The Real Rate of Interest on International Financial Markets

International Finance Discussion Papers Number 136

April 1979

THE REAL RATE OF INTEREST ON INTERNATIONAL FINANCIAL MARKETS by

David H. Howard

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access to unpublished material) should be cleared with the author or authors.

The Real Rate of Interest on International Financial Markets by

David H. Howard*

Recent experience with high nominal interest rates and inflation rates has raised the question of the behavior of expected real rates of interest -- defined as the nominal interest rate less the expected rate of inflation and called simply the real rate of interest in this paper -- during this period. This paper examines real domestic interest rates in four major industrialized countries (Canada, Germany, the United Kingdom, and the United States) during the period 1971:Q1 - 1977:Q3. The approach taken is to construct timeseries models for consumer-price inflation in each of the countries. These models yield predicted inflation rates which are then used to calculate a short real rate of interest for each country. Questions regarding the behavior of the real rate of interest over time and across countries are addressed. In particular, the questions of the existence of a constant real rate and a world real rate of interest are investigated.

The empirical evidence presented in this paper indicates that the real rate of interest varies over/ and differs across countries. Only when market forward rates are used to express the real rates in terms of U.S. dollars is it found that real rates across countries

are equal or differ only by some capital control and risk terms.

*/ International Finance Division, Federal Reserve Board. This paper represents the views of the author 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. I would like to thank Betty Daniel, Richard Freeman, Peter Garber, Dale Henderson, George Henry, Peter Isard, Val Koromzay, Frank McCormick, Larry Promisel, Kenneth Singleton, and Ted Truman for their comments on earlier versions of this paper.

I. The Real Rate of Interest

The expected real rate of interest (r) is defined here to be: (1) r=R- p*,

where R is the nominal rate of interest, and p* is the expected inflation rate, during the relevant time interval, in consumer

prices, The problem with equation (1) is that it involves two variables that are not readily observed. There are two commonly

used methods of solving this problem: one is to assume that the expected real rate is constant, or at least essentially constant; the other is to specify a particular way by which inflation expectations are formed. Eugene Fama (1975, 1977) reports evidence consistent with

the assumption of a short-term real rate of interest that is constant (or practically so). Other analysts, commenting on Fama's

work, report evidence of a variable real interest rate. For example, in the papers by John Carlson and by Charles Nelson and William Schwert the second method mentioned above is employed in that particular measures of p* are used to calculate (at least implicitly) r series, which then serve as evidence to contradict Fama's results. Using complete macroeconomic models for the determination of r, J.W. Elliott also reports evidence that indicates that the real rate of interest is not constant over time.

The approach taken in this paper is to construct forecast models for consumer-price inflation (P,) in each of the four countries studied here. These models yield predicted inflation rates which are then taken to be p* in equation (1) and are used to calculate a short

real rate of interest series for each country.

The procedure for deriving the inflation-forecasting model is first to estimate an autoregressive integrated moving average (ARIMA) model for inflation using the past history of the inflation series itself. Next, ARIMA models of various possible leading indicator

i.e., the whitened series, series are estimated. Then the residuals/from all of these models are cross-correlated. Significant cross-correlations can be interpreted as evidence of causality as defined by C.W.J. Granger and are used here as the criterion for deciding whether or not the consumer will use a particular leading indicator to forecast inflation. It is suggested by Edgar Feige and Douglas Pearce that such inflation expectations may very well represent economically rational inflation expectations in that at least some attention is given to the costs and benefits of obtaining and utilizing information. In any case, the approach taken here is a useful way of approximating an essentially unobservable variable. Table 1 presents the ARIMA models for price

inflation. 2/

Denote the forecasts from the Table 1 equations as t.- Examination of the cross-correlations between the whitened inflation series and the whitened series for wage (w,) and M1 (m1,) growth in all four countries and exchange-rate growth (e,) in all but the United States indicates that 4, cannot be improved on in Germany and the United States, but that in the United Kingdom past wage data significantly improve the inflation forecast while in Canada past Ml data improve the forecast. (The ARIMA models for variables other than p, and the cross-correlations are not reported here.) Thus, for Germany and the United States the inflation-forecasting equation is: PE = fe; for Canada and the United Kingdom it is pf = Pr, where for

Canada:

TABLE 1

ARIMA Models for Price Inflation

Canada: 1960:Q2 - 1977:94

(1 - BY) =.415B + .31284)p, = 00408 + up; G11) (11)

=

Q(30) = 23.9

Germany: 1960:Q2 - 1977:Q4

(1 - BY*)p, = .00124 + (1 + .418B7)u,; (.11)

Q(30) = 23.8

United Kingdom: 1948:Q2 - 1977:Q4 (see footnote 2)

4 . 4 (l-B) (1- B)p. = - .00066 + (1 - .903B dues . (05) -

Q(30) = 22.1

United States: 1960:Q2 - 1977:Q4

(1 - B)p_ = .00025 + (1 + 3368" ug

Q(30) = 25.2

Notes: Bis the backshift operator; figure in parentheses is the standard error of the estimated parameter directly above it; Q(K) is the Box-Pierce Q-statistic calculated for K lags;u, is the difference between actual and predicted P.; P, is the inflation rate between quarters t-1 and t, expressed at an annual rate.

