Central bank policy reaction and the expectations hypothesis of the term structure

Central Bank Policy Reaction and theExpectations Hypothesis of the TermStructure

Peter KuglerDepartment of Economics, University of Bern, CH-3012 Bern, Switzerland

This paper applies the monetary policy reaction model developed by McCallum to theterm structure of interest rates. First, it contains the solution of a rational expectationsmodel of the central bank policy reaction, with respect to the current long short-spreadfor the N period long rate case. Second, it applies this model rather successfully torecent weekly data for four countries. # 1997 by John Wiley & Sons, Ltd.

Int. J. Fin. Econ. 2, 217±224, 1997

No. of Figures: 0 No. of Tables: 1 No. of References: 12.

KEYWORDS: expectations hypothesis; term structure of interest rates; policy response

SUMMARY

The (rational) expectations hypothesis of the termstructure of interest rates, which states that the longrate is an average of the current and (rationally)expected future short rate, plus a constant termpremium, is rejected by numerous empiricalstudies. The sole explanation of this result, byvariation of the term premium, seems not veryconvincing given the pattern of results obtainedover the whole maturity spectrum. Of course,irrational expectations could be the reason for thelacking empirical support for the expectationshypothesis. However, conduct of monetary policymay play another important role for the empirical®ndings. This idea was introduced by Mankiw andMiron who observed that the spread between a USlong and a short rate had substantial predictivepower in line with the expectations hypothesisbefore the founding of the Fed. These authorsargue that interest rate stabilization by the Fedleads to zero expected short rate changes. There-fore, the spread only re¯ects variations of the termpremium and has no predictive power for the short

rate. This argument was recently extended andformalized by McCallum, who considered theeffect of the use of the spread as an indicator formonetary policy. His solution of a correspondingrational expectations model for the two period longrate shows that a strong policy response to changesin the spread and strong positive autocorrelation ofthe term premium produce predictive power of thespread for the short rate and, therefore, empiricalresults in favour of the expectations hypothesis.

The contribution of this paper is twofold. First,the McCallum model is solved for the general Nperiod long rate case, and it is shown that theresults for the two period case are also valid for thegeneral case. Second, the approach is applied toone and three months interest rates for the USA,Japan, Germany and Switzerland using a weekly1982±92 sample. This exercise points to a strongpolicy reaction by the Japanese, German and Swisscentral banks to the spread, whereas for the US it isrelatively low. The model nicely explains theresults of the standard regression test of theexpectations theory: for the Japanese case a strongreaction of the central bank and strong autocorrela-

*Correspondence to: P Kugler, Department of Economics, University of Bern, Gesellschaftsstrasse 49, CH-3012 Bern, Switzerland.

CCC 1076±9307/97/030217±08 $17.50# 1997 by John Wiley & Sons, Ltd. Int. J. Fin. Econ. 2: 217±224 (1997)

tion of the term premium leads to substantialpredictive power of the spread for short ratechanges. Therefore, the standard test of expecta-tions theory does not reject this hypothesis. How-ever, lower autocorrelation of the term premium (inparticular for Germany and Switzerland) or a lowerreaction coef®cient of the central bank (in particularthe USA) leads to rejections of the expectationstheory by the standard test for the remainingcountries.

1. INTRODUCTION

It is a widely recognized and well documented factthat the constant term premium version of theexpectations theory of the term structure is rejectedby the data. Of course, this ®nding may beattributed to time variation of the term premium.However, there is an increasing evidence againstthis explanation of the empirical failure of theexpectations theory (e.g. Froot, 1989; Evans andLewis 1994). An alternative explanation is based onthe effects of the conduct of monetary policy onexpectations. First, Mankiw and Miron (1986)consider the effect of short term interest ratestabilization by the central bank. Brie¯y, thisimplies that variation of the long short spread onlyre¯ects random changes of the term premiumwhen expected future short rates are equal to thecurrent short rate. Thus, the spread has nopredictive power for the future short rate andtherefore the standard tests reject the expectationshypothesis. The analysis of US data before andafter the founding of the Federal Reserve (byMankiw and Miron) as well as cross- countrystudy for the recent ¯oating rate period, by Kugler(1988, 1990) give some empirical support to thishypothesis. Second, there are attempts to relate therejection of the expectations theory to uncertaintywith respect to the regime of monetary policy.Indeed, the application of a Markov Switchingmodel to the US ten years bond rate and the threemonths treasury bill rate by Hamilton (1988)produces results in line with the expectationstheory. Similar analyses for the short term maturityspectrum by Lewis (1991) and Kugler (1996)con®rm this ®nding, at least for the USA.

