-~12-

both cannot hold when tax rates are nonzero and inflation rates are not
identical. In this paper a bit of evidence is presented which is
consistent with the arbitrage condition for real after tax interest
rates prevailing (roughly) for a substantial period, but the main point
of the paper is that neither condition can be expected to prevail
consistently either over time or across currencies. Neither condition
can substitute adequately for a general equilibrium model in which both
the real exchange rate and inflation are determined as endogenous

variables.


which reduce to the familiar interest rate arbitrage condition: Ry =
Ry +e. (Note that it is specified that taxes are levied on nominal
interest income.) In Howard and Johnson, it is shown that if
conditions (1) and (2) hold, a change in expected inflation in one
country implies that either the real exchange rate must change, that is
PPP will not hold, or there must be a differential impact on real after
tax interest rates across countries, even if tax rates are equal. Some
combination of these two effects is also possible.2/

In the above analysis, no relationship between uy and lo, is
stated. Conditions (1) and (2) apply to investors who face a country-
specific combination of tax rates and expected inflation. However,
these investors can observe all such combinations, and some are in a
position to change their location or set up a subsidiary in order to
seek out the highest real after tax rate of return. A piece of
evidence of this kind of behavior is the existence and use of tax
havens. The fact that such havens are heavily utilized indicates that
at least a significant portion of investors are concerned with after
tax rates of return and are willing to move funds and operations across
national boundaries in order to take advantage of various tax
incentives. Such investors presumably move funds between assets
denominated in different currencies and located in different countries
until their expected after tax real rates of return are equal, at least

in the simple case examined in this paper in which the assets are

perfect substitutes and there are no barriers to such movements.


- 16 -

Purchasing power parity, e = T) > Mos into the interest rate
arbitrage condition, Ry = Ry +e. As mentioned in the text, the
evidence presented by Frenkel indicates that purchasing power parity
is not an attractive proposition about market expectations. The
specification of PPP which is implicit in their analysis plus neglect
of the role that taxes play in the portfolio allocation decisions of
international investors may be important reasons why the evidence
Presented by Kane and Rosenthal, although perhaps suggestive, is not
entirely convincing.

The Kane and Rosenthal evidence is not convincing chiefly for
two reasons. First, Kane and Rosenthal interpret low t-ratios as
supporting their hypothesis when, in fact, the t-ratios could just
be reflecting the imprecision of their estimates. Second, even
accepting the t-ratios as valid evidence, there is a large
Proportion of high t-ratios in the results reported. In Kane and
Rosenthal's Table 4B, nearly half (31 out of 65) of the regressions
contain at least one t-ratio greater than 1.73 (the critical value
for 95 percent confidence level) in absolute value. The authors
split their sample period (February 1974 - June 1979) in half and
implicitly argue that the first half's experience is less relevant
because it took time for agents to become familiar with a floating
exchange rate regime. This division is, of course, arbitrary and
one might argue that a 32 month learning period seems a bit long.
Nevertheless even in the second half of Kane and Rosenthal's sample
Period there is a very large Proportion of regressions with one or

more t-ratios exceeding 1.73; in Table 4B, for months 33 through


rates of return. As such it represents just another force acting to
Prevent the PPP condition from holding, even in the long run.
Nevertheless, it is tempting to investigate to what extent it is low
inflation countries that tend to have currencies that have appreciated
in real terms.

Figure 1 summarizes the inflation and bilateral real exchange
rate experience of eight major European industrialized countries from
1975 to 1978. These eight countries are ones where it is not
unreasonable to expect both capital and goods markets to be highly
integrated, although, to be sure, some restrictions on capital
movements and trade between these countries do exist and prevent the
markets from being completely integrated. By 1975 the initial impact
of the real oil price shock of 1973-1974 had already occurred and, to a
large extent, the differences across countries in the 1975-1978 period
reflect differences in policies (especially monetary policy) chosen to
deal with the remaining price and income effects of the initial real
shock. In the figure, countries are arranged in order of their
consumer price inflation rates over the entire period, with Switzerland
being the lowest. A plus sign indicates an appreciation of the real
exchange rate (measured using consumer price indices) of the currency
of the country listed vertically in terms of the currency of the
country listed horizontally over the three year period. (Both prices
and exchange rates are measured on an annual average basis.) A minus
sign indicates depreciation of the real exchange rate, The implication
of expression (6) is that such an ordering by inflation rate (if
expected inflation roughly corresponded to actual inflation) should
generate an array with pluses above the diagonal. For the period 1975-

