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Adverse incentives in the taxation of foreigners
Journal of International Economics 27 (1989) 283-297. North-Holland
NTIVES IN T
Matthew B. CANZONERI* Georgetown University, Washington, DC. 20057, USA Received January 1988, revised version received March 1989 Sovereign policymakers will opt for too much of the public good if their tax falls partially on foreigners. They myopically calculate that an increase in public spending is only partially financed by a decrease in home consumption; the rest comes from foreign consumption, which they do not care about. This paper presents an example with seignorage taxes. In a two-country model with cash-in-advance constraints, the inefftciency is characterized by an inflation bias, too Imuch public spending, and large fiscal deficits. Curiously, the countries most able to impose such taxes seem to have abstained from doing so.
I. Introduction
This paper illustrates an ine@ciency in sovereign policymaking that has not been discussed in the policy coordination literature. In a two-country model with cash-in-advance constraints, the ineficiency is characterized by an inflation bias, too much public spending, and large fiscal deficits. The inefficiency does not come from competition over the terms of trade, or from problems with time inconsistency, or from inflations distortionary et.& on decisions about labor versus leisure, cash versus credit goods, ar real balances; these distortions have been purposely excluded from the model.’ Rather, the inefficiency is due to the sovereign’s ability to tax foreigners. In the present example foreigners are hit with a seignorage tax, but clearly the problem is more general than the question of seignorage. Each country is composed of infinitely lived citizens ,who value both public and private spending; each country’s policymaker sets the level of public spending and taxation to maximize his citizens’ welfare. Brivate agents behave competitively, but each policymaker knows that his actions will affect *I wish to thank Roberto Chang, Mark Gertler, Dale Henderson, Gary Hufbauer, Pat Kehoe, Carol Rogers, Anne Sibert, Lars Svensson and an anonymous referee for helpful comments. They are in no way responsible for what follows; I suspect several of them would have done things quite differently. ‘In particular, I am not discussing the time consistency problems of Calvo (1978) or Lucas and Stokey (1383); 1 have purposely excluded factors that would lead to time inconsistency. 0022- 1996/89/$3.50 0 1989, Elsevier Science Publishers l3.V. (North-Holland)
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the behavior of the other policymaker (as well as the private sector). Thus, the equilibria inve;tigated in this paper are Nash solutions to a game between sovereign policymakers. Public spending in each country can be financed by an income tax on its own citizens. If the policymaker uses this tax, he realizes that an increase in public spending. must come at the expense of his own citizens’ private spending. The policymaker has the interests of his citizens in mind, so he makes the local decision between public and private spending efficiently. In fact, since other distortions have been excluded from the model, the result is globally efficient. When policymakers are restricted to the tax that falls exclusively on. their own citizens, the Nash solution to the game between policymakers is the outcome a world economic planner would choose. However, iublic spending can also be financed by a seignorage tax, part of which falls cn foreigners. The efficient world outcome can be supported by seignorage taxes, income taxes, or some combination of the two, but this felicitous outcome seems unlikely if the policymaker is allowed to resort to a tax on foreigners, whose welfare he does not care about.2 In choosing the level of public spending, he now thinks that an increase in his spending need not imply an equal decrease in his citizens’ spending; part of the increase can be financed by the tax on foreigners. Thus, there is a Nash solution in which policymakers eschew the income tax, in favor of a seignorage tax, and expand public spending. Compared with the efficient outcome, this Nash solution !s characterized by too much public spending, too much inflation, and large fiscal deficits. The seignorage example p?:zsented here is really rather puzzling, and that is one reason it was chosen to illustrate the more general problem of allowing governments to tax foreigners. The puzzle is that the bad Nash solution does not seem to be observed in the real world. The U.S. dollar is still the major vehicle for world trade, ye1 the United States only finances a small fraction of its spending with seignorage. Why is U.S. monetary policy SO siable? The German mark and the Japanese yen are also vehicle currencies, but only the Japanese appear to depend on seignorage to any great extent. This paper suggests two questions for future research. First, why is seignorage not used to a greater extent by key currency countries? (Or is this why they are key currency countries?) Second, how important is the more general problem, when all taxes on foreigners income are taken into account? Section 2 outlines the model use,d in the seignorage example and establishes Proposition 1, which states that a competitive equilibrium can support an efficient world outcome if tax rates are chosen properly. Section 3 ‘There may be many Nash solutions to a dynamic game such as this. Some rnq achieve the efficient outcome through the use of trigger mechanisms. II do not look for solutions that incorpcratc trigger mechanisms.
M.B. Canzoneri, Taxation of foreigners
285
describes the Nash game between sovereign policymakers and illustrates the inefficiency of allowing them to tax foreigners; Proposition 2 states that the efficient world outcome will not result if policymakers are allowed to use the seignorage tax, which falls partially on foreigners. Section 4 discusses the seignorage example in particular. It suggests sevtral approaches for future research on the puzzle described above, and it highlights a limitation of the analysis presented in sections 2 and 3. Section 5 looks beyond the seignorage example to assess the scope of the problem when all taxes on foreigners are taken into account; it suggests that the taxation of foreigners is very widespread and that the inefficiency that results should be tgken seriously.
2. A two-country model with income an seignorage taxes Think of a world consisting of just two countries. Tb,e home and foreign countries produce y, and yf units of a good that can be used for either public or private consumption. (Asterisks designate foreign country supplies, demands or prices; all quantities are measured in per capita terms.) Production is exogenous; for simplicity, let y,=y:'=y.
(1)
World output is fixed at 2Ji each period. The home country is composed of identical, infinitely hved households whose utility in period zero is given by
u= f
Go
S’(logc,-I-logg,),
where gt and c, are public and private consumption. The foi*r=lgncountry is similarly composed of identical, infinitely lived households whose utility is given by
U”= f 5’(logc,*+logg,*). t=O
There are 2j units of output available each period, and ho
(2’)
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286
public and private consumption equally; it is easy to calculate an efficient allocation of goods. Lemma 1.
A Pareto optimal allocation
is given by
A world social planner might well choose this allocation;3 however, the policymaker considered here cannot simply allocate goods. He must tax or borrow to finance his purchases, and he is subject to a cash-in-advance constraint that has yet to be specified. His taxes include an income tax that falls on his own citizens and a seignorage tax that falls on whoever holds the currency he issues. Now, consider the cash-in-advance constraints4 Each period begins with
a financial exchange and ends with a goods market. In the financial exchange, income taxes are collected, interest is paid on debt, new debt (in the form of either money or bonds) is issued, and governments and households acquire the cash they will need in the goods market that follows. In the goods market, shoppers pay for goods with cash; barter is not possible. At the end of each period, firms deliver the cash they have received to the households that own them; these cash holdings are the base for the seignorage tax. If seignorage taxes are to be well defined, the model must exhibit distinct demands for the two currencies ? This requires an arbitrary restriction on the cash-for-goods exchanges that can be made. Helpman and Razin (1984) show that a variety of restrictions will do. In their buyer’s system, the buyer’s currency is used in exchange; buyers must use their own country’s currency to pay for goods. In their seller’s system, the seller’s currency is used; sellers can only accept their own country’s currency in payment for goods. Either of these restrictions will produce a distinct demand for individual currencies, and seignorage taxes will be well defined. However, it turns out that the seller’s system allows the seignorage tax to fall on foreigners while the buyer’s system does not. In this section and the next the seller’s system is postulated; these points will be discussed further in section 4. 3More specl‘fitall y, the allocation described in Lemma 1 is the solution to the world planner’s problem: r
max Wc 6’(10gC,+10gg,)+(1-W) 2 6’(logc,*+logg,*) Icr.8r.ct.sll r=o i r=o I subject to c,+g,+cF+g,*sy,+yfr=2J, with w set equal to 0.5. ‘The model in this section owes much to Helpman and Razin (1984), which in turn owes much to Lucas (1980) and Stockman (1980). More elaborate discussions of the general set-up described in this paragraph and the next may be found in these papers or in chapter 5 of istinct money demands are also needed to avoid the exchange rate indeterminacy allace (1981).