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(2) Be = ¥@e-1,.,.,Pe-m,@et-1,...,Ml¢-m)3

and for the United Kingdom:

where ¥ and Q are unconstrained distributed lag functions. Table 2

presents the estimates of the coefficients in equations (2) and (3) .2/

The predictions of the models in Tables 1 and 2 are taken to. be p*¥ in equation (1) and must be subtracted from a nominal three-month interest rate in order to obtain the real interest rate. It is important that the nominal rates of interest be reasonably comparable across countries and that the dating of the interest rate correspond to the period for which the inflation rate is predicted. The interest rates

quarterly averages of used in this study are/three -month rates selected for their comparability for publication in the Federal Reserve Bulletin. Appendix Tables 1-5

contain the data on nominal interest rates, expected and actual infla-

tion, and the calculated series for expected and actual, i.e., ex post,

real rates of interest.

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II. Testable Hypotheses

Two types of hypotheses will be tested in this study. One has to do with the real interest rate in each individual country, and the other has to do with the relationship across countries of the real interest rate,

The first hypothesis, which is associated with Fama in the above discussion, is:

Hl: the real rate of interest in each country is constant.

The second set of hypotheses has to do with the international interdependence of interest rates. One hypothesis is:

H2: the real rate of interest is equal across countries .4/

A less extreme hypothesis is:

H3: there is a stable relationship among individual countries’

real rates of interest.

Hypotheses H2 and H3 have to do with relationships between the real rates of interest that might enter into the countries' respective investment expenditure demand functions. The final hypothesis to be investigated in this paper has to do with the relationship between the real rates of interest relevant to international portfolio investment, When making his portfolio investment decision, the investor residing in country i compares the expected return available in all countries. That is, he compares Ry - Pi with Ry +e¥, +e}, Ry- Pie where the subscript denotes the country and eit denotes the expected appreciation of the value of country j's currency in

terms of the currency of country i. Note that the comparison is in terms of

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a country i consumption bundle. In a well-developed international market, the two rates of return would be forced to equality or to differ only by

some risk terms, Thus, ignoring risk,

* * * *

From equation (4) it is readily seen that

¥* (5) ey, = (R, - R,)/(1 + R;).

* The properties of [(Rj - R)/Q + R;)] as a predictor of ess allow one to

test the following hypothesis:

H4: international financial markets force real rates of return in terms of any one currency to be equal, i.e.,

uncovered interest parity holds.2/

Nearly all of the above hypotheses pertain to the question of the ability of a government to influence the level of the real rate of interest in its own country. Hypothesis H4 involves the substitutability of financial assets and the interdependence of international financial markets and has implications for the effects of monetary and exchange-rate policies. The policy implications of the results obtained from testing the

above hypotheses will be discussed below.

III. Empirical Results

A. Constancy of the Real Rate

A constant real rate of interest will be defined as one where the expected value of r is equal to a constant, k, regardless of other information available. In other words the differences between r and k are white noise. There are several ways in which this proposition can be tested. The

first method used here is to estimate

that is, simply regress r on a constant, and examine the residuals. Table 3

presents these results.

A second method is first tc estimate (7) R= k +#p*

using ordinary least squares. The residuals are examined and the estimate of B is compared to unity. A constant real rate of interest implies that k will be the mean of r, that the estimate of 8 will not be significantly different from unity, and that the residuals from the regressions will be

white noise. These results are presented in Table 4.

The final method used here for testing the constancy of the real interest rate is one used by Fama (1975). Fama presents several tests, but

the one used here involves:

(8) p= + BR.

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TABLE 3

OLS Estimates of: (6) r=k

United United Canada Germany Kingdom States Eurodollar

k -.005 -014 - .048 -.005 -005

(.004) (.006) (.013) (.003) (,004) Q(12) 18.17 21.46 10.30 20.18 23.43 DW -82 99 1.38 81 66 P, 259% 50% 231 55% 62% Po .1l -.02 .08 .39* 46% P, -.05 ell -.17 239% -40* P, -.02 .27 13 11 .19

SS ce de

Notes: Sample size = 27; figure in parentheses is the standard error of the estimated parameter directly above it; 9; is the i*)-order sample autocorrelation; */ indicates a sample autocorrelation that exceeds twice its standard error.

Q(12)

DW

Notes:

-11-

TABLE 4

OLS Estimates of: (7) R=k +8 p*

United Canada Germany Kingdom .036 .040 - 066 (.011) (.012) (.011) -483 -528 215 (.128) (.192) (.067) 22.62 44.35 33.31 -58 41 .55 -70* 79% .71* -26 51* .50* 11 34 14 -07 16 .03 . 6362 -232 -290

Sample size = 27,

United States Eurodollar 022 - ,034 (.004) (.006) 599 -576 (.058) | (.077) 7.95 13.62 1.27 .90 035 .53* 03 -20 24 225 .09 ~20 -810 -689

-12-

Fama's hypothesis -- involving both a constant real interest rate and efficient markets -- is that - equals the mean of r, 5 equals unity, and the residuals are white noise. That is, Fama's hypothesis has to do with the properties of nominal interest rates as predictors of actual inflation

(p). In Table 5, the results from estimating equation (8) are presented.

