Tests of Covered Interest Rate Parity by ngs20854

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Daniel L. Thornton

Daniel L. Thornton is an assistant vice president at the Federal
Reserve Bank of St. Louis. David Kelly provided research
assistance.




Tests of Covered Interest Rate
Parity



       ECEN’FLY there has been considerable in-                         ticular way. Indeed, this relationship is fre-
terest in and investigations of whether the cov-                        quently imposed in open-economy macroeco-
ered interest parity (CIP) holds. At the inicroeco-                     nomic models. Finding that the relationship
nomic level, CIP is important because is it a                           among these variables implied by CIP does not
direct consequence of covered interest arbi-                            hold would leave their relationship uncertain.~
trage. Its failure to hold would suggest 1) that
                                                                          Generally, there have been two types of em-
markets are inefficient in the sense that traders
                                                                        pirical investigations of CIP. The first are de-
do not take advantage of known profit oppor-
                                                                        signed to determine whether markets are effi-
tunities, 2) that legal restrictions and regula-
                                                                        cient in the sense that all known profit oppor-
tions, such as capital controls, exist or 3) that
                                                                        tunities are arbitraged.~These tests investigate
costs have been unaccounted for, such as in-
                                                                        whether the actual forward premium deviates
dividual borrowing constraints or differences in
                                                                        from that implied by CIP by more than the
political risks across countries.’
                                                                        transaction costs using the most efficient ar-
  At the aggregate level, CIP is important be-                          bitrage. The issues are whether the forward
cause it implies that interest rates and spot and                       premia ever exceed estimates of the transaction
forward exchange rates are related in a par-                            costs and, if they do, whether they persist. The

  ‘In a sense, there are no tests of covered interest ar-                terest rates will immediately get translated into their ex-
   bitrage. It is axiomatict If tests revealed that CIP was              change rates and vice versa. This is particularly true if the
   violated so that known riskiess profit opportunities were             forward rate is an efficient predictor of the future spot rate.
   being ignored for long periods of time, such results would            Even if this is not the case [for example, see Chrystal and
   undoubtedly be explained in various ways, such as alleg-              Thornton (1988)], both forward and spot rates would likely
   ing that relevant costs were ignored.                                 be affected since they tend to move together. Further-
  ~lfCIP does not hold, it does not necessarily mean that                more, if CIP holds, such economies may be influenced
                                                                         more by external events, such as changes in U.S.
   there is no other exact linear relationship among these               monetary policy, than if CIP does not hold. See Dufey and
   variables or their subsets. It only means that the nature of          Giddy (1978) and Kubarych (1983) for a discussion of
   the relationship would be uncertain.                                  some of the policy implications.
   The policy implications of CIP may be especially important           3
                                                                          For example, see Deardorff (1979), Callier (1981),
   for small open economies where the U.S. interest rate can             Bahmani-Oskooee and Das (1985) and Clinton (1988).
   effectively be taken as exogenous. If CIP holds, attempts
   by such countries’ policymakers to move their domestic in-



                                                                                                                      JULY/AUGUST 1989
                                                                   56


evidence is that frequent violations of CIP oc-                         absence of transaction costs. Other linear com-
cur, hut do not persist.4                                               binations of the variables need not equal zero.
                                                                        Tests of CIP that rely on the markets’ reactions
  The second tests are designed to examine
whether CIP holds on average.5 Specifically,                            to economic news or events make use of the
they test whether domestic and foreign inEerest                         fact that the particular linear combination of
rates and spot and forward exchange rates res-                          asset prices implied by CIP is zero. To see this,
pond in a way consistent with CII’ to economic                          assume that U.S. and foreign interest rates and
news that affects each market individually.                             the spot and forward exchange rates can he
                                                                        represented by the following equations:
  This article provides a generic representation
of the latter tests and shows that, under ap-                           (2) Aln(1+i,)           = a, +
propriate conditions, similar tests can he per-
formed that do not require testing the markets’                         (3) al~U+~) = a,                   +

