Term structure and interest differentials as ... - Semantic Scholar

Applied Financial Economics, 1998, 8, 615 — 625

Term structure and interest differentials as predictors of future inflation changes and inflation differentials G U G L I E LM O M A RI A C A PO RA L E and N I K I TA S P I T TI S* Centre for Economic Forecasting, ¸ondon Business School, Sussex Place, Regent’s Park, ¸ondon N¼1 4SA and *Department of Economics, ºniversity of Cyprus, Kalipoleos 75, P.O. Box 537, Nicosia, Cyprus

The paper tests the unbiasedness of interest differentials and term structure as predictors of inflation differentials and inflation changes, respectively, using three-, six- and twelve-month maturities in eight major industrial countries over the period 1981—1992. The first hypothesis requires rational expectations (RE) and equality of ex-ante real interest rates, which in turn holds only in the presence of uncovered interest parity (UIP) and ex-ante purchasing power parity (PPP). The second is correct if, in addition to RE, the Fisher hypothesis and constancy of ex-ante real rates are satisfied. The empirical results lead to the rejection of both null hypotheses, although interest differentials and term structure do appear to be relatively useful for forecasting purposes. In particular, the interest differential model performs better than simple ARMA models at the shortest end of the maturity spectrum in out-of-sample forecasting.

I. INTRO DUCTI ON Some new evidence on two hypotheses of interest to both macroeconomists and policy-makers is reported, namely the unbiasedness of interest differentials as predictors of future inflation differentials, and of the term structure as a predictor of future inflation changes. While existing studies tend to focus on one or the other, and to consider only the period up to the beginning of the 1980s, a systematic analysis of both propositions in eight major industrial countries is presented using three-, six- and twelve-month maturities over the period 1981—1992. The issue of the information contained in the term structure of interest rates is an important one because if the relationship between interest rates for different maturities could help predict future inflation the yield curve could be used as a guide for monetary policy. Fama’s (1975) seminal paper found that real interest rates are constant over time, with fluctuations in nominal interest rates mainly reflecting changes in expected inflation (the so-called Fisher effect).

Similar conclusions have been reached by other researchers for the United States (Nelson and Schwert, 1977; Mishkin, 1981; Fama and Gibbons, 1982). Mishkin (1990) finds that the constancy of real rates is rejected in the United States. The term structure appears to contain a great deal of information about future inflation at its shortest end (maturities of six months or less). Conversely, longer maturities provide information about the term structure of real interest rates. The evidence for other OECD countries (Mishkin, 1984a) also rejects the constancy of real rates and the existence of a Fisher effect. Concerning the latter, a more recent study by the same author (Mishkin, 1992) finds that in the United States there is no short-run correlation between interest rates and inflation; however, there is a long-run Fisher effect in which inflation and interest rates have a common stochastic trend when they exhibit trends. As for the hypothesis that interest differentials are unbiased predictors of future inflation differentials, and hence that ex-ante real interest rates are equal under floating in the presence of a high degree of capital mobility, it is of interest

For the related issue of whether the term structure can predict real economic activity, see Estrella and Hardouvelis (1989) 0960—3107  1998 Routledge

615

G. M. Caporale and N. Pittis

616 for three main reasons. First, the equality of real rates would imply that monetary policy is not an effective stabilization tool in an open economy as real economic activity could not be influenced through the real interest rate. Second, real interest rate equalization across countries requires that UIP and PPP be satisfied. Therefore, it is a test of the monetary approach to exchange rates (Frenkel, 1976) versus models which depend on real rates differing between countries in the short run (Mussa, 1982). Third, policies which increase domestic savings can only increase the rate of investment and hence productivity if real rates are not equal across countries (Feldstein, 1982). Concerning the empirical literature, Mishkin (1984a) uses a latent variable statistical model to test for real rate equality, and cannot reject the equality hypothesis in bilateral tests of the United States vis-a` -vis six industrialized countries. Mark (1985), in contrast, finds that neither pre-tax nor net-of-tax real rate equality are well supported by the data. The contribution of the present study is mainly empirical; however, some relevant theory is also reviewed in order to make the economic interpretation of the results clearer. The layout of the paper is as follows. Section II presents a testing strategy for the two hypotheses of interest. In Section III the predictive power of the two models is assessed by evaluating the information contained in the yield curve and the interest differential, respectively, and by comparing their forecasting performance with the forecasting performance of simple ARMA models. Some concluding remarks are offered in Section IV, in which the policy implications of our findings are spelt out.