of
M.B. Canzoneri, Taxation of foreigners
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Taking account of two arbitrage conditions simplifies the analysis. The two countries’ goods are perfect substitutes, so Pt = etPL
(3)
where pt and p: are the home and foreign currency prices of the good, and et is the exchange rate in the financial exchange. In addition, government bonds are perfect substitutes, so It = met
0
+ &A
where I, and I,” are the gross nominal rates of return on home and foreign government bonds. ( 3j and (4) imply that gross real rates of return equalize: R, = UptIp, + I) = V(P,*/P,*, I) = RF
(5)
Home household utility can be rewritten as:
u=t~~S’rlog(e,,+c,,)+loggtl
(6)
where cht and cft are the household’s spending on home and foreign goods. In the seller’s cvstem, the home household’s decisions are constrained by mht
2 PtCht,
mht
+ etmft
m,t
2
Pi%,,
+ lht + etlft
(7)
+ 2)tTt
where )tihtand ml,are the household’s demands for home and foreign money, &t and Ift are its demands for home and foreign bonds, and z, is a lump-sum income tax. The first constraint is the cash&advance constraint; the second is the intertemporal budget constraint for the financial exchange. The first two terms on the right-hand side of (8) are cash received fr firms for last period’s sales. Home households are assumed to own half of equity in the firms of both countries. Thus, home households hold half of last period’s home currency balances and ha of last period’s foreig balances; they pay half of the ‘;torne seig
M.B. Canzoneri, Taxation offoreigners
288
of foreign equity that drives the results that follow, a justification
of the fixed
ownership assumption is warranted. In a stochastic version of the model, risk diversification could be used to explain foreign equity holding. Such an extension would, however, not be trivial; it will not be attempted here. Instead, it will be assumed that initial equity shares are as postulated for historical reasons. In equilibrium, domestic and foreign inflation rates will equalize; so real returns on domestic and foreign equity will equalize, and households will be willing to hold the postulated shares. This, however, is not enough to justify the analysis that follows. When a policymaker calculates his Nash policy, he considers the value of a marginal increase in his seignorage tax. This will cause a marginal differential in inflation rates, and thus a marginal differential in the rates of return on domestic and foreign equity. However, in what follows, transactions costs will be assumed to be . large enough to make portfolio changes unprofitable for these marginal changes in inflation rates. The budget constraint, (8), can be expressed more conveniently in real terms. Dividing through by pt, and using (3), (4) and (5), it becomes:
=
WPt - IlPJY, - 1 +wPE-
IlPl*)Y,*_1+
4
- lb:-
19
(9)
where bt = (Z,Jp,)
+ (I,Jp,*) is the households’ total demand for government debt. Additional simplicity comes from the fact that I, and I: are greater than one in the equilibria considered in this paper. NIonies are dominated assets that are only held for transactions purposes; the cash-in-advance constraints, (7), are always binding. Therefore, (7) and (9) can be combined:
chr+cfr+bp+r,=~~.5(pl-l/p,)y,-1+0.5(plr-l/p~)y,*-1
+R,&-,.
(10)
Finally, letting c, = Cht+ cft, the home household budget constraint can be
written as? ,Eo %@t-rJ=
f
at+ lCWPt/Pt+ l)Yt+WP1*/P,*,
t=o
+0*5(m- l/PO)-t 0*5(m*_ I/PO*),
AY,“l (11)
where m _ l and m? l are initial cash balances,’ and the a, are real discount 6The period-y-period constraints in (10) are collapsed into the single constraint (11) by using the constraints iteratively to eliminate the 6: and then assuming that lima&.+0 as T+m. ‘These initial conditions are consistent with starting the economy a period earlier; the home households would have reeked a half of the period - 1 currency balances as receipts from the firms’ period - 1 sales.
M.B. Camoneri, Taxation ojforeigners
289
factors; that is, u, 5 (&RI.. . R, _ I)_ 1 and a0 = 1. Analogous steps lead to the foreign household budget constraint: Q) c 4 (e-e?=
t=O
i a,+ICO.S(P,IPt+,)Y,+O*~(P~/P,S;~~Y,*l t=O
+OS(m-l/po)+0.5(mI ,/p$
(W)
I=Iome and foreign households choose c, and cr to maximize utilities subject to budget constraints. Their first-order conditions are: 6’(c,/c,) = a, = S’(c$/c,*).
(12)
These conditions ensure the intertemporal efficiency of consumption. Governments also face cash-in-advance constraints and budget constraints. If the home government purchases home output, then (13)
mtt 2 Pt&
is its cash-in-advance constraint. The home governmen% budget constraint is: (m!iJPJ+R,-lb,-,
=vaw-mt-,)/P,+bt.
(14)
In the financial exchange it must acquire cash for purchases in the goods market that follows, and it must pay principle and interest on last period’s bonds; these transactions can be financed withI income taxes, seignorage or new bonds. Collapsing (13) and (14) into a single constraint, the home government budget constraint becomes: a3
c
wr= f ~tC~t+bv-~t-JPtl* r=O t=O
Similarly, the foreign government budget constraint is: a0
c
a,[$ +(ml*-m,*_,)/p:]a r=o
a,s,” = f
r=O
The equilibrium conditions are: Cht+Cg+gl=yt=jt
and
qr+cf*t+gl*=yr*=y,
(15)
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290
mht + &
+ mtt = &hr
+ 6
+ 8,) = ml;
mf,+m~+m~~= p,*(c,t+c,*,f!e)=m~*
(17)
These conditions can be more conveniently expressed as: m,= pty,;
mt = pf
(18)
y&
and c,+g,+c,*+g,*=y,+y,*=2j.
(19)
Letting the monetary instruments be defined by growth rates, h, = (m, -m, _ J/m,
and
h,*= (m,*- rnf!-Jm,*,
(20)
seignorage revenues in equilibrium are: (mr- m, _ Jpt = h,y, and (rn: - rnf?-&‘p,*= h,*y,*.
(21)
Using (HI), (20) and (21), the household budget constraints become: c0 Q, a,c, = c c at ( Yt-5
t=O
t=O
30 c a,c,*= i
t-o
-
fMh,y, - O.Sh,*yf),
a,(y,*-r,*-OSh,y,-OSh,*y,*),
t=O
c2’2) (W
and the government budget constraints become: 00 c W, = f a,(%+ hYJ9
t=O
t=O
(23)
Q) c
a,gf
t=O
= i
r=o
a,( r,* +
h: y,*).