response to particular sets of information. In so                       (4) AlnF,          a, + b,n,, and
doing, this article extends empirical investiga-
tions to a larger set of countries and over a                           (5) AInS,    =a + h n,,
                                                                                       4    4
longer time period.a
                                                                        where n, denotes the new information that
DOES CLP HOLD ON’ AVERAGE?                                              becomes available in the interval over which the
                                                                        t’i’ observation is made. Each asset may respond
  (IF is a direct consequence of covered in-                            differently to the same news.
terest arbitrage! In the absence of transaction
                                                                          Investigations of CIP rely on testing the
costs, the CIP condition requires that
                                                                        markets’ responses to specific information by
(I)   mU +iJ’-lnU    +i,’)—lnF’,+lnS,     =   0,                        identifying a par’ticular component of n, and by
                                                                        making an assumption about the stochastic pro-
where i~and i are the foreign and U.S. interest
rates, respectively, and F, and 5, are the for-                         perties of the rest. One approach is to estimate
ward and spot foreign exchange rates (dollars                           the equations
per unit of foreign currency), respectively.~The                        (6) Aln(1+i,)           = a + d,L,          +   e,,,
maturity of the U.S. and foreign assets and the
forward contract are identical. Moreover,                               (7) Aln( 1   +   i,*)   =       a, + d,I,   +    e,,,
foreign and U.S. securities are assumed to be
                                                                        (8) ah~F,          a, + d,l, + e,,, and
identical except for the currency in which
future payments are denominated.                                        (9) AInS,    =     a        +   d 1,   +
                                                                                     4     4
The Markets’ Reactions to                                               where I, denotes specific information that
                                                                        becomes available during the period in which
Economic JVCMTS
                                                                        the t’’ observation is made, and e,,= (be,)
  Equation I asserts that a particular linear                           denotes an individual market’s response to all
combination of these variables is zero in the                           other inforniation made available during the in-
 4
   Much of this literature shows that the difference between              Germany. Roley’s data covers the period from October 6,
  the actual forward premium and that implied by CIP often                1977, through May 30, 1985, while Husted and Kitchen’s
   falls outside of the neutral band given by transaction                 data covers the period from February 8, 1980, through
  costs, e.g., see Bahmani-Oskooee and Das (1985) and                     August 27, 1982.
  Clinton (1988). For example, Clinton finds “that while the
   longest sequence of profitable trading opportunities is five         ‘Deardorff (1979) shows that covered interest arbitrage re-
                                                                          quires that the forward rate deviate from that implied by
  observations [days], the most common run does not ex-                   CIP by no more than t+t ÷t,+tJ,where t, t , t, and t,
  tend beyond a single observation. Thus, in general, profit              are the transaction costs (proportional to the size of the
  opportunities appear to be both small and short-lived, even            transaction) in the United States and foreign securities
  though they are not rare.” See Clinton (1988), p. 367, He
  suggests, however, that it is unlikely that the quality of the          markets and the spot and forward foreign exchange
                                                                          markets, respectively. He also shows that the “neutral
  data will ever be sufficient to provide a rigorous test of              band” is narrower than this if “one-way” arbitrage is con-
  market efficiency. i.e., that there are no unexploited profit
                                                                          sidered. This band has been further narrowed by Callier
  opportunities.                                                          (1981), Bahmani-Oskooee and Das (1985) and Clinton
 5                                                                       (1988).
   To date, this work has relied exclusively on investigating
  markets’ responses to money announcements. See Roley                  8
                                                                          AlnF, and AlnS, are weighted by an annualizing factor
  (1987), Husted and Kitchen (1985) and Tandon and Urich                  equal to 12 divided by the number of months in the for-
  (1987).                                                                 ward contract.
 6
   Roley (1987) considers Japan and only the Gensaki rate,
  while Husted and Kitchen (1985) use data for Canada and



FEDERAL RESERVE SANK OF St LOUIS
                                                                   57


terval, c,.9 Estimnating this equation system in-                       specific information to 3 am. after the informa-
volves the additional assumption that E(e,) 0.               =          tion is released. ~I’hechange in the exchange
Equations 6-9 are estimated and the restrictions                        rates is defined similarly. Undem- these assump-
d   —  d,    d, + d4
                —        a,
                         =     a,
                                —    a, + a4
                                         —     0         =              tions, changes in the interest and exchange
are tested. If CIP holds, the intercept and slope                       rates reflect informnation that is common to
coefficients of equations 6-9 will satisfy the par-                     both, as well as the information unique to each.
ticular homogenous linear restriction implied by                        For example, changes in the interest rates will
CIP.                                                                    reflect the markets’ reaction to information be-
                                                                        tween 3 am. and 11 a.m., but this information
  An asymptotically equivalent test can be per-
                                                                        will not necessarily be reflected in the change
formed by estimating the equation
                                                                        in the exchange rates. Likewise, changes in the
(10) Aln(1 +i,) AlnU+it)—AlnF, + AInS,
                    —                       a +          =              exchange rates reflect the markets’ reaction to
        dl, + f,,                                                       information from 3 am. to Ii a.m. the next day,
                                                                        but this information will not he reflected in the
and testing the hypothesis that a       d    0. ln
                                             =       =
                                                                        changes in the interest rates. Consequently, the
this form, the error term, f,      e,,
                                     =   e,,    c, +
                                                 —       —
                                                                        error term of equation 10 comes potentially
e4,, vanishes under the null hypothesis that the
                                                                        from differences in the information in the asset
markets respond to the new information in a                             prices due to non-synchronous data, as well as
way consistent with CIP, that is, b—b,
                                                                        from changes in the log of tmansaction costs.” it
—  b, + h4 0. A more satisfactory interpretation
            =
                                                                        could not come from the common information
of f,, therefore, comes from recalling that equa-
                                                                        because, as vve have already noted, this compo-
tion I holds identically only in the absence of
                                                                        nent of the error term vanishes under the null
transaction costs, so that I’, represents the
change in the log of these costs.’°                                     hypothesis.

   Another interpretation of f, stems from the                          Tests of the Linear Restrictions
fact that the observations used to examine C1P                          Implied by LiP
generally are not taken at the same time. To il-
lustrate the effect of this, assume that observa-                          A comparison of equations 6-9 and equation
tions on U.S. and foreign interest rates are                            10  reveals another interesting aspect of these
taken at 3 a.m. EST, while the observations on                          tests. The hypothesis that a = 0 is a test that
the spot and forward exchange rates are taken                           the linear combination implied by CIP, but not
at 11 am. EST. The change in interest rates is                          accounted for by I,, is zero. If CIP holds, this
measured from 3 a.m. before the release of the                          will he true at all times, not simply when the


