
p incipie,
p o ide insigh s on he e ec s o he de ini i e sys em. In he same way as
Keen
(1987,1989.a)
cons uc s his ha monizing e o m unde he des ina ion p incipie in such a way
ha
(neglec ing income e ec s)
wo ld
p oduce p ices a e unchanged, he coun e pa o his
analysis
unde he o igin p incipie
does
no a ec
wo ld
consume p ices.
This
pa alellism
ansla es in o modi ying he common
a ge
owa ds
which
coun ies ha monize hei indi ec
ax
s uc u es,
which
does
no depend on
local
demand esponses bu on
local
supply
esponses. The s uc u e o he
pape
is as
ollows.
In sec ion 1 he basic model is se up.
Sec ion
2 conside e ax ha moniza ion as a po en ial Pa e o imp o emen . Sec ion 3 poses he
ques ion whe he he speci ic
kind
o ha monizing e o m being analyzed can also esul in an
ac ual
Pa e o imp o emen .
Sec ion
4
includes
some addi ional commen s.
1.
The model
The
basic amewo k is a s anda d model o in ema ional
ade
[Dixi
and No man
(1980)]
in
which
wo coun ies, labelled as "home" and "ab oad",
ade
in N commodi ies.
Each
coun y's
a iables
a e ep esen ed by lowe case and uppe case le e s espec i ely, and
he e
is a single consume
in
each o hem. The only dis o ions a e due o consump ion axes,
le ied
on an o igin basis, so
ha
commodi ies a e axed a he a es
p e ailing
in he coun y in
which
hey a e p oduced, his being he coun y
which
collec s he ax e enue.
Since,
assuming away anspo cos s, he applica ion o he o igin p incipie implies
ha
consume
p ices
in each coun y a e he same, we ha e he ollowing ela ionship be ween consume
p ices,
q-Q, p oduce p ices in each coun y, p and P, and he ax ins umen s, and
T:
[1]
P = q- P=q-T
whe e axes a e exp essed in speci ic e ms.1
1
Since he applica ion o he o igin p incipie implies ha expo s a e axed and impo s a e exemp ed, he home
(ab oad)
coun y's consume mus be indi e en , in
equilib ium,
be ween
payingp + (P + T) o domes ically-
p oduced goodsand P + T (p + ) o impo ed
goods.
Thus,
consume p ices a e equalized ac oss coun ies, i.e.,
q = Q. On he wo king and consequences o he o igin p incipie see Cnossen and Shoup (1987) and Keen
(1990,1993).
2
The
home and o eign consume s can be cha ac e ized by hei expendi u e unc ions,
e{q,ü)
and
E(q,
U),
whe e u and U s and o he
u ili y
le éis
achie ed by he consume in each
coun y. Tax e enue is e u ned o he
indi iduáis
as a lump sum paymen . As o he
p oduc ion
side,
i
is
assumed
ha
bo h coun ies beha e
compe i i ely,
and hei beha iou can
be esumed in he e enue unc ions
(p)
and
R(P).2
Since
he
pa ial
de i a i es
o he expendi u e and e enue unc ions
yield,
espec i ely,
he compensa ed demand and supply unc ions, he
wo ld
ma ke -clea ing condi ions o he N
commodi ies a e
gi en
by:
[2]
e¿q,u)
+ E¿q,
U)
= p(p) + Rp(P)
whe e
he subindices
deno e
he
( ec o
o )
pa ial
de i a i es
o he ele an unc ions.
Consume
expendi u e in each coun y equals na ional income a domes ic p ices plus
ax
e enue.
Using
he sign' o
deno e
ansposi ion, he
budge
cons ain s
in
each coun y can
be
w i en
as:
[3]
e(q,u) = (p) + ' p(p) + qxz
[4]
E(q,U)
= R(P) + T'R iP)-qlz
whe e
' p(p) and T' R (P) exp ess ax e enue in each coun y. The e m z ep esen s a
ans e o commodi y
1
om he o eign coun y o he home one. I s pu pose is o cha ac e ize
e o ms
en ailing a po en ial Pa e o imp o emen , in he sense
ha
u can be inc eased o a
gi en
alué
o U. The ole o z
is
jus
ha
o assu ing
ha
he o eign
u ili y
le el
does
no
change. On he o he hand, z = 0 in [3] and [4] when he ocus is on cha ac e izing an ac ual
Pa e o imp o emen , i.e., a si ua ion in
which
bo h « and U inc ease wi hou any need o an
in ema ional
ans e .
