Tax E asion, Technology Shocks, and he Cyclicali y o
Go e nmen Re enues
Jo di Caballé
Uni e si a Au ònoma de Ba celona and MOVE
Judi h Panadés
Uni e si a Au ònoma de Ba celona and MOVE
Ma ch 7, 2011
Abs ac
This pape analyzes he beha io o he ax e enue o ou pu a io o e he busi-
ness cycle. In o de o eplica e he empi ical e idence, we de elop a simple model
combining he s anda d Ak g ow h model wi h he ax e asion phenomenon. When
indi iduals conceal pa o hei ue income om he ax au ho i y, hey ace he
isk o being audi ed and hence o paying he co esponding …ne. Unde he empi i-
cally plausible assump ions ha he in e empo al elas ici y o subs i u ion exhibi s
a su¢ cien ly small alue and ha p oduc i i y shocks a e se ially co ela ed, we
show ha he elas ici y o go e nmen e enue wi h espec o ou pu is la ge
han one, which ag ees wi h he empi ical e idence. This esul holds e en i he
ax sys em displays ‡a ax a es. We ex end he p e ious se up o gene a e la ge
…scal de…ci s when he economy expe iences a ecession.
JEL Classi…ca ion Numbe : H23, H26, O41
Keywo ds: Tax e asion, Technology shocks, G ow h
Financial suppo o bo h au ho s om he Spanish Minis y o Educa ion h ough g an ECO2009-
09847 and he Gene ali a o Ca alonia h ough g an SGR2009-00350 and, o he … s au ho om
he ICREA Academia p og am, is also g a e ully acknowledged.
Co espondence add ess: Jo di Caballe. Uni e si a Au ònoma de Ba celona. Depa amen
d’Economia i d’His ò ia Econòmica. Edi…ci B. 08193 Bella e a (Ba celona). Spain.
E-mail: jo [email protected]
1. In oduc ion
In his pape , we ollow he app oach in oduced by Kydland and P esco (1982) o
s udy he ole played by eal echnology shocks in d i ing business ‡uc ua ion. We will
ocus ou analysis on he esponse o go e nmen e enue o echnology shocks. The
beha io o go e nmen e enue o e he business cycle has ecei ed some a en ion in
he empi ical li e a u e o ecen yea s. I is well known ha economic ecessions end
o educe he ax e enue and his makes di¢ cul o go e nmen s o und hei exis ing
spending p og ams. Mo eo e , du ing expansion pe iods ax e enue inc eases and his
c ea es a new addi ional poli ical p essu e on he go e nmen o inc ease public spend-
ing. The e o e, he empi ical analysis o his ques ion ocuses on ob aining es ima es o
he income elas ici y o ax e enue in o de o …nd ou whe he ax e enues exhibi
a mo e han p opo ional esponse o ou pu ‡uc ua ions.1I is impo an o dis in-
guish be ween he long- un income elas ici y o ax e enue, which shows how e enues
will g ow o e ime as pe manen income g ows, and he sho - un income elas ici y
o ax e enue, which shows how much e enues will ‡uc ua e o e he business cycle.
Fo ins ance, Holcombe and Sobel (1997) es ima e bo h he sho - un pe sonal income
elas ici y o ax e enue and he sho - un pe sonal income elas ici y o he ax base
o U.S. s a es and …nd ha on a e age hey a e equal o 1.392 and 1.192 espec i ely.2
Hence, he a e age elas ici y es ima e sugges s ha a one pe cen inc ease in pe sonal
income should esul in a 1.4 pe cen inc ease in he ax e enue. Recen s udies by
Dye and Me iman (2004) and B uce e al. (2006) p o ide mo e accu a e es ima es
ha also suppo he idea ha he sho - un pe sonal income elas ici y o he ax base
ends o be la ge han one.
The main objec i e o his pape is o p o ide a heo e ical se up ha can be con-
sis en wi h hese empi ical …ndings. The s anda d Ak g ow h model wi h ‡a ax a es
p edic s ha he go e nmen e enue o ou pu a io emains cons an when a echnol-
ogy (o o al ac o p oduc i i y) shock akes place. Unde ‡a ax a es, a echnology
1See Dye (2004) o a e iew o his li e a u e.