 ~Thisspecification assumes that there is no idiosyncratic in-          “For simplicity, let Ai = Aln(1 + i~’)— Aln(l + C) and AR, =
  formation that affects one market but not the others. It is            AlnF, — AInS., so that CIP implies that Al — AR = 0,
  difficult to see how such idiosyncratic information could               under the simplifying assumption of zero transaction costs.
  exist in the reduced-form equations 6-9, or how such an                 Now let Ai, = o, + a,SI, + d,c + d,rj. and AR =            +
  assumption could hold under the null hypothesis. For a                   + dc, + d,co~Here, c, denotes the information not con-
   model that looks at the implications of non-synchronous                tained in I, that is reflected in both interest rates and ex-
  trading using the assumption of idiosyncratic information,              change rates, ~ denotes the information reflected in Ai,
  see Lo and MacKinlay (1989).                                           that is not reflected in AR and w, denotes the information
loIf transaction costs vary symmetrically around a non-zero               reflected in AR that cannot be reflected in Ai,. Since there
   mean, the change in the log of transactions costs will not             is little lustification to do otherwise, it is assumed that Ai,
  vary symmetrically around zero. This stems directly from                responds the same to and ~ likewise, the response of
  the concavity of the log function. This means that if the               AR is the same for c and w~ Note that if the response of
                                                                          these markets to information is consistent with CIP, i.e.,
  distribution of transactions cost is symmetric, the distribu-
  tion of the log of the change in the transaction costs will            (a, — i30) = (a, — f~) (d, — d) = 0, Ai — AR, differs
                                                                                                      =

                                                                         from zero by 6, q, — d,w,, the response to the non-
  be asymmetric.                                                          synchronous information. [Estimation requires a normaliza-
“Since the markets may eventually respond to all informa-                 tion; however, this does not affect the conclusion].
  tion, the non-synchronous data implies that changes in
   asset prices taken at different periods of time will be                Roley (1987), p. 65, asserts that, “when testing whether
  serially correlated. In terms of equations 6-9, this means              the responses of these variables to a specific piece of new
                                                                          information are inconsistent with covered interest parity,
  that the error terms will be cross-sectionally autocor-                the exact alignment of the data is not necessary.” The
   related. In terms of equation 10, this implies that f will be          above illustration demonstrates that this is not necessarily
  serially correlated. Indeed, when equation 10 was
  estimated using all of the daily data, this was the case,               the case. The error term of equation 10 and, hence, the
                                                                          precision with which the parameters can be estimated is
  The results reported in this paper are for estimates of                 clearly dependent on the degree to which the data are
  equation 10 only on days when the specific information
  was available. Not surprisingly, in nearly all cases, these            synchronous.
  error terms were serially independent.



                                                                                                                      JULY/AUGUST 1989
                                                                 58


markets react to specific information. Tests of                        rates. Anticipated changes in Ml are the median
UP using the markets’ response to specific in-                         forecasts from the Money Market Services sur-
formation generally are performed using data                           vey, and the forecast error is the difference be-
only for days when the information is released;                        tween the forecasted change and the change in
however, evidence on CIP can be obtained dir-                          first-announced Ml. The interest rates are
ectly from the changes in these four asset                             reported as of 3 am. EST and the exchange
prices even if information that the markets res-                       rates are reported as of 11 am. ES’I’. The in-
pond to is not identified or is not available.                         terest rates are bid rates from the Bank of In-
                                                                       ternational Settlements.’~ The exchange rates
   Rejecting the hypothesis that this linear com-
                                                                       are the average of bid and ask rates from the
bination of changes in asset prices is zero is
                                                                       London foreign exchange market.
strong evidence against CIP. A failure to reject
the null hypothesis is not strong evidence in                            The test of CIP using money announcements
favor of it, however, because the same could be                        involves estimating the equation
true for other linear combinations of these asset
prices. If asset prices follow a random walk                           (11) Aln(1+i,)    — Aln(1+i~)      —   AInF,+AlnS,     =   a       +

without drift, the same could be true for any                                 d,UM   +   d,ME, + e,.
linear combination of the change in these asset
                                                                       Both anticipated money, ME, and unanticipated
prices, not simply for the linear combination im-
plied by CIP. Consequently, stronger evidence                          money, UM, are included because, as a number
consistent with UP would be obtained if the                            of researchers found, these asset prices re-
null hypothesis is not rejected for the linear                         sponded in a statistically significant way to both
combination implied by CIP, but is rejected for                        anticipated and unanticipated changes in the
other linear combinations.                                             money stock.’~The finding that the individual
                                                                       markets respond significantly to ME is, itself,
                                                                       frequently taken as evidence that the markets
EMPIRICAL EVIDENCE                                                     are informationally inefficient.’~For the purpose
                                                                       of testing for CIP, however, the only relevant
  Tests of CIP using the markets’ response to
                                                                       issues are whether the markets respond to ME
specific information have relied exclusively on
                                                                       and whether the responses net out in a way
their response to money announcements. In this
                                                                       consistent with CIP.
section, the broader test outlined above is ap-
plied to daily data for the period from October                         It has been common to estimate equations like
5, 1979, to September 14, 1988. Tests of CIP us-                      6-9 or equation 11 over different subsamples to
ing the markets’ response to information in the                       see if the markets’ response to money announce-
form of money announcements also are under-                           ments changes in response to changes in the
taken. The reported tests using money an-                             Federal Reserve’s operating procedure.” Since
nouncements are only fot days on which there                          the interest here is only in testing for CIP,
was an announcement.                                                  however, there is no need to split this sample
                                                                      for this purpose: the difference in magnitude of
  The data used in this study are one-, three-,
                                                                      the market’s response is unimportant.
six- and twelve-month Eurocurrency rates for
the United States (U.S.), United Kingdom (U.K.),                          It is important to split the sample for another
Canada (CA), Germany (GB), Switzerland (SW),                           reason, however: the null hypothesis that d,                   =