As
a ma e o
no maliza ion,
commodi y
1
is aken o be he nume ai e (so q = 1) and
is
assumed o be un axed in bo h coun ies
(i.e.,
= T =
0).
In o de o
a oid
excessi e
no a ion, ec o
p ices
will
he ea e be in e p e ed as being oiN-
dimensión.
By
Wal as'
Law
one o he N+2 equa ions in
[2]-[4]
can be d opped, so we can
d op
he equilib ium condi ion
o
commodi y 1. The e o e he sys em in
[2]-[4]
can be desc ibed as N+l independen
equa ions
wi h
N+l a iables. In he sea ch o a po en ial Pa e o imp o emen he la e a e
N-l
ela i e consume p ices, q, he home
u ili y
le el,
u, and he size o he in ema ional
2
The
e enue
(o
GNP)
unc ion, exp essing he
alué
o p oduc ion a gi en p oduce p ices (and amoun s o
he
p ima y
ac o s), is ex ensi ely discussed in Dixi and No man (1980, ch. 2).
3
ans e , z, gi en he ax pa ame e s and T as
well
as he o eign
u ili y
le el,
U. Al e na i ely,
in
he sea ch o an ac ual Pa e o imp o emen he N+l
a iables
a e q, u and U and he
pa ame e s a e / and T.
2. Tax Ha moniza ion as a Po en ial Pa e o Imp o emen
Conside
i s
ax ha moniza ion as a po en ial Pa e o imp o emen , so
ha
he policy
leads o an inc ease in one coun y's wel a e when i is accompanied by an app op ia e
in ema ional ans e o he
o he
coun y so
ha
i s wel a e
le el
is kep cons an . We can
hus
e alúa e
in
[2]-[4]
he wel a e e ec s in e ms o he
home
coun y's wel a e, du, o an
a bi a y ax e o m, {d ,dT}, coupled
wi h
he ans e , dz, equi ed o hold U unchanged.
Di e en ia ing
in
[2]-[4]
wi h
dU = 0, we ha e:
[5]
eq/iu
+
[eqj
+
EC í-
pp - Rpp]dq +
ppd
+
RPPdT
= 0N.i
[6]
e,¿lu+[eq- p- pp ydq
+
' ppd -dz
= 0
[7]
[Eq-Rp-RPPT],dq+T'Rppd +dz = 0
whe e is he (N-1)- ec o o ze oes.
Thus,
elimina ing dz in
[6]
and
[7]:
du] = -( ' ppd +T'RPPdT) •
dq [
-{ ppd
+ RppdT)
whe e A = +
Egj
- pp -
Rpp,
i.e, he ma ix o he de i a i es o he compensa ed wo ld
excess demand o he non-nume ai e
goods
wi h
espec o he non-nume ai e p ices, is
nega i e semi-de ini e. I
will
be assumed
h oughou
ha
he e
is enough subs i u abili y in
demand o p oduc ion be ween he nume ai e good and he
o he
goods
o ensu e
ha
A
will
be
nega i e de ini e.3
The
sys em in
[8]
allows
one o ob ain an exp ession o he change in
home
u ili y,
du,
as a unc ion o he e o m associa ed
wi h
d and dT:
-{ '
ppd
+ T'
RppdT)
-( pp
+
RPPT)'
-( ppd + RppdT) A
whe e:
3
See Dixi and No man (1980, ch. 5).
[8]
-( pp +RPPT)'
'qu
[9]
du -
4

[10]
a = eu + ( pp +
RPPT)
'A^e^
and i can be shown ha a is posi i e whene e an inc ease in he home coun y's endowmen
o
he
i s
commodi y, a cons an ax a es and o eign
u ili y,
implies a s ic po en ial Pa e o
imp o emen . We
will
assume his is he case.
The
no ion o ha moniza ion is usually aken o mean making he ax sys ems mo e
"uni o m".
This
en ails bo h a p ocess o con e gence owa ds a common
a ge
and he
sugges ion o de e mining his
a ge
as some
kind
o a e age o he
exis ing
ax s uc u es. The
i s
ques ion can be app oached as a p og am o domes ic ax e o ms
implying
a uni o m
p opo iona e con e gence o he ax a es in bo h coun ies owa ds a ce ain common s uc u e
H,
i.e.:
whe e H is a N-l ec o and /3 is a
small
posi i e scala
which
measu es he
"size"
o he
e o m.
