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

International Finance. Discussion Papers Number 280

April 1986

TAXATION OF CAPITAL GAINS ON FOREIGN EXCHANGE TRANSACTIONS AND THE NON#NEUTRALITY 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to International Finance Discussion Papers (other than an acknowledgment by a writer that he has had access to unpublished material) should be cleared with the author or authors.

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 purehasing power parity and equalization of real after-tax interest-rates (or constancy of the real after-tax interest-rate differential) cannot hold similtaneously. Furthermore, cases in which real returns are taxed are.

also considered.

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.

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 lIt 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.

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. Secondcly, the paper attempts to clarify the conditions under which the basic H-d 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

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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.

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.

20ne 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 determ:.ne 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.

-y - 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 a

Fisherian hypothesis represented below as

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

(1b) i*(1-1*) = r¥® + 1%,

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)

SaAaAre i

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

derived as

(2) r- r*® = i(t-t) - i*(1-1*) - (a - W*) .

In general, the differential will be nonzero. H-J (1982) show that a change 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.

-5 - Let St be the domestic currency price of foreign currency, and define ep=(1+tez)=E_(St/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-t).

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

then (4) holds:

(4) et= mth 7 1 .

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

(5) r-r*® = i*(t*-1) - et.

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

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

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

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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) i(1 - 1) = i*(1- t) te.

Substituting equation (6) into (2) yields

(7) r- r*® = i*(a%1) te - (n- W*) .

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

(8) r- r® = iX(t*-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.

-T -

III. Exact Arbitrage Relations for Three Tax Regimes3 The General Set-up

Fisherian relations in exact form are written as follows:

(9a) 1 + i(1-t) = (1+#r)(14+m) ,

(9b) 1 + i*(1-1t*) = (14+r*)(1+7*) . From (9), the real after tax interest-rate differential is (10) r= r* = [1 + i(t-t)I/01 + wd - 01 + e101 + oD,

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

follows: (11) eg= C1+mp]/C1+0¢] .

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).

-8 -

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

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 + i(i-t)

C1 + i*(1-1*) Je ; (13) 1 + i(1-1t) = [1 + i*(1-1t)Je ; and,

(14) 1 + i(t-t) = 1 + C01 + i*)e - 1](1-1) .

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."

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

“9 -

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

interest income.

IV. 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) r- r* = (1 + i*(1-a*)Je/E1 + ew) - 01 + i*(-c*) ]/01 + n*]

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

-10 -

16) r-r*® = (1 + i*(-t)Je/[1 + 1] - [1 + Wad-o)Vt1 +0].

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

(7) r- et = (it(tt-) 1 + wd].

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* = C(1+i*)(1-c)etr (tem) - C1+iR(i- te) IC 4m)

-11 -

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

(19) r= r* = a(n) /(14m)(1en*) + i*(r*-a)/(14n*) ,

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 aire 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 lqwer 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

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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) r = [(1+i)/(1+m) - 1](1-1), and

(200) r*= CO+i*)/(4n*) - 1]C1-1*)

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

(21):

(21) rert= (+i) (-a)/( 4m) -— (14i*)-)/4a) = (ret).

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

-13 -

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

respectively:© (22) rer*= a*/(14+0*) - w/(1+n) - (t¥=1) ;

(23) r-or*= i*(a*-1)/(1 +0") + a*/(140*) - W(1+t) - (1*-1)

. ,

and,

(24) rer*= [(14+4*)/(140*) - 1)(1*-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.

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References

Ben Zion, Uri and J. Weinblatt, "Purchasing Power, Interest Rat? 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.

IF DP

NUMBER

280

279

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270

B15 -&

International Finance Discussion Papers EE BE SCussion Papers

TITLES

1986

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

The Prospect of a Depreciating Dollar and Possible Tension Inside the Ems

The Stock Market and Exchange Rate Dynamics

Can Debtor Countries Service Their Debts? Income and Price Elasticities for Exports of Developing Countries

Post-+simulation Analysis of Monte Carlo Experiments: Interpreting Pesaran's (1974) Study of Non#nested Hypothesis Test Statistics

A Method for Solving Systems of First Order Linear Homogeneous Differential Equations When the Elements of the Forcing Vector

are Modelled as Step Functions

International Comparisons of Fiscal Policy: The OECD and the IMF Measures of Fiscal Impulse

An Analysis of the Welfare Implications of Alternative Exchange Rate Regimes: An Intertemporal Model with an Application

1985 (partial listing)

Expected Fiscal Policy and the Recession of 1982

Elections and Macroeconomic Policy Cycles

Assertion Without Empirical Basis: An Econometric Appraisal of Monetary Trends

in ... the United Kingdom by Milton Friedman and Anna J. Schwartz

ee Pleese address requests for

Papers, Division of International

the Federal Reserve System, 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

copies to International Finance Discussion Finance, Stop 24, Board of Governors of

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316 &

International Finance Discussion Papers

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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

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

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 Mar quez Jaime Mar quez Henry S. Terrell

Rod Mills

Neil R. Ericsson David F. Hendry