(23”)
The last terms in these budget constraints arc the seignorage taxes. Each government’s seignorage tax is shared equally by the citizens of both countries, while its income tax falls exclusively on its own citizens. The e tax is shared because each household owns half of the equity of tries, and receives half of the currency of both countries at the end
M,B.Canzoneri, Taxation of foreigners
291
An equilibrium must satisfy the equilibrium conditions, (18) and (I9), the households’ first-order conditions, (12), and three of the four budget const:aints, (22), (22*), (23) and (23*). (One is redundant).* Equilibria do exist. In fact, an efficient world allocation can be supported by a competitive economy if world tax rates are set properly. Proposition I. The eficient xo r!d &cation described in Lemma I is an equilibrium outcome if r,, h,, 7: and h,S are set to satisfy z, + h,y’= O.Sj and zf + hrj = My.
Proposition 1 can be verified directly. All of the budget constraints are satisfied on a period-by-period basis; that is, b, = b: = 0. There are high and low inflation ways of supporting the eflicient outcome. If money growth is set equal to zero and income taxes finance public spending, then inflation is equal to zero. At the opposite extreme, if income taxes are set equal to zero, then _PCPL-1 Pt
= h, = 0.5
and
n,* E pr*-f:Pt
1 = h,* = 0.5.
3. A Nash solution to the game betweem There is no reason to think that politically sovereign policymakers will settle on any of the efficient alternatives suggested by Proposition 1. The home policymaker’s objective is to max f S(log c, + logg,) ~~tr~tr~t.Ct,~f*Qt~ r=O subject to the equilibrium condition, (19), the first-order conditions, (12), and three of the four budget constraints, (22), (22*), (23) and (23*). The foreign policymaker’s objective is to *For example, (22), (23) and (23*), in conjunction with the equilibrium condition (14), imply (22*). To see this, sum the conditions in (14) to get: ,~Oa,(c,+n,+c?+g:)=
f a,2P I=0
Then, sum (22), (23) and (23*) t3 get: f a,(c,+g,+g,6)= I=0
i a,(~+TIZ+0.5h,~+O.Sh,*~). r=O
Finally, subtract the second expression from the first to obtain (22’).
M.B. Canzoneri, Taxation of foreigners
292
max f S’(logcf + log gf) {$I?, r?.ht,cp,Ct,at) t = 0 subject to the equilibrium condition, (19), the first-order conditions, (12), and three of the four budget constraints, (22), (32*), (23) and (23*). Sovereign policymakers care only about the welfare of their own citizens, and they have the ability to tax foreigners. Proposition 2 describes the probable outcome of this game between sovereign policymakers. Proposition 2. There exists a Nash solution to the game which is ineflcient. Nash strategies are given by:
h,= q=
213, h,* = 2/3, b,=O,
The corresponding
z,*=b,*=O. Nash outcomes are:
c, = (1/3)j& c,*= (l/3)5 71,= h, = 213, I$ = h,;:= 2,‘3. In this Nash solution, policymakers eschew the income tax in favor of the seignorage tax, half of which falls on breigners. In deciding upon the level of public consumption, each policymaker calculates that an increase in public spending will only lower his citizens’ private consumption by half the amount; the rest comes at the expense of foreign consumption. Consequently, he expands public spending beyond the efficient level. Compared with the efficient outcome of Proposition 1, the Nash solution is characterized by too much public spending, high fiscal deficits and excessive inflation. This is an example of the inefficiency of sovereign policymaking when there is an externality in policymaking: policymakers are allowed to tax foreigners. N#te that the policymakers may be fully aware of the selfdefeating nature of their competitive taxation. Each must engage in it anyway, because he knows the other will. The rest of this section is devoted to a proof of Proposition 2 and a word (in the last paragraph) about the time consistency of consumption plans, public and private. Readers who already believe in validity of Proposition 2 may wish to skip to section the two maximization proble by using the first-order con ition, (12), to e
M. B. Canzoneri, Taxation of foreigners
293
(25)
f s’[~-a,-(1/2)(hty,+h,sy~)]/c, t=o
(1 -S)-‘= and (1-q-l
= i s’[B-?~-(1/2)(h,y,+h,*y,S)]/c,S, t=O
and the government budget constraints
become:
syz,+h,y,)/c,
g 5’gJc, = ? t=O t-z
(26)
and S’g,*/c,*= f St@,* + h,*y,*)/c,*.
i t=O
WY
t=o
Then, dropping the foreign household budget constraint, maker’s problem reduces to: max
f
the home policy-
(27)
8(log c, + logg,)
~gt,~t*~t*ct*ct~ t=O
subject to (l!?), (23, maximization are:
(26) and (26*). The first-order
c,*:
-A, - pY(z,* +
h,:
-y~‘(l/~)y,fc,+~~sy,lc,=o,
c,:
d'/c, -
I, - yS’[j -
- W%t
+ hty, -
. 7,.
- yiY/q +
g,:
5’/gt -
h,*yf
conditions
-g,*)/c,*2 = 0,
7, -
( l/2)( h,y, + h,*y:)]/c;
g,)/c:= 0,
tp/c,=0,
A,- ?$‘/c,= 8,
where A,, y, q and p are the Lagrange multipliers corresponding constraints (19) (29, (26) (and (26*). In a similar manner, th e fotcign policymaker’s problem can max
for this
f
(et,rr,M,c?,cl t =0
#(log c,yI+ log gfc)
to the
f28”)
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294
subject to (19), (i5*), (26”) and (26), and an analogous set of first order conc”iti0ns, (28*), results. Proposition 2 will be established if the policies and outcomes it specifies are seen to satisfy the first-order conditions, (28) and (28*), the equilibrium condition, (19), and the four budget constraints, (25), (25*), (26) and (26*). Proposition 2 is indeed consiseent with the budget constraints; the constraints are satisfied on a period-by-period basis, with b, = b: = 0. Moreover, the specified levels of public and private spending add up 1:3 2j; the equilibrium condition, (19), is satisfied. Now, consider the first-order conditions, (X). Since hry,*=gr and a,l =O, the first equation in (28) implies that &=O. The second implies that ~=(1/2)y, and since [*]=c, and (a)=0 in the third, y=l and q= l/2. Then, the fourth imp!ies that 1 *.
bt
=
-( 1/2pt/ct
where i is the Lagrangian function. So, r, is reduced to zero. Finally, the last equation says that gt =cJq = 2c,, which is what Proposition 2 specifies. In an analogous manner, the proposition can be shown to be consistent with the foreign policymaker’s first-order conditions, (28*). This completes the proof of Proposition 2. Finally, note that time consistency is not a problem here. If policymakers reoptimize in some future period, they will have the same budget constraints (since b, =O), and they will calculate the same first-order conditions. They will ci;rry out the plans calculated at t = 0. For similar reasons, consumers plans are time consistent; see footnote 7. e sei;;norage example an some limitatif .ISof the
So why has it not happened? Some would indeed argue that there has been too much inflation, too much public spending, and too much deficit spending in the industrial nations, but it would be hard to blame this litany of woes on the temptation to create seignorage. Fischer (1982) has calculate? the seignorage collected by over sixty countries between 1960 and 1978. In fourteen industria! countries seignorage averaged about 1 percent of GNP and accounted for only 6 percent of the total revenue collected. In the United States, the country that would seem best able to impose a seignorage tax on foreigners, seignorage averaged about 0.5 percent of GNP and only 2 or 3 percent of total revenue collected. There are countries for which the seignorage tax was an important source gf revenue. In Italy it accounted for about 15 percent of total revenue between 1973 and 1978, and in Argentina et-cent of revenue between 1960 and 1975.
