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A STUDY OF INTEREST RATES IN THE LONGER RUN: NOW YOU KNOW THE REST OF THE STORY [*].

Paul Schnitzel [**]

Abstract

Do nominal rates of interest change with inflation expectations, changes in expected real rates of interest or both? By 1996, nominal interest rates, inflation, and money supply growth in the United States and six industrial countries had significantly retreated from peak levels in the early 1980s. In explaining the rise of nominal yields, in these countries, up to the 1980s, this paper finds evidence for both higher inflation and higher real rates of interest. In contrast with the idea that variations in nominal yields are principally the product of variations in expected rates of inflation, this paper finds evidence that real rates of interest were non-constant in all countries. After 1981, lower rates of inflation in all countries were eventually manifested, sooner or later, in lower rates of interest. Simple tests of significance provide more support for the inflation-interest rate connection than do cointegration tests. While simple tests of significance suggest evidence that changes in real rates of int erest contributed to changes in nominal yields, tests of cointegration provide little or no support for this position.

INTRODUCTION

The Nominal Rate of Interest and its Components

The riskless, nominal rate of interest, [r.sub.n], may be thought of as the sum of the expected real rate of interest, r, and the expected rate of inflation, p. Over time, movements in this nominal yield reflect changes in one or both of these components, as suggested by the arithmetic approximation:

[r.sub.n] = r + p (1)

In a 1981 article, Santoni and Stone (S&S), used this idea to explain why the average levels of four U.S. interest rates were significantly higher during 1967-81 than they were during 1954-66. [1] The 1967-81 years were marked by higher average rates of inflation and monetary growth.

S&S advanced three principal conclusions: (1) there was no convincing, circumstantial evidence of a significant increase in the unobserved, expected real rate of interest to explain the higher nominal rates of interest; (2) the percentage point increases in four average rates of interest after 1966 were not significantly different from the percentage point increase in the average rate of inflation; (3) the higher, average rate of inflation after 1966 was fully explained by more rapid monetary growth, having nothing to do with any increase in velocity V or slowdown in the growth of real GNP, Y, as suggested by the equation of exchange:

P = M + V - Y (2)

The empirical literature on the Fisher relationship has been divided on the question of whether variation in the expected nominal rate of interest is attributable solely or largely to variation in the expected rate of inflation, Fama (1975), Mishkin (1993) and Evans and Lewis (1995) or not, Friedman and Schwartz (1982, pp 522-3).

This paper examines the behavior of the average levels of two nominal interest rates, in each of seven countries including the United States, in the context of their longer-run determinants using the methodology of S&S in addition to the techniques of unit root and cointegration testing. The disinflation of 1981-97 both reflected and contributed to: a reduced faith in activist, monetary policy; a consensus that there is no long-run trade off between lower inflation and lower real growth (observable in the evidence, below); greater willingness to accept that low inflation is conducive to economic efficiency and growth, Bernanke and Mishkin (1997 P. 104)

Research Methodologies

Tests Of Significance: S&S

Using simple tests of statistical significance this paper compares an average, nominal, quarterly yield between two time samples. A student t-statistic is used to test for a significant change in the average yield in the later over the earlier sample. By Eq. (1), it is next determined, via t-statistic, if there was a statistically significant change either in the real rate of interest Proxy or the measured rate of inflation proxy for the expected rate of inflation. Eq. (1) suggests that a significantly higher nominal yield could be explained by a significant increase in inflationary expectations, a significant increase in the real rate of interest, or both.

Others, Peterson (1996), Nigel Duck (1993), have argued that this Fisherine, quantity theory is a useful way of characterizing the interest rate-inflation-money nexus. The evidence here, from tests of significance, for seven countries, does not contradict this approach yet, finds somewhat looser connections between nominal yields and expected inflation, as well as inflation and money. The evidence from cointegration tests finds mixed support for the interest rate-inflation connection, strong support for the money-inflation connection, and little support for a nominal-real interest rate connection.

Using Tests of Cointegration

If the connections among nominal yields, real rates of interest, and inflation, implied by Eq. (1) are of a longer-term nature, perhaps these series are cointegrated within the meaning of Engle and Granger (1987). Specifically, if the nominal yield contains a unit root, is it because of a unit root in the rate of inflation or the real rate of interest? If the three relevant series contain a unit root, do they share a common variable trend?

Data

Figures 1-7 contrast the behavior of two interest rates in each of six countries, with that of interest rates in the U.S. Over the period 1957-96. [2] In Canada, France, the Netherlands, and the U.K, the pattern of interest rate behavior over the 40 years is strikingly similar to that for the U.S., resembling an inverted "V." Interest rates climbed irregularly from 1957 to peak levels around 1981, but have since receded from those peaks. Interest rates in Germany and Switzerland exhibited a more gentle, irregular increase between 1957 and about 1975, but, showed no secular down trend beyond 1975.

