Stanley Diller

English

Research Papers in Economics

This PDF is a selection from an out-of-print volume from the National
Bureau of Economic Research
Volume Title: The Seasonal Variation of Interest Rates
Volume Author/Editor: Stanley Diller
Volume Publisher: UMI
Volume ISBN: 0-87014-205-A
Volume URL: http://www.nber.org/books/dill70-1
Publication Date: 1970
Chapter Title: Summary and Conclusions
Chapter Author: Stanley Diller
Chapter URL: http://www.nber.org/chapters/c3374
Chapter pages in book: (p. 104 - 107)CHAPTER 5
Summaryand Conclusions
THERE IS COMPELLING evidence of the presence of repetitive seasonal
movements in both long- and short-term interest rates in the years
between 1955 and 1960. Outside this period, both before and after,
the evidence is less conclusive, and certainly the seasonal movements
are smaller. Nevertheless, a seasonal pattern apparently existed in
most of the rates studied over a period substantially longer than the
brief period of peak seasonality. This result is largely predicated on
the demonstrated similarities among the seasonal patterns of the
several rates, as well as the relative uniformity of the pattern for a
given rate over an extended period. The study's primary focus is on
the quality of the evidence for these conclusions.
The seasonal factors for short-term rates are found typically to
decline from a relative high in January through the spring months to
a trough in June and then sharply increase to September, from which
they rise gradually to a peak in December. This pattern is conspicuous
in the late fifties but occurs with some variation throughout the
postwar period. The amplitudes, however, vary considerably, rising
gradually after the early fifties through 1957 or 1958 and falling off
quite rapidly thereafter. By 1965 the seasonal movement had all but
vanished, although recent evidence not considered in this study
indicates some resurgence in the seasonal.
104SUMMARY AND CONCLUSIONS 105
The seasonal pattern for yields on bankers' acceptance is, perhaps,
the most stable of those examined, although its amplitude is somewhat
less than that of Treasury bill rates. During part of the period of
peak seasonality, the amplitudes, that is the variation from seasonal
high to seasonal low, exceeded 20 per cent of the level of the series.
These amplitudes dropped sharply after 1959. By 1963, the seasonal
pattern for bankers' acceptances virtually disappeared. The seasonal
pattern for Treasury bills appears to have continued through 1965,
the end of the study period, although its amplitude then was barely 2
per cent of the level of the series. The seasonal movement in
commercial paper rates is far less stable and its amplitude smaller
than those of the other two series.
While this study did not specifically evaluate the relation between
seasonal amplitude and term to maturity, there is an obvious decline
in both seasonal amplitude and the period over which thereis
a measurable seasonal factor, as the maturity of Treasury securities
increases. The patterns of the seasonal factors of long-term rates are
less stable than those of the short-term rates (except commercial
paper) and have a much smaller amplitude. In the early fifties the
pattern typically starts with a January low that falls to a trough in
March, then rises to a plateau extending from June to October,
before declining to an intermediate position for the last two months.
The patterns for all the private long-term bonds are alike with respect
to their midyear highs and January lows, the characteristic distinguish-
ing these patterns from those of the same securities in the later
period, as well as from the patterns of the short-term rates. Starting
in1955 the seasonal patterns of private long-term bond rates
change—the January factors from lows to highs and the June and
July factors from highs to lows. The troughs remain in March and
April and the peaks in September and October. As in the case of
the short-term rates the amplitude is greatest in the late fifties and
tapers off thereafter. By 1965, the amplitude is very low and in some
cases nonexistent.
While this evidence strongly supports the view that seasonality
exists in the interest rate series, questions relating to the methods, as
well as the desirability of adjusting the data for seasonal variations
remain. In addition to the sampling problem of drawing from a
hypothetically stable population (a common problem of empirical106 THE SEASONAL VARIATION OF INTEREST RATES
economics), the estimation of seasonal factors must cope with the
effects of a shifting population. That is, the seasonal factors for a
given month estimated for different years differ not merely because
of random fluctuations but also because the true value, apart from
randomness, may itself be varying. The difficulty in empirical seasonal
analysis is to distinguish the random from the systematic variation of
the seasonal factors. While itispossible to devise tests of the
significance of differences in estimated factors for nonoverlapping
periods, a continuous reading of their accuracy from year to year is
elusive. Visual comparisons of the adjusted with the nonadjusted data
(or, correspondingly, the seasonal factors with the ratios-to-moving
average) may help to determine whether the estimated seasonal
component captures the systematic seasonal movements of the raw
data. Unfortunately, this method ties the conclusions to the particular
analyst and invites differences in judgment. Because of the subjectivity
of this element, the study merely suggests the periods within which the
factors are deemed relatively accurate.
While the similarity in the patterns of all the long-term rates
considered is strong evidence of a seasonal element in the rates, the
patterns themselves may not be sufficiently stable to warrant an
attempt to eliminate this element. The question whether a seasonal
pattern existsisdistinct from the question whether the seasonal
movement is sufficiently stable to justify seasonally adjusting the data
and risking the introduction rather than the elimination of variation.
Itis often maintained that a seasonal pattern in long-term rates
would not persist because of the profits available to those who would
arbitrage the seasonality away by buying securities in periods of sea-
sonally high rates and selling them when the rates are seasonally low.
This argument is true only to the extent the seasonal amplitude is
sufficient to cover the costs of arbitrage, including the risk that on
any given occasion the cyclical, trend, or random components may
swamp the seasonal effect, and to the extent the seasonal movement
is sufficiently stable to make the arbitrage more than a mere specula-
tion. The greater the importance of these two effects—swamping by
other components of variation and instability from year to year—the
greater will be the seasànal amplitude that will survive arbitrage.
Municipal bond yields, for example, a series with a large irregularSUMMARY AND CONCLUSIONS 107
component and an unstable seasonal component, has a relatively high
seasonal amplitude.
The cause of the variation in seasonal amplitudes, the salient
characteristic of the seasonals observed in this study, is a complex
issue. At the risk of oversimplification this study considered the
problem in the light of the supply of and demand for money. On the
assumption that the seasonal variation in the demand for money is
relatively constant from year to year, the change from year to year
in the seasonal patterns for short-term interest rates would depend on
that of the seasonal patterns for the supply of money. In years when
the seasonal factor for, say, January in money outstanding is high the
corresponding seasonal factor for interest rates would be low; and
when the former is low the latter would be high. The observed rela-
tionship between the changing seasonal factors of money supply and
short period interest rates is, indeed, inverse. Hence the data are
consistent with the hypothesis that the rise in the amplitude of the
seasonal variations in interest rates during the 1950's and its virtual
disappearance during the 19 60's is attributable to changes (in the
opposite direction) in the seasonal movements in money supply. This
inverse relationship is more conspicuous when allowance is made for
seasonal movements in the quantity of bills outstanding, a finding con-
sistent with the hypothesis that the Treasury made some attempt to
benefit from the seasonal variation in interest rates. Failure to take
account of this effect, which involves a change in demand in the same
direction as the change in supply, obscures the relation between
money supply and interest rates. When this change in demand is
statistically nullified the full effect of the change in supply is ob-
servable.

The Seasonal Variation of Interest Rates

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