In Table 3, one or more of the sample autocorrelations in the Canadian, German, U.S. and Eurodollar regressions are inconsistent with the hypothesis that (r-k) is white noise, ©/and the U.K. 0} has a fairly large t-ratio (1.63). These autocorrelations are inconsistent with the hypothesis that the real rate of interest as defined in this paper was constant during the sample period. Turning to Table 4, in all five cases the estimate of ® is significantly different from unity, but, of course, the presence of positive autocorrelation biases the standard errors downward, In Canada, Germany, the United Kingdom, and the Eurodollar case, the sample autocorrelations suggest that the residuals are not white noise. In the U.S. regression the residuals appear to be white, although 0, is fairly large with a t-ratio of 1.84. Thus the results reported in Tables 3 and 4 indicate that in the five cases investigated here during the period

1971-1977, the real interest rate probably was not constant.

The estimates presented in Table 5 are more favorable to the hypothesis of a constant expected real rate of interest. Only in the German regression is the estimate of g significantly different from unity. In addition, in the German and Eurodollar equations the autocorrelations suggest that the residuals are not white noise. Nevertheless, in the three other regressions -- i.e., in Canada, the United Kingdom, and

the United States -- Fama's joint hypothesis seems to be confirmed.

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TABLE 5

OLS Estimates of: (8) p=U+565R

United United

Canada Germany Kingdom States Eurodollar ul 034 026 -.033 - .006 - 005

(.019) (.012) (.044) (.011) (,014) 8 634 407 1.812 1.170 .997

(.247) (.151) (.427) (.167) (.190) Q (12) 10.93 40.05 10.47 10.60 12,81 DW 1.28 1.67 1.36 1.38 1.03 5 36 .12 31 29 48% P, 04 - 59% 02 -.36 -.06 0, -.03 -.03 - 62h -.03 .07 o, 14 .51* 06 .18 16 Re .209 224 .418 .663 2524

Notes: Sample size = 27.

- 14 -

However, following Nelson and Schwert, the hypothesis can be subjected

to an additional test by estimating the following equation : (9) p =u + 5R + Apx,

If p* significantly improves the predictive power of the equation compared to that of equation (8), then Fama's hypothesis is falsified and the real rate is variable and/or markets are inefficient. Table 6 presents the results obtained from estimating equation (9).

In Table 6 the inclusion of p¥ results in a significant \ and -- except for the U.K. regression -- an insignificant 6 as well. In addition, in each case the R? values increase substantially when p*

al! If it is assumed that markets are efficient, the results

is include in Tables 5 and 6 taken together lead to the conclusion that the expected real rate of interest is not constant, thus corroborating the conclusion

reached on the basis of Tables 3 and 4 8/

B. Relationships Among Interest Rates

For the purpose of investigating the relationships among the various countries' interest rates it is useful to begin by examining the simple correlations between rates. Table 7 presents these correlations. Except for the correlation between the real U.S. rate and the real Eurodollar rate the correlations are quite emall Thus the Table 7 results seem to indicate little or no relationship among the real interest rates

on assets denominated in different currencies.

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TABLE 6

OLS Estimates of: (9) p=H +65 R + Ape

United United

Canada Germany Kingdom States Eurodollar u O11 008 - .047 003 009

(.012) (.009) (.012) (.011) (.012) § -.108 105 492 467 131

(.189) (.122) (.134) (.357) (.276) K 992 686 978 520 724

(152) (.133) (.054) (.238) (.191) Q (12) 5,16 5.16 8.06 10.40 9.79 DW 2.26 1.46 2.37 1.56 1.55 Ps -.12 -.23 -03 Ol 207 , -.07 -.04 -.14 -l7 14 RZ -715 .631 -961 719 702

Notes: Sample size = 27,

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TABLE 7

Correlations Between Real Interest Rates

United United Canada Germany Kingdom States Eurodollar Canada I -.38 --08 26 . 26 Germany 1 37 -.18. -.14 United Kingdom 1 16 -10 United States 1 96

Eurodollar 1

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Hypotheses H2 and H3 can be tested by estimating an equation

of the forn:

expected If/real rates are equal across countries, i.e., H2 is true, then

G@=Oand"=1. If there is a relationship between the two rates, i.e., H3 is true, then ™ #0, If the residuals from the regression are not white noise, then there may be omitted variables in equation (10) and the relationship postulated is only an approximation of the true relationship. Table 8 presents the results of estimating equation (10) using in turn the interest rates on the two U.S, -dollar-denominated assets as the right-hand-side variable,

The method for testing the hypothesis that real rates of return in terms of any one currency are equal, i.e., H4, utilizes equations (4) and (5). However, in order to allow for the possibility of a capital control and risk premium, equation (4) must be changed to

* * * * (4°) Ry-PgsRyteysteysRj- pyre, where c -- the capital control and risk premium -- is composed of a constant component as well as one that varies with the nominal interest rate.72

That is, c=b + a (14R;) and equation (5) becomes

(5") 54 = (Ry-Ry)/(14R5) + b/(14R;) +a.