All series consist of quarterly observations taken from the 12/96 IMF International Financial Statistics CD. For all index numbers, 1990 = 100. The government bond yield, GBY, and the treasury bill rate, TBR, were used as proxies for the riskless, nominal rate of interest. Due to limited series length of the TBR, 3-month Euro-currency LIBORs were used for the Netherlands and Switzerland. [3] The measured rate of inflation, [delta] CPI, is the annualized rate of change in the CPI index number. S&S used the GNP deflator to construct their measured rate of inflation. M2 is the sum of seasonally adjusted Ml plus quasi-money. [delta]M2 is the annualized rate of change in M2 and takes the place of M in Eq. (2). [delta]RGDP which replaces Y in Eq. (2) is the annualized, quarterly change in the real GDP index number. What S&S call V in Eq. (2), the annualized rate of change in quarterly, M1B velocity, is [delta]V, herein, the annualized, quarterly, rate of change in M2 velocity.

S&S argued that the average, measured rate of inflation was a reasonable proxy for the average, expected rate of inflation for the following reason: Since they found no detectable change in the expected real rate of interest after 1966, it was more likely that the measured rate of inflation was an unbiased estimate of the true rate of inflation. The unobserved, true rate of inflation includes the prices of all goods and services, including not only short-lived, consumer goods, but also capital or long-lived goods. An (A) increase (decrease) in the expected real rate of interest would tend to raise (lower) the price of short-lived relative to the price of long-lived goods. In the presence of an (a) increase (decrease) in the real rate of interest, the measured rate of inflation would tend to overstate (understate) the true rate of inflation due to an under-representation of relatively lower (higher) priced, longer-lived goods. With no change in the expected real rate of interest, the measured rate of inflation is more likely to be an unbiased estimate of the true rate of inflation even though measured rates of inflation principally measure changes in the p rices of short-lived goods, and largely exclude the prices of long-lived assets.

The "Proxy" series, bottom row, Table 1, is the ratio of the CPI index number to the share price index number. The numerator represents the average price of short-lived goods; the denominator, the average value of equity shares, represents the average price of long-lived goods. [4] While changes in the expected real rate of interest are not directly observable, it may be possible to detect the repercussions of such a change, by observing the behavior of the relative price of short-lived to long-lived assets. A rise in the real rate of interest reduces the dollar amount of current consumption that must be sacrificed to obtain another dollar's worth of future consumption. This implies a reduction in the present value of long-lived assets compared to the present value of shorter-lived assets. Over time, an (a) increase (decrease) in the average, real rate of interest would manifest itself as an increase (decrease) in the Proxy. I am unaware of any use in the literature of such an empirical real rate proxy. The real rate of interest is sometimes measured as the difference between the observed nominal rate of interest and some measure of the ex post rate of inflation, Strauss and Terrell (1995, p. 1051).

S&S conjectured that the U.S. real rate of interest did not likely increase from 1954-66 to 1967-81. This paper found evidence suggesting significant variation in the real rate of interest in all seven countries including the United States as well as evidence consistent with the presence of a unit root in the levels of proxy series for all countries save Canada and Germany. [5] For four of seven countries, at least one nominal yield was cointegrated with the real rate proxy, only in the presence of the log-differenced CPI. For the most part, bivariate combinations of the nominal yield and proxy were not cointegrated.

Rising Nominal Rates of Interest: 1957--81

Columns 2, 4, 6, and 8, Table 1, report average rates of interest (upper entries) along with their respective standard deviations (lower entries, in parentheses), for all countries, over four, roughly contemporaneous, sub-sample periods, along with summary t-test (upper) and F-ratio lower statistics in columns 5, 7, and 9. In all countries, significant t-statistics in column 5 (upper entries) show that average rates of interest were significantly higher in the second, compared to the first sub-sample period, column 4 versus column 2. F-statistics in column 5 (lower entries) report significant increases in the variances of the average rates of interest from the first to the second sub-samples in five of seven countries. [6] These findings agree with those of S&S for the U.S., namely, average rates of interest were both significantly higher and more variable in the second, compared with the first sub-sample period. t and F values, column 7, compare third and second sub-sample, average yields and variances; t an d F values in column 9 compare fourth and third sub-sample, average yields and variances.

Were the Higher, Average, Second Sub-sample Interest Rates Wholly Traceable to Higher Average Rates of Inflation as Found by S&S in the U.S. Case?

In the second sub-sample, four countries: Canada, France, Netherlands, and Switzerland report both higher average inflation and Proxy. The UK reported significantly higher inflation and no change in the Proxy. In Germany, higher nominal yields were associated with higher inflation, but no conclusions could be made about the Proxy. In the U.S., Proxy 1 decreased significantly, Proxy 2 did not change.