II . SOM E T HEORY As stated above, the aim is to test (a) whether the interest differential is an unbiased predictor of the future inflation differential between countries, and (b) whether the term structure is an unbiased predictor of the future inflation path in individual countries. As a first step, a theoretical framework is discussed which sheds light on the conditions under which these two null hypotheses can be expected to hold, and also some estimable equations are derived. Consider the two propositions of interest in turn. Starting from the unbiasedness of interest differentials, assume that uncovered interest parity (UIP) holds: E (s !s )"iK%#!iK* (1) R R>K R R R where s is log of the spot exchange rate, defined as DM for foreign currency, m is the maturity of the interest rate, and

the interest differential is between Germany (GE) and each of the other countries. We adopt the convention that Germany is the domestic economy because of its role as the centre country in the EMS, which sets a nominal anchor. Also assume that ex-ante purchasing power parity (PPP) holds: E (s !s )"E (n%# !n* ) (2) R R>K R R R>K R>K where n is the inflation rate defined as log P !log P . R>K R Combining Equations 1 and 2 and assuming rational expectations (RE) yields: n%# !n* "(iK%#!iK*)#(u%# !u* ) R>K R>K G R R>K R>K

(3)

where u%# "n%# !E n%# R>K R>K R R>K (4) u* "n* !E n* R>K R>K R R>K Equation 3 states that if UIP, ex-ante PPP and RE hold, then the interest differential should be an unbiased predictor of the future inflation differential. However, the validity of Equations 1 and 2 also implies equality of the ex-ante real interest rate between the two countries. To see that, subtract Equation 2 from Equation 1 to obtain: 0"(iK%#!E n%# )!(iK*!E n* ) R R R>K R R R>K (5) "E rK%#!E rK* R R R R where r is the real interest rate, and the second equality follows from the Fisher hypothesis. Therefore, we can conclude that the interest differential will be an unbiased predictor of the future inflation differential only if ex-ante real rates are equal. The joint hypothesis of RE and equality of ex-ante real rates can be tested by estimating the following equation: n%# !n* "a#b(iK%#!iK*)#e (6) R>K R>K R R R>K where the null hypothesis of the unbiasedness of the interest differential as a predictor of the inflation differential is (a, b)"(0, 1) and e is a white noise error process. R Turning now to the unbiasedness of the term structure as a predictor of future inflation changes, we shall show that for this proposition to hold ex-ante real interest rates must be constant over time, and hence the Fisher hypothesis has to be satisfied. More formally, consider the Fisher hypothesis for maturities m and n: iK"rK#E n R R R R>K iL"rL#E n R R R R>L

(7)

For further evidence on real interest parity, see Mishkin (1984b), Cumby and Obstfeld (1984), Cumby and Mishkin (1986), and Gaab et al. (1986), who all find that real interest rates are not perfectly correlated across countries. For some evidence on asymmetries in the EMS see Giavazzi and Giovannini (1987). Concerning Equation 2, it should be pointed out that researchers have found it rather difficult to reject the unit root hypothesis for real exchange rates (see MacDonald and Taylor (1992) for a survey of the empirical evidence).