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TABLE 8

U.S. Real Rate on RHS

OLS Estimates of: (10) T; = & + Tri

Eurodollar Real Rate on RHS

United United United Canada Germany Kingdom Eurodollar Canada Germany Kingdom States (.00 4) (.006) (.013) (.001) (.004) (.006) (.013) (.001) bi .364 -,340 . 666 1.119 .316 -.233 .353 833 (.273) (.377) (. 816) (.061) (.235) (.327) (. 709) (.045) Q(12) 15,60 17.24 — 11. 26 18.42 16. 33 17.80 . 11.35 19.43 DW . 86 1.01 1,41 68 - 83 1.00 1.38 83 py 57* 48% .29 64% .5g* 49% -30 57% P5 .00 11 -.20 .05 Ol 12 -.19 -.02 Re . 066 .032 . 026 .931 067 .020 .010 .931 Notes: Sample size = 27.

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Table 9 presents the results of regressing actual exchange rate changes on [ (R4-Rj)/(1+Rj)], [1/(1+R})], and a constant. If the resulting regression residuals are white noise and if the coefficient of [ (Ry-Rj)/ (1485) ] is significantly different from zero and not significantly different from unity, hypothesis H4 cannot be rejected. An alternative -and less exacting -- test of H4 uses the actual market forward premium (£54) as a measure of ey and proceeds as described above. These results

are reported in Table 10.

In Table 8 only two of the estimates of & -- both for Canada -are not significantly different from zero and the estimates of 7 are not significant except for those between the U.S. and Eurodollar rates. Therefore hypothesis H2 can be rejected in all cases and H3 can be rejected for all but the U.S.-Eurodollar relationship. When the U.S. real rate is taken to be the right-hand-side variable in the U.S.-Eurodollar relationship, Table 8 indicates that 7 is not significantly different from unity and the relationship is one where the Eurodollar rate is different from the

positive U.S. rate by a (positive) constant term only. There is evidence of/firstorder autocorrelation in the Canadian, German, and Eurodollar-U.S. regressions, which would bias the results in favor of rejecting the null hypotheses, © ™ 0, 7 = 0. This may present a problem with regard to the above conclusions about % but not those concerning % except for the estimate of 7 in the Eurodollar-U.S. regressions. As a check, a Cochrane- Orcutt procedure was used to re-estimate those equations exhibiting autocorrelation in Table 8. These results -- not presented here -- indicate insignificant a's in the two “erman equations, and an that is not signif-

teantly different from unity in either U.S.-Eurodollar equation.

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TABLE 9

OLS Estimates of: (11) ej; = a +b [1/(1 +R;)] +¥[ (Ry - R,)/(1 + R;)]

Q(12)

DW

7) P3

A

Notes:

U.S. Rate as R, United Canada Germany Kingdom

019 574 .199 (.662) (2.070) (1.554)

-.022 ~ .468 -0.198 (.620) (1.947) (1.459)

622 -3.612 ~274 (.812) (3.133) (2.204)

32.50 16.04 5.30 83 1.83 1.57 53% .07 17 .09 -.40* -.06

-.21 2.15 -.03 -.51* -.23 . ,06.. .031 — .079 .005

Sample size = 27.

Eurodollar Rate as Ry

Canada

- 083 (.677)

. 068 (.630)

-677 (.689)

33.43 84

-53*

Germany

.372 (2.037)

-.248 (1.898)

-3.344 (3.175)

17.82

1.83

.08

United Kingdom

-.109 (1.556)

.091 (1.444)

. 768 (1.866)

5.02

1.60

16

.07

O11

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TABLE 10

OLS Estimates of: (12) £5; = a+b [1/(1 + R,)] +Y [QR - R,)/(1 + Ry)]

Q(12)

DW

Notes:

U.S. Rate as Ry

Canada -.065

.066 (.041)

1.105 (.052)

36.93

72

64%

2958 ©

Sample size = 26,

Germany -.099 (.156)

(.147)

. 168 (.245)

11.95

1.22

Unite Kingdom

.297

(.745) -

-.275 (.070)

1,082 (.105)

5.36 1.80 08

-.09

Eurodollar Rate as R;

United Canada Germany Kingdom -.121 -.131 288 .(,039) (.150) (.067) .- 108 142 -.280 (.037) (.140) (,062) 948 247 931 (.039) (.239) (.079) 40.24 14.76 8.78 52 1.12 1.53 -65* -43* 21 25 -08 02 -.44* -.20 -.37 968 051 953

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In Table 9 there «re no statistically significant coefficients, the R2'5 are very small, and four of the six regressions exhibit some evidence of autocorrelation. These results are inconsistent with hypothesis H4.