There is a related problem of empirical ®nance:namely the rejection of the hypothesis that the

forward rate is an unbiased predictor of the spotexchange rate. This well known result may beagain explained by a highly volatile risk premium(Fama, 1984). However, a recent paper by McCal-lum (1994a) provides a very interesting newexplanation for bias of the forward rate. He showsthat the reduced form of a rational expectationsmodel with simultaneous interest rate smoothingand leaning against the wind with respect to theexchange rate by the central bank implies anegative relationship between the change in thespot rate and the lagged forward premium, asfound in most foreign exchange market ef®ciencystudies. This ®nding suggests the conjecture thatthe empirical results about the relation betweenshort rate change and lagged spread may be causedby a similar reason, namely the instantaneousreaction of monetary policy to changes in thespread, which are interpreted as signals of changesin future in¯ation expectations. Indeed, McCallum(1994b) solved a corresponding model for the twoperiod long rate and obtained a reduced formrelating the short rate change with the laggedspread by a coef®cient differing from twoÐthevalue implied in standard tests of the expectationstheory. In addition, he provides a solution for amodel using an approximation of the expected oneperiod rate of return for the general N period longrate case, and it appears that this frameworkaccounts for most of the results of tests of theexpectations hypothesis with US data.

The aim of this paper is twofold. First, we extentMcCallum's exact two period solution to thegeneral N period long rate case. Second, we applythis approach to one and three month Eurorates forthe US$, Yen, DM and Swiss Franc using a weekly1982±92 sample. The remaining part of this paper isorganized as follows: Section 2 presents the modeland its solution. The empirical results are given inSection 3 and some conclusions are offered inSection 4.2.

2. THE MODEL

Consider the following linearized version of theterm structure equation:

Rt �1

N�rt � re

t�1 � ret�2 . . .� re

t�Nÿ1� � xt; �1�

218 P. Kugler

Int. J. Fin. Econ. 2: 217±224 (1997) # 1997 by John Wiley & Sons, Ltd.

where Rt is the N period (long) rate, rt is the oneperiod (short) rate and re

t�j denotes expected valuesgiven information available in period t. xt is a termpremium which follows a stable AR(1) schemewith innovation ut which is exogenous with respectto rt and Rt:

xt � rxtÿ1 � ut

ut � IID�0; s2u�; jrj < 1

�2�

For expository purposes a constant term is omittedfrom Equation (2), but the estimation is carried outincluding a constant.

By contrast to standard analyses of the termstructure which do not use an explicit model for theshort rate we postulate, following McCallum(1994a), a policy reaction function:

Drt � l�Rt ÿ rt� � zt �3�where zt is a white noise error term withzt � IID�0; s2

z� representing exogenous short rateshocks, whereas the ®rst term in the right-handside, with coef®cient l > 0, accounts for theendogeneity of monetary policy: The central bankincreases the short rate when a widening spreadsignals higher expected future in¯ation and corre-spondingly higher future short rates. That is,Equation (3) mimics a forward-looking countercyclical policy by the central bank in a highlystylized way, ignoring other indicators consideredby the central bank.1 The model above is ageneralization of the analysis of the two periodterm structure by McCallum (1994b), who dis-cusses the rationale for this speci®cation of policybehaviour in more detail.

This model can be conveniently solved under therational expectations hypothesis using the methodof undetermined coef®cients. The minimal statevariable solution discussed by McCallum (1983) isgiven by

rt � f1rtÿ1 � f2xt � f3zt: �4�For N� 2, McCallum achieves, at the bubble freesolution, with f1�1, f2� 2l=(27 lr), f3� 1. Inaddition, for N� 3, the solution is f1�1,f2� 3l=(37 l(2z� z2), f3� 1. Therefore, we mayconjecture that f1�f3� 1 also holds for N largerthan 3. Indeed, the validity of this restriction f1�1can be easily demonstrated when rt and Rt arecointegrated I(1) series: This implies that 1 has to be

one as rt would be stationary when jf1j is smallerthan 1. Moreover, combining Equations (1) and (3)we get

�1� l�rt � rtÿ1 �lN�rt � re

tÿ1 � � � � ret�Nÿ1� � lxt � zt:

