Inflation and nominal tax system in an open economy

European konomic

Review 24 (1984) 23-37. North-Hotlaud

University of Geneva, 1211 Geneva 4, Switzerland Received February

1982

This paper provides au analysis of the imp&cations of the interaction between inflation and a rCrx system which is not fully indexed within the contrxt of an open economy. The model used I-, c laracterkd by perfect foresight, full employment, imperfect substitutability between dlomesti; arid foreign assets, and an endogenous stock of capital. Three distinct channels through whn an increase rn the inflation rate disturbs, the initial equilibrium are analysed separately. Th#: gobal eB
Several features of current tax codes were clearly not intended for inflationary times an .I have not been amended despite the high rates of infiation of the last decade. As long as the general price level is constant, the facts that the income taxes are based on a nominal schedule and arc leviea on nominal interest income and nominal capital gains, that nominal interest payments are deductible and that capital depreciation is only possible OT!a historic cost basis do not really matter. But, with positive rates of inflation, these features increase the tax burden of the private sector, lower (increase) the after-tax real returns (costs) relative to the pre-tax real returns (costs) for lenders (borrowers), and decrease the returns to equit:, owners, all of which generate real distortions. The existing literature ’ has dealt with the problem of the interactions between inflation and the nominal features of present tax sysre comparing steady states of closed economies characterized inflation rates. The purpose of.’this aper is to broaden the to focus on the same i studies in two directions: first, we wa the specific fra,mework., which is more adequate for Euro can co~~~~~~es,of 3 *This paper P . .:4written during a stay as a Visiting Scholar at the Depar?lnent of Economics of MIT arrd then at the University of Geneva. I am grateful to Professor Robert M. Solow and nts. 1141remaining errors are naturally mint. ~~~~~~~,~~ sup to John Rust for s of the SAss Nation pie, Feldstein (1976). C&en an S

t?Ct4-2921/84/$3.00 0 1984, Elsevicr Science Publishers B.V. (North-Holland)

e a fill$ dynastic model which h short a.nd Ion usbdnent proce n on the long-E-Pi

e~~n~~llly; !3txond, we will pro

omy and the fi:xed exchange rate of our modei, rate can be thol~ght of as exogenous changes iw the t of the world.. Tbrou@prlout this paper, we wilt assume that these changes flation rate leave the pm-tax real returns on foreign assets assum~t.i~n enables us to focus on the distortions generated the nominal. tax system of the small open economy and abstract from used by the nominal features of the foreign tax n section 2. Section 3 shows that with a nominal in the inflation rate can be divided into three distinct aaalysed separately as far as their short and longens are concerned. &&on 4 gathers the partial results of the n and discusses them with respect to the net position of the as debtor or creditor to t’he rest of the world. The implications for elicit wiiEalso be briefly considered.

for tbi~ ana’iysis describes a small open economy under exchange rates and a. bond financed pubhc deficit. Its main

re is only one good for which the economy is a price taker. Since that no devaluation will occur, the price level and the inflation ed exogenously on the world market. The goods market urn is restored t.hrodgh the instantaneous adaptation of the trade to any discrep;-zncy betwxn domestic production: and absorprion. ssets are present in the model: money, foreign bonds, ee assets are assumed to be gross e last two are assume Q be perfect substitutes. rsonal income tax which is levied ob labour not retain earnings), nominal interest income, ominal interest payments are deductible. As far a~iowances at historic cos’t are rate income tax which onomic effect such a tax

(e) Since our main concern i,, * the long run, we have simplified the S~GW run features of the model by assuming perfect foresight and full employment, and b;r evaluating the capital stock at replacement cost2 2.1. Norration The exogenous variables are noted with a tilde over them. --=volume of domestic production net of physical depreciation; 4 W*Y = household real wealth and real disposable income; c, s -volume of household consumption and saving; i =volume of net investment; =-volume of goods purchased by the government; g = trade balance; X I& =stock of capital; =real stocks of government and foreign bonds; 8,;; =rea.l stocks of government bonds held by the central bank and the households; !$,I$ -real stocks of toreign bonds held by the central bank and the households; rm -real stock of money; rs, *f_ = pre-tax real returns on government and foreign bonds; =Igovernment controlled real spending; & =personal income tax rate; t =domestic and foreign rate of inflation. p” 2.2. The structure of the model The short-run model is composed of twelve equations and involves nine endogenous variables and three state variables w, k and b,: q(k) = c(y) w) -I- i[q’( k) - a . ii - r,J + g + x,

q”4,

Qtc, 4,

c,>o,

4‘ I=-0,

i’>,O, i(O)=S.

om in the lit~xature, simce it dces not a s~rn~~~~esthe short-run dynamics. See fir example, bcifh 4197%.

