18
used to update the previous policy path and so on. This iterative process
between x, and ¥y continues until 1}, oe? 4,0, where s is the sth

iteration.

Experimental Design

The first step in empirically implementing our analysis is to
parametrize the social welfare function. In this paper we use the following

parametrization:

ye ar ar 2
min E(W) =E } w.(Ye,- as,)° + m. (Kage Pay)
te1de2 a1) tt it te1de2 jars st Sat

where we have assumed the following form for the K matrix in the welfare

function, equation (21):

T . 0 M.0
K = area »T= a “S5 ’ W=6, iWa> MRO iMi> j=1...4,

and 855 is the Kronecker product.

The target variables we consider are:

Yue growth rate for real oi] revenues of OPEC, Agr;

Yor growth rate of OCs, aw’;

Y3= growth rate of LDCs, any®; and

YQ inflation rate of manufacture exports of OCs, apd.

: 14
The policy instruments we use are:


39
insensitive to changes in fiscal policy's weight. This means that there
are, in our model, other more efficient instruments to promote growth in
LDCs. In contrast, however, welfare losses for DCs and OPEC are quite
sensitive to changes in fiscal policy's weight. In particular, given a
weight of 4.5 for oil prices, a reduction in the weight on government
expenditures from 99999 to 5000 raises welfare losses to both DCs and OPEC.
This is because with a weight of 4.5, of] prices tend to follow their target
values quite closely, which include a fall in oil prices. As noticed
earlier, there exists in the context of our analysis a positive association
between oi] prices and government expenditures. Thus a decline in oi]
prices leads to a fall in government spending and this latter decline
generates the adverse effects on DCs and OPEC. We also notice that, despite
the decline in the average growth rate of oil prices, there is an increase
in the amount of capital transfers to LDCs. This increase in transfers is
necessary to offset the impact of lower government expenditures in DCs on
the LDCs, since the beneficial aspects of lower oi] prices are being offset
by the reduction in growth of DCs.

In contrast to the previous situation, a reduction in the wei ght
of government expenditures from 99999 to 5000, coupled with a reduction in
the weight of oi] prices to 0.1, results in significant reductions in
welfare losses for both DCs and OPEC despite a decline in average capital
transfers to LDCs and unchanged oi] prices. This result arises because DCs‘
government expenditures are now substantially (and unrealistically) higher,
increasing exports of LDCs and their foreign exchange receipts which
allows a small reduction in the average increase in capital transfers (see

Figure 7).


35

explained by the large weight differential between these two instruments.

In order to eliminate the influence of a large weight differential
on the welfare tradeoffs, we reduce the weight of government expenditures
from 99999 to 5000. As a result, we find that this weight reduction leads
to declines in welfare losses of 1.0 percentage points for DCs (2.6 minus
1.6) and of 1.6 percentage points for OPEC with almost no effect on LDCs'
welfare losses despite an increase of 1.7 percentage points in the average
growth rate of oi] prices. These last results suggest that the adverse
effect of higher oi] prices on both DCs' and LDCs' growth are being offset
by the stimulative effects of increases in government expenditures of DCs,
given that fluctuations in this instrument now have attached a lower cost
(see Figure 5).

We also examine the impacts of further increases in the weight for
DCs' growth target. In effect, this amounts to raising the cost of
deviations in DCs' growth target from their desired path relative to the
cost of deviations in the instruments from their desired paths. Thus we
consider an increase in the weight of DCs' growth target from 10 to 200,
while keeping the weights for of] prices and government expenditures at 4.5
and 5000 respectively. Our results indicate that when the weight for NCs
equals 200, their welfare losses decline by 1.1 percentage points with
respect to the base solution. There is also a similar decline in OPEC's
welfare losses despite a decline in the average oil price growth rate. This
implies that OPEC's reduction in welfare losses arises out of the increase
in the volume of oi] exports induced by the higher growth in developed
economies. Finally, the LDCs experience a decline in welfare losses of 0.2

percentage points because the effects of higher government expenditures


44
ENDNOTES

*an earlier version of this paper was presented at the 5th IAEE Annual North
American Meetings, June 1983, and the 4th IFAC/IFOR conference on The
Modeling and Control of National Economies, June 1983. We are grateful to
F. Gerard Adams, Matt Canzoneri, David Kendrick, Lawrence Klein, Peter
Tinsley, Janice Shack-Marquez, Edward Green, Geoffrey Heal, and James Sweeny
for their comments. We are also grateful to Gregory Chow for providing the
software used in our analysis. Any remaining errors belong entirely to us.
This paper represents the views of the authors and should not be interpreted
as reflecting the views of the Board of Governors of the Federal Reserve
System or other members of its staff.

See Niehans (1968), Hamada (1979), Johansen (1982), Canzoneri and Gray
(1983), Rogoff (1983), and Oudiz and Sachs (1984). However, these analyses
have been characterized by deterministic, static, two-country models, with
little or no empirical content (an exception is Oudiz and Sachs 1984). Our
approach is more empirically oriented and thus we use a three-country,
stochastic, dynamic model.

* there is a considerable amount of work analyzing the possibilities for
policy coordination between the North and the South. Suffice to mention
the work of the UNCTAD for the last twenty years. For the academic
literature, see Bhagwati (1977), Cline (1979) and Johnson (1967). The
possiblities for policy coordination between OPEC and the North have been
analyzed by Adelman (1984), who cites the Teheran agreement of 1971 as a
failure of such arrangements. However, conclusions reached by focusing on
only two country blocs are conditional on the third country bloc which is
left out. Thus it seems that a more realistic approach to the problem of
policy coordination is to include the North, the South, and OPEC. Taylor
(1981) has examined this issue from a theoretical standpoint, and the
Present paper could be seen as an empirical implementation of Taylor's
work,

* hs a corollary of our analysis, we offer an approach to determining oi]
Prices which is different from the classical wealth maximization approach
developed in the literature (Hotelling 1931, Dasgupta and Heal 1979). We
recognize that OPEC faces not only the problem of allocating oi1 production
through time (the classical approach), but also a tradeoff between
exploiting the direct price inelasticity of oi] demand on the one hand, and
avoiding the income feedback effects of oi] price increases on the other.
This tradeoff arises only in a more general equilibrium model such as the
one developed below. See Marquez and Pauly (1984) for an analysis of the
implications of these tradeoffs for OPEC's pricing policy.

* Financial links also exist among these three blocks of countries, and there
have been several attempts at modeling these financial links. For instance
Sachs (1983a) develops a model that captures both trade and financial links.
However, he assumes the parameter values for his relationships casting some
doubts on the generality of his results. Minford (1984) uses a model with
both trade and financial linkages coupled with rational expectations. Some
of his parameters are assumed and some are estimated; yet "full dynamic
simulation tests have not yet been possible." (Minford 1984:7). Clearly,


12

Model simulations are needed to quantify the total--direct and indirect--
effect of an oil price increase. To this end, we have simulated the model
of section II for the period 1973-1983 under three alternative

9
noncooperative scenarios:

I. A sustained ten percent increase in the price of oil.

II. A sustained ten percent increase in the price of oi] coupled with a
restrictive fiscal policy.

III. The same as case II in conjunction with an increase in aid to

developing countries.

Table 2 contains the dynamic income multipliers for each of these cases.

