-19-

(non-rational expectations) game-theoretic analyses of two-country monetary
policy, we have also analyzed money market and goods market demand
disturbances. It is worth noting that the model developed here is
considerably easier to manipulate than previous non-game-theoretic,
rational expectations, two-country macro-models, even though it yields the
same qualitative results about the transmission of disturbances. The
algebra here is simpler because time-consistent rational CPI inflation rate
expectations and exchange rate depreciation expectations turn out to be

static (unless there is a regime shift).


-36-

36/ Rogoff (1983b) and Canzoneri (1983) discuss institutional responses to
the central bank's time-consistency problem in a closed economy context.

37/ Apart from its game-theoretic aspects, the model is quite similar to
nes employed by Henderson and Waldo (1983), Daniel (1981), and Canzoneri
and Gray (1983). Daniel's two-country model includes intermediate imports
instead of wage indexation. Canzoneri and Gray's model does not
incorporate rational expectations but like the present one, is highly
symmetric.

38/ As Gray (1976) demonstrates, full price-level indexation is sub-
optimal in the presence of supply (productivity) shocks.

39/ In the discussion below, we sometimes refer only to domestic variables
and equations if discussion of their foreign counterparts is redundan:.

40/ Making notional labor supply depend on the real wage, as in Rogoff
(7983b), would not qualitatively affect the results here.

41/ The assumption that A < .5 implies that, in each country, the marginal
Propensity to consume out of real income is less than one. (A is the
marginal propensity to consume either one of the two goods.)

42/ The solution procedure may be described as follows: First, we assume
that rational expectations are equivalent to static expectations for CPI
inflation and the rate of change of the exchange rate. Imposing this
assumption, we solve the model of equations (19) - (22) as a function of
m, m*, Ww, Ww, T> at and the disturbances. Then in the text, we use the
resulting partial derivatives (see equations an below) to solve for the
time-consistent values of W, W*, 7 mf, and F 1) - e,. This procedure
confirms that time-consistent excharige rate ani (eae inflation rate
expectations are indeed static.

43/ Daniel (1981) discusses these transmission channels, as do Canzoveri
and Gray (1983). If 8 = 0, so that there is no wage indexation, and if the
income elasticity of money demand, 4, equals one, then ap/am*,

an/am* < 0. If Bg > 0, then an/am* may be positive even if 9 =

44/ In models in which employment is the only objective (such as Henderson
and Waldo (1983)), both the Nash and cooperative equilibria involve fully
restoring n and n* to their pre-shock levels. A shift in demand from the
foreign good to the home good produces no conflict. In models in which
money growth (rather than inflation) is a second government objective (such
as Canzoneri and Gray (1983)), m is decreased and m* increased, but not
enough to cause n and n* to return to pre-shock levels. With money growth
targets, the cooperative solution always involves a greater response to
aggregate demand shifts than does the Nash solution, and thus greater
exchange rate and employment stability. With inflation-rate targets, as in
the present model, the cooperative solution does not necessarily involve
greater exchange rate and employment stability than in the Nash solution.


-13-

contemporaneous information, then the home monetary authority may no longer
have sufficient information to fully offset home money demand disturbances.
Consequently, these disturbances will have some effects both at home and
abroad. If the only problem is incomplete information, however, there is
no reason to presume that a cooperative monetary policy regime will lead to
better outcomes in response to money demand disturbances than would a fully
discretionary non-cooperative regime. (If the central banks place weight
on achieving their money supply targets, as in Canzoneri and Gray (1983),
then the cooperative and non-cooperative response to money demand shocks
will no longer be equivalent.)

Goods market demand shocks do not disturb the Nash equilibrium only
because we have made the simplifying assumption that both countries
experience the same goods market demand disturbance. (This assumption is
relaxed in Appendix B.) Provided that both countries alter their money
supplies equally to offset the mutual disturbance, there will be no effect
on home and foreign prices and employment. The level of world real
interast rates will move to offset the disturbance, but the real exchange
rate will remain fixed. The resulting equilibrium is Nash because neither
side will have an incentive to unilaterally alter its money supply
further.

On the other hand, aggregate supply disturbances do affect the price
levels which arise in Nash equilibrium in spite of our simplifying
assumption that the home and foreign supply shocks are perfectly
correlated. The reason is that an aggregate supply shock creates a trade-
off between price level stability and employment stability. As we

discuss more fully in Appendix A, an aggregate supply shock alters the


-23-

both cdomestic- and foreign-currency denominated bonds. The demand for real
money balances in each country is a decreasing function of the nominal

interest rate and an increasing function of real income:
(20a) m- py =-ar + o(p +y - Py) +,
(20b) m* - py = -art + o(p* + y* - pf) + v*,

where m is the logarithm of the nominal money supply and v is the money
market. disturbance term; v ~ N(0, oe), ve ~ N(O, on)s and v and v* are
independent.

Nomestic- and foreign-currency denominated bonds are perfect

substitutes so that uncovered interest parity holds:
(21) Et (eg41) - etree rt.

Agents are assumed to have full period t information (including
knowledge of the period t disturbances) in making their portfolio and
investment decisions.

3. Goods market demand
Jemand for the good produced in each country is a decreasing function

of its relative price, an increasing function of real income at home and

abroad, and a decreasing function of the real interest rate:

(22a) yg = nq - 8'{r - ExlPrctary) * Pret + ale + y - Py)
+ a(p* + y* - pf) tu' + x,
(22h) yh = -nq - 6'{r* - Exlptctary] + Pfel + a(p + y - Py)

+ A(p* + y* - pH) t+ ul - x,


-4-

where A (A*) is the home (foreign) social loss function. Star superscripts
denote foreign country variables, t subscripts denote time, and lower case
letters are used to represent logarithms. (Henceforth, we will discuss
only domestic variables and equations in circumstances where discussion of
their foreign counterparts is superfluous.) Employment is given by n, and
TM is the rate of consumer price level inflation; e.g., TH = (Pye -
(Prey where Py is the consumer price lever _/ The socially-preferred
values of n and m, are denoted by nv and 7. x is the relative weight which
society places on inflation stabilization versus employment stabilization.
As with most of the technological and behavioral parameters of the model of
Appendix A, x is assumed to be the same for both countries (though 1 and
7 may differ).2/ The objective functions (1) are static, but the results
below would be unchanged even if we replaced equations (1) by objective
functions which also depended on expected future values of inflation and
employment. The same results would obtain because the real effects of

unanticipated monetary policy last for only one period, the length of the

wage cont racts 2!