The higher inflation-to-higher rate of interest evidence for seven countries differs in an important way from the evidence for the U.S. experience. S&S found that in their second, compared to their first sub-sample period, average levels of four rates of interest were anywhere from 3.84 to 4.20 percentage points higher while the average rate of inflation was 4.24 percentage points higher. Standard tests of significance found no difference between the average increases in the rates of interest and the increase in the rate of inflation. This study found that in five of seven countries, including the U.S., the average increase in the rate of inflation was significantly greater than the average increase in the rate of interest. [7] Only the Netherlands and the U.K. resemble the U.S. in S&S' study.

The evidence for the first two sub-sample periods suggests a possible explanation why average rates of interest did not increase by as much as average rates of inflation. A significant increase in the real rate of interest, by reducing the relative prices of long-lived compared to short-lived goods, would tend to cause the measured rate of inflation to rise by more than the expected rate of inflation. This might explain why measured inflation rose by more than average yields in Canada and France. For Germany, the record is incomplete. For the U.K., the Proxy showed no significant increase, however, its second sub-sample standard deviation was more than double that observed for the first sub-sample. Similarly, Proxies 1 and 2 exhibited significantly greater variances in the U.S., in the second sub-sample. These findings raise the likelihood that U.K. and U.S. measured rates of inflation may have been biased estimates of the expected rates of inflation.

Was Inflation in the Second Sub-sample a Monetary Phenomenon?

More often than not the answer is no. [8] Monetary growth rates did not increase significantly in France, Germany, Netherlands and Switzerland. But, they did rise significantly in Canada and the UK

Eq. (2) reminds us that a higher average rate of inflation may be associated with slower growth in Y and/or an increase in V. For the U.S., Canada and the UK, higher inflation in the second sub-sample appears to be the result of faster M2 growth and is traceable neither to slower RGDP growth nor to an increase in velocity.

For Germany, the Netherlands and Switzerland, the record is incomplete with regard to ARGDP and [delta]V. France shows evidence of a significantly slower rate of growth in RGDP that may be connected with more rapid inflation, but no significant change in M2 velocity.

In general, there is evidence of a potentially greater role played by the real rate of interest in explaining the significantly higher average nominal rates of interest observed during the second sub-sample period. Also, there is evidence suggesting no role for money supply growth in accounting for the higher average inflation in four of the six countries during the second sub-sample period.

1981-96: Generally Lower Nominal Rates of Interest

By the end of the fourth sub-sample, 1996.3, interest rates in all seven countries had retreated from the cyclical peaks of the second sub-sample. In general, in the third and fourth sub-sample periods, nominal rates of interest, inflation and monetary growth rates reached average levels that were significantly below earlier peak levels, in all countries. [9] Real GDP, and velocity, in general, showed little tendency to change. The real rate of interest Proxy, showed a greater tendency to change. Lower average rates of interest and inflation also exhibited significantly lower variability.

Nominal Interest Rates in the Third Sub-sample

GBY and TBR remained significantly above second sub-sample average levels in the U.S., Canada and the UK. Nominal yields were significantly lower in the Netherlands and Switzerland, but exhibited no significant change in France and Germany.

Nominal Interest Rates in the Fourth Sub-sample

On average, 13 nominal interest rates changed [10] by 0.89 percentage points from the second to the third sub sample. 14 nominal interest rates changed [11] by -- 1.75 percentage points from the third to the fourth sub-sample. GBY and TBR were significantly lower in the U.S., Canada, France, and the UK. The GBY in Germany was significantly lower; its TBR showed no significant change. Nominal yields showed no significant change in the Netherlands and Switzerland.

Contributions of Changes in Real Rates of Interest to Changes in Nominal Rates of Interest: Third and Fourth Sub-samples

Between the second and third and the third and fourth sub-samples, significant changes in the average Proxies were observed in twelve of sixteen scenarios. All countries showed a significant decrease in the real rate Proxy in the last sub-sample. When the Proxy changed significantly, at least one of two nominal yields changed significantly and in the same direction, in eight of twelve instances.

The above evidence suggests some "causative" role for the real rate of interest in explaining movement in nominal yields. An increase (decrease ) in the longer-run average rate of growth in real GDP may also serve as a proxy for an increase (decrease) in the real rate of interest, Dewald (1998). One byproduct of an increase (decrease) in the trend rate of growth of real GDP is an increase (decrease) in the demand for credit. S&S' findings for the U.S. were consistent with this idea: No detectable change in either Y or the real rate proxies. Here, despite circumstantial evidence of significant change in real rate Proxies in seven countries, no corroborating evidence exists of significant change in real GDP growth rates.

Was There An Inflation Rate-To Interest Rate Connection in the Third and Fourth Sub-sample Periods?