1978, this result is obtained in nearly all cases. Indeed the few


It is also interesting to note that the preceding analysis
implies a particular kind of "vicious" or "virtuous" circle with regard to
exchange rates and inflation. The term vicious/virtuous circle is not
well defined in the literature. As Henry Wallich and Jo Anna Gray (p. 50)
point out, "virtually any succession of price-level increases (decreases )
and exchange-rate depreciations (appreciations) experienced by a country
may be labelled a vicious (virtuous) circle without doing violence to
currently accepted uses of the term." A common theme in this literature
is the observation that low inflation countries tend to have currencies
that appreciate which in turn tends to slow inflation further and that the
opposite is true for high inflation countries. The timing relationships
involved in this process suggest a causal ordering, but, as Frenkel points
out (198la, p. 163), exchange rates and prices are endogenous variables
that react to shocks with different speeds. Thus the observed timing
relationship should not be interpreted as evidence of causality.
Expression (8) has as an implication an empirical regularity -- a tendency
for the currencies of high (low) inflation countries to depreciate
(appreciate) in real terms -- that is a type of vicious (virtuous) circle.
This empirical regularity does not depend on a causal relation between
exchange rates and inflation rates.

II. Alternative Tax Regimes

In the preceding section, the tax regime considered is one in
which each country's tax rates are approximately equal and in which taxes
are levied against nominal interest payments. Alternative tax regimes
include the more general case where tax rates can differ substantially
across countries and regimes in which taxes are levied on inflation-

adjusted, that is, real, interest payments.


If expected after tax real rates of return are specified to
be equal across countries ,4/ it follows from conditions (1) and (2)
that:
(3) (1 - t)Ry 7m (1 - to) (Ry -e) - To
If condition (3) holds, then

e = Ry + (my = my)/(1 - ty) - [CL - ty), V1 - ty),
or,
(4) es (") - m)/(1 - ty).
if ty = toe Condition (4) states that the expected rate of change of
the exchange rate is systematically related to relative rates of
inflation in a way that ensures a violation of PPP as long as the tax
rate is not zero. (Note that PPP implies e = TM]- T+) The expected
change in the real exchange rate (x), that is, the exchange rate
adjusted for price level changes, is defined to be:

(5) X=@-1, +715.

1 2

Substituting for e in equation (5) using condition (4), one obtains:
(6) x= [to/(l = ty)] (my = 1).

According to expression (6), investors expect the currencies of low
inflation countries to appreciate in real terms and those of high
inflation countries to depreciate in real terms. As long as the
inflation differentials do not change, these movements in expected real
exchange. rates will continue, which may help explain Frenkel's

observations that departures from PPP often appear to be persistent and

cumulative.


-17-

65, one third of the reported regressions contain one or more t-
ratios greater than 1.73.

Recent papers by Robert Cumby and Maurice Obstfeld and by
Frederic Mishkin present evidence that real interest rates are not
equal across countries. Like Kane and Rosenthal, Cumby, Obstfeld,
and Mishkin do not take taxes into account in their empirical work.
Indeed, the neglect of the role of taxes in these studies may be
one reason for their negative findings. It is interesting to note
that Cumby and Obstfeld regard their evidence against PPP as
implying a rejection of real interest rate equality across
countries; however, as shown in the present paper, when the role of
taxes is taken into account such evidence is consistent with after
tax real interest parity. Robert Hodrick reports mixed evidence on
the equality of real interest rates across countries; Hodrick also

omits the role of taxes in his empirical analysis.


rates involved. Thus, the tax effect identified in that paper
disappears if taxes on interest payments are adjusted for inflation.

