-19-

2) _ 2,2, 2
Syl yg = Avy)" Coy + (2)
Ol yg = (C,/8,)7(02 +a) + Uc, #0,)/8,)°02 + (G,/d,)°of + (6,/A,)702, (13)
Y'ac 31 e?
Cy) = mb, + bum, © Cy = Yom, ~ MY eq?
cy = Yo>, + biy,> Ay = + myC, + byC,.

Since db. > m, and it has been assumed that my > bys Cy + Cy and the sum of

the second and third terms in ay are positive, Thus, if oy = oe = a = 0 and

+ 2 2 2 2 . . : *
either a, or & > 0, lac to. leet This result can still be obtained if
my <by but (11) ig positive or if (11) is negative but yy(myb, + bym,) >
2. .2_ 2 2 2 _ 2
ly (my; ~ bym,)|. Ifo, =o, = 0 and O)s Og, or o, > 0 then 0 = Flee
oy lac"

IV. PERMANENT DISTURBANCES AND FINANCIAL POLICY RESPONSES IN A SINGLE OPEN
ECONOMY
This section contains a brief description of some implications of
alternative financial policy responses when a single open economy experiences
permanent as well as transitory disturbances, The analysis of the effects
of transitory disturbances above proceeds under the assumption that private
agents know exactly the structure of the economy which is embodied in the
coefficients of an economic model, including the intercept terms of that
model, However, they are ignorant of the current values of the transitory
disturbance terms when they set the nominal wage given the announced constant
values of the financial policy instruments. While the average level of output
is its full employment level, there are variations in output about this level,

It is into this environment that permanent disturbances are introduced.


-40-

Most of this paper is devoted to analyzing the effects of serially
uncorrelated transitory disturbances under alternative financial policy
regimes when current output and price variations are unobservable in at least
one country and nominal wages do not deviate from preset paths. The lessons
of such analysis seem more relevant when equilibrium in the model is
assumed to refer to a "period" of a half year or a year rather than a
month or a quarter. The longer the equilibrium period, the more sense
it makes to regard disturbances as serially uncorrelated and to presume that
alternative financial policy regimes can lead to measurably different out-
comes. However, the longer the equilibrium time period, the less plausible
it is to assume that current output and price variations are unobservable
and to suppose that nominal wages are not adjusted. It is comforting to
note that similar results can be obtained in models with serially correlated
disturbances for which it seems more natural to take the equilibrium period
to be a quarter.

It has been emphasized that in order to decide between alternative
pure policy regimes and in order to implement more complicated financial
policy regimes that involve rules for changing policy instruments, the
authorities need a considerable amount of information. In particular they
must know the nonstochastic coefficients of the economic structure and the
parameters of the joint distribution of additive disturbances. In studies
which attempt to give empirical content to analytical frameworks of the
same general type as the one used here, estimates of the relevant coefficients
and parameters from existing econometric models have been employed. ‘There
is evidence to suggest that this approach can yield useful results 2! Of

course, such a procedure is open to the objection that this type of analytical


-36-

Some of the more obvious pitfalls encountered in attempting to
interpret changes in the consolidated balance sheet of the financial
authorities are well recognized and can be avoided by an alert obsexver.

A balance sheet must be presented in terms of a single unit of account,

for example, home currency units. If the home currency value of the
authorities’ foreign currency securities or of other reserve assets such

as gold, Special Drawing Rights (SDR's), or International Monetary

Fund position changes, the home currency value of: reserves- ehanges

without any intervention policy actions. Such "valuation changes" ust

be removed to arrive at the relevant changes in reserve totals. New
allocations of SDR's lead to changes in reserves when no intervention policy
action has occurred, so these must be taken out. Increases or decreases

in foreign currency assets matched 'by increases or decreases in liabilities
denominated in the same foreign currency lead to changes in gross reserves
but not net reserves. It is changes in net reserves that constitute inter-
vention policy action. The foreign currency denominated Carter bonds issued
by the U.S. Treasury are examples of the type of foreign currency borrowing
by the financial authorities which must be included in calculations of net
reserves. Arriving at a net reserve figure is sometimes tricky because

a country's foreign currency borrowing, say, by the Treasury may be reported
at a different point on the consolidated balance sheet than its foreign
currency assets held, say, by the exchange stabilization fund,

Less obvious pitfalls remain, Outright forward exchange contracts
entered into by the financial authorities are "off balance sheet items" and

information about them is not usually available, at least to most private


~A4e

In section III it is assumed that

m= nm, /x, + m3 > by = k@, + ny)/x, + km, (A13)
which can be rewritten as
(CL - k)/k] (my + m3x,) >n). (A14)

This condition is more likely to be satisfied the smaller k, the proportion
of wealth minus money demand allocated by residents of both countries to
home currency securities; the larger TM35 the effect of an increase in home
output on home money demand; the larger Xy> the increase in home output
associated with an increase in the price of the home good; and the larger
(smaller) m(n)), the effect of an increase in the price of the home good on
home (foreign) money demand.

*
In section VI it is assumed that Ye = Ve where

y,

- - eo -
et ela (l - h) + athly + at(y + ¥) + 8G - cat + heat FH),

* =. = * * = * =
Ve cfa (1 -h)- axh]Y +h'(y¥+ Y) + h(1 - ca)¥ + (1 - h)c(M + B).

If in the equilibrium at which the approximation is made home and foreign
output are equal when measured in the same units (Y = ¥ so that h=1 - hh),
the responsivenesses of the desired ratio of wealth to income to the two
expectec. real interest rates are equal (a, = ax), and the total of home
currency assets is equal to the total of foreign currency assets when both
totals ere measured in the same currency (M+ B= N+ F), then the effects
of a depreciation of the home currency on the demands for home and foreign
output are equal in absolute value GO, = 3) Y (M+ B) can be compared

*
with Y (N + F) in the equilibrium at which the approximation is made because

12

E=b=P=1,


Bo

X

Xo
Mo

Bo

Xi

Figure 1


*(PUPTIOH WIA0N iWeprezsuy) Ueuyog uosg Jo TOO UT

‘skessq :squowkeg JO oouejeg oy} pue sejey odueyox’ O1q4TXO Ta ‘(*Spe)

‘qe8zaqeTpury *d setzeyg pue ueudty *g uyor ut ,,‘seToITQ snonjzaTA pue
snotora pue AdTTOq UOTIBZTTTGeIS, (1861) ‘AeA BUuUY Of pue ‘DO AtUaH SYSTTTEM

-n’-


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*[tady ‘sotwouocg AzejeuoW. JO TeUINOL ,,‘squowesueray KreQouo_
quering tepuq Aot[og Areqeuoq Jo Yonpuog ayy, (8/61) ‘°H UPTIV ‘29Z7TOW

*Aqne ‘ueqshg aaresoy

[elapeq ay3 JO sroursa0cg jo preog ‘¢gT ‘ou ‘siedeg uotssnosTg eoueUTY

yeuotjzeureqUy ,,Sesueyoxy pzeMiog pue jodg 203 yeyzeW ey? pue ‘eTWaIg ySTY
Ssuotqeqoedxq yeuotjzey,, (0861) fuojeT3urg *f yQouusy pue *y preyoty fasoayq

*(sseig ATsreatug
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Kuouodg FOEIFTOT SUL (761) ‘*spe ‘e33TM “| PIeTITM pue “gq puomsey ‘erquoq

*yorey
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FOYT UOAQ TPUTIAO,, (€261) ‘POPTTEM TION pur YoUENW seMoYT ‘uYyor ‘usxerey

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*Z *ton ‘Koto ot1q4ng

uo seT19g eDUeTeZUOD ejseYyooy-eT8eureg ‘sjzi10dxq ABoTOuyoe, pue Azoeyy

Jorquog ‘seToTTog Teutado ‘(*spa) ‘zezITeW °*H UeTTY pue JeuUNzg [1ey UT

ufkot[og ArejauoW uny—Jz0yg UT uoTIeMIOJUT ABT{TxnNy BUTIE3TTZ UO, (LL6T)
399118) oTUUOg pue Arteg souRL YITM AeTSUT] *y Tejeq pue *Yy UYOr ‘xouUErquoTEY

*uoTIeILessTp [e10JD0p peyst{qhdun ‘AjrTsreatuQ ate, ,,‘wezsks AreJOUOW
[euoT}eureUT ey; pue AoUsTOTZZq ButTyeMADTIOg, (6/61) *T2BUSTH'*D ‘sau0L

“key ‘MoTAey oTMOU0Dg
UedTiomy ,,‘seTwoUCdy uedQ UT SeTOTTOg TeTOURUTY, (6/61) ‘°M eTed ‘uQsaopudq