III. The Conflict Between Wage Setters and the Central Banks

The tension between wage setters and the central bank within each
country derives from the assumption that n, society's target employment
rate, is greater than n, wage setters' target employment rate. Possible
factors which might distort the labor-leisure decision, thereby causing
wage setters to target levels of employment which are too low and levels of
real wages which are too high, include income taxation and unemployment

insurance 20/ Monopolistic unions might also cause the average real wage


-34-

17/ See Appendix A. We are restricting our attention to contemporaneous
money supply feedback rules since, in the setup of the text, "prospective"
(lagged) feedback rules are not time consistent; see Rogoff (1983b). If
time consistency were not a problem, lagged feedback rules would still be
inferior to contemporaneous feedback rules since both inflation rate
stabilization and employment stabilization enter the social objective
function. Lagged feedback rules succeed in decreasing the variance of
employment only by increasing the unconditional variance of inflation; see
Canzoneri, Henderson and Rogoff (1983). A similar problem with lagged
feedback rules arises in the presence of multiperiod overlapping
contracts.

18/ The second-order conditions for a local minimum are met; because of
the quadratic forms of (1), the minimum is global.

19/ Central banks could try to fool wage setters by indicating that they
have no plans to cooperate, and then turning around and doing so. They
could not achieve systematic gains this way, however.

20/ Here is the first of many times where we make use of the fact that
certainty equivalence obtains because the objective functions are
quadratic; see Sargent (1979).

21/ We are assuming that the same regime is expected to remain in place
permanently, though this assumption is easy to modify. Note that
expectations of future money growth are not static; it is precisely because
expectations of next period's money supplies are affected by current period
disturbances that CPI inflation rate expectations are not affected. The
fact that rational expectations for the rate of exchange rate deprecation
are also static follows because the two goods have equal weights in both
countries’ CPI's.

22/ Although the real exchange rate does not turn out to move in the Nash
equilibrium, the fact that it can move (out of Nash equilibrium) plays a
major role in everyone's decisions. In Appendix B, we allow for relative
shifts in demand between home and foreign goods. In this case, the real
exchange rate does fluctuate in both the Nash and the cooperative regimes.

23/ A simpler method of obtaining equations (5) is to solve (3) for Pt and
pf holding q = 0. Then ye t-1 ral eee Abe: the ryt ting
expressions and form (p4)” - Ey_1 (Pz) and - Eg_y (pt)

24/ If q varied, we would need to substitute into the social objective
functions for q, p, and p* in terms of W, W*, dm and dm* in order to solve
for the Nash equilibrium. This more algebraically cumbersome approach is
sketched in Appendix B.

25/ To prove uniqueness of the Nash equilibrium, take t-1 expections
across equations (3), and subtract the resulting expressions from (3) to
obtain two equations in dpy, dp#, and dqy. Use equations (26) of Apsendix
A to substitute out for thése three variables in terms of dm and dm*. The
result is two linear, independent equations in dm and dm* and the solution
is unique; see Appendix B.


-20-

Appendix A: The Underlying Two-Country Macroeconomic Model

Here we describe the two-country, two-good, rational expectations cum
wage contracting model on which the results of the text are based.2/
Monetary policy can have short-run real effects here because nominal wage
contracts are negotiated a period in advance; these contracts are only
partially indexed to the current-period consumer price level 38/ To
facilitate algebraic manipulation, the technological and behavioral
parameters in the two countries are constrained to be equal.

1. Aggregate Supply

The good produced by home-country firms differs from the good produced
by foreign-country firms. But within each country, all firms have identical
Cobb-Douglas production functions. Using lower case letters to denote

logarithms, the aggregate production functions can be written as
(12a) y = ¢g + ok + (1 - a)n +z,

(12b) y*® = ch + ak* + (1 - a)n*® + 2*,

where star (*) superscripts indicate the foreign country ,22/ y is output, k

is the fixed capital stock, n is labor, Cy is the constant term, and z is a
serially uncorrelated aggregate productivity disturbance; z ~ N(0, oA). z
and z* are assumed to be perfectly correlated so that z = z*. Tine
subscripts are omitted where the meaning is obvious; throughout, all
parameters are non-negative.

Firms hire labor until the marginal value product of labor equals the

nominal wage rate, w:


(26d) Pp = WwW + (w+ H)(m - w + My - v) - vd(m* - We + ATE - ve)

+ AHu/s - H(o + 4/8)Z/a + [HA/6 - 2w(o + 1/0) ]x,

(26e) py} = WE + (WJ + H)(m* - We + AR - ve) - v(m - W + Amy - Vv)

+ AHu/6 - H(¢ + A/6)Z/a - [HA/S - 2vd(o + 1/8) I]x,

(26f) n=Ai+ (Q + Rv)(m-wWt ATy - v) = Ru(m* - We + dae - v*)

+ Qau/d + Of-$ - 2/6 + 1/(1-8)]z + [Qa/5 - ARv( go + 1/0) Ix,

(26g) n* = fi* + (Q + Rv) (me - We + AME - vt) - Rv(m - W + AT - Vv)

+Qau/6 + QL-¢ - 4/6 + 1/(1-8)]z - [OA/5 - ARv(o + 1/6) Ix,
v = [2(n + «)/e + 2on + (1 - ort > 0,
H = (1 + 0/6 + 98)! > 0,

S = HEKp - (1 - 9)/2 + x + n)/81 30,

a
mw

H{.59C(1 - a)/a + 1] + /6C.5(1 - a)/a + nJ} > 0,

Q = [ol - a) + a(1 - a)/s + a/(1 - 8)J7! > 0,

n
im

O{-5Lo - 1/(1 - 8)) + an/o} 3 0.

Using equations (26), and imposing the assumption that the income
elasticity of money demand 6 <1, we can determine the sign of the following
partial derivatives (holding w, w* , on and 7 constant):

aq/am, dp/am, ap ,/am, an/am, ap/ du, ap ,/au, an/ ou > 0;

an/ ox > 0;

ap ,/ ax, aq/ ax, ap ,/am*, ap ;/ az, ap/az < 0.

The partial derivatives ap/ax, ap/am*, an/am*, an/az, may be positive


-22-

agree to supply (ex-post) whatever amount of labor is demanded by firas in
period t, provided firms pay the negotiated wage. The actual levels of
employment in period t are thus found by substituting the wage equations
(15) into the labor demand equations (13):

(17a) n= + y(p- &) - q+ 2/a,

(17d) n* = fi + y(p* - W*) + 1q + Z/a,

where y = (1 - 6)/a, t = .58/a, and

(18) q=e+ p* - p.

As described in the text, wage setters choose w to minimize

E (n, - ny’, where E, denotes rational expectations based on period t-1

t-1 t-1
information. This implies that w = E, fp, - -58q,/(1-8)], and
we = E,_ Cet + -5¢q,/(1-)1.