As o he second ques ion, i.e., he choice o he common
a ge
o
which
bo h
coun ies "ha monize" hei axes, he coun e pa o he p oposi ion shown in
Keen
(1987)
e e s o he pa icula class o ha monizing e o ms [11]
which
imply
a con e gence owa ds
he ec o
The
in e p e a ion o
[12]
becomes clea e when i
is
ew i en as:
[13]
H=<P +(INA-<P)T
whe e
<P
= [ pp + Rpp]'l pp and is he iden i y ma ix o o de N-l, so
ha
(Ip¡_i
-
<P)
=
[ pp + RpP]'1Rpp. As shown in
[13],
His a
ma ix
weigh ed a e age o he ax s uc u es in he
wo coun ies whe e he weigh s depend on
local
supply esponses. In pa icula , i
hese
local
supply
esponses a e iden ical a he s a ing posi ion, i.e., pp = RPp, [13] becomes
H=
(l/2)(í+7),
and each componen o His loca ed jus midway be ween he co esponding
componen s o he
ini ial
domes ic ax s uc u es and T.
Now
we can show
ha
he ha monizing e o m unde examina ion leads o a wel a e
imp o emen :
[11]
[12]
H=
[ pp + RppY pp +
RPPT)
5
P oposi ion 1: When
axes
a e
le ied
acco ding o he o igin p incipie, and
gi en
any
a bi a y
ini ialposi ionin
which * T, he ha monizing e o m in
[11]-[13],
consis ing in a
p opo iona e
con e gence
owa ds
an
app op ia e
weigh ed
a e age
o he
exis ing
domes ic
ax
s uc u es,
gene ales
a
po en ial
Pa e o
imp o emen .
P oo . The p oo uns pa allel o
ha
o
Keen
(1987)
and hinges on he ac
ha
[11]-[13]
imply:
[14]
ppd +
RppdT
=
OAM
whose subs i u ion in
[9]
gi es ise o:
[15]
du=
±( ' pPd +T'RppdT)
= ^-{T- yRPp$(T- )>0
whe e he inequali y ollows om he ac
ha
he ma ix
Rpp<P=
Rp [ pp + Rpp' 1 pp =
Tpi
+ Rpp}1 is posi i e de ini e.
Q.E.D.
Some in ui ion on he esul can be ob ained i we neglec income e ec s o he non-
nume a ie goods, i.e., i e^ =
0p¡. .
Subs i u ing in
[8]
and using
[14]
p o ides dq-
OJV-I,
so
ha
wo ld
consume p ices do no
a y.
The e o e, he ha monizing e o m is designed o lea e
consume p ices unchanged. As a consequence,
wo ld
demand,
e¿ q,u)
+
E< q,U),
will
no
change, as nei he
will
wo ld
supply, p(p) +
Rp(P).
The only e ec o he policy is he
" ealloca ion"
o p oduc ion be ween coun ies so
ha
he
agg ega e
wel a e loss om dis o ing
axes is dec eased.
A
g aphical explana ion is p o ided
in
Figu e
l.4
I shows he
simpli ied
case in
which
he wo coun ies ha e he same supply schedule o a single axed good whose consume
wo ld
p ice is q. The excess bu den associa ed
wi h
he axes and T in each coun y is gi en
by ABC
in coun y 1 and
ADE
in coun y 2. In his case in
which
supply esponses a e he
same, i he wo coun ies ha monize hei axes a he
le el
(1/2)
( + T) implied by
[12],
he
educ ion in
excess
bu den in he high- ax coun y is
BCFG,
which
exceeds he inc ease in he
low- ax
coun y,
DEFG.
Since he dis ances y
¿y
and y y a e he same,
agg ega e
supply
does
no
a y.
P o ided he app op ia e in ema ional ans e is made, one coun y can imp o e
wi hou he o he one expe iencing any wel a e change.
Figu e
1 is he eoun e pa in he p esen con ex o he analysis o ha moniza ion unde he des ina ion
p incipie
in Keen (1990,1993). I am indeb ed o Ben Lockwood o
sugges ing
his diag am in his discussion o
he pape a he Copenhagen mee ing o he
HCM
esea ch ne wo k on
"Fiscal
Implica ions o Eu opean
In eg a ion".