*EL *T0a ShoTTOd OTT qGng UO satizag sdUerezUOD

Aeysoyooy-eTZeurey “sseo01g ADTTOg 9yz pue suoTInjtysuy Are OUCH

*(° spe) ‘20Z3129W °H UBT TY pue TeuUNag Taey UT ,,‘juemM0D y ITT TqQetsey
aqey esueyoxy Zutonpey 103 sjuswesuerzy ButzAyeuy,, (0861) ‘°m eTeq fuoszepusg

*Sutmooyzz03 ‘Amoucdg [TPOTITTOd JO [eUANOL
uf Stskeuy ITaZauoucsg uy :sezey jodg eanyng Jo s10jz0tpeig Tewt3do
se soyey e8ueyoxy PAPMIOT,, (0861) ‘AOTAPOH “fF Jteqoy pue *g sie] ‘uasuey

*(sseag O8edTYD JO

Aqtsreayun :08eotyg) waysks AxeyouoW TeuoT}eUTE JU] oy pue SaTOT]Og

Zaeyouoyy TBuoTIeN *(*pe) ‘seqtTy °Z Ieqoy UT ,,‘seTOTTog AreJOUOW Jo
souspusdepzequy, ey} pue suayshs ojey eSueyoxY oATIeUIEITY, (7/61) ‘TYOTOY ‘epemeYy

*(@2TFJO BuTIuTAg

Juewuzeacy *s*n :u0zZuTYseM) sqUewisnt py. ajey esueYyoXY JO. 830937q. OUL

‘(*spa) ‘heusemg *¢ paeyoTy pue annoy *q stuueg *yIeTD °g 1030 ut

u{S278Y VBueyoR” OTqtxeTZ pue pexIg Jepug sjJessy o1}sewog pue ustez0g
UT suoTzeiedg yUeg TPI3U2D,, (//61) ‘UOSIepueH *M eTeq puke soURT fU0II1TD

-@-


-F5-

27/ If B'B' were flatter than x, there would be more variation in home
(foreign) output under floating (fixed) exchange rates than under fixed
(floating) exchange rates.

28/ A game theoretic approach to this and other policy conflicts in open
economies has been employed by Hamada (1974), Jones (1979), and Niehans (1968).
29/ Black (1980) discusses the issues addressed in this section among others.
30/ For a more detailed discussion of this equivalence see Girton and
Henderson. (1977).

31/ This approach is used by Tinsley, Spindt, and Friar (1980).

32/  Kalchbrenner, Tinsley, Berry, and Garret (1977) describe a number of

refinements.


-23-

policy whereas under similar assumptions in a closed economy a money supply

16/

constant policy dominates an interest rate constant policy.— An aggregates
constant policy is superior (inferior) to a rates constant policy for large
values of the degree of substitutability between home and foreign securities
(the responsiveness of home good demand to changes in the exchange rate).

Tae authorities should proceed differently in a second environment in
which tne only difference is that they can observe and respond to current
movements in the two financial variables not chosen as policy instruments 22/
In this environment one policy instrument can be kept fixed. However, the
authorities should choose and announce a linear rule which tells them how
to vary the other policy instrument in response to deviations of the remaining
two financial variables from their expected values 28/ These remaining
two financial variables can be regarded as information variables since
deviations in these variables from their expected values provide a basis
for making estimates of the current values of the disturbance terms. In
general, the coefficients of the decision rule will be functions of both the
coefficients of the model and the parameters of the joint distribution of
the additive disturbance terms. While the decision rule is the same period
after period, the value of the variable policy instrument is changed from
period to period since the authorities can learn something about the shocks
in the current period from observations on the two information variables.

It has been assumed that the authorities change a financial policy instrument
in response to current information while the nominal wage remains fixed

at a value set before other market meet. That the authorities rather than
private agents should adjust to current information even if it is available

to both sets of agents seems reasonable since the costs associated with


-41-

framework calls for exact knowledge of coefficients and parameters, not
estimates. Much progress has been made in modifying the analytical framework
to take account of the fact that only estimates of coefficients and
parameters will ever be available to the authorities 22/

In this paper intervention policy has been viewed as part of macroeconomic
financial policy in open economies rather than as a tool for stabilizing
so called disorderly foreign exchange markets, While the empirical relevance
of intervention policy for financial policy has not been firmly established,
the interest of the authorities in intervention policy suggests that it is
worthwhile to make clear what role it might play. More empirical work
attempting to isolate the effects of intervention policy is badly needed.
It has been argued that managed floating would be best from the viewpoint
of individual countries, Further theoretical work that determines whether
this conclusion holds when more attention is paid to the problem of
distinguishing between permanent and transitory disturbances would be helpful.
It has also been emphasized that the authorities in various countries might
find it in their interests to manage the float differently. How conflicts
that arise over the proper overall stance of intervention are resolved
and how they could be resolved more satisfactorily is another promising

area for further research,


it is returned again to its original value before the operation is complete.
Suppose the authorities sell a foreign currency security to private agents.
They obtain foreign money but sell it back to private agents for home money,
temporarily reducing the home money supply. However, they then purchase a
home currency security from private agents, thus restoring the home money
supply to its original value, in order to complete the intervention operation.

There is a widely held view that if the authorities sell a foreign
currency security, say, in order to prevent the home currency from depreciating,
they reduce the home money supply either unintentionally or intentionally.
From the description of an intervention operation above it is easy to
see that the home money supply could be lower if the authorities did rot
complete the intervention operation by purchasing a home currency security.
Failure to complete the intervention operation would never be unintentional
That is, if the authorities allow the home money supply to remain lower, it
is because, given the other choices available to them, they want it to be
lower. The view is taken in this paper that if the authorities sell a foreign
currency security and do not purchase a home currency security with the home
money they acquire, their action can most clearly be understood as being
a combination of the intervention operations and monetary operations defined
above. If this view is adopted, only monetary operations change the home
money supply.

It is interesting to define intervention operations in the way suggested
above and to study the effects of such operations only if home currency and
foreign currency securities are imperfect aubstitutes in the portfolios of

private agents, If these two types of securities were perfect substitutes, an


-34-

D, = ane * Do, = bi + bys
1 Yy¥y ~ YyVye 3.7 Yebs * Meth?
D, = [bYG# ~ y$) + bL yy - yy] D, = vgbh + bY
27 Mylty 7 FY ary ye 4 vy?
=p?!
Ay bed, + yoo
ays . . 2 2 2 2
Dy» Doo Des Dy» and Ay are all positive, Thus, if = F ot 0 and °% > 0,
2 2 2_ 2_ . 2
then oy pp, let and en < %§l pr: If > % = 0 and either O, or
2 _ _ 2 2 . .
o, > 0, then 0 = len < oy pr and 0 = O€ | py < ai By manipulating
the coefficients of oe in (22), (23), (24), and (25) it can be shown that
if 3 = a = o = 0 and oe >.0, then Orley oler but Flop z tle when
bly: ae z bie « When Daye is greater (less) than b! ey | the B'B' schedule is steeper
Y’y*

(flatter) than the xx schedule in Figure 3 since
CD gigs — E/E = (bEFE - PBy)/ CLP
VII. KEEPING TRACK OF INTERVENTION POLICY

This section is a description of some of the difficulties encountered
by financial authorities and private agents in trying to keep track of the
overall stance of intervention policy which is the net result of the
intervention policies in many countries 22/ In the last section examples were
provided of two types of disturbances for which the authorities in two
countries could agree on the overall stance of intervention policy and one
type for which they would have different views about the appropriate overall
stance of intervention policy. Such examples make it clear that the authorities

in a given country need information about other countries’ intervention operations

in order to negotiate effectively:-with the authorities in those countries


\ -20-

As an example of a permanent disturbance consider a once and for all
shift up in the demand for the home good. Of course, if private agents know
that this disturbance has occured and take it into account when setting the
nominal wage, it has no effect on the average levels of output and employment.

Now suppose that private agents do not realize that this permanent
disturbance has occurred. It seems reasonable to assume that the nominal
wage would not be changed, at least for a while. During this time the average
real wage would be lower and the average level of output would be higher
than their full employment values under either an aggregates constant or a
rates constant financial policy regime. The results regarding the effects
of transitory disturbances under alternative financial policy regimes carry
over with minor modifications to cases in which a permanent disturbance is
also present. For an unrecognized permanent disturbance in the market for
the home good (markets for home money and home currency securities) the
deviation of average output from its full employment level is smaller (greater)
under an aggregates constant policy than under a rates constant policy.

After a while private agents would recognize that levels of output above

the full employment value were being observed more frequently than would be
suggested by what was known about the joint probability distribution of the
transitory disturbances, would conclude that the economic structure had
changed, and would change the nominal wage. Important research on how private
agents would go about trying to separate permanent from transitory disturbances
under various sets of conditions is well under way, but it is not reported

13/

on here —'


-26-

values of 8 represent decreases in the demand for the foreign good matched
by increases in demand for the home good.

