-18-

the follower and sets policy to maximize its own utility subject to the
constraint implied by that reaction function.

Two leader-follower policy regimes are considered. The first is
the Stackelberg Regime. In this case, the follower's committed response
is to simply take the leader's policy as given and maximize its utility.
The leader chooses its own utility maximizing policy subject to the
follower's reaction function. The rules of this game are well-defined
and require no verification since each player is following a utility
maximzing policy. The second is the Fixed-Rate Regime. In this regime,
the follower's committed response is to fix its bilateral exchange rate
with the leader by matching the leaders money growth rate. Once again,
the leader maximizes its own utility subject to the constraint implied by
the follower's reaction function. The rules of this game are also well-
defined, and since bilateral exchange rates are readily observed,
adherence to the rules is also easily verified. The basic difference in
the attractiveness of these two regimes lies in the difference in the
reaction function the follower offers to the leader.

It should be noted that our view of the Fixed-Rate Regime is not
the usual one. 22/ Here it is modelled as a non-cooperative game, with
the follower enforcing the fixed rates. It is not modelled as the
outcome of direct cooperation and coordination of Policies; in fact, we
have questioned the feasibility of such regimes because of their
vulnerability to cheating. In our view, the Fixed-Rate Regime is an
alternative that the follower will want to impose upon the leader if it
Produces an outcome more favorable than the Stackelberg or Nash

solutions.


-33-

All are positive since Py > Pos For the parameter values specified in

footnote 14, 6g, = 2, dg, = 1.6 and 6g, = .8.

17/ The Pareto-efficient set of outcomes is the locus of tangencies of
the US and ROW ellipses; that is, the points (6g, ég*) such that
Usge/Usg ze UF 5ge/U* sq The formula for this locus is rather
complicated but discriminant analysis confirms that it is a hyperbola and

that it must run through the points B, F and B*,

18/ The point S must be distinct from N and in the direction indicated
because the slope of the US indifference is infinite at N. See

footnote 15.

19/ With the symmetric-negative constraints, both players would rather
be followers in a Stackelberg Regime. The US for example can be seen to
prefer S* to S as follows: The US indifference curve at S* (not
pictured) has infinite slope (see footnote 15), so S* must be prefered to
S if 69S 6 89% (that is, if ROW's policy as a Stackelberg leader is less
expansionary than as a Stackelberg follower). Since S$ must lie below the
45° line (see footnote 18), a. < Sgt, and by symmetry, 895 = 89% 3 SO
finally 59h = 896 < $e. Both players are better off in a Stackelberg

solution than in the Nash solution, but neither wants to lead.

20/ Since the ROW indifference curves are the mirror image of the US
indifference curves, a ROW indifference curve must be tangent to the 450

line at the same point a US indifference curve is. Clearly, the strength


-29-

rise; the price of ROW output falls. This is “inflationary” if ROW wages
are indexed to a weighted average of the prices of ROW and U.S. output,
not the price of ROW output alone. Under these circumstances, ROW
nominal wage rates rise in absolute terms and relative to the price of
ROW output. It is in this sense that the rise in import prices is built
into the cost of production in the ROW. The resulting rise in the ROW
real product wage will, in the absence of corrective monetary policy,
produce a fall in ROW output.

Suppose now that ROW policy makers choose to prevent part of this
output reduction through an exapansionary monetary policy. Under the
assumptions of our model, the increase in the rate of growth of the ROW
money supply will be built into inflationary expectations. Thus, from
the ROW's point of view, the depreciation of their exchange rate presents
them with a choice between two undesirable alternatives: less output or
higher expected inflation.

If ROW wages are indexed to a sufficiently high degree, a US
monetary contraction produces not only a depreciation of the ROW currency
but a rise in the ROW inflation rate during the adjustment period. It
can be argued, as with the depreciation, that there is a sense in which
this short run rise in inflation is built into the system in a way that
worsens the ROW's output-inflation trade-off. Accordingly, while short-
run inflation and exchange rate movements do not enter policy makers'
utility functions directly, they do enter indirectly through their impact
on the ultimate targets of policy -- output and inflationary

expectations.


-38-

References

Argy, V. and J. Salop. “Price and Output Effects of Monetary and Fiscal
Expansion in a Two-Country World Under Flexible Exchange Rates,"
International Monetary Fund, DM/79/33, May 1979.

Blinder, Alan S. "Monetary Accommodation of Supply Shocks Under Rational
Expectations". Journal of Money, Credit and Banking, 13 (1981)
pp. 425-438.

Bruno, M. and J. Sachs. “Macro-Economic Adjustment with Import Price
Shocks: Real and Monetary Aspects," NBER Working Paper, No. 340,
(April 1979).

Bryant, Ralph C. Money and Monetary Policy in Interdependent Nations,
The Brookings Institutfon, Washington, 1980.

Canzoneri, M. and J. Gray. "Oil Price Changes and Monetary Policy in a
Three Country Framework." Manuscript, Board of Governors of the
Federal Reserve Systme (June 1982a).

Canzoneri, M. and J. Gray. "Monetary Policy Games and the Consequences
of Non-Cooperative Behavior," (November 1982b).

Caprio, Jerry, and Clark, Peter. "Oil Price Shocks in a Portfolio-
Balance Model". Board of Governors of the Federal Reserve System,
International Finance Discussion Paper #181, (June 1981).

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

Findlay, Ronald, and Rodriguez, Carlos. "Intermediate Imports and
Macroeconomic Policy Under Flexible Exchange Rates". The Canadian
Journal of Economics 10, No. 2 (May 1977), pp. 208-217.

Gray, J. “Wage Indexation: A Macroeconomic Approach," Journal of

Monetary Economics, 2 (1976), pp. 221-235.

Hamada, Koichi, “Alternative Exchange Rate Systems and the
Interdependence of Monetary Policies." In National Monetary
Policies and the International Financial System, ed. Robert Z.
Aliber, University of Chicago Press, Chicago, 1974.

Hamada, Koichi. "A Strategic Analysis of Monetary Interdependence."
dournal of Political Economy, Vol. 84, August 1976, pp. 677-700.

Hamada, Koichi. “Macroeconomic Strategy Coordination under Alternative
Exchange Rates." In International Economic Policy, eds. Rudiger
Dornbusch and Jacob Frenkel, Johns Hopkins University Press,
Baltimore, 1979.



©

é/+) denotes the deviaz‘on of
from its full equilibium no-snocs vaiues .
represents the deviation of tne iog vaiue am ourons “se
vaiue of its fuli employment jieve:. For sma.: chase

approximates the nercentage daviacian of 7 varie 2

ngeshock value,

the currant tion fk a

seen

Productise *¢

(Al) 6x = (ies) dh

She = 61* = S0* = a(1/fah[Bliwteig*) + (4-8)

where = § = {W/P)L/E MS

Factor osicing and price indices:

(A3)  6w = yépi
Swe = y*épi*

6q = 6g + spi



-12-

time horizon to which the constraints apply is the “adjustment period", a
period of time determined by the length of labor contracts.

To close the model, the manner in which agents form their
expectations must be specified. Expectations formation in the muda! is
rational in a limited sense. Specifically, agents' price expectations
are rational given their (static) assumptions about US and ROW monetary
policies and OPEC's oi] pricing policy. If their views about these
policies are correct, then their price predictions will be realized,

For our purposes, the most important way in which the
constraints (5) differ from each other is in their specification of the
spillover effects of monetary policy. These spillover effects, in turn,
depend on the channels through which a country's monetary policy is
transmitted abroad. A number of possible channei: may be identi fied. 2/
We will focus on four. The first two of the four. an interest rate
channel and a goods demand channel, are well-known. The other two were
selected because of their increasing relevance for a number of countries
over the past decade. One stems from the now common practice of
contractually linking nominal wage rates to an index that includes the
prices of imported goods as well as domestically produced goods. The
other arises from the nature of OPEC's oi] pricing policy; the price of
of] is denominated in dollars and it not always adjusted quickly in
response to changes in the purchasing power of the dollar.

The first of our transmission channels was formally introduced by
Mundell (1963). This channel, which depends critically on capital
mobility, operates through the real interest rate to produce negative

spillover. In the absence of fully indexed input prices, an expansionary

monetary policy in one country raises that country's output and lowers


-20-

output. Given a fixed dollar price of oil, the real price of oi] in
terms of U.S. output necessarily falls. The effect on the price of oil
in terms of ROW output is even stronger. The change in the ROW real
Product price of oi] is equal to the change in the U.S. real product
price less any change in the relative price of ROW output. Since the
U.S. expansion results in a rise in the relative price of ROW output, any
reduction in the price of oi] in terms of U.S. output means an even
greater reduction in terms of ROW output.

By contrast, an expansionary ROW monetary policy has an ambiguous
effect on the U.S. real product price of oi]. In motivating this result,
we begin by noting that the fixed dollar price of oi] does not provide a
direct channel of transmission from ROW monetary policy to the U.S, real
Product price of oi] and, therefore, U.S. output. A ROW expansion
effects the U.S. real product price of oil indirectly through its impact
on the price of U.S. output. The ROW expansion is transmitted to the
Price of U.S. output through the real interest rate and goods demand
channels already discussed. The overall sign of the spillover effects
transmitted through these two channels may be positive or negative --
that is, the price of U.S. output as well as the level of U.S. output may
either rise or fall. Accordingly, the real price of oil in terms of U.S.
output may either rise or fall.

The one asymmetrical game examined in the next section involves
the special case in which the spillover effects of U.S. monetary policy
are positive while the spillover effects of ROW monetary policy are
negative. In the version of our model considered here, this will occur

for sufficiently large values of + and sufficiently small values of a.


~2-

We begin, in section II, by constructing a three-country model
with one oil producing country (OPEC) and two oil importing countries
(the U.S. and the ROW). This framework is used to develop the
constraints for the game played by policy makers in the two oi] importing
countries. As indicated above, an important element of these constraints
is the spillover effects of monetary policy. These spillover effects, in
turn, depend on the channels through which a country's monetary policy is
transmitted abroad. A number of possible channels may be
indentified2/. The present paper focuses on four. The first was
formally introduced by Mundell in the early 1960's. This channel, which
depends critically on capital mobility, operates through the real
interest rate. The second channel is also well-known, This channel,
which depends on the existence of two or more goods in the model,
operates directly through the demand for goods. The other two channels
were selected because of their increasing relevance for a number of
countries over the past decade. One stems from the now common practice
of contractually linking nominal wage rates to an index that includes the
prices of imported goods as well as domestically produced goods. The
other arises from the nature of OPEC's oil pricing policy; the price of
oil is denominated in dollars and is not always adjusted quickly in
response to changes in the purchasing power of the dollar.

The first channel described above produces negative spillover, a
beggar-thy-neighbor effect. In the absence of fully indexed inpu~
prices, an expansionary monetary policy in one country raises tha:
country's output and lowers its real interest rate. The real interest
rate movement is transmitted abroad, where its net impact is

deflationary. (The lower real interest rate produces a fall in the




~6-

growth of the U.S. and ROW money supplies. Shocks to the model take the
form of unexpected once-and-for-all changes in these policy variables.
The model can be summarized as follows:
Notation
Note: With the exception of interest rates, lowercase letters
denote the log value of a variable and uppercase letters denote the
variable itself. An asterisk refers to the ROW, while a superscript "o"
refers to OPEC.

real output

the composite input, consisting of equal numbers of units of
labor and oi]

labor employed in production of x
oil employed in production of x
nominal wage rate

vu to

domestic currency price of x

consumer price index

dollar price of oil

the exchange rate (units of ROW currency per dollar)
degree of wage indexation

z

‘°

degree of oi] price indexation

real expenditure

real income

terms of trade (relative price of U.S. output)

OPEC's net holdings of real bonds issued by U.S. residents
OPEC's net holdings of real bonds issued by ROW residents
the real interest rate

i the nominal interest rate

m the nominal money stock

octet kK OX KX OD

1c
+

9 the rate of growth of the money stock

6(+) denotes the deviation of the current value of a variable
from its full equilibium no-shock value. Thus, for example, 6x
represents the deviation of the log value of output from the log
value of its full employment level. For small changes, 6(+)
approximates the percentage deviation of a variable from it's full
equilibrium no-shock value.


-10-

In equation (5), total spending in each of the two oil importing
countries is shown to be an increasing function of domestic net income
and a decreasing function of the real rate of interest. Both spending
and income are measured in terms of the same consumption basket used to
define the price levels of the two countries.

A critical feature of the model is the assumption that OPEC is
unable to immediately adjust its level of consumption to changes in the
level of its income. Specifically, OPEC is assumed to have short-run
marginal propensity to save of one. This assumption is captured by
equation (6).

Real income in the two oil importing countries is given by
equation (7).2/ Real income in each country is an increasing function of
the level of its output and the relative price of its output. It is a
decreasing function of its real oil bill, OPEC's ‘net holdings of its
bond, and the real interest rate paid on those bonds. The relative price
of U.S. output is defined in equation (8) to be "the" terms of trade.

Equation (9) states that OPEC's net accumulation of each oi1
importing country's. bond is equal to that country's excess of sperding
over income. Thus OPEC's total saving -- or, equivalently, its current
account surplus -- is equal to the sum of U.S. and ROW dissaving.

Equation (10) is the log deviation form of the goods market
equilibrium conditions.o/ The demand for each good must equal its
supply. Demand for each good is an increasing function of total
expenditure in the two oi] importing countries and a decreasing function
of its relative price.

Equation (11) gives the equilibrium conditions for the U.S. and ROW

money markets. For simplicity, the income elasticity of money demand


-44-

Jones, Michael. “Automatic Output Stability and the Exchange
Arrangement: A Multi-Country Analysis". Review of Economi:
Studies, Vol. 69, 1982a, ppp. 91-107.