2Resea che s dis inguish be ween wo ax measu es when es ima ing elas ici ies: he ax base o he
ax e enue. Tax e enue da a by he ype o ax is easily a ailable o se e al de eloped coun ies bu
hey can embed ax a e changes and his leads o a bias in he sho - un elas ici y es ima o .
1
shock a¤ec s symme ically ou pu and go e nmen e enue since go e nmen e enue
is a cons an p opo ion o ou pu . The e o e, he s anda d Ak g ow h model wi h ‡a
ax a es does no o¤e a plausible explana ion o he empi ical e idence as he alue
o he sho - un income elas ici y o ax e enue p edic ed by he model is equal o one.
The e a e se e al candida e explana ions o he high empi ical income elas ici y
o ax e enue. One ob ious explana ion consis s o dispensing wi h he assump ion
o cons an ma ginal ax a es and conside ing ins ead a p og essi e ax schedule on
income. Clea ly, as he a e age ax a es inc ease wi h income he go e nmen e enue
will inc ease mo e han he agg ega e income.
Ano he al e na i e explana ion o he high income elas ici y o go e nmen e -
enue elies on he beha io al esponses o income shocks. When he economy de e i-
o a es, indi iduals migh inc ease hei sa ings and educe consump ion, especially o
i ems like du able goods. Then, a e he economy s a s o eco e , hey migh make
some o he pu chases ha had p e iously been pu o¤ du ing he ecession. I he
go e nmen collec axes on consump ion, hen he p e ious beha io o consump ion
along he business esul s in a high elas ici y o e enue.
In his pape we p o ide an al e na i e mechanism gene a ing he desi ed pa e n
o cyclicali y o go e nmen e enue. This mechanism complemen s he p e ious ones
since elies exclusi ely on a di¤e en assump ion, namely, he exis ence o ax e asion
unde a ‡a ax a e on income. We will show ha e en his simple ax s uc u e is able
o gene a e an income elas ici y o ax e enue la ge han one unde se ially co ela ed
p oduc i i y shocks when he alue o he in e se o he in e empo al elas ici y o
subs i u ion (IES, hence o h) is la ge han one. O cou se, unde a p og essi e ax
sys em ou mechanism based on ax e asion will ein o ce he p e ious esul and, hus,
he go e nmen e enue will o e shoo e en mo e as a esponse o a p oduc i i y shock.
The same can be said i axes we e imposed on o he p ocyclical endogenous a iables
like consump ion. No e ha ou model displays an income elas ici y o go e nmen
e enue la ge han one e en o economies ha ing ax sys ems cha ac e ized by ‡a
ax a es.3
3In his espec , i should be men ioned ha du ing he las decade some coun ies made an impo -
an e o m o hei sys em o income axa ion. They eplaced hei p e ious p og essi e ax s uc u e
by a pu e ‡a ax a e. Fo ins ance, Russia, Se bia, I aq, Slo akia and Uk aine se a ‡a ax a e o
13%, 14%, 15%, 19% and 13%, espec i ely.