M.B. Canzoneri, Taxation o$foreigners
295
Italy and Argentina would ,lot seem to be in a position to impose a seignorage tax on foreigners. Japan is the only reserve currency country that looks at all suspicious in Fischer’s data; in Japan seignorage averaged about 13 percent of GNP, and it accounted for about 12 percent of total reveau~. Why have policymakers not fallen into the Nash solution describe Why has U.S. monetary policy been so stable? Two approaches may yield answers to these questions in future research. First, there may be an important cost of inilation that has been omitted m the model outlined in section 2. Slow progress in work on the time consistency of monetary policy also suggests (to me, anyway) that such a cost is missing in most ‘maximizing’ models.’ Second, policymakers may be using reputationai strategies that lead to a different, low intlation Nash solution. There is already a welldeveloped literature on inflation biases and policy coordination that may be relevant here.’ o Good answers to these questions would presumably include an explanation of why one currency emerges as a ‘vehicle’ for trade while another does not, but this would require a majGi advance in monetary theory. A certain lack of robustness in the analysis presented above may also be due to the current state of monetary theory. It will be recalled that Helpman and Razin’s (1984) seller’s system was postulated to obtain distinct demands for the two currencies* purchases had to be made in the seller’s currency. Helpman and Razin also define a buyer’s system; in this system, buyers use their own currency, and sellers end up holding both domestic and foreign money balances at the end of the goods market. Here, it might be thought that Proposition 2 wc;luldgo through without any assumption about foreign equity hoiding. ThL is not the case; if fact, the proposition does not go through at all. Helpman and Razin point out that sellers will only accept both currencies if they result in the same profits for next period’s financial exchange; the arbitrage condition (3) must therefore be replaced by Pr=et+lPt
* l
‘Calve (1978) and Grossman (1988) find that (in the absence of some form of precommitment) policymakers would produce infinite rates of inflation. Grossman attributes this to the lack of costs to actual (as opposed to anticipated) inflation in their models; however, Grossman finds refuge in reputational equilibria, and does not try to specify the missing costs of innation. “Policymakers sometimes try to tie their hands with a k percent rule (or a targeting procedure). If the rule h,= h,*= 0 is credibly imposed, then the policymakers have to finance their spending with the income tax, which falls on their own citizens; it can be shown that a Nash solution to this game results in the efficient world outcome. Rogoff’s (1985) suggestion that monetary czars with (perversely) anti-inflation tendencies have been appointed to reduce the Inflation bias amounts to the same thing. In addition, trigger mechanisms and reputational strategies may have r3ade sovereign policymaking efficient without resort to rules or outside intervention. See Rogoif (1987; for a discussion of the literature stemming from arro and Gordon’s (1983) inflation bias model and Canzoneri and enderson (1988) for a discussion of the eficiencyof sovereign policymak;Tg via trigger mechanisms and reputational strategies.
296
M.B. Canzoneri, Taxation of foreigners
An equation like (8) will still result for the home household budget constraint, but in going fiorn eq. (8) to eq. (9), using the new arbitrage condition, one obtains:
The firms’ currency arbitrage does away with the foreign base for the seignorage tax, whether or not there is foreign ownership of the &ms. This lack of mhustness is more a comment on the state of monetary theory than an indictment of the proposition about seignorage taxes. In the cash-in-advance paradigm, some arbitrary restrictions must be placed on the use of the various currencies if the model is to produce distinct demands for individual currencies and well-defined seignorage taxes. The validity of statements like Proposition 2 will turn on which restriction is chosen. And this is not a peculiarity of the cash-in-advance paradigm. The lesson of Kareken and Wallace (1981) is that similar problems arise in overlapping generations mod&. Without a deeper theory of currency substitution, one cannot expect anything else. e general problem of taxing foreigners
The inefficiency described here is not limited to seignorage taxes. There are many ways in which governments tax foreigners. Corporate income is taxed before it can be passed on to domestic or foreign shareholders, and then taxes are withheld on dividends (and interest) going to foreigners.” The incidence of taxes on imports is shared with foreign producers; the incidence of taxes on exports is s?,ared with foreign consumers. In short, the taxation of foreigners is widespread. It would be very interesting to know what pczticq 4 public spending in the OECD co;;lltries is fnanced by foreigners. The simple seignorage example affords a clean view of the ineaciency that ~stllts from allowing sovereign poli symakers to tax foreigners. Most of the EZX~;‘.~ mentioned above distort the price structure directly, as would the zl~ntir~~~ tax if say a labor-leisure decision were added. Adding them to the . atl;i,! jys 7~~~:~‘. 3 complicate matters in at least two ways. First, time consistency often becomes a problem when policymakers can tax fixed money balances in order to avoid financing future spending with distortionary taxes; finding time consistent solutions can be difficult. Second, distortionary taxes are a source of inefficiency in and of themselves; in assessing the costs of “In soli>ecasesthe withholding is limited by treaty. Horst and Hufbauer (1983) describe these taxes briefly; ufbauer et al. (1988) review the existing tax treaty network in some detail and assess the consequences of an extension of the network.
M.B. Canzoneri, Taxation of foreigners
297
sovereign policymaking, it would be difftcult to separate the inefficiencies associated with the price distortions from the inefficiency coming from the taxation of foreigners. In any event, one guiding principle shines through: allowing sovereign policymakers to tax foreigners gives them adverse incenti-.-es; it should probably be discouraged.’ 2 12This is certainly the case when, as in the seignorage example, there are no other distortions in the economy. The usual caveat about second-best solutions is relevant here.
References Barro, Robert and David Gordon, 1983, Rules, discretion and reputation in a model of monetary policy, Journal of Monetary Economics 12, 101-122. Canzoneri, Matthew and Dale H:Tderson, 1988, Is sovereign policymaking bad, CamegieRochester Conference Series on Public Policy 28, 93-148. Calvo, Guillermo, 1978, On the time consistency of optimal policy in a monetary economy, Econometrica 46, 1411-1428. Fischer, Stanley, 1982, Seignorage and the case for a national money, Journal of Political Economy 90, no. 21,295-3 13. Grossman, Herschel, 1988, Inflation and reputation with generic policy preferences, unpublished manuscript, Sept. Helpman, Elhanan and Assaf Razin, 1984, The role of saving and investment in exchange rate determination under alternative monetary mechanisms, Journal of Monetary Economics 13, 307-325. Horst, Thomas and Gary Hufbauer, 1983, International tax issues: Aspects of bas:rc i&&e tax reform, in: Charles Walker and Mark Bloomfield, eds., New directions in federal tax policy for the 1980s (Balkinger Publishing Ctimpany, Cambridge, MA). Hufbauer, Gary, Kimberly Elliot and Eduardo Maldonado, 1988, Tax treaties and American interests, A Report to the National Foreign Trade Council, August. Kareken, John and Neil Wallace, 1981, On the indeterminacy of equilibrium exchange ratet, Quarterly Journal of Economics 96, no. 2, 207-222. Lucas, Robert, 1980, Equilibrium in a pure currency economy, Economic Inquiry 18, no. 2, 203-220. Lucas, Robert and Nancy Stokey, 1983, Optimal fiscal and monetary policy in an economy without capital, Journal of Monetary Economics 12, 5:-90. Rogoff, Kenneth, 1985, The optimal degree of commitment to an intermediate monetary target, Quarterly Journal of Economics 100, 1169-l 189. Rogoff, Kenneth, 1987, Reputational constraints on monetary policy, Carnegie-Rochester Conference Series on Public Policy 26, 141-l 8 1. Sargent, Thomas, 1987, Dynamic Macroeconomic Theory (Harvard University Press, Cambridge). Stockman, A!x, ‘1380,A theory of exchange rate determination, Journal of Political Economy 88,673-698.