Jones, Michael. “Optimal Foreign Exchange Market Intervention: ividence
from the Bretton Woods Era". Unpublished manuscript (November
1982b).

Krugman, Paul. “Oil and the Dollar". In Economic Interdependence and

Flexible Exchange Rates, edited by J. Bhandari and B. Putnam,
M.I.T. Press, Cambridge, forthcoming.
Mundell, Robert A. "Capital Mobility and Stabilization Policy Under

Fixed and Flexible Exchange Rates". Canadian Journal of Economics

and Political Science, Vol. 29 (November 1963), pp. 475-485,
Mussa, Michael. “Macroeconomic Interdependence and the Exchange Rate

Regime". In International Economic Policy: Theory and Evidence,

eds. Rudiger Dornbusch and Jacob Frenkel. The Johns Hopkins
University Press, Baltimore (1979).
Sachs, Jeffrey. “Energy and Growth Under Flexible Exchange Rates: A
Simulation Study". NBER Working Paper No. 582, (November 1980).
Schmid, Michael. "A Model of Trade in Money, Goods and Factors".
Journal of Internatioan] Economics 6, (1976), pp. 347-361.

Thomas, George B. Jr. Calculus and Analytic Geometry, 3rd Ed., Addison-

Wesley, Reading, 1960.


FIGURE 1B: THE BEGGAR-THY-—NEIGHBOR POLICY WORL

2.54
$69



=34-

of this result depends on the symmetry we have imposed on the utility
functions. In particular, if wu were not equal to u*, then F would not be

in the Pareto-efficient set.

21/ The latter result should also be clear from Figure 1; the Fixed-Rate
Regime offers the US a better "budget constraint" than the Stackelberg
Regime. However, it can also be verified directly by comparing the US

utility at S, Lys with US utility at F, Upe It turns out that

(088) *u7 Tu + ey (01 + 205)]
Cu + (0, - bo) “Iu(u + on)? + of(u + of - 03)

Up = Us = >0

22/ The expression for UE - UR is rather complicated, and as it turns
out, unsigned. We have found for example that if Po TM P) = 1 (5 must be
Tess than °1) and yw is sufficiently large, then Ug > Ug (as in Figure 1).
On the other hand, if Po TM Py = 1 and uw is sufficiently small, then

Ur < Ug.

23/ Again, discriminant analysis confirms that the indifference curves
are ellipses, and the angle a of rotation of the major axis for the US
ellipses 1s given by cot 2(180° - a) = (og =e + u)/2og05 (see

footnote 14). a is greater than 135° for all parameter values and goes

to 180° as u goes to #, The US reaction curve is

89 = (040684 - e4ogdg*)/(u + oa)


-19-

As equations (16) and (17) show, the spillover effects of monetary
policy are not only ambiguous in sign in this case, they are also
asymmetric. For both countries, the real interest rate and goods demand
channels of the previous case are still present .tL/ As before, the real
interest rate channel produces negative spillover, the goods demand
channel produces positive spillover, and the spillover effects generated
through these channels are symmetrical for the two countries. For
simplicity, the degree of wage indexation has been set equal to zero for
both countries. Accordingly, the wage indexation channel is not present
in this version of our model.

The asymmetry of spillover effects in this case stems from the
fact that the price of oi] is set in dollars and is not adjusted in the
short run for movements in the prices of U.S. or ROW output. The fourth
channel of transmission considered in this paper is, then, the one
associated with a less than fully indexed dollar price of oi]. In making
Production decisions, U.S. firms are concerned with the real price of oil
in terms of U.S. output, while ROW firms are concerned with the real
price of oi] in terms of ROW output. We will demonstrate the asymmetry
of the spillover effects that are transmitted through our fourth channel
by examining, in turn, the impact an expansionary U.S. monetary policy on
the ROW real product wage and the impact of an expansionary ROW monetary
policy on the U.S. real product wage.

An expansionary U.S. monetary policy lowers the real produce price
of oil for the ROW. In understanding this result, it is useful to begin
by noting that the expansion lowers the U.S. real product price of oil.

This is because the expansion generates a rise in the price of U.S.


-3-

the results in Canzoneri and Gray (1983). That paper analyzes a three
country model with two oil-importing countries, the US and the ROW, and
one oil producing country, OPEC. US and ROW monetary policy “matter" in
this model, as does OPEC's pricing policy, because of contractually set
wage rates in the US and the ROW. In conducting policy, monetary

policy makers face a tradeoff between short-run employment objectives and
long-run inflationary expectations. This tradeoff is due to a public
sector credibility problem that is captured, in an ad hoc way, by the
assumption that private sector expectations concerning monetary policy
are static. That is, a new policy must be run for a period before it is
fully reflected in wage setters' expectations.

The game aspects of the paper derive from the spillover effects of
monetary policy -- that is, the way one country's monetary policy affects
output in the other -- and the global shock that creates an adjustment
problem in the first place. In Canzoneri and Gray (1983), the global
shock is an oi] price increase, but here it can be interpreted more
generally. The exact nature of the spillover effects depends upon
structural and institutional features of the three economies involved.

In our model, two important determinants of the sign and symmetry of the
spillover effects are the degree of wage indexation in each of the oil-
importing countries and the role played by oil.

Three of the many possible specifications of the spillover effects
of monetary policy are singled out for consideration. The first
specification produces a beggar-thy-neighbor policy world in which an
expansionary monetary policy in either country causes a contraction in
the other. Our model suggests that this specification may be relevant in

periods when indexing and oi] play no major role. The second produces a


-21-

III]. Policy Games

We turn now to some of the game theoretic aspects of monetary
policy in an interdependent world. The formal analysis underlying the
discussion of this section is contained in Canzoneri and Gray (1982b).
Only a subset of the results of that paper are presented here.

Three policy games are examined in this section. Each game
corresponds to one of the three types of policy spillover described in
the preceding section: negative symmetric, positive symmetric, and
asymmetric. Both the non-cooperative and the cooperative solutions to
these games are presented. The implications of our results for measuring
the size and distribution of the adjustment burden following an oil price
shock are then discussed.

We begin by describing the social welfare function of the policy
makers in each of the two oi] importing countries. Policy makers use the
one tool at their disposal-- monetary policy -- to maximize this
objective function subject to the macroeconomic constraints developed in
the last section. Consideration of OPEC's maximization problem is, by
contrast, altogether omitted from our analysis; the price of oil is
assumed to be exogenous.

The monetary authority in each oi] importing country is assumed to
be concerned only with domestic employment and long-run expectations of
the domestic rate of inflation. Specifically, the policy makers' utility

functions take the following form:

(18) U = -(6x)2 ~ um, ue = (ox)? - pote?


-22-

Here 6x and 6x* represent deviations of output from their full employment
values in the U.S. and the ROW, and m and m* are long-run inflationary
expectations.

By assumption, all games are initiated by an unanticipated
increase in the price of oi] that will, in the absence of corrective
policy, cause output to deviate from its full employment level. Such
deviations are temporary; they persist for only one period which is
referred to as the adjustment period. At the end of the adjustment
period, labor contracts are renegotiated with the new price of oi] in
mind, and, absent further unanticipated shocks, output returns to its
full employment level.

Monetary policy can be used to offset some or all of the output
effects of an oil price shock, but only at the cost of changing the
inflation rate expected to prevail in periods subsequent to the
adjustment period. This is because private agents are assumed to expect
the money growth rates established during the adjustment period to be
permanent. This assumption is intended to capture, in a very simple way,
the notion that policy makers are subject to a credibility constraint.
The important implicit assumption is that the monetary authority cannot
convince the private sector of a change in policy by simply announcing
it. Agents expect past policy to continue until confronted with an
actual policy change. Once a new policy has been in place for a period,
it, then, is believed to be permanent 22/

Thus, the tradeoff faced by policy makers following a shock such
as an oil price increase is this: They can increase the rates of growth

of their money supplies and increase employment during the period of


-24-
(21) U= (8x) = ulny + 69)%, Ue = -(6x4)? = ua(ne + ag*)”,

The dependence of output levels in the U.S. and ROW on the two
policy instruments, g and g*, is somewhat more complicated. As the
analysis of the last section demonstrated, a variety of specifications
are possible; we have selected three. In all three specifications, the
own effects of monetary policy are assumed to be positive; an
unanticipated increase in the rate of growth of a country's money supply
raises that country's output. It is the cross effects of monetary policy
that distinguish the three specifications and produce the three different
game situations studied in this section. In the symmetric-negative
specification, an expansionary policy in either country exports
unemployment to the other. In the symmetric-positive case, an
expansionary policy in either country increases employment in the other.
In the asymmetric game, a U.S. expansion increases employment both at
home and abroad, but a ROW expansion causes unemployment in the U.S.

At the beginning of the adjustment period, the U.S. and ROW
monetary authorities see the exogenous oi] price shock, and set the rates
of growth of their money supplies to maximize the utility functions (21)
subject to the relevant set of macroeconomic constraints. We now
consider, in turn, the games corresponding to each of the three output
specifications described above.

The Symmetric-Negative Game

With the symmetric-negative constraints, the spillover effects of

monetary policy are negative; an expansion in one country causes a


-27-

Some discussion of the flexible exchange rate case is contained in
Hamada (1974). Under the objective function postulated by Hamada for the
fixed exchange rate game, the flexible exchange game is degenerate.
Accordingly, Hamada suggests alternative objective functions for policy
makers in the case of flexible exchange rates -- functions that include
domestic output and the domestic interest rate. The analysis of the
present paper, by contrast, postulates one objective function that
applies regardless of exchange rate regime or other variations in the
“rules of the game". Indeed, in our analysis regime selection is an
outcome of the postulated objective function and world economic

structure.

4/ Many comparisons of fixed and flexible exchange rate regimes
emphasize the source of distrubances; see, for example, Canzoneri (1982)

and the references therein.

5/ Fiscal and commercial policy instruments are less flexible than
monetary policy instruments in most countries; however, in some
situations we might expect them to come into play as well. In such
cases, other longer run objectives would be added to the utility
functions, Or, if no one authority controlled all of its country's

instruments, new players would be added.

6/ This assumption is necessary in order to make corrective monetary
policy costly, given the nature of the utility functions (1). There are,

of course, alternative modelling strategies, fully consistent with


-19-

The way US and ROW policy makers rank the Nash, Stackelberg and
Fixed-Rate solutions will in general depend upon the spillover effects
of monetary policy. As the structural constraints implied by these
spillover effects change, so will the relative merits of the Nash,
Stackelberg and Fixed-Rate Regimes. In the next section, we describe how
the JS and ROW policy makers rank these regimes under the three sets of

cons*raints given by equations (5) of the preceding section.

IV. Adapting Regimes to an Evolving World Economy

In this section we explore the relative merits of Nash, Stackelberg
and Fixed-Rate Regimes under each of the three sets of macroeocnomic
constraints developed in section II. Our view is that each set of
constraints may have been relevant at a different point in history.
Accordingly, the discussion of this section is organized in what we
regard as a plausible chronological order.

A. A Beggar-thy-neighbor Policy World:

The world economic structure characterized by the symmetric-
negative constraints (5a) is one in which the interest rate channel for
the transmission of monetary policy dominates. It's theoretical
foundations may be found in Mundell (1963). It's policy implications are
consistent with the competitive devaluations and beggar-thy-neighbor
policies of an even earlier period. Our discussion in section II also
suggests that it describes a period in which neither wage indexation nor
of] played an important role.23/ The time period for which this game is
most likely to have been relevant, then, is the post WWI era -- a period
in which policy makers found refuge in a Fixed-Rate Regime. As we will

show below, these observations are consistent with our model. Fixed


-23-

and 1960's, which do not meet either of these requirements. When
spillover is positive and symmetric, we find that the ROW has an
unambiguous preference for a Fixed-Rate Regime, while the US may find
itself in the position of opposing fixed rates.

For the symmetric-positive constraints, the situation is
illustrated by Figure 2. (Figure 2B is an enlargement of the boxed area
in Figure 2A.) Again, B and B* are the US and ROW bliss points. The US
indifference ellipses and NS reaction curve are tilted downward,
reflecting the fact that a more expansionary ROW policy decreases US
unemployment and allows the US to economize on inflation. 22/ N, S, S*
and F again represent Nash, Stackelberg and Fixed-Rate solutions. The
locus of Pareto-efficient points is a hyperbola (not shown) running from
B to F to B*, The shaded area represents the set of outcomes that are
Paretc-superior to the Nash solution.

The US prefers the leadership role in a Stackelberg Regime to the
Nash Regime; this is confirmed by the observation that in the Stackelberg
Regime, the US chooses S over nc! However, the ROW is worse off at S
than at N; S is further from the ROW's bliss point (moving along NS*}
than N. Were it possible, of course, the ROW would opt to lead in a
Stackelberg regime; this is ruled out by assumption. As long as the ROW
is unable to coordinate its actions, it runs the risk of being exploited
as an unwilling follower in a Stackelberg game. One might expect the ROW
to make its dissatisfaction with this arrangement evident. A likely
complaint, reminiscent of the 1970's, would be that the US is shirking
its critical role as a locomotive in leading the world out of recession.

With the symmetric-positive constraints, the ROW finds the Fixec-

Rate Regime superior to both the Stackethecg and Nash Regimes. Tha os


FIGURE 1A: THE BEGGAR-THY—NEIGHBOR POLICY WORLD
254 7



-28-

rational expectations, that would produce games identical to those we
study in Sections III and IV. But these alternatives have their own
drawbacks. We could, for example, use curremt inflation rates in the
objective functions (1) rather than "long-run" inflationary expectations.
This formulation, however, is inconsistent with our presumption that
policy makers are reluctant to run corrective policies because the
resulting price increases somehow get “built into the system". Our
present formulation does capture this notion. Further discussion of this

point is contained in footnote 7.