2
In o de o endow he s anda d Ak g ow h model wi h ax e asion, we assume ha
indi iduals ha e o choose in each pe iod he amoun o income hey wan o consume
and he amoun o income hey wan o e ade. When indi iduals conceal pa o hei
ue income om he ax au ho i y, hey ace he isk o being audi ed and hence o
paying he co esponding …ne. Bo h axes and …nes de e mine indi idual sa ing and
he a e o capi al accumula ion. Thus, wo ypes o shocks coexis in his model:
he agg ega e shock, which is gi en by changes in he o al ac o p oduc i i y o he
economy and he idiosync a ic shock, which is in oduced by means o he ax inspec ion
policy. The main esul o ou analysis says ha , when echnology shocks a e se ially
co ela ed, he alue o he IES ully de e mines he beha io o he go e nmen e enue
o GDP a io. In pa icula , when he in e se o IES is la ge han one, he go e nmen
e enue inc eases mo e han ou pu in he p esence o a posi i e echnology shock. In
his case, he elas ici y o ax e enue wi h espec o GDP is la ge han one, which is
consis en wi h he a o emen ioned empi ical egula i y. Mo eo e , when ei he he IES
is equal o one o echnology shocks a e no se ially co ela ed, he uni a y elas ici y o
ax e enue is eco e ed. The in ui ion o his esul lies in he ac ha , when shocks
a e se ially co ela ed, an inc ease in cu en o al ac o p oduc i i y means ha he
expec ed o al p oduc i i y and, hus, he expec ed e u n o in es men in he nex
pe iod will be highe . The e o e, sa ing will inc ease o dec ease depending on he
alue o he IES. Mo eo e , unde ax e asion, unde epo ing he ue income is also
a mechanism ha allows indi iduals o ans e p esen income o he u u e. This
means ha , i indi iduals decide o sa e mo e (less) as a esponse o a eal business
shock hey will also decide o e ade mo e (less) axes and his will esul in less (mo e)
e enues aised by he go e nmen .
In he nex sec ion we de elop he basic dynamic model o ax e asion. In Sec ion
3, we will discuss he implica ions o a echnology shock on he go e nmen e enue o
GDP a io. In sec ion 4, we ex end ou model o cope wi h he implica ions o he
budge de…ci s un by he go e nmen . Some …nal ema ks conclude he pape .
2. The Model
Le us conside a compe i i e economy in disc e e ime wi h a con inuum o ex-an e
iden ical indi iduals who a e uni o mly dis ibu ed on he in e al [0;1] :Each indi-
3
idual ihas access o a common echnology ep esen ed by he p oduc ion unc ion
yi; =A ki; whe e A >0is he andom o al ac o p oduc i i y (TFP), yi; is he
ou pu pe capi a o indi idual iand ki; is he capi al pe capi a o indi idual iin
pe iod .4We assume ha capi al ully dep ecia es a e one pe iod.
We assume ha he s ochas ic p ocess o s ic ly posi i e TFP shocks A g ollow
a loga i hmic au o eg essi e p ocess,
ln A +1 =ln A +u +1;(2.1)
whe e 2[0;1] and u +1 is i.i.d. and no mally dis ibu ed wi h ze o mean and a iance
2:No e ha he ealiza ion o TFP shocks a e he same o all indi iduals. The e o e,
p oduc ion is exposed o mac oeconomic (o non-idiosync a ic) TFP shocks.
Ou pu can be de o ed o ei he consump ion o in es men . A e p oduc ion has
aken place, each indi idual idecides bo h his consump ion ci; and he amoun xi; o
decla ed income, and hen pays he co esponding income ax a he a e 2(0;1) :I
he is inspec ed by he ax en o cemen agency, he o al amoun o un epo ed income
is disco e ed and he axpaye has o pay a penal y a he ‡a a e  > 1;which
is imposed on he amoun o e aded axes (as in Yi zhaki, 1974).5Inspec ion o a
pa icula indi idual is an e en ha occu s wi h p obabili y p2(0;1) :We also assume
ha p < 1in o de o ensu e posi i e ax e asion.
The amoun o ou pu emaining a e consump ion has aken place and axes and
(po en ial) penal ies ha e been paid cons i u es he capi al s ock ki; +1 ha is used
o p oduc ion in he nex pe iod. The e o e, he budge cons ain o an audi ed
indi idual is
A ki; xi;  (A ki; xi; ) = ci; +ki; +1;
whe eas he budge cons ain o a non-audi ed indi idual is
A ki; xi; =ci; +ki; +1:
We assume ha he amoun o axes collec ed by he ax agency is de o ed o
…nancing go e nmen spending ha en e s in o he ins an aneous u ili y o indi iduals
4See Rebelo (1991) o a model whe e he Ak p oduc ion unc ion a ises endogenously when physical
and human capi al a e pe ec subs i u es. In his case he capi al s ock kembodies bo h ypes o
capi al.
5I he penal y a e we e smalle han one, ax e asion would be encou aged by he ax au ho i y.