France (FR) and Japan (JA), the corresponding                          d, =    0 will not be rejected either if the markets
forward exchange rates and the spot exchange                           do not mespond to money announcements or if

“The interest rates are from the BlS data tape at the Board            ME from equation 10 is likely to have little bearing on the
 of Governors of the Federal Reserve System. These are                 test because ME and UM are nearly orthogonal. Further-
 bid rates taken from several markets. The Money Market                more, while the evidence on the importance of ME may be
  Service survey data through 1986 were provided by Graig              weak, the cost in terms of lost efficiency for including it is
  Hakkio.                                                              small.
‘~For xample, this is true of Tandon and Urich (1987),
       e                                                              “While this type of test is generally valid, there are some
  Husted and Kitchen (1985) and Belongia and Sheehan                    important limitations, For a discussion of these, see
  (1987). Deaves, Melino and Pesando (1987), however,                    Pesaran (1987), especially chapter 8.
  show that the significance of expected money on U.S. in-            “In October 1982, the Fed switched from a nonborrowed-
  terest rates is due to a few outliers, while Belongia, Hafer          reserves to a borrowed-reserves operating procedure. See
  and Sheehan (1986) have shown that the response of U.S.               Thornton (1988a) for a discussion of the borrowed-reserves
  interest rates to anticipated money is very sensitive to the
                                                                        operating procedure.
  sample period. In any event, the presence or absence of


FEDERAL RESERVE SANK OF St LOUIS
                                                                      59




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their response is consistent with CIP on                                     THE RESULTS
average.
                                                                                Table 1 reports t-statistics for tests of various
  It is well-documented that the markets,                                    linear combinations of changes in U.S. and
especially U.S. interest rates, responded in a                               foreign interest rates and spot and forward ex-
statistically significant way to unanticipated                               change rates, including the linear combination
changes in the money stock through the early
                                                                             implied by CIP. The t-statistic for the linear
part of 1984. Their response after early 1984 is
                                                                             combination implied by CIP is denoted T,; t-
more problematic, however. Consequently, the
                                                                             statistics for two other linear combinations of
period was divided into two subperiods: Oc-
tober 5, 1979, to January 29, 1984, and January                              the changes in these asset prices are denoted ‘I’,
30, 1984, to September 14, 1988.’~Equations in                               and T,. The alternative linear combinations are
the form of 6-9 were estimated for both per-                                 interesting because T, is the t-statistic for a test
iods, and both anticipated and unanticipated                                 of a linear combination of changes in these
changes in the money stock had a statistically                               asset prices that is correlated with that implied
significant effect only during the first subperi-                            by CIP, while T, is the t-statistic for a test of a
od.” Consequently, estimates of equation ii are                              linear combination that is orthogonal to that im-
presented only for the period ending in 1984.                                plied by CII’.” Consequently, if the null
Results for the more general test are presented                              hypothesis that CIP holds cannot be rejected, it
for the entire period.                                                       would not be surprising to find that ‘I’, >T,>T,.

    ‘7For example, Dwyer and Hafer (1989) found that essential-               case for U.S. and Canadian interest rates at all maturities,
     ly there was no statistically significant response of U.S. in-           except the 12-month maturity for Canada, and is generally
     terest rates to money announcements after July 1984.                      true for both the forward and spot exchange rates. It is not
     More importantly, estimates of equations of the form of 6-9               true for other foreign interest rates, with the exception of
     found no statistically significant response to either an-                 the one-month Euroyen rate.
     ticipated or unanticipated changes in the money stock dur-              “Let R , R and R denote the three restrictions on the vec-
     ing the second subperiod.                                                 tor of’chainges in’ asset prices that correspond with T,, T
    “Estimates of equations like 6-9 for the first subperiod in-               and T,, respectively, e.g., R, =(1, — I, — I, 1). Then the
     dicate that the markets frequently responded significantly                correlation between R, and R is — .50, while R and R,
     to anticipated changes in the money stock, This was the                   are uncorrelated.