�3a�Clearly, imposing f1�1 we get

rt � rtÿ1� f2xt � f3zt; �4a�

and taking into account (4a) and (2) we obtain ret�j

as

ret�1 � rtÿ1 � f2xt � f3zt � f2rxt;

ret�2 � rtÿ1 � f2xt � f3zt � f2rx� f2r

2x2;

ret�j � rtÿ1 � f2�1� r� � � � � r j�xt � f3zt;

for j � 3; . . . ;N ÿ 1:

Substituting rt and ret�j into (3a) we get

�1� l��rtÿ1 � f2xt � f3zt�

� rtÿ1 �lN

Nrtÿ1 � f2

PNÿ1

j�0

�N ÿ j�r jxt � Nf3zt

" #� lxt � zt:

Equating coef®cients of rt71, xt and st on both sidesof the equation above results in

rtÿ1:1� l � 1� lN

N

zt:�1� l�f3 � l3 � 1

xt:�1� l�f2 �lNf2

PNÿ1

j�0

�N ÿ j�rj

" #� l:

The ®rst equation listed above con®rms theargument that f1�1 holds, whereas the secondand third equations provide

f3 � 1;

f2 �lN

N ÿ lPNÿ1

j�1

�N ÿ j�r j

:

Thus, the solution for rt is

rt � rtÿ1 �lN

N ÿ lPNÿ1

j�1

�N ÿ j�r j

xt � zt: �5�

Central Bank Policy Reaction 219

# 1997 by John Wiley & Sons, Ltd. Int. J. Fin. Econ. 2: 217±224 (1997)

Given these values for f1, f2, f3 we can rewrite thespread as

Rt ÿ rt�1

N�re

t�1ÿrt � ret�2 ÿ rt �� re

t�Nÿ1 ÿ rt� � xt:

Substituting the solution for rt and ret�j results in

Rt ÿ rt �1

Nf2�r�N ÿ 1� � r2�N ÿ 2�

�� rNÿ1� � 1

�xt;

Rt ÿ rt �1

N

lN

N ÿ lPNÿ1

j�1

�N ÿ j�r j

PNÿ1

j�1

�N ÿ j�r j � 1

2666437775xt;

Rt ÿ rt �N

N ÿ lPNÿ1

j�1

�N ÿ j�r j

xt: �6�

Finally, let us derive the reduced form relationshipbetween the interest rate change Drt and the laggedspread. Under the AR(1) assumption for xt we get

Rt ÿ rt � r�Rtÿ1 ÿ rtÿ1� �N

N ÿ lPNÿ1

j�1

�N ÿ j�r j

ut: �7�

Equating this expression to Equation (6) we obtain

xt �N ÿ l

PNÿ1

j�1

�N ÿ j�r j

Nr�Rtÿ1 ÿ rtÿ1� � ut

Substituting xt in (5) yields

rt ÿ rtÿ1 � rl�Rtÿ1 ÿ rtÿ1� �Nl

N ÿ lPNÿ1

j�1

�N ÿ j�r j

ut � zt:

�8�Equation (8) shows that the spread has nopredictive power for the short rate change when lis equal to zero. This result is easily understood, asEquation (3) indicates a random walk behaviour forthe short rate for l � 0. Of course, this is the case ofinterest rate smoothing by the central bank ®rstdiscussed by Mankiw and Miron (1986). Moreover,even if l is different from zero, if r is equal to zero,there is no predictive power of the spread for theshort rate. This ®nding can be interpreted asfollows: the predictive power of the spread for

the short rate is based on the predictable policyreaction of the central bank to the spread. However,if r is zero, there is no predictable exogenousmovement of the spread which results in predict-able policy reactions.

The coef®cients r and l can be estimated byapplication of indirect least squares to Equations(7) and (8). Moreover, our model implies that thespread is strongly exogenous when the two whitenoise errors are mutually uncorrelated: (Rt7 rt)and Drt follow a contemporaneously and dynami-cally recursive structure in this case and l can beestimated by OLS. Finally we should note that thetwo reduced form coef®cients of �Rtÿ1 ÿ rtÿ1� areindependent of N.