Foreign output must also be equal to aggregate supply which depends
negatively on the Clogarithm of the) real wage measured in terms of the

foreign good:

¥ =k) - HG - 2). (15)
The (logarithm of the) real wage is equal to the (logarithm of the) foreign
nominal wage Gi) minus the (logarithm of the) price of the foreign good. It
is assumed that the nominal wage is set each period before other markets meet
at the constant value ®) which would insure that employment would equal its
desired level and output would equal its corresponding full employment level

*
(¥,) if all disturbances were zero:

*
w

2%

. (16)

Equilibrium schedules for the home good, the foreign good, and home
currency assets are shown in Figure 3. In order to construct these schedules
it is necessary to eliminate p and > from these markets with the use of the
relationships between p and Y and between > and ¥ implied by the aggregate
supply functions when w and . are set equal to w and 3 XoXo is an equilibrium
schedule for the home good. An increase in Y which reduces excess demand must
be matched by a rise in ¥ which increases demand. i is an equilibrium
schedule for the foreign good, An increase in Y which raises demand must be
matched by a rise in ¥ which reduces excess demand. The XX schedule is steeper
than the XX schedule, The absolute value of the reduction in excess demand for
the home good caused by a rise in Y which increases home saving as well. as

home imports exceeds the increase in excess demand for the foreign good

caused by a rise in Y which increases not only foreign exports (home imports)


-22-

of the two financial variables they do not set when implementing their
monetary and intervention policies.

Suppose the authorities operate in an environment in which they know,
or have unchanging beliefs about, the nonstochastic coefficients of the three
linear market equilibrium relations and the joint distribution of the
additive disturbance terms, Suppose also that they cannot observe output and
the price of the home good, and cannot observe or, at least, do not respond
to current movements in the two financial variables they do not set when
implementing their monetary and intervention policies. In this environment
it makes sense to compare alternative pure financial policies under which
values for the two financial variables chosen as policy instruments are set
before markets meet each period and are not changed once markets meet. The
aggregates constant and rates constant policies considered above are examples
of such pure financial policies. Once a policy is found to be superior it is
followed period after period unless there are changes in the parameters of

the system or the joint distribution of the stochastic disturbances,24/

The analysis of section III suggests one kind of conclusion; for

example, given the coefficients of the system and all of the other parameters
of the joint distribution of the disturbances, there exists a variance of the
disturbance term in the market for the home good large enough to insure that an
aggregates constant policy leads to lower expected loss than a rates constant
policy. Additional conclusions must be based on explicit calculations of
expected losses. Suppose that the three equilibrium relations are normalized on
income and that the variances of the normalized disturbances are equal 22/ An

aggregates constant policy may or may not be better than a rates coristant


-35-

about what actions are required in order to achieve a desirable overall
stance for intervention policy, Private agents also need information about
intervention policy so that they can base their decisions on reliable
forecasts of financial variables including exchange rates, Up to this point
it has been assumed that the authorities in each country hold their
international reserves only in the form of stocks of government securities
denominated in the currencies of other countries and that changes in these
stocks reflect the intervention policies of the authorities. In this section
additional forms of international reserve assets are considered. Changes
in the stocks of these assets as well as certain other transactions described
below can also reflect the intervention policies of the authorities.
Unfortunately keeping track of the intervention policies of the
authorities in all the relevant countries is often not an easy task either
for the authorities themselves or for private agents. Of course, one source
of difficulty is that data on the balance sheet of a country's financial
authorities, the consolidated balance sheet of the treasury, the central
bank, and the exchange stabilization fund, often become available only with
a lag, but this is not the most important source, Far more important sources
of difficulty are that the balance sheet is often not presented in a way
which makes it easy to isolate and determine the net result of intervention
policy actions of the financial authorities which are reflected in different
places on the balance sheet and that not all policy actions properly regarded
as intervention policy actions are even recorded on the balance sheet of

the financial authorities.


-17-

Two other possible sources of stochastic shocks to equilibrium are
(1) shifts in home residents’ preferences between home money and foreign
securities which cause movements in the MM schedule and (2) shifts in home
residents' preferences between home money and home securities which cause
movements in both the MM and BB schedules. In both these cases, a rates
constant policy leads to less variation in output than an aggregates constant
policy. Under a rates constant policy the transmission of financial market
disturbances to the market for the home good through interest rate and

exchange rate changes is prevented.

The Derivation of the Results

This subsection contains a formal derivation of the results of the
previous subsection, It is convenient to work with the model in a somewhat
more compact form, (2) and (3) are substituted into (1), and (5) is substituted
into (4). The modified version of (4) is solved for p, and the result is
substituted for p wherever it appears in the other equations, Each of these
other equacions with the disturbances set equal to zero is subtracted from

the same equation with the disturbances free to take on any value to obtain

a a “
O=~y¥-yoityer+a+B, (8)
M= mY -mitmetry+é, (9)
Be- by¥ + biitbe-yte, (10)


Home money demand depends positively on the price of the home good, the
exchange rate, the price of the foreign good, and home output. Increases
in all of these variables raise the transactions demand for money balances.
Money demand depends negatively on the nominal interest rate on home currency
securities and on the expected nominal return on foreign currency securities
measured in home currency which is equal to the nominal interest rate on
foreign currency securities plus the expected rate of depreciation of the
home currency. Money demand depends positively on two disturbance terms,
y andé. Positive values y (6) represent shifts of home residents' asset
preferences toward home money and away from home currency securities (foreign
currency securities).

The supply of home currency securities (B) must equal the demand for
these securities by both home and foreign residents:

B=b -~bp-b,p-baY+bi-b,d+e-e)

0 1 2 3 4 5
(7)

(Gi-F+e)- db + doe - bY
+ boi - e + e) - bp + bee - gy ~ Yt &

It is assumed that both home and foreign residents determine the home currency
amount that they will hold in securities by subtracting their money demands
measured ‘in home currency from the home currency value of their wealth and

allocate tthe same fraction of this amount to home currency securities. The

resulting demand for home currency securities depends negatively on the prices

of the hone and foreign goods, on home and foreign output, on the expected
nominal return on foreign currency securities measured in home currency, and

on the nominal interest rate on foreign currency securities, Increases in

prices and outputs raise the transactions demands for money of both home and


-32-

somewhat more compact form. (2) and (3) are substituted into (1) and (14);
(5) is substituted into (4), and (16) is substituted into (15). The modified
versions of (4) and (15) are solved for p and 3 respectively and the results
are substituted for p and > wherever they appear in (1), (6), (7), and

(14). The further modified versions of (1) and (14) and the sum of the
modified versions of (6) and (7) with the disturbances set equal to zero

are subtracted from the same equations with the disturbances free to take

on any values, and i is set equal to zero to obtain

a “ +
O=- yy + ye + ya¥ ta +8, (17)
es ** *
O= yy¥ - y,e - yE¥ - B, (8)
~ a ms '%
= + -
B byY + ble - DAY +6 +. (19)

B' is the deviation of B from its expected value in addition to the deviation

that is equal in magnitude and opposite in sign-te the deviation of: the money

a a «
supply from its expected value (B = B' = MJ, ‘Vy and y, are defined: above, and

= *

= - - ‘em
y¥ = y+ Ly, - Gy + y3)C - DDI /x,, by =m - by,
* * * =. * *
eo - ts
ye=s+y, + ly, + Cy, + y,)(1 - h) + ¥5)/x,, bl =m +b,
* * = te * *

= - - ts
Ye = ¥, + Yo. - Bh) = yah + ys, > b)/x, + b>.
*

* * *
yz tly, ~ (yy + yghl /x,,

It is assumed that income, relative price, and wealth effects outweigh

. : *
possibly "perverse" expected real interest rate effects so that Yys Yoo and


-29-

similar argument can be employed to demonstrate that the demand shift
under consideration causes xx to shift farther to the right than XX at a
constant ¥ (aga, > ay2,)- A series of demand shifts of the type under
consideration would trace out the xix, schedule in Figure 3.