4

in an addi i e way. The e o e, he ma ginal a e o subs i u ion o p i a e consump ion
be ween wo a bi a y pe iods is no a¤ec ed by he le el o go e nmen spending. Since
consume s ake as gi en he pa h o go e nmen spending, he u ili y acc uing om his
spending can be supp essed om he consume s’objec i e unc ion. Indi iduals a e
assumed o maximize he ollowing expec ed discoun ed sum o ins an aneous u ili ies:
1
X
s=0
 E [U(ci; +s)] ;(2.2)
whe e 2(0;1) is he discoun ac o and E []is he condi ional expec a ion gi en he
in o ma ion a ailable a pe iod . We assume ha he ins an aneous u ili y unc ion is
isoelas ic,
U(ci; ) = (ci; )1
1;
whe e he pa ame e alue plays he usual double ole as he alue o he (cons an )
ela i e isk a e sion index and as he alue o he in e se o he IES.
The amoun o un epo ed income in pe iod o each indi idual iis i; =A ki; xi; :
Hence, we can use he p e ious budge cons ain s o w i e he s ochas ic law o mo ion
o capi al pe capi a as
ki; +1 =8
>
>
<
>
>
:
(1 )A ki; ci; (1)i; ;wi h p obabili y p;
(1 )A ki; ci; +i; ;wi h p obabili y (1 p);
o , equi alen ly,
ki; +1 = (1 )A ki; ci; +i; hi;(2.3)
whe e hiis a andom a iable wi h he ollowing p obabili y unc ion:
(hi) = 8
>
>
<
>
>
:
p o h= 1 ;
1p o h= 1;
(2.4)
o all i2[0;1] :Mo eo e , he a iables hia e independen ly dis ibu ed ac oss indi-
iduals. No e ha E(hi) = 1 p > 0as we ha e assumed ha p < 1. We de…ne he
ne ue income pe capi a as
ni; = (1 )A ki; :(2.5)
5
Then, using (2:3) we can w i e ni; +1 as
ni; +1 = (1 )A +1 (ni; ci; +i; hi):(2.6)
Taking ni; as he s a e a iable o indi idual iin pe iod , and ci; and i; as he
con ol a iables, he Bellman equa ion o he s ochas ic dynamic p oblem aced by
his indi idual in pe iod be o e knowing i he is going o be audi ed o no is
V(ni; ) = Max
ci; ; i; g((ci; )1
1+E [V(ni; +1)]);(2.7)
whe e ni; +1 sa is…es (2:6) :I is well known ha he alue unc ion o his p oblem
is he isoelas ic unc ion, V(ni; ) = D
1(ni; )1wi h D > 0(see Hakansson, 1970):
The e o e, using (2:6) and compu ing he condi ional expec a ion E [V(ni; +1)], he
op imiza ion p oblem aced by a axpaye wi h ini ial a e - ax ue income ni; becomes
Max
ci; ; i; g((ci; )1
1+E D
1[(1 )A +1 (ni; ci; +i; hi)]1);(2.8)
Di¤e en ia ing wi h espec o he con ol a iables ci; and i; ;we ob ain he ollowing
… s o de condi ions o he p e ious p oblem:
(ci; )=DE h((1 )A +1)1(ni; ci; +i; hi)i;(2.9)
and
E [(1 )A +1 (ni; ci; +i; hi)]hi= 0:(2.10)
Using he independency be ween A +1 and hiand he dis ibu ion o he andom a i-
able higi en in (2:4) ;condi ion (2:9) becomes
(ci; )=D(1 )1 (1 p) (ni; ci; +i; )+p(ni; ci; +(1 )i; );
(2.11)
wi h
 E h(A +1)1i;
while condi ion (2:10) becomes
(1 p) (ni; ci; +i; )=p(1) (ni; ci; +(1 )i; ):(2.12)
Sol ing o ci; and i; in he sys em composed o equa ions (2:11) and (2:12), we ob ain