The third sub-sample evidence was inconsistent. Counter evidence was provided by the U.S. and Canada in the third sub-sample where significantly higher GRY and TBR were associated with significantly lower inflation. Third sub-sample evidence consistent with the hypothesis was observed in five cases: the Netherlands and Switzerland: three nominal yields and inflation were significantly lower; the UK: significantly higher average GBY and TBR were accompanied by significantly higher inflation. In France and Germany significantly lower rates of inflation were accompanied by nominal yields that exhibited no significant change in the third sub-sample. In the fourth sub-sample, eleven of fourteen scenarios were consistent with the lower inflation-to-lower nominal yield hypothesis.

Was Inflation in the Third and Fourth Sub-samples A Monetary Phenomenon?

The answer to this question is half of the time. In 14 scenarios, one observes same-direction changes in monetary growth and average inflation in seven cases, Table 1. The UK and the U.S. provide four egregious counter examples.

In six cases, significant changes in average inflation were accompanied by no change in money growth. Can any of these be explained by a significant decrease in real GDP or increase in velocity? In three of six instances: Canada, Germany, and the UK, a significant fall in average inflation was accompanied by a significant fall in velocity. Real GDP exhibited no significant change in seven countries after the second sub-sample.

Comparing the Percentage Changes in Nominal Interest Rates With Percentage Changes in Rates of Inflation

In S&S' study, the higher U.S. rates of interest after 1966 seemed to be fully explained by higher rates of inflation. They recorded no significant difference in the percentage increase in four interest rates and the percentage increase in the rate of inflation. By contrast, this study found, in seven of ten cases, second sub-sample percentage increases in interest rates were significantly greater than the percentage increases in inflation, see fn. 7.

Comparing percentage point changes in the rate of interest and the rate of inflation: second to third sub-sample

Again, the evidence is uneven. In the Netherlands, a 5.12 percentage point decrease in the rate of inflation was significantly different from both a 0.70 percentage point decrease in the GBY and a 2.80 percentage point decrease in the TBR. In Switzerland, a 1.75 percentage point decrease in the rate of inflation was significantly different from a 0.48 decrease in the GBY. However, in the U.K., a 3.85 percentage point increase in the rate of inflation was not significantly different from a 3.53 and a 3.49 percentage point increase, respectively, in the GBY and the TBR. [12]

Comparing percentage point changes in the rate of interest and the rate of inflation: third to fourth sub-samples

In Canada, a 2.85 percentage point decrease in the rate of inflation was not significantly different from a 2.54 percentage point decrease in the GBY, but was significantly different from a 3.83 percentage point decrease in the TBR. In France, a 3.20 percentage point decrease in the rate of inflation was not significantly different from either a 3.39 percentage point decrease in the GBY, or a 2.81 percentage point decrease in the TBR. In the UK, a 7.51 percentage point decrease in the rate of inflation was significantly different from a 3.74 percentage point decrease in the GBY, and a 1.62 percentage point decrease in the TBR.

The role of inflation uncertainty and expectations

More than half of the time, there was a divergence between expected and measured rates of inflation. Ball and Cecchetti (1990) have argued that high inflation gives rise to increased uncertainly about inflation. During a time (second sub-sample) of significantly higher measured inflation rates and yields, market participants acquired higher inflation expectations. Thereafter, they did not respond quickly to lower measured rates of inflation. In all countries, but the UK, the third sub-sample period was marked by significantly lower measured rates of inflation. Market participants responded at different rates of speed in different countries to these lower inflation rates. In the U.S. and Canada two nominal yields rose significantly; in France and Germany two nominal yields remained unchanged. Only as they became convinced of sustained, lower rates of inflation, did they build these into lowered, expected rates of inflation and lower nominal rates of interest. With the exception of the UK, the third and fourth sub-samples were characterized by sustained lower rates of inflation producing lower nominal yields sooner, as in the Netherlands, and Switzerland or later, as in the U.S., Canada, France, and Germany. High inflation and more uncertain inflation may help to account for more frequent and prolonged departure of the paths of interest rates and inflation and may help account for findings (below) of noncointegration observed about as often as cointegration between interest rates and rates of inflation.

In nine instances where a significantly lower rate of interest was associated with a significantly lower rate of inflation, the percentage point decrease in the rate of inflation was significantly greater than the percentage point decrease in the rate of interest in five. Meanwhile, during the third sub-sample: in the U.S. and Canada: GBY and TBR increased significantly in the face of a significant decrease in inflation; France: GBY and TBR did not change in the face of a significant decrease in the rate of inflation; Germany: GBY and TBR did not change in the face of a significant decrease in inflation; Germany: fourth sub-sample: TBR exhibited no change in the face of a significant decrease in inflation. [13]

Are Interest Rates and Rates of Inflation Cointegrated?