Now consider the effect of a depreciation of the home currency. This
depreciation raises demand for the home good and lowers demand for the
foreign good. If these two demand effects were equal in absolute value,
depreciations (and, of course, appreciations) would also trace out the
EK schedule in Figure 3. In many two-country models the two demand
effects are necessarily equal in absolute value when depreciations in the
neighborhood of balanced trade are considered because the only effect of a
depreciation on the markets for the home and foreign goods is to raise the
relative price of the foreign good. This increase leads to changes which
are equal in absolute value in the markets for the two goods. However, in this
model a depreciation affects expected real interest rates and real wealth in
addition to the relative price of the foreign good, so the two demand effects
of the depreciation are not necessarily equal in absolute value. There is a
set of quite stringent assumptions which, in combination with assumptions
already made, is sufficient to insure that the two demand effects are equal
in absolute value 24/ In order to simplify the analysis and to make the
results readily comparable to those of other models that set of assumptions
is adopted here .22/ Given these assumptions depreciations (appreciations)
of the ‘home currency move the XX and xx schedules down (up) so that they
continue to intersect on the UK, schedule,

Now the analysis of the effects of a shift up in the demand for the

home good matched by a shift down in the demand for the foreign good which is


~6-

from the single foreign good. Home output (Y) must be equal to aggregate

demand for the home good:
= (wad T+y,(e+p-p)+ taeh. (1)
Y= yg + y,(¥ +¥) - yor - yar + y,(e +p - p) + yce — yep ta +B.

Here, and in what follows, all coefficients except intercept terms are positive.
Aggregate demand depends negatively on the expected real interest rates

on home currency securities (r) and on foreign currency securities () and on
the (logarithm of the) home currency price of the home good (p). Increases

in expected real interest rates raise home and foreign saving. Increases in
the price of the home good reduce home and foreign real wealth measured in
terms of the home good, and therefore, raise home and foreign saving .£/
Aggregate demand depends positively on home output, on foreign output @),

on the (logarithm of the) exchange rate (e) defined as the home currency

price of foreign currency, and on the (logarithm of the) relative price of

the foreign good (e + > - p), where > is the (logarithm of the) foreign
currency price of the foreign good. Increases in home and foreign output

raise income at home and abroad and, therefore, spending on the home good.2/
It is assumed that the marginal propensities to consume the home good (y),
to consume the foreign good Gs» and to save (s = 1 - 7 i) are the same
in both countries and are all positive .o/ A depreciation of the home currency
(rise in e) increases the home currency value of foreign currency assets
thereby raising home and foreign wealth and reducing home and foreign saving.
An increase in the relative price of the foreign good shifts home and
foreign spending toward the home good and raises foreign income measured

in terms of the home good thereby stimulating foreign spending on the home

good. Aggregate demand depends positively on two disturbance terms, a and8.


intervention operation as defined above would have no effect on the economy.
Financial. policy would consist only of monetary operations, and whether the
money supply were changed through exchanges for home currency securities or
for foreign currency securities would be of no consequence. There is no
general agreement among economists that home currency securities and foreign
currency securities are imperfect enough substitutes that intervention operations
of a reasonable size have any important or lasting effect on the economy.
Empirical evidence is accumulating on this issue, but it remains unresolved .2/
The analysis of this paper proceeds under the assumption that home and
foreign currency securities are imperfect enough substitutes for one another
to warrant inclusion of intervention policy in the study of open economy

financial policy.

III. TRANSITORY DISTURBANCES AND FINANCIAL POLICY RESPONSES IN A SINGLE

OPEN ECONOMY

In this section a discrete time stochastic model of a single open
economy in which agents have rational expectations is employed to analyze
the effects of some transitory disturbances to macroeconomic equilibrium
under two pure financial policy regimes, an aggregates constant policy and
a rates constant policy .4/ In the first subsection the model is described,
and the results are presented and explained! In the second subsection the

results are derived more formally.

The Model and the Results

In the real sector of the economy attention is focused on aggregate

demand for and aggregate supply of the single home good which is different


-18-

where

* =
yisty, + ly, + (yy + y3)h + y5]X)> b= by/x, + b3,

Y
Ye 7947 YL --B) + yg + ys, bp = bg +P

my = m/x + m5, by = bs + by + by.
a, = m, + ms

A hat over a variable indicates the deviation of that variable from its
constant expected value. It .is assumed that relative price and wealth effects
outweigh possibly "perverse" expected real interest rate effects so that

Ye is positive. Foreign variables do not appear in (8), (9), and (10) because
they are fixed by the foreign authorities.

The difference between the slopes of the MM and BB schedules of Figure 1 is
GID) vg - G/Y) a3 = (myb; - bym,)/(bm,). (11)

It has been assumed that my > by. This assumption is sufficient to insure

that the MM schedule is steeper than the BB schedule since b, > m, and therefore
b; > m,. The intuitively appealing result that an increase in the demand for
the home good (a > 0) causes the home currency to appreciate under an

aggregates constant policy is obtained if and only if the MM schedule is steeper
than the BB schedule.

The variances of home output (og) under a rates constant (RC) and an

aggregates constant (AC) financial policy regime are given by


The (logarithm of the) real wage is equal to the (logarithm of the) nominal
wage in the home country (w) minus the (logarithm of the) price of the home
good. It is assumed that private agents want to supply each period a given
amount of labor which does not change when the real wage changes. If this
amount of labor is fully utilized in production, the full employment level
of output (Y,) results, However, since the process of wage negotiation

is costly, private agents enter into a labor contract each period before
other markets meet, They agree to supply whatever amount of labor firms
want at the prevailing real wage. Thus, output can exceed its full employment
level if the real wage is low enough. They also agree to set the nominal
wage at the constant value (w) which would insure that employment would

equal its full employment level if all disturbances were zero:
wew (5)

In order to calculate w, private agents must know the parameters of the
economic model and the announced values of the financial authorities' policy
instruments.

In the financial sector of the model, attention is focused on the
markets for two assets, home money and home currency securities. Home
(foreign) residents hold home (foreign) money but no foreign (home) money.
The supply of home money (M) must equal the demand for home money by home

residents:

* * —
M= mp) +mp+m(e +p) +mY-mi-m(ite-e)+y+6é. (6)


=24-

changing a financial policy instrument are much smaller than the costs
associated with renegotiating the nominal wage.22/

The implication that one financial instrument, for example the
exchange rate, can be kept fixed depends crucially on the assumption that
. the authorities and private agents are concerned only about: expected: squared
deviations of Y from ¥_ If the authorities and private agents were also
concerned, for example, about expeeted squared: deviations: in interest-sensitive
consumption from some desired level, optimal financial policy would involve
variations in both financial policy instruments, so the exchange rate would have
to vary no matter whether it was chosen as a policy instrument or was used as
an information variable, Thus, in general circumstances it will always be

optimal for an individual country to opt for a managed floating exchange

rate rather than a fixed or freely floating exchange rate.

VI. TRANSITORY DISTURBANCES AND THE SCOPE FOR AGREEMENT ON FINANCIAL
POLICIES IN A TWO-COUNTRY WORLD ECONOMY
Up to this point it has been assumed that the authorities in tthe
foreign country have enough information and a sufficient number of policy
instruments to set foreign output and the price of the foreign good in
addition to the interest rate on foreign securities, It seems more natural
to suppose that the foreign authorities are no better informed than the
home authorities and, therefore, cannot fix foreign output and the price
of the foreign good so that transitory disturbances such as those considered
above affect outputs in both countries of the two-country world ecoaomy.
Here the model of section III is extended to incorporate this assumption.2//

For simplicity it is also assumed that the authorities in each country use


International Finance Discussion Papers
Number 202

February 1982

THE ROLE OF INTERVENTION POLICY
IN OPEN ECONOMY FINANCIAL POLICY:
A MACROECONOMIC PERSPECTIVE

by

Dale W. Henderson

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an

acknowledgment by a writer that he has had access to unpublished material)
should be cleared with the author or authors.


Footnotes

* Economist, Board of Governors of the Federal Reserve System. This paper
was presented at the Pennsylvania State University Conference on the Political
Economy of Domestic and International Monetary Policy held in June 1980 and
will appear in Lombra and Witte (1982). Discussions with Donald Adams,
Matthew Canzoneri, Michael Dooley, Jo Anna Gray, Kenneth Rogoff, and Jeffrey
Shafer led to improvements in the paper. The analysis and conclusions of
this paper should not be interpreted as representing the views of the Board

of Governors of the Federal Reserve System or any other member of its staff.

1/ There is no discussion of the use of intervention policy to counter
“disorderly markets" or such features of exchange market dynamics as runs

or bandwagons. Shafer (1982) addresses these issues among others.

2/ Dooley (1979) provides a thorough discussion of intervention operations.
Girton and Henderson (1977) compare the effects of intervention operations

and monetary operations in a model of financial markets.

3/  Frankel's (1979) evidence suggests that home and foreign currency
securities are perfect substitutes. Obstfeld (1980), Hansen and Hodrick (1980),
and Meese and Singleton (1980) present evidence that is consistent with home
and foreign currency securities being imperfect substitutes. When Obstfeld
simulates an intervention operation, he finds that the effects are quantitatively

significant but relatively short lived.