The results from case I suggest that a permanent 10 percent
increase in the price of oi] reduces real income for all country blocs
considered here. More specifically, the DCs experience an annual average
real income loss of 1.5 percent, while real income in LDCs
falls by an annual average of 1.0 percent. OPEC's terms-of-trade
improvement raises their real income only temporarily. The dynamic effects
of higher oi] prices on oi] demand, and the ensuing worldwide recession are
transmitted to OPEC as a significant decline in their oi] exports reducing
their real income by an average of 0.3 percent per year.

A restrictive fiscal policy response to the oil price increase
only exacerbates the real income losses, as the results from case II
indicate. Here the annual average income loss for DCs is 3.7 percent, 0.8
percent for OPEC, and 1.5 percent for the remaining developing countries.
This worldwide recession is initiated by the cutback in aggregate demand in

DCs, which reduces exports of both OPEC and LDCs and thus the revenue to


Nordhaus,

Oudiz, G.

50

W. (1980). "Oil and Economic Performance in Industrial Economies,"
Brooking Papers on Economic Activity, No.2:341-401.

and J. Sachs (1984). "Macroeconomic Policy Coordination Among The
Industrial Countries," Brookings Papers on Economic Activity,
No.1:1-64.

Pindyck, R. (1977). "Optimal Economic Stabilization Policies Under

Rogoff, K.

Sachs, J.

Sachs, J.

Sachs, J.

Taylor, |.

Terrel, H.

Decentralized and Conflicting Objectives," IEEE Transactions on
Automatic Control, Vol. ac-22, No.4:517-530.

(1983). "Productive and Counterproductive Cooperative Monetary
Policies," International Finance Discussion Paper No.233, Board of
Governors of The Federal Reserve System.

(1979). "Wages, Profits and Macroeconomic Adjustment: A
Comparative Study," Brookings Papers on Economic Activity,
No.2:269-319.

(1983a). "Energy and Growth Under Flexible Exchange Rates," in J.
Bhandari and B. Putnam (eds.) Economic Interdependence and

Flexible Exchange Rates, Cambridge: MIT Press.

(1983b). "Real Wages and Unemployment in the OECD Countries,"
Brookings Papers on Economic Activity, No.2:255-289.

(1981). "South-North and Southern Growth. Bleak Prospects from
the Structuralist Point of View," Journal of International
Economics, Vol.11, No.4:589-602.

(1984). "Bank Lending to Developing Countries: Recent
Developments and Some Considerations for the Future," Federal
Reserve Bulletin, Vol.70, No.10:755-763.

United Nations (1982). Trade and Development Report, 1982, New York: United

Nations.

World Bank (1982). World Development Report, New York: Oxford University

Press.


22
ensure the existence of both the welfare function we have postulated and its
associated coordinated policies. However, this is such a formidable task
that only in very small models can one actually derive the appropriate set
of weights (see Oudiz and Sachs 1984). In this paper we take a more
pragmatic approach and begin with an initial set of weights, which are then
changed to examine the effects of different (quadratic) welfare functions on
cooperative policy mixes. We start with an egalitarian welfare function,
j.e., Wit 1 for i=1,...,4, which implies that the tradeoffs between targets
that may arise here are due only to the behavioral constraints embedded in
our model, to the stochastic structure (as represented by 2), and to the
values given to the instruments' weights.

The choice of values for the instruments' weights (the m's) is
complicated by the fact that the iterative algorithm to solve for Xt (closed
loop) is sensitive to the values of instruments' weights, especially low
values (similar findings are reported by Klein and Su 1980, Bellman 1961).
To get around this problem, we recognize that policy changes are costly and
thus are not likely to be frequent or to result in large deviations from
historical standards (Klein 1983). Thus large weights are given to both
real government expenditures of DCs (m=99999) and nominal net capital
transfers to LDCs (m, =1500), effectively constraining the instruments.

Interest rates are assigned a weight m =20, and oil prices are assigned a
2

weight m,=4.5. While it is true that this choice of weights is arbitrary,
we examine below the sensitivity of our results to changes in these

weights.

Empirical Results
Although the notion of cooperation among the major country blocs

has a good deal of appeal in theory, it remains to be seen whether it is


40

Evaluation of Sensitivity Analysis Results

Several interesting results emerge from the sensitivity analysis
performed so far. First, although instrument instability did not
materialize for the weights we have used, there are cases where small weight
values result in paths for instruments that are not entirely consistent with
the policy environment where these instruments are determined. In other
words, even though a policy mix might be efficient, it may lack credibility
when compared to historical standards. To be specific, we find that in
order to accelerate economic growth in LDCs, capital transfers would have to
exceed their (already high) targets by an annual average of $US 20 billion
in some cases. Given today's current financial situation for some
developing countries, it seems unlikely that such large transfers will take
place.” Second, there are certain combinations of weights (see Figures 3,
5, 7) which lead to rather expansionary fiscal policies, implying myopic
behavior on the part of individuals. This is an area where more work is
clearly needed.

Third, the results suggest that certain instruments can substitute
for each other in supporting a given target growth path. More specifically,
either lower oi] prices or higher government expenditures reduce the need
for capital transfers to developing countries. On the other hand, we find a
complementary relationship between government expenditures and oi] price
growth, provided growth considerations override inflationary
considerations.

Fourth, we find that the "ceteris paribus" oi] price path
consistent with OPEC's best interests is higher than the oi] price path
consistent with either DCs' or LDCs' best interests. The measurement of
ceteris paribus oi] price paths in our context is difficult because other

instruments are changing at the same time as all oi] prices do. Thus we


3
The analysis begins in section II where we present a three-region

econometric world model used to study the effects of exogenous oi1

price increases on worldwide economic activity and international trade.

In section III we use model simulation to estimate the effects that changes
in oi] prices, and uncoordinated policy responses, have on each region's
growth prospects. We find that a sustained increase in the price of o7]
deteriorates growth prospects for all countries and that this situation is
only aggravated if (uncoordinated) restrictive policy responses are put in
place. While in principle a worldwide recession, and the bleak prospects
for the future, may justify a call for policy coordination on a global
scale, empirical estimates of the benefits of such a policy move are hard to
come by raising questions about its viability. Thus, in section IV we focus
on the possibility of coordinating policies among the North, the South, and
OPEC aimed at generating a sustained recovery of the world economy. This
question is analyzed empirically by applying stochastic optimal control to
the estimated econometric model.

The fact that cooperative policies may exist, and that they night
be implemented, does not imply that all the parties involved will benefit to
the same extent. As it turns out, the actual distribution of income gains
is crucially dependent on the specification of the welfare function. Thus
we also examine in section IV the sensitivity of the distribution of income
gains (or losses) between DCs, OPEC, and non-OPEC LDCs to alternative
specifications of the welfare function: Finally, section V contains our

conclusions.


33

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19

Xe growth rate for oil prices, Aw? 5

Xo long term nominal interest rate of DCs, rd;
Xg= real government expenditures in DCs, 64; and
Xqe nominal net capital transfers to Locs: "cr,

and thus xt=(Xigs Xop» Xgpo Xap >

Our choice of target variables is particularly useful in analyzing
the implications of a sustained recovery of the world economy for oi]
prices, stabilization policies, and transfers to LDCs. In addition, it
lends itself to the study of the distribution of income gains arising from
changes in the bargaining position of each country. The inflation rate of
manufacture exports, a proxy for the overall inflation rate, is also
included in the welfare function to capture policy makers' concern with
allocative inefficiencies and distributional effects of high and uncertain
inflation rates (Niehans 1968, Cukierman 1983).