All these results strongly depend on the assump-tion that zt is not autocorrelated. When we assumethat zt follows a stable AR(1) process with para-meter y it is easily demonstrated that we get thesolution

rt � rtÿ1 �lN

N ÿ lPNÿ1

j�1

�N ÿ j�r j

xt

� N

N ÿ lPNÿ1

j�1

�N ÿ j�y j

zt

Rt ÿ rt �N

N ÿ lPNÿ1

j�1

�N ÿ j�r j

xt

� 1

N ÿ lPNÿ1

j�1

�N ÿ j�y j

PNÿ1

j�1

�N ÿ j�y jzt

�9�

Clearly, we no longer have a simple recursivestructure, i.e. there exists a rather complicatedfeedback relation between Drt and (Rt7 rt). We canwrite Equation (9) in matrix notation as

zt � Cet �10�where e0t � �xt; zt�, z0t � �Drt; Rt ÿ rt� and the matrixcontains the coef®cients depending on l, r, y andN. Our assumptions with respect to the error termscan be written in a VAR(1) form:

et � Betÿ1 � et;

B � r 0

0 y

� �; e0t

�ut; vt

�:

9>=>; �11�

220 P. Kugler


From (10) and (11) we get now

et ÿ Betÿ1 � Cÿ1zt ÿ BCÿ1ztÿ1

et � Cÿ1zt ÿ BCÿ1ztÿ1

zt � CBCÿ1ztÿ1 � Cet

9>=>; �12�

Thus, zt follows a VAR(1) model with coef®cientsdepending on the structural parameters l, r and yin a rather complicated and highly non-linear way.Of course, these parameters are not so easy toestimate from the reduced form as in the basicmodel. However, estimates of l and y are easilyobtained by applying the instrumental variablemethod with AR(1) error with instrumentsDrtÿ1; Rtÿ1 ÿ rtÿ1 to Equation (3).

What are the implications of our basic modelwithout autocorrelation of the policy reactionequation error term for the standard regressiontest of the term structure? This test is based on thefollowing equation relating a weighted sum ofexpected future short rate changes to the currentspread, which is implied by the basic termstructure, Equation (1), with a zero term premiumPNÿ1

j�1

�N ÿ j�Dret�j � b�Rt ÿ rt�: �13�

The slope coef®cient b of this equation is equal toN. This implication of the expectations hypothesisis tested by regressing observed future short ratechanges on the current spread and considering thehypothesis b � N , taking into account the meanzero MA(N-1) error term representing expecta-tional errors.

Given the reduced form of Equations (7) and (8)for the short rate change and the spread we easilyget Dre

t�j � lr j�Rt ÿ rt�. Therefore, the followingvariant of Equation (13) in the framework of ourstructural model is obtained:PNÿ1

j�1

�N ÿ j�Dret�j� l

PNÿ1

j�1

�N ÿ j�r j�Rt ÿ rt�: �14�

The slope coef®cient is, in general, different fromN. It is zero when the central bank does not react tothe term structure and=or when the termpremium is not autocorrelated. As discussed abovethese conditions result in random walk behaviorofDrt.

In our empirical analysis we apply our basicmodel to weekly data for one and three month

interest rates. Thus, the short rate is not the oneperiod rate as in the standard case outlined above.However, the model is easily adapted to thissituation: the basic term structure equation is nowgiven by

Rt �1

3�rt � re

t�4 � rer�8� � xt: �1a�

Of course, this formulation involves an approxima-tion error since months are not exactly equal to fourweeks. However this error should be rather smalland is neglected. Given the derivation of thesolution for the standard case, we easily obtain

rt � rtÿ1 �3l

3ÿ l 2P4j�1

rj �P8j�5

rj

! xt � zt �5a�

Rt ÿ rt �3

3ÿ l 2P4j�1

rj �P8j�5

r j

! xt: �6a�

This results in the two reduced form equations

Rt ÿ rt � r�Rtÿ1 ÿ rtÿ1� �3

3ÿ l 2P4j�1

rj �P8j�5

r j

! ut

�7a�

Drt � rl�Rtÿ1 ÿ rtÿ1� �3l

3ÿ l 2P4j�1

rj �P8j�5

r j

! ut � zt:

�8a�

Therefore, the two reduced form coef®cients of�Rtÿ1 ÿ rtÿ1� are the same as in the one period shortrate framework. Moreover, Equation (13) is nowwritten as

2P4j�1

Dret�j �

P8j�5

Dret�j � b�Rt ÿ rt�: �13a�

Without a policy reaction model and with aconstant term premium we expect b � 3 under



rational expectations, whereas the policy reactionmodel implies

b � l 2P4j�1

r j �P8j�5

r j

!:

In our following empirical analysis we estimate thereduced form Equations (7a) and (8a). This allowsus to estimate a slope coef®cient for the standardtest equation for the expectations theory under ourpolicy reaction model. This implied value iscompared with the estimate obtained by the directapplication of OLS to Equation (13a) with observedshort rate changes.