6
3.
Tax Ha moniza ion as an Ac ual Pa e o Imp o emen
While
he p e ious sec ion has a gued
ha
he ha monizing e o m
[11]-[13]
is wel a e
imp o ing
in he sense
ha
i inc eases he
u ili y
le el
o a coun y p o ided he
o he
coun y's
wel a e
is kep unchanged, he ques ion
ha
a ises is whe he his e o m may also imply an
ac ual Pa e o imp o emen , i.e., a gain in bo h coun ies' u ili y wi hou any need o an
in ema ional compensa ion.
This
is he ques ion discussed in
Keen
(1989.a) when axes a e
le ied
acco ding o he des ina ion p incipie unde he assump ion
ha
he a e no income e ec s
o
he N-l axed commodi ies
(i.e.,
—
Equ - 0#_i in e ms o he
p esen
model).
The
analysis can now be ca ied ou o cing z = 0 in
[2]-[4]
and in e p e ing he N+l
a iables
as N-l consume p ices, q, and wo u ili y
le éis,
u and
U,
o gi en
alúes
o he ax
pa ame e s and
T.
Di e en ia ing o ally
we
ob ain:
[16]
e^/iu +
EqUdU
+ Adq +
ppd
+
RppdT
=
Oy.i
[17]
eudu
+ [eq- p -
pp ]'dq
+
' ppd
= 0
[18]
EudU+[Eq-Rp-RpPT]'dq+T'RppdT =0
1
Using
[16]
o isola e dq, he e ec s on wel a e, du and dU, associa ed
wi h
an a bi a y
e o m
{d ,dT} a e he solu ion o he sys em: 5
[19]
c«
-
(eq
- p -
pp )
'A' eq4 - {eq - p - pp )
'A
EqU
-
{Eq-RP-
RppT)'A'Xeqi
E -(Eq-RP-RPPT)'A'lEqU_
dU}
=
L
dU i
-
'
ppd
+ (eq - p - pp ) 'A'
( ppd
+ RppdT)
T'RppdT
+{Eq-Rp-
RppT)'A~ ppd +
RppdT)
_
We
can now assume, as in
Keen
(1989.a),
ha
he e
a e no income e ec s o he N-l
axed
goods,
i.e.:
[20]
Zqu
=
Equ=0 í-l
so
ha
all
income e ec s a e h ough he un axed nume ai e.
This
allows
one o ew i e
[19]
as:
{eq- p- pp yAA
[21]
eju
EudU
' +(eq- p- pp )'A~
(Eq-Rp-RpPT)'A
1
T'
+{Eq-Rp-RPPT)'A
ppd
RppdT
Sol ins
o
du
we ob ain:
[22]
du = M[ ' - (eq - p -
pp )']AA ppd
- (eq - p -
pp )
'A'lRPPdT}
and a
simila
exp ession o dU. Focusing on he ha monizing e o ms
[11]-[13],
and ecalling
ha
hey imply
ppd
+
RppdT
= 0#-i,
[22]
becomes:
[23]
du= —{ 'S - 'ST)
5
In
he
pa icula
case o he ha monizing e o ms [11]-[13], and using [14], he igh hand side in [19] becomes
-
í
' ppd
, -
T'RppdT']
' -
We can obse e ha adding he exp essions o
du
and dU
in
[19] we md a weigh ed
sum
o he wel a e changes expe ienced by bo h coun ies:
[eu + { pp
+
RppT)'Aleq^du
+
[E
+
( pp
+
RPPT)'A'X
Eqjj dU
-
- (í
' ppd
+
T
'RppdT)
> 0
whe e he weigh s a e a (> 0) in [10] and i s coun e pa A (> 0) o he o eign coun y. Since his is posi i e
using he igh hand side in [15], he ha monizing e o m [11]-[13] is wel a e-enhancing in he
sense
ha i
inc eases he
alué
o a social wel a e unc ion W = au + AU, i.e., an addi i e measu e o wo ld wel a e whe e
he weig hs a ached o each coun y a e a
and
A. Ac ually, his esul is no su p ising when compa ed o ha
in
sec ion 2, and he p ocedu e in ha sec ion has he ad an age o ocusing on he ole o he in ema ional
ans e
dz
equi ed
o
du
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