Predictors of inflation differentials and changes

617

Taking the difference of the two interest rates with different maturities and assuming RE yields: n

!n "(rK!rL)#(iK!iL)#(u !u ) (8) R>K R>L R R R R R>K R>L Equation 8 states that if the ex-ante real rate is constant over time (i.e. rK"rL) and expectations are rational then the R R term structure of nominal interest rates is an unbiased predictor of future inflation changes between periods m and n. The joint hypothesis of RE and constancy of the ex-ante real rate can be tested by estimating the following equation: n !n "a #b (iK!iL)#gKL (9) R>K R>L   R R R where the null hypothesis is (a , b )"(0, 1) and g is again   R a white noise process. To summarize, we have shown in this section that the unbiasedness of interest differentials as predictors of future inflation differentials requires rational expectations (RE) and equality of ex-ante real interest rates (which in turn holds only in the presence of uncovered interest parity (UIP) and ex-ante purchasing power parity (PPP)), whereas the term structure will be an unbiased predictor of future inflation changes if, in addition to RE, the Fisher hypothesis and constancy of ex-ante real rates are satisfied.

Fig. 1. Recursive estimate of b in Equation 9$2S.E. — France 

II I. E MP IR ICAL R ES UL TS ¹ests of unbiasedness Our dataset consists of London Eurocurrency interest rates with three-, six- and twelve-month maturity and consumer price indices for eight major economies, covering the period from June 1981 to December 1992. The reasons for using Eurocurrency rates are that they are market clearing, and they should not be affected by capital controls. Before proceeding to estimating Equations 6 and 9, one should note that the OLS estimates of the standard errors will be invalid. This reflects the presence of serial correlation which is due to the fact that the number of periods for the interest and inflation rates are greater than the observation interval. This is the well known overlapping observations problem, which may cause the error term to follow an MA (m!1) process, where m is the maturity of interest rates. In order to derive asymptotically valid standard errors, we employ the Generalized Method of Moments (GMM) developed by Hansen and Hodrick (1980) as modified by White (1980) to allow for conditional heteroscedasticity and by Newey and West (1987) to ensure that the variance—covariance matrix is positive definite.

Fig. 2. Recursive estimate of b in Equation 9 $2S.E. — Italy 

A further issue to be addressed is that of the time series properties of the differentials which appear in Equations 6 and 9. Standard unit root tests turned out to be rather inconclusive as to whether the null hypothesis that the variables of interest contain stochastic trends should be rejected. Because of the low power of such tests, we decided to follow our prior that the differentials are stationary stochastic variables, which implies that the inference using the t-distribution is valid, and that the forecasting ability of the specified equations can be correctly assessed (Mishkin, 1992).

It is also implicity assumed that the ‘pure’ expectations hypothesis holds, i.e. that long-term interest rates should simply be a geometric average of expected future short-term interest rates. To determine the order of integration of the variables we followed the sequential testing strategy described in Perron (1988), starting from the most general specification and testing down to more restricted specifications. This led us to estimate the Dickey—Fuller (DF) regressions without a constant and a deterministic trend, because neither of them was found to be statistically significant (the test statistics are not reported for reasons of space).

618

Fig. 3. Recursive estimate of b in Equation 9$2S.E. — Nether lands

Fig. 4. Recursive estimate of b in Equation 9$2S.E. — Japan 

Fig. 5. Recursive estimate of b in Equation 9$2S.E. — Switzerland 

G. M. Caporale and N. Pittis

Fig. 6. Recursive estimate of b in Equation 9$2S.E. — ºK 

Fig. 7. Recursive estimate of b in Equation 9$2S.E. — ºSA 

Fig. 8. Recursive estimate of b in Equation 9$2S.E. — Germany 

Predictors of inflation differentials and changes

619

Table 1. Estimation of Equation 9 a

FR IT NL JA SZ UK US GE

FR IT NL JA SZ UK US GE

FR IT NL JA SZ UK US GE

0.0077 (0.0006) 0.0140 (0.0006) 0.0041 (0.0014) 0.0045 (0.0007) 0.0080 (0.0015) 0.0140 (0.0018) 0.0095 (0.0011) 0.0042 0.0017 0.0153 (0.0008) 0.0274 (0.0008) 0.0070 (0.0042) 0.0087 (0.0024) 0.0133 (0.0038) 0.0276 (0.0039) 0.0208 (0.0020) 0.008 0.0041 0.0230 (0.0012) 0.0420 (0.0016) 0.0090 (0.0059) 0.0130 (0.0074) 0.0240 (0.0058) 0.0426 (0.0052) 0.0305 (0.0032) 0.011 0.006

b

s.e.