!El

‘+?J=:: J,’ -

I&$ W-jE &I, yt),

o
s,
WV (W

e long-run mode!, which defines the initial and final steady states, is fromthe short-run one by equating the right-side term of (lOj, (11.) to zero. The variables w, k and 15,must then be considered as (I) is the goods market equilibrium condition. Notice that investment na: between the corrected marginal product of capital nes& real return. This corrected marginal return is Z to the net marginal product of capital, q’(k), minus a term, a *fi, which negative effect on firms capital yield of depreciation :Sncesat historic cost in the presence of inflatiou, Eqr;. (2) and (3) are the equilibrium conditions for the money and foreign ,tively. Because of the wealth constraint, the following met:

e afl;er-tax

real

6. ,Hsthev,,fnJlation and nom&u1tax system

27

government bonds is equal to (I-- f) ~(r, + fi) -_ fi, i.e., ( I- Q ’ rp - f* @. A similar exprest;ioa~ involving ?r instead of r8 is also valid for foreign bonds. q. (4) defnes the household real wealth. ‘Weassumed that households do not consider the actual value of future tax payments as a present liability and, therefore9 include the stock of government bonds as net wealth. Eq. (5) defines the household disposable income. It differs from the usual formulation as, the tax ‘burden depends on the inflation rate, since we assumed that the tax system is a nominal institution, The term - F.(bi+ b: -t-ik)*p represents the additional taxes on household compensation for real losses suffered from holding bonds as well as on nominal capital gains. Finally, the ter;n -a * k - p” is our proxy for the negative fiscal effect on corporate income due to inflation and historic cost depreciation. Eqs. (5) and (7) assert that both government and foreign bonds have to be held either by the central bank or the households. Eq. (8) is the central bank balance sheet. Eq. (9) states that the government controts exogenously in real term its goods purchases plus its gross of tax nominal interest payments on its debt toward the households minus the nominal income it gets from the central bank’s holding of foreign bonds. With this assumption, the model can be shown as locally stable.3 With these nine equations, the instantaneous equilibrium is defined given the exogenous variables and the state variables w, k and br. Eqs. (IO), (1 I) and (12) complete the model by providing the dynamics of these state variables. Their evolution through time is governed by the household saving. the net investment, and the current account, respectively. Notice that, due to the wealth constraint, these three equations implicitly define the dynamics of the stock of government bonds. Indeed, by combining (4) (5). (7) and (8) and b?: differentiating with respect to time, we have

Furthermore, using (9), (IO), (I I) and (12) we get

we use (8) a;ld (9),

3A

formatproofof st

economy is provided by Christ (1979).

bonds depends on the ~ffer~~~ its tax revenue plus the

results, we need two more assumptions

WhiCh

in ,the household stock of government bonds ct on their saving, since the wealth ettect, s2 * dhi ~0, &an the income effect, s1 - ( 1 -I) - rB - dk$ >*(I, we will th effect always dominates, whatever the personal tax re, w’emust have

are not

has an has an assume rate is.

sume that the elasticity of the demand for foreign bonds to rg is greater in absinlute value than the corresponding r mohey demand. When the economy is a net creditor to the rest ( -) SO, this assumption is equivalent to

otiee that

inequality is alwa.ys true when the economy is a net rest of the world* f( ’ ) l 0. last

tial sterPdy state

ur analysis, we will assume that, in the initial steady o not hold government bonds, the rate of inflation is to zero, aad both real returns on government and foreign bonds are

rg = f-r.