Equations (12) and (17), together with the assumption that

Cy = ok + (1 - a)n, imply that the aggregate supply equations can be

written as
(19a) y, = 0(p - W) - «q + 2/a,
(19b) yg = e(p* - W*) + Kq + Z/a,

where 6 = (1-a)(1-8)/a and x = .5(1-a)6/a.
2. Money and bond markets
Only domestic residents hold the domestic money and only foreign

residents hold the foreign money. However, residents of both countries hold


-35-

26/ This result is due to the quadratic form of the objective functions.

27/ Rogoff (1983b) demonstrates how to extend a framework such as the
present one to the case where central banks have incomplete contemporaneous
information,

28/ Henderson (1984) derives a similar result.

29/ We note again that the presence of intermediate imports in the
production function would imply a similar result.

30/ There are other, asymmetric, cooperative schemes which, holding wages
Constant, lead to Pareto improvements over the Nash equilibrium,
Qualitatively, all of these schemes are similar in that they involve
higher money growth at home and abroad than in the Nash equilibrium, The
symmetric scheme analyzed in the text is a logical one to consider since
the two countries are identical in almost every respect. Canzoneri and
Gray (1983) have emphasized that fixed exchange rate regimes may be non-
cooperative in that either country can unilaterally precommit to fix the
exchange rate.

31/ Canzoneri and Gray (1983) analyze a one-time supply disturbance and
find that the cooperative response to this disturbance may call for either
smaller or larger changes in the money supply than in the Nash
equilibrium. In their framework, the authorities try to stabilize
employment and money growth. The present framework may also yield the
result that Idpy | < |dpy| when the central banks adopt the money supply as
an intermediate monetary target, along the lines discussed in Rogoff
(1983b).

32/ An alternative proof is possible : Define pz, = dpy, and find the
value of po which minimizes T as defined in equations (6). This value turns
out to be the same as for (dp,) .

33/ A still better cooperative equilibrium could be achieved if the two
countries could eliminate their labor market distortions at low cost.

34/ Buiter (1981) specifies optimal contingent rules. There are, of
course, many problems involved in designing an insitutional framework in
which to implement such rules.

35/ McKinnon (1982) suggests a cooperative monetary reform. His specific
proposal to fix the path of the world money supply would definitely be an
improvement over money-supply targeting by individual countries in a world
where the main source of disturbances is currency substitution.


-17-

y > x (since x > 0), and note that x' > xy. Q.E.D.

So the cooperative regime produces a better response to unanticipated
supply disturbances, but a higher expected inflation rate. Whether social
welfare is higher under the cooperative or non-cooperative regime thus
depends, in part, on the variance of the supply shock and on the size of
the labor market distortion. Note that it is perfectly possible for the
country with the smaller labor market distortion to prefer the cooperative
regime, while the other country would be better off under a non-cooperative
regime. (If the home country had no labor market distortion, it would
always prefer the cooperative regime regardless of the variance of the

disturbances.)

VII. Institutional Designs for Superior Cooperative Regimes

The possibility that the regime we have labeled "cooperative" might be
inferior to the "non-cooperative" regime does not violate the basic tenets
of gane theory: the central banks are assumed to cooperate with each
other, but not with private sector wage setters. Of course, if the central
banks were able to credibly guarantee that they would not systematically
try to raise employment, and would only use monetary policy to offset
disturbances, then it would be possible to achieve a superior and truly
cooperative outcome 23/ The present analysis does suggest cases in which
government to government cooperation might lead to better institutional
reforms. Suppose, for example, each country passed a binding law fixing
the fiture path of its money supply except for prespecified responses to

specific disturbances 24/ If the two countries designed their monetary


~9-

the underlying macroeconomic model of Appendix A,
ye = ( aq/adm*)/(ap*/adm*) = -¥; that is holding base wage rates constant, a
unilateral foreign money supply increase has exactly the opposite effect on
the real exchange rate q as a unilateral home money supply increase.
Appendix A also demonstrates that (y - t¥) > 0; i.e., an unanticipated
increase in the home money supply raises home employment.

Wage setters are assumed to correctly anticipate whether a cooperative

or Nash regime will be in place in the ensuing period 22/

By examining
the first-order conditions (3), wage setters can choose base wage rates so
that the expected real wage equals their target real wage. The underlying
macromodel is constructed so that wage setters' target (logarithm of the)
real wage is zero, and so that Eid (44) = 0. Taking t-1 expectations

across (3), and setting expected real wages and the expected real exchange

rate equal to zero yields 20/
' - \N N -N
(4a) (We) = Epp (PE) = Pe_y + 544) + my
- N -
(4b) (wg) = By (oR) = wey - Sag + GS.

where a = TM + (y - w¥)(n - n)/x(1 + .5¥), and
(wt) = Te + (y - TY) (N* - HF)/y(1 + .5¥),

By choosing w and w* according to equations (4), wage setters assure
themselves that the non-cooperating central banks will, in the absence of
disturbances, produce price levels consistent with wage setters' target
real wages. We see by inspection of equations (4) that the rate of nominal

wage growth is an increasing function of the difference between the


~32-

Footnotes

*/ Board of Governors of the Federal Reserve System. An earlier version
Of this paper was written while the author was on leave at the Research
Department of the International Monetary Fund. The views expressed in this
Paper are the author's own, and should not be interpreted as the official
views of either institution. The author has benefited from discussicns
with Matthew Canzoneri and Dale Henderson, and from comments on an earlier
draft by seminar participants at Columbia University, Princeton University,
and the University of Virginia.

1/ Hamada (1976) was the first to analyze the strategic interactions of
two (or more) governments in conducting monetary stabilization policy.
More recently, Jones (1982, 1983) as well as Canzoneri and Gray (1983) have
examined some game-theoretic aspects of monetary policy under fixed and
flexible exchange rates. The above analyses do not incorporate raticnal
expectations. Other recent multi-country analyses of monetary policy
include Carlozzi and Taylor (1983), Henderson (1984), Macedo (1983),
McKinnon (1982), Miller and Salmon (1983), and Sachs (1983).

2/ The focus of the present analysis is game-theoretic and not
Information-theoretic. This is not to suggest that the information-
theoretic aspects of exchange rate management are unimportant. Indeed, our
empirical knowledge of the determinants of exchange rate movements is, as
yet, rather limited; see Meese and Rogoff (1983).

3/ The analysis. of the strategic interactions of private agents and the
Monetary authorities within a given country is based on Phelps (1967),
Kydland and Prescott (1977), Barro and Gordon (1983a) and Rogoff (19&3b).

4/° Whether or not it is really possible to implement a cooperative
monetary system is, regrettably, an issue which is beyond the scope cf this
paper. Hamada (1976) stresses that the problem may best be thought of as
one in which the central banks cooperate to construct a regime with the
best possible (self-enforcing) non-cooperative equilibrium.