                                                                                                                              JULY/AUGUST 1989
                                                                  60


   In every instance, the t-statistics for the test                        Scatter plots of the dependent variable and
of CIP are extremely small, suggesting that CIP                         unanticipated changes in the money stock for
holds on average over the sample period. While                          the four instances in which the coefficient on
supportive of CII’, the fact that the null hypoth-                      tiM was statistically significant are presented in
esis cannot be rejected is not compelling evi-                          figures 1-4. In the case of the six-month maturi-
dence because the same could be true of other                           ty for Japan shown in figure 1, it appears that
linear combinations of these variables. Tests of                        two extreme observations (see arrows) could ac-
other linear combinations produce t-statistics                          count for the significant positive coefficient on
that are considerably larger than those for that                        UM. The same two observations appear as ex-
implied by CII’, although in no case was the null                       treme observations for the 12-month maturity
hypothesis rejected. In the majority of cases,                          for Japan in figure 2. To see if the results for
however, T,>T,,                                                         Japan are sensitive to these observations, they
                                                                        were deleted and the equation was re-estimated.
Tests of the Response to Specjfie                                       In both instances the coefficient on UM was no
Information                                                             longer statistically significant at the 5 percent
                                                                        level.”
   Estimates of equation 11 along with the t-sta-
tistics for tests of linear combinations of the                           The remaining scatter plots reveal no similarly
changes in these variables for the period from                          dramatic outliers. They do indicate what the
October 5, 1979, through January 29, 1984, are                          low adjusted B-squares suggest: a relatively
presented in table 2.20 Two F-statistics are                            weak relationship between the dependent vari-
reported. F, is a test that all of the coefficients                     able and unanticipated changes in the money
are zero. F, is a test that the two slope coeffi-                       stock.’~Given the spherical nature of the scatter
cients are zero.                                                        plots and the extremely low adjusted R-squares,
                                                                        these results do not represent a serious
   ‘l’here were four instances in which the coef-
                                                                        challenge to the null hypothesis that CIP holds
ficient on unanticipated changes in money was
                                                                        on average.
statistically significant at the 5 pet-cent level and
three instances in which the null hypothesis                              Tests of linear combinations of changes in
that both slope coefficients are zero is rejected.                      these variables reported in table 2 are similar to
In no instance was the coefficient of anticipated                       those for the entire period reported in table 1.
money alone significant at the 5 percent level.                         The major difference is the T, statistic is signifi-
                                                                        cant at the 5 percent level for Germany, France
  The occasional statistically significant response                     and the United Kingdom for all maturities.”
to unanticipated changes in the money supply is                         This provides strong evidence that CIP holds on
odd given the general lack of such responses.                           average during the period. This finding is con-
Even more surprising, one of these occurs at a
                                                                        sistent with that of Clinton (1988) who found
maturity of six months while the other three                            that, even though thei’e were numerous in-
occur at a maturity of 12 months, despite the                           stances when deviations from interest rate pari-
fact there was no statistically significant re-                         ty were larger than those implied solely by
sponse at shorter maturities.” This fact along                          transactions costs, no profitable arbitrage oppor-
with the extremely low adjusted R-squares leaves                        tunities exist on average.
open the possibility that the statistically signifi-
cant responses are due to the influence of a                              Unlike Roley (1987) who rejected CIP for
ielatively few observations.”                                           Japan, these results suggest that it holds for the


‘°Francedevalued its currency three times during this                    changes in the money stock are due to relatively few
  period, causing excessively large movements in the                     observations.
  Eurofranc rate. These observations were deleted from                  “The observations are March 7, 1980, and June 10, 1983.
  tests involving money announcements for France. They                    The t-statistics for the coefficient on UM are 0.97 and 1.69
  were October 5, 1981, June 14, 1982, and March 21,1983.                for the six- and twelve-month maturities, respectively.
“Most of the empirical evidence suggests that the response              4
                                                                       ‘ Given the results reported here, there is little reason to
  of U.S. interest rates to money announcements is the                    perform formal statistical tests for the stability of the coeff i-
  strongest at the short-term maturities, For example, see
                                                                         cients, In any event, such tests likely will be of low power
  Dwyer and Hafer (1989) and Hafer and Sheehan (1989).                    given the low adjusted R-squares for these equations.
“Thornton (1988b, 1989) has shown that some of the                     “Separate tests indicate that many of these asset prices do
  reported statistically significant responses of U.S. interest           not follow a random walk,
  rates, exchange rates and stock prices to unanticipated



FEDERAL RESERVE SANK OF St LOUtS
                                                                                                                                                                                    61


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                                                                                                                                                                                        OOS                                  185
                                                                                                                                                                                                                               /
                                                                                                                                                                                                                                                                  013                            04                                 MN                           13?


     OR              N                                                                     ~t34                       ~ozs                             ‘~1~N                       ~                                     002                                      015                            06                             20                      -~g1%
      N                                       ~*1                              NbttN                                                       /                                                                                 N
                                                                                                                                       >///N~                                                                                            //                                      N                                                          N                                    N   N


                                                      45r                                  SI,                      ~-~Ø7~                                 165                     -S                                        ía”                                  ~                              a                  -~                                  -loG
                                                      ~                        ~                                                                                                                                                                                                                              N

                                                                                                 ‘N,       1kN~~”N’N/                                                              N’                                                                                                                         /         /           N                   /NN                      N

    ~tJKN”                                            0t26                                 Q’N,,                      S’’                          4rnt~                                002                              ØØ4N                                     oso                                         N




       A”,                                    \N                                                 /~                  ~                                                                  007                                  $27                          N/Ga                                   0&’                            iS                  ‘-23
                                              ~t*~                         NPSNNfl~



     Th$EE MONTh,                                                                                                                                              N

     CA       t-Ofl               ‘                                        NN.04a,~//’mw                                                            fl3f~                               012                              2.06                                     235                                               ‘                                                9
             N                                                                                                                                                                                                   N                                    ,                     /,                                                                                           N


    mg’                                                                            ~ãtN~                              00’                      /N0-                        ‘            009~                                 “~‘                                  001                    /&1N..,,3~                                                      =142
                                              ,ftftt                   /                                   N’(4$N//                        /               /        T                                   /    /                                                    N                                                         /           /                N




      OR             N,                       =0~ N=OG,’~07                                                                            /           ~G~It                                bD7                                  052                                  027                            01                 —a                          /       =220
                                              (1 )~ wiit:   flNN                                                                                       /,/                 /                            /
N                                     /                                                /           N’           /              /               /                                    / /