(20) 1) in the hong-rug model, together with (l9), implies that (21)

6. Huber, Injlation

ad nominal tax system

29

remains unchange for any portfolio reshuffling between1 government and foreign bonds. will not analyse the more difficult case of uneqpal initia returns for thes owever, since both short and long-run multipliers arc continuous with respect to bi, j5, rg and Fr, our results will also be valid for initial situations characterized by a small government debt toward househoids, a low rate of tion, and a small difference between domestic and foreign real returns. ue to the complexity of the model, all comparative statics exercises and the analysis of stability for this model were done with the help of a computer program designed by the author. Pe short-rub

In this section, we provide a disaggregated analysis of both short-rtin and long-term caasequences of an increase in the inflation rate. However, since QW concern is the real distortions related to the nominal tax system, we will disfcard several initial effects induced by a higher inflation rate which will also be present if the tax system was fully indexed, i.e., the decrease in the real return of money” or Tobin effect, the decrease In household disposabic income due to the higher intIation tax on money ballances,’ ar ’ the change in government goods purchases because of its spending behavic J.‘~ Even with these simplifications, an s?xogenous increase in the inflation rate will still disturb the existing long-run equilibrium through three distinct channels. For the remainder of this section, we will only consider the case where the economy is a net creditor to the rest Q and h,h:>O, and assume that the convergence to the final steady state is monotonic. 3.1,. The income effect

As the inflation rate increases, the household disposable income decreases (dJ’
(3, (13) ad

in se ct is timne. E.E.R:-

B

30

G. Wuber, hjkxtion and nominal tax system

s will decrease both Due f[o their iower disposable income, ~v~n~~and ~onsunlpt~~n. Consequen al vrealilh will decline (4i,ala). the goods market equilibriu nce (dai->9), thigh wiB induce the stock of use of higher tax revenues, the government budget l&l us and, therefore, the stock of government 1bond.swiB1 Finally, notice that the househotd wealth equiilibriurn is by the dtec;lxw in their di!;lposable income (dm =~d@‘=:d@= on~que~t~, the i tment Ievel and the government goods s remam uncha:nged (dg =_&= 0). iven the prevailing domestic real return and with no central bank on the foreign bonds market, the new short-run equilibrium is n &eess flow demand on the capital and government arket’ and excess flow supplies of both money and foreign bonds aw ~ui~~~,~a on assets maricets will be restored through a continuous e;cline in the domestic real return (fg ~0). As the increase in the stock of bonds has to be he?d by households as such or as money, and since sit~v~tyof the foreign bonds demand is greater than the sensitivity of ~~~n~~~ demand..lo we are sure that the household foreign bonds holding will &crease through time (6; ~0). However, it is not possible to determine vely whether the central bank stock of foreigrr bonds, i.e,, the money ill increase or decrease (GI= 6,”=?). er its initial drop, the household disposable income will continue to se (9 ~0) as household real wealth declines and the lowering domestic I rt:tum induces a portfolio reshuffling toward non interest bearing assets. tke naticnal income expands with the growth of foreign bonds holding, government iqcoru;; must increase since household ce tax revenue decreases, the rise in government income B only be explained by tbe increase of its net income related to the holding bonds and domestic liabilities. Consequently, government goods wilI increase through time (g>(I), ‘because of its spendiqg viour assumed in eq. (9). above, the ecanomy is on a path leading to a long-run racteriied in table 1, provided the ace~umulation processes for down and end. This will be the case for the stock of t bonds since the lowering h,ousehold disposable iacome means amI, therefore, a smaller budget s s. As far ar +’ stock ent expands rts goods enues increase (g r Q), inducing a that point, we are still not sure

6. Huber, inj7ation nz;! non,inal tax system

Table 9 The short and long-run kmuitipliers. ---

_-l_l-

Income effe,d Short-run

Long-run

r*, g, m, bi, b:, b,b,b,, 12 0

JI: -D.y;i’-r;s,.i,.e~m,
Y:YpcO

k: -tD*y;i

ti:s, .y,
bi,b,: +D~y;i’~[s,~r;[I(

[sb--sl*ra~l(

)]=m,>O ) +e-n,,]--s,,*(l

+e-/;I

-s,.I,.e]cO X,

m,b,b: +D.y,;i’.l,*e.s,>O

l&: -q-y,>0

b$ +D.y;i’.e-[f,.s,-s,.r;n,,]>O

I;B:-Y,>O

b,: -D.yy,.i’.e.Cb,.s,+s,.r;n,,]=m,>O g: +D.y;i’.r;FsL.12.e-s,

*re’[::