Table 10 presents some positive results. In each Canadian equation, the estimate of Y is significantly positive and in the Canadian-

Eurodollar case Y is not significantly different from unity. (In the

Canadian-U.S. case Y is just slightly greater than unity.) Both capital control and risk terms are significant in the Canadiansignificant Eurodollar regression, while neither is/in the other Canadian regression. The R?'s are quite large in the Canadian equations and there is evidence of first-order autocorrelation. In each of the U.K. regressions reported in Table 10, at least one capital control and risk term enters significantly and the estimates of Y are significantly positive and not significantly different from unity. Furthermore, the R“'s are large and there is no evidence of autocorrelation. In contrast to the rest of the results in the table, the German regressions indicate that there is no relationship between U.S. dollar and German real rates of interest even when forward rates are used as the measure of exchange-rate expectations. As in the Canadian equations, there is some evidence of first-order autocorrela-

tion in the German regressions. Cochrane-Orcutt estimates of the

Canadian and German equations in Table 10 are reported in Table 11.

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TABLE 11

Cochrane-Orcutt Estimates of: (12) fyi =a+tb {1/(1 + R;)] +¥ [(Ry - R;)/(1 + R;))

Q(12)

DW

Notes:

U.S. Rate as Ry. Eurodollar Rate as R; Canada —___— Gé rmany ana ermany -.050 - 434 . 036 -.375 (.066) (.253) (.036) (.212) 053 -430 -.035 ~ .367 (.061) (.237) (.034) (.197) 1.169 1.141 1.004 1.099 (.080) (.300) (.038) (.231) 8.04 6.77 9.66 9.23 1.80 1.61 1.84 1.45 .09 18 -02 27 .21 .21 .08 25 -.21 -.23 -.19 -.10 -.03 -.33 -.19 -.32 -678 795 797 809 (.147) (.121) (.121) (.118) 975 352 993 464

Sample size = 25;0 is the autoregressive parameter calculated in the Cochrane-Orcutt procedure.

- 24 -

In Table 11 the only estimate of Y that is significantly different from unity is in the Canadian-U.S,. regression and even-that one is fairly close to unity. However, even though the point estimates of

the German Y's are not statistically different from unity, their

and U.K. standard errors are substantially larger than are those of the Canadian/ point estimates reported in Tables10 and 11. In addition, the R's for the

German equations are considerably lower than those for the other equations. Thus it seems that in the German case the true relationship may Table 10.

be somewhat more complicated than the one represented by equation (12) in/

_the Canadian regressions in Similarly the presence of autocorrelation in/Table 10 -- and corrected for in Table ll -- indicates the possibility of omitted variables in equation (12), Nevertheless, the results are broadly consistent with hypothesis H4, i.e., that real interest rates in terms of any one currency -- in this case U.S. dollars -- are equal or at least differ only by some capital

control and risk terms when market forward premia are taken to be the

ll relevant measure of expected exchange rate changes.

As mentioned in the preceding paragraph, there is evidence that equation (12) may be missing some significant explanatory variables for Canada and Germany. Jacob Frenkel and Richard Levich (1975, 1977) have attributed deviations from covered-interest parity to transactions costs. Their work suggests that these costs may be an omitted variable. (Frank McCormick has called into question the size -- but not the relevance -of the transactions costs involved.) Changes in capital controls are

12/ another potentially important factor omitted in this study.

Finally, it should be pointed out that the real rates

of return used in this study do not take taxes into account. Cross-country differences in taxation as well as changes in tax rates over time could very well be important factors in determining the international investor's decisions and thus represent another set of potentially important factors

omitted in this study.

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IV. Conclusion A. Summary of Empirical Findings

The results reported above indicate that at least during recent years the (expected) real rates of interest studied here were not constant. Furthermore these rates were not equal across countries, In fact in only the U.S.-Eurodollar case is there found evidence of a significant relationship between real interest rates. In this case the U.S. and Eurodollar rates differ by a constant term only. When the real rates of interest are put in terms of one currency -- in this study U.S. dollars -- there appears to be no significant relationship across countries except when forward rates are used as the measure of exchange-rate expectations.

This paper's empirical findings depict international financial markets that are sufficiently integrated and interdependent that coveredinterest parity holds (at least approximately) between comparable assets issued in different countries. However, the results do not support the stronger hypothesis of uncovered-interest parity. Thus unless the assumption is made that forward premia represent the market's forecast of exchange-rate changes, this paper's empirical results indicate that international financial markets are not so integrated and interdependent that expected real rates of return expressed in one currency are forced either to equality or to differ

only by some capital control and risk terms.

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B. Policy Implications

The empirical results indicate that each country's real rate of interest varies over time, and that there is no significant relationship between countries' real interest rates. These results imply that the real rate of interest is at least potentially susceptible to manipulation by policy makers.

The international interdependence of financial markets may affect the policy makers’ ability to influence some economic variables. In his survey of modern theories of international finance, Dale Henderson (pp. 191-92) states that if home and foreign securities are perfect substitutes, a domestic open-market operation or an exchange-market operation will affect the exchange rate but that the nominal interest rate will change only by the amount of the change in the expected rate of depreciation. The demand for domestic-currency assets, including money, will increase in the case of an expansionary policy action if the home-country residents have net assets denominated in foreign currency. (The resulting depreciation of the home currency increases. the home currency value of net foreign-currency assets.) This last effect is termed the "valuation effect” by Henderson. The evidence presented in this paper indicates that international financial assets are substitutes for each other in that their real rates of retura expressed in terms of one currency tend ‘to be equal or differ only by some capital control and risk terms only if market forward rates are taken to be the relevant measure of exchange-rate expectations.23/ Therefore this study's results indicate that the effects

of open-market and exchange-market operations may depend, inter alia, on

whether or not forward premia represent the market's forecast of exchange-

rate changes.