NTIVES IN T
Matthew B. CANZONERI* Georgetown University, Washington, DC. 20057, USA Received January 1988, revised version received March 1989 Sovereign policymakers will opt for too much of the public good if their tax falls partially on foreigners. They myopically calculate that an increase in public spending is only partially financed by a decrease in home consumption; the rest comes from foreign consumption, which they do not care about. This paper presents an example with seignorage taxes. In a two-country model with cash-in-advance constraints, the inefftciency is characterized by an inflation bias, too Imuch public spending, and large fiscal deficits. Curiously, the countries most able to impose such taxes seem to have abstained from doing so.
I. Introduction
This paper illustrates an ine@ciency in sovereign policymaking that has not been discussed in the policy coordination literature. In a two-country model with cash-in-advance constraints, the ineficiency is characterized by an inflation bias, too much public spending, and large fiscal deficits. The inefficiency does not come from competition over the terms of trade, or from problems with time inconsistency, or from inflations distortionary et.& on decisions about labor versus leisure, cash versus credit goods, ar real balances; these distortions have been purposely excluded from the model.’ Rather, the inefficiency is due to the sovereign’s ability to tax foreigners. In the present example foreigners are hit with a seignorage tax, but clearly the problem is more general than the question of seignorage. Each country is composed of infinitely lived citizens ,who value both public and private spending; each country’s policymaker sets the level of public spending and taxation to maximize his citizens’ welfare. Brivate agents behave competitively, but each policymaker knows that his actions will affect *I wish to thank Roberto Chang, Mark Gertler, Dale Henderson, Gary Hufbauer, Pat Kehoe, Carol Rogers, Anne Sibert, Lars Svensson and an anonymous referee for helpful comments. They are in no way responsible for what follows; I suspect several of them would have done things quite differently. ‘In particular, I am not discussing the time consistency problems of Calvo (1978) or Lucas and Stokey (1383); 1 have purposely excluded factors that would lead to time inconsistency. 0022- 1996/89/$3.50 0 1989, Elsevier Science Publishers l3.V. (North-Holland)
284
M.B. Canzoneri, Taxation of foreigners
the behavior of the other policymaker (as well as the private sector). Thus, the equilibria inve;tigated in this paper are Nash solutions to a game between sovereign policymakers. Public spending in each country can be financed by an income tax on its own citizens. If the policymaker uses this tax, he realizes that an increase in public spending. must come at the expense of his own citizens’ private spending. The policymaker has the interests of his citizens in mind, so he makes the local decision between public and private spending efficiently. In fact, since other distortions have been excluded from the model, the result is globally efficient. When policymakers are restricted to the tax that falls exclusively on. their own citizens, the Nash solution to the game between policymakers is the outcome a world economic planner would choose. However, iublic spending can also be financed by a seignorage tax, part of which falls cn foreigners. The efficient world outcome can be supported by seignorage taxes, income taxes, or some combination of the two, but this felicitous outcome seems unlikely if the policymaker is allowed to resort to a tax on foreigners, whose welfare he does not care about.2 In choosing the level of public spending, he now thinks that an increase in his spending need not imply an equal decrease in his citizens’ spending; part of the increase can be financed by the tax on foreigners. Thus, there is a Nash solution in which policymakers eschew the income tax, in favor of a seignorage tax, and expand public spending. Compared with the efficient outcome, this Nash solution !s characterized by too much public spending, too much inflation, and large fiscal deficits. The seignorage example p?:zsented here is really rather puzzling, and that is one reason it was chosen to illustrate the more general problem of allowing governments to tax foreigners. The puzzle is that the bad Nash solution does not seem to be observed in the real world. The U.S. dollar is still the major vehicle for world trade, ye1 the United States only finances a small fraction of its spending with seignorage. Why is U.S. monetary policy SO siable? The German mark and the Japanese yen are also vehicle currencies, but only the Japanese appear to depend on seignorage to any great extent. This paper suggests two questions for future research. First, why is seignorage not used to a greater extent by key currency countries? (Or is this why they are key currency countries?) Second, how important is the more general problem, when all taxes on foreigners income are taken into account? Section 2 outlines the model use,d in the seignorage example and establishes Proposition 1, which states that a competitive equilibrium can support an efficient world outcome if tax rates are chosen properly. Section 3 ‘There may be many Nash solutions to a dynamic game such as this. Some rnq achieve the efficient outcome through the use of trigger mechanisms. II do not look for solutions that incorpcratc trigger mechanisms.
M.B. Canzoneri, Taxation of foreigners
285
describes the Nash game between sovereign policymakers and illustrates the inefficiency of allowing them to tax foreigners; Proposition 2 states that the efficient world outcome will not result if policymakers are allowed to use the seignorage tax, which falls partially on foreigners. Section 4 discusses the seignorage example in particular. It suggests sevtral approaches for future research on the puzzle described above, and it highlights a limitation of the analysis presented in sections 2 and 3. Section 5 looks beyond the seignorage example to assess the scope of the problem when all taxes on foreigners are taken into account; it suggests that the taxation of foreigners is very widespread and that the inefficiency that results should be tgken seriously.
2. A two-country model with income an seignorage taxes Think of a world consisting of just two countries. Tb,e home and foreign countries produce y, and yf units of a good that can be used for either public or private consumption. (Asterisks designate foreign country supplies, demands or prices; all quantities are measured in per capita terms.) Production is exogenous; for simplicity, let y,=y:'=y.
(1)
World output is fixed at 2Ji each period. The home country is composed of identical, infinitely hved households whose utility in period zero is given by
u= f
Go
S’(logc,-I-logg,),
where gt and c, are public and private consumption. The foi*r=lgncountry is similarly composed of identical, infinitely lived households whose utility is given by
U”= f 5’(logc,*+logg,*). t=O
There are 2j units of output available each period, and ho
(2’)
M.B. Canzoneri, Taxation of foreigners
286
public and private consumption equally; it is easy to calculate an efficient allocation of goods. Lemma 1.