3, 6-month: m"6, n"3 0.102 0.003 (0.135) 0.477 0.004 (0.139) 0.145 0.007 (0.175) 0.932 0.008 (0.207) !0.573 0.007 (0.577) 1.070 0.010 (0.480) !0.205 0.005 (0.327) 0.92 0.005 0.721 6, 12-month: m"12, n"6 0.313 0.005 (0.081) 0.787 0.007 (0.348) 1.550 0.009 (1.010) 1.460 0.008 (0.840) !0.306 0.011 (1.060) 0.953 0.014 (0.938) !0.787 0.007 (0.485) 1.979 0.009 0.923 3, 12-month: m"12, n"3 0.275 0.007 (0.176) 0.676 0.007 (0.219) 2.230 0.012 (1.050) 1.430 0.011 (0.707) !0.678 0.013 (0.614) 1.234 0.017 (0.516) !0.605 0.009 (0.305) 1.52 0.011 0.83

R

(a, b)"(0, 1)

0.00

604

0.24

713

0.00

9.54

0.01

46.61

0.01

33.27

0.05

73.4

0.01

77.91

0.03

17.8

0.11

480.9

0.17

327

0.05

23.56

0.04

18.9

0.01

18.49

0.02

55.6

0.05

101.74

0.08

44.18

0.11

527

0.38

1181

0.12

10.28

0.07

19.69

0.01

16.77

0.11

100.1

0.06

88.52

0.08

30.38

Sample 85:1—92:12

The argument for stationarity can be summarized as follows: given the evidence that the log of the exchange rate is I(1), UIP implies stationary interest differentials unless there is an I(1) risk premium, which seems unlikely (MacDonald and Taylor, 1992).

The estimates of Equation 9, which test whether the term structure is an unbiased predictor of future inflation changes, lead to the following conclusions. The null hypothesis (a , b )"(0, 1), which implies that the ex-ante   real interest rate is constant over time, is rejected for all

620 countries and for any maturity. Most estimates are not significantly different from zero or negative. This points either to misspecification or the fact that the slope of the real term structure is not constant over time (Mishkin, 1990). To interpret the results, one should note that the composite error term gKL includes both the forecast errors R of inflation, which are orthogonal to the regressors by the RE hypothesis, and an additional term that disappears if the slope of the real term structure is constant, thereby making the OLS estimates consistent. One the contrary, if the slope is not constant, the probability limit of b will be different  from 1, and a will also be an inconsistent estimate of a ,   which can be shown to be the mean slope of the real term structure. Consequently, the term structure can be seen to contain information about future inflation changes if b  is significantly different from 0, while the slope of the real term structure is not constant if b is statistically different  from 1. As the estimates of b imply a time-varying slope of the  real term structure, we investigated the evolution over time of the parameters by estimating Equation 9 recursively. Figures 1 to 8 (m"12, n"6) show that indeed the parameter b is rather unstable in the first years of the sample.  The EMS countries, especially Italy and France, exhibit most instability. This is hardly surprising, since the early EMS period was characterized by large and frequent realignments which resulted in quite a volatile term structure. We therefore reestimated Equation 9 for the period starting in January 1985. The results are reported in Table 1. The null hypothesis is again strongly rejected, but now the estimates of b are mostly significant and positive though  different from one. In the case of the United Kingdom the estimates of b are very close to one for all points in the  maturity spectrum. In contrast, for Switzerland and the United States the estimates of b remain negative even  during the period of structural stability, which indicates that the term structure in these countries fails to predict even the direction of future inflation changes. This is in contrast to the findings of Mishkin (1990), who reports that in the United States the term structure of nominal interest rates contains a great deal of information about the future path of inflation at the longest end of the maturity spectrum. In the rest of the countries b is statistically significant  and positive, with the implication that the term structure does have some information about changes in future inflation. The estimated coefficients are generally higher at longer maturities, indicating that more information about future inflation changes is contained at the longest end of the maturity spectrum. This is what one would expect, since