The close inflation rate-interest rate connection observed up to the end of the second sub-sample loosened thereafter as market participants showed inertia in adapting their expectations to falling measured rates of inflation. The nominal yield and the rate of inflation can drift away from each other. But if they do not drift too far from each other, they may be cointegrated. If they drift too far from each other, they are nor likely to be cointegrated.

Cointegration testing is especially suited to searching for relationships among series that are non-stationary, unit root processes. It will be shown that most of the levels' series for nominal yields, real rate Proxies and measured inflation rates are non-stationary, trending away from their starting points, drifting over time. If an OLS cointegrating regression (COIR) of the GBY (TBR) on [delta]CPI and the Proxy produces a non-unit root, stationary residual series, this is evidence that three parent series are cointegrated despite each containing a unit root. The presence of a unit root in the COIR residual series is evidence of non-cointegration.

Therefore: (1) each level and differenced series was tested for the presence of a unit root via a procedure suggested by Holden and Perman (Rao 1994 pp. 64-5); (2) possible cointegration is examined in trivariate and bivariate combinations via a test due to Johansen (1991), (1995).

Testing For Unit Roots in Univariate Series

The augmented Dickey-Fuller (ADF) unit root test equations are:

[delta][y.sub.t] = a1 + b1[y.sub.t-l] + c1T + [sigma][d1.sub.j][delta][y.sub.t-j] + [e1.sub.t]. (3)

[delta][delta][y.sub.t]t = a2 + b2[delta][y.sub.t-l] + c2T + [sigma][d2.sub.j][delta][delta][y.sub.t-j] + [e2.sub.t], (4)

[delta] and [delta][delta] are, respectively, first and second difference operators. T is a time trend. To determine the number of d1 and d2 augmentation terms, the Akaike Information Criterion (AIC) was used over sixteen lags. In all instances, a Breusch-Godfrey test statistic found no fourth-order serial correlation. Eq. (3) tests for the presence of a unit root in GBY, TBR, LNCPI, LNM2, and the Proxy. Eq. (4) tests for the presence of a unit root in [delta]GBY, [delta]TBR, [delta]LNCPI, [delta]LNM2, and [delta]Proxy.

Tests results, Table 2, suggest the presence of a zero frequency unit root in the levels of nominal yields of all countries save Germany where the GRY appears to be stationary. [14] [delta]GBY and [delta]TBR appeared to be stationary. However, [delta]EG3 appeared to contain a single unit root.

The annualized inflation rate [delta]LNCPI appeared to contain a unit root in all countries but Switzerland where ALNCPI appeared to be stationary. Contrast this with Swiss nominal yields that appeared to drift, But, in general, GBY(TBR) and [delta]LNCPI were non-stationary.

The evidence suggests a unit root in five countries' Proxy series (two for the U.S.). The real rate Proxy in Canada and Germany appear to be stationary, Table 2. Four series yielded a significant coefficient on time: Proxy (Germany); [delta]LNM2 (France and UK); [delta]LNM2 (UK).

Lloyd and Rayaer (1993), for example, have documented the fragility of these ADF procedures. The presence of moving average (MA) components in series may compromise the power of ADF statistics. Therefore, residual series from all estimates of Eqs. (3) and (4) were examined for the presence of MA terms up to an order of eight. There was at least one significant MA term at the 5% level in 28 of 68 residual series with the Netherlands and the UK the most afflicted, while the U.S. was least afflicted. [15]

Testing for Cointegration

Trivariate combinations

Implementation of Johansen's methodology was that found in the Eviews 2.0 software. A VAR of GBY(TBR), [delta]LNCPI, and Proxy was searched for the optimum lag structure via AIC up to a maximum of sixteen. Deterministic trends were not included in cointegration test routines. The Johansen test proceeds to test various restrictions on the VARs that would be consistent with cointegration.

Table 3 reports cointegration tests results for the following systems: France. two: GBY(TBR), [delta]CPI, and Proxy; Netherlands: two: GBY([delta]EG3), [delta]CPI, and Proxy; Switzerland: two: GBY(ESF3), [delta]CPI, and Proxy; UK: two: GBY(TBR), [delta]CPI, and Proxy; and the U.S.: four: GBY10(TBR), ACPI, and Proxy (2). The optimum AIC lag-length structure for the unrestricted VAR is shown in parentheses.

Evidence consistent with cointegration was found in nine of twelve cases. Non-cointegration was found in three cases: Netherlands: GBY; Switzerland: GBY; and the U.S.: TBR, Proxyl. However, closer inspection of the nine cointegrated systems, indicates the presence of the wrong sign (negative) in estimated COIRs, suggesting that a higher nominal rate of interest is associated with either a lower rate of inflation or a lower real rate of interest: France: both cases; Netherlands: one: wrong sign on [delta]CPI; Switzerland: one; the UK: two, and the U.S.: two of four: wrong sign on the Proxy. Among cointegrated, trivariate systems, only the U.S. provided examples of COIRs (both in the presence of Proxy 1) with the theoretically anticipated positive signs.