)+e*n,,]

+s,*(l+e.b,)]>O w: -s,~m,/s,<0,

r,:q”.m,
x: -i,.nf,
Marginal product &ct Long-run

Short-run y, rg9

g,

m, bi, @, i$‘,b,: ?t, 6: 0

y, r,,, x, m, b!, E$‘,w, b,: 0

S;: -I-a<0

bi,b,: +D.a.i’.r;s2.(I--~.\V-II.T:-mbr!>0

x,&: +?,a>0

k: -mm,,
g: -r;m,,
Real return eflect Short-run

Lung-run

b;, b,: 0

y_w, m, b;: 0

y: +d.r,-(1-f)2.w.nZp=mg~;0

k: +D.i’.r;s,.l;f=tnkiO

m,bF: -d.(t-f).w*n,,=m,,>O

bi,b,:

r,: -!+,,>o;

bf,b,: +B.i’.r;s,.e-t’.n2,-r/r,<0

b:: --mlb
l&b,,<0 g:r;m,,>O . b,:f*r;mfb>O

x,1;,: +d~[rs+-f)Wn,,

~(l-c,+c,~?)-r$J~O

-D,i’.r;s,.f.(l,Se.n,,)-m,,>Q

r,:q”~r,l,>@: x: -rf*mf9

g. -r;m,,
G. Hvber,

32 ng ~~r~~~~

will

Irrjlation

and nominal tax system

decline since the foreign interes,t payments increase e acceleration in the

ahss

lXX3tlliCZ Qn

the

therefore, induce households to hold more money, ntra2 banlk to buy more foreign bonds. The further increase in ill once again boost its goods purchases. It will up to a point where the current account will slowing down the accumtllation of foreign bonds. ted the capital stock. Due to the decrease in the s uGll expand their investment, inducing a 0) As it increases, the decline of its marginal vest, decelerating capital accumulation. Notice the positive investment wiElfurther deteriorate of foreign assets. Finally, as dissave will diminish so that ith wiii stabifize at its long-run equilibrium value. ,)

ond chamel

through which am increase in inflatisn rate disturbs

decrease lthe corrected marginal product of use of depreciation allowances at historic cost, i&ate a capital decline (i 0). As in section 3.1, the

i~itia2 equilibrium 5 f available to firms

‘Notice that the decrease in the domestic :?a.1 return decelerates the decline in the capital stoc accelerates the growth in the stock of government bonds. At first, the decrease in the capital stock dominates; however, there will. be a point of time where the growth in the stock of government bonds wiIHcompensate the desrp ,_,ase in the capital stock, and then surpass it. At ‘rhat poi.nt, the stock iof foreign bonds is decreasing since the household real wealth is doing so, h’,=&-t-6,-t-k’= G ~‘3, and there is an excess fiow demand for foreign bonds and excess flow supplies of cspital, government bonds, and mosey. Therefore., the domestic real return will rise (I:g~O), inducing a positive effect on the household disposable income. When this positive e&t will dominate the negative effects of both decreases in domestic production (i 0). At that point, the economy is on a path (G>O, &CO, 6, ~0, & < 0) simiiar tc the one described in section 3.1, although of opposite sign. The same mechanism.s, which will not be repeated here, will slow down the accumulation processes for these various stocks and end them. The economy will therefore converge to its final long-run equilibrium. However, the characteristics of this steady state must now be described, since the variations of most endogenous variables have changed signs along the transient path. Notice first that there is only one level of household disposable incorn,,p which is consistent with government budget equilibrium. Indeed, by differentiating (5) and (16), together with (19), we have” d&-f~(l-Z)-1

-dy=O.