4/ Mundell (1968) and Stein (1963) were pioneers in the analysis of open

economy financial policy, Their analysis is extended by Tower and Willett (1976).
A recent contribution to this analysis has been made by Kaminow (1979).

Bryant's (1980) analysis of the effects of disturbances under alternative
financial policy regimes is similar to the one of this paper. The approach

used here is also employed in Henderson (1979 and 1980).


-1l-

and the price of the home good in the current period. They can choose as
policy instruments, and set values for, any two of the four financial variables
M, B, i, and e, The values of the other two variables are determined by

the model, The discussion of the home authorities' balance sheet in section II
implies that if the home authorities seek to change B without changing M,
they must: also change the supply of foreign currency securities available

to the public through intervention operations. It is assumed that the home
authorities follow either an aggregates constant policy or a rates constant
policy. Under an aggregates constant policy M and B are kept unchanged,
while under a rates constant policy M and B are allowed to vary to keep i

and e constant. Under each policy regime, the home authorities set and
announce the same values for two financial policy instruments before markets
meet each period; that is, they either do not observe or elect not to

respond tio movements in the financial variables for which they do not set
values. The announced values of the two financial policy instruments can

be chosen arbitrarily because private agents set the nominal wage so that the
expected value of Y is equal to Ye given these announced values. In this

and the next two sections it is assumed that the foreign authorities can
observe the level of foreign output ® and the price of the foreign good

(p) in the current period and that they act to keep these variables as well
as the interest rate on foreign currency securities ) fixed at constant
values denoted by ¥, z and ¥/ Given the nature of the disturbances and
the behavior of the authorities, it is rational for agents to expect in any
period that the values of the price of the home good and the exchange rate

in the next period will be equal to the constants p and e, respectively, and


-10-

foreign residents partly at the expense of their demands for home currency
securities. It is assumed that both home and foreign residents regard the
three assets they hold as strict gross substitutes. Therefore, the negative
effect of an increase in the expected rate of return on foreign securities

(the nominal interest rate on foreign securities) on the demand for home
securities resulting from the increased relative attractiveness of foreign
currency securities dominates the positive effect on this demand

resulting from reduced home (foreign) money demand. The demand for home
currency securities depends positively on the nominal interest rate on home
currency securities, on the expected nominal rate of return on home cu:rrency
securities measured in foreign currency which is equal to the nominal interest -
rate on home currency securities minus the expected rate of depreciation

of the home currency, and on the exchange rate. Increases in the nominal
interest rate on home currency securities (the expected rate of return on

home securities) make these securities more attractive relative to foreign
securities and reduce home (foreign) money demand. Therefore, by > m,. It

is assumed that the postive effect of an increase in the exchange rate on the
demand for home currency securities resulting from the increased home currency
value of world wealth dominates the negative effect on this demand resulting
from increased home currency denominated demand for both home and foreign money
for transactions purposes. The demand for home securities depends negatively
(positively) on the disturbance term y (€). Positive values of y (€) sepresent
decreases (increases) in the demand for home currency securities matched by
increases (decreases) in the demand for home money (foreign currency securities).

Now the behavior of the home and foreign financial authorities is

described, It is assumed that the home authorities do not observe home output


~A2-

* *
r,r, and A +A are given by

- = x *
r=i-h222.l a - ny eet+ bd), (43)
P E 3
- - = x o*
* * - - - =, - -
r=t+E2#-pPe?_-a-pme=#+2 4, (a4)
P E z
*
A+tAZM+BHtE(N+F). (A5)

The aggregate supply equations for the home and foreign goods are given

by
y=x®, x, =-X', (A6)
x ok 4 * *,
¥=xQ, eo - Re. (AT)
P

*
It is assumed that X' and X' <0, so both the approximation coefficients are
positive,

The asset market equilibrium conditions are given by

n= ae (a8)
Q
m =L-m, m= 1), m =- Los
m, = (L - L,¥)(1 - h), ms = - Ly,
* ED x E-E *
EN = UC Y,i-“—o, ), (A9)
- * ** i. _ * _ *
ny = Gd - L,Y) > n= L,, Ln Ly,
* *
ny =L-n, no =- Ly,


-31-

shifts down and XX and x shift up along xi xk, until a new equilibrium
is reached along the line segment ag as above a. Thus, for shifts in
asset preferences between home currency and foreign currency assets there is
less variation in both home and foreign output under fixed exchange rates,
and there is no policy conflict.

Finally consider a shift up in home demand for the home good at the
expense of home saving. Suppose the initial equilibrium is at a: This
disturbance initially affects only the XX schedule which is shifted from

X,X, to X,X.

‘o%o Xi" Under fixed exchange rates the new equilibrium is at age

Home output rises, and as a result of induced home demand for foreign goods,
foreign output rises. When the B'B' schedule is steeper than the xx
schedule, there is pressure on the home currency to appreciate 26/ Under
fixed exchange rates this pressure is countered with intervention operations
which cause the B'B' schedule to shift down from BoB. The new B'B'
schedule (not shown) passes through ag- Under flexible exchange rates the
home currency appreciates dampening the rise in home output but exaggerating

the rise in foreign output. The B'B' schedule shifts down, and the XX and

x * x * Ox
XX schedules shift up along the new XXXK schedule XK, XX, until a new

equilitrium is reached on the line segment aya above age Thus, for shifts
in demand for the home good corresponding to shifts in saving there is more
variation in home (foreign) output under fixed (floating) exchange rates

than under floating (fixed) exchange rates 22/ and there is a policy conflict .28/

The Derivation of the Results

This subsection contains a formal derivation of the results of the

previous subsection, As before it is useful to work with the model in a


-F2-

5/ This model is a partly linear and partly log linear approximation to a

non linear model sketched out in the appendix, Explict expressions for

the approximation coefficients are presented in the appendix.

6/ In order to consider a fixed interest rate policy in the model of

this section under the assumptions about the behavior of the foreign autaorities
spelled out below or to consider fixed interest rate policies in the -two-country
model of section VI, it is sufficient but not necessary to assume that real
wealth enters the aggregate demand function of at least one country and that
tax liabilities corresponding to government securities are not perfectly
discounted. For an explanation of why such assumptions are sufficient in the
context of a closed economy model, see Canzoneri (1980). For an explanation

of why they are not necessary, see Canzoneri, Henderson, and Rogoff (1981).

2/ ¥ and ¥ can be added together because units are chosen so that the

relative price of the foreign good is one in the equilibrium about which

the approximation is made.

8/ Home and foreign residents are assumed to have the same tastes so that
shifts of wealth between countries through current account surpluses and
deficits will have no effects on the variables of the model, Without this
assumption a more complicated, dynamic analysis would be required.

9/ The foreign authorities must use monetary operations and two fiscal policy
instruments, for example the level of balanced budget government spending and
its allocation between the home and the foreign good, to achieve these constant
values. Strictly speaking, it is foreign disposable income and not foreign
output that is kept constant. Turnovsky (1976) and Flood (1979) make different

assumptions about the behavior of the foreign authorities.
10/ This statement is strictly true only if it is assumed that there are "no
speculative bubbles", Sargent (1973) explains the implications of this assumption

in the context of a closed economy.


~30-

KK
equal in absolute value can be completed. The shifted XX and XX schedules

XX a XX
are X)X) an ye

point as. The shift in preferences for goods causes home output to rise

Under fixed exchange rates the new equilibrium is at

and foreign output to fall. Both of these movements tend to raise the
demand for home currency assets, so the home currency tends to appreciate.
However, the authorities undertake intervention operations, sales of

home currency securities in exchange for foreign currency securities waich
shift the B'B' schedule down. The new B'B' schedule labeled BiB) passes
through ase Under flexible exchange rates the home currency appreciates
dampening the rise in home output and the fall in foreign output. The B'B'
schedule shifts down and the XX and xe schedules shift up along xi) until
an equilibrium is reached somewhere on the line segment ag a5 above ase Thus,
for shifts in demands between home and foreign goods there is less variation
in both home and foreign output under floating exchange rates, and there is
no policy conflict.

Now consider a shift in asset preferences toward home currency assets
and away from foreign currency assets. For convenience, suppose that the
initial equilibrium is at age The change in asset preferences shifts the
B'B' schedule from BiB) to BoBg: Under fixed exchange rates the new
equilibrium is at acs which is also the initial equilibrium. The shift in
asset preferences puts pressure on the home currency to appreciate. Under
fixed exchange rates this pressure is met by intervention operations, sales
of home securities in exchange for foreign securities, which shift the B'B'
schedule from B'B' back to B'B'. Under flexible exchange rates the home

00 rr

currency appreciates lowering home output and raising foreign output. B'B'


-7-

Positive values of a (8) represent increases in the demand for the home
good at the expense of saving (demand for the foreign good). These stochastic
variables and those introduced below to represent other disturbances are
assumed to have zero means and to be mutually and serially uncorrelated.