With our choice of policy instruments we can examine the type of
policy mix--fiscal, and (only indirectly) monetary--that can be implemented
by developed economies in order to achieve a non-inflationary growth path
for the world economy: Also, it is possible to study the financial
requirements of developing countries resulting from a sustained target
growth. Finally, we determine the optimal price of oi] from a cooperative
policy point of view, and examine how it might differ from OPEC's optimal
price when considered in isolation.

The desired values for the growth and inflation targets (the a's)

are shown in Table 3. To determine these values we postulate a transition


25
percent in 1984, but rises again to 5.8 percent by 1990. The initial
decline in and is due to both the fall in oi] prices in 1983 and the
reduction in economic activity of DCs in 1982.

The overall picture that emerges from applying optimal control to
our (albeit very simple) model is that it is feasible to achieve relatively
high growth rates for developed, OPEC, and non-OPEC developing countries for
the remainder of this decade, provided international policy cooperation
results in (1) nominal oi] prices growing at an average of six percent per
year, (2) nominal capital transfers to non-OPEC developing countries growing
at 10.0 percent per year, (3) long term interest rates declining to 8.0
percent, and (4) real government expenditures continuing their (modest)
expansionary path. Recall, however, that these results are conditional on
the weighting scheme for the welfare function chosen a priori. We now

analyze the sensitivity of our results to changes in these weights.

The Distribution’ of Income Gains or Moving Along the Contract’ Curve

One of the characteristics of the optimal control solutions shown
in Figure 1 is the divergence between desired and fitted (mean) paths for
the target growth rates. Furthermore, this divergence is not uniform across
targets, which means that even though there are cooperative policies capable
of restoring a sustained recovery to the world economy, not all countries
benefit equally from this increase in world output. This unequal gain
distribution, or the extent to which growth in one country takes place at
the expense of growth in another country ("welfare tradeoffs") is crucially
dependent on the weights used in the welfare function. And an interesting

question that arises in this context is the sensitivity of the tradeoffs


21

Table 3

Base Optimal Control Solution
Desired Values for Targets and Instruments

(1982-1990)

Targets

sy? AR? asy* ass
1982 2.5 1.0 4.0 7.0
1983 3.4 1.0 4.8 6.5
1984 4.0- 4.0 5.5 5.5
1985 4.3 6.0 6.0 5.0
1986 4.8 7.0 6.5 5.0
1987 5.2 8.0 7.0 5.0
1388 5.5 9.0 7.0 5.0
1989 5.8 10.0 7.0 5.0
1990 5.8 10.0 7.0 5.0
Instruments

a dq

4eP, r G CP
1962 0.0 14 1.0 1.0
1983 -15.0 11 1.01 1.11
1984 6.5 10 1.02 1.23
1985 6 10 1.03 1.37
1986 6 & 1.04 1.52
1987 6 8 1.05 1.70
1986 6 & 1.06 1.87
1989 6 & 1.07 Z.ue
1990 6 8 1.08 2.31

CF is defined as nominal net capital transfers to developing countries,
which are estimated at $52.7 billion in 1982. 64 is defined as government
purchases in 1970 prices and 1970 exchange rates, with a value of $450.9
billion in 1982.


34

. Figure 5
Mean Fittec Values for Targets and Instruments: Case 2
Desirec Path ——} (m=2.3, m3=99999)-—~—} (my=0.1, mg= 5000)—— — —
(TEREST RATES (GOVERNMENT EXPENDITURES
en a ee | as) TT TT TT TT 125
= 413 7
r watts
\ L a 4
H "1 _ =
XL — 105
= — 49 =
ppp gp jp pt t 7 [es ee ee ee ee ee 0.95
yee 1984 1986 1988
yee 84 86 1988 1990 4 7B cs 98: 1990
TriétegegsedtT 20 TrsereteTt tt 2.60
—-p~. .
r\/ Nas v0 2.00

= -_——
\// ~~
~. )

10
[ee ee ee ee 10)
1982 1984 1986 1988 1990
(INFLATION RATE
rTTTrTrtrTrit 8
7
6
5
Lit pt jf ft tt y4
1982 1984 1986 1988 1990
OPEC'S GROWTH
rT TTttfeftfT iT «+71 20
— 10
-
MKT
—= = fe)
L ar
pot py py ft | 20
1982 1984 1986 1988 1990

e
oe oe

jt

140

|_} 0.80

1986

1988

1990

fy yp tp

141 ise
1982 1984 1986 1988 1990
GROWTH LDCS

TTT 49
7 7

Zz
L 2 745
f
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16

min E(W) = Ef } (yf 4, )'K (E> 4) (21)
tel ~
subject to ye= £( Yes eae Xe> Sta? Zee 8) +e >» (22)
where
YF column vector of endogenous variables,
f = vector of functions,
x column vector of controllable exogenous variables or instruments,
Z,= vector of non-controllable exogenous variables,
8 = vector of parameters,
e = vector of random errors, e ~ N(Q,2),

Q = estimated covariance matrix,

Xe = I

4)»

K = positive semidefinite diagonal matrix of weights,

d,= column

vector of desired values for targets and instruments.

The cooperative policy vector is obtained as the solution of the

first-order conditions for the above minimization problem which, in our

case, takes the form of a linear feedback rule:

The cooperative policy mix x

Gy

(8.9% dps K) Yee + 9 (23)

p> as derived here, is conditional on the

(estimated) parameters of the model, @ and 2, the desired values for

instruments and targets, 4d.» and the weights in the welfare function, K.


OPEC

The only behavioral relation we model for OPEC is their absorption
of oil revenues. For this we relate their imports of manufactures, we in
equation (13), to a distributed lag of real oil revenues, R°, which are
defined in equation (12). The absorption elasticity in the first year is
0.31, 0.36 in the second year, and 0.04 after four years. The long run

absorption elasticity is 0.98.

Non-OPEC Developing Countries

Gross output, ey* in equation (14), is determined using a two
level nested CES production function with capital, K*, and oi] consumption,
0, as arguments in the first nest. The parameters of this function are
estimated using the first-order conditions for cost minimization; the
estimated elasticity of substitution between oi] and capital is 0.05 in the
short-run and 0.73 in the long-run.

Capital formation, 1* in equation (15), is modeled as a function
of changes in the rental price of capital, Pes relative to the price of oil
and on gross output changes. However, we amend this neoclassical
formulation to allow for a non-constant speed of adjustment. In particular,
we model this speed as a direct function of the availability of foreign
exchange reserves in real terms, Ry / 4, since it seems reasonable to
expect that the availability of financial resources will determine how much
investment can take place in a given year (see Coen 1971). We find

investment to be quite responsive to changes in foreign exchange reserves


31
The influence on OPEC's growth target of alternative DCs' fiscal

policies is examined here by lowering the cost of fluctuations in this
instrument from 99999 to 5000. The results point to a rather expansionary
fiscal policy leading to an unambiguous reduction in welfare losses for each
bloc of countries. This "Pareto" improvement is possible, in our model,
because the optimal response of government expenditures in developed
economies is rather expansionary, exceeding its target by an annual average
of $US 55 billion, whereas the optimal fiscal policy response with a large
weight exceeds its target only by an average of $US 8.6 billion. This
expansionary fiscal policy raises OPEC's oi] exports which, when combined
with the higher oil prices, explains the reduction in welfare losses to
OPEC. Similarly, we find a substantial reduction in welfare losses to LDCs
despite (1) increases in the average growth rate of oi] prices, and (2)
virtually no deviations of capital transfers from their desired values.
Again, this result can be explained by the stimulative effect of higher
government expenditures in DCs on exports of LDCs, which increases their
foreign exchange reserves and thus eliminates the need for higher capital
transfers. Therefore, the expansionary fiscal pol‘cy serves as a substitute
instrument for capital transfers to Locs.

