-11 -

If ppp holds, (11) can be Substituted into (18) to yield

(19) r= * = (nay s(n) (1 en*) + UC a)/(an*)

This is the original H-J result, in exact form. Even with equal tax rates,
equalization of real after-tax interest rates does not hold as long as tax
rates are non-zero. Recall that ina two-country world where only interest
income Is taxed, and where tax rates in both countries are identical,
purchasing power parity is consistent with real after tax interest rate
equalization. One can then conclude that the existence of the capital
gains tax, not the tax on interest receipts, creates this non-neutrality.
If capital gains on foreign exchange transactions are taxed at
rates lawer than interest receipts, as shown by Blejer (1983), one can
without loss of generality normalize the tax rate on capital gains to be
zero. ‘This case can then be analyzed as if only interest income were taxed
at home, as analyzed above. If tax rates differ, changes in anticipated
inflation will alter the interest-rate differential, whereas if tax rates

are equal, neutrality is preserved.

V. Non-neutrality when Real Returns Are Taxed

It was shown above that ina two-country world in which nominal
returns are taxed, in which interest parity exists, and in which purchasing
power holds, taxing capital gains on foreign exchange transactions

introduces a non-neutrality; changes in anticipated inflation will alter


-2-

and abroad drive a wedge between real interest rates that would otherwise
be equal (i.e., why. should the imposition of a proportional tax on all
goods create reallocations of resources?)?

The purpose of this paper is twofold. First, the paper
demonstrates that the source of the wedge between real rates is not the
existence of a tax on interest income but instead the implicit assumption
that capital gains are taxed as if they were interest income. Secondly,
the paper attempts to clarify the conditions under which the basic H-J
proposition holds "exactly" (rather than as an approximation) -- the
proposition that in a world in which interest income is taxed, both
purchasing power parity and equalization of real after-tax interest-rates
(or constancy of the real after-tax interest-rate differential) cannot hold
simultaneously. Furthermore, cases in which real returns are taxed are
also considered.

Three tax regimes are considered: the first is one in which
interest receipts are taxed where they are earned; the second is one in
which interest receipts are taxed at home regardless of where they are
earned; and the third is one in which both interest receipts and capital
gains on foreign exchange transactions are taxed at home. Double taxation
is not considered. All cases are considered in "exact" rather than
"approximate" form.

The results of the paper can be summarized as follows. In the
first regime, if purchasing power parity holds, changes in anticipated
inflation will not alter the equilibrium real after-tax interest-rate in

either country, regardless of the relative rates of taxation. In the


B15 A

International Finance Discussion Papers

IFDP
NUMBER TITLES
1986
280 Taxation of Capital Gains on Foreign
Exchange Transactions and the Non*neutrality
of Changes in Anticipated Inflation
279 The Prospect of a Depreciating Dollar
and Possible Tension Inside the EMS
278 The Stock Market and Exchange Rate Dynamics
277 Can Debtor Countries Service Their Debts?
Income and Price Elasticities for Exports
of Developing Countries
276 Post-+simulation Analysis of Monte Carlo
Experiments: Interpreting Pesaran's (1974)
Study of Non#nested Hypothesis Test Statistics
275 A Method for Solving Systems of First Order
Linear Homogeneous Differential Equations
When the Elements of the Forcing Vector
are Modelled as Step Functions
274 International Comparisons of Fiscal Policy:
The OECD and the IMF Measures of Fiscal
Impulse
273 An Analysis of the Welfare Implications of
Alternative Exchange Rate Regimes: An
Intertemporal Model with an Application
1985
(partial Tisting)
272 Expected Fiscal Policy and the Recession
of 1982
271 Elections and Macroeconomic Policy Cycles
270 Assertion Without Empirical Basis: An

Econometric Appraisal of Monetary Trends
in... the United Kingdom by Milton Friedman
and Anna J. Schwartz

Pleése address requests for copies
Papers, Division of International Finance,

the Federal Reserve Systen, Washington, D.C. 20551.