Bivariate systems

Is the nominal yield cointegrated with the rate of inflation (real rate Proxy), but not with the real rate Proxy (rate of inflation)? The findings concerning bivariate cointegration were about evenly divided on the inflation-interest rate connection, but more often than not pointed to no connection between real and nominal yields. Bivariate results reported in Table 3 are summarized:

Six instances of cointegration of nominal yields and inflation: (GBY-[delta]LNCPI): Canada, UK and U.S. (TBR-[delta]LNCPI): Germany, U.S. ([delta]EG3-[delta]CPI): Netherlands. By contrast, Strauss and Terrell (1995, p. 1052) found non-cointegration among inflation rates and nominal yields in approximately the same countries.

Five instances of non-cointegration of nominal yields and inflation: (GBY-[delta]CPI): France and the Netherlands; (TBR-[delta]CPI): France; (GBY- [delta]NCPI): Switzerland; (TBR-[delta]CPI): UK.

Two instances of cointegration of nominal yields and Proxy: France (GBY-Proxy); Netherlands ([delta]EG3-Proxy)

Ten instances of non-cointegration of nominal yields and Proxy: (GBY-Proxy): Netherlands, Switzerland, UK, U.S., both proxies. (TBR-Proxy): France, UK, U.S., both proxies. (ESF3-Proxy): Switzerland. Only in the cases of the UK and the U.S. were the bivariate results consistent with the S&S findings: GBY and TBR were noncointegrated with either Proxy 1 or Proxy 2, but were cointegrated with the rate of inflation.

Trivariate systems were initially ruled out for Canada and Germany because Proxy series in both countries were stationary. The same was true of the GBY in Germany. For Canada (two cases) and Germany (one case), bivariate systems consisting of the nominal yield and the rate of inflation were examined for the presence of cointegration. In all three instances, the null of non-cointegration was rejected. As shown in Table 3, the correct sign appeared in two of three COIRs.

Conclusions

In seven countries, variations in average, nominal rates of interest, in general, reflected variations in average rates of inflation over four consecutive, sub-sample time periods beginning in 1957 and ending in 1996. Up to the end of the second sub-sample, significantly, higher, average rates of inflation were rapidly reflected in significantly, higher, average rates of interest in all countries.

As to whether higher rates of inflation exhibit greater variability as well, the evidence generally runs counter. Three countries (U.S., Canada, and Switzerland) experienced significantly higher second sub-sample inflation variances; three reported either significantly lower inflation rate variances: (France, Netherlands, U.K.) or an unchanged variance: (Germany).

By the end of the fourth sub-sample, interest rates in all seven countries had responded to significantly lower rates of inflation with varying degrees of speed consistent with what Milton Friedman has referred to as monetary policy's long and variable lag.

By contrast, the evidence from cointegration tests proved to be even more ambiguous than tests of statistical significance concerning the longer-run connections between interest rates, inflation and the real rate of interest. Only in the U.S. was there, consistent, robust evidence for a cointegrated interest rate-inflation connection and a non cointegrated nominal yield-real rate connection.

With the exception of Germany and the UK, money supply growth rates were significantly lower during the third and fourth sub-samples than during the second sub-sample. However, by tests of significance, the money-to-inflation connection proved less dependable than the inflation-interest rate connection. Where data permitted, there was no evidence that velocity or real output behaved in a way that would offset or cancel the effects of changes in the money supply.

The higher monetary growth-to-higher inflation hypothesis found more support from tests of cointegration. From the Johansen test, the alternative hypothesis of cointegration could not be rejected for bivariate combinations of [delta]LNM2SA and [delta]CPI for all countries, but Switzerland and the UK. In Switzerland, cointegration could not be rejected for LNM2SA and LNCPI. For the U.K., cointegration could not be rejected for LNM2SA and [delta]CPI.

Finally, the evidence from simple tests of significance uncovered in this study suggested an important role for the expected real rate of interest in explaining nominal yields. However, in the context of bivariate cointegration analysis, there was evidence that nominal yields were connected to the real rate proxies in two of seven countries: France (GBY-Proxy), Netherlands ([delta]EG3-Proxy)

Meanwhile, when examined in the same context of bivariate cointegration analysis, there is no evidence that nominal yields were connected to the real rate proxies in five of seven countries: the U.S., all scenarios, France (TBR-Proxy); Netherlands (GBY-Proxy); Switzerland, all scenarios; UK, all scenarios.