That a highly expansionary policy may be beneficial to all the
parties involved should not come as a surprise. In the present context, it
implies that individuals are willing to consider their holdings of
government debt as part of their wealth without realizing that the increased
debt service may call for increased taxes in the future. Since it is quite
unlikely that individuals will sustain such a view indefinitely, it seens
clear that such an expansionary move will not be observed in reality. This

forward-looking expectation element is absent from our model and is one


28

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5

Table 1
Main Behavioral Relations in
Global Econometric Model

Developed Economies

cF = cope yay Po w
= ry4, ry (2)
mee M(PL/ PE Y) (3)
ARPS =P(ASP, ASP), ABP, U) (4)
ays @(L,£k,E(0,C)}) (5)
04 = GP, Pos Pas Py GY) (6)
ad = 0% oS (7)
als ad. xtipyy p, av) (8)
XS ya + Mp (9)
wae wd + ad + xt (10)

ye od 4 gba xd 24 (11)

OPEC
= d, gy, pd
R= (PoAGt AG)/ Pa) (12)
me= WO(R°) (13)

Non-OPEC Developing Countries

Gye= g(K*(KE , Ka), 0°) (14)
i = 1(a(Pe/ P.), acre Re/P4) (15)
Me = mh, R*/ Pa) (16)
o* = F( Pe/P, , GY*) (17)
nt = of 08% + x (18)
xe = x(Pdy pe, v4) (19)

2 phyd d Qo yk 2 2
nee ply + pM + PoRe- PEMD - Po + CF + RE, (20)


4
II. A GLOBAL MODEL OF OIL PRICE EFFECTS

The model we use is simple but comprehensive; it is desigried to
analyze the international transmission of oi] price effects, and its
theoretical justification can be found in models developed by Taylor {1981}
and Marquez (1983). The world economy is divided into three regions: (1)
the North, which is represented here by the group of developed countries,
DCs,(2) the OPEC countries, and (3) the South, which we characterize as the
group of non-OPEC developing countries, LDCs. Economic activities in these
different regions are linked to each other through international trade flows
and prices. The international trade flows we model are (1) oi], sold by
OPEC to both DCs and LDCs; the latter also export oi] to DCs; (2)
manufactures, exported by the DCs to both OPEC and LDCs; and (3)
manufactures and raw materials exported by the LDCs to OCs.

The model contains 37 equations, 15 of which are behavioral
relationships. The parameters of the model are econometrically estimated
using annual data for 1960-1979, although some of the relationships are
estimated using data only up to 1977. The estimation method we use is OLS
since the advantage of alternative parameter estimators such as 2SLS, 3SLS,
and FIML hold only in large samples. For small samples such as ours, the
choice of OLS might be justified (see Malinvaud 1970:569, Mariano 1978, and
Juage et. al. 1982:638). We now describe the main behavioral equations
which are shown, in general form, in Table 1 (an appendix to this paper,
available upon request, contains all the equations of the model as well as a
list of indicators of the dynamic simulation performance of the model inside

and outside the estimation sample).


V7

The policy mix at a point in time depends on the effects of past policy
decisions as summarized in Yap with the weights in the linear feedback
rule being updated recursively by a set of matrix Riccati equations.
Moreover, the policy mix can be modified over time as information about the
behavior of the endogenous variables becomes available. Notice that since a
stochastic framework is being used, x attempts not only to minimize the
WX a! but also to minimize the covariance matrix of deviations between y,
and Ey,

By combining the expression for the cooperative policy vector with
the econometric model, we obtain an "enlarged" econometric model where
cooperative policies, as represented by equation (23), and the behavior of

the world economy, as represented by equation (22), are determined

simultaneously:
Ue = Ee Meng? Xt> Xeeae Zt> 9) * et > (22)
*
X = 6. (9, 2, de Ket +a (23)

The solution algorithm for this problem is explained in full detail in Chow
(1975, 1981).° Greatly simplified, it begins with equation (22) and an
initial policy path for Xe Oe to determine the effects of the given
policy path on the endogenous variables, lee These effects are then used
(with a lag of one period) in equation (23) to obtain a second policy path
ran which, by using equation (22), generates a second path for the

2
economic activity targets, {y he This second round of effects is, in turn,


taken place after the first oi] shock in 1973. The estimated growth rate
for potential output prior to 1973 is 4.7% and 2.9% for the period
afterwards. A Chow test for the null hypothesis of structural parameter
stability could not be accepted.

The conditional demand for oil, of in equation (6), is derived
from a three level CES production function, equation (5), whose arguments
are labor, L, capital, K, oil, 0, and coal, C. Thus capital-energy and
interfuel substitution possibilities are both taken into account. This
conditional demand for oil depends on the prices of oil, coal, labor, and
the rental price of capital as well as on gross output. ey4, We estimate a
linearized version of this demand function with a distributed lag (4
periods) for prices and income with a sample split in 1972. The long run
oil price elasticity declines from -0.27 to -0.57. The long run coa’ price
elasticity increases from 0.29 to 0.91. The estimated income elasticity
declines from 1.70 to 1.34. These changes in the parameter estimates turned
out to be quite significant as a Chow test for the null hypothesis of
parameter stability could not be accepted. Finally, the hypothesis of
homogeneity of degree zero in prices cannot be rejected.

DCs' total imports of oil, ad in equation (7), are equal to the
difference between oi] demand and the exogenously given oi] supply, os,
OPEC is assumed to be the swing producer, and therefore imports of oi] from
OPEC, ag in equation (8), are equal to total oi] imports minus oi] imports
from LDCs, x » which in turn depend on the price of oi] relative to the
price of coal and on gross output of DCs. Finally, total exports, x4, total
imports, nf, and real income are determined in equations (9), (10), and ‘11)

7
respectively.


23

viable in practice or whether the outcome is worth the effort. Our purpose
here is to examine these empirical questions with the econometric model of
section II for the period 1982-1990, given the targets and weights described
above.

Figure 1 displays the cooperative policy paths consistent with a
sustained recovery of the world economy. In particular, we find that
nominal oi] prices increase by 3.2 percent in 1982, decline by 8.8 percent
in 1983, and increase in 1984 by seven percent; nominal oi] price growth
remains in the six percent range for the 1985-1990 period. The path for
optimal real government expenditures in DCs shows an average growth of 1
percent per year while optimal nominal capital transfers grow at an average
of 10 percent per year. Finally, interest rates fall from 13 to 8 percent.
As Figure 1 shows, these last three instruments exhibit virtually no
deviations from their desired values.