                                                      Uss’                                 ~                         JOG                            0543                           /N0Q9~D41~ 003                                                                                                02               ,‘=iG                                      SW
N      /         /                                                                 (fl/%                                   NkN,N                                                        /                                                                 /




      (1K’                                    =002                                         012’GSt’N’                                              øZ~SN                                ,006                                 125                                  t$2                /                        /                     29                  —244
                                              (0$~’ ~178~
                     /                         esí,~ ‘ileN\_aoNns4N                                         NP/N
                                                                                                                                                                                   —oos                     //
                                                                                                                                                                                                                             07~
                                                                                                                                                                                                                                     /                        /
                                                                                                                                                                                                                                                                  047                    /01                                        /  /
                                                                                                                                                                                                                                                                                                                                    20NN=20
                                                                                                                                                                                                                                                                                                                                                                     N



                                              ~NN                                  ~a,                              (~\                                N                                    /                N                                                               N               /            /




     $)XMONTK                                         N       ‘                    /             ‘N’        /       /“/,                                                       /                                                 N            /                                              ‘‘                                                     /

                                                      oa*                                  ~                    ‘~7                                 0. $                           -~,0O7                                    ‘154                                 0.25           ‘~-0S                              --34                                  -99
N            /           /        /                       4        /               flfl’                            /S)\                                                            N           N                /       /       N                                                       /



                                      N                                                    006                       1004N                         0105                            —007                                      0’68                                 020                            04                 -34                                  —1,48
                                                                                                                                                       N

                                                                                                                                                    ~jst                           —ao                                           a                                oss                            Os                 —36                                 =zs
      NN                                       ~?3)                                •                                ~i                                             N                                                                              N

             N                                                                     NN                                      N

                                 NN           N       SN                                   ~                 “4$~                                          5$4                     .~-1Jo3                                   093                                  072                            01                 —2                                  =326
                             NN               ~                            N,02,                           //(1~                           N                                                                                                                                                          N



                                      ~-tJaI~                                              11                   /S                             ~                                        r9                                   Ms                                                                               N

                                                                                                  N//N                                                     /                   N                                                              /                   /              /       /                                      /               ‘N’                          /
                     /                    N                                                       /   /                                        N       N           N       ‘N’                      /                                                                                    /                                                                       /




                                                                                                                                                                                                                                                                                                                                                JULY/AUGUST 1989
                                                                                62


                   N                                       N,                                 N    N
                        N

                                                                           /   N,         N”’~



     thIs 2 ( ontntued)
 The Markets’ Reaction to Money                                          Anno           ments 0 tóber 5, 19 9
 January27, 1984
                                                                                                                      es,t of LInear
        ____                                   Estimates of Eq~wtion7                                                 Combtotts

 Matutity!
                   Constant’                                    ,               If       N’                    Tt               ______-



 a                          050          021             024        0337        09>       88       312           00         32            2
                       (1)           208)           (158)
 1’WE VS MONTH
 CA         043                          004          004           0220        006                 o~o         .oi         a
                            67)     055)            (045)

  W                         014       006             007           0288        008      039       0             00         2             148
                       (069)         068            (064)

                         02           01                 ‘005       07          010                     2        04         St            as

                       (175         (202}

 FR                      003             026             019        0364        019        18          22        02                       S2~
                       (010)        ( 38)               ItS)
 UK                      -03          000                OtS        0230        008      166       003           04         25                4
                       (203)        (005)           (     4)

 JA                      072          029           =021            0377        023     535*       358           0          27            3
                       (283)        (49)            (120)

  Actual cbs rctehl               10 2 mae ma epe?tea ceettleten

     fndicates stat           i   i~ntticana at the 5 percent teve

 T,M(1             )        AIrtI rJ           IF        415        0
 T~ 1     (    t            And     i)      4n           MnS

        tn(    -            Aif          -i-AlIt                =0




I uroven rate. Roles used the Gensaki rate and
attributed his failut e to support CII to capital
                                                                                                                      -
controls. Since the Eurocut enc~rates used
here are not affected h~capital controls the
results are not inconsistent with Roley s To-                                            1 he T stati tics repot ted in table   are much
gether hov~ er they suggest that there should
             c\                                                                       smallei than the t-statistics fot the intei cept
be relati~~ls u eak substitutability bet%\ een the                                    terms, ome of u hich n crc ignificant at the 5
Furoven and Gensaki rates.                                                            percent level.’6 One explination for thi \\.hn h


2 Equation 11 was also estimated using all of the daily data,                         terms were not much different from the t-statistics for the
  not simply for days when there was a money announce                                 linear combination of the e asset price implied by dR
  ment Not surprisingly the t-statistics for the intercept                            reported in table 2.