G. M. Caporale and N. Pittis

Fig. 9. Recursive estimate of b in Equation 6$2S.E. — France—  Germany

the coefficient b gets larger as the variability of the real  term structure slope declines relative to the variability of expected inflation (Mishkin, 1990). In terms of the constancy of the ex-ante real interest rates, the evidence suggests that the ex-ante real rate is virtually constant over time in the United Kingdom, while it is quite time-varying in the United States and Switzerland. Concerning the estimation of Equation 6, which tests whether the interest differential is an unbiased predictor of the future inflation differential, our findings suggest the following: such a model is much more structurally stable than the term structure model. This can be seen from Figs 9 to 15 (for interest rates with a twelve-month maturity), which graph recursive estimates of the coefficient b. In most cases they do not exhibit much variation over time. The two main exceptions are again France and Italy, for which the estimates of b move towards one as more data points are added. It is noteworthy that the recursive estimates become positive towards the end of 1985, which almost coincides with the beginning of the EMS regime normally referred to as the ‘hard’ EMS (Giavazzi and Spaventa, 1990). It should be noted that the closeness of b to one is an indication of the extent to which UIP and ex-ante PPP hold. The charts show that as the EMS was becoming more credible b was approaching one, which can be interpreted as evidence that the risk premium was decreasing over time, making UIP more relevant. The reduction in the risk premium could reflect either a decrease in the exchange risk premium due to the regime change or a decrease in the political risk premium due to the gradual abolition of

A note of caution is appropriate here, as it is also possible that the higher volatility of the estimates at the beginning of the period is due to a small sample size effect. Similar considerations apply to the recursive estimates for Equation 6. Mishkin (1990) also analyses the relationship between movements in the nominal and real term structure of interest rates. More information about the real term structure is found in the observable nominal term structure for maturities of six months or less.

Predictors of inflation differentials and changes

621

Fig. 10. Recursive estimate of b in Equation 6$2S.E. — Italy—  Germany

Fig. 13. Recursive estimate of b in Equation 6$2S.E. — Switzer land—Germany

Fig. 11. Recursive estimate of b in Equation 6$2S.E. — Nether lands—Germany

Fig. 14. Recursive estimate of b in Equation 6$2S.E. — ºK—  Germany

Fig. 12. Recursive estimate of b in Equation 6$2S.E. —  Japan—Germany

Fig. 15. Recursive estimate of b in Equation 6$2S.E. — ºSA—  Germany

G. M. Caporale and N. Pittis

622 Table 2. Estimation of Equation 6 a FR IT NL JA SZ UK US GE FR IT NL JA SZ UK US GE FR IT NL JA SZ UK US GE

b

0.0011 (0.0012) !0.0030 (0.0017) 0.0010 (0.0016) 0.0005 (0.0013) !0.0038 (0.0009) 0.0045 (0.0020) !0.0034 (0.0008) —

0.114 (0.029) 0.100 (0.002) !0.013 (0.206) 0.061 (0.047) 0.228 (0.078) 0.242 (0.054) 0.086 (0.025) —

0.0030 (0.0020) !0.0046 (0.0032) 0.0015 (0.0017) 0.0006 (0.0013) !0.0090 (0.0013) 0.0054 (0.0036) !0.0064 (0.0021) —

0.271 (0.056) 0.232 (0.058) !0.059 (0.187) 0.161 (0.053) 0.642 (0.097) 0.425 (0.075) 0.152 (0.058) —

0.0084 (0.0040) !0.0063 (0.0046) 0.0021 (0.0023) 0.0014 (0.0021) !0.0016 (0.0046) 0.0090 (0.0100) !0.0110 (0.0050) —

0.559 (0.059) 0.485 (0.067) !0.295 (0.273) 0.297 (0.256) 0.694 (0.388) 0.858 (0.168) 0.297 (0.148) —