AUTHOR(s)

Garry J. Schinasi

Jacques Melitz

Michael K. Gavin
Jaime Marquez
Caryl McNeilly

Neil R. Ericsson

Robert A. Johnson

Garry Schinasi

Andrew Feltenstein
David Lebow
Anne Sibert

William H. Branson
Arminio Fraga
Robert A. Johnson

Kenneth Rogoff
Anne Sibert

David F. Hendry
Neil R. Ericsson

to International Finance Discussion
Stop 24, Board of Governors of


-7 -

III. Exact Arbitrage Relations for Three Tax Regimes3

The General Set-up

Fisherian relations in exact form are written as follows:

(9a) 1+ i(t-t) = (1tr)(1+n) ,

(9b) 1 + i*(1-1*) = (14r*)(14+0*) .

From (9), the real after tax interest-rate differential is

(10) p= r* = [1 + it) # od - 01 + Per + oD.

Furthermore, an exact form of ppp is required and is represented as

follows:

(11) eg= [14mg l/U1+af] .

Three Exact Arbitrage Relations

One can think of at least two other relevant tax regimes
(treaties) to consider. The first regime is one in which interest payments
(nominal, or real) are taxed only by the country in which they are earned.
The second regime is one in which interest is taxed only in the country

where ore resides. One can of course also consider cases of double

3Similar results can be found in approximate form in Blejer (1983).


II. Taxing Capital Gains as Interest Income and the Non-neutrality
Proposition: The Case of Approximate Arbitrage Relations

In a two-country world in which nominal interest receipts are
taxed, real interest rates in the two countries are assumed to obey 4

Fisherian hypothesis represented below as

(1a) i(i-t) = r+, and

(1b) i*(1-1*) = r¥ + a,

where, * indicates foreign and,

= nominal interest rate

= tax rate on nominal interest receipts

expected inflation rate

= inflation adjusted after-tax interest rate (or the "real after-tax"
interest rate)

Saar
4

From (1), the real after tax interest-rate differential can be

derived as

(2) r= r® = (tet) - i%(1-1*) - Cn - o*)

In general, the differential will be nonzero. H-Jd (1982) show that a
ehange in anticipated inflation in the home country would create a change
in the differential, even if tax rates were equal. This result is
reproduced here, and it is then shown to depend on the assumption that
capital gains on foreign exchange transactions are taxed as if they were

interest income.


-3-

second regime neutrality exists only when tax rates are equal. In the
third regime, where interest and capital gains are both taxed, real
after-tax interest rates will change even if tax rates are equal, but only
because capital gains are taxed as if they were interest receipts. If
capital gains on foreign exchange transactions are taxed at rates below
taxation of interest receipts, then it can be shown that the results in the
second regime hold. For cases in which neutrality prevails, it can further
be shown (trivially) that the real after-tax interest differential will be
zero.2

When real returns are taxed instead of nominal returns, taxing
capital gains as interest income preserves neutrality, while taxing only
interest income introduces non-neutrality.

Section II briefly reviews the H-J results. Section III
specifies the exact interest parity conditions for three relevant tax
regimes: (treaties). Section IV derives results for the case in which
nominal. returns are taxed and section V derives results for the case in

which real returns are taxed.

2one can assume, without loss of generality, that the real after-tax
interest-rate differential is zero. After substituting various interest
parity conditions in the interest-rate equalization equation, one cah then
determine whether or not ppp holds. In instances where the two are
consistent (not consistent) it can be shown that the real interest
differential will be zero (nonzero) and changes in anticipated inflation
will be neutral (nonneutral) in the sense that changes in anticipated
inflation will not (will) alter the initial interest-rate differential.
Note that in general the differential as represented in eq. (2), and
particularly eq. (10) will be nonzero.


IFDP
NUMBER
269

268

267

266

265

264

263

262

261

260

259

258

257

256

255

254

316 #

International Finance Discussion Papers

TITLES
Canadian Financial Markets: The Government's
Proposal for Reform

Was It Real? The Exchange Rate Interest
Differential Relation, 197381984

The U.K. Sector of the Federal Reserve's
Multicountry Model: The Effects of
Monetary and Fiscal Policies

Optimal Currency Basket in a World of
Generalized Floating: An Application to
the Nordic Countries

Money Demand in Open Economies:
Substitution Model for Venezuela

A Currency

Comparing Costs of Note Issuance Facilities
and Eurocredits

Some Implications of the President's Tax
Proposals for U.S. Banks with Claims on
Developing Countries