Data Appendix

(Unless otherwise specified, data are not seasonally adjusted.)

Consumer prices

For Canada, the consumer price index is from the Quarterly

Canadian Forecast: Historical Supplement and the Canadian Statistical

Review. The German consumer price data are taken from International Financial Statistics, The British price data are from the Central Statistical Office's Economic Trends and are the all-items retail

price index. The U.S. consumer price index is the BLS all-items index,

Wages ‘The Canadian wage series is average weekly wages (industrial composité) from the Quarterly Canadian Forecast: Historical Supplement ~-and the Canadian Statistical Review, For Germany the wage data are wage and salary rates (hourly basis, overall economy) from the Monthly Report of the Deutsche Bundesbank, The wage data for the United Kingdom are from

- Economic Trends atid “are average earnings (in Great Britain) in all in-

‘dustries and services covered.” For ‘the United States, wages are the “average hourly earnings index for private nonfarm manufacturing. The U.K. and U.S, wage data-are seasonally adjusted.

Money Supply (M1) The Canadian money stock data are from the Bank of Canada Re-

view and from data supplied by the Bank of Canada. The data for the

German money supply are from the Monthly Report of the Bundesbank. The

- 29 .

British money data are adjusted for breaks in the series by the Bank of England and are available on request from the Bank. The U.S.

money stock data are from the Federal Reserve Board.

Exchange Rates

Exchange rate data are from the Federal Reserve Bulletin

and the Federal Reserve's Annual Statistical Digest. The data are

expressed as U.S, cents per unit of foreign currency,

Forward Rates | All forward premia are three-month rates expressed as annual

rates and are from the Federal Reserve.

Interest Rates

All interest rates are three-month rates. For Canada, the Canadian finance paper rate is used; for Germany, the Frankfurt interbank loan rate is used; for the United Kingdom the London local authority rate and the London interbank sterling bid rate were spliced to form one series; and for the United States, the CD rate is used, These data as well as the Eurodollar rate are from the Federal Reserve and are selected for their

comparability.

- 30 -

Appendix Table lL:

Canada

Real Rate of Interest

Expected

Inflation Next Period

Expected

Nominal Rate of

Actual Actual

Interest

Period

ANON

ee @

oat? t

onom e a te

oonn

tN © 0 e e e Non s+

asreas Ino

aHonere.

mor st st

moar mann

BNMN oO wootnr

SIN

tn inin

AM NO ee e

Anan

AON wo

co 0 0

OOHO

ate

~ON oO e e@« © e@ tnt OM en

onsn eo 8 AHANde a |

onnNs DF 00

ANNO DONG

ANIA e e e e ~N On

1975:Q1 Q2 Q3 Q4

NOMS ANNO

BRMTON e e e e Amo ©

NH OO eeee owen

mon None

tyNnNeO AAA

1976:Ql1

sno Caan

aro nae

1977:Q1

- 31

Germany

Appendix Table 2:

Real Rate of Interest

Expected

Inflation

Nominal Rate of

Next Period

Actual

Actual

Expected

Interest

Period

———ae

me stun ee 8 @ ANMO et

ATINO

Nn

ARN WY eee @ WN st 0

Noto tage

wttwoo e se e e ~RORR

WORHON aHHHOo

mnNnwWN ee @ @ STOOD

oaonn

wOoNnNnanre

moon

ooom

Nm Ore eeee NNO OS

OOM A oe © 0 ~ Om OO

ennn a}

amo ee ee

ONS OE aed

moon tAGeA

wOoNNA os e @ +tTNA0

ontn onainn

SNA Otaon

atto aaa

wy oO Mm 0

ON +0

WeoOrt ed e ee» e@ @ wo +t +t +

TNM 4 ee @ 6 NOMN OM

NAtnwo eee e tte ed

NIMOO wonn

orom oeee OANMO

aannr mot

Q2 Q3 Q4

1976:Q1

nan e oOMmnm

oto . Otte

tio WHO

Ooo ee es @ Non

~~ St eee ttt

1977:Ql

Real Rate Actual

of Interest

Expected

————

- United Kingdom Actual

Inflation Next Period

Expected

Appendix Table 3:

Nominal Interest

Rate of

Period

wour NDA Nate Toon rao e oO OMN NOD e e e e e e e e e e e e e e e e e e e e e e e e e e SHA ON NAN © AMN OY ON Oo +t Nott wo Oorn ~H oO ' ' tes ’ toa al te 0! too ' ot ' ' ‘ NRE N OADM woaonn woMHN +TotN INO FF onMma . . e e e e e e e e e e e e e e e e ° e se e e e e Won +t Wann NOOO ~+taoOmM oats RARER ~te DD ‘