ci; = ni; ;(2.13)
6
and
i; =
(ni; ci; );(2.14)
whe e
 =1
1 + D(1 )1 (1 p)(1 + )+p(1 (1))1= ;(2.15)
and
=1p
p(1) 1= 1
1+(1) 1p
p(1) 1= >0:(2.16)
Applying he en elope heo em, ha is, U0(ci; ) = V0(ni; );i mus hold ha
c
i; =Dn
i; :(2.17)
Subs i u ing (2:13) in (2:17) and using (2:15) we ob ain
D=1
1 + D(1 )1 (1 p) (1 + )+p(1 (1))1= :
The e o e, sol ing o Din he p e ious equa ion we ge
D="1
1((1 )1 H)1= #
;(2.18)
whe e
H= (1 p) (1 + )+p(1 (1)):
Subs i u ing (2:18) in o (2:15) ;and using (2:13), and (2:14) ;we ge he ollowing
consump ion and e asion policies:
ci; =h1(1 )1H 1=ini; ;(2.19)
and
i; =
(1 )1H 1= ni; :(2.20)
No e ha , when p = 1, we ha e ha = 0 and, hence, H= 1. The e o e, when
p = 1;indi iduals do no e ade axes, i; = 0 o all i2[0;1] :Mo eo e , unde his
ull en o cemen policy conduc ed by he ax agency, he op imal consump ion policy
is he one appea ing in absence o ax e asion,
ci; =h1(1 )1 1=i(1 )A ki; :
7
In o de o ob ain he alue o he agg ega e a e - ax ue income n +1 in equilib-
ium, which is gi en by (2:6) ;we compu e
n +1 =Z[0;1]
ni; +1di = (1 )A +1 "Z[0;1]
ni; di Z[0;1]
ci; di +Z[0;1]
i; hidi#
= (1 )A +1 "Z[0;1]
ni; di Z[0;1]
ci; di + Z[0;1]
i; di! Z[0;1]
hidi!#
= (1 )A +1 [n c +(1 p) ];
whe e he hi d equali y ollows om he independence be ween he a iables hiand
i; a he beginning o pe iod ; whe eas he las equali y comes om he law o la ge
numbe s o a con inuum o i.i.d. andom a iables, acco ding o which R[0;1] hidi =
E(hi)=1p; and om he de…ni ions o agg ega e consump ion c R[0;1] ci; di,
agg ega e e asion  R[0;1] i; di; and agg ega e a e - ax ue income n R[0;1] ni; di.
In consequence, as ollows om (2:19) and (2:20) ; he agg ega e alues o consump ion
and e aded income a e
c =1(1 )1H 1=
| {z }

n ;(2.21)
and
 =
(1 )1H 1= n =
(1  )n :(2.22)
In o de o analyze he e¤ec o a TFP shock on e aded income and on consump ion,
we mus compu e he alue o  :Gi en ha he andom a iable u +1 is no mal
and hus he echnology shock A +1 is log-no mal, he condi ional expec a ion  
E h(A +1)1iis equal o
 =A(1)
exp (1 )22
2:(2.23)
The nex sec ion discusses he e¤ec o a TFP shock on bo h he amoun o e aded
income and he go e nmen e enue o GDP a io.
3. E¤ec s o TFP shocks
In o de o analyze he e¤ec o a echnology shock on go e nmen e enue o ou pu
a io, we should … s compu e he e¤ec o an inc ease o he TFP alue A on he
e asion o income a io  =y :Since agg ega e ou pu sa is…es y =A k and he he
8
(4.3) ha
(1 + g )1=A1
[(1 )H]1= A(1)=
1(1 + (1 p)) exp (1)22
2
so ha
E 1[1+g )]1=E 1A1

[(1 )H]1= A(1)=
1(1 + (1 p)) exp (1)22
2
=A
1e2=2
[(1 )H]1= A(1)=
1(1 + (1 p)) exp (1)22
2
=1
[(1 )H]1= A=
1(1 + (1 p)) exp (13+2)2
2;(4.6)
whe e he second equali y comes om he ac ha
E 1A1
=A
1e2=2;
and he hi d comes om some s aigh o wa d simpli…ca ion.