J/ It has been suggested that the second argument in our utility
functions should be either the short-run domestic inflation rate or the
rate of depreciation of the exchange rate during the adjustment period.
One reason policy makers may care about these short-run phenomena ‘is the
possibility that the resulting price increases will somehow get “built
into the system." In fact, this possibility is allowed for in the macro
model that underlies our paper. Further, the deleterious effects of
short-run inflation and exchange rate movements are captured in our
specification of policy makers' utility. These points may be
demonstrated by considering the effects of a contractionary U.S. monetary
Policy on the ROW. This exercise is analyzed in detail in Canzoneri and
Gray (1983), which provides the formal macroeconomic underpinnings for
the present paper. In that framework, a contraction in the US causes an
appreciation of the U.S. dollar and a depreciation of the ROW currency
that reflects a deterioration in the ROW's turns of trade. Both the

absolute and relative prices of the good the ROW imports from the US


-16-

asymmetric game, both would be better off if the US inflated more while
the ROW inflated less.

In each of the three games we consider, there are a variety of
Pareto-improving outcomes and a Pareto-efficient set characterized by the
contract curve. The basic problem with all of these “better" outcomes is
that they provide incentives for one or both of the players to cheat.
Consider once again the symmetric-positive game, and suppose the US and
ROW policy makers have agreed to the swap described above; that is, each
has promised a more expansive policy than implied by the Nash solution.
In this situation, the US policy maker has an incentive to cheat on the
agreement and run a less expansionary policy. This is because the more
expansionary policy promised by the ROW would increase US employment,
making it optimal for the US to economize to some extent on inflation.
Put another way, if the US policy maker did not cheat and actually
carried out the agreed upon policy, the outcome would look too
inflationary to a public that did not fully understand the nature of the
solution and discounted the possibility of foreign repercussions in
response to a tighter US monetary policy. The political pressure to
cheat could well be enormous.

The cheating problem is compounded by the difficulty of defining
and verifying cooperative solutions, and by the moral hazard this
implies. The various OECD countries have different procedures for
implementing monetary policy and different definitions for monetary
aggregates; both can be altered in subtle ways that allow policy makers
to violate the spirit, without violating the letter, of their
committmernts. Further, the effect of a monetary policy that is well-

defined in terms of implementation procedures and aggregates can always


-36-

11/ Once again, the nominal exchange rate depends on the ratio of the
money supplies; that is,
be = (1 + 2)%(8 + + + 9)(1/04)(69 - 89*)

This result is used in Canzoneri and Gray (1982b).

12/ Recall that we are assuming that agents‘ expecations are "rational"
given their assumptions about monetary policy. If their views about
monetary policy (and the price of oil) are correct, then their price

predictions will be realized.

13/ It is clear from the money demand functions that in full employement
equilibrium the rates of product price inflation are g and g*. Since the
terms of trade is fixed in full equilibrium the rates of inflation of the
general price levels (pi and pi*) are also equal to g and g*.

14/ With the utility functions (21),
au/adg = -2(6x)(36x/a6g) - a(n + 6g) = 2p 4840, >0
du*/adg* = 2p 4840, >0
when T= 1% = 0 and &g = 6g* = 0.
15/ It may be interesting to note that some unemp1oyment will remain
as long as any weight is given to inflation in the utility functions.

The conditions Usq = 0 and UF sgxTM 0 (which define the Nash equilibrium)

imply


-23-

adjustment to the oi] price shock, but only at the price of higher
expected rates of inflation in the period that follows. Policy makers
have two choices in dealing with these expectations in the post -shock
Period. They can accomodate them, thereby achieving full employment
output. Or they can lower them by lowering the rates of growth of their
money supplies, thereby forcing their economies through a second
adjustment period. The terms m and 7* enter the utility functions (1)
because each of these choices has undesirable consequences in subsequent
periods -- higher steady state inflation in the first case and additional
periods of adjustment and unemployment in the second.

Under the assumptions discussed above, the long run expected rates

of inflation in the U.S. and the ROW are simply3/

(19) T= 9, w= gt,

where g and g* are the rates of growth of U.S. and ROW money supplies

during the adjustment period. Note that
(20) T=) + 69, Sita = 16 + 69%,

where 1, and 74 are the rates of inflation in the full-information

0
equilibrium that is assumed to have Preceded the adjustment period.
These are the inherited rates of inflation that each country enters the
adjustment period with. For most of our analysis, we assume that the
inherited rates in both countries are zero. Using equations (20), the

utility functions (18) may be re-written as


-8-

(6) é¢ =0

(7) ay = (A/¥)(6x+.58t) - (0/PT)(0/¥)(Sq-6pi+60) - (rB/Y)6b = (B/Y)ér

8y* = (X/Y)(Sx*=.56t) ~ (Q/PI)(0/Y)(Sq-6pi+60*) = (rB/Y) 8b*
- (B/Y)8r
(8) ét = 6p - dp* - dp*
(9) sb = (¥/8)(8e ~ by)
sb* = (¥/B)(Sc* = dy*)
(10) 8x = .5(C/X)[ée + Se - (142p)6t]

6x* = .5(C/X)[6c + dc* + (1+2y)dt]

(11) mS = 6p + 6x = Adi

ém*®> = Sp* + 6x* = Adi*

(12) éi = 6r + SP, - OP

it = ort
Si* = br + opty = ope
(13) m= my +g
me = ms + gt

Equation (1) gives the production technologies of the two oi]

importing countries. Output of each consumption good is proportional to


~8-

makers are subject to a credibility constraint. The important impl‘cit
assumption is that the monetary authority cannot convince the private
sector of a change in policy by simply announcing it. Agents expect: past
policy to continue until confronted with an actual policy change. Once
the new policy has been in place for a period, it, then, is believed to
be permanent.

Policy makers have two choices in dealing with the higher
inflationary expectations generated by their responses to the oil price
increase. They can accomodate them, thereby maintaining full employment
output in subsequent periods. Or they can lower them by lowering the
rates of growth of their money supplies, thereby forcing their economies
through additional adjustment periods. The terms 7 and m* enter the
utility functions (1) because each of these choices has undesirable
consequences -- higher steady state inflation in the first case and
additional periods of adjustment and unemployment in the second._/

Under the assumptions discussed above, the long-run expected rates

of inflation in the U.S. and the ROW are simply

(2) sg, wee,

where g and g* are the rates of growth of the US and ROW money supplies
during the adjustment period. The oi] price shock has no direct effect
on long-run expected rates of inflation; it affects inflation
expectations only if it affects money growth rates. Letting 6g and 6g*
represent the changes in the growth rates of US and ROW money that occur

in response to the of] price shock during the adjustment period, we have


-25-

the case. 2/ However, our conclusions are unaffected by the location of
the Nash relative to the 45° line.

As noted earlier, the Nash solution does not exploit the
comparative advantage of US monetary policy enough. Both players would
be made better off by a more expansionary US monetary policy and a less
expansionary ROW monetary policy. The Pareto-improving outcomes lie in
the shaded area.

Both the US and the ROW prefer the Stackelberg Regime to the Nash
Regime. In Figure 3, S is better for both players than N. It is better
for the ROW because it lies back along its NS reaction curve in the
direction of B*, and it is better for the US because the US chooses it
explicitly over n.28/

The Fixed-Rate Regime, by contrast, comes off poorly under the
asymmetric constraints. With the US leading and the ROW enforcing the
fixed-rate structure, the outcome will be point F in Figure 3. In this
setting, Fixed rates do not lead to a Pareto-efficient outcome; in fact,
F is not even a Pareto-improving outcome. It is is worse than N, and
thus S, for the Row ;22/ The ROW has no incentive to enforce a fixed-rate
structure under these circumstances. Furthermore, the US may also prefer
S to F, as is the case pictured in Figure 3. In this situation, the US
will lead in a Stackelberg Regime. However, it is also possible for the
US to prefer the Fixed-Rate Regime to both the Stackelberg and Nash

Regimes. If this occurs, US and ROW interests conflict and, as before,

we venture no guess on the outcome.


-15-

terms of trade, an excess demand for ROW money will result in a fall in
both ROW prices and output. We conclude, then, that the spillover
effects of monetary policy that operate through the real interest rate
channel alone are negative.

The second of our transmission’ channels, which depends on the
existence of two or more goods in the model, operates directly through
the demand for goods. In and of itself (abstracting from the real
interes: rate channel), this channel produces positive spillover. To see
this, consider once again an increase in the rate of growth of the U.S.
money supply. The resulting increase in U.S. output leads, at an
unchanged real interest rate, to an equal increase in U.S. expenditure.
At an unchanged terms of trade, this expenditure increase would fall
equally on the U.S. good and the ROW good, generating an incipient excess
supply of the U.S. good and an excess demand for the ROW good. This
induces, in turn, an equilibrating rise in ROW output and fall in the
terms of trade.2/

Of course, increased production of the ROW good will occur only if
the ROW real product wage falls. This is possible because the increased
demand for the ROW good causes a rise in its relative price -- a fall in
the terms of trade. A rise in the relative price of ROW output can
produce a rise in its absolute (domestic currency) price even if the
overall ROW price level falls 20/ This, in turn, lowers the ROW
real product wage and induces increased production of ROW output. It
follows that the output response to the increased demand for the ROW good
will be larger, the larger is the terms of trade change it produces.
Further, if the induced terms of trade effect is sufficiently strong, the

positive spillover channeled through goods demand will dominate the


-17-

channel will always dominate the negative spillover effects channeled
through the real interest rate.

The three channels of transmission discussed above, and the
spillover effects they generate, are symmetrical for the two oil
importing countries. The effects of a U.S. expansion on ROW output are
identical to the effects of an ROW expansion on U.S. output. A
sufficiently high degree of wage indexation Produces the positive
symmetric game of the next section, while the absence of full indexation
and a sufficiently high elasticity of relative goods demand with respect
to relative price produces the negative symmetric game of the next
section. We consider next a version of our model that produces a
transmission channel that does not operate symmetrically for the U.S. and
ROW. The essential feature of this version is that the price of oil is
set in dollars and is not indexed to any price or basket of prices during
the adjustment period.

A Fixed Dollar Price of 0i1

Equations (16) and (17) below give the solutions for U.S. and ROW
output for the special case in which wage rates in both oil importing

countries and the price of oi] are fixed in nominal terms (y=yt=y? = 0).

(16) 6x = £459 + pgdg* - 664
(17) éx* = p¥sg* + pkg - 684
where

bq = (1/D,D5)(1+a)2(o+9) {eaL2r(1+ate) + 4(6+26) + 26]
+ O(Ev+t)} > 0

Pg = (1/D,D5)(1+A)2(6+9)x0(E4-t-Ev) (unsigned)

= (1/0 ,D5)2D, EL (14A) ag + vae] > 0

A)
a
"


-18-

of = (1/0,D9)(1+A)?[re(Ea-r-Ev) + 2EerLav(o+g) + A(1+A+e+9)]}
(unsigned)
oF = (1/D,D2)(1+A)*{Ea(ore)Ea(ore) + (2ta)] + 2engr (142)
+ 40(6+9)[1 + Ev(1-27)]} (unsigned)

D) = A(O+ptt) +1 + 16+ 90

2EA(1+A48) + 248 > 0

i=)
Ixy
"

Other parameters are defined as before.

As before, an increase in the price of oil reduces output in both
the U.S. and the ROW, and does so by the same amount in the two
countries. An increase in the rate of growth of U.S. money has the same
qualitative effect on U.S. output that it had in the previous case.
However, for the same degree of wage indexation, this effect is stronger
in the present case because the rise in the price of U.S. output
associated with the monetary expansion lowers the real product price of
oi] as well as the real product wage.

The effect of an expansionary ROW monetary policy on ROW output
may, in this case, be either positive or negative, whereas in the
Previous case it was unambiguously positive. The intuition behind this
anomalous result is as follows: As before, the spillover effects of ROW
monetary policy may be either positive or negative. If they are
negative, the price of U.S. output declines, which can raise the real
Product price of oi] for both the U.S. and the ROW. If the rise in the
ROW real product price of oi] is sufficiently large, it can dominate the
positive effects normally associated with a monetary expansion and

Produce a decline in ROW output.


-24-

prefers F to N, and therefore to S as well. The US may or may not prefer
F to S, but it certainly prefers F to ne28/ Once again, the Fixed-Rate
Regime achieves a Pareto-efficient outcome. If the US does prefer fixed
rates, it is assumed that fixed rates will prevail. However, for some
parameter values, the US prefers to lead in a Stackelberg Regime. This
is the case pictured in Figure 2. Here, again, US and ROW interests
conflict and our analysis provides no theoretical presumption about which
policy regime will be established. The ROW can be expected to seek the
implementation of fixed exchange rates, while the US will oppose such
efforts.

C. An Asymmetric Policy World:

The world economic structure characterized by the asymmetric
constraints (5c) is one in which the spillover effects of US monetary
policy are positive, but the spillover effects of ROW policy are
negative. In section II, we describe a model that results in these
constraints because oi] is priced in terms of dollars; we speculate (but
have not shown) that a similar model with a high degree of wage
indexation in the ROW and a lesser degree of wage indexation in the US
could also result in these constraints. Oil and wage indexation have
played important roles in the more recent, flexible-rate era, and indeed
we will show that the Stackelberg Regime (which assumes flexible exchange
rates) is more attractive than the Fixed-Rate Regime in this case.