5/ There seems to be little harm in abstracting from the macroeconomic
effects of sterilized intervention, since those effects appear to be
extremely limited. See, for example, Rogoff (1983a).

6/ A similar specification of the social loss function is used by Barro
‘and Gordon (1983a), and by Kydland and Prescott (1977).

7/ See equations (16) of Appendix A.

8/ Most rational expectations cum wage contracting analyses include only
output or employment deviations directly into the social loss function A,
and do not include the level of the inflation rate. It is indeed difficult
to rigorously justify including the anticipated component of the inflation
rate into A. Some costs of perfectly anticipated inflation include the
administrative costs of posting new prices, the costs of adjusting the tax
system to be fully neutral with respect to inflation, and the costs
incurred because high rates of inflation force private agents to economize
on their holdings of non-interest bearing money. The optimal rate of


-29-

(28b) (dm*)N = ~ dm,

where, from equations (26), ay(ay - ao) + x1 (b) - b3) > 0, but aya, + yb bz 0.
A positive x represents a shift in world demand from the foreign good to

the home good; home CPI inflation falls and home employment rises. Ina
time-consistent Nash equilibrium, the home country may set unanticipated

money growth at a positive a or negative level, depending (in part) on x,

the relative weight placed on inflation deviations versus employment

deviations 4/

Provided that the responses to relative demand shifts are symmetric,

the cooperative Pg and (we)° are as in the text (equations (9)), and
(29a) dm® = ~ [(ay- ay)ag + x(by- bo)b4]x/E(ay- ay)? + x(by- by)2I,
(29b) (dm*)© = - dm°,

c and am are of opposite

Ally

Since a, 0, it is perfectly possible that dm
signs.

Finally, we note that while the symmetric cooperative equilibrium
characterized by (29) indeed lies on the contract curve, and indeed provides
better stabilization than the Nash equilibrium, it may be especially
difficult to achieve when n - 1 and n* - n* are strictly positive. In that
case, either country could gain by unilaterally deflating in a no-shock
cooperative equilibrium. Thus, (ex-post) the country which is asked to

raise its money supply more than in the no-shock equilibrium might be

reluctant to agree to take the aggregate demand disturbance into account.


-6-

(2a) Ag = Czp/a+ y(p_ - HE) - rap - (WF - A)?

+ xfP_ - Pe-y + -5(d¢ - Gt_7) - #7

(2b) Ag = Czg/a + ype ~ WE) + aa, - (A - *)T?
+ xCpf - £7 - Slade - ae_7) - 7H,

where p is the home-currency price of the home good, p* is the foreign-
currency price of the foreign good, and q is the real exchange rate:

q =e + p* - p (e is the home-currency price of foreign currency).

w (W*) is the home (foreign) base nominal wage rate, and z is a supply
shock common to both countries.

The first term in the home social objective function A represents
squared deviations of home employment from its socially-desired value; it
consists of four components: The first component depends on the
productivity disturbance, z, and on the coefficient of the Cobb-Douglas
production function, a. The second component depends on the difference
between the actual period t price level, Py» and the base wage rate w; w is
set a period in advance equal to the expected value of the consumer price
index. The coefficient y is equal to (1-g)/a, where g is the degree to
which wages are indexed to unanticipated changes in the CPI. It is assumed
that O< B< 1.23/ The third component involves the real exchange rat2, q,
and arises because wages are indexed to a price index which includes the
foreign good. (The two goods have equal weights in the cpr.24/) By
construction of the model of Appendix A, the expected value of q is zero
and t = .58/a. A similar component in q would arise if, as in the modal of
Daniel (1981), the foreign good entered as an intermediate good in the

domestic production function. The fourth and final component


-5-

to be too high to sustain society's target employment rate n.

Despite the fact that their targets are socially suboptimal, wage
setters are able to frustrate any effort by their home central bank to
systematically raise the level of employment or lower real wages. They can
do so by setting base nominal wage increases at a sufficiently high level
so that, in the absence of disturbances, the central bank will not choose
to inflate the money supply beyond the point consistent with wage setters'
desired real wage 2l/ At this sufficiently high level of inflation, the
central bank finds that the marginal utility gain from inflating (further)
to raise employment above wage setters' desired level is fully offset by
the marginal disutility from the added inflation. Thus equilibrium is
characterized by “stagflation. "22!

It is, of course, possible to consider a cooperative equilibrium
between wage setters and their home central bank, in which the central bank
promises not to systematically inflate for the sake of raising the average
level of employment. The problem is how to design a system to enforce such
a promise without constraining the ability of the central bank to offset
unanticipated shocks. For example, if it were possible to anticipate every
type of disturbance, one could write a law specifying a path of the money
supply contingent on each possible disturbance. We shall return to this

issue in Section VII.

IV. Mutual Elements in the Home and Foreign Central Bank Objective

Functions and the Potential for Cooperative Stabilization Policy

Using equations (16), (17) and (18) of Appendix A, we can rewrite the

home and foreign social objective functions as


~18-

constitutions independently, the prespecified response to common supply
disturbances would probably be Nash, whereas if they designed their systems
jointly, the prespecified response might be closer to the cooperative
one 22! The behavior of governments in other countries will, in general,
be a consideration in evaluating any institutional response to the time-
consistency problem discussed here.28/ Thus it should be clear that an
optimally-designed cooperative regime is superior to any non-cooperative
scheme.
VIII. Conclusions

Even though monetary policy cooperation produces superior res onses to
supply shocks and to unanticipated relative shifts in aggregate demand, a
fully-discretionary cooperative regime may still be inferior to a fully
discretionary non-cooperative regime. The reason is that a non-cooperative
regime yields systematically lower time-consistent expected rates of
inflation. Each central bank's incentive to inflate is lower in a non-
cooperative regime because, once base wage rates are set, unilateral money
supply growth causes real exchange rate depreciation. This depreciation
exacerbates the inflationary consequences of money growth and, in the
presence of wage indexation, reduces the employment gains. Inter-central
bank cooperation may nevertheless be beneficial when the variance of the
disturbances is high, or in institutional settings where the incentive to
systematically inflate is controlled or eliminated.

The present analysis extends the recent game-theoretic literature on
two-country monetary policy by incorporating rational expecations, and by
examining paths along which wages and price expectations are time

consistent. In addition to considering supply shocks as in other recent


-8-

supply. This simplification can only be rigorously justified because both
countries are assumed to experience identical goods market demand and
productivity disturbances. (The analysis in Appendix R allows for relative
shifts in aggregate demand, and explicitly treats the money supplies as the
control variables.)