Monetary Stabilization Policy in an Open
Economy

Anticipatory Capital Flows and the Behaviour
of the Dollar

Simulating Exchange Rate Shocks in the MPS
and MCM Models: An Evaluation

Trade Policy for the Multiple Product
Declining Industry

Long Memory Models of Interest Rates, the
Term Structure, and Variance Bounds Tests

Currency Substitution and the New Divisia
Monetary Aggregates: The U.S. Case

The International Transmission of Oil Price
Effects and OPEC's Pricing Policy

U.S. Banks' Lending to Developing Countries:
A LongeraTerm View

Conditional Econometric Modelling:
An Application to New House Prices
in the United Kingdom

AUTHOR(s)
Garry J. Schinasi
Richard Meese
Kenneth Rogoff

Hali J. Edison

Hali J. Edison
Erling Verdal

Jaime Mar quez

Rodney H. Mills

Allen B. Frankel

Marcus H. Miller
Arnold Kling
Arnold Kling
Catherine Mann
Gary S. Shea
Jaime Marquez
Jaime Marquez
Henry S. Terrell

Rod Mills

Neil R. Ericsson
David F. Hendry


-6-

one tax rate is non-zero. Furthermore, anticipated changes ir inflation
will alter the interest-rate differential betweeen countries as long as the
home tax rate is nonzero, even if tax rates are equal.

However, if only nominal interest receipts are taxecl, the
existence of equal tax rates alters these conclusions. When only nominal

interest receipts are taxed, the appropriate arbitrage relation is eq. (6)

(6) iQ@- t) = it - tte.

Substituting equation (6) into (2) yields

(7) p- * = i8(t¥-t) +e - (n- W*).

If ppp holds, (4) can be substituted in (7) to yield

(8) r= r® = i*(c¥-t).

In a world where only interest receipts are taxed and ppp holds, real

after-tax interest rates differ between the two countries and changes in

anticipated inflation alters this differential only when tax rates differ.

Stated differently, when only interest receipts are taxed and when tax
rates at home and abroad are equal, real after-tax interest-rate

equalization is fully consistent with ppp.


International Finance. Discussion Papers
Number 280

April 1986

TAXATION OF CAPITAL GAINS ON FOREIGN EXCHANGE TRANSACTIONS
AND THE NONANEUTRALITY OF CHANGES IN ANTICIPATED INFLATION

by

Garry J. Schinasi

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished
material) should be cleared with the author or authors.


-9 -

country. And in (14) home taxes are paid on capital gains as well as

interest income.

1V. Non-neutrality when Nominal Returns Are Taxed

Taxes on Interest Income Paid where Earned

In the first tax regime, where interest is taxed where it is
earned, arbitrage relation (12) is relevant. Substitution of (12) into

(10) yields

(15) ree = [1 + akC-t*)Je/01 + we) - C1 + ater) + WD.

Under the assumption that ppp holds we can substitute (11) into (15) and
find that the real interest-rate differential is zero. In the first tax
regime, equalization of inflation-adjusted after-tax interest rates is
fully consistent with purchasing power parity, and changes in anticipated
inflation will not create changes in real after-tax interest rates in
either country.

If interest receipts are taxed where they are earned, and ppp
holds, investors in each country consider domestic and foreign tax rates in
portfolio decisions. Nominal interest rates fully reflect tax
differentials as well as inflation differentials.

Taxes on Interest Income Paid to Home Country

Now consider the second tax regime, where residents are taxed
only in their own country. Arbitrage relation (13) is relevant in this

regime and substitution into (10) yields


-8 -

taxation, where interest earned abroad is taxed by both the foreign and
home countries, but this appears to be less relevant.4

Each of these tax treaties implies a different foreign exchange
arbitrage relation. Equations (12) and (13) represent arbitrage relations
for the first and second tax regimes, respectively, while (14) reproduces
in exact form, the arbitrage relation used by H-J in which both interest

income and capital gains are taxed at the home country tax rate:>

(12) 1 + iC-t) = C1 + ike) Je 5
(13) 1 + i(i-t) = [1 + i*(1-1)Je 5 and,

(4) 1 + i(-t) = 1 +001 + i*)e - 111-1).