For the asymmetric constraints, the situation is illustrated by
Figure 3. The US ellipses and NS reaction curve are tilted upward, while

26/

the ROW ellipses and NS reaction curve are tilted downward.— The Nash

solution pictured in Figure 3 lies above the 45° line. This need not be


-28-

employment effect. The interesting point here is that the Nash solution
does not exploit sufficiently the positive externalities embodied in the
spillover effects of monetary policy. The basic arguments are the same
as in the symmetric-negative game, only the signs of the spillover
effects are reversed, as are the conclusions, At the margin, a more
expansive U.S. policy would increase ROW employment without significantly
affecting the U.S. policy maker's utility, and vice-versa. Both would be
better off if they could mutually agree to inflate more.

As in the preceding case, it is not clear how a cooperative
solution would be achieved in a world of decentralized policy making.
There are many cooperative solutions and policy makers will not be
indifferent among them. Further, in the absence of binding contractual
arrangements, all cooperative solutions are subject to credibility
Problems. As before, we might expect a solution close to the Nash
solution with each country attempting to influence the other's monetary
Policy. In this case, however, the pressure would be in the direction of
more, rather than less, inflationary policies.

The Asymmetric Game

With the asymmetric constraints, the spillover effects of U.S.
policy are positive, while the spillover effects of ROW policy are
negative. This means that U.S. policy has a comparative advantage over
ROW policy in combating the unemployment caused by an unanticipated rise
in the price of oi]. The Nash and cooperative solutions to this game are
quite different from those of the two symmetric games already discussed.

If inherited inflation rates are zero, each policy maker knows

that the other is going to inflate. However, in this case the two policy


-5-

a better outcome in a non-cooperative setting. The non-cooperative
Stackelberg and Fixed-Rate Regimes we propose appear to be historically
relevant and they avoid some of the moral hazard problems associated with
direct cooperation.

In section IV, it is shown that the Stackelberg and Fixed-Rate
Regimes can indeed provide Pareto-superior outcomes to the Nash. With
the symmetric-negative constraints, two outcomes are possible. The
Fixed-Rate Regime may be the preferred set of rules for all players, in
which case it is assumed that fixed rates will be implemented. However,
it is also possible that the ROW will prefer to have the US lead in a
Stackelberg game, while the US prefers fixed rates. In this situation
there is no theoretical presumtion about how the conflict over policy
regime will be resolved. A similar situation arises with the symmetric-
positive constraints. Fixed rates may be preferred by all. But it is
also possible that the US will prefer to lead in a Stackelberg game while
the ROW prefers fixed rates. Again, our analysis does not suggest a
resolution to this conflict. Finally, the case in which spillover is
asymmetric is the only case in which it is certain that fixed rates will
not be the preferred outcome. Either both players will prefer the
Stackelberg Regime, or there will be disagreement, with the US favoring
the Stackelberg Regime and the ROW supporting fixed rates.

The methodology, rather than the specific results, of Section IV
are what we wish to emphasize in this paper. Some of our direct
comparisons depend upon the form of the welfare functions that are
postulated. Further, we consider only global shocks as the driving force
behind all of the games ~/ But more importantly, no formal structure for

the game of regime selection is presented. In all the games we consider,


-4-

locomotive policy world in which an expansionary policy in either country
causes an expansion in the other. This specification is particularly
relevant for periods in which a high degree of wage indexation prevails.
The third specification produces an asymmetric policy environment in
which an expansion in the US induces an expansion in the ROW, while an
expansion in the ROW induces a contraction in the US. Our model suggests
that this specification may be relevant when OPEC is setting a dollar
price of oil in the short-run. We speculate that the first, or
symmetric-negative, specification is most likely to have been relevant
(if ever) in the early post-war era; the symmetric-positive and
asymmetric specifications refer to more recent periods.

In section III, the inefficiences associated with the Nash
solution are characterized, and a rationale is developed for considering
non-cooperative, leader-follower regimes as realistic alternatives to the
Nash. The nature of the inefficiences associated with the Nash solution
depend upon the macroeconomic constraints under which the game is played.
In the beggar-thy-neighbor policy world, the Nash solution is too
expansionary; each country would be better off if both countries could
somehow manage to inflate less. The converse is true for the locomotive
policy world. Welfare in both countries would be raised by more
expansionary policies. In the asymmetric game, all would be better off
if the US inflated more while the ROW inflated less.

The argument for considering other non-cooperative regimes as
alternatives to the Nash is based upon the difficulties inherent in
defining and verifying directly coordinated policies and the moral hazard
that this implies. These difficulties suggest that it may be more

realistic and more productive to model policy makers attempts to achieve


-17-

be altered by changing the regulatory environment in financial markets.
These factors provide great scope for cheating in any direct attempt at
coordination of policies.

In the remainder of this section we explore ways in which a group
of politically sovereign policy makers can achieve outcomes superior to
the Nash solution and at the same time avoid some of the pitfalls of
direct attempts at cooperation. Our approach is to ask whether policy
makers can design well-defined and easily verified rules of the game that
will produce a Pareto-improving outcome. To do this, we must first
discuss the nature of the players in our games. We can then consider the
kinds of policy regimes that they might be capable of instituting.

Up to now, we have treated the US and ROW policy makers in a
completely symmetric manner. This is probably unrealistic. The US is a
single country with one monetary authority; the RCW on the other hand is
an aggregation of a number of smaller countries, each with its own
monetary authority. This suggests that the degree of coordination ROW
policy makers can hope to achieve among themselves is limited. If
coordinated actions are difficult for the ROW, the role of "leader" in
the global policy games we are concerned with naturally falls to the US.
In fact, the US appears to have played a dominant role in the policy
games cf the post World War II era and may continue to do so in the
1980's. Therefore, the alternative rules of the game we have chosen to
examine assign the role of leader to the US and the role of follower to
the ROW. A follower, in our terminology, is a player (or group of
players in the case of the ROW) that is committed to a well-defined
reaction in response to any particular policy the dominant player, or

leader, may choose. The leader knows the reaction function of


-7-

full employment values in the U.S. and the ROW, and w and a* are long-run
inflationary expectations. While the first argument in each of these
utility functions requires no special justification, the second may. The
case for including an inflation term of this particular form will be
taken up later in the section.

There would, of course, be no policy game if policy makers had
available as many independent instruments as they have targets.
Accordingly, we assume that policy makers in each country have at their
disposal only one policy tool -- the rate of growth of the domestic money
supply -- to use in pursuing their dual objectives.

By assumption, all games are initiated by a global shock that
will, in the absence of corrective policy, cause output levels in
both countries to deviate from their full employment values. In
Canzoneri and Gray (1983), the global shock is an unanticipated increase
jin the price of of]. We will continue to use that example here. The oil
price shock affects output levels, and monetary policies "work", because
of contractually set nominal wage rates in the two countries. Neviations
of output from full employment are, however, temporary; they persist for
only one contract period, which is referred to as the adjustment period.
Absent further unanticipated shocks, output returns to its full
employment level in the period following the adjustment period.

Monetary policy can be used to offset some or all of the short-run
output effects of an oil price increase, but only at the cost of
increasing the inflation rate expected to prevail subsequent to the
adjustment period. This is because private agents are assumed to expect

the money growth rate established during the adjustment period to be

6
permanent <! In a very simple way, this captures the notion that policy


-37-

6x = -(u/o,)(89 + T))

8x* = -(u*/p,)(6g* + 1H)

So if 6g > -1, and Sg* > -n*

v then 6x and 6x* are negative as Jong as y

0
and u* are positive.

16/ At the Nash solution, U., = 2p (-8x) < 0 because 6x < 0; see

$69

footnote 12. Similarly, Us = 2p 9(-8x*) <0.

g
17/ See Canzoneri and Gray (1982b) for a demonstration that such a

solution exists.

18/ See Canzoneri and Gray (1982b) for a derivation of the contract
curve.

19/ Our model does have implications for the size of the adjustment
burden that are independent of its game aspects. If, for instance, the
oil price shock raises the price of domestic output in the two countries,
it will be true that the adjustment burden is an increasing function of
the degree of wage and oil indexation. In contrast to most other models
in which indexing has been studied, however, the oi] price shock does not
necessarily raise output prices in our framework. Thus, the conclusions
for indexing in the present paper are not clear cut. This point and
other implications of our macroeconomic structure in the one good case

are discussed in Canzoneri and Gray (1982a).


-30-

IV. Measuring the Adjustment Burden

The analysis of the last section has one major implication for the
size of the adjustment burden following an oil price shock. The absence
of cooperation betweeen policy makers unambiguously increases the size of
the adjustment burden for all players, where the adjustment burden is
measured by the reduction in policy makers' utility functions ly
Perhaps equally important and interesting, however, are the lessons to be
derived from the present section concerning the appropriate measurement
of the size and distribution of the adjustment burden.

The appropriate measure of each country's adjustment burden
following an oi] price shock is presumably the reduction in socia
welfare, somehow measured, experienced by that country following the
shock. In the game framework of the present paper, that reduction is
measured by the utility loss suffered by policy makers. This loss is a
weighted average of the changes in output and inflationary expectations
that follow the shock, and can not be directly observed. Clearly, an
observable proxy for the actual adjustment burden -- a measure that is
perfectly correlated with social welfare -- would be useful.

One candidate proxy for the adjustment burden born by any
individual country following an oil price increase is the fall in its
level of output. A casual reading of the popular literature suggests
that this proxy is already in wide use. It appears to be common »ractice
to gauge the overall impact of an oil shock by its aggregate effect on
output levels, and the distribution of that impact by its effect on

relative output levels. However, the analysis of this section suggests


Papers address this question in a multi-country setting that explicity
models OPEC's short run savings behavior. Examples include Caprio and
Clark (1981), Krugman (1980), Sachs (1980), and Schmid (1976).
Unfortunately, none of these papers provides the analysis we require of
both an oi] price shock and the spillover effects of monetary policy.

For further discussion of this point, see footnote 1.

4/ In calculating the post shock equilibrium, which is necessary in
solving the model, it is assumed that the real value of the original
dollar increase in the price of oil is preserved. That is, the dollar
price of oil is adjusted in the post shock period for any changes in the
U.S. price level which occur subsequent to the pre shock equilibrium.
Thus, the real value of the oi] price increase can only be temporarily

eroded during the adjustment period.

5/ The level of real income in each country is defined to be nominal net
national income deflated by the domestic consumer price index.

Accordingly, Y and Y* are given by
Y = (P/PI)X = (Q/PI)O - rB
Ye = (P*/PI*)X* = (Q/PI)O* - rB*

Because consumption patterns are identical in the two countries, and
because the law of one price holds, (Q/PI) = (Q*/PI*); the real price of
oil in the U.S. is equal to the real price of oil in the ROW. Log
linearizing Y and Y* around their no-shock equilibrium values yields

equations (7).


-21-

The Stackelberg Regime has much to recommend it. Both the US and the ROW
achieve higher utility at S than at N. The ROW is better off because S
lies back along its reaction curve in the direction of its bliss point,
B*, The US must be better off since it explicitly chooses S$ over y.28/
The US is, however, off of its reaction curve at S. For this to be a
viable regime, the US must be convinced that any attempt to move away
from S toward its own reaction curve will only result in a movement along
NS*. This condition will be met as long as the ROW is committed to the
response function NS* and the US is aware of that committment.

It is interesting to note that in this beggar-thy-neighbor policy
world the US may be regarded as a reluctant leader. (This is not true
with the symmetric-positive constraints (5b), as will be seen below.)
Were it possible, the US would opt for a Stackelberg Regime in which the
ROW was the leader; that is, S* is better for the US than 5.19/ Our
assumptions preclude this possibility. However, this comparison does
suggest that the US might view its leadership role in this Stackelberg
Regime as a burden.

With symmetric-negative constraints, the Fixed-Rate Regime may
dominate both the Nash and Stackelberg Regimes for both the US and the
ROW. In the Fixed-Rate Regime, the ROW policy makers commit their
monetary policies to fixing their dollar exchange rates; in our model,
this amounts to the ROW setting its money growth rate to match whatever
money growth rate the US adopts. In terms of our diagrams, the ROW
offers the US the 45° line as its reaction curve instead of NS*; the US

chooses point F, which happens to be a Pareto-efficient outcome. In this

case then, the Fixed-Rate Regime is one way of achieving a cooperative

20/
solution in a non-cooperative setting.


International Finance Discussion Papers
Number 219

February 1983

TWO_ESSAYS ON MONETARY POLICY IN AN INTERDEPENDENT WORLD:

I, MONETARY POLICY GAMES AND THE CONSEQUENCES
- Vv A\

II. SOME ASPECTS OF THE ADJUSTMENT PROBLEM
N E IDENT WORLI

by

Matthew B. Canzoneri and Jo Anna Gray

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.


-34-
§/ The demands for the two goods (in levels) are given by

xt (PI/P)(P*E/P)¥ (C4C#) + OPEC demand

xed = (pre/px)(P/p*E)Y (CHC) + OPEC demand

Equations (10) are obtained by log linearizing x4and yd around their no-
shock equilibrium values, setting the change in OPEC's demand for both
goods equal to zero, and equating output demand to output supply. The y
which enters equation (10), then, is the negative of the own relative
price elasticity of the expenditure Shares of the two goods. The term
(1+2p) which enters equation (10) is the negative of the own relative

price elasticity of the levels of expenditure on the two goods.

J/ An unitary income elasticity of money demand means that each
country's nominal money balances are effectively deflated by the price of
domestic output in the equations describing money market equilibrium. If
this were not the case, valuation effects would be another source of

spillover.

8/ The solution of equations (1) through (13) of the text requires
calculating the one period ahead expectation of the price of U.S. and ROW
output. This expectation appears in equation (12) as a determinant of
the nominal interest rate. To find SPyy> we begin by differencing
equation (13), substituting the result, along with equation (12), into

equation (11), and updating the result by one period.