The growth outlook consistent with the above cooperative macro
policies is shown in Figure 1. Growth in developed economies, after
experiencing a decline of one percent in 1982, shows a steady increase from
3.2 percent in 1983 to 4.5 percent in 1990. Non-OPEC developing countries
exhibit positive growth for the entire planning period starting with a three
percent growth rate in 1982, which increases to 5.6 percent by 1990; their
(nine year) average annual growth rate is 3.5 percent. OPEC's real oil
revenues decline. sharply in 1982 and 1983 (16 percent in each year) because
of both the recession in developed countries and the decline in oi] prices.
However, these revenues increase by 10.8 percent in 1984, and 6.5 percent in
1985, with an annual average growth rate of 5.8 percent for the period 1986-

1990. The inflation rate, ane’, decreases from 5.9 percent in 1982 to 3.9


International Finance Discussion Papers

Number 247
December 1984

COOPERATIVE POLICIES AMONG THE NORTH, THE SOUTH, AND OPEC:
AN OPTIMAL CONTROL APPROACH

by

Jaime Marquez
Peter Pauly

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 materials)
should be cleared with the author or authors.


46

“Notice that the number of targets exceeds the number of instruments, given
that we have to minimize the variances of the deviations between the actual
and the expected value for each target. In effect, there are eight targets
and four instruments. The variance-covariance matrix 9 is estimated using
the OLS residuals.

> Although capital transfers to non-OPEC LDCs can hardly be considered a
variable under their control, developed countries do benefit from such
transfars as the simulation results from case III indicate. Capital
transfers here are net of amortization and interest payments, and thus they
represent “new money". There are, in principle, several sources of capital
transfers: OPEC cumulated unspent oi] revenues (as in scenario III), debt
relief (Kenen 1977), and profit sharing from seabed activities (Cooper
1977). Nevertheless, these capital transfers have traditionally been a
source of political controversies and ethical considerations (see Bhagwati
1977, Cooper 1977, and Kenen 1977).

limplicitly we are assuming the monetary authorities carry out open market
operations with a corresponding effect on the interest rate.

Nn similar target growth rate is found in the United Nations Development
Report (United Nations 1982).

*8Real of1 prices are defined here as nominal oi] prices relative to the
export price of manufactures of developed countries.

This the growth rate corresponding to the "high-case scenario" of the
World Bank Report for 1982 (World Bank 1982:35). More recently, Terrel
(Terrel 1984:759) has estimated that in order to restore a sustained growth
to developing countries, transfers should grow at a rate of 6 percent per
year starting from a base of $40 billion transfers for the period 1983 and
1984. The discrepancy in estimates is due to the lower target growth rate
of Terrel's analysis.

2" Cooperative policies derived for the period 1973-1983 (not shown) indicate
that growth for each region could have been higher than historical growth
rates. However, we do not find this kind of exercise very informative since
one can always do better with hindsight. From the point of view of
evaluating cooperative policies between the three country blocks considered
here, an extrapolation into the future seems more relevant, especially when
combiried with a sensitivity analysis as we do here.

I this is average growth rate is higher than the "high scenario" target
growth rate for developing economies (3.3%) of the 1982 report of the World
Bank (World Bank 1982:37). This seemingly small difference in growth rates
results in significant differences in the levels of real income after 9
years.

2 they also find that Japan and Germany reduce government spending in
response to an increase in the price of oil. However, Oudiz and Sachs point
out that, becauses of the large size of the U.S. in the world economy, the
U.S. plays a very influential, and asymmetrical, role in the world economy.
Thus it is entirely conceivable to observe, at our (OECD) aggregate level, a
positive association between government spending and oi] prices. Finally,


10
depend on the export price of manufactures of DCs relative to the export
price of manufactures of LDCs, paps, and on the real GDP of DCs. Our
estimates point to an income elasticity of 2.7 and a (relative) price
elasticity of 0.7 . Nominal foreign exchange reserves, R*, are determined,
in equation (20), as the balance of payments plus foreign exchange reserves

lagged one period.

III. THE ANATOMY OF OIL PRICE EFFECTS

There is little doubt that oi] price increases, and the associated
policy responses, have a significant impact on the outlook of the world
economy. In this paper the effects of oi] price increases are decomposed
into direct and indirect effects. More specifically, the direct effect is
the transfer of real income from oil importers to OPEC, which in the case of
the DCs takes the form of a deterioration of the real balance of payments,
given the increased cost of oi] imports in terms of manufactured goods. In
the case of the LOCs, the transfer takes the form of a reduction in foreign
exchange resources, which has subsequent indirect dynamic effects on output
growth through the influence on capital good imports and investment.

The indirect effects of oi] price increases operate, in our
model, through OPEC's revenue recycling and increases in manufactures '
export price. An increase in oil prices raises oi] revenues of OPEC who in
turn recycles a fraction of it to import manufactures from DCs. This
increase in OPEC's imports represents a stimulus to activity in the 0Cs--one
which may offset the direct negative effect. In turn, this stimulus to real
activity in the DCs increases exports of LDCs, enlarging their foreign

exchange resources and thus allowing greater capital good imports and faster


9
(an elasticity in excess of one), although not quite as responsive with
respect to changes in relative prices and real income.

Imports of manufactures, we in equation (16), are derived from the
second nest of the production function, where the economy-wide capital stock
is modeled as an aggregate of a domestically made capital component, Ki and
a foreign made capital component, Kf with a positive (but finite)
elasticity of substitution. Following Marquez (1984), the optimal level of
the foreign capital stock is proportional to the optimal level of the
economy-wide capital stock, and by taking time derivatives, we obtain
imports of manufactures as a function of net investment, rt, We assume,
again, a lagged adjustment model for imports with the speed of adjustment of
manufacture imports directly related to the availability of foreign exchange
reserves. Our empirical results for manufacture imports point to an import
elasticity of 0.8 with respect to net investment and an elasticity i1 excess
of one with respect to (real) foreign exchange reserves.

The conditional demand for oil, o* in equation (17), is derived
from the first level of the (two level CES) production function, and it
depends on relative factor prices and gross output, ey, Oi1 imports, mn,
are assumed to come from OPEC only, and they are derived using the identity
between world oi] consumption and world oi] production, equation (18). This
identity establishes that LDCs' of] imports are equal to LDCs' oi] demand
minus (the exogenously given) of] supply, os**, plus the amount of oi]

exports of LDCs to DCs.

Finally, exports of manufactures to DCs, x in equation (19),


42
Table 7

Impact of Acceleration in Oi1 Price
Changes on World Income Distribution.

Average Effects

1983-1990
Case I
nm M3 Ds OPEC LOCs (4%?)
4.5 99999 0.6 -3.9 0.1 3.8
2:3 99999 0.3 -3.8 0.3 5.6
0.1 99999 13 ~3.9 0.5 15.5
Case II
m M3 Os OPEC LOCs A(A#P 9)
4.5 99999 0.5 -0.9 0.4 1.8
2.3 99999 0.6 “13 0.5 2.8
0.1 99999 0.9 22.1 0.5 4.9

Case I: Greater weight to OPEC's revenue target.
Case II: Greater weight to DC's growth target.

Entries for a particular weighting scheme represent deviations of welfare
losses from welfare losses for the base solution.


30
their welfare losses only by inducing an increase in welfare losses to the
other countries.