The expected real interest rate on home currency securities is
equal to the nominal interest rate on these securities (i) minus the
expected rate of increase in the average home currency price of the

consumption bundle of both home country and foreign country residents:
= oo *¥ *
r*i-h(p-p)-(1-h)\(e-e+p-p). (2)

h is the proportion of spending that would be allocated to the home good

by residents of both countries if all of the disturbance terms were zero.

Pp, e, and z are the constant values of p, e, and P expected in any period

to prevail in the next period. The expected real interest rate on foreign
currency securities is equal to the nominal interest rate on these securities
(es) plus the expected rate of depreciation of the home currency minus the

expected rate of increase in the average home currency price of the world

consumption bundle:

*
r:

Hoe

+e-e-hlp-p)-G-h(e-e+p-p). (3)

Home output must also be equal to aggregate supply which depends
negatively on the (logarithm of the) real wage measured in terms of the

domestid¢ good:

Ye X47 x, (w - p). (4)


-21-

Up to this point only the case of a single permanent disturbance has been
considered, Such a disturbance would not call into question the feasibility
of a rates constant policy unless it were large enough to require, for example,
the sale of most of the authorities’ foreign currency securities in intervention
operations. However, if there were a series of even moderate-sized permanent
disturbances that required the sale of foreign currency securities by the
author:.ties, such as a succession of permanent shifts in asset preferences
away fiom home currency securities and toward foreign currency securities,
a rates constant financial policy regime, even though desirable, might not
be feasible because the financial authorities might exhaust their holdings

of foreign currency securities.

V. TRANSITORY DISTURBANCES, INFORMATION, AND FINANCIAL POLICIES IN A SINGLE
OPEN ECONOMY

‘The analysis of this section proceeds under the assumption of section III
that the economy experiences only transitory disturbances. In section III
conclusions were drawn about which of two alternative financial policy regimes
the authorities should choose if all disturbances were in the home good market
or if all disturbances were in financial markets. Here it is asked how the
financial authorities should proceed when the economy is buffeted by all
of the types of transitory disturbances considered above, It is assumed that
both the authorities and private agents wish to minimize the expected
squared deviations of output from ¥,. What financial policy is optimal depends
on wha: information the authorities have about the structure of the economy,

about the disturbances to which it is subjected, and about the current values


-38-

policy stance of the authorities can not be accurately determined.

As part of their intervention policy the financial authorities
can persuade private banks or government related institutions to undertake
transactions that have the same effect as their own intervention operations
would have had, These transactions which are examples. of what some have: called
the "orgranization" of capital flows are reflected on the balance sheets
of the private banks or the government related institutions and not on the
balance sheet of the financial authorities, so it is difficult if not
impossible for other financial authorities and private agents to monitor
them, One common example of this type of transaction involves the financial
authorities and private banks in a country. The financial authorities buy
spot foreign currency from private agents. Instead of using this spot
foreign currency to buy foreign currency securities for their own reserves
they sell it to a private bank and agree to buy it back forward, sometimes
at a price more favorable than the market price, in a so-called swap
transaction. The private bank sells a domestic currency security in order
to obtain the spot home currency needed to buy the spot foreign exchange
from the authorities, The private bank uses the spot foreign exchange
obtained from the authorities.to buy a foreign currency security. Thus the
effect on the supplies of government securities denominated in home and
foreign currencies available to private agents other than home country banks is
the same as if the financial authorities had performed a standard intervention
operation, The foreign exchange exposure of the home private bank is
unchanged because its foreign currency security is matched by a forward
contract to receive home currency, and the balance sheet of the financial

authorities is unchanged because the forward contract is an off balance sheet

item.


=39-

Another common example of intervention policy not reflected in
the balance sheet of the financial authorities is directed borrowing by
government related enterprises. These enterprises issue foreign currency
denominated debt instead of domestic currency denominated debt thereby
making the supplies of home currency and foreign currency securities
closely related to government securities which are available to private
agents different from what it otherwise would have been. Foreign currency
borrowing by government related enterprises is usually matched by forward
contracts with the financial authorities.

It appears that the organization of capital flows which has occurred
from time to time over at least the past decade may now be assuming a more
important role in overall intervention policy, Innovations in such hidden
intervention that make it more difficult to detect are liable to proliferate.
These development will make the assessment of the overall stance of
intervention policy more difficult for both financial authorities and

private agents.

VIII. SOME CONCLUDING REMARKS

An important advantage of the approach used here is that it yields
suggestive qualitative results. For example, it was shown in section VI that
when disturbances arise from stochastic shifts in asset preferences, the
authorities in different countries have a mutual interest in intervening to
reduce exchange rate variability. This result helps to explain interest in
coordinated official intervention to minimize the exchange rate effects of
changes in desired portfolio composition by the oil-producing countries and

central banks of some other countries.


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-27~

Figure 3


-3-

is an extended version of the model of Section III. Since intervention
policy conflicts can arise, the financial authorities in different countries
have an interest in keeping track of the overall stance of intervention
policy. Some of the practical difficulties encountered by financial
authoriries (and private agents) in trying to accomplish this task are
discussed in Section VII. Section VIII contains some concluding remarks

about the usefulness of the analysis and some suggestions for extending it.

II, DEFINITIONS OF MONETARY OPERATIONS AND INTERVENTION OPERATIONS

The stylized balance sheet of the financial authorities in a hypothetical
country which is called the home country has the home money supply as a
liability and both home and foreign currency securities as assets. The home
authorit:ies' holdings of foreign currency securities are their only foreign
exchange reserves. At a given exchange rate, changes in the three balance
sheet it:ems must sum to zero, so values for only two of the three items can
be chosen independently. The authorities conduct financial policy using
two kinds of financial market operations:: (1) monetary operations, exchanges
of home money for home securities with private agents and (2) intervention
operations, exchanges of home currency securities for foreign currency
securities with private agents.2/ Monetary operations alter the mix of money
and securities denominated in the same currency available to the public,
Interverition operations alter the supplies of securities denominated in
different currencies available to the public. The intervention operation
just described is often referred to as "sterilized intervention" because it
leaves toth the home money supply and the foreign money supply unchanged.

Although the home money supply may change during the course of the operation,


rot

a(*)

ne

Hoe

=*

X(+)
*
X(+)

-A5-
The symbols are defined as follows:

home currency price of home good

foreign currency price of foreign good

home currency price of foreign currency

aggregate demand for and aggregate supply of home good
aggregate demand for and aggregate supply of foreign good
home residents’ wealth measured in home currency

foreign residents' wealth measured in home currency

proportion of spending allocated by both home and foreign residents
to home good

constant speed of adjustment of actual to desired wealth by both home
and foreign residents

desired ratio of wealth to income for both home and foreign residents
expected real interest rate on home currency securities

expected real interest rate on foreign currency securities
nominal interest rate on home currency securities

nominal interest rate on foreign currency securities

home currency money wage of home residents

foreign currency money wage of foreign residents

aggregate supply function for home good

aggregate supply function for foreign good

supply of home money measured in home currency

supply of home currency securities measured in home currency
supply of foreign money measured in foreign currency

supply of foreign currency securities measured in foreign currency

home currency average price of consumption bundle of both home and
foreign residents

demand for real balances of home money measured in terms of consumption
bundle of both home and foreign residents

demand for real balances of foreign money. measured in terms of consumption
bundle of both home and foreign residents

proportion of wealth minus money demand held in home currency securities
by both home and foreign residents


-A3-

*
Bekai-i-&

Ey ta + K- quc:) - ak], (A10)

E

* *
b, = k(m, +n)), b, = k'(A - L) + km, bd) = kA - L) = kny,

b, = km, + n)), bs = k'(A - L) ~ km, bo = kK(N + F -m) -n,),
. oud .F =
b, = km,, be = KI - £) + kn), by = kny,
E- *
er = (1- ki - F-2=jpa+k- que) - a1. (all)
Q is given by
- ek.
Q = hp + (1 - HEB. . (a12)

* * OE
It is assumed that 0 <k <1; that Lj, Ly, k', de LY), @ - LY), @- 14),

and Gh - t) > 0; and that Ly» Ly, i and i, <0. These assumptions imply that all
the asset market approximation coefficients except bs by» and bg are positive.
The assumption that wealth holders in both countries regard the. thre: assets
they hold as strict gross substitutes implies that bs and by are positive,

that is, that the positive effect of the increase in the ratio of wealth

minus money demand that home (foreign) wealth holders want to hold in home
currency securities exceeds the negative effect of the increase in home
(foreign) money demand. It is assumed that bg is positive, that is, that

the positive effect of the increase in wealth on the demand for home currency
securities exceeds the negative effect of the increase in money demaads. Note
that A = aY and k = at in the equilibrium at which. the approximation is made.
Adding (A8), (A9), (A10), and (Al1) yields the identity (A5), so only three

of the four asset market equilibrium conditions are independent. In this

paper the equilibrium condition for foreign currency securities, (All), is not used.