-40-

(Al2) 64 = 6r + 6P,, 7 OP

i* = + §p*. - Sp*
67 ér Spt) 6p

(Al13) om =mi+g

m* = my + gt

Equations (A7) and (Al0) may warrant clarification. To arrive at
(A7), we define the level of real income in each oil-importing country to
be nominal net national income deflated by the domestic consumer price

index. Accordingly, Y and Y* are given by
Y = (P/PI)X = (Q/PI)O - rB
Ye = (P*/PI*)X* = (Q/PI)O* - rB*

Because consumption patterns are identical in the two countries, and
because the law of one price holds, (0/PI) = (Q*/PI*); the real price of
oil in the US is equal to the real price of oi] in the ROW. Log
linearizimg Y and Y* around their no-shock equilibrium values yields
equations (A7).

The demands for the two goods (in levels) are given by

x7 = (P1/P)(P*E/P)Y(C#C*) + OPEC demand

xed 2 (pre/pe)(p/PHE)Y (CHC) + OPEC demand

Equations (Al10) are obtained by log linearizing x4and xed around their

no-shock equilibrium values, setting the change in OPEC's demand for both


-10-

policy in either country increases output in the other. In the
asymmetric case, a US expansion increases output abroad, but a ROW
expansion causes output to fall in the US.

The three game situations just described are embedded in three
models of output determination which are summarized by equations (5a),
(5b), and (5c) below. These reduced form models describe the dependence
of output in each country (6x and 6x*) on the changes in the money growth
rates of both countries (6g and 6g*) and the oi] price shock (8q), They
constitute three possible sets of contraints that may be faced by policy
makers as they attempt to maximize the objective functions given by
equations (4).

(5a)  Symmetric-Negative Constraints:
5x = 9159 - pydg* - 1464, 8x* = p15g* - p89 - 9464
where 94 > 0 for i = 1, 2, 3 and Py > Pos

{5b) Symmetric-Positive Constraints:
8x = 9 48¢ + pgdg* - 664, Sx* = p48g* + 589 - 664

where p > 0 for i = 4, 5, 6 andp pp.
j 4 5

(5c) Asymmetric Constraints:
6x = 9769 = 9 g69* - P64, Sx* = p&6g* + egg - P94

where p, > 0 and et > 0 for i = 7, 8, 9.


-9-

+ 69, 1 = ms + Sg*,

where 1, and TM% are the rates of inflation in the full-information
equilibrium preceding the adjustment period. These are the inherited
rates of inflation that each country enters the adjustment period with.

Using equations (3), the utility functions (1) may be re-written as
(4) Us =(8x)? = u(ng + 69)%, UF = =(8x8)? = ue(ng + 59%)?

For most of our analysis, we assume that TH and TM% are zero and that uy
equals u*.

The dependence of output levels on the price of of] and on the two
monetary policy instruments is somewhat more complicated. In most macro-
models concerned with the short-run determination of output, output
responds negatively to unanticipated increases in the prices of imported
inputs and positively to unanticipated increases in the rate of growth of
the domestic money supply. However, there exists no such consensus on
the spillover effects of monetary policy, which depend on the structural
and institutional features of the economies involved and the role played
by oi]. The sign and symmetry of these spillover effects are important
because they produce the game aspects of our paper.

In the case of symmetric-negative spillover, monetary policy is a
“begger-thy-neighbor" policy. An expansionary policy in either country

exports unemployment to the other. In the case of symmetric-positive

spillover, monetary policy has a "locomotive" effect. An expansionary


-7-

The Model
Note: The model has been log-linearized around its no-shock
equilibrium and written in log deviation form. For real variables, the
model's no-shock equilibrium is identical to its pre-shock equilibrium.

A bar over a variable indicates its no-shock (or, equivalently, its pre-
shock) equilibrium value. The two oi] importing countries are assumed to

be identical in all respects in the pre-shock equilibrium. The
superscripts d and s denote demand and supply. Subscripts refer to time.

Unless otherwise indicated, Greek letters represent parameters.

(1) 8x = (1-a)éh
8x* = (lea) 6h*

where (l-a) = C(W/P) + (0/P)H/X

(2) 6h = 61 = 60 = -(1/a)[B(Sw-dp) + (1-8)(6q-5p)]
6h* = 61* = 60* = =(1/a)[B(dw*-dp*) + (1-8) (8q-de-sp*) J

where 6 = (W/P)L/L(W/P)L + (/P)0]

(3) 6w = yépi
éw* = y*6pi*

6q = 6g + y°Spi

(6) Spi = .5(Sp + Sp* + Se)

Spi* = .5(dp* + dp - de)

(5) 6c = 6y = ofr

6c* = éy* - or


-36-

25/ The US ellipses and reaction curve have the oroperties describec in
Footnotes 74 and 15; the ROW ellipses and reaction curve have the
properties described in footnote 23. Again, the parameter values are

sors 6c = o*6g = = pt = 3/ neous Uf4
04 = 08 € 30¢, $64 1, ps °% 3/4 ancou 1/4,

2) For cea Nash solution, we nave

5

and 8 are 5ig,
If Py is large

small, the Nash wi?!

ROW utility must be Tower at F than at N if 69 is less than

use the ROW ellipse et N has a zero slope. 59p must be less thar 39x,

oecause the US indifference ellipse at N has an infinite slope.


-31-

that these measures are inadequate approximations of policy makers'
utility in a wide range of circumstances.

Consider, for example, the problem of comparing the overall size
of the adjustment burden in a non-cooperative game setting with the size
of the burden in a cooperative setting. The move from a non-cooperative
solution to a cooperative solution raises the utility of all players.
However, if spillover is negative, this move is also associated with a
greater output loss and lower long run inflation for all players.
Accordingly, the size of the output loss does not, in this case, provide
a correct indication of policy makers’ utility. In general, the
relationship between output losses and social welfare will depend on the
nature of the spillover effects of policy which, in turn, depend on the
structural and institutional features of the countries involved.

The difficulty of appropriately capturing the changes in social
welfare following an oil price shock is even more evident when the
question of the distribution of the adjustment burden is addressed. If
one allows for differences in the relative weights assigned to output and
inflation across countries, no systematic relationship between social
welfare and output can be established, even for a given macroeconomic
structure. A country with a very high aversion to inflation may, for
example, suffer a substantial output loss compared to a country with a
very high aversion to unemployment, and yet experience a lower overall

utility loss.


FIGURE 3B:

6g

ASYMMETRIC POLICY WORLD

1 \ NS
1.54 a
CV \ A
j Wer FA line
\ 7
\ (4
\\ ' YA
1.04 SOA Va
1 5: N
] /
: f F
|
j va
9.54
: Yj
VA
V4 NS*
7
7
1 7
0.6 Mans \ sgt
-0.5 0.0 0.5 io 1.5


-41-

goods equal to zero, and equating output demand to output supply. The w
which enters equations (A10), then, is the negative of the own relative
price elasticity of the expenditure shares of the two goods. The term

(1+2)) which enters equations (A10) is the negative of the own relative

price elasticity of the levels of expenditure on the two goods.


FIGURE 3A: ASYMMETRIC POLICY WORLD

6g

6g

Or


-14-

positive spillover. The actual spillover effects of monetary policy
depend, then, on the relative importance of these three channels.

The first of our three transmission channels was formally
introduced by Mundell in the early 1960's. This channel, which depends
critically on capital mobility., operates through the real interest rate.
In tracing this channel, we observe first that an increase in the rate of
growth of the U.S. money supply leads to a lower real interest rate.

This occurs, in our model, because an expansionary monetary policy raises
U.S. output and, simultaneously, U.S. oil imports. This, in turn, leads
to a rise in OPEC's income. Because OPEC's short run marginal propensity
to save is assumed to be one, the increase in OPEC's income generates an
equal increase in their desired saving. At an unchanged real interest
rate, this produces an incipient world excess supply of goods. A fall in
the real interest rate is required in order to equilibrate the goods
markets.

The fall in the real interest that accompanies an expansioriary
U.S. monetary policy has, in and of itself, a contractionary impact on
the ROW. This can be seen most easily by considering the ROW money
market. At unchanged ROW prices and output, a fall in the real interest
rate induces a fall in the ROW nominal rate and an excess demand for ROW
money. At an unchanged terms of trade, this excess demand can be
eliminated by either a fall in the ROW price level, a fall in ROW output,
or both. If the terms of trade are held constant, a fall in the ROW
price level means a fall in the price of domestic output. In the absence
of full indexed wage rates, this produces a rise in the ROW real product

wage and, accordingly, a fall in ROW output. Thus, at an unchanged


-6-

conflict of interests may arise. Consider, for example, the game played
under the symmetric-negative constraints. As already noted, the ROW may
prefer the Stackelberg Regime to both the Nash and the Fixed-Rate
Regimes, while the US always finds the Fixed-Rate Regime the most
attractive of the three. The ROW cannot force the US to lead in a
Stackelberg game, and the US cannot force the ROW to fix its exchange
rate against the US dollar. Who will win out if this situation occurs?
On the basis of the analysis presented in this paper, we have no way of
telling. Our approach does, however, suggest which solutions or regimes
a given policy maker will prefer in a given economic environment. Even
in situations in which interests conflict then, it may provide some
insight into the posturing and compromises of policy makers as they adapt

world policy regimes to an evolving world economic structure.

II, Utility Functions and Macroeconomic. Constraints

This section begins with a description of the social welfare
function that policy makers in each country attempt to maximize. We then
develop the macroeconomic constraints for the game played by these policy
makers as they strive to achieve their objectives.

Policy makers in each oi] importing country are assumed to be
concerned with domestic employment and long-run expectations of the
domestic rate of inflation; their utility functions take the following

form:

(1) Us -(8x)? - ur, Ut = -(8x*)2 - were?

Here 6x and 6x* represent deviations of employment or output from their


exchange rates may be the preferred policy regime in a world
characterized by the symmetric-negative constraints (5a) or, for that
matter, the symmetric-positive constraints (5b) to be discussed later.
For symmetric-negative constraints, the situation is illustrated by
Figure 1. (Figure 1B is an enlargement of the boxed area in Figure 1A.}
B and B* are the US and ROW bliss points; indifference curves take the
form of ellipses, with larger ellipses representing lower utility
Tevels.-4/ The straight lines labeled NS and NS* are the US and ROW
reaction curves for the Nash and Stackelberg games. The US curve, for
example, gives the US utility maximizing response to any ROW poticy.2/
It and its ROW counterpart are referred to as the NS reaction functions
in the discussion that follows. The Nash solution is labeled N, the
Stackelberg solutions are S and S*, and the Fixed-R=te solution is Ft6/
The Nash soluticn is located at the intersectisn of the two
NS reaction curves. Neither the US nor the ROW has an incentive to nove
unilaterally from this point. However, as discussed in the last section,
there exist alternative feasible outcomes that are better for one or both
players. All of these Pareto-improving points are included in the shaded
area of figure 1B; the Pareto-efficient outcomes lie on a hyperbola (not
pictured) running from 8 to F to pe tl/ The incentive to cheat at any of
these points, also discussed in the last section, is indicated by the
fact that one or both of the players must be off his NS reaction curve.
In the Stackelberg Regime, the US chooses a utility maximizing
policy conditioned on the ROW's Nash reaction function. In our diagrams,

the ROW restricts the US opportunity set to the curve NS*; the US picks

point S, the point of tangency between NS* and a US indifference ellipse.


=32-

Footnotes

1/ The game theoretic aspects of policy making in an interdependent
world have been recognized by a number of earlier writers. See, for
example, Bryant (1980), Hamada (1974, 1976 and 1979), and Johansen
(1980).

2/ There is of course a voluminous jiterature devoted to the
international transmission of monetary disturbances; however, explicit
analyses of two (or more) country models are relatively scarce. We are
unaware of any set of papers that present just the analyses we need here,
although many of the individual pieces of our desired framework do appear
in various other papers. Mundell (1963) for exar le, develops symmetric-
negative constraints in a model with fixed prices and static
expectations. Mussa (1979) presents an exceilent discussion of
macroeconomic interdependence which includes an exposition of Mundell's
results. Argy and Salop (1979) present a model very like the two-good
extension of the Canzoneri and Gray (1982a) model we discuss below,
though they postulate static expectation formation. Daniel (1981)
presents a rational expectations model that is also very like our two-
good extension; her use of intermediate goods serves the function of our
indexing. Bruno and Sach's (1979) simulation model has all of the

ingredients necessary to derive the three sets of constraints we employ.

3/ There exist a number of papers that explore the effects of an oii
price shock in a single country context; see, for example, Blinder

(1981), Bruno and Sachs (1979), and Findlay and Rodriguez (1977). A few


5.

II. A Three-Country Model

In this section, we develop an analytical framework that is used
to study the effects of both an oil price shock and the monetary policy
responses to that shock. Of particular interest are the spillover
effects of monetary policy. It is these effects that produce the policy
games analyzed in section III of the paper.