In the present paper, where a relationship between real after tax
interest rates across countries is specified, it is not the case that
the identified effect of taxes disappears when taxes are levied on real
interest payments rather than nominal interest payments: the path of
the real exchange rate can be affected by tax rates even in an
inflation-adjusted tax environment.

The particular tax regime involved affects the path of the
real exchange rate. Thus any serious empirical investigation of the
Propositions put forward in this paper must take cross-country
differences in tax regimes into account. In the next section of the
Present paper some informal empirical evidence is presented in which it
is specified, reasonably, that taxes are levied on nominal interest
rates and, not so reasonably, that tax rates are equal across
countries. Given the modest use made of the evidence, such an
assumption is probably acceptable, but clearly there is scope for a
more complete empirical investigation in which actual tax regimes are
taken into account.

III. Behavior of Real Exchange Rates, 1975-1980

Expression (6) is not intended to be a theory of real
exchange rate determination. The factors working against the PPP
condition -- see the preceding discussion for a list of some of them --
as well as the goods arbitrage implicit in the PPP condition itself
also help to determine the path of the exchange rate. Expression (6)
merely is the logical implication of a well integrated international

capital market in which investors are concerned with real after tax


International Finance Discussion Papers
Number 222
May 16, 1983

PURCHASING POWER PARITY AND REAL AFTER TAX INTEREST RATE ARBITRAGE

by

David H. Howard and Karen H. Johnson*

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 hy a writer that he has had access to unpublished
material) should be cleared with the author or authors.


-10-

minus signs in the diagram result mostly from cases where the real
exchange rate change was in fact negligible and where the differences
in inflation rates were quite small.

Continuous real appreciation of the sort pictured in Figure 1
cannot be expected to continue indefinitely. The arbitrage
possibilities in goods markets implicit in a divergence from PPP plus
other forces tending to affect the equilibrium real exchange rate, such
as the oi] price shock of 1979, would be expected to counteract the
asset market arbitrage forces being highlighted in this paper. Indeed,
in 1978-1980, a reversal of the conditions illustrated in Figure 1 did
occur, as Figure 2 shows. Nevertheless, to the extent that 1975-1978
was a period during which, for these countries, monetary policy
differences largely determined differences in expected and actual
inflation and few other exogenous factors were present to alter the
paths of real exchange rates, Figure 1 seems to corroborate the
existence of the economic relationships summarized in expression (6).
IV. Conclusion

Tax considerations and the existence of a substantial number
of investors in a well integrated international capital market who tend
to equalize their expected real after tax rates of return introduce
another potential reason for exchange rates to deviate from their
purchasing power parities, even in the long run. Indeed, literal
intepretation of expression (6) indicates that even if all shocks are
monetary in nature, PPP will not hold as long as tax rates are nonzero.
(Compare Frenkel, 198la, p. 162.) There is a fundamental tension

between the rates of return and goods arbitrage conditions involved;


Switzerland
Germany
Netherlands
Belgium

France

Sweden

United Kingdom

Italy

FIGURE 1

Real Bilateral Exchange Rate Changes: 1975-1978

Switzerland Germany Netherlands Belgium France Sweden U.K. Italy

+ + + + + + +
- - + + + +

- + + + +

+ + + +

+ - +

- +

Note: The countries are listed in order of (consumer price) inflation rate during the
period, with Switzerland having the lowest rate. A plus (minus) sign signifies an
appreciation (depreciation) of the real bilateral exchange rate of the currency of
the country listed vertically with respect to that of the country listed
horizontally. For example, the Swiss franc appreciated in real terms against
the German mark.


Consider the regime in which taxes are levied on nominal
interest payments but tax rates need not be approximately equal. In
this case,

(7) x = [tp/(1 - ty)I(n, - 49) + [(ty - ty)/(1 - ty)IRy,
which, of course, is the complete version of expression (6). The
second term on the right-hand-side of equation (7) indicates that if
nominal interet rates are high enough, differential tax rates may
reverse, or at least weaken, the tendency of currencies of low
inflation countries to appreciate in real terms.