The solution algorithm used here may be described as follows: In the
two-country macro-model of Appendix A, we solve for the effects of home and
foreign money supply changes, holding base wage rates constant and assuming
that CPI inflation rate expectations and exchange rate depreciation
expectations are static. In the analysis of the text, we employ the partial
derivatives obtained in Appendix A to solve for the time-consistent path of
wages. We will then confirm that static CPI inflation rate and exchange
rate depreciation expectations are indeed rational (provided there are no
regime changes).

Once base wage rates are set and the current-period disturbances are
observed, the first-order conditions for the two non-cooperating central

banks are given byl8/

(3a) (any/apy)% = aty = wwIlzy/a + ripe - fie) - rap - (A - AY]
Ne

+ 2x(1 + .5¥)Epy - Pe-y + -5(de - G1) - a) = 0,

(3b) (ang/apg) = 2¢y + c¥*)Ezp/a + y(pe - HE) + tap - (A - FDI

+ 2x(1 - .5¥*)CpE - py - -5(a¢ - de) - FHI = 0,

where N superscripts stand for "Nash" equilibrium, and
¥ = (aq/adm)/(ap/adm) > 0 (m is the home money supply, v is a home money

demand disturbance, dm = m, - v,- Egy (my - Ve))« Due to the symmetry of

t t


-24-

where u' ~ N(0, oe), x ~ N(O, o) and A< 5 Al The common goods market
demand disturbance is u', and x represents a shift in demand from the
foreign good to the home good. Using equations (16), equations (22) can be

rewritten as

(22a') yg = nq - S{r - EslPy(eez)] + Pref tut x,

(22b') Ya = -ng - 6{ré - E CPE t+] + pte} t+u- x,

where 6 = 6'/(1-2A), and u = u'/(1-2A). In deriving equations (22'), we
have made use of the fact that, because the CPI weights are the same in both
countries and because home and foreign bonds are perfect substitutes, real
consumption interest rates are always equal even though the real exchange
rate may fluctuate in the short-run. Otherwise, the different real interest
rates faced by both home and foreign consumers would enter separately in
(22').
4. Solution of the model

To close the model, it is necessary to specify how wage setters and

investors form expectations of future prices.22/

The procedure for deriving
time-consistent, rational, price expectations is discussed in the text.

. -N
There we demonstrated that ElP retary - Py, is constant and equal to m, or

I
€ depending on whether the equilibrium between central hanks is non--
cooperative or cooperative. (See equations (4) and (9) of the text.) Using
equations (16) and (21), it is easy to deduce that

* - - . . sas s
t+) - ear roe my - ye In the time-consistent equilibrium,

E,le
rational expectations of exchange rate appreciation are static. Exchange
rate appreciation and CPI inflation expectations would change, of course, if

the governments' objective functions changed. We are now prepared to solve


International Finance Discussion Papers
Number 233
December 1983

PRODUCTIVE AND COUNTERPRODUCTIVE COOPERATIVE MONETARY POLICIES

by

Kenneth Rogoff

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.


-ll-

Feasibility of the q = 0 Nash equilibrium is confirmed by examining
equations (23),(25) and (26) of Appendix A; q = 0 and dp, = dpt if and
only if dm = ame 24/ One can also prove that the Nash equilibrium is
unique 22! Note that although the two countries may have different
expected inflation rates, the unanticipated component of home and foreign
price movements is the same.

To compare social welfare under the Nash regime with social welfare
under a cooperative regime, it will be necessary to compute
Ey y(a,)% and E, y(t)". using the fact that q\= 0, it is possible to

decompose the social loss functions into three components:

(6a) Epp (ag )N = (fF - ye + yah + 1,

(6b) Egy (agyN = (mR - He)e + CN + (rey,

where aN = (3,)% - 3,72, (ne) = ccag)N - Get’,
TNs Ey y{lzg/a + (doy)? + xt (dp,)TM1?}, and (re) = r%, since (ap)" = (dps).

The first element of Ea) is nonstochastic and depends on the
difference between the socially optimal level of employment, n, and wage
setters' target level of employment, n. Because monetary policy cannot
systematically raise the employment rate, this term can be reduced only by
directly addressing the underlying cause of the distortion. (This issue is
beyond the scope of the present paper.) The second term, ya’, measures the
extent to which the expected CPI inflation rate exceeds society's target

rate. This second term is also independent of current-period disturbances,


-10-

central banks' target employment rate, n, and wage setters' target
employment rate, i. Nominal wage growth is a decreasing function of the
weight society places on stabilizing inflation versus stabilizing
employment. Using the fact that Ey - 4-1) = “41> it is easy to
deduce from (4) that the expected rate of change of the CPI,

Ey (Peay + 5d447) - (p, + -5a,). is constant and equal to a Thus,
rational CPI inflation rate expectations are indeed static. 2Y/

Using equations (3) and (4), one can analyze the responses of the non-
cooperative system to unanticipated disturbances. Because the twc
countries are completely identical except for their labor market
distortions and target inflation rates, and because they experience
identical goods market demand and aggregate supply (but not money demand)
shocks, the real exchange rate q always turns out to be zero in Nash
equilibrium, regardless of the realization of the disturbances!

To confirm that q = 0 is indeed always a Nash equilibrium, first substitute

(4) into (3), and calculate (p,)" and (pf N under the assumption that q = 0.

Subtract Ee (0) and E,(¢)" from the resulting expressions to obtain:
23/
(5a) (pe) = Ey_y (pe )N = (dpg)N = -zp/aly + x(1 + .5¥)/(y - TY),
(5b) (pg)N - ey _y(pg)% = (apg) = -zy/aly + y(1 + .5¥)/(y - t¥)T.


-31-

Jones, Michael, "Automatic Output Stability and the Exchange Rate
Arrangement: A Multi-Country Analysis," Review of Economic Studies,
Vol. 89, No. 155 (January 1982), pp. 91-107.

ae , "International Liquidity: A Welfare Analysis," Quarterly
Journal of Economics, Vol. 98, No. 1 (February 1983), pp. 1-23.

Kydland, Finn E. and Edward C. Prescott, "Rules Rather than Indiscretion:
The Inconsistency of Optimal Plans," Journal of Political Economy,
Vol. 85, No. 3 (June 1977), pp. 473-92.

Macado, Jorge Braga de, "Policy Interdependence under Flexible Exchange
Rates," unpublished paper, Princeton University (July 1983).

McKinnon, Ronald I., “Currency Substitution and Instability in the World
Dollar Standard," American Economic Review, Vol. 72, No. 3 (June
1982), pp. 320-348.

Meese, Richard A. and Kenneth Rogoff, “Empirical Exchange Rate Models of
the Seventies: Do They Fit Out-of-Sample?" Journal of International
Economics, Vol. 14, No. 1/2 (February 1983), pp. 3-24.