-14-

affecting the allocation of spending between home and foreign goods either

at home or abroad. If the authorities pursue an aggregates constant policy,
levels of output between Yy and Yo result. For example suppose an increase
in the demand for the home good shifts the XX schedule to XX,

to excess demand for the home good. Output tends to increase, creating

and gives rise

an excess demand for home money and an excess supply of home securities,
These disequilibria can be removed only by a rise in i and an appreciation
of the home currency (fall ine). An appreciation of the home currency
raises excess supply in the markets for the home good, home money, and home

currency securities, As the home currency appreciates, the X, and

2%p+ MoMy»
BoBy schedules shifts toward one another until they intersect at a point in
the shaded triangle above XXo-

If instead the authorities pursue a rates constant policy, levels of
output between Yy and Y result. If the XX schedule shifts to XXos then the
new equilibrium point is at point a. Since there is no change in the exchange
tate the XX schedule does not shift back from XX + The MM and BB schedules
are shifted to the right by monetary and intervention operations until they
pass through point a. An expansionary monetary operation, a purchase of home
securities with home money, shifts both MM and BB to the right. However, BB
is shifted farther since increases in income raise the demand for money by
more than they reduce the demand for home currency securities. Thus, in order
to keep both the exchange rate and interest rate constant, the authorities
must undertake an intervention operation, a sale of home securities in exchange

for foreign securities, so that the BB schedule does not shift farther to

the right than point a. When the only source of shocks to equilibrium is


-16-

Figure 2


and there is no intervention, so the interest rate and the exchange rate
vary when disturbances are experienced. Under a "rates constant policy"
monetary operations and intervention operations are employed to keep the
interest rate and the exchange rate fixed. The tool of analysis is a
discrete time stochastic model in which agents have rational expectations.
It is shown that for disturbances to the market for the home good an
aggregates constant policy results in less variation in output and that
for disturbances to financial markets a rates constant policy results in
less variation in output. Section IV is a demonstration that similar results
can be obtained when the economy is subject to one kind of permanent
disturbance as well as transitory disturbances.

To establish that the nature of the truly optimal financial policy
regime depends on the kind of information available to the authorities
about the structure of the economy and about the disturbances to which it is
subjected is the purpose of Section V. There it is argued that under
general conditions it is not optimal for the authorities in a single
open economy facing transitory disturbances either to rigidly fix the
exchange rate or to allow it to fluctuate freely.

In Section VI attention is turned to the interactions in a two-country
world economy that must be considered when choosing financial policies. It
is emphasized that the overall stance of intervention policy is the result
of the intervention policies of both countries, Then it is shown that for
two kinds of transitory disturbances the two countries would agree on what
the overall stance of intervention policy should be while for another kind

of transitory disturbance a policy conflict would arise. The tool of analysis


-37-

agents. Forward foreign exchange operations are equivalent to intervention
policy actions in their impact on financial variables. The net return

in terms of home currency to a private agent who sells a home currency
security to and purchases a foreign currency security from the financial

authorities is

a+n-Q+n, (26)

milo

where E is the spot price of foreign currency in terms of home currency,

and £ is the unknown spot price of foreign currency in terms of home currency
that will prevail in ninety days. The net return to a private agent

who sells (1 + r) units of home currency forward to the authorities in

return for forward foreign currency is

(l+#4r)- (+r), (2)

rit 2

where F is today's home currency price of foreign currency for delivery in

ninety days. Covered interest arbitrage ensures that
*
(Q4r-+Z2Q+4). (28)

Substitution of the right hand side of (28) for the first (1 + r) in (27)
reveals that (27) and (26) are equal, Private agents regard the: security

exchange which is implied by an intervention operation and the purchase
of the forward contract from the authorities as equivalent transactions

30/ :
because they have the same net return.—— Thus, these two types of transactions
have the same effect on financial variables, and in the absence of knowledge

of the authorities’ forward foreign exchange operations the intervention


=25-
monetary operations to fix the interest rate on securities denominated
in the currency of their country, The overall stance of intervention policy
is the net: result of the intervention operations of the two sets of
authorities, Taken together they can choose as a policy instrument and set
a value for either the total supply of home currency securities (and, by
implication, the total supply of foreign currency securities) or the exchange
rate, In this environment it is interesting to consider whether the authorities
in the two countries could agree on a fixed or a freely fluctuating exchange

rate, In the first subsection the necessary modifications to the model are

described, and the results are presented and explained, In the~ second

subsection the results are derived more formally.

The Modifications to the Model and the Results

The only additional market which must be considered explicitly is the
*
market for the foreign good. Foreign output (Y) must be equal to aggregate

demand for the foreign good:

* * * x. * ** * * w*
¥ = yo + y,(¥ + ¥) - yor - ygr - y,(e +P - p) — yoe - yep - Be (14)

Aggregate demand depends negatively on expected real interest rates, on the

relative price of the foreign good, on the exchange rate, and on the price

of the foreign good. Increases in the exchange rate and the price of the
foreign good reduce home and foreign real wealth measured in terms of the
foreign good.and, therefore, raise home and foreign saving, Aggregate demand
depends positively on home and foreign output. It is assumed that trade

is initially balanced so that the effect of an increase in the relative

price of the foreign good on the demand for the foreign good is equal

in absolute value to the effect on the demand for the home good 22/ Positive


The Role of Intervention Policy
in Open Economy Financial Policy:

A Macroeconomic Perspective
by
Dale W. Henderson*

I, INTRODUCTION

This paper is an analysis of the extent to which alternative financial
stabilization policies can be expected to dampen the effects of shocks to
macroeconomic equilibrium in open economies. According to the view emphasized
here intervention policy is an integral part of open economy financial
policy.2! Intervention operations have effects on macroeconomic variables
which can be distinguished from those of monetary operations, Thus the
specification of a financial policy regime is not complete until both the
intervention and monetary policies of the financial authorities have been
described. An alternative view according to which intervention operations
have no effects so that the specification of a financial policy regime
requires only a description of monetary policy is also discussed briefly.

Intervention operations and monetary operations are defined in
Section [I. Whether one open economy financial policy regime is better than
another usually depends on the source of disturbances to the economy. In
Section III this observation is illustrated by a comparison of the effects
of different kinds of transitory disturbances to macroeconomic equilibrium
in a single open economy under two alternative pure financial policy regimes.

Under

“aggregates constant policy" the money supply is kept unchanged


~-F3-
11/ Flood (1979), Parkin (1978), and Wallich and Gray (1981) analyze open
economy financial policies under the assumption of rational expectations,
12/ For an explanation of the exact restriction that this assumption places
on the parameters of the underlying model see the appendix.
13/° Meltzer (1978) has emphasized the importance of the distinction between
permanent and transitory disturbances. In Rogoff (1980) private agents must

"

attempt to sort out transitory and "lasting" disturbances and therefore adjust

their expectations slowly new lasting disturbances.
14/ This kind of analysis was first employed by Poole (1970) and has been
extended by Friedman (1975).

15/ That is, suppose equations (8), (9), and (10) are divided through by

Yy» My, and by respectively; that (a +8)/yy =B', (y +6 Yim, = 6", and

C-y¥+ eddy = e' are disturbances that may be mutually correlated; and that
2
ca
16/ See Poole (1970).

i= os = Ole
17/ It would be interesting to consider optimal behavior for the authorities

in yet a third environment in which they cannot observe or elect not to

respond to current movements in the financial variables not chosen as

policy instruments but in which the coefficients of the economic model are
stochastic variables which have a joint distribution with the additive stochastic
terms that: is known to the authorities, as in Brainard (1967), and to private agents.
18/ A rulle of this kind was first developed by Poole (1970), Kareken, Muench,

and Wallace (1973) and Friedman (1975) significantly generalize and extend Poole's
results. Boyer (1978) derives an optimal decision rule in a model in which home

and foreign currency securities are perfect substitutes and exchange rate
expectaticns are static. Roper and Turnovsky (1980) show how this rule is affected

by the incorporation of a more general hypothesis regarding the formation of


-33-

* :
Yy are all positive. my, by» n> and bo are defined above. It has been
ts one
assumed above that my > by» so by is positive.
**
The difference between the slopes of the XX and XX schedules of

Figure 3 is
36 -. os ;
QD) yy - (Y/Y) = Cys - yyye)/ (yaye). (20)

xk * *
The XX schedule is steeper than the XX schedule since Vy > Yy and yt > ¥y-
B'B' has a positive slope but this slope may be greater or less than the

Pr ek :
slopes of XX and XX. The difference between the shifts in XX and XX schedules

at a constant value of Y given a positive 8 is
a
*
Y.