‘37

(-A

)

Since govermnent controlled spending is assumed to be constant (d& ==O), household disposable income and (because of their saving function) household real wealth are unchanged in the long run (d:v= drr:.=0). Furthermore, by d.ifferentiating (5), together with (I9), (20) and (21), we get

Or, using (4), O-dy=(l

-Z).r;dm.

Consequently, the money stoc of foreign bonds are also unchanged in the long-run. st remain unaffect domestic real return

is ~~r~c~~l~~~d[d4!3,! ==&.I~ -t dk = tit.

I Sinw

in

equal to the us dW&We, the capi te (dk e 0). Equilibrium of the capital ller in the final st&y mds ma;&% is restored as the increase i3 government actty the decrease in the capital stock (dbi r= -dk > 0). e increase of its debt toward households, the: government will ds purchases in the long run (dg 4) by au amount equal to slice that this amount is exactly equal to the decrease of dq = 4”. dk = rg. dk =. - t, .dbi. ‘Wift-iunchanged consampent, it means that the trade balance is unaffectc;;d Err the iB5

&Cl

:'bE

1 rather than real interest inco?mes are taxed, an increase in ion rate cause!; a decrease in both the after-tax real returns on domestic Ilds,L3 which creates an excess demand on the money market, I,). d@>Q, and excess supplies on the capital and t tinds marketPI d(bi+k)d = --2~w~(bz+b3)~d@c0, and om the --Pw-(f2+,f3).d$<0. markets will be restored by an increase of the mestic real return (dr,:>O), and a central bank purchase o’fforeign the money stock (dm = d@ = -- db,”> 0). Since heir portfolio against interest bearing assets, szbie income is now lower (dy CO). The subsequent decrease in ving ~-3 induce a decline in their real wealth (tit<). Simultaneously, of ~~ve~~~~t bonds will grow (6%=6: >O), as the government @es a budget deficit due to lower tax revenue.15 However, as its e increases, it will enpatnd l-s goods purchases (dg > 0). Because r domestic real return, the firms will d&vest and initiate a in the stock (f CO),, The sign of the change in the trade gr!zwth for the stock of foreign bonds is ate, as ~~~vestrne~~and consu ption decrease and government s ~~~;r~~~ (dx = & = ?). final steady state will not mcnts as in sections 3.1 a gsish two opposite cases concerning the trade balance. the characteristics of the final steady state.

ever the CfO§§ one. iS.5comideyed in section3.1.

e sxr~ reason as in section 3.2, we can show th,at housr disposable income and real wealth, money stock, and, th’e centrai nank stock of foreign bonds are unchanged in the long run (dy =dw -dnt =:.db,”= 0). Since the after-tax foreigm real return is now lower, the ilong-run equiiibrium of the money market is possible only if the after-tax domestic real return is higher (dr,>O). ft means also that the household stock of foreign bonds has decreased (d!$cO), and that the tota! stock of capital and government bonds is larger (dk + db! >O). But, as the capital stock must be smaller (dk CO) because of the higher domestic real return, we are sure that the household holding of government bonds has increased in the long run (db,b>O). Finally. the government goods purchases are smaller in the long run, since its debt toward households is larger (dg< 0), and therefore 1he trade balance has improved (d:c>O), as both consumption anti investment remain unchanged.

Bef%lrepresenting the global results of an increase in the inflation rate, a look at table 1 will convince us that all short and long-run multiphers do not depend upon whether the economy is a creditor or a debtor to the rest of !hc world, since neither f(s) nor b: appears in their formulation.‘6 However, the exogenous income effect may be affected by this net position. Let us define 6: as the national debt” to the rest cf the world which induces a zero income effect in the case of a higher inflatron rate. Algebraically. 6: is defined by -F(b;+&t-k)-,.k=O. Pn table 2, we have summarized at first the quallitative signs of the long-

run multipliers for the three partial effects considered in section 3. In a second part, these partial effects are added qualitatively depending upon k: in order to present the global implications of a higher fnflatioa rate. Table 2 The long-term implications of a higher rate 4 inflation. -.rB

k ---.-

y

---

12’

m

h!