R

(a, b)"(0, 1)

0.20

1439.54

0.005

0.26

4676.01

0.008

0.01

47.63

0.009

0.00

402.05

0.004

0.11

297.1

0.009

0.25

946.8

0.004

0.24

1384.7

s.e. 3-month rates 0.005

— 6-month rates 0.007

—

—

0.41

470

0.006

0.49

1047

0.008

0.00

0.008

0.10

200

0.005

0.33

158.94

0.011

0.36

250

0.007

0.26

218.6

— 12-month rates 0.008

—

76.2

—

0.73

407.53

0.008

0.74

187.03

0.007

0.03

52.12

0.009

0.14

10.62

0.008

0.23

50.34

0.014

0.48

23.59

0.011

0.32

25.44

—

—

—

Sample 85:1—92:12

capital controls. Even in the ‘hard’ EMS, though, real interest differentials which are difficult to explain by risk premia and capital market imperfections have persisted (Giovannini, 1992).

Estimation of Equation 6 was carried out for the whole sample period and for the period starting in January 1985. The two sets of estimates are remarkably similar, and for reasons of comparison with the term structure model we

See Frankel and MacArthur (1988), who show that the real interest rate differential can be decomposed into the covered interest differential, or political premium, and the real forward discount, or currency premium, which can further be decomposed into the exchange risk premium and expected real depreciation.

Predictors of inflation differentials and changes

623

report in Table 2 the results for the latter period. The joint hypothesis (a, b)"(0, 1) is again rejected for all countries and for all forecasting horizons. The estimates of b, though, are statistically significant and positive, suggesting that the interest differential does contain some information about the future inflation differential. It is interesting to note that the value of the estimates of b increases with the interest rate maturity. This might be due to the fact that long-term interest rates are not as sensitive to (short-term) exchange rate expectations (e.g. expectations of realignments within the EMS) as short-term rates. Moreover, PPP, which is part of the null, becomes more relevant in the long run. However, as we will show next, it does not follow from these findings that long-term rates perform better than short-term rates in out-of-sample forecasting. It is also worth noting that the only country in which the estimate of b is negative and not significantly different from zero is the Netherlands. As the Dutch Guilder was anchored to the DM, it is not surprising that UIP and PPP appear not to hold in this case. On the whole, these results are consistent with the evidence presented by Mark (1985) for the period from May 1973 to February 1982, although he takes a different approach. His method is to estimate agents’ forecast of the real

rate differential by using optimal linear prediction rules, and then to perform tests of equality based on current and past real interest rate differentials, and past and current money growth and inflation rates. Obviously this procedure has the pitfall that it is valid only as long as the set of variables chosen to construct agents’ forecasts are actually contained in their information set. Out-of-sample performance of the term structure and interest differential models The econometric estimates reported above show that, although the unbiasedness hypothesis is rejected for both the term structure and the interest differential models, the significant and positive values of b and b obtained for some  countries may contain some useful information for forecasting inflation or inflation differentials. In order to evaluate the forecasting performance of these models we compare their out-of-sample accuracy with that of a simple AR(1) model which yielded the lowest root-mean-squared errors (RMSE) and mean absolute errors (MAE) among all the ARMA models examined. The results are quite interesting (see Table 3), indicating that the interest differential model

Table 3. Forecasting equations (a) Inflation differentials 3-month Int. Diff.

FR IT NL JA SZ UK US

6-month AR(1)

Int. Diff.

12-month AR(1)

Int. Diff.