Miller, Marcus and Mark Salmon, "Dynamic Games and the Time Inconsistency
of Optimal Policy in Open Economies," unpublished paper, University of
Warwick, (June 1983).

Phelps, Edmund S., "Phillips Curves, Expectations of Inflation and Optimal
Unemployment Over Time," Economica, Vol. 34, No. 135 (August 1967),
pp. 254-281.

_ > "Inflation in the Theory of Public Finance," Swedish
Journal of Economics, Vol. 75, No. 1 (January/March 1973),

Rogoff, Kenneth, "On the Effects of Sterilized Intervention: An Analysis
of Weekly Data," (unpublished, Washington, May 1983a).

__ > "The Optimal Degree of Commitment to an Intermediate
Monetary target: Inflation Gains versus Stabilization Costs,"
International Finance Discussion Paper No. 230, (Board of Governors of
the Federal Reserve System, Washington, September 1983).

Sachs, Jeffrey, "International Policy Coordination in a Nynamic
Macroeconomic Model," National Bureau of Economic Research Working
Paper No. 1166 (July 1983).

Sargent, Thomas J., Macroeconomic Theory (New York: Academic Press,
1979).


-30-

References

Barro, Robert J. and Navid B. Gordon, "A Positive Theory of Monetary Policy
in a Natural-Rate Model," Journal of Political Economy, Vol. 91, No. 4
(August 1983a), pp. 589-610.

> "Rules, Discretion and Reputation in a Model of Monetary
Policy,” Journal of Monetary Economics, Vol. 12, No. 1 (July 1933b),
pp. 101-121.

Buiter, W. H., "The Superiority of Contingent Rules over Fixed Rules in
Models with Rational Expectations," Economic Journal, Vol. 91, No. 363
(September 1981), 647-670.

Canzoneri, Matthew B., Dale W. Henderson and Kenneth Rogoff, "The
Information Content of the Interest Rate and Optimal Monetary Policy,"
Quarterly Journal of Economics, Vol. 98, No. 4 (November 1983), pp.
545-566.

Canzoneri, Matthew B., and Jo Anna Gray, “Two Essays on Monetary Policy in
an Interdependent World," International Finance Discussion Papers No.
219 (Board of Governors of the Federal Reserve System, Washington,
February 1983).

Canzoneri, Matthew B., "Monetary Policy Games and the Role of Private
Information," unpublished paper, Board of Governors of the Federal
Reserve System (Washington, November 1983).

Carlozzi, Nicholas and John B. Taylor, "International Capital Mobility and
the Coordination of Monetary Rules," unpublished paper, Federal
Reserve Bank of Philadelphia (June 1983).

Daniel, Betty C., "The International Transmission of Economic Disturbances
under Flexible Exchange Rates," International Economic Review, Vol.
22, No. 3 (October 1981), pp. 491-509.

Gray, Jo Anna, "Wage Indexation: A Macroeconomic Approach," Journal of
Monetary Economics, Vol. 2, No. 2 (April 1976), pp. 221-36.

Hamada, Koichi, "A Strategic Analysis of Monetary Interdependence," Journal
of Political Economy, Vol. 84, No. 4 (August 1976), pp. 667-7010.

Henderson, Dale W., “Exchange Market Intervention Operations: Their Role
in Financial Policy and Their Effects," in J.F.0. Bilson and R.C.
Marston, eds., Exchange Rate Theory and Practice, (Chicago:
University of Chicago Press, 1984), forthcoming.

Henderson, Dale W. and Douglas Waldo, "Reserve Requirements on Euro-
currency Deposits: Implications for the Stabilization of Real
Outputs," in J.S. Bhandari and B. Putnam, eds., Economic
Interdependence and Flexible Exchange Rates (Cambridge: M.1I.T.
Press, 1983).



-7-

depends on the difference between society's and wage setters' target levels
of employment, n - n.

the second term in the social objective function is the squared
difference between the actual rate of CPI inflation and society's target
rate. Again, the real exchange rate enters. Obviously, it is the presence
of the real exchange rate in both objective functions which creates
opportunities for cooperation or conflict 22! We shall begin by

considering the non-cooperative or "Nash" equilibrium.

V. Equilibrium When Central Banks Do Not Cooperate

to Achieve Their Stabilization Objectives

Each central bank has only one instrument at its disposal, the money
supply 20! Once base wage rates are set, any unilateral effort by either
central bank to influence its own country's price level will also have an
effect on the real exchange rate (except in the case of complete wage
indexation, 8 = 1) 2 Only if the two central banks inflate jointly can
they raise prices in both countries without altering the real exchange
rate,

Here we will examine the Nash equilibrium which obtains when each
central bank perceives that it cannot improve its own objective function
through unilateral action. To focus on the game-theoretic aspects of the
model, we will assume that central banks and private investors have full
current-period information. To further simplify, we will treat the home
price of the domestically-produced good as the home central bank's control

variable, though implicitly it is actually controlling the home money


-21-

(13a) Cg + log(1 - a) + K - ong+z=w-p,

(13b) c§ + log(1 - a) + ok* - an§ + z = we - pr,

where p is the nominal price of the domestically-produced good, and ny is
aggregate labor demand. The notional labor supply curve is assumed
inelastic :40/

(14a) no =f,

(14d) ng = ai,

To simplify algebra, n is set equal to k + (1/a)[log(1 - a) + Col, n= n*,
k = k*, and c

= a
0 = S:

CPI-indexed wage contracts for period t are negotiated at the end of
period t-1. The base wage rate is w (w*), and the indexation parameter is
B:

(15a) w= W + B(py - W),

(15b) we = We + B(pt - W), O< B< 1,
where

(16a) py = .5p + .5(p* +e),

(16b) py} = .5p* + .5(p - e);

e is the (logarithm of the) exchange rate (the domestic currency price of

foreign currency). The nature of the employment contract is that laborers


-27-

or negative. For example, when there is no wage indexation, a foreign money
supply shock will raise or lower domestic output and employment, depending
on whether the expenditure-switching effect of the real appreciation of the
domestic curency outweighs the expenditure increasing effect of lower world
real interest rates 43/ Wage indexation increases the possibility that the
foreign money supply shock will raise domestic employment.

In the text, we require knowledge of ¥ = (aq/am)/(ap/am), holding m*,

wy we, at and at constant. One can easily demonstrate, using (26), that ¥ >0.


-3-

may find it useful to at least glance at Appendix A before proceeding to
the main body of the text.