The e o e, using (4.5) and (4.6), he amoun o go e nmen spending in da e is
G =y 1
E 1[1+g )]1=A 1k 1
E 1[1+g )]1
=A 1k 1[(1 )H]1= A=
1(1 + (1 p)) exp (1 3+2)2
2
=A(+)=
1k 1[(1 )H]1= (1 + (1 p)) exp (1 3+2)2
2:
No e ha he go e nmen spending in depends on he alues o wo a iables known
a 1;namely, he capi al k 1and he he TFP shock A 1:
Conce ning he e¤ec i e go e nmen spending o GDP a io in pe iod , no e ha
G
y
=G
(1 + g )y 1
=
(1 + g )E 1[1+g )]1=
[(1 )H]1= A=
1(1 + (1 p)) exp (13+2)2
2
A [(1 )H]1= A(1)=
1(1 + (1 p)) exp (1)22
2=A
1e2=2
A
;(4.7)
whe e he second equali y comes om (4.5) and he hi d om (4.3) and (4.6).
15

As we ha e shown in he p e ious sec ion, he go e nmen e enue o GDP a io can
‡uc ua e in each pe iod wi h he echnological shock A in he p esence o ax e asion
(i.e., when p < 1) e en i he ax a e emains cons an ac oss pe iods (see (4.9)).
Mo eo e , we ha e jus seen in his sec ion ha he go e nmen spending o ou pu
a io a also ‡uc ua es wi h he shock A as he amoun o go e nmen spending was
decided in pe iod 1:
Conce ning he …scal de…ci o GDP a io, we can compu e G R
y om (4:7) and
(4:9) :No e om (4:7) ha he go e nmen spending o GDP a io s ic ly dec eases
wi h he inno a ion shock in A :Howe e , he go e nmen e enue o ou pu a io
inc eases (dec eases) wi h he inno a ion shock in A i  > 1(<1) when  > 0;while
i does no a y wi h A i ei he = 0 o = 1:The e o e, we ge he ollowing esul :
P oposi ion 4.1. Fo a gi en alue o A 1; he go e nmen de…ci o ou pu a io
G R
y is dec easing in he alue A o TFP i 1and  > 0. Mo eo e , he same
esul holds o all  > 0when = 0.
P oo : No e ha , i 1and  > 0; hen he go e nmen e enue o ou pu a io
weakly inc eases wi h A and, since he go e nmen spending o GDP a io s ic ly
dec eases wi h A o a gi en alue o A 1; he esul immedia ely ollows. When
= 0; he go e nmen de…ci is dec easing since he go e nmen e enue o ou pu
a io is no a¤ec ed by changes in A ;while he go e nmen spending o ou pu a io
s ic ly dec eases wi h A o a gi en alue o A 1:
The p e ious esul ag ees wi h he empi ical e idence since ell us ha , unde he
empi ically ele an case wi h 1and  > 0;…scal de…ci s inc ease when he cu en
a e o g ow h is lowe han he expec ed one. No e in his espec ha , as we ha e
shown a he beginning o his sec ion, he de ia ion o he ac ual a e o g ow h in
pe iod and i s expec a ion a 1 o a gi en alue A 1in pe iod 1is ully
explained by he ealiza ion A o he TFP in pe iod : Howe e , o he empi ically
mos implausible case  < 1;i TFP shocks a e posi i ely co ela ed,  > 0; he o e all
e¤ec on he public de…ci o GDP a io is ambiguous. In his case he e enue o GDP
a io dec eases when he e is a posi i e shock on TFP, which coupled wi h he dec ease
in he go e nmen spending o GDP a io, gi es aise o an ambiguous e¤ec on he
go e nmen de…ci o ou pu a io.