Arbitrage at home implies that the (expected) after-tax noninal
return (cost) at home must equal the (expected) after-tax return (cost)
abroad. Eq.(12) represents the arbitrage relation when interest income is
taxed where it is earned so different tax rates appear on either side of

the relation. In (13), home taxes are paid on interest earned in either

4 according to Blejer (1983, page 5, footnote 2), "Japan, the Netherlands,
and some other industrial countries do not distinguish for tax purposes
between regular income and exchange gains. The United States, Canada, and
the United Kingdom apply rates of capital gains,..., to foreign exchange
transactions...." "An additional distinction refers to the timing of
taxation. While most countries tax foreign exchange gains and losses when
they are realized, the United States, Japan, Canada and the United Kingdom
also tax accrued gains and losses. In the Federal Republic of Germany,
unrealized gains are not taxable until realized wherever unrealized losses
are deductible when incurred."

5This exact arbitrage relation was also used by Ben Zion and Weinblatt
(1984).


-5 -

Let St be the domestic currency price of foreign currency, and
define ey=(1+e_)=Ey(S_/St-1) so that « represents the expected depreciation
of the home currency. The arbitrage relation assumed in H-J is

(3) i= i* +.

This approximate arbitrage relation has at least two interpretations:
either arbitrageurs ignore taxes; or domestic interest, foreign interest,
and capital gains are taxed at equal rates at home. In this second
interpretation the arbitrage relation can be written as

(3)" i(i-t) = i*(1-1) + e(1-1).

If purchasing power parity (ppp) holds, as H-J (1982) assumes,

then (4) holds:

(4) eg= mE - 1E

Substitution of (4) into (3) and then of (3) into (2) yields

(5) ro rt = i*(r%-1) - et.

In a two-country world, where Fisher relations hold for domestic trades but

ahere interest parity condition (3) holds, equalization of real after tax

interest rates and purchasing power parity cannot both hold when at least


Taxation of Capital Gains on Foreign Exchange Transactions
and the Non-neutrality of Changes in Anticipated Inflation
by Garry J. Schinasi

I. Introduction

In a two-country world with perfect capital markets and no taxes,
the existence of purchasing power parity is fully consistent with interest
parity and the equalization of real interest rates across countries. In
such a world, changes in anticipated inflation in either country will not
alter the world equilibrium real interest rate. In a world in which taxes
exist, real after-tax interest rates need not be equal, and changes in
anticipated inflation may create arbitrage opportunities, thereby creating
capital flows between countries and thereby altering equilibrium
interest-rate differentials.

It was argued in Howard and Johnson (1982) that in a two-country
world the "existence of taxes on nominal interest receipts" introduces a
"non-neutrality" in the sense that changes in anticipated inflation cause
either a change in the real after-tax interest-rate differential or a
departure from purchasing power parity. H-J (1983) further showed that if
real after-tax interest rates are equalized across boundaries then
purchasing power parity will not hold.’ It was argued that each
proposition holds even if tax rates in both countries are equal; these
propositions are counter-intuitive. Why should the introduction in each

country of an equal, proportional tax on interest receipts earned at home

1It was further shown in H-J (1983) that if a tax is imposed on real
interest instead of nominal interest, departures from purchasing power
parity can also occur. This is further discussed in the final section of
this paper.


-12 -

the real after-tax interest differential even when tax rates are equal.
Taxing only interest receipts preserves the type of neutrality that would
exist in a world without taxes. The non-neutrality occurs because in the
first world the inflation differential (i.e., the expected change ir. the
exchange rate) is taxed while in the second it is not.

If real returns are taxed instead of nominal, these conclusions
are reversed. Taxing capital gains as if they were interest receipts
preserves neutrality while taxing only interest receipts introduces a
non-neutrality. Governments intent on taxing real returns will preserve
neutrality if they tax capital gains on foreign transactions as interest
income. These propositions will now be demonstrated.

When real returns are taxed the relevant Fisher relations are
(20a) or = [(1#i)/( +m) - 10-1),
and

(200) r*= [(1+4*)/(140*) = 10(1-1*)

Subtracting (20b) from (20a) yields the real interest-rate differential in

(21):

(21) rerte (14i) = 1)/(1 4m) = (14) (1-4) = Cea).