The one period, discrete time model of this section is a two-good
extension of the framework developed in Canzoneri and Gray
(1982a).=/ There are three countries, one oi] producing country
called OFEC and two oi] importing countries called the U.S. and the rest
of the world (or ROW). Oi] is an intermediate good that is used by the
U.S. and ROW to produce two consumption goods which are consumed in all
three countries. Each oi] importing country is specialized in the
production of one of these consumption goods. Labor is the only other
variable input employed in the production of each consumption good; it is
used in fixed proportions with oi]. OPEC sets the price of oi] in terms
of U.S. dollars, but this price may be partially or fully linked to a
consumer price index. The nominal wage in each oil importing country is
contractually fixed in terms of the local currency, but may also be
partially or fully linked to an index of consumption good prices. The
absence of completely flexible wage rates introduces the possiblility of
short run deviations of output from its full employment level. There are
three assets in the system: U.S. money which is held only by U.S.
residents, ROW money which is held only by ROW residents, and a real bond
that is held by the residents of all three countries. The model includes

three exogenous policy variables: the price of of] and the rates of


-29-

makers do not react to that fact in the same way. The U.S. will inflate
more to compensate for the negative spillover effects of ROW policy,
whi"e the ROW will inflate less because of the positive spillover effects
of U.S. policy. So the Nash solution exploits the comparative advantage
of U.S. monetary policy in this asymmetric game.

The interesting point, however, is that the Nash solution does not
exploit the comparative advantage of U.S. policy enough. Both policy
makers would be better off if the U.S. inflated more and the ROW inflated
less. The argument should by now be familiar. At the Nash solution,
there is no cost for either policy maker to making a marginal change in
the rate of growth of his money supply. However, the ROW benefits from a
more expansionary U.S. policy, and the U.S. benefits from a less
expansionary ROW policy.

Once again, it is not clear how a cooperative solution would be
achieved in a world of decentralized policy making. A solution close to
the Nash might be expected, with each country attempting to influence the
other's monetary policy. In this case, however, the ROW will attempt to
induce the U.S. to inflate more, while the U.S. will attempt to induce
the ROW to inflate less. Thus, the pressures exerted by the two
countries as they strive for a better outcome might be interpreted to
reflect differing objectives while, in fact, the objective functions of

the two countries are identical.


-35-

am? ~ §Pyy = OX, - AGF = ACSP4y - SP Hy)
Because of the way we have chosen to specify output supply and demand, 6x
and 6r are expected to be equal to zero in the post shock equilbrium,
The term (6P,> - 8P 44) is simply the change in the expected rate of
inflation in the post shock equilbrium, which is simply equal to the
change in the rate of growth of money, or 6g. The term
amy is the deviation of the money stock in the post shock period from
the value it would have assumed in the absence of shocks. Since the post
shock period is the second period in which altered money growth rate
is applicable, this term is equal to 26g. Substituting these values into
the equation above and simplifying gives

5p ,, = (2+r)6g
An exactly analogous expression for the post shocx price of ROW output
can be derived. Once these expressions are substituted into equation

(11) of the text, the solution of the model is a matter of

straightforward algebra.

9/ The nominal exchange rate also deprecitaes; that is,
se = (1 +2)°(6 + x + 9)(1/0,)(89 = 694)
This result is used in Canzoneri and Gray (1982b) to define the Fixed-

Rate Regime.

10/ In fact, in the case of a fixed real price of oi], the ROW price

level necessarily falls following a U.S. expansion,


-12-

A Fixed Real Price of Oil

output 2/

Equations (14) and (15) below give the solutions for U.S. and ROW

for the special case in which the price of oil is fully

indexed (8°=1) but the degree of wage indexation may lie anywhere

between zero and one, inclusive (O<y=y*<1l). Each country's output is a

linear function of the unanticipated changes in the model's three policy

variables -- the rates of growth of U.S. and ROW money and the price of

oil.
(14)

(15)

8x = 9169 + ppdg* - 0369
5x* = py5g* + po6g - 36

where

by = (1/D,D9)(1+a)?(1-y)of{eaLe(aty) + (1+A)(g+2r)+ 270(1-y)]
+ 10(1-y)} > 0
(1/0 Dp)(1+A)2(1-y)o{eaLe(aty) + (144)9] - 1A8(1-v)]
(unsigned)

°2

3 = (1/D,D9)2D,EL(1+A)ag + vae(1-y)] > 0
and

(¥7X)(1+4y) > 0

a
1

a = (¥/X)[(1-r)o +(B7Y)] > 0
— = 1/(1-8) > 0

v = (l-a)(1-8) > 0

@ = (1-a)B/a > 0

@ = (1-a)(1-8)/a > 0

Dy = A(O+p+t) + 1 + TO(l-y) + By + o> 0

Dp = 2EA(1#A) + 28(1-y)(Ea+d) > 0


-31-

to our wage indexation channel. Argy and Salop (1979) present a model
very like the model developed in Canzoneri and Gray (1983), though they
postulate static expectation formation. Daniel (1981) presents a
rational expectations model that is also very like our model; her use of
intermediate goods serves the function of our indexing. Bruno and Sach's
(1979) simulation model has all of the ingredients necessary to derive

the three sets of constraints we employ.

11/ Henderson and Quandt (1971) and Bryant (1980) provide useful
discussions of the Nash and Stackelberg solution concepts we use in this

section.

12/ Bryant (1980) and Hamada (1979) have used the Stackelberg solution
concept in describing international policy games. Henderson (1979)
discusses cases in which a degeneracy between targets and instruments
allows Stackelberg solutions to exist when Nash solutions do not. As far
as we know, we are the first to use the Fixed-Rate Regime as a solution

concept in a non-cooperative game setting.

13/ As noted earlier, we can let 6q in the constraints (5) represent any
global supply side disturbance; it need not represent an oi] price

increase.

14/ These ellipses are obtained by substituting the constraints (5a)
into the utility functions (4) to eliminate 6x and éx*, The resulting
formulae are rather complicated, but discriminant analysis (see Thomas

(1960), pg. 496) confirms that they are indeed ellipses. The angle a of


-25-

contraction in the other. Reliance upon such “begger thy neighbor"
policies can, in a non-cooperative setting, result in an excessively
inflationary outcome.

If 1, and 1

0 0
adopt expansionary policies. The oi] price shock would cause

are both zero, then both policy makers will want to

unemployment if they did nothing, and if T% and TM% are both zero the
marginal utility of avoiding some of this unemployment outweighs the
marginal disutiltity of the inflationary expectations engendered. 24/
And when each policy maker realizes that the other is going to expand, he
will want to adopt an even more expansionary stance to make up for the
negative spillover of the other's policy.

The non-cooperative or Nash solution is the policy configuration
from which neither player can move unilaterally to make himself better

off. If both 7, and TM are zero, both players will adopt expansionary

0
policies in the Nash solution. ve/

To us, the interesting point to note is that the negative
spillover effects of monetary policy give the Nash solution an
inflationary bias. ach policy maker knows that the other will expand,
and each must therefore run an even more inflationary policy to make up
for the negative spillover of the other's policy. In fact, it turns out
that there is a certain amount of needless competitive inflation (or
devaluation) going on in the Nash solution. The Nash solution is always

dominated by a range of cooperative solutions that are less inflationary

and make both policy makers better off.


-32-

rotation of the major axis for the US ellipses (see Thomas (1960), pg.
493) is given by cot 2a = (8 - 0 + u)/200 93 so the rotation is less
than 45° for all permissible parameter values and goes to zero as y goes
to, The ROW ellipses are of course the mirror images of the US
ellipses if, as we assume, uy = u*. The ellipses in Figure 1 reflect the

parameter values p, = 064 =1, Pos 3/4 and » = 1/4,

15/ The US reaction function is found by maximizing U for a given 6g*;

the US function is
89 = (910464 + pypp69*)/(u + o*)

Note that the slope of this curve is less than one since Py > Pos The
slope of a US indifference curve is equal to Usgx/Y eq? and since Ugg =0
for any point on the US reaction function, the US reaction curve cuts the
US ellipses at points where their slope is infinite. The ROW reaction
function is the mirror image of the US function; it cuts the ROW ellipses

at points where their slope is equal to zero.
16/ The US policies in the Nash, Stackelberg, and Fixed-Rate Regine are
89y = 010 464/(u + Oe = 0195)
N v3 1 2

pp 36d(u + °° + pyPo)(u + o° - 5)

u(u + pe) + plu + o - pa)?

895

89, = (0) - ,)0,80/Lu + (0, - 6)",


-1-

I, Introduction and Summary

In a world characterized by short-term wage or price rigidities,
unanticipated supply-side disturbances such as an oi] price increase may
cause temporary deviations of output from its full-employment level.
While corrective monetary or fiscal policies may be effective in
neutralizing the effects of such shocks on output and employment, they
may co so at the cost of a higher price level and increased inflationary
expectations. These short-run macroeconomic costs constitute an
important part of the adjustment burden that is shouldered by the world
economy following global disturbances such as the oil price increases of
the 1970's. The purpose of the present paper is to identify some of the
ways in which the interdependence of the world's economies affects the
adjustment to an oi] price shock and the associated adjustment burden.

The focus of our analysis is on the spillover effects of monetary
policy -- that is, the way in which one country's monetary policy affects
output and employment in other countries. These spillover effects depend
on the structural and institutional features of the individual countries
involved, and may be positive or negative for any given country. They
create a situation in which policy makers in one country may be expected
to condition their actions on the policies pursued in other countries;
policy has unavoidable game aspects .2/ In studying the outcome of this
global policy game, we find that the overall size of the adjustment
burden is unambiguously increased by the absence of cooperation among
policy makers. It is further noted that the output losses associated
with an oi] price shock do not, in general, provide an adequate measure

of the reduction in social welfare caused by such disturbances.


FIGURE 2A: THE LOCOMOTIVE POLICY WORLD

2.254
4

6g

1.754

0.254
j

-0.25-4

-0.75-

T T * 7 T T T
-0.75 -0.25 0.25 0.75 1.25 1.75 2.25


-4-

just described. It can be reasonably argued that as the institutional
structures of the world's larger economies have changed, so have the
relative importance of these channels. This perspective may be
particularly useful in attempting to understand apparent inconsistencies
in policy prescriptions over time and across countries.

In section III of the paper we show that regardless of the
specific nature of the game played by world policy makers, the non-~
cooperative solution to that game is destructive in the sense that there
generally exist coordinated policies that would make all players better
off. In a symmetric game in which spillover effects are negative, the
non-cooperative solution is too inflationary; both countries would be
better off if they could both somehow manage to inflate less. The
converse is true for a symmetric game in which spillover effects are
positive. Welfare in both countries would be raised by more expansionary
policies. In the asymmetric game in which the dollar price of oil is
fixed, all would be better off if the U.S. inflated more while other
countries inflated less. Clearly, then, the overall size of the
adjustment burden following an oil price shock is increased by the
absence of cooperative behavior on the part of policy makers.

The games discussed in section III are treated in more detail
in Canzoneri and Gray (1982b). Stackelberg and fixed exchange rate
solution concepts are also discussed in that paper; only a sample of the
results are presented here. Section IV concludes with a brief discussion
of the difficulties involved in selecting an observable measure of the
adjustment burden borne by an individual country or by the world economy
as a whole following an oi] price shock. Output losses are shown to be a

generally inadequate measure of this burden.


-13-

As expected, each country's output responds positively to an
increase in the rate of growth of its own money stock as long as wages
are not fully indexed. Monetary policy "works" due to the absence of
completely flexible wages in the short run. An unexpected increase in
the rate of growth of U.S. money, for example, produces an incipient
excess supply of money that is offset, in part, by a rise in the U.S
price level. Provided U.S. wages are not fully indexed, this "price
surprise" lowers the U.S. real wage product and induces an increase in
U.S. output and employment.

A rise in the real price of oi] lowers output in both oi]
importing countries. It does so by increasing the price firms must pay
for the composite input. This reduces the amount of the composite input
employed in production and, therefore, the level of output.

As equations (14) and (15) show, the spillover effects of monetary
policy are symmetrical but ambiguous in sign. For a sufficiently high
degree of wage indexation, we see that these effects are positive. That
is, an expansionary monetary policy in one country raises output in the
other. If the degree of wage indexation is less than one, spillover can
be negative; an expansionary monetary policy in one country may produce a
contraction in the other. The larger is t -- that is, the higher is the
responsiveness of relative goods demand to relative price -- the more
likely is this outcome. Some intuition into these results can be gained
by considering three competing "channels" through which one country's
monetary policy may be transmitted to other countries. The first of the

three channels produces negative spillover, while the other two produce


-2-

alternatives may be characterized by a set of assumptions about the way
in which individual players' actions are constrained. The two sets of
assumptions, or “rules of the game", we focus on are referred to as the
Stackelberg Regime and the Fixed-Rate Regime. Each Regime is modelled as
a leader-follower game with the US as the leader and the rest of the
world (or ROW for short) as the follower. The Stackelberg solution
concept fs familiar, but our use of fixed exchange rates as a solution
concept in a non-cooperative leader-follower game is new.2/ In the Fixed-
Rate Regime, the follower commits itself to fixing its bilateral exchange
rate with the leader. The leader then chooses an optimal policy subject
to the committed response of the follower. Fixed exchange rates are,
then, viewed as an alternative non-cooperative solution that the ROW may
be able to impose upon the US.

The relative desirability of the Nash, Stackelberg and Fixed-Rate
Regimes depends on the structural features of the world economy alluded
to earlier, features that have been changing over time. Thus our
analysis suggests one explanation for the way international policy
regimes have adapted to an evolving world economic structure.