Section II describes the home and foreign welfare functions, which
depend cn own employment and CPI inflation. Section III details the
objectives of wage setters, as well as the nature of a time-consistent
equilibrium. Section IV describes the cross-effects of home and foreign
monetary policy; the real exchange rate plays a key role here. Section V
derives the stochastic equilibrium path of the world economy when central
banks conduct stabilization unilaterally, and are unable to guarantee to
wage setters that they will not try to systematically raise employment.
Section VI contrasts the results of Section V with social welfare under a
regime in which central banks again lack credibility with wage setters, but
are able to cooperate with each other in conducting stabilization policy.
Section VII stresses that an optimal cooperative regime -- one which
contains institutional constraints on systematic inflation -- is definitely

superior to any non-cooperative regime.

II. Donestic and Foreign Social Objective Functions

Each central bank attempts to minimize a social loss function which

depends on deviations of own-country employment and inflation from their

optimal (socially-desired) values -©/

(la) Ae = (mg - 2 + xCmpy - Hy),

!
S
7
1

(1b) ag = He)? + Cnty - FH),


-14-

market-determined full information real wage; that is, the real wage which
wage setters would agree on after observing the productivity disturbance.
Because the base nominal wage is set a period in advance, and because wage
indexation is incomplete, the central bank can effect wage setters' desired
movements in the real wage only by allowing some price level adjustment in
response to supply shocks. But while such price level movements are
consistent with one social objective, employment stability, they are
inconsistent with another social objective, price level stability. In the
next section we demonstrate that, holding base wage rates constant:, the
cooperative response to supply shocks is superior to the non-cooperative

response.

VI. Equilibrium When Central Ranks Cooperate to Achieve

Their Stabilization Objectives

Examining the first-order conditions for the Nash equilibrium
(equations (3)), we see that the incentives of the central banks to
unilaterally inflate are reduced by their fears of the concommmitant
effects on the real exchange rate. The real exchange rate depreciation
caused by unilateral home money growth raises consumer price level
inflation. Aside from the direct disutility of the higher inflation
rate, the home country enjoys less of an increase in employment from
unanticipated money growth than it would if the real exchange rate were to
remain constant. The reason is that nominal wages are indexed to the CPI,

which includes the domestic price of the foreign good .22/


-16-

"]

+

where (#1)° v(t = x,

uw

(9b) (wt)S = Ey _ ype)" = pe_y + (74)°,
where (##)° = WE + y(fi* - T*)/x,

(10) (pg )° = Egy (DE)® = (dpy)© = (dpgy® = -zy/aly + x/¥),

(11) 0 = (o8/a2)Ey/(y? + x1 = (18)%,

Comparison of equations (9) with their Nash counterparts, equations
(4), reveals that the mean rate of CPI inflation is higher under the
cooperative regime than under the non-cooperative regime. The intuitive
explanation is simple: wage setters anticipate that the two central banks
will have stronger incentives to inflate in a regime where each can count
on the other's cooperation, so that the benefits of inflation are not
reduced by real exchange rate depreciation.

A comparison of equations (10) and (5) reveals that

|(dp,)°| > (dp, 1. In the Nash equilibrium, the central banks allow the
supply shock’ to affect employment more, and inflation less, than in the

cooperative equilibrium. 2// It is easy to prove that the cooperitive

response to disturbances is superior; ij.e., re < ph 32/

Proof: Note that expressions (11) and (7) can be written in the same
general form since W(" +) = 2 + Py" + x)’. Differentiating the
expression (y? + ort? + yy? with respect to y yields

ayy - Ole?e + yy. Note that this derivative is strictly positive for


discretionary, inter-central bank cooperation can also lead to
systematically higher expected rates of inflation: private sector wage
setters will choose higher rates of nominal wage growth if they rationally
fear that the central banks will coordinate their efforts to lower real
wages and raise employment. (The conflict. between wage setters and the
central banks is generated by some type of labor market distortion which
causes the natural rate of unemployment to be too high.) Therefore,
monetary policy cooperation is unambiguously beneficial only in
institutional frameworks which eliminate or ameliorate the central banks’
credibility problem vis-a-vis wage setters /

Except for the fact that it incorporates rational expectations (cum
wage contracting), the stochastic, two-good, two-country model we employ is
quite similar to ones which have been used to characterize the benefits of
inter-governmental cooperation. Although sterilized intervention is
ineffective here (since bonds denominated in different currencies are
perfect substitutes) ,2/ domestic open market operations can still be used
to temporarily offset the real effects of unanticipated disturbances.
Nominal wage contracts, negotiated a period in advance and only partially
indexed to the current price level, provide the fulcrum for monetary
policy. Unanticipated foreign monetary policy similarly can have real
effects on the domestic economy (through the real exchange rate and through
real interest rates). The equations and solution of the underlying

Macroeconomic model are relegated to Appendix A so as to focus on the game-

theoretic aspects of the analysis in the text. Nevertheless, many readers


-25-

for the expected values of the real exchange rate, outputs, and real
interest rates. Taking t-] expectations across equations (19) and (22') and
recalling that wage setters set w = Eyl, - +58q,/(1-8)] and wk = Ee lPt

+ .56q,/(1-8)], one can solve for
(23) Egg (ap) = 0 = W - Eg_y (PE) = W - Ey (pe),
(24a) Eg_y(r - Fy) = Egy (yt) = 0, and
(24d) Eq_y(r* - 7H) = Egy (yf) = 0.

We can use the above equations together with equations (2) to

obtain
(25a) Eg_y(my) = = Amy,
(25b) Eg_y(mg) = We - anf.

We are now prepared to solve for q, Pp, p*, Pr Pt. n and n* as functions of

Ww, WT] ,7f, Z, Uy xX, Vv, and v*. These solutions are given below

(26a) q = vE(m - W+ Amy - v) - (m* - We + AT - v*) - 2(6 + 1/6)x],

w

(26b) p= W+ (vS + H)(m - W+ Amy - v) = vS(m* - Wwe + Am - v*)

+ xHu/6 - H(g + A/6)z/a + [AH/6 - 2vS(g + 1/8) ]x,

(26c) p* = we + (vS + H)(m* - We + dah - ve) - vS(m - W + Amy - v)
+ aHu/6 - H(g + A/6)z/a - [AH/6 - 2vS(g + 1/8) Ix,


Productive and Counterproductive Cooperative Monetary Policies

by Kenneth Rogoff*

I. Introduction
Schemes to increase coordination among central banks of employment and
inflation-rate stabilization policies have received renewed attention

Vy

recently.— Unfortunately, most of these schemes focus entirely on how
central banks might cooperate to offset unanticipated disturbances, and pay
little or no attention to the problem of systematically maintaining low
expected rates of inflation. The present paper is an effort to provide a
simple macroeconomic framework in which to examine both issues .2/ Within
the context of a two-country model of a managed floating exchange rate
system, we simultaneously analyze the strategic interactions of sovereign
monetary authorities across countries, and the strategic interactions of
private agents and the monetary authorities within a given country .2/

The main result of this paper is that, contrary to the usual
conclusion (and presumption) of earlier analyses, increased monetary policy
cooperation between two governments does not automatically increase welfare
in either country. In fact, welfare in one or both countries may be higher
when central banks conduct their monetary policies independently. It is
true that a cooperative regime does produce better responses to certain

types cf unanticipated disturbances (such as supply shocks or relative

shifts in aggregate demand). But when monetary policy is fully


-33-

inflation may nevertheless be non-zero; it may be optimal to make some use
of the seignorage tax when other methods of taxation are also
distortionary. See Phelps (1973).