-

t5: i$ ---

bg

___.____~ ii

g x _-~.-__ _.~

Partial efiects

income effect (b,h> F;) margir.ai product effect ied return effect Global effects 9°F : : 85;a
----

@I?lC bent f(., appears section 2.3, it does not matter. 17@’is likely to be negatlvc.

i-

-

-

--

f

_-

0 +

0 0

0 Cl

0 G

? -

? + + 8 0 0 -+ + + $ __________.____~

-

imgSic;ely

in

'

-I-

6

f

-

0

-i

+

P

+’

-

0

t

:’ + f

‘? --

+ 0 +

‘I + A-

the iodiicieni

fJfJ;

bLit, becalise

+

0

*

‘? --

‘7 ‘I i + -.--.--- ~~ ot’ e< [St+) in

the

in.cmme cfkct18

by ass~mi

that !$ is eqtial to RF, the are a Iswer capital stock, a household diisposable ese re ::3.’ 2.e quite si ar to those for a closed

now a laqp ~~~Q~~ dlebt to the rest of the iworld &‘c&‘), costive &.ome e&ct, the decline in the capital stock is reinforced and real we~th and disposable income increa.se in the long the economy has a sma!ler national et creditor to the res!t of the world jb,h>B@), i.e., a negative long-term variation of the capital stock is indeterminate T#eenthe forces generated by the income effect ts. This variation may well be positive if the ition of the economy is sufticiently laqse. However, the I wealth and disposable income will decline. at a ne~~ve income effect induces an increase in the capital cruci:ally on the assumption of a bond financed public deficit. If ney financing, the flow disequihbria considered in section n an excess flow money demand and excess flow supplies other markets. It means that the domestic real return would have run decline in the capital stock.“’ Pn this case and tion toward the rest of the world, an increase in the ation rate v& unambiguously lead to a smaller capital stock in the long mary, BE have shown 2o that, due to the nominal features of the 5ysttxx1, IM immase in the inflation rate leads to a smaller longstock and. an unchanged household disposable income, provided initial e&t on household irlcome is sterilized. If this likely not sterilized, then the decrease in the long-run or even reversed.22 However, the long-term partial income effect rely on the assumption of a bond If’ the government budget imbalance is money initial income effect leads to a further decrease of

income 4kct.s ;Hong the adjustment paths for the two other partial and the inkh~~~ tax on mouey balances were not considered al! he world is large.

G. .Huber, lnj7arion and nonlirtal fax sysfIam

3?

11~order to prove the local, stability of the model, we must fitrst determine

the coefficients of the characteristic equation of the system. After computation, the characteristic equation becomes ao.z3+a,.z”fal.u7+a3=8,

where a,=(l-g)*b2*w~0,

a1=4~--aa,~t’~q”~0,

a;= +i’.~.[(1-~.rr,.s,.nf,-I,.s,-fi*s,+/2.~.rJ

+i’*[I( )*(l-&rr,~sl-s,pO, e= +(l -f)-

WVq"
With our qualitative assumptions, it can easily ix shown that a,, a,, a?. l/3 and a, . a2 -a, 1a3 are all strictly positive. The model is then locally stable.

Christ, CF.,

1979. On fiscal and monetary policies and rhe government budget restmix% American Economic Review 69,526-538. Feldstein, M., 1976, Inflation, taxes and the rate of interest: A theoretical analysis, American Economic Review 66,809-820. Feldstein, M., J. Green and E. She&in&i, 1978, Inflation and iaxes in a growing economy -&irh (debt and equity fmance, Journal of Political Economy 86, 53-70. Green, J. and E. Sheshinski, 1977, Budget displaceit?ent effects of in??ationary finance, institute k?f Mathematical Studies in. Social Sciences report no. 180 (Stanforc; Umversily, Stanford, CA!. Huber, G., 1981a, Government spending in the long c~!:u:The case of a small open economy under a fixed exchange !ratce,Unpublished manuscript. Huher, 6.. 1981b, ‘The long term iXI@imtiOnS of vsrious taxes in a small open economy under a W-ipr. fixed exchange rate and a money financed r.tiblic deficit, Unpublish LC:s when. the Smith, G., 1979, The long run conse~uen~~:~ govermnent budget is not balanced, journal of 1