To borrow from Friedman and Schwartz (1991, p. 39) "...there is no magic formula for wringing reasonable conjectures from refractory and inaccurate evidence." The above evidence from tests of significance and cointegration did not always speak with one, unambiguous voice. It is fair to say that when it came to the higher inflation rate-to-higher interest rate connection, there was greater support from tests of significance than from cointegration. Tests of significance offered some support for the existence of a connection between nominal yields and real rates of interest whereas cointegration analysis offered little support.

(*.) Figures and Tables are available from the author upon request.

(**.) Professor of Finance, California State University, Los Angeles

Notes

(1.) The Aaa corporate bond rate, the 20-year government bond rate, the 90 day commercial paper rate, and the 3-month treasury bill rate.

(2.) The countries are: Canada, France, Germany, the Netherlands, Switzerland and the U.K. GBY and TBR refer to the government bond yield and treasury bill rate, respectively. GBY10 is the ten-year government bond yield. NETHEG3 and SWIESF3 refer to the 3-month Euro-Dutch guilder and Euro-Swiss franc LIBORs, respectively.

(3.) As shown in Tables 1-7, short-maturity interest rate series for France, Germany, the Netherlands, and Switzerland were not available back to 1957. The same is true for series on GDP, both nominal and real, as well as for series on share prices used for the construction of the "Proxy" series used to capture the consequences of a change in the real rate of interest.

(4.) For the United States, two proxy measures of the real rate of interest were employed: Proxy1 is the ratio of the price index number for consumer finished goods to the producer price index for capital equipment. Proxy2 is the ratio of the WPI series to the index number for securities prices.

(5.) Garcia and Perron (1996) found evidence that the ex post real rate of interest exhibited different means and variances for the periods: 1961-73, 1973-80, and 1980-86.

(6.) The F-ratio for the Netherlands, column 5, reports no significant increase in the second over the first sub-sample variance of the GBY. All t-test and F-ratio statistics were obtained using the Quattro Pro, version 6, for Windows 3.1 statistical routines.

(7.) For the U.S., the average CPI rate of inflation was 5.29 percentage points higher during the second sub-sample period. By contrast, average levels of GBY10 and TBR were, respectively, 3.18 and 3.70 percentage points higher during the second sub-sample period. A t-test statistic was used to test the null hypothesis of no significant difference between the mean increase in the rate of interest and the mean increase in the rate of inflation. For the GBY10 and the rate of inflation, the estimated t-value was 5.72; for the TBR and the rate of inflation, the t-value was 3.91. Both were sufficient to reject the null hypothesis. For the remaining countries, I report the percentage point increase in the second over the first sub-sample, average rate of inflation; the percentage point increase in the second over the first sub-sample, average rate of interest and the estimated t-value, respectively: Canada: inflation: 6.29; GBY: 3.88; t-value: 6.65; TBR: 4.35; t-value: 3.93; France: inflation: 5.55; GBY: 4.30; t-va lue: 2.56; Germany: inflation: 2.56; GBY: 1.50; t-value: 3.62; Netherlands: inflation: 3.21; GBY: 3.39; t-value: 0.33; Switzerland: inflation: 2.80; GBY: 1.80; t-value: 2.33; U.K.: inflation: 5.19; GBY: 3.66; t-value: 1.82; TBR: 2.70; t-value: 1.84.

(8.) In this study, the theory of inflation as monetary phenomenon refers to average rates of inflation and monetary growth measured over longer periods of time. Whether on a month-to-month, or a quarter-to quarter basis, changes in the money supply contribute anything to the explanation of macroeconomic aggregates, see Friedman and Kuttner (1992) for the negative view, Haslag (1990) for the positive. For evidence of the presence of cointegration between inflation and the M3 and L versions of money in the U.S. see Schnitzel (1994).

(9.) Table 1 shows that the third sub-sample period began in 1974.4 and 1975.1, respectively, in Switzerland and the U.K., and in 1981.4 in four remaining countries. The fourth sub-sample period began anywhere from 1984.3 to 1991.1.

(10.) Six rose significantly, three declined significantly, four exhibited no significant change.

(11.) None increased significantly, nine declined significantly, five exhibited no significant change.

(12.) For the Netherlands, the average CPI rate of inflation was 5.12 percentage points lower during the third sub-sample period. By contrast, average levels of GBY and TBR were, respectively, 0.70 and 2.80 percentage points lower during the third sub-sample period. A t-test statistic was used to test the null hypothesis of no significant difference between the mean increase in the rate of interest and the mean increase in the rate of inflation. For the GBY and the rate of inflation, the estimated t-value was 11.48; for the TBR and the rate of inflation, the t-value was 4.13. Both were sufficient to reject the null hypothesis. For the remaining countries, I report the percentage point change in the third over the second sub-sample, average rate of inflation; the percentage point change in the third over the second sub-sample, average rate of interest and the estimated t-value, respectively: Switzerland: inflation: -1.75; GBY: -0.48; t-value: 3.18; U.K.: inflation: 3.85; GBY: 3.53; t-value: 0.36; TBR: 3.49; t- value: 0.40.