16
Le us …nish his sec ion wi h some commen s abou he selec ion o he ax a e
when he amoun o go e nmen spending is chosen a pe iod in ad ance. No e ha we
ha e bee implici ly assuming in ou p e ious analysis ha he selec ion o ax a es is
subjec o less disc e ion han go e nmen spending, ha is, ha ax a es a e se o
longe pe iods han he amoun o go e nmen spending. In ac , we we e making he
ex eme assump ion ha he alue o he ax a e was exogenously gi en. One way o
a ionalize his assump ion and make i consis en wi h balanced budge in he long
un consis s o assuming ha he go e nmen (o he legisla i e body) chooses a da e
0, be o e obse ing any echnological shock, he ax a e in o de o minimiza ion o
he uncondi ional expec ed squa e o he go e nmen de…ci o ou pu a io. The e o e,
he objec i e o he go e nmen is o choose he ax a e in o de o minimize
EG R
y 2
This a ge is ully achie ed achie ed when
ER
y =EG
y ;
which acco ding o he go e nmen spending objec i e becomes
ER
y =: (4.8)
as, om he law o i e a ed expec a ions, E(G /y ) = E(E 1(G /y )) = . Combin-
ing (3:2) wi h (3:1) we ob ain he go e nmen e enue o GDP a io
R
y
=(1 p)[H(1 )]1= A(1)=
exp (1 )22
2!:(4.9)
The uncondi ional expec a ion (i.e., he expec a ion a he ini ial da e 0 be o e obse -
ing any ealiza ion o he TFP shock) o he p e ious go e nmen e enue o GDP a io
can be easily compu ed by aking in o accoun he ollowing uncondi ional expec a ion:
EA(1)=
= exp 2(1 )22
22(1 2)!:
Plugging he p e ious exp ession in he uncondi ional expec a ion o he a io (4:9) ;
we ge
ER
y =(1 p)[H(1 )]1= exp 2(1 )22
22(1 2)!exp (1 )22
2!
17
=(1 p)[H(1 )]1= exp (1 )22
21 + 2
(1 2)!:
I is immedia e o see ha he p e ious expec a ion is s ic ly inc easing in he ax
a e and ends o 1 as con e ges o 1 and o a nega i e numbe when app oaches 0.
The e e o e, he e exis s a unique alue o he ax a e sol ing he equa ion (4.8) o
2(0;1). This is he ax a e ha balances he go e nmen budge in (uncondi ional)
expec ed e ms and ha is kep cons an o all pe iods in ou analysis.
5. Final Rema ks
In his pape , we ha e shown ha , by in oducing ax e asion in he s anda d Ak
model g ow h wi h ‡a ax a es, i is possible o ob ain an elas ici y o ax e enue
wi h espec o ou pu la ge han one, which ag ees wi h he empi ical e idence.
The e o e, ax e asion o¤e s by i sel an explana ion o he high income elas ici y o
go e nmen e enue ha complemen s o he explana ions elying ei he on p og essi e
income axa ion o on axes imposed on p ocyclical a iables. we ha e ex ended he
model o accoun o he cyclical beha io o …scal de…ci s when go e nmen has a
a ge conce ning he alue o i s spending ela i e o GDP. we show ha , unde a
plausible pa ame e es ic ion, …scal de…ci s become la ge in ecessions.
We ha e used o ou analysis a e y simple model o capi al accumula ion whe e he
s a ic po olio choice model o ax e asion p esen ed by Allingham and Sandmo (1972)
has been ex ended o a dynamic se up.8In his amewo k, consume s’decisions abou
how much income hey wan o epo no only a¤ec hei p esen consump ion bu
also hei u u e consump ion. The e o e, he esponse o consume s o posi i e TFP
shocks a¤ec s bo h he ax e asion decision and go e nmen e enue. In his se up, we
ha e shown how he e¤ec o a posi i e echnology shock on he go e nmen e enue
o GDP a io is ully cha ac e ized by he alue o IES pa ame e when TFP shocks
a e se ially co ela ed. In pa icula when he IES exhibi s a su¢ cien ly small alue,
a posi i e echnology shock makes indi iduals o lowe mo e han p opo ionally hei
amoun o e aded income in o de o main ain a smoo h pa h o consump ion o e ime.
The e o e, he go e nmen e enue inc eases mo e han ou pu and in consequence he
income elas ici y o ax e enue becomes la ge han one.
8See Lin andYang (2001) o a simila con ex .
18
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20