A Pareto optimal allocation
is given by
A world social planner might well choose this allocation;3 however, the policymaker considered here cannot simply allocate goods. He must tax or borrow to finance his purchases, and he is subject to a cash-in-advance constraint that has yet to be specified. His taxes include an income tax that falls on his own citizens and a seignorage tax that falls on whoever holds the currency he issues. Now, consider the cash-in-advance constraints4 Each period begins with
a financial exchange and ends with a goods market. In the financial exchange, income taxes are collected, interest is paid on debt, new debt (in the form of either money or bonds) is issued, and governments and households acquire the cash they will need in the goods market that follows. In the goods market, shoppers pay for goods with cash; barter is not possible. At the end of each period, firms deliver the cash they have received to the households that own them; these cash holdings are the base for the seignorage tax. If seignorage taxes are to be well defined, the model must exhibit distinct demands for the two currencies ? This requires an arbitrary restriction on the cash-for-goods exchanges that can be made. Helpman and Razin (1984) show that a variety of restrictions will do. In their buyer’s system, the buyer’s currency is used in exchange; buyers must use their own country’s currency to pay for goods. In their seller’s system, the seller’s currency is used; sellers can only accept their own country’s currency in payment for goods. Either of these restrictions will produce a distinct demand for individual currencies, and seignorage taxes will be well defined. However, it turns out that the seller’s system allows the seignorage tax to fall on foreigners while the buyer’s system does not. In this section and the next the seller’s system is postulated; these points will be discussed further in section 4. 3More specl‘fitall y, the allocation described in Lemma 1 is the solution to the world planner’s problem: r
max Wc 6’(10gC,+10gg,)+(1-W) 2 6’(logc,*+logg,*) Icr.8r.ct.sll r=o i r=o I subject to c,+g,+cF+g,*sy,+yfr=2J, with w set equal to 0.5. ‘The model in this section owes much to Helpman and Razin (1984), which in turn owes much to Lucas (1980) and Stockman (1980). More elaborate discussions of the general set-up described in this paragraph and the next may be found in these papers or in chapter 5 of istinct money demands are also needed to avoid the exchange rate indeterminacy allace (1981).
of
M.B. Canzoneri, Taxation of foreigners
287
Taking account of two arbitrage conditions simplifies the analysis. The two countries’ goods are perfect substitutes, so Pt = etPL
(3)
where pt and p: are the home and foreign currency prices of the good, and et is the exchange rate in the financial exchange. In addition, government bonds are perfect substitutes, so It = met
0
+ &A
where I, and I,” are the gross nominal rates of return on home and foreign government bonds. ( 3j and (4) imply that gross real rates of return equalize: R, = UptIp, + I) = V(P,*/P,*, I) = RF
(5)
Home household utility can be rewritten as:
u=t~~S’rlog(e,,+c,,)+loggtl
(6)
where cht and cft are the household’s spending on home and foreign goods. In the seller’s cvstem, the home household’s decisions are constrained by mht
2 PtCht,
mht
+ etmft
m,t
2
Pi%,,
+ lht + etlft
(7)
+ 2)tTt
where )tihtand ml,are the household’s demands for home and foreign money, &t and Ift are its demands for home and foreign bonds, and z, is a lump-sum income tax. The first constraint is the cash&advance constraint; the second is the intertemporal budget constraint for the financial exchange. The first two terms on the right-hand side of (8) are cash received fr firms for last period’s sales. Home households are assumed to own half of equity in the firms of both countries. Thus, home households hold half of last period’s home currency balances and ha of last period’s foreig balances; they pay half of the ‘;torne seig
M.B. Canzoneri, Taxation offoreigners
288
of foreign equity that drives the results that follow, a justification
of the fixed
ownership assumption is warranted. In a stochastic version of the model, risk diversification could be used to explain foreign equity holding. Such an extension would, however, not be trivial; it will not be attempted here. Instead, it will be assumed that initial equity shares are as postulated for historical reasons. In equilibrium, domestic and foreign inflation rates will equalize; so real returns on domestic and foreign equity will equalize, and households will be willing to hold the postulated shares. This, however, is not enough to justify the analysis that follows. When a policymaker calculates his Nash policy, he considers the value of a marginal increase in his seignorage tax. This will cause a marginal differential in inflation rates, and thus a marginal differential in the rates of return on domestic and foreign equity. However, in what follows, transactions costs will be assumed to be . large enough to make portfolio changes unprofitable for these marginal changes in inflation rates. The budget constraint, (8), can be expressed more conveniently in real terms. Dividing through by pt, and using (3), (4) and (5), it becomes:
=
WPt - IlPJY, - 1 +wPE-
IlPl*)Y,*_1+
4
- lb:-
19
(9)
where bt = (Z,Jp,)
+ (I,Jp,*) is the households’ total demand for government debt. Additional simplicity comes from the fact that I, and I: are greater than one in the equilibria considered in this paper. NIonies are dominated assets that are only held for transactions purposes; the cash-in-advance constraints, (7), are always binding. Therefore, (7) and (9) can be combined:
chr+cfr+bp+r,=~~.5(pl-l/p,)y,-1+0.5(plr-l/p~)y,*-1
+R,&-,.
(10)
Finally, letting c, = Cht+ cft, the home household budget constraint can be
written as? ,Eo %@t-rJ=
f
at+ lCWPt/Pt+ l)Yt+WP1*/P,*,
t=o
+0*5(m- l/PO)-t 0*5(m*_ I/PO*),
AY,“l (11)
where m _ l and m? l are initial cash balances,’ and the a, are real discount 6The period-y-period constraints in (10) are collapsed into the single constraint (11) by using the constraints iteratively to eliminate the 6: and then assuming that lima&.+0 as T+m. ‘These initial conditions are consistent with starting the economy a period earlier; the home households would have reeked a half of the period - 1 currency balances as receipts from the firms’ period - 1 sales.
M.B. Camoneri, Taxation ojforeigners
289
factors; that is, u, 5 (&RI.. . R, _ I)_ 1 and a0 = 1. Analogous steps lead to the foreign household budget constraint: Q) c 4 (e-e?=
t=O
i a,+ICO.S(P,IPt+,)Y,+O*~(P~/P,S;~~Y,*l t=O
+OS(m-l/po)+0.5(mI ,/p$
(W)
I=Iome and foreign households choose c, and cr to maximize utilities subject to budget constraints. Their first-order conditions are: 6’(c,/c,) = a, = S’(c$/c,*).
(12)
These conditions ensure the intertemporal efficiency of consumption. Governments also face cash-in-advance constraints and budget constraints. If the home government purchases home output, then (13)
mtt 2 Pt&
is its cash-in-advance constraint. The home governmen% budget constraint is: (m!iJPJ+R,-lb,-,
=vaw-mt-,)/P,+bt.
(14)
In the financial exchange it must acquire cash for purchases in the goods market that follows, and it must pay principle and interest on last period’s bonds; these transactions can be financed withI income taxes, seignorage or new bonds. Collapsing (13) and (14) into a single constraint, the home government budget constraint becomes: a3
c
wr= f ~tC~t+bv-~t-JPtl* r=O t=O
Similarly, the foreign government budget constraint is: a0
c
a,[$ +(ml*-m,*_,)/p:]a r=o
a,s,” = f
r=O
The equilibrium conditions are: Cht+Cg+gl=yt=jt
and
qr+cf*t+gl*=yr*=y,
(15)
M.B. Canzoneri, Taxation of foreigners
290
mht + &
+ mtt = &hr
+ 6
+ 8,) = ml;
mf,+m~+m~~= p,*(c,t+c,*,f!e)=m~*
(17)
These conditions can be more conveniently expressed as: m,= pty,;
mt = pf
(18)
y&
and c,+g,+c,*+g,*=y,+y,*=2j.