NONN Oo 4 00 WT Metta one + NEO Ss mw orn otro e e @ e ee. UmU°¢ e e e e e e e e e e e e e. 86° e NMmnMo nNROAN NOSNn nNoOonw

CMAM NMOM OFTMN DOOM OFTRNH RONDO tro en en ee} [ee en ee *. @e@ e e@ e ss . e* @ s ee @ @ NOODD CMOH NONYT MNON HATH Coon ano

owoeor ANKE O ONON tone NOME AN IW! ooo

e e e e e e e e e e e e e es e e e e e e e e ~wonst +tnORM co ONN + NaANN AaAnNnOr Norns et 00 10 et ete aa es ee eet Aaae et

aN OS t+ aN OS st aa on t ANOS ANOS HAN OT AN mM an N arse) + n wo ~ ~ ~ ~N ~~ n n nt ron fon Oo an On ro a et et et re ei eo es

-33 -

United States

Appendix Table 4:

Real Rate of Interest

Expected

Inflation Next Period

Expected

Nominal Rate of

Actual Actual

Interest

Period

onan Sond

~oaoann eee 8 @

AONA '

mONN Stas

tONO Vine

annns ting

1971:Q1 Q2 Q3 Q4

aane Anaad

orton

° ee onNAnAO et

NMIAN onan

ONN A ° ee

Orn et eo eee Lo ba 2)

tomo eee @ wonwon

1975:Q1 Q2 Q3 Q4

Oo eth + eee oun ON

OWN + et ee ee eoo°o

mnonNn nog nh

OnAnR e e « e rene

mito o

w

Wins

NaN ee

anon ows

© wn © e e e ~ ow

Sas sini

Eurodollars

Appendix Table 5:

Real Rate of Interest

Expected

Inflation (U.S.)

Nominal Rate of

Next Period

Expected

Actual

Actual

Interest

Period

aonmnn

ONnNM

amo +t Nast on

NOonn toa

tono ee ee NOME

nat none

Neno e 08 © @

WINN WY

1972:Ql Q2 Q3 Q4

oOronrt oe ee onan Oo

ot

tmnor ee e ~ OHO

Q2 Q3 Q4

1973:Q1

owron ee © Nt etn

Ot et co e Um. e

ett et

NM OO aad

Ntan ooco

tonn wowm

OretN et e eUe e ~woro

wonnea eee ¢@ remo r Oo

+tToatan s @ e e oQonrr

~oouw ee 8 @ oroo

HiNnwoON e e e e Mode

aanrnr ooee tan ts

Nano eee e nunn

anc row

eon eee mnwo

1977:Q1

- 35 -

Literature Cited

R.Z. Aliber, "The Interest Rate Parity Theorem: A Reinterpretation,"

Journal of Political Economy, November/December 1973, 81, 1451-59.

G.E.P. Box and G.M. Jenkins, Time Series Analysis: Forecasting and

Control, rev. ed., San Francisco, 1976.

J.A. Carlson, "Short-Term Interest Rates as Predictors of Inflation: Comment ,."" American Economic Review, June 1977, 67, 469-75.

M. Dooley and .. Isard, "Capital Controls, Political Risk and Interest Disparities,” International Finance Discussion Papers, no. 125, september 1978.

J.W. Elliott, "Measuring the Expected Real Rate of Interest: An Explora-

tion of Macroeconomic Alternatives," American Economic Review,

June 1977, 67, 429-44,

E.F. Fama, "Short-Term Interest Rates as Predictors of Inflation,"

American Economic Review, June 1975, 65, 269-82,

E.F. Fama, "Interest Rates and Inflation: The Message in the Entrails,"

American Economic Review, June 1977, 67, 487-96.

x

El. Feige and D.K, Pearce, “Economically national Expectations: -.re Innovations in the Rate of Inflation Independent of Innovations

.in Measures of Monetary and Fiscal Policy?," Journal of Political

Economy, June 1976, 84, 499-522.

- 36 - J.A. Frenkel and R.M. Levich, "Covered Interest Arbitrage: Unexploited

Profits?," Journal of Political Economy, April 1975, 83, 325-38.

J.A. Frenkel and R.M. Levich, "Transaction Costs and Interest Arbitrage: Tranquil versus Turbulent Periods," Journal of Political Econo ’ December 1977, 85, 1209-26.

K. Garbade and P, Wachtel, "Time Variation in the Relationship between Inflation and Interest Rates," Journal of Monetary Economics, November 1978, 4, 755-65.

C.W.J. Granger, "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, July 1969, 37, 424-38,

D.W. Henderson, "Modeling the Interdependence of National Money and Capital Markets," American Economic Review, February 1977, 67, 190-99,

P. Isard, Exchange-Rate Determination: _ A Survey of Popular Views and Recent Models, Princeton Studies in Intemational Finance, no. 42, 1978,

F. McCormick, "Covered-Interest Arbitrage: Unexploited Profits: Comment,"

Journal of Political Economy, forthcoming.