3. EMPIRICAL RESULTS

The reduced form Equations (7a) and (8a) as wellas the usual term structure test equation (13a) wasestimated using weekly end of period Euromarketdata for the US$, Yen, DM and Swiss Franccovering the period from October 1982 to July1992.2

This sample period was selected mainly because of

the unborrowed reserves operation procedureapplied by the Fed from fall 1979 to fall 1982.These three years clearly exhibit a differentbehaviour of US interest compared with precedingand subsequent periods. In addition, the strongmovement of the US-interest rate was transmittedto other currencies to a substantial extent.3

Table 1 contains the estimates for l and robtained by the application of indirect leastsquares. The r estimates are in a rather narrowrange between 0.73 (Germany, Switzerland) and0.81 (Japan). The differences in the l estimates arelarger. They are between 0.25 and 0.41. Mostinterestingly we note a higher l estimate for Yen,DM and Swiss Franc than for the US$. This resultis, of course, in line with the more anti-in¯ationarystance of monetary policy in the former countries.The value implied by this estimate for the slope ofthe regression of the term structure test equation isclose to 3 for the Yen, but a lower persistence of thespread (equal to the persistence of the termpremium) and slightly lower reaction coef®cientresults in estimates which are substantially lowerthan 3 in the German and Swiss case. For the US$the relatively low reaction coef®cient l is the main

Table 1. Estimation results for the policy reaction function model for the term structure of one and three months interestrates, weekly data 1982=10±92=07.

Drt � c1 � lr�Rtÿ1ÿ rtÿ1� �

3l

3ÿ l 2P4j�1

rj �P8j�1

rj

! ut � zt

�Rt ÿ rt� � c2 � r�Rtÿ1 ÿ rtÿ1� �3

3ÿ l 2P4j�1

r j �P8j�1

r j

! ut

R2 DW=O�36�r l Drt Rt ÿ rt Dr Rt ÿ rt l

�2P4j�1

r j �P8j�5

r j

�b�2�

USA 0.777 0.254 0.035 0.604 2.05/47.9 2.11/55.9 1.33 1.38(14.8)(1) (2.23) (2.88)

Japan 0.807 0.414 0.134 0.655 1.99/147.8 1.96/124.2 2.42 2.94(23.1) (6.80) (11.3)

Germany 0.731 0.364 0.059 0.535 2.00/37.2 1.99/50.5 1.62 1.44(12.2) (4.81) (3.18)

Switzerland 0.726 0.354 0.051 0.528 1.90/79.6 1.98/109 1.54 1.68(10.6) (2.97) (5.01)

(1)t-values in parentheses. White standard errors.(2)Direct OLS estimate of the slope coef®cient of the standard term structure test, Equation (13a), t-values based on MA(7) andheteroscedasticity corrected standard errors.

8>>>>>>>>>><>>>>>>>>>>:8>>>>><>>>>>:

222 P. Kugler


reason for the relatively low implied slope coef®-cient of the standard term structure test regression.Finally, we have to stress that the directly estimatedslope of the regression term structure test is veryclose to the estimate implied by our structuralmodel: indeed, the slope coef®cient implied by thepolicy reaction model is within a two standarderror band of the directly estimated coef®cient.

These empirical results are surprisingly good forour highly stylized policy reaction model. Ofcourse, the slope of the term structure is surelynot the only indicator used by the central bank inorder to determine the stance of monetary policy.Moreover, we may argue that it is not the three toone month spread which is relevant for monetarypolicy, but the spread between a long rate and ashort rate. The sometimes signi®cant Ljung±Boxstatistics with 36 lags, pointing to higher orderresidual autocorrelation, can be considered asevidence for omitted policy indicators. In fact, itcould be argued that the predictive power of thespread is caused by the reaction of the central bankto some indicator other than the current spread,like for example the lagged short rate changes. Inorder to investigate this objection we estimated thepolicy reaction, Equation (3) with an AR(1) errorterm as brie¯y outlined in Section 2. However, theIV estimates for l are only marginally differentfrom those reported in Table 1. Therefore, ourempirical results clearly point to the relevance of asystematic monetary policy reaction to the spreadas a cause of the apparent empirical failure of theexpectations hypothesis of the term structure ofinterest rates.