AR(1)

RMSE

MAE

RMSE

MAE

RMSE

MAE

RMSE

MAE

RMSE

MAE

RMSE

MAE

0.006 0.006 0.008 0.020 0.003 0.007 0.003

0.004 0.005 0.007 0.008 0.002 0.005 0.002

0.006 0.007 0.007 0.010 0.004 0.012 0.005

0.006 0.006 0.006 0.008 0.004 0.011 0.005

0.005 0.005 0.008 0.009 0.005 0.006 0.005

0.004 0.005 0.007 0.008 0.004 0.005 0.004

0.007 0.006 0.010 0.009 0.007 0.011 0.004

0.006 0.005 0.009 0.008 0.006 0.008 0.004

0.009 0.011 0.004 0.024 0.009 0.022 0.027

0.008 0.010 0.003 0.023 0.008 0.021 0.027

0.004 0.006 0.006 0.017 0.011 0.010 0.012

0.003 0.006 0.005 0.017 0.011 0.008 0.009

(b) Inflation rates 6—3 month Term structure

FR IT NL JA SZ UK US GE

12—6 month

AR(1)

Term structure

12—3 month

AR(1)

Term structure

AR(1)

RMSE

MAE

RMSE

MAE

RMSE

MAE

RMSE

MAE

RMSE

MAE

RMSE

MAE

0.003 0.003 0.007 0.008 0.004 0.011 0.002 0.006

0.002 0.002 0.006 0.007 0.003 0.010 0.002 0.005

0.003 0.003 0.007 0.009 0.004 0.010 0.002 0.004

0.002 0.002 0.006 0.007 0.003 0.010 0.002 0.004

0.004 0.005 0.010 0.007 0.006 0.015 0.004 0.011

0.003 0.004 0.009 0.005 0.005 0.012 0.004 0.011

0.004 0.004 0.012 0.003 0.006 0.011 0.002 0.004

0.003 0.004 0.011 0.003 0.005 0.007 0.002 0.003

0.005 0.006 0.018 0.013 0.006 0.015 0.006 0.018

0.004 0.005 0.017 0.012 0.005 0.014 0.006 0.018

0.005 0.004 0.006 0.008 0.006 0.012 0.002 0.005

0.004 0.003 0.006 0.006 0.005 0.010 0.002 0.004

In-sample estimation: 85:1—91:12

Out-of-sample estimation: 92:1—92:12

G. M. Caporale and N. Pittis

624 outperforms the AR(1) model in out-of-sample forecasting when interest rates with three- and six-month maturities are employed. Conversely, the AR(1) model performs consistently better in the case of interest rates with a twelve-month maturity. The forecasting performance of the term structure model is rather poor: in no case does this model predict more accurately than the simple autoregressive model.

tary policy can influence an open economy through the real interest rate channel.

AC KN OWL ED GEM EN TS We are grateful to the co-editor for useful comments and suggestions.

IV . C ON CL US IONS In this paper we have presented some additional empirical evidence on the hypothesis formulated by Mishkin (1990) about the term structure as an optimal predictor of the inflation path, and the other hypothesis found in the literature concerning the unbiasedness of interest differentials as predictors of future inflation differentials. Both issues are of extreme relevance to policy-makers, in particular to the monetary authorities, as the validity of the first hypothesis would enable them to use the maturity structure as a guide for monetary policy, and only if the second was rejected would it be possible to affect the level of economic activity through the real interest rate. The statistical tests we carried out lead to the rejection of the null in both cases. The two models, though, appear to contain some information which can help predict the direction of future changes. The term structure predicts future inflation better for longer maturities, and interest differentials have extra predictive power for future inflation differentials when UIP holds. In the case of the EMS countries there is evidence of structural instability, and both the term structure and the interest differential model seem to be a better forecasting tool in the second EMS period, when a stable structure of exchange rates became an objective for the member states, and realignments became less common. It is probable that the resulting reduction in interest rate volatility and in the risk premium account for the improved performance of both models from 1985. However, formal tests of forecasting accuracy indicate that only the interest differential model at the shortest end of the maturity spectrum predicts better than simple time series model. The policy implications of our findings are the following. First, the yield curve should not be seen as an unequivocal indicator of future inflation, and hence should not be adopted as a guide to monetary policy. As already pointed out by Mishkin (1990), the predictive power of the term structure model for future inflation depends on the relative variability of expected inflation and real term structure, which would change if the slope of the yield curve was used to determine the conduct of monetary policy. Second, the fact that ex-ante real rates appear not be constant over time and not to be equal across countries implies that monetary tools can be used effectively for stabilization purposes. In spite of the degree of openness and liquidity of international financial markets, UIP does not seem to hold, and hence mone-