ER) yy — Oe 3s = Cg - FPIGBD. (a)

xX

*
The XX schedule shifts down farther since vy > yye It can be shown that
*.
kK ~
the XX schedule shifts farther to the right than the XX schedule at a constant
. * *
value of Y given a positive B since Yy > Yye

: * .
Under the assumption that Ye = Ye the variances of home output (of) and

foreign output (0%) under fixed (FI) and flexible (FL) exchange rates are

Y
given by
obey = GRID, O, + LG - ¥~)/D,]7o9, (22)
ley 7 GylPy)ay + [Gy - ¥y/D,]" 05, (3)
Og lg, = (Dy/M,)702 + [ONG - ygD/M]7 0p + Uvg las — HP/AgI CoG + 02), (24)
8 lay = (D,/4,)?02 + biG - Yy)/Bq]7op + ly Gy - Fy/Aol Cag + 2), (25)


Appendix

The model of the text is a partly linear and partly log linear
approximation to the model sketched out briefly in this appendix. The
symbols used are defined at the end of the appendix. The approximat:ion
is made at the equilibrium which would emerge if all the disturbance
terms were zero and trade were balanced. In this equilibrium all of
the endogenous variables take on their constant expected values, which
are represented by the symbols for these variables with bars over them,
and units are defined so that E = 3 =P= 1. The coefficients displayed
below or beside a given equation are the coefficients of the approximation

to that equation.

The aggregate demand equations for the home and foreign goods are given by

= n€Byppy + EY - cfa(r, 1) (PY + EPY) - (A+ An, (Al)
* *

yy h(l - ca), Y= h'(¥ + Y) + h(1 - ca)Y,

¥p = 0a,¥, Ys 7 heW +F),
*.

¥3 = caky, Ye =he(A + A),

*
EPY = [1 - hey ifpy + ERY - cla(r,r)(PY + ERY) - (A+ AD], (a2)

a = (1 = h)(1 - ca), y, = hla + % + ha - cay¥,

* * *

Yo = cay, ¥5 = (1 - h)c(M +B),

3, = cat, ¥g= = bye +d),

It is assumed that 0 <h, ca <1 and that as ax, and h' 50, so all the

approximation coefficients are positive, and 0 < Vp i, <1. In der:ving Yo,

¥3> J 35. and yy, use is made of the facts that in equilibrium h(Y + % =Y,
and (1 - h)(Y + % =¥ and that with balanced trade hy = (4 - h)Y. ca is

represented by s in the text.


-28-

but also foreign saving. The increase in excess demand for the home good
caused by a rise in ¥ which increases not only home exports (foreign imports)
but also home saving is less than the absolute value of the reduction in
excess demand for the foreign good caused by a rise in ¥ which increases
foreign saving as well as foreign imports. BORG is an equilibrium schedule
for the combined market for home money and home currency securities. Attention
is focused on this combined market for home currency assets because the home
authorities alter the supplies of home money and home securities with
monetary operations to satisfy any change in the composition of home currency
assets desired by private agents at a constant interest rate on home currency
securities. An increase in Y which raises the demand for home money plus
home currency securities must be offset by a rise in ¥ which raises the demand
for foreign money partly at the expense of the demand for home currency
securities, The slope of the B'B' schedule may be greater than or less than
the slopes of both the XX and xX schedules or it may be greater than the slope
of the xx schedule but less than the slope of the XX schedule as shown in
Figure 3,23

It is useful to consider first the effects of a shift up in the
demand for the home good matched by a shift down in the demand for the “oreign
good which is equal in absolute value. These shifts can be represented by

. pad
hel and in the XX schedule from
*

* wk * **
XoXo to XX ° At a constant value of Y, XX shifts down farther than XX

movements in the XX schedule from XoXo to X.

*
(aga, > aya,) since in the market for the home good a fall in Y reduces not
only home exports (foreign imports) but also home saving, while in the market

for the foreign good it raises foreign saving as well as foreign imports, A


-12-

for home residents to set the nominal wage at the constant w each period
before other markets meet ,10/ Ly/

Equilibrium schedules for the markets for the home good, home money,
and home currency securities are shown in Figure 1. In order to construct
these schedules it is necessary to eliminate p from these markets with the
use of the relationship between p and Y implied by the aggregate supply
function when w is set equal to w. XoXo is an equilibrium schedule for the
home good, An increase in i, which lowers demand, must be accompanied
by a decline in Y, which raises excess demand. MoMy is an equilibrium

schedule for home money. An increase in i, which reduces money demand, must

be offset by a rise in Y, which raises money demand. is an equilibrium

Bo®o
schedule for home currency securities. An increase in i, which raises
demand, must be matched by an increase in Y which lowers demand. It is
assumed that the effect of an increase in Y on the demand for home money is
greater than the absolute value of the effect of an increase in Y on the
demand for home currency securities t2/ In the next subsection it is denonstrated
that this assumption is sufficient to insure that MoMy is steeper than ByBy
as shown in Figure 1, and the implications of relaxing it are discussed,
XyXq> MoMy > and BoBy are the equilibrium schedules which would result if all
disturbances were zero, so they intersect at Yee Changes in the exchange rate
or the home authorities' holdings of home and foreign securities cause the
schedules to shift in a manner described below.

Consider the effects of stochastic shifts in the XX schedule in
the range between XX) and XX, shown in Figure 1, These shifts might result

from disturbances affecting home or foreign saving behavior or from disturbances


-F4-

of exchange rate expectations and an additional type of disturbance. Boyer
(1980) considers decision rules for the authorities in a model which is the same
as the one used here in all essential respects except that exchange rate
expectations are static. Fischer's (1977) and Frenkel's (1980) optimal

rules are derived in models quite different from the one employed here.

19/ It could be assumed that the nominal wage was "indexed" to the two
financial variables not chosen as policy instruments and that neither financial
policy instrument was changed. If such an indexing rule were determined
optimally, it would result in the same variation in output as would the
authorities' decision rule, It appears that labor contracts involving
indexing to financial variables are not negociated, and conventional indexing
is not a perfect substitute for this type of indexing.

20/ It also depends on the assumption that the coefficients of the system

are known with certainty.

21/ Sweeney (1983) analyzes open economy financial policy using a two-country
model.

22/ See the appendix for a demonstration that the assumption of balanced

trade has this implication.

23/ Whenever a result depends on the relative slope of the B'B' schedule,

this fact is mentioned in the footnotes.

24/ These assumptions are spelled out in the appendix.

25/ If they were not, the analysis would be somewhat more complicated. If
depreciations cause the XX and 55 schedules to trace out a line wich a negative
slope, as seems most reasonable, all the results except for those regarding a
shift in demand between home and foreign goods are necessarily the same in
qualitative terms, but the results for a demand shift may be e{fected.

26/ If B'B' were flatter than xR, there would be pressure on the home

currency to depreciate.


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-15-

stochastic shifts in the XX schedule, an aggregates constant policy leads
to less variation in output than a rates constant policy. Under an aggregates
constant policy disturbances to the home good market induce changes in the
interest rate and the exchange rate that dampen the movement in output.
A different kind of conclusion is reached when shocks to financial
markets are considered. For purposes of illustration, attention is focused
on a type of shock for which intervention operations are the appropriate
remedy. Consider stochastic shifts in the BB schedule between BiB) and
BBS shown in Figure 2, These shifts result from changes in preferences
between home and foreign securities either at home or abroad. If the authorities
pursue an aggregates constant policy, levels of output between Yy and Yo

result. Suppose a shift in asset preferences toward home securities and

away from foreign securities causes the BB schedule to move to BAB The

‘2°
increase in the demand for home securities leads to a decrease in i, which
in turn creates excess demand for home money. In order for equilibrium in
financial. markets to be reestablished, the home currency must appreciate.

Appreciat:ion causes the three schedules to shift together as before, so the

new equilibrium must lie in the shaded triangle below BoB Output may fall,

0°
rise, or remain the same since the changes in financial variables have opposite
effects on demand for the home good.

If instead, the authorities pursue a rates constant policy, output
definitely remains unchanged. The BB schedule is shifted back to BOBy by an
intervention opration consisting of a sale of home securities and purchase
of foreign securities. When the only source of shocks to equilibrium is

stochastic shifts in the BB schedule, a rates constant policy leads to less

variation in output than an aggregates constant policy.