(19)
Letting the monetary instruments be defined by growth rates, h, = (m, -m, _ J/m,
and
h,*= (m,*- rnf!-Jm,*,
(20)
seignorage revenues in equilibrium are: (mr- m, _ Jpt = h,y, and (rn: - rnf?-&‘p,*= h,*y,*.
(21)
Using (HI), (20) and (21), the household budget constraints become: c0 Q, a,c, = c c at ( Yt-5
t=O
t=O
30 c a,c,*= i
t-o
-
fMh,y, - O.Sh,*yf),
a,(y,*-r,*-OSh,y,-OSh,*y,*),
t=O
c2’2) (W
and the government budget constraints become: 00 c W, = f a,(%+ hYJ9
t=O
t=O
(23)
Q) c
a,gf
t=O
= i
r=o
a,( r,* +
h: y,*).
(23”)
The last terms in these budget constraints arc the seignorage taxes. Each government’s seignorage tax is shared equally by the citizens of both countries, while its income tax falls exclusively on its own citizens. The e tax is shared because each household owns half of the equity of tries, and receives half of the currency of both countries at the end
M,B.Canzoneri, Taxation of foreigners
291
An equilibrium must satisfy the equilibrium conditions, (18) and (I9), the households’ first-order conditions, (12), and three of the four budget const:aints, (22), (22*), (23) and (23*). (One is redundant).* Equilibria do exist. In fact, an efficient world allocation can be supported by a competitive economy if world tax rates are set properly. Proposition I. The eficient xo r!d &cation described in Lemma I is an equilibrium outcome if r,, h,, 7: and h,S are set to satisfy z, + h,y’= O.Sj and zf + hrj = My.
Proposition 1 can be verified directly. All of the budget constraints are satisfied on a period-by-period basis; that is, b, = b: = 0. There are high and low inflation ways of supporting the eflicient outcome. If money growth is set equal to zero and income taxes finance public spending, then inflation is equal to zero. At the opposite extreme, if income taxes are set equal to zero, then _PCPL-1 Pt
= h, = 0.5
and
n,* E pr*-f:Pt
1 = h,* = 0.5.
3. A Nash solution to the game betweem There is no reason to think that politically sovereign policymakers will settle on any of the efficient alternatives suggested by Proposition 1. The home policymaker’s objective is to max f S(log c, + logg,) ~~tr~tr~t.Ct,~f*Qt~ r=O subject to the equilibrium condition, (19), the first-order conditions, (12), and three of the four budget constraints, (22), (22*), (23) and (23*). The foreign policymaker’s objective is to *For example, (22), (23) and (23*), in conjunction with the equilibrium condition (14), imply (22*). To see this, sum the conditions in (14) to get: ,~Oa,(c,+n,+c?+g:)=
f a,2P I=0
Then, sum (22), (23) and (23*) t3 get: f a,(c,+g,+g,6)= I=0
i a,(~+TIZ+0.5h,~+O.Sh,*~). r=O
Finally, subtract the second expression from the first to obtain (22’).
M.B. Canzoneri, Taxation of foreigners
292
max f S’(logcf + log gf) {$I?, r?.ht,cp,Ct,at) t = 0 subject to the equilibrium condition, (19), the first-order conditions, (12), and three of the four budget constraints, (22), (32*), (23) and (23*). Sovereign policymakers care only about the welfare of their own citizens, and they have the ability to tax foreigners. Proposition 2 describes the probable outcome of this game between sovereign policymakers. Proposition 2. There exists a Nash solution to the game which is ineflcient. Nash strategies are given by:
h,= q=
213, h,* = 2/3, b,=O,
The corresponding
z,*=b,*=O. Nash outcomes are:
c, = (1/3)j& c,*= (l/3)5 71,= h, = 213, I$ = h,;:= 2,‘3. In this Nash solution, policymakers eschew the income tax in favor of the seignorage tax, half of which falls on breigners. In deciding upon the level of public consumption, each policymaker calculates that an increase in public spending will only lower his citizens’ private consumption by half the amount; the rest comes at the expense of foreign consumption. Consequently, he expands public spending beyond the efficient level. Compared with the efficient outcome of Proposition 1, the Nash solution is characterized by too much public spending, high fiscal deficits and excessive inflation. This is an example of the inefficiency of sovereign policymaking when there is an externality in policymaking: policymakers are allowed to tax foreigners. N#te that the policymakers may be fully aware of the selfdefeating nature of their competitive taxation. Each must engage in it anyway, because he knows the other will. The rest of this section is devoted to a proof of Proposition 2 and a word (in the last paragraph) about the time consistency of consumption plans, public and private. Readers who already believe in validity of Proposition 2 may wish to skip to section the two maximization proble by using the first-order con ition, (12), to e
M. B. Canzoneri, Taxation of foreigners
293
(25)
f s’[~-a,-(1/2)(hty,+h,sy~)]/c, t=o
(1 -S)-‘= and (1-q-l
= i s’[B-?~-(1/2)(h,y,+h,*y,S)]/c,S, t=O
and the government budget constraints
become:
syz,+h,y,)/c,
g 5’gJc, = ? t=O t-z
(26)
and S’g,*/c,*= f St@,* + h,*y,*)/c,*.
i t=O
WY
t=o
Then, dropping the foreign household budget constraint, maker’s problem reduces to: max
f
the home policy-
(27)
8(log c, + logg,)
~gt,~t*~t*ct*ct~ t=O
subject to (l!?), (23, maximization are:
(26) and (26*). The first-order
c,*:
-A, - pY(z,* +
h,:
-y~‘(l/~)y,fc,+~~sy,lc,=o,
c,:
d'/c, -
I, - yS’[j -
- W%t
+ hty, -
. 7,.
- yiY/q +
g,:
5’/gt -
h,*yf
conditions
-g,*)/c,*2 = 0,
7, -
( l/2)( h,y, + h,*y:)]/c;
g,)/c:= 0,
tp/c,=0,
A,- ?$‘/c,= 8,
where A,, y, q and p are the Lagrange multipliers corresponding constraints (19) (29, (26) (and (26*). In a similar manner, th e fotcign policymaker’s problem can max
for this
f
(et,rr,M,c?,cl t =0
#(log c,yI+ log gfc)
to the
f28”)
M.B. Canzoneri, Taxation of foreigners
294
subject to (19), (i5*), (26”) and (26), and an analogous set of first order conc”iti0ns, (28*), results. Proposition 2 will be established if the policies and outcomes it specifies are seen to satisfy the first-order conditions, (28) and (28*), the equilibrium condition, (19), and the four budget constraints, (25), (25*), (26) and (26*). Proposition 2 is indeed consiseent with the budget constraints; the constraints are satisfied on a period-by-period basis, with b, = b: = 0. Moreover, the specified levels of public and private spending add up 1:3 2j; the equilibrium condition, (19), is satisfied. Now, consider the first-order conditions, (X). Since hry,*=gr and a,l =O, the first equation in (28) implies that &=O. The second implies that ~=(1/2)y, and since [*]=c, and (a)=0 in the third, y=l and q= l/2. Then, the fourth imp!ies that 1 *.