C.R. Nelson, Applied Time Series Analysis for Managerial Forecasting, San

Francisco, 1973.

C.R. Nelson and G.W. Schwert,. “Short-Term Interest Rates as Predictors of Inflation: On Testing the Hypothesis that the Real Rate of

Interest is Constant,” American Economic Review, June 1977, 67,

- 37 -

D.A. Pierce and L.D,. Haugh, "Causality in Temporal Systems: Character-

izations and a Survey," Journal of Econometrics, May 1977, 5, 265-93,

L/

- 38 -

For a discussion of ARIMA models, see Ceorge Box and Gwilym Jenkins

or Charles Nelson. See David Pierce and Larry Haugh for a discussion of causality and causality tests. Granger causality can be summarized as follows: x causes y if information about some present and past x improves the forecast of present y, given other information, including

past y.

See the appendix to this paper for a discussion of the data used in this study. The U.K. sample is longer than the other samples because it was necessary to investigate the effectiveness of the U.K.'s many incomes policies. Inspection of the residuals of the fitted model during incomes-policy periods indicated that inflation expectations

probably would not be affected by such policies.

One might expect the consumer to combine P. and B, to obtain his actual forecast of P,- Since both Pe and P. are unbiased, a linear combination of the forecasts is: A Pe = OP, + (1-p)p, + u, ,

or,

-39-

A ~ A

OLS estimates of » for both Canada and the United Kingdom were not significantly different from unity. Therefore the equation Py = P, is used here. In equations (2) and (3) lag lengths of 10 were assumed. No constraints were placed on the curves because of the absence of prior notions of what the curves might look like (even smoothness cannot be expected). The collinearity of the data means that caution must be used when interpreting the individual coefficient

estimates in Table 2,

H2 could be combined with H1 to yield the hypothesis that not only is there a world interest rate but also that it is constant. This hypothesis will not be tested here explicitly, although it will be

teenid immlicicl,y wher. 4] and H2 are investigated.

If the forward premium is substituted for eft in equations (4) and (5), hypothesis H4 states that covered interest parity holds. In fact, hypotheses H2 and H4 could be viewed as being derived from the proposition of covered interest parity in a series of steps. First, covered interest parity asserts:

Ry = Rj + fiji + £54R ’ where fai is the forward premium of country j's currency with respect to country i's currency. Covered interest parity states that arbitrage removes all riskless profit opportunities. The next step would be to assert that arbitrage removes all expected profit opportunities. Thus ert would replace fsa and one would obtain equations (4) and (5), i.e.,

then hypothesis H4, To obtain hypothesis H2, one could/assume that exchange-

-40-

rate expectations are equal to expected inflation differentials, i.e.,

*

* . * - Py and that the term e5iR; is small enough to be ignored.

Cy, ~ Pi

6/ A "twice-the-standard-error" rule cf thumb is used here ana in similar situations throughout this paper as the test for statistical

significance. Notethat the hypotheses in this paper refer to the

average interest rate during the quarter.

7/ F-tests indicate that the increases in the R?!

s due to the inclusion of p* are significant. That is, information on p* is not just duplicating the information in R; rather, p* contains more information

about p than does R.

8/ Kenneth Garbade and Paul Wachtel present evidence that U.S. markets are

efficient and that the U.S. real rate of interest is not constant.

9/ On the other hand, the correlations between nominal interest rates are

as follows:

Canada Germany U.K. U.S. Eurodollar

Canada 1 .10 78 .65 52 Germany — 1 039 w73 76 U.K. 1 -66 053 U.S. . 1 97

Eurodollar 1

10/

11/

- 41 -

For a discussion of exchange and political risks, see the study

by Robert Aliber.

The proposition of covered-interest parity is fairly well established

empirically with regard to Eurocurrency deposits; see the survey by

Peter Isard, p. 12, note 8 and the studies cited there. The results

reported in the present study go somewhat further in that both the

country of issue as well as the currency denomination of the

financial assets can differ. |

See the study by Michael Dooley and Isard for a discussion of the

effects of German capital controls and uncertainties about future

controls on interest-rate differentials during the period 1970-1974.

It is interesting that the four largest (in absolute value) residuals in

the German regressions reported in Table 10 are in 1972:Q3, 1973:Q1,

1973:Q2, and 1974:Q1. (The first three are underpredictions, while

the fourth is an overprediction.) According to the chronology of reported

German capital controls/in Dooley and Isard, the German government

took measures to prohibit purchases of domestic fixed-interest securi-

ties by non-residents in 1972:Q3, and in 1973:Q1 the government ex-

tended the prohibition to include many other capital transactions with

non-residents as well. In 1974:Q1 most of the restrictive measures .

were terminated. Thus three of the four largest residuals (in terms of

absolute value) in the German regressions in Table 10 correspond to

quarters in which there were changes in capital controls and this

correspondence suggests that changes in capital controls probably are an

important omitted factor in the German case.

- 42 -

13/ Henderson's criterion for perfect substitutability is whether or not the home (nominal) interest rate equals the foreign (nominal) interest rate plus the expected rate of depreciation, which is

essentially the same criterion as the one used here.