FEDERAL RESERVE SANK OF St LOUIS
                                                                                         63



 —a



    Figure 1
    Scatter Plot For Japan: Six-Month Maturity
    Ainii       ~‘   iii   —   Ainil   +    i~i Mn
                                                 —        Ft       +   Aiitst
    .012


    .008


    .004


    ~000


—.004


—   .006


—.012



—016


—.020


—024



—028



—   .032



—036
        —5                 —4          —3        —2            —l               0   1    2     3   4   5   6   7   8   9
                                                                                        (UM)




Figure 2
Scatter Plot For Japan: 12-Month Maturity
Mnit        +    i~i— Mnii + ifl             —   Ainrt         +   Airts,
    .008


    .004


    .000


     -004



    .008


    .012



    .016


    .020


     024


     028


     .032

    • 036


—040
           —5              —4          —3            —2            —1
                                                                                        (UM)




                                                                                                                           JULY/AUGUST 1989
                                                                                 64




           Figure 3
           Scatter Plot For Germany: 12-Month Maturity




            —   _~JIJ,
                    —5                —4        —3        —2        —1   0   1     2    3   4   5   6   7   8   9
                                                                                 (UM)




            Figure 4
            Scatter Plot For France: 12-Month Maturity
            Am    it        tti   —   Alit it    ,i   —   Alt, m~   Am
                .012                                                                                                    .012

                 .010                                                                                                   .010

                -008                                                                                                    .008

                .006                                                                                                    .006

                 .004                                                                                                   .004

                 .002                                                                                                   .002

                 .000                                                                                                   .000

            —002                                                                                                    —   .002

            —    .004                                                                                               —004

            —006                                                                                                    —   .006

            —-008                                                                                                   —   .006

            —~010                                                                                                   —-010

            —012                                                                                                    —   .012

            —    .014                                                                                               —014

            —016                                                                                                    —.016

            —.018                                                                                                   —018
                        5               4       —3          2       —1   0   1    2     3   4   5   6   7   8   9
                                                                                 tuMi




FEDERAL RESERVE SANK OF St LOUIS
                                                               65



is consistent with the frequent—though not
persistent—violations of CIP using transaction
cost data, is that shocks to the market in the
form of money announcements are destabiliz-
ing, causing large deviations from CIP on these
days2’ If this is the case, deviations from CIP
should be larger on money-announcement days.
Consequently, not only will the means be larger,
but the variance of the dependent variable
in equation 11 should be larger on money-
announcement days as well.28

  Table 3 reports test of the equality of the
variances of the dependent variable of equation
11 against the alternative that the variance is
larger on money-announcement days. These
tests are performed only for the period ending
in 1984 because, as has been noted, the in-
dividual markets do not respond significantly to
unanticipated changes in the money stock
thereafter.
  In general, the results are not consistent with
the hypothesis that the variance is larger on
money-announcement days. There are six in-                           CONCLUSIONS AND
stances in which the null hypothesis of the
equality of the variances is rejected in favor of                    IMPLICATIONS
the alternative at the 5 percent significance                          Despite a few occasions in which there was a
level, but there are seven instances in which
                                                                     statistically significant response to unanticipated
the variance of the dependent variable is signif-
                                                                     changes in the money stock, the results of tests
icantly lower on money-announcement days.29
                                                                     of the markets’ response to economic news are
Moreover, two of the former cases are for the
                                                                     consistent generally with the hypothesis that
six- and 12-month maturities for Japan. Since
                                                                     CIP holds on average. In two of the four in-
the previous results for these maturities were
strongly influenced by these observations, they                      stances in which there was a significant re-
were deleted and the tests repeated. When this                       sponse to unanticipated changes in the money
was done, the null hypothesis was no longer re-                      stock, the results appeared to be due to the
jected in favor of the alternative in either                         nature of the data and the sensitivity of least-
case3°Consequently, the occasional significant                       squares to extreme observations. Also, the few
intercept term and the occasional significantly                      instances in which the means of the dependent
larger variance on money-announcement days                           variable implied by CIP were significantly dif-
are not strong evidence against CIP holding on                       ferent from zero on money-announcement days
average.                                                             do not constitute strong evidence against C1P.
27
  Another is that the difference in these results are due to          stances where this was not the case, the actual frequency
 the distributions of the dependent variable. Though not              in the first and last group exceeded the actual frequencies
 reported here, the distributions of the dependent variable           in the second and third and 11th and 12th groups. The
 have their probability mass more highly concentrated                 null hypothesis of normality was rejected in every case at
 about the mean and have thicker tails than normally                 very low significance levels by formal chi-square
 distributed random variables. Consequently, sample means             goodness-of-fit tests.
 vary considerably, even in what conventionally would be            28
                                                                       0ne way to conceptualize this is simply to note that there
 large samples. The evidence of this is obtained from tests          is an extra source of variation on money-announcement
 derived from histograms constructed by dividing the inter-          days. For an example, see Thornton (1988b).
 val from ±2.33 standard deviations around the mean into            29This may not be too surprising given the transaction-cost
  11 equal-length groups centered on the mean, The first
 and last group were open-ended, theoretically containing 1           interpretation of the error term because Bahmani-Oskooee
 percent of the sample in each. These histograms were                 and Das (1985) report that their estimates of transaction
 created for all observations and for days when there were            costs were highly unstable.
                                                                    30The F-statistics for the six- and 12-month maturities are
 and were not money announcements for the first
 subperiod. In nearly all instances, the actual frequency in          0,72 and 114, respectively. Indeed, for the six-month
 the first and last group exceeded—in many cases, greatly             maturity, the variance is significantly smaller on money-
 exceeded—the expected frequency. But even in those in-               announcement days.