We begin in section II by postulating a social welfare function
that policy makers in each country attempt to maximize. The welfare
function includes domestic output and the long-run rate of inflation.
Also described are the macroeconomic constraints that are relevant to
policy makers in each country as they use the one policy tool at their
disposal, domestic monetary policy, to maximize this objective function.
These constraints explain how domestic and foreign monetary policy affect

domestic output and long-run inflation. This section draws heavily on


-39-

(A4) Spi = .5(ép + Sp* + Se)

6pi* = .5(ép* + dp - 6e)

Consumption functions, income definitions, and the terms of trade:

(A5) 6c = 6y = o6r

6c* = éy* = oér

(A6) éc° = 0

(A7)  éy = (X/Y)(8x+.56¢) = (N/P1)(9/Y)(6q-6pi+so) = (rB/Y)Sb - (B/Y)ér

8y* = (X/Y)(8x*=.56t) = (0/PI)(0/Y)(Sq-6pi+s0*) - (rB/Y) 6b*
- (B/Y)6r

(A8) 6t = 6p - Sp* = ép*

Bond accumulation and goods market equilibrium;

(A9) 6b = (¥/B)(ée = sy)

Sb* = (Y/B)(6c* = by*)

-5(C/X)[Sc + Sc* = (142) st]

6x* = .5(C/X)[6c + Sc* + (142p)6t]

(A10) 6x

Money mar<ets:

(All) 6m = 6p + 6x = ASI

ém* = 6p* + Sx* = ASi*


-37-

Appendix

Here we present the structural model that generates equations (5)
of the text. Only the equations for the adjustment period are given. A
more complete description of the model and its solution can be found in
Canzoneri and Gray (1983). The model is expressed in log deviation form,
which is consistent with the solutions presented in the text.

Note: With the exception of interest rates, lowercase letters
denote the log value of a variable and uppercase letters denote the
variable itself. An asterisk refers to the ROW, while a superscript "o"
refers to OPEC.

x real output

the composite input, consisting of equal numbers of units of
Tabor and oi]

} labor employed in -production of x

° oi] employed in production of x

wW nominal wage rate

p domestic currency price of x

pi consumer price index

q dollar price of oil

e the exchange rate (units of ROW currency per dollar)
Y degree of wage indexation

wad degree of oi] price indexation

c real expenditure

y real income

t terms of trade (relative price of U.S. output)

b OPEC's net holdings of real bonds issued by U.S. residents

b* OPEC's net holdings of real bonds issued by ROW residents
r the real interest rate

i the nominal interest rate

m the nominal money stock

a

the rate of growth of the money stock


-16-

negative spillover channeled through the real interest rate. The change
in the terms of trade will be larger, the lower the responsiveness of
relative demands to relative price, or the lower t (which is positively
related to the elasticity of relative goods demand with respect to
relative price). Thus we see from equations (14) and (15) that a
sufficiently small t will always produce positive spillover, or a
positive Poe

Our third transmission channel, for which the terms of trade
change discussed above is a prerequisite, is wage indexation. It is a
channel which has become increasingly relevant for a number of countries
over the past two decades. Like the goods demand channel, it produces
positive spillover. To demonstrate this effect, we consider once more
an expansionary U.S. monetary policy. As already noted, such an
expansion is accompanied by a rise in the relative price of ROW output.
Even if the absolute (domestic currency) price of ROW output remains
unchanged, this relative price change will produce an increase in ROW
output as long as ROW wages are indexed to some extent. This occurs
because ROW wages are indexed to a weighted average of the prices of ROW
and U.S. output, not to the price of ROW output alone. If the absolute
price of ROW output remains unchanged, a rise in its relative price will
be associated with a fall in the overall price level. Provided wages are
indexed to some extent, this will result in a fall in the ROW nominal
wage rate, and accordingly, a fall in the real product wage (the nominal
wage rate deflated by the price of domestic output). This, in turn,
leads to a rise in ROW output. Examination of the terms entering Po
reveals that for a sufficiently high degree of wage indexation (a

sufficiently large y) the positive spillover effects associated with this


-13-

its real interest rate. The real interest rate movement is transmitted

abroad, where its net impact is deflationary. This is because the lower
real. interest rate produces a fall in the foreign nominal interest rate

and this, in turn, ©....gases foreign money demand. The increased money

demand results in downward pressure on foreign prices

and output. Thus, the spillover effects that are channelled through the
real interest rate are negative and symmetric across countries.

The second transmission channel we consider, which depends on the
existence of two or more goods in the model, operates directly through
the demand for goods. An expansion in one country raises output and
expenditure in that country. Some, but not all, of the increased
expenditure falls on each country's good, generating an excess supply of
the expanding country's good and an excess demand for the other country's
good. As a result, both the relative price and the output of the second
country's good rise. Thus, the goods demand channel generates spillover
effects that are positive and symmetric across countries.

Our third channel of transmission, wage indexation, depends
critically on the terms of trade change generated through the goods
demand channel. As discussed above, an expansion in one country raises
the relative price of the good produced by the other country. If nominal
wages are linked to a price index that includes the price of imports as
well as the price of domestically produced output, the second country's
real product wage falls and its output increases. Accordingly, the
spillover effects produced through this transmission channel are also
positive and symmetric.

The channel associated with the fixed dollar price of oi] is, in

contrast to the other three channels, an asymmetric one. An expansionary


~3-

foreign nominal rate and this, in turn, increases foreign money demand.)
Thus, the spillover effects that are channelled through the real interest
rate are negative and symmetric across countries. By comparison, the
channels that operate through goods demand and wage indexation generate
spillover effects that are positive and symmetric. An expansion in one
country raises output and expenditure in that country. Some, but not
all, of the increased expenditure falls on each country's good,
generating an excess supply of the expanding country's good and an excess
demand for the other country's good. As a result, both the relative
price and the output of the second country's good rise. Thus, an
expansion in either country increases output in the other by generating
increased demand for the other country's good. Our third channel of
transmission, wage indexation, depends critically on the terms of trade
change generated by this increased demand. Consider again an expansion
in one country and the accompanying rise in the relative price of the
good produced by the other country. If nominal wages are linked to a
consumer price index, the second country's real product wage falls and
its output increases. The channel associated with the fixed dollar price
of oi] is, in contrast to the other three channels, an asymmetric one.
An expansionary U.S. policy lowers the real price of oil, for both US and
ROW producers and this can lead to an increase in output in the ROW. An
expansionary ROW policy, on the other hand, has an effect on real oil
prices that is ambiguous in sign. Accordingly, the spillover effects
Produced by this channel are positive for U.S. policy but are ambiguous
in sign for ROW policy.

The nature of the game that is actually played by policy makers

depends on the relative importance of the four channels of transmission


-9-

the amount of the composite input employed in its production. One unit
of the composite input consists of one unit of labor and one unit of oi] :
which are used in fixed proportions.

The conditions for profit maximization yield equation (2), which
gives the derived demands for the composite input, as well as the derived
demands for labor and oi] in each oi] importing country. These demands
depend on the real product price of the composite good -- that is, on its
price in terms of the domestically produced consumption good. This, in
turn, is equal to the sum of the real product wage and the real product
price of of]. Accordingly, equation (2) shows derived demands in each
country to depend negatively on the domestic currency prices of labor and
oil, and positively on the price of domestic output.

Nominal wage rates and the dollar price of oil are determined
by equation (3). As in Gray (1976), nominal wages are set at the
beginning of each period (before any oi] price or monetary policy shocks
are realized) at a level that is expected to clear the labor market.

In addition, each country's nominal wage is linked to its price level by
an indexing parameter y (or y*) which is generally assumed to lie between
zero and one, inclusive. The price of oi] is set in dollars and is
linked to the U.S. price level by the indexing parameter 7°. The term 6q
represents unanticipated disturbances to the dollar price of oil, or oil
price shocks4/,

Equation (4) defines each country's price level as a weighted
average of the domestic currency prices of the two consumption goods.

Since the two countries are identical in all respects in the pre-shock

equilibrium, the two goods are assigned equal weights of one-half.


-15-

illustrate this point, consider a game characterized by the symmetric-
positive constraints described in the last section. In this game polity
makers are faced with a global disturbance that will, in the absence of
corrective policy, produce unemployment in both the US and ROW. Policy
responses are designed to balance the benefits of decreased employment.
losses against the costs of increased inflationary expectations. Both
Players opt for an expansionary monetary policy. ach is aware of the
beneficial effect of the other player's expansion on home employment and
appropriately internalizes that information by expanding less than he
would in the absence of the other player's response. However, neither
player takes into account the beneficial impact of his own actions on the
other player. As a result, the Nash solution does not exploit the
positive externalities associated with monetary policy enough; both
policy makers would be better off if they could agree to expand more.
This result is demonstrated formally in the next section, but its
logic is fairly straight-forward. In the Nash solution, the US policy
maker has increased the rate of growth of the US money supply to the
point where any further marginal change would have no effect on US
utility. However, further increases in the growth rate of US money would
increase ROW utility by lowering ROW unemployment. Similarly, a marginal
increase in the rate of growth of the ROW money supply would have no
effect on ROW utility, but it would increase US utility. Clearly, both
policy makers would be better off if they could agree to expand more.
Analogous inefficiencies characterize the Nash solutions to the
other games studied in this paper. In the symmetricenegative game, both

players would be better off if they could agree to inflate less. In the


-1-

I. Introduction and Summary

In an interdependent world, rational policy makers in one country
may be expected to condition their actions on the policies pursued in
other countries; policy making has unavoidable game aspects../ In the
absence of direct cooperation or side-payments, it is well-known that the
outcomes of such games are socially inefficient; there are alternative
policies that would, if implemented, make all parties better off.
Unfortunately, policy makers generally have an incentive to cheat in
these Pareto-improving outcomes, and politically sovereign policy makers
seem to have difficulty achieving them.

In this paper we describe the games that may be played by policy
makers in two structurally identical countries following a common
external shock such as the oil price increase of 1973. The analysis has
two objectives. The first is to investigate the nature of the
inefficiencies associated with the non-cooperative Nash solutions to
these games. In our framework, whether the Nash solution is too
expansionary or too contractionary depends on structural features of the
world economy. These structural features have changed over the post-war
Period and with them, it is argued, the inefficiencies associated with
the Nash outcome. Thus, our analysis of the costs of non-cooperative
behavior differs from previous work, particularly that of Hamada, which
places its emphasis on the preferences of policy makers </

Our second objective is to explore means of achieving outcomes
superior to the non-cooperative Nash solution. Because of the
difficulties inherent in implementing and enforcing cooperative
solutions, it is suggested that policy makers look to other non-

cooperative solution concepts as alternatives to the Nash. Each of these


-30-

8/ A number of papers explore the effects of an oil price shock in a
single country context; see, for example, Blinder (1979), Bruno and Sachs
(1979), and Findlay and Rodriguez (1977). A few papers address this
question in a multi-country setting. Examples include Caprio and Clark
(1981), Krugman (forthcoming), Sachs (1980), and Schmid (1976).
Unfortunately, none of these papers provides the analysis we require of
both an oi] price shock and the spillover effects of monetary policy.

For further discussion of this point, see footnote 10.

9/ Of course, if policy makers' actions were appropriately constrained,
our specification of the model could be made fully consistent with
rational expectations. Suppose, for example, that the game described in
section II is known to be a one time only game -- that the monetary
policy adopted in response to the oi] price shock is to be (perhaps
legislatively) fixed for all time. Then the static expectations we

ascribe to private agents would be fully rational.

10/ There is of course a voluminous literature devoted to the
international transmission of monetary disturbances; however, explicit
analyses of two (or more) country models are relatively scarce. We are
unaware of any set of papers that present just the analysis we need here,
although many of the individual pieces of our desired framework do appear
in various other papers. Mundell (1963) for example, develops symmetric-
negative constraints in a model with fixed prices and static
expectations. Mussa (1979) presents an excellent discussion of
macroeconomic interdependence which includes an exposition of Mundell's

result. Hamada (1978) describes a transmission channel similar in spirit


~26-

The intuition behind this result is fairly straight-forward. At
the Nash solution, each country has pushed its money growth rate to the
point where its effect on domestic utility is zero at the margin. And
yet a decrease in either country's money growth rate will increase output
-- and, therefore, utility -- in the other count ry 28/ Clearly,
both policy makers would be better off if they could mutually agree to
inflate less.

The trouble with cooperative solutions is that they require
cooperation. In any cooperative solution, there is always an incentive
to cheat. Suppose the U.S. and ROW policy makers agree to a less
inflationary, Pareto Optimal solution.t2/ In any such cooperative
solution, at least one of the two countries can increase its welfare by
increasing its money growth rate, provided the other country does not
respond by altering its own money growth rate. Thus, at any cooperative
solution, unemployment will seem high, and the risk of inflation low, to
a public that does not fully understand the nature of the solution and
the possibility of foreign repercussions. The political pressure to
cheat on cooperative solutions could well be great.

More generally, it is difficult to see how two very independent
policy makers would come to agree upon a cooperative solution in the
first place. There is a continuum of cooperative solutions defined by a
"contract" curve; some are more favorable to the U.S., while others are
more favorable to the row.18/

More likely, it seems to us, the outcome would be closer to the
Nash solution, with each country attempting to induce the other to run a

less expansionary policy. At the Nash solution the ROW, for example,


=22-

The Fixed-Rate Regime is clearly better than the Nash Regime for
both the US and the ROW. For the US, it is also unambiguously superior
to the Stackelberg Regime 22/ However, the ROW may or may not be better
off at the point F than at 5.22/ If the ROW prefers fixed rates (as
pictured in Figure.1), it is assumed that fixed rates will prevail.
However, the ROW may prefer the Stackelberg Regime to fixed rates. In
this situation US and ROW interests conflict, and our analysis provides
no theoretical basis for determining the resolution of that conflict. In
principle, of course, the ROW may commit itself to any reaction function
it pleases. If it prefers S to F, it can choose to present the US with
its NS reaction function instead of the 45° line. However, the US is not
obligated to choose the point S in this situation. It can, instead,
“punish” the ROW by moving up toward the Nash solution. This imposes
costs on the US as well as the ROW. But if the US can coerce the ROW
into its preferred regime through such action, the US may find it a
profitable course to pursue. Unfortunately, our framework is not rich
enough to allow us to evaluate and compare the costs and benefits of such
strategies.