bt
=
-( 1/2pt/ct
where i is the Lagrangian function. So, r, is reduced to zero. Finally, the last equation says that gt =cJq = 2c,, which is what Proposition 2 specifies. In an analogous manner, the proposition can be shown to be consistent with the foreign policymaker’s first-order conditions, (28*). This completes the proof of Proposition 2. Finally, note that time consistency is not a problem here. If policymakers reoptimize in some future period, they will have the same budget constraints (since b, =O), and they will calculate the same first-order conditions. They will ci;rry out the plans calculated at t = 0. For similar reasons, consumers plans are time consistent; see footnote 7. e sei;;norage example an some limitatif .ISof the
So why has it not happened? Some would indeed argue that there has been too much inflation, too much public spending, and too much deficit spending in the industrial nations, but it would be hard to blame this litany of woes on the temptation to create seignorage. Fischer (1982) has calculate? the seignorage collected by over sixty countries between 1960 and 1978. In fourteen industria! countries seignorage averaged about 1 percent of GNP and accounted for only 6 percent of the total revenue collected. In the United States, the country that would seem best able to impose a seignorage tax on foreigners, seignorage averaged about 0.5 percent of GNP and only 2 or 3 percent of total revenue collected. There are countries for which the seignorage tax was an important source gf revenue. In Italy it accounted for about 15 percent of total revenue between 1973 and 1978, and in Argentina et-cent of revenue between 1960 and 1975.
M.B. Canzoneri, Taxation o$foreigners
295
Italy and Argentina would ,lot seem to be in a position to impose a seignorage tax on foreigners. Japan is the only reserve currency country that looks at all suspicious in Fischer’s data; in Japan seignorage averaged about 13 percent of GNP, and it accounted for about 12 percent of total reveau~. Why have policymakers not fallen into the Nash solution describe Why has U.S. monetary policy been so stable? Two approaches may yield answers to these questions in future research. First, there may be an important cost of inilation that has been omitted m the model outlined in section 2. Slow progress in work on the time consistency of monetary policy also suggests (to me, anyway) that such a cost is missing in most ‘maximizing’ models.’ Second, policymakers may be using reputationai strategies that lead to a different, low intlation Nash solution. There is already a welldeveloped literature on inflation biases and policy coordination that may be relevant here.’ o Good answers to these questions would presumably include an explanation of why one currency emerges as a ‘vehicle’ for trade while another does not, but this would require a majGi advance in monetary theory. A certain lack of robustness in the analysis presented above may also be due to the current state of monetary theory. It will be recalled that Helpman and Razin’s (1984) seller’s system was postulated to obtain distinct demands for the two currencies* purchases had to be made in the seller’s currency. Helpman and Razin also define a buyer’s system; in this system, buyers use their own currency, and sellers end up holding both domestic and foreign money balances at the end of the goods market. Here, it might be thought that Proposition 2 wc;luldgo through without any assumption about foreign equity hoiding. ThL is not the case; if fact, the proposition does not go through at all. Helpman and Razin point out that sellers will only accept both currencies if they result in the same profits for next period’s financial exchange; the arbitrage condition (3) must therefore be replaced by Pr=et+lPt
* l
‘Calve (1978) and Grossman (1988) find that (in the absence of some form of precommitment) policymakers would produce infinite rates of inflation. Grossman attributes this to the lack of costs to actual (as opposed to anticipated) inflation in their models; however, Grossman finds refuge in reputational equilibria, and does not try to specify the missing costs of innation. “Policymakers sometimes try to tie their hands with a k percent rule (or a targeting procedure). If the rule h,= h,*= 0 is credibly imposed, then the policymakers have to finance their spending with the income tax, which falls on their own citizens; it can be shown that a Nash solution to this game results in the efficient world outcome. Rogoff’s (1985) suggestion that monetary czars with (perversely) anti-inflation tendencies have been appointed to reduce the Inflation bias amounts to the same thing. In addition, trigger mechanisms and reputational strategies may have r3ade sovereign policymaking efficient without resort to rules or outside intervention. See Rogoif (1987; for a discussion of the literature stemming from arro and Gordon’s (1983) inflation bias model and Canzoneri and enderson (1988) for a discussion of the eficiencyof sovereign policymak;Tg via trigger mechanisms and reputational strategies.
296
M.B. Canzoneri, Taxation of foreigners
An equation like (8) will still result for the home household budget constraint, but in going fiorn eq. (8) to eq. (9), using the new arbitrage condition, one obtains:
The firms’ currency arbitrage does away with the foreign base for the seignorage tax, whether or not there is foreign ownership of the &ms. This lack of mhustness is more a comment on the state of monetary theory than an indictment of the proposition about seignorage taxes. In the cash-in-advance paradigm, some arbitrary restrictions must be placed on the use of the various currencies if the model is to produce distinct demands for individual currencies and well-defined seignorage taxes. The validity of statements like Proposition 2 will turn on which restriction is chosen. And this is not a peculiarity of the cash-in-advance paradigm. The lesson of Kareken and Wallace (1981) is that similar problems arise in overlapping generations mod&. Without a deeper theory of currency substitution, one cannot expect anything else. e general problem of taxing foreigners
The inefficiency described here is not limited to seignorage taxes. There are many ways in which governments tax foreigners. Corporate income is taxed before it can be passed on to domestic or foreign shareholders, and then taxes are withheld on dividends (and interest) going to foreigners.” The incidence of taxes on imports is shared with foreign producers; the incidence of taxes on exports is s?,ared with foreign consumers. In short, the taxation of foreigners is widespread. It would be very interesting to know what pczticq 4 public spending in the OECD co;;lltries is fnanced by foreigners. The simple seignorage example affords a clean view of the ineaciency that ~stllts from allowing sovereign poli symakers to tax foreigners. Most of the EZX~;‘.~ mentioned above distort the price structure directly, as would the zl~ntir~~~ tax if say a labor-leisure decision were added. Adding them to the . atl;i,! jys 7~~~:~‘. 3 complicate matters in at least two ways. First, time consistency often becomes a problem when policymakers can tax fixed money balances in order to avoid financing future spending with distortionary taxes; finding time consistent solutions can be difficult. Second, distortionary taxes are a source of inefficiency in and of themselves; in assessing the costs of “In soli>ecasesthe withholding is limited by treaty. Horst and Hufbauer (1983) describe these taxes briefly; ufbauer et al. (1988) review the existing tax treaty network in some detail and assess the consequences of an extension of the network.
M.B. Canzoneri, Taxation of foreigners
297
sovereign policymaking, it would be difftcult to separate the inefficiencies associated with the price distortions from the inefficiency coming from the taxation of foreigners. In any event, one guiding principle shines through: allowing sovereign policymakers to tax foreigners gives them adverse incenti-.-es; it should probably be discouraged.’ 2 12This is certainly the case when, as in the seignorage example, there are no other distortions in the economy. The usual caveat about second-best solutions is relevant here.
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