9/ Even with one-period contracts, it would be necessary to explicitly
allow for multiperiod objective functions in order to analyze reputational
equilibria; see Barro and Gordon (1983b) or Canzoneri (1983). Sachs (1983)
examines monetary policy cooperation in an interesting dynamic setting; his
model does not incorporate rational expectations. Miller and Salmon (1983)
examine dynamic games in a very general dynamic open-economy model. The
main conclusion of the present paper would not be altered in a framework
with more dynamic elements.

10/ See Barro and Gordon (1983a).

Ji/_ Each individual group of wage setters is indeed concerned with the
inflation rate, just as society is. But because the impact of an
individual firm's contract on the aggregate inflation rate is small, they
have little incentive to temper their nominal wage increases.

12/' Phelps (1967) and Kydland and Prescott (1977) demonstrate why a time-
consistent macroeconomic equilibrium might be characterized by stagflation.
While we focus here on labor market distortions, there are other factors
which may cause the time-consistent rate of inflation to be too high.
Examales include seignorage and the existence of nominal government debt;
see Barro and Gordon (1983a).

13/_ It would, of course, be attractive to extend the present model to
‘allow for an endogenous determinaton of 8. For the full information setup
of the text, one can show that individual groups of wage setters would
choose gp = 0 if g is bounded between zero and one. Wage setters have no
need to worry about aggregate goods market demand and money demand
disturbances, because these are fully offset by the central banks. However,
wage setters want the central banks to allow some price level movement in
response to productivity shocks in order to stabilize employment around the
level which would arise if nominal wages were fully flexible. (See Appendix
A.) But because the central banks also care about price level stability,
they do not allow sufficient price level movement to fully stabilize
employment. Thus, from the point of view of wage setters at an individual
firm, indexation would only serve to further damp desired movements in the
real wage. .

14/ The assumption that home and foreign consumers have identical
consumption baskets yields considerable algebraic simplification, but is
not essential to any of the main conclusions here.

15/ Sachs (1983) also stresses the role of the real exchange rate as the
key variable interlocking the objective functions of the two governments.

16/ There will obviously be no trade-offs and no conflicts if the central
banks have as many independent instruments as objectives.


-28-

Appendix B: Relative Shifts in Demand

Throughout the text, shifts in the demand for each country's good are
assumed to be perfectly positively correlated; that is, x = 0, so that
there are no relative shifts in demand between the two goods. This
assumption is analytically convenient because it turns out to imply that
the real exchange rate q does not move in either the Nash or the symmetric
cooperative equilibrium. To solve the model when x ~ NO, 02), use
equations (26d) - (26g) to substitute into equations (1) for n - ny

n* - i*, ay and Tf:

(27a) A = (adm + agdm* + a3x + fi - ny2

+ x(bydm + bodm* + b3x + W - pe_y - 7),

(27b) A* = (aydm* + apdm - agx + i* - wey?
+ x(bydm* + bodm = b3x + W - pt_y - ¥)?,
where dm = m-W+ An - v, dm* = m* - we + ant - v¥, and the coefficients

a; and b, are the same as in (26d) - (26g). (As a minor expositional
convenience, we are abstracting from the common disturbances u and z.) In
the Nash equilibrium, 2A/adm = 0 = aA*/adm*. The procedure for finding a
and (wey is the same as in the text, and the resulting equations are the
same as equations (4) of the text.

Furthermore,

(28a) dN = - (aya3 + xbyb3)x/[ay(ay- ap) + yby(by- bp) J,


-12-

but as we shall later confirm, it is a function of the policy regime. The
final term, nan measures the extent to which the central bank succeeds in
stabilizing the employment rate and the CPI inflation rate arouncl their
expected market-determined values. Note that although the central banks
actually attempt to stabilize inflation and employment around their
socially-preferred values, in a time-consistent equilibrium the central
banks appear to respond to disturbances as if they were trying to stabilize
inflation and employment around their mean market-determined values .20/ To

evaluate rN substitute in for (dp, using equation (5a):
(7) N= (Bsa? )ECx1)? + Px? + x')? = Cr)",

where a is the variance of the zero mean supply shock, Ey (Ze) and
x' = yx(1 + .5¥)/(y - TY).

The reason that money demand shocks do not appear in equation (7) is
that, to the extent the shocks are known (here information is perfect=2’),
they can be completely neutralized. For example, consider a temporary
disturbance to home money demand. The home central bank can temporarily
raise the home money supply and, as one may confirm from the model of
Appendix A, prevent any effect from being transmitted abroad through
exchange rates or interest rates. Furthermore, the resulting stabilization
of the domestic price level is consistent with both home price level
stability and home employment stability. Thus the home central bank will
react to the disturbance in the same fashion whether or not it takes the
utility funtion of the foreign central bank into account .22/ Clearly, if

we relax the asumption that investors and central banks have complete


-15-

From the above discussion, it would appear self-evident that each
central bank would prefer to increase its money supply beyond the level
consistent with Nash equilibrium, provided it could count on the other
central bank to increase its money supply. In this section we will assume
that the two central banks agree to fix the real exchange rate at the same
level which would arise if all the disturbances were zero, and to confer
with each other on the most mutually advantageous set of price levels
consistent with that real exchange rate.20/ We will demonstrate below that
such an agreement is mutually beneficial only if the variance of supply
shocks is large relative to distortions in the labor markets.

Under the cooperative fixed real exchange rate (q = 0) regime, the
first-order conditions for minimization of the home and foreign social

welfare functions (equations (2)) are given by equations (8) below:
(8a) y[ze/a + y(Pp - we) - (A - A) + x(P_ - Pe_y - 7) = 0,
(8b) y[zy/a + y(pf - WE) - (A* - fi*)1 + x(pf - pty - Tf) = 0-

In deriving equations (8), we have made use of the fact that aq/adm is
zero ‘n the cooperative equilibrium, since each central bank can count on
the other to match any further unanticipated change in its money supply.
Equations (9), (10), and (11) are derived using the same algorithm used to
derive equations (4), (5), and (7) of the previous section: "c"

superscripts stand for “cooperative regime".

(9a) (g)© = Ey_7 (4) = ver + Cap)S,