When tax rates apply to real interest payments, arbitrage
conditions (1) and (2) become:

(8) rm=(l- ty) (Ry - )) = (1 - ti) (Ry +e - 1),
(9) rs (1 - to) (Ry -e- T)) = (1- to) (Ro - 19).

Equating these real after tax rates of return (r¥ and r3) and using

equation (5), one obtains:

(10) x= E(t) - ty)/(1 - ty)1(R, - 14).

Thus, as long as tax rates differ and the nominal interest rate (Ry)
does not equal the inflation rate (4), the real exchange rate will
change over time even in the absence of any shocks. In the particular
case where Ry exceeds > that is, where the real interest rate as
conventionally defined is positive, the currencies of low tax rate
countries will appreciate in real terms in this tax regime.

In an earlier paper (Howard and Johnson) it is shown that if
taxes are levied on real interest income and no relationship is
specified about real after tax interest rates across countries, the
paths of real exchange rates and/or real after tax interest rates need

not be affected by a change in expected inflation regardless of the tax


exchange rate movements. (See, for example, Frenkel, 1981b.) The
present paper examines the relationship between the goods market (i.e.,
PPP) and capital market (i.e., interest rate) arbitrage conditions. It
is shown that in a world in which there is a well integrated
international capital market and where investors are concerned with
their real after tax rates of return, one would not necessarily expect
PPP to hold even in the long run even if all shocks are monetary in
nature .2/ In such a world, the real exchange rate is not independent

of relative inflation rates.

I. Interest Rate Arbitrage with Taxes

In order to examine the implications of a well integrated
international capital market, the following notation is introduced:2/
Ry = nominal rate of interest on an asset denominated in the
currency of country i,
ma; = expected rate of inflation in country i,
P. = price level in country i,
r. = expected real after tax rate of interest in country i,
t, = marginal rate of tax on income in country i (t;< 1),
E = exchange rate (units of currency 1 per unit of currency 2),
e = expected rate of change of E.
It is specified that an individual investor equates the expected real
after tax rates of return expressed in terms of a single currency, on
similar assets (e.g., bonds) denominated in different currencies, at
least up to a perhaps time-varying risk premium. If the bonds are
perfect substitutes, arbitrage will ensure that:
(1) ry= (l-t)) Ry - m= (1 - ty) (Ra +e) - 7,
(2) r

= (= t5) (Ry =e) - my = (1 - ty) Ry - 1p,


-13-

Literature Cited

Blejer, Mario I., "Financial Market Taxation and International Capital
Flows," IMF Departmental Memorandum, April 14, 1983.

Branson, William H., "Comments: ‘The Collapse of Purchasing Power
Parities during the 1970's' by Frenkel," European Economic
Review, 16, May 1981, 167-171.

Cumby, Robert E. and Obstfeld, Maurice, "International Interest-Rate and
Price-Level Linkages Under Flexible Exchange Rates: A Review
of Recent Evidence," in Bilson, John F.0. and Marston, Richard C.,

eds., Exchange Rates: Theory and Practice, Chicago, 1983.

Frenkel, Jacob A., "The Collapse of Purchasing Power Parities during

the 1970's," European Economic Review, 16, May 198la, 145-165.

> "Flexible Exchange Rates, Prices, and the Role of the 'News':

Lessons from the 1970s," Journal of Political Economy, 89,

August 1981b, 665-705.

Hodrick, Robert J., "Some International Evidence on the Equality of
Expected Real Interest Rates," Working Paper, Graduate School
of Industrial Administration, Carnegie-Mellon University, 1979.

Howard, David H. and Johnson, Karen H., “Interest Rates, Inflation, and
Taxes: The Foreign Connection," Economics Letters, 9, 1982,
181-184.

Kane, Alex and Rosenthal, Leonard, "International Interest Rates and

Inflationary Expectations," Journal of International Money

and Finance, 1, April 1982, 97-110.