The efficacy of alternative instruments in achieving OPEC's growth
target can be examined by varying the instruments’ weights in the welfare
function. Intuitively, the smaller the value of the weight for a given
instrument the more willing we are to use that instrument to improve OPEC's
growth target. A reduction in the weight of of] prices' growth from 4.5 to
0.1 raises the average growth rate of oil prices by 11.7 percentage points,
inducing further increases in welfare losses to both DCs and LDCs--by 1.3
and 1.5 percentage points respectively--while reducing OPEC's welfare
losses even further. The increases in welfare losses of DCs and LDCs are
not more pronounced because as oi] prices accelerate, the optimal fiscal
policy response becomes more expansionary and thus tends to offset the
adverse effects of increases in oi] prices on income growth (see Figure 3).

That the optimal fiscal policy response to higher oi] prices might
be a1 expansion of government expenditures is a plausible result given that
the overriding consideration in our specification is the sustainability of a
given growth path. Experimentation (not shown) with a higher weight for
inflation leads to a decline in government expenditures. In addition, the
expansionary policy response to higher oil prices is consistent with
previous historical attempts at international coordination of macropolicies.
For instance, the "locomotive" and "convoy" strategies that were tried
during the seventies were a clear response to the higher oi] prices (see
Sachs 1979:270). Furthermore, Oudiz and Sachs have found (Oudiz and Sachs
1984:41) that the optimal fiscal policy response in the U.S. to an exogenous

22
increase in the price of oil is an expansion of government expenditures.


47

Burbidge and Harrison (1984) have found, using Vector Autoregressive
simulations, that an increase in the price of oi] leads to increases in the
money supply in the U.S., Japan, and the U.K., which is clearly an
expansionary response to the oi] price shock.

*3Vhile it is true that an increase of one dollar in exports can offset a
one dollar decline in foreign aid while keeping foreign exchange reserves
constant, it is also true that an increase in exports may enhance domestic
activities to a greater extent than aid. These domestic considerations make
the notion of substitutability a subtle one, and its analysis is beyond the
scope of the present paper.

"another instance of unrealistic instrument paths' is the case of greater
weight to OPEC's growth target using a low weight for government
expenditures. Under these circumstances, these expenditures exceed their
targeted values by an annual average of $55 billion in real terms. Again,
given today's concern with government budget deficits, it seems unlikely
that such an expansion of government expenditures will materialize.

2> . eos .

One way of relaxing the assumption of cooperation is, for instance, to
include in the welfare function only OPEC's targets and instruments and have
reaction functions for DCs and LDCs. A second approach is to have a welfare
function for each of the players who have conflicting objectives (Pindyck
1977). Alternatively, one could examine the implications for growth of
Cournot-Nash and Stackbelger solutions (see Canzoneri and Gray 1983).
Notice that we have not dealt with the (difficult) problem of policy
coordination in the face of uncertainty about the underlying economic
structure. Using a highly stylized version of the model used in this paper,
we have examined cooperative pricing policies in a Bayesian framework
allowing for learning about the structure. The results, while preliminary,
are available upon request.


29

. Figure 3
Mean Fitted Values for Targets and Instruments: Case I
Desired Path 5 (my=2.3, m3=99999)— — — -; (my=0.1, m3=5000)— - — —
(NTEREST RATES GOVERNMENT EXPENDITURES
5 TTrrer TT ites
= om +
8 Ye NLL
It Le 7 15
" —
9 5 ==
a —— 4 105
7 = 4
, ty tf t ft 5 [a ee ee ee ee ee 0.95
wee 984 1986 1988 1990 y982 1984 1986 1988 1990
On PRKE GROWTH ‘TRANSFERS TO LDCS
TTTrtTtftditdtt 60 Trererrttit 2.60
' /a40 “J 00
, — — 2.
7 :
- 7 20 - 7
meer eee 7 .
NU ASS z 4 140
\/ °
| ns es ee es es es 20 pi ft i tf j | ft 0.80
1982 1984 1986 1988 1990 1982 1984 1986 1988 1990
INFLATION RATE GROWTH DCS
rtttft iT iT iT] 850
4
L Jf 74750
eo
L > + 6.50
Z.\ |
t- 5.50 ie)
|
fot to} ft jf tt 4.50 [ee ee ee ee 2
1982 1984 1986 1988 1990 1982 1984 1986 1988 1990
OPEC'S GROWTH GROWTH LDCS
TTT? tt tf 16 TT T TT TT 9 9
L —7
8 2
L “745
47
ie) oo
rTM~ oc” 438
J Nee
| es Gs es Gs 8 [es ee es GG 1
1982 1984 1986 1988 1990 1982 1984 1986 1988 1990



Developed Economies

Private consumption, cd in equation (1), is modeled following the
permanent-ircome hypothesis. The measure of income we use is nominal value
added, Py y, deflated by the consumption price index pas the estimate of
the short run mpc is 0.47 and the estimated long run income elasticity is
one. Investment, 19 in equation (2), is a function of a distributed lag of
both real income and long term nominal interest rates r; the estimate of
the short run mpi is 0.13 and the estimated long run elasticity with respect
to income is 1.18; the long run interest rate elasticity is -0.20. Imports

of raw materials from LDCs, Mo

r in equation (3), depend on the price of raw

materials, in relative to the export price of manufactures of DCs, pa > and
on the real income of DCs, Y4; the long run relative price elasticity is
-0.69 and the long run income elasticity is 0.63.

The inflation rate of exports of manufactures, ane in equation
(4), is modeled as a markup on factor prices while allowing for supply
constraints. The factor prices considered are wages, raw materials, and
oil. A one percent increase in the rate of change of nominal wages, Aw os
raises the inflation rate by 0.33 percent, which is quite close to the
effect of a one percent increase in the inflation rate of raw materials on
aap’, A one percent increase in the inflation rate of oil prices, Aw o>
raises (with a lag) the inflation rate by 0.10 percent. Finally, capacity
utilization U, measured as the difference between potential and actual
output, is included as an explanatory variable to capture the effects of
supply constraints on the inflation rate. A one percent increase in excess
capacity lowers (with a lag) the inflation rate by 0.2 percent.

Potential output, Y*, is estimated as a trend of actual output.
We split the period of estimation into two subperiods--1960-1972 and 1973-

1979--to allow for the possibility of structural changes that might have


20

of the world economy from a ‘no-growth' path to a ‘high-growth’ path with
reduced inflation. The desired growth rate for developed economies is
assumed to increase steadily from 2.5 percent in 1982 to 5.8 percent in 1989
and 1990. For developing countries, the desired growth rate increases from
four percent in 1982 to seven percent for the period 1987-1990. Real oi]
revenues of OPEC, R°, are targeted to grow at one percent during 1982 and
1983. These growth rates are small relative to the standards of the 1970's,
but they are ambitious given the sharp declines in real oi] revenues for the
1982-1983 period. We increase this desired growth rate from four percent in
1984 to ten percent in 1989 and 1990. Finally, the desired inflation rate
for manufacture exports steadily declines from seven percent in 1982 to five
percent in 1985 and thereafter.