RE F ER E N C E S Cumby, R. and Mishkin, F. S. (1986) The international linkage of real interest rates: the European—US connection, Journal of International Money and Finance, 5, 5—24. Cumby, R. and Obstfeld, M. (1984) International interest rate and price level linkages under flexible exchange rates: a review of recent evidence, in Exchange Rate ¹heory and Practice, eds J. Bilson and R. Marston, University of Chicago Press, Chicago, IL. Estrella, A. and Hardouvelis, G. A. (1989) The term structure as a predictor of real economic activity, Federal Reserve Bank of New York, Research Paper no. 89-07. Fama, E. F. (1975) Short-term interest rates as predictors of inflation, American Economic Review, 65, 269—82. Fama, E. F. and Gibbons, M. R. (1982) Inflation, real returns and capital investment, Journal of Political Economy, 9, 297—324. Feldstein, M. (1982) Domestic savings and international capital movements in the long-run and the short-run, NBER Working Paper no. 947. Frankel, J. A. and MacArthur, A. T. (1988) Political vs. currency premia in international real interest differentials, European Economic Review, 32, 1081—1121. Frenkel, J. A. (1976) A monetary approach to the exchange rate: doctrinal aspects and empirical evidence, Scandinavian Journal of Economics, 78, 200—24. Gaab, W., Granziol, M. J. and Horner, M. (1986) On some international parity condition: an empirical investigation, European Economic Review, 3, 683—713. Giavazzi, F. and Giovannini, A. (1987) Models of the EMS: is Europe a greater Deutschmark area? in Global Macroeconomics, eds R. C. Bryant and R. Portes, St. Martin’s Press, New York. Giavazzi, F. and Spaventa, L. (1990) The new EMS, CEPR Working Paper no. 369. Giovannini, A. (1992) European monetary reform: progress and prospects, Brookings Papers on Economic Activity, 2, 217—91. Hansen, L. P. and Hodrick, R. J. (1980) Forward exchange rates as optimal predictors of future spot rates, Journal of Political Economy, 88, 829—53. MacDonald, R. and Taylor, M. P. (1992) Exchange rate economics: a survey, IMF Staff Papers, 39, 1, 1—57. Mark, N. C. (1985) Some evidence on the international inequality of real interest rates, Journal of International Money and Finance, 4, 189—208. Mishkin, F. S. (1981) The real rate of interest: an empirical investigation, in ¹he Cost and Consequences of Inflation, CarnegieRochester Conference Series on Public Policy, 15, 151—200. Mishkin, F. S. (1984a) The real interest rate: a multi-country empirical study, Canadian Journal of Economics, 17, 283—311. Mishkin, F. S. (1984b) Are real interest rates equal across countries? An empirical investigation of international parity conditions, Journal of Finance, 39, 1345—58.

Predictors of inflation differentials and changes Mishkin, F. S. (1990) What does the term structure tell us about future inflation?, Journal of Monetary Economics, 25, 77—95. Mishkin, F. S. (1992) Is the Fisher effect for real? A reexamination of the relationship between inflation and interest rates, Journal of Monetary Economics, 30, 195—215. Mussa, M. (1982) A model of exchange rate dynamics, Journal of Political Economy, 90, 74—104. Nelson, C. R. and Schwert, G. W. (1977) Short-term interest rates as predictors of inflation: on testing the hypothesis that the real rate of interest is constant, American Economic Review, 67, 478—86.

625 Newey, W. and West, K. (1987) A simple, positive definite, heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica, 53, 703—8. Perron, P. (1988) Trends and random walks in macroeconomic time series: further evidence from a new approach, Journal of Economic Dynamics and Control, 12, 297—332. White, H. (1980) A heteroskedasticity-consistent covariance matrix estimator and direct tests for heteroskedasticity, Econometrica, 48, 817—38.