(13.) In three of the remaining four, no significant difference was observed between the lower rates of interest and inflation. In one instance, a 3.83 percentage point decrease in the fourth sub-sample, Canadian TBR was observed to be significantly greater than the 2.85 percentage point decrease in the CPI rate of inflation.

(14.) For counter evidence to the characterization of nominal interest rates as unit root processes, see Wu and Zhang (1996).

(15.) The presence of seasonal unit roots at different frequencies in potentially cointegrated series would rule out cointegration testing for said series according to Hylleberg, et al. (1988). The presence of seasonal unit roots in time series means that such series must be seasonally differenced in order to render them stationary. Quarterly series that contain fourth-order, (second-order) seasonal unit roots will have auto-correlation functions (ACFs) of their first-differences with large spikes at lags 4, 8, 12, 16, etc. (2, 4, 6, 8, etc.). For all series tested in Table 2, sample ACFs suggested the possibility of fourth-order unit roots in the following four series: Germany: [delta]LNCPI, [delta]LNM2SA; Netherlands: [delta]LNM2SA and the U.K.: [delta]LNM2.

References

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Bernanke, Ben S. and Mishkin, Frederic S. "Inflation Targeting: A New Framework for Monetary Policy?" Journal of Economic Perspectives 11(Spring): 97-117.

Dewald, William G. (1998) "Bond Market inflation Credibility." Monetary Trends (February): 1.

Duck, Nigel W. (1993) "Some International Evidence on the Quantity Theory of Money." Journal of Money, Credit, and Banking 25 February: 1-13.

Engel, Robert F., and Granger, C. W. J. (1987) "Cointegration and Error Correction: Representation, Estimation, and Testing." Econometrica 55(March): 251-76.

Evans, M. D. D. and Lewis, K. K. "Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation?" Journal of Finance 50(March): 225-53.

Fama, Eugene. (1975). "Short-Term Interest Rates as Predictors of Inflation." American Economic Review 69(June): 269-82.

Friedman, Benjamin M., and Kuttner, Kenneth N. (1992) "Money, Income, Prices, and Interest Rates." American Economic Review 82, (June): 472-93.

Friedman, Milton and Schwartz, Anna J. (1991) "Alternative Approaches to Analyzing Economic Data." American Economic Review 81 (March): 39-50.

----. (1982). Monetary Trends in the United States and the United Kingdom: Their Relation to Income, Prices, and Interest Rates 1867-1975. Chicago: University of Chicago Press.

Garcia, R. and Perron, P. (1996) "An Analysis of the Real Interest Rate under Regime Shifts." Review of Economics and Statistics 78 (February): 111-25.

Haslag, Joseph H. (1990) "Monetary Aggregates and the Rate of Inflation." Federal Reserve Bank of Dallas Economic Review: 1-13.

Holden, Darryl and Perman, Roger. "Unit Roots and Cointegration for the Economist." In B. Bhaskara Rao (ed.) Cointegration for the Applied Economist. New York: St. Martin's Press, Inc.

Hylleberg, S., Engle, Robert F, Granger, C. W. J., and Yoo, B. S. (1988) "Seasonal Integration and Cointegration." Discussion Paper No. 88-32, Department of Economics, University of California, San Diego.

Johansen, Soren. (1991) "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models." Econometrica 59: 1551-80.

-----. (1995) Likelihood-based Influence in Cointegrated Vector Autoregressive Models. Oxford University Press.

Lloyd, T. A. and Rayner, A. J. (1993) "Co-integration Analysis and the Determinants of Land Prices: Comment." Journal of Agricultural Economics 44: 149-56.

Mishkin, Frederic. (1993) "Is the Fisher Effect for Real." Journal of Monetary Economics (February): 195-215.

Peterson, Willis L. (1996) "Does Money Still Matter?" Cato Journal 16, (Fall: 253-65.

Santoni, Gary and Stone, Courtenay. "What Really Happened to Interest Rates? A Longer-run Analysis." In Thomas M. Havrilesky and Robert Schweitzer (eds.) Contemporary Developments in Financial Institutions and Markets. Arlington Heights, Illinois: Harlan Davidson, Inc., 1983.

Schnitzel, P. E. (1994) "On the Disappearing Money-to-Inflation Connection." Atlantic Economic Journal 22, (September): 24-37.

Strauss, Jack and Terrell, Dek (1995). "Cointegration Tests of the Fisher Hypothesis with Variable Trends in the World Real Interest Rate." Southern Economic Journal 61, (4): 1047-56
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