                                                                                                                JULY/AUGUST 1989
                                                                 66


‘rhis is so because the hypothesis that the mean                      Clinton, Kevin- “Transactions Costs and Covered Interest
of the dependent variable implied by CIP is zero                         Arbitrage: Theory and Evidence’ Journal of Political
                                                                         Economy (April 1988), pp. 358-70.
was never rejected for larger samples using all
                                                                      Cornell, Bradford. “The Money Supply Announcements
of the daily observations.                                               Puzzle: Review and Interpretation,” American Economic
                                                                         Review (September 1983), pp. 644-57.
   ‘l’here is no evidence that the data are con-
                                                                      Deardorff, Alan V. “One-Way Arbitrage and Its Implications
sistently more variable on money-announcement                            for the Foreign Exchange Markets;’ Journal of Political
days. Furthermore, the t-statistics for tests that                       Economy (April 1979), pp. 351-64.
linear combinations other than that implied by                        Deaves, Richard, Angelo Melino, and James E, Pesando.
CIP were zero were much larger than those for                            “The Response of Interest Rates to the Federal Reserve’s
                                                                         Weekly Money Announcements: The Puzzle of Anticipated
that implied by CIP and, in several instances,                           Money’ Journal of Monetary Economics (May 1987), pp.
the null hypothesis was rejected during part of                          393-404.
the sample period. Hence, CIP appears to hold                         Dufey, Gunter, and Ian H, Giddy. The International Money
on average for these data.                                               Market (Prentice-Hall, 1978),
                                                                      Dwyer, Gerald P, and R. W. Hafer. “The Response of Inter-
  There are several policy implications of the                           est Rates to Economic Announcements,” this Review
finding that, on average, an exact linear rela-                          (MarchlApril 1989), pp. 34-46,
tionship exists between the U.S. and foreign in-                      Engle, Robert F. “Autoregression Conditional Heteroscedas-
terest rates and the spot and forward exchange                           ticity With Estimates of the Variance of United Kingdom In-
rates. For example, if the U~S.interest rate is                          flation,” Econometrica (July 1982), pp. 987-1008.
taken as exogenous, foreign central banks can-                        Hater, R. W., and Richard C, Sheehan. “The Response of
                                                                         Interest Rates to Unexpected Weekly Money: Are Policy
not independently and simultaneously control                             Changes Important?” unpublished manuscript, March
both their interest rates and their exchange                             1989.
rates, This means that small open economies are                       Hardouvelis, Gikas A. “Market Perceptions of Federal
susceptible to exogenous changes in US, mone-                            Reserve Policy and the Weekly Monetary Announcements;’
                                                                         Journal of Monetary Economics (September 1984), pp.
tary policy. Finally, the results indicate the CIP                       225-40.
assumption used in many theoretical models is                         Husted, Steven, and John Kitchen, “Some Evidence on the
appropriate, so long as it is not required to hold                       International Transmission of US. Money Supply An-
at every point in time, These results, however,                          nouncement Etfects’ Journal of Money, Credit and Banking
do not ptovide evidence for the question of                              (November 1985), pp. 456-66.
market efficiency which characterizes many                            Kubarych, Roger M. Foreign Exchange Market in the United
                                                                         States, revised ed, (Federal Reserve Bank of New York,
discussions of CIP and covered interest                                  1983),
arbitrage.                                                            Lo, Andrew W., and A, Craig MacKinlay. “An Econometric
                                                                         Analysis of Nonsynchronous Trading;’ NBER Working
                                                                         Paper No, 2960 (May 1989).
                                                                      Pesaran, M. Hashem. The Limits to Rational Expectations,
                                                                         (Blackwell, 1987).
REFERENCES                                                            Roley, V. Vance. “U.S. Money Announcements and Covered
Bahmani-Oskooee, Mohsen and Satya P. Das. ‘Transaction                   Interest Parity: The Case of Japan;’ Journal of International
                                                                         Money and Finance (March 1987), pp. 57-70.
  Costs and the Interest Parity Theorem,” Journal of Political
  Economy (August 1985), pp. 793-99.                                  Sheehan, Richard C. “Weekly Money Announcements: New
Belongia, Michael t, and Richard C. Sheehan. “The Infor-                 Information and Its Effects;’ this Review (August/September
  mational Efficiency of Weekly Money Announcements: An                  1985), pp. 25-34.
  Econometric Critique,” Journal of Business and Economic             Tandon, Kishore, and Thomas Urich, “International Market
  Statistics (July 1987), pp. 351-56.                                    Response to Announcements of US. Macroeconomic
Belongia, Michael t, R. W. Hafer, and Richard G. Sheehan.                Data’ Journal of International Money and Finance (March
  “A Note on the Temporal Stability of the Interest Rate—                1987), pp. 71-83.
  Weekly Money Relationship,” Federal Reserve Bank of St.             Thornton, Daniel L. “The Borrowed-Reserves Operating Pro-
  Louis, Working Paper 86-002 (1986).                                    cedure: Theory and Evidence’ this Review (Januaryl
Callier, Phillips, “One-Way Arbitrage and its Implications for           February 1988a), pp. 30-54.
  the Foreign Exchange Markets;’ Journal of Political                            “Why Do Market Interest Rates Respond to
  Economy (December 1981), pp. 1177-86.                                 Money Announcements?” Federal Reserve Bank of St.
Chrystal, K. Alec, and Daniel L, Thornton. “On the Informa-              Louis Working Paper No. 88-002 (1988b).
  tional Content of Spot and Forward Exchange Rates;’ Jour-           _______    “The Effect of Unanticipated Money on the Money
  nal of International Money and Finance (September 1988),               and Foreign Exchange Markets;’ Journal of International
  pp. 321-30.                                                            Money and Finance (forthcoming).

								
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