B. A Locomotive Policy World:

The world economic structure characterized by the symmetric-
Positive constraints (5b) is one in which the goods demand and indexing
channels for the transmission of monetary policy dominate. It is most
likely to be relevant in periods in which a high degree of wage
indexation is prevalent and in which the price of oi] is fixed in real
terms (indexed to a commodity price index), rather than being fixed in

terms of dollars. The 1970's meet at least the first of these

requirements. However, (5b) may also describe periods such as the 1950's


Monetary Policy Games and the Consequences
of Non-Cooperative Behavior

by
Matthew Canzoneri
and
Jo Anna Gray*
Federal Reserve Board
Washington, D.C. 20551

December, 1982
Revised January, 1982

*We would like to thank Robert Cumby, Robert Flood, Dale Henderson,
Robert Hodrick, Preston Miller, Kenneth Rogoff and Jeffrey Sachs for
helpful discussions. Catherine Crosby coaxed our ellipses out of the
computer. Any errors are, of course, the responsibility of the authors
alone,


References

Argy, V. and J. Salop. “Price and Output Effects of Monetary and Fiscal
Expansion in a Two-Country World Under Flexible Exchange Rates,"
International Monetary Fund, DM/79/33, May 1979.

Blinder, Alan S. "Monetary Accomodation of Supply Shocks Under Rational
Expectations". Manuscript, Princeton University and the NBER
(December 1979).

Bruno, M. and J. Sachs. "“Macro-Economic Adjustment with Import Price
Shocks: Real and Monetary Aspects," NBER Working Paper, No. 340,
(April 1979).

Bryant, Ralph C. Money and Monetary Policy in Interdependent Nations,

The Brookings Institution, Washington, 1980.
Canzoneri, Matthew. “Exchange Intervention Policy in a Multiple Country

World," Journal of International Economics, vol. 13, 1982,

pp. 267-289.
Canzoneri, Matthew and Jo Anna Gray. “Some Aspects of the Adjustment
Problem in an Interdependent World." In The Future of the

International Monetary System, edited by Tamir Agmon, Robert

Hawkins and Richard Levich, forthcoming in 1983.

Caprio, Jerry, and Clark, Peter. "“Oii Price Shocks in a Portfolio.
Balance Model". Board of Governors of the Federal Reserve System,
International Finance Discussion Paper #181, (June 1981).

Cooper, Richard N. The Economics of Interdependence: Economic Policy in

the Atlantic Community, McGraw-Hill, New York, 1968.
Cooper, Richard N. “Macroeonomic Policy Adjustment in Interdependent

Economies". Quarterly Journal of Economics, Vol. 83, No. 1

(February 1969), pp. 1-24,


-26-

Footnotes

1/ The game theoretic aspects of policy making in an interdependent
world have been recognized by a number of earlier writers. See, for
example, Bryant (1980), Cooper (1968 and 1969), Hamada (1974, 1976 and
1979), Henderson (1979), Johansen (1980), and Jones (1982a,b).

2/ In Hamada (1974), for example, exchange rates are assumed to be fixed
and monetary policies are determined by policy makers preferences cver
output on the one hand and the balance of payments on the other. In
Hamada (1976), policy makers objectives include inflation (rather than
output) and the balance of payments. In either framework, Nash policies
will be "too" contractionary if the net desire for balance of payments
surpluses exceeds the creation of international reserves. Similarly,
policies will be too expansionary if the net desire for balance of
payments surpluses falls short of reserve creation. Which of these
situations occurs depends on each country's balance of payments target
and the relative importance of that target in the country's welfare

function. Analogous results are obtained by Johansen (1980).

3/ Most of the literature on the game theoretic aspects of monetary
policy in open economies assumes fixed exchange rates. A notable
exception is Jones (1982a,b). He discusses both cooperative and Nash
solutions in a multi-country setting with various exchange rate
intervention strategies. His model includes more countries than ours and

is tractable, in part, because he assumes commmodity prices are fixed.


-35-
and cuts the US indifference curves where their slope is infinite. The
ROW indifference curves and reaction curve are mirror images of their US
counterparts. The US Nash, Stackelberg and Fixed-Rate policies are

59y = gr gS4/E(u + 04) + pyre)

Pg gSd(u + of = pgog)(u + of - of)

69
s u(u + 4)? + oe(u + of - p)*

(4 + P5)pg64/Eu + (py + 66)

59

Figure 2 reflects the same parameter values used in Figure 1; that is,
Py 9664 =, Pee 3/4 and » = 1/4. For those parameter values,

59y = .50, 89 = .40 and 89, = ,53.

24/ S must be distinct from N and further out along the ROW reaction

curve since the US indifference curve has infinite slope at N.
25/ With the symmetric-positive constraints,

(0688) 7u7oelu + o4(o4 ~ 206))

Cu + (04 + es) Mu(u + 04)”

Ue - Ue =
ws + oa(u +04 = pg) ]

and can take either sign.


-39-

Johansen, Leif. “The Possiblity of an International Equilibrium with Low
Levels of Activity," unpublished manuscript. University of Oslo,
May 1980.

Krugman, Paul. “Oil and the Dollar". In Economic Interdependence and
Flexible Exchange Rates, eds. J. Bhandari and B. Putman, M.I.T.
Press, Cambridge, forthcoming.

Mundell, Robert A. “Capital Mobility and Stabilization Policy Under
Fixed and Flexible Exchange Rates". Canadian Journal of Fconomics
and Political Science, Vol. 29 (November 1963), pp. 475-485.

Mussa, Michael. "Macroeconomic Interdependence and the Exchange Rate
Regime". In International Economic Policy: Theory and Evidence,
eds. Rudiger Dornbusch and Jacob Frenkel. The Johns Hopkins
University Press, Baltimore (1979).

Sachs, Jeffrey. “Energy and Growth Under Flexible Exchange Rates: A
Simulation Study". NBER Working Paper No. 582, (November 1980).

Schmid, Michael. "A Model of Trade in Money, Goods and Factors".
Journal of International Economics 6, (1976), pp. 347-361.



FIGURE 2B:

THE LOCOMOTIVE POLICY WORLD

0.754
| \\
45° line
1 \ /
i 1 /
/
1 /
| /
| /
1 . /
Fy ———[S=_
O——
VAI
0.504 xe
/*N
| WA \
| ye NS
/
/ Ss
/
| /
v4
| /
i
2547
§ 9.560 O.75


-1l-

In Canzoneri and Gray (1983), we analyze in some detail a model
that can generate all three sets of constraints given above 2/ A
formal description of that model is presented in the appendix. The
remainder of this section contains a summary of the model's central
features and a discussion of the different structural assumptions that
produce equations (5a), (5b) and (5c).

The framework developed in Canzoneri and Gray (1983) consists of
three countries, one oi] producing country (OPEC) and two oi] importing
countries (the US and the ROW). Oil is an intermediate good that is used
by the US and ROW to produce two consumption goods which are consumed in
all three countries. Each oil importing country is specialized in the
production of one of these consumption goods. Labor is the only other
variable input employed in the- production of each consumption good. OPEC
sets the price of oi] in terms of US dollars, but this price may be
partially or fully linked to a consumer price index. The nominal wage in
each oi] importing country is contractually fixed in terms of the local
currency, but may also be partially or fully linked to an index of
consumption good prices. The absence of completely flexible wage rates
introduces the possiblility of short-run deviations of output from its
full employment level.

The model includes three exogenous policy variables: the price of
oil and the rates of growth of the US and ROW money supplies. The impact
of changes in these policy variables on output levels depends on
structural parameters such as the degree of wage indexation in the US and
ROW. The constraints given by equations (5) describe these effects under

differing sets of assumptions about the sizes of such parameters. The


-ll-

has bee set equal to unity 2/ Nominal interest rates are defined

in equation (12). And the evolution of the U.S. and ROW money stocks is
described by equation (13). Monetary policy in each country takes the
form of setting a constant rate of growth, g (or g*), of the domestic
money stock. Any change in monetary policies -- that is, any change in g
or g* -- is assumed to be unexpected and, once it occurs, permanent.

The model outlined in equations (1) through (13) above involves
expectazions of future prices and policy variables. To complete the
model the manner in which agents form their expectations must be
specified. It is assumed that agents' expectations are "rational" given
their assumptions about U.S. and ROW monetary policies and OPEC's oil
pricing policy. If their views about these policies are correct, then
their price predictions will be realized.

The remainder of this section will be spent discussing the model's
solutions for the levels of U.S. and ROW output. Of particular interest
are the effects of the monetary policy adopted in one of the two oil
importing country's on the output of the other. For simplicity,
attention is limited to two special cases of the general model outlined
in equations (1) through (13) above. We treat first the special case in
which the degree of wage indexation in the two oi] importing countries
is variable, but the price of oi] is fully indexed. This case produces
the macroeconomic constraints necessary to yield the two symmetric games
studied in the next section. We then turn to the special case in which
both noninal wage rates and the dollar price of oi] are fixed. This case

produces the one asymmetric game studied in section III.


~27-

would have every incentive to maneuver the U.S. into running a less
inflationary policy. If the U.S. acquiesed, ROW employment would be
stimulated, but at the expense of U.S. employment. As a result, the ROW
would find it desirable to reduce its own money growth rate, moving back
along its own reaction curve in the direction of cooperative solutions
more favorable to the ROW.

In general, the opportunities for such manipulation appear to be
limited. Outright political pressure and the engineering of public
opinion, whatever else they achieve, appear not to be very effective
means of altering the policies pursued in other countries. An
alternative strategy would be for one country to commit itself to a lower
inflation rate in return for a similar promise by the other country.
Unfortunately, such movements toward a Pareto Optimal solution require an
effective means of precommitment. This requirement is extremely
difficult meet in a world composed of politically sovereign players. Any
policy maker attempting to strike such a bargain confronts the problem
that his promises, as well as the promises of other policy makers, are,
in the jargon of game theory, “incredible”.

The Symmetric-Positive Game

With the symmetric-positive constraints, the spillover effects of
montary policy are positive; an expansion in one country causes an
expansion in the other. The "locomotive" aspects of policy produce, in a
non-cooperative setting, a solution that is not sufficiently
inflationary.

Each policy maker knows that the other is going to inflate and,

therefore, that he does not have to inflate as much to get a given


-43-

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

Findlay, Ronald, and Rodriguez, Carlos. “Intermediate Imports and
Macroeconomic Policy Under Flexible Exchange Rates". The Canadian
gournal of Economics 10, No. 2 (May 1977), pp. 208-217.

Hamada, Koichi. "Alternative Exchange Rate Systems and the
Interdependence of Monetary Policies." In National Monetary
Policies and the International Financial System, edited by Robert

Z. Aliber, University of Chicago Press, Chicago, 1974.
Hamada, Koichi. "A Strategic Analysis of Monetary Interdependence."
Journal of Political Economy, Vol. 84, August 1976, p. 677-700.

Hamada, Koichi. “Macroeconomic Strategy Coordination under Alternative

Exchange Rates." In International Economic Policy, edited by

Rudiger Dornbusch and Jacob Frenkel, Johns Hopkins University
Press, Baltimore, 1979.

Hamada Koichi and Makoto Sakurai. "International Transmission of
Stagflation under Fixed and Flexbile Exchange Rates," Journal of
Political Economy, Vol. 86, Oct. 1978, p. 877-896.

Henderson, Dale. "Financial Policies in Open Economies". American
Economic Review, May 1979, pp. 232-239.

Henderson, James M. and Richard E. Quandt. Microeconomic Theory, 2nd
ed., McGraw-Hill, New York, 1971.

Johansen, Leif. “The Possibility of an International Equilibrium with
Low Levels of Activity," unpublished manuscript. University of

Oslo, May 1980.


Some Aspects of the Adjustment Problem
in an Interdependent World*

by
Matthew Canzoneri
and
Jo Anna Gray
Federal Reserve Board
Washington, D.C. 20551
September, 1982

Revised October 1982
Revised December 1982

*Forthcoming in The Future of the International Monetary System, eds.
Tamir Agmon, Robert Hawkins and Richard Levich. We would like to thank
Robert: Cumby, Dale Henderson, Robert Hodrick, Preston Miller and Jeffrey
Sachs for helpful discussions. Any errors are, of course, the
responsibility of the authors alone.



-14-

US policy lowers the real price of oi] for both US and ROW producers. In
and of itself, this leads to an increase in output in both countries. An
expansionary ROW policy, on the other hand, does not directly affect the
real price of oi]. It acts indirectly through its effect on the U.S.
price level -- an effect that is ambiguous in sign. Accordingly, the
spillover effects produced by this channel are positive for U.S. policy
but are ambiguous in sign for ROW policy.

The nature of the game that is actually played by policy makers
depends on the relative importance of the four channels of transmission
just described. The relative importance of these channels, in turn,
depends on the structural features of the economies involved -- features
that have changed dramatically over time. On the one hand, a fully
indexed price of oi1, no indexation of wages, and a sufficiently high
price elasticity of relative goods demand produces the negative symmetric
spillover of equations (5a). By comparison, a fully indexed of] price
and a sufficiently high degree of wage indexation produce the positive
symmetric spillover of equations (5b). Among the conditions that produce
the asymmetric spillover of equations (5c) are a fixed dollar price of
oi] and a large price elasticity of relative demand. The reader js
referred to Canzoneri and Gray (1983) for a more extensive discussion of
the economic intuition, as well as the formal analysis, underlying these
results.

TIT. The Costs of Non-Cooperative Behavior and Alternative Rules of
the Game

It is well known that, in general, the non-cooperative Nash

solution to a game is inefficient AL/ there typically exist alternative

feasible outcomes that would increase the utility of all players. To