The desired values for the instruments (the r's) are also shown in
Table 3. Nominal oi] prices are targeted to have a zero growth rate in
1982, a decline of 15 percent in 1983, and a six percent increase for the
1984-1990 period implying a one percent increase in real oil prices for this
last period. Long term nominal interest rates, rd, are targeted to decline
from 14 percent in 1982 to eight percent by 1986, remaining at this level
until 1990. For government expenditures we assume an average annual growth
rate of only 0.9 percent reflecting the concern of current administrations
over increasing government budget deficits. Nominal capital transfers to
LDCs are assumed to grow at an 11.2 percent growth rate per years.
Government expenditures and capital transfers enter into the welfare
function as indices with 1982=1.0 to avoid the problems that arise from
interactions between the units of measurement of the instruments and the
weights in the welfare function.

Ideally, we would like to obtain a set of weights that would


37

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SON[eA pasjsap SI} WIJ aLqejeA Jaber aya Jo SUopIefAaP
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qi XV soa7 9340 5,90 fw tw
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72642, YIMOJ S,I07 JOS YBfam saIeIIH z]]] aSed
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38
. Figure 7
Mean Fitted Values for Targets and Instruments: Case 3

Desired Path 3 (m,=0.1, m3=99999)— — — -; (m,=0.1, m3= 5000)——- — —
WITEREST RATES GOVERNMENT EXPENDITURES
[ee ee ee | i) TTTTTtidls tft 114
= 413 = ae 110
= "
= 9
tof tf tf ft | tf 7 pot ft tt} 0.98
w82 1984 1986 1988 1990 1982 1984 1986 1988 1990 |
CL PRIZE GROWTH ‘TRANSFERS TO LDCS
TT??? t?td?T TST 472 TT T?Td?tftStTST éiie60
2.00
ie)
\ 140
i — 10
|e ee 10) }o} j j fj ft | tj oso
1982 1984 1986 1988 1990 1982 1984 1986 1988 1990
INFLATION RATE GROWTH DCS
ToT T TT T TTT 7.50
6.50
5.50 al
A )
/
|e es ee ee ee 4.50 fof jf yf tf tt 2
1982 1984 1986 1988 1990 1982 1984 1986 1988 1990
OPEC's GROWTH GROWTH LOCS
“Tt TTT T T TT 16 TTg?Tt?tdftt tt 8
= I 8
= 7 a 0
Lo? 48 /
~~ 4
i es es 16 Jo} f tf | J} 2

“1982 1984 1986 1988 1990 1982 1984 1986 1988 1990


26
among the different targets to changes in the parameters in the welfare

function.

More formally, a welfare tradeoff is said to occur when an
improvement in the performance of the ith target implies a deterioration in
the performance of another target variable. One useful measure of the

performance of a given target, relative to its desired values, is:

1990
We = (1/9 J (Yap ea
i t-f9a2 it

i”, i1,2,3,
where Ws is a measure of the average deviation of the fitted (mean) value of
target variable Y; from its desired value ay. Therefore, the smaller is Wj»
the smaller is the "welfare" loss of the ith country bloc. In this context,
a welfare tradeoff is defined as a situation where a decrease in W,entails a
simultaneous increase in Wy for j # i.

A distinct type of tradeoff that arises in our formulation is the
degree of substitutability among different instruments in achieving a
specific target. In particular, a desired growth path for LDCs could be
achieved with alternative policy mixes for capital transfers and government
expenditures in DCs. Thus it is conceivable that an expansionary fiscal
policy in DCs, by raising exports of developing countries, could reduce the
amount of capital transfers, or aid, needed to support a target growth rate
for LDCs. While presumably, the expansionary effect of direct transfers to
LDCs is larger, the DCs should prefer conventional expansionary fiscal
policy since it avoids the direct transfer of resources. The question is
what is the extent to which these two policies can substitute for each

other.


2

analyses have focused on policy coordination among the major developed
countries. The possibility of policy coordination with other country blocks
such as OPEC or the group of developing countries has received considerably
less attention. And yet two of the most significant developments of the
last decade, the increase in oi] prices and the unprecedented level of LDCs‘
debt, have had a significant impact on developed economies' growth outlook
and therefore on the viability of policy coordination agreements among them.
Ignoring the role played by OPEC and other developing countries in the world
economy may be too great an abstraction to make.

The purpose of this paper is to address the issue of policy
coordination among developed countries (the North), OPEC, and other

developing countries (the South). We consider specific questions such as:

-- What are the paths for oi] prices, government expenditures, interest
rates, and resource transfers to LDCs consistent with a non-inflationary
recovery of the world economy?

-- What are the optimal stabilization policy responses in industrial
economies to changes in oi] prices?

-- Can lower oil prices eliminate the need for higher capital transfers to
LDCs? Can these capital transfers be avoided by coordinated expansionary
fiscal policy in DCs?

-- What is the nature and sensitivity of the distribution of income gains
(and losses) among DCs, OPEC, and non-OPEC LDCs to different coordinated
policy mixes?

-- How different is the oi] price path that maximizes growth for oi]

exporters from the oil price path that maximizes growth for oil importers?


45

the absence of financial links is a limitation of our model. However, the
ongoing modeling effort still suggests the existence of tradeoffs between a
reasonably sized model including most of the relevant linkages, reliability
of parameter estimates, technical limitations of numerical optimization
algorithms, and model validation.

>the theoretically correct specification should use the real interest rate.
This specification, however, yielded the wrong sign in estimation, and thus
could not be used. This sign reversal could be due to the combination of
our (large) level of aggregation and a positive variance in the distribution
of inflationary expectations, or to the non-neutrality of the distributuion
of the inflation rate with respect to changes in relative prices. This non-
neutrality arises when the one-good assumption of most macro models is
removed. See Cukierman (1983), and Sachs (1983b:260-261) who examines the
effects of this non-neutrality in the distribution of relative price changes
on the labor market.

“Gross output is defined as real value added plus oi] imports in real terms.

Developed countries also export to DCs. These intra DCs trade flows cancel
each other out in equation (11); trade flows between DCs and Centrally
Planned Economies are treated exogenously.

* see Marquez (1983), Fried and Schultze (1975), Nordhaus (1980), MacAvoy
(1982), and Griffin and Teece (1982). In this paper we are considering
increases in the price of oi] for expositional purposes. We have found that
in general the effects of oil price changes are almost symmetrical.
Nonetheless, empirical results suggest the existence of a lower threshold
for oil prices for debt-riden countries (Mexico, Nigeria, Venezuela) below
which oil price changes are no longer symmetrical.

9 . . . . .
We use historical values as the baseline simulation.

OPEC's real GDP can be approximated by OPEC's real oi] revenues. This
approximation works best for analyses with long term horizons such as ours,
and for the large oil producers which account for most of OPEC trade and for
which oi] revenues represent a sizeable fraction of GDP.

eon computational purposes, we need to express the model in its state-
space representation. This is accomplished by redefining variables with
lags of order greater than one as new variables. As a result, the state-
space representation of the model has variables with lags of order no
greater than one. The size of the model, in its state-space representation
has 101 equations.

In effect, the original number of targets is increased by the number of
variances and covariances that has to be minimized.

Sin order to be fair, we should point out that optimal control applications
are not problem free. In particular, Kydland and Prescott (1977) argue that
policies derived using optimal control need not be optimal if agents have
rational expectations. The main problem is, as they indicate, the absence
of a mechanism inducing future policymakers to take into account the effects
of today's policymakers' decisions on today's agents' decisions. However,
the issue is far from resolved since Chow (1981) shows how to apply optimal
control theory allowing for rational expectations.