4. SUMMARY AND CONCLUSION

This paper applies the endogenous policy reactionmodel developed by McCallum (1994a), whichexplains the bias of the forward foreign exchangerate as a predictor of the spot rate, to the termstructure of interest rates. First, it generalized thesolution of the corresponding model for the two-period long rate case by McCallum (1994b) to thegeneral N period framework. Second, it applies thismodel to recent data of four countries The modelconsists of the expectations theory term structureequation with an autocorrelated term premium and

a policy reaction function. The latter equationrelates the short rate change to the long shortspread re¯ecting the central bank reaction tochanges of expected future in¯ation. The estima-tion of the rational expectations reduced-formsolution using weekly data for the three and onemonth rate and period 1982±92, shows a highreaction coef®cient for the Japanese, German andSwiss central banks to the spread, whereas for theUS it is relatively low.

The model nicely explains the results of thestandard regression test of the expectations theory:for the Yen, a strong reaction of the central bankand strong autocorrelation of the term premiumleads to substantial predictive power of the spreadfor short rate changes. Therefore, the standard testof expectations theory does not reject this hypoth-esis. However, lower autocorrelation of the termpremium (in particular, DM, Swiss Franc) or alower reaction coef®cient of the central bank (inparticular, USA) leads to rejections of the expecta-tions theory by the standard test for the remainingcountries.

ACKNOWLEDGEMENTS

The author would like to thank Ben McCallum forsuggesting the approach applied in this paper andfor helpful comments on an earlier draft as well asChiente Hsu for outstanding research assistance.Moreover, helpful comments of an anonymousreferee are gratefully acknowledged. Of course, allremaining errors are mine.

END NOTES

1. Equation (3) has an immediate appeal when thecentral bank uses the short rate as its instrument.However, I would suggest that Equation (3)remains a valid description when the central bankuses other instruments, as these actions areimmediately transmitted to the short rate, as a rule.

2. The data source is INTLINE Databank, WEFA,middle rates. The estimation of the model withmonthly data resulted in large l estimates withvery large standard errors. Besides the problem of arelatively small monthly sample this result seems



to be partly caused by low persistence of the termstructure error term xt with monthly data implyinglow and imprecise estimated values. Moreover, itmight be argued that the policy reaction functionadopted is less appropriate for monthly thanweekly data, as more policy indicators are availablemonthly.

3. However, it should be mentioned that aextended sample (1979±92) produced similar re-sults.

5. REFERENCES

Evans, M. D. D. and Lewis K. K. (1994) Do risk stationarypremia explain it all? Evidence from the TermStructure. Journal of Monetary Economics, 33, 285±318.

Fama, E. F. (1984) Forward and spot exchange rates.Journal of Monetary Economics, 14, 319±338.

Froot, K. A. (1989) New hope for the expectationshypothesis of the term structure of interest rates.Journal of Finance, 44, 283±305.

Hamilton, J. D. (1988) A rational expectation analysis ofchanges in regime: an investigation of the term

structure of interest rates. Journal of Economic Dynamicsand Control, 12, 385±423.

Kugler, P. (1988) An empirical note on term structure andinterest rate stabilization policies. Quarterly Journal ofEconomics, 53, 689±692.

Kugler, P. (1990) The term structure of euro interest ratesand rational expectations. Journal of International Moneyand Finance, 9, 234±244.

Kugler, P. (1996) The term structure of interest rates andregime shifts, some empirical results. Economics Letters,50, 121±126.

Lewis, K. K. (1991) Was there a `peso problem' in the USterm structure of interest rates: 1979±1982?. Interna-tional Economic Review, 32, 159±173.

Mankiw, N. G. and Miron J. A. (1986) The changingbehavior of the term structure of interest rates.Quarterly Journal of Economics, 101, 211±228.

McCallum, B. T. (1983) On-uniqueness in rationalexpectations models: an attempt at perspective. Journalof Monetary Economics, 11, 139±168.

McCallum, B. T. (1994a). A reconsideration of theuncovered interest parity relationship. Journal ofMonetary Economics 33, 105±132.

McCallum, B. T. (1994b). Monetary policy and the termstructure of interest rates. NBER Working Paper No.4938.

224 P. Kugler


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Central bank policy reaction and the expectations hypothesis of the term structure