Substituting the various arbitrage relations (12), (13), and (14) into (21)


-14 -

References

Ben Zion, Uri and J. Weinblatt, "Purchasing Power, Interest Rate Parities
and the Modified Fisher Effect in Presence of Tax Agreements," Journal
of International Money and Finance ,3, (1984), p.67-73.

Blejer, Mario I., "Financial Market Taxation and International Capital
Flows," in Taxation, Inflation, and Interest Rates, edited by Vito
Tanzi, International Monetary Fund, 1984.

Howard, D.H. and K.H. Johnson,"Interest Rates, Inflation, and Taxes: The
Foreign Connection," Economic Letters, 9, (1982), p.181-4.

, “Purchasing Power Parity and Real After Tax Interest
Rate Arbitrage," International Finance Discussion Paper #222 ,May 1983.



Taxation of Capital Gains on Foreign Exchange Transactions
and the Non-neutrality of Changes in Anticipated Inflation

Garry J. Schinasi, Economist*
International Finance Division
Federal Reserve Board
April 1986

* The author would like to acknowledge the extensive and enlightening
discussions with Karen Johnson and David Howard; the paper is much improved
as a result of these discussions. Comments and suggestions from other
menbers of the International Finance Division were also helpful. The
author assumes full responsibility for any remaining errors and ‘omissions.


Abstract

In a two-country world with perfect capital markets and no taxes,
the existence of purchasing power parity is fully consistent with interest
parity and the equalization of real interest rates across countries. In
such a world, changes in anticipated inflation in either country will not
alter the world equilibrium real interest rate. If asset returns are
taxed, the existence of taxes may drive a wedge between real after-tax
interest rates, and changes in anticipated inflation may create arbitrage
opportunities, thereby creating capital flows between countries and thereby
altering equilibrium interest-rate differentials.

The purpose of this paper is twofold. First, the paper
demonstrates that the source of the wedge between real rates is not the
existence of a tax on interest income (as argued in the literature on this
subject) but instead the implicit assumption that capital gains are taxed
as if they were interest income. Second, the paper attempts to clarify the
conditions under which the basic proposition first argued by Howard and
Johnson (1982) holds "exactly" (rather than as an approximation) -- the
proposition that in a world in which interest income is taxed, both
purchasing power parity and equalization of real after-tax interest-rates
(or constancy of the real after-tax interest-rate differential) cannot hold
simaltaneously. Furthermore, cases in which real returns are taxed are

also considered.


-10 -

(6) r= r® = C1 + aXe Je/tt + nd - 01 + 8) + ry.

If ppp holds, (10) can be substituted in (16) to yield

(7) ee et = C8 +].

When interest receipts are taxed at home, changes in anticipated inflation
alter the real after-tax interest-rate differential only when tax rates
differ. Because foreign tax rates do not directly affect domestic nominal
interest rates, foreign and domestic portfolio decisions for hcme-country
investors are not directly affected by foreign tax rates. Nominal interest
rates will not fully reflect tax differentials and the real after-tax rates
will differ; the non-neutrality exists. When tax rates are equal, the home
tax rate conveys the same information as the foreign tax rate. Nominal
interest rates fully reflect all tax information in both countries and the

real after-tax differential is zero.

Tax on Interest and Capital Gains Paid to Home Country

When taxes are paid on both interest income and capital gains, the H-J
exact arbitrage relation is appropriate. Substituting (14) into (10) yields

the real after-tax interest-rate differential,

(18) r= r= C1 +i*)C1-t)ett (14m) - [14ik(i- te) 1/140).


-13 -

and assuming purchasing power parity yields (22), (23), and (24),

respectively:

(22) ports O/(14n*) = (14m) - (2) ;

(23) ror*= U(r) (en) + VC 4n®) = (14m) - (2) 5

and,

(24) rer®= C(14i*)/(14n*) - 110% 1).

By inspection it can be seen that only in the case when capital gains are

taxed as interest income (eq. (24)) will equal tax rates in both countries

preserve neutrality.

6strictly speaking, the arbitrage relations derived earlier do not apply in
a world in which real returns rather than nominal returns are taxed.
Arbitrageurs would behave differently if real returns were taxed. It can
easily be shown that the results derived in section V are correct, however.