43
function, and quite importantly, on the assumption of cooperation among the
three country blocs considered here. Clearly, more research is needed in
each of these areas. Furthermore, capital flows are not being modeled here,
and no allowance is made for endogeneity of exchange rates. Taking into
account the above considerations, the sensitivity analysis we have performed
suggests the following conclusions: (1) if growth is the overriding concern
of authorities, then there is a positive relationship between the optimal
response of government expenditures and optimal oi] price changes; (2) low
oil prices and expansionary fiscal policy in DCs reduce the need for net
capital transfers to developing countries; (3) there exists a conflict of
interests between oi] importers and oi] exporters since the oi] price path
that reduces OPEC's welfare losses is higher than the oil price path

required to reduce welfare losses for both DCs and LDCs.


13
Table 2
Dynamic Income Multipliers for

O11 Price Shocks, Fiscal Policy Responses
and Transfer Policies

1973-1983
DCs OPEC Non-OFEC LDCs

IT @ mm Fr Hm ror mw
1973 -0.5 -0.5 -0.5 7.9 7.9 7.9 -0.05 0.05 -0.05
1974 -0.6 -1.4 -1.4 2.9 2.3 2.3 -0.1 0.1 -0.1
1975 -0.8 -2.0 -1.8 0.8 ~0.4 -0.2 -0.2 0.2 0.01
1976 -0.9 -2.4 -1.7  -0.1 -1.4 -0.8 -0.4 0.5 0.8
1977. -1.2  «--3.0 --1.5—-0.5 -2.0 -0.5 -0.7 0.8 2.6
1978 -1.4 -3.5 -1.4 -0.6 -1.9 0.2 -1.0 1.3 5.1
1979 -1.6 -4.1 -1.5 -0.6 -1.4 1.1 -1.3 -1.7 8.0
1980 -1.8 -4.7  -1.6 -1.1 -1.4 1.3 -1.5 2.2 11.0
1981 -2.1 -5.4 -1.8 -2.8 -2.9 0.8 -1.7 -2.7 13.9
1982 -2.5 -6.4 -2.1 ~-4.4 -4.2 0.7 -1.8 -3.2 16.6
1983 -2.9 -7.2 -2.5 -4.4 -2.8 1.8 -1.8 -3.5 19.0
Average-1.5 -3.7 -1.6 -0.3 -0.8 1.3 -1.0 -1.5 7.0

Effect

Dynamic multipliers are computed as
b j b
m = (ys, - ys,) * 100/y.
ijt it it it
b . . th . :
where Vit is the base solution for the i variable at time t,

vie is the, solution for the jth endogenous variable at time t under
the jv alternative simulation, j = 1, II, III.

Simulation I: 10 percent shock to oi] prices in 1973, which crows
at historical rates afterwards.

Simulation II: As simulation I, but with a cut in government purchases
in 1974 of 8 US$ billion, 2 percent of total purchases;

Simulation III: Same as simulation II, but allowing greater capital transfers
tranfers from OPEC to non-OPEC LDCs, by an annual average of US
$24 billion.


15
off. And it is precisely in this state of "low equilibrium" levels of
income growth where the gains from policy coordination among the different

country blocs are highest (Johansen 1982).

IV. COOPERATIVE POLICIES AMONG THE NORTH, THE SOUTH, AND OPEC

Formulation of the Problem

While the benefits of a global policy coordination effort are
known in theory, empirical estimates of the gains of such a move are
difficult to come by casting doubts on whether global policy coordination
will ever occur. In this section we assess, empirically, the viability of
cooperative policies among DCs, OPEC, and LDCs. In effect, we reverse the
focus of analysis of the previous section, and ask now what are the
implications for oil prices, stabilization policies in DCs, and transfers to
LDCs if a sustained recovery of the world economy is to materialize.

We begin our analysis by making the (strong) assumption that
economic policies in DCs, OPEC, and LDCs, are determined in a cooperative
setting. This assumption amounts to postulating a social welfare function
which is used to evaluate the desirability of alternative coordinated policy
mixes (for details see Niehans 1968, Oudiz and Sachs 1984). Furthermore, we
assume that this welfare function is quadratic in deviations from a given
set of targets. To derive the optimal coordinated policy "mix", we minimize
the expected cost of not achieving the given set of growth targets for each
of the regions considered here, subject to the behavioral constraints and

iL
identities embodied in the econometric model of section II:


1. INTRODUCTION

During the last ten years, we have witnessed a number of events
which are bound to have a long lasting impact on the future course of the
world economy. Since 1973, oil prices have increased by more than 1000
percent generating a significant income redistribution from oi] importers to
OPEC. These income transfers, and the associated policy responses, have
hampered growth in developed economies from a historical average of 5
percent to an average of 2 percent for the 1974-1980 period. More recently,
these countries have experienced negative growth rates. The developing
countries, facing a sharp increase in their oi] bill and a contraction in
their export markets, managed to keep an annual average growth rate of 5
percent until 1980 by borrowing to unprecedented levels. However, the sharp
increase in international interest rates slowed growth in these economies to
less than one percent for the 1982-83 period. And their growth outlook
seems closely linked to their ability to service their external debt, which
crucially depends on the levels of international interest rates and thus on
stabilization policies beyond their control. Economic performance in OPEC
countries has not been as spectacular as previously thought. The worldwide
recession and the dynamic effects of higher oil prices have induced a 50
percent decline in oil exports constraining considerably their ability to
finance further growth. In view of the long lasting impacts of these
turbulent developments, it seems reasonable to ask whether they could be
avoided in the future by implementing coordinated policies among the major
participating countries.

Although questions of international policy coordination have been

1
receiving an increasing amount of attention in the literature, so far the


36

(higher growth in DCs) and lower oi] price growth are transmitted to them
via international trade, enlarging their foreign exchange resources, which
affords faster capital accumulation and enhances output growth. Notice that
this faster output growth does not call for capital transfers above the
targeted levels. Thus, once again, we find that increases in DCs'
government expenditures and lower oi] prices serve as substitute instruments

for capital transfers to LDCs.

Case III: Greater Weight to LDCs Growth Target

We now examine the effect on coordinated policies of an increase
in the weight of LDCs' growth target from one to ten while keeping the
weights for the other targets equal to one. We also reduce the cost
attached to fluctuations in capital transfers from 1500 to 100. Our results
are shown in Table 6 and depicted in Figure 6; Figure 7 displays the mean
paths for targets and instruments for selected weight combinations.

An increase in the weight of LDCs' growth target reduces their
welfare losses by an average of 1.1 percentage points with respect to the
base solution for all the combinations of weights considered here. More
specifically, reducing the weight for oi] prices from 4.5 to 0.1, while
keeping the fiscal policy weight unchanged, does not increase welfare losses
to LDCs despite a 7 percentage points increase in the annual average growth
rate of oil prices. Growth in LDCs is isolated from the adverse effects of
higher of] prices by the increase in capital transfers, which now exceed
their (already high) targets by an annual average of $US 19.5 billion.

Although fiscal policy can, in principle, serve as an instrument

to promote growth in LDCs, we find that LDCs' welfare losses are fairly


24

Figure 1
Mean Fitted Values for Targets and Instruments: Baseline Solution

BITEREST RATES OCS’ GOVERNMENT EXPENDITURES
ToT T TT TT TT 7 ToT TT TT TTT a4
—_——_ DESIRED ————_ = DESIRED

- FITTED 415 | ——