-15-

Footnotes

International Finance Division, Federal Reserve Board. This paper
represents the views of the authors and should not be interpreted as
reflecting the views of The Board of Governors of the Federal Reserve
System or other members of its staff. We would like to thank Maureen
Walsh for her assistance with the data used in this study and Jerry
Caprio, Richard Freeman, Dale Henderson, Peter Isard, Raymond Lubitz,
Larry Promisel, and Ralph Smith for their useful comments and
suggestions.

Kent Kimbrough presents a model in which unanticipated monetary
shocks produce deviations from purchasing power parity. The
conclusions of the present paper hold for anticipated shocks;
unanticipated shocks are not analyzed specifically.

The notation and analysis follows that presented in Howard and
Johnson.

Mario Blejer has extended the Howard-Johnson analysis by working out
the implications for different tax regimes, including the important
case in which foreign exchange gains and losses and interest payments
are taxed at different rates.

A recent paper by Alex Kane and Leonard Rosenthal presents some
evidence that they contend indicates that real interest rates are
equal across countries. Unfortunately Kane and Rosenthal do not take

taxes into account. Their hypothesis is that R =R

17 TM1* "2.7 "2
which follows immediately from substituting expectations of


The behavior of exchange rates during the floating rate
regime of the 1970s and early 1980s has given rise to renewed interest
in the ability of the purchasing power parity (PPP) doctrine to predict
changes in nominal exchange rates. Jacob Frenkel (1981la, 1981b) points
out that PPP predictions have not performed well during the recent
floating rate period and contrasts this performance with that of the
1920s, when PPP predictions appear to have been much more reliable.
Frenkel offers a number of reasons for the poor performance of PPP,
including: shocks that require changes in relative prices and changes
in equilibrium real exchange rates themselves (on this point, see also
William Branson); transportation costs; commercial policies; and the
inherent difference between exchange rates ~-asset prices -- and
national price levels with regard to their short-run responsiveness to
new information ("news"). This last reason pertains to short-run
departures from PPP only, but the first three can mean that PPP need
not ever hold, regardless of the length of the period involved. Indeed
Frenkel points out that during the 1970s departures from PPP often
appear to have been persistent and cumulative. Frenkel's analysis
leads him to conclude that when real shocks require changes in relative
prices, PPP may not hold in the long run and that the usefulness of PPP
“is in providing a guide as to the general trend of exchange rates in
particular in circumstances where the main shocks underlying the trend
are of a monetary origin," (198la, p. 162).

Another theme in the literature on exchange rates is

concerned with the connection between changes in interest rates and


Abstract

This paper examines the relationship between the goods market and
capital market arbitrage conditions. It is shown that in a well integrated
international capital market in which investors are concerned with real
after tax rates of return, purchasing power parity will not necessarily hold
even in the long run even if all shocks are monetary in nature. In such a
world, the real exchange rate is not independent of relative inflation
rates. Alternative tax regimes are investigated and some informal empirical

evidence is presented.


-ll-

FIGURE 2

Real Bilateral Exchange Rate Changes: 1978-1980

Switzerland Germany Netherlands Belgium Sweden France U.K. Italy

Switzerland - - - - - - -
Germany + + - - - -
Netherlands + - - - -
Belgium - - - -
Sweden - - -
France - -
United Kingdom +

Italy

Note: see note to Figure 1.


-14-

Kimbrough, Kent P., "Price, Output, and Exchange Rate Movements in the

Open Economy," Journal of Monetary Economics, i, January 1983,

25-44,

Mishkin, Frederic S., "Are Real Interest Rates Equal Across Countries?
An Empirical Investigation of International Parity Conditions,"
NBER Working Paper No. 1048, December 1982.

Wallich, Henry C. and Gray, Jo Anna, "Stabilization Policy and Vicious
and Virtuous Circles," in Chipman, John S. and Kindleberger,

Charles P., eds., Flexible Exchange Rates and the Balance of

Payments: Essays in Memory of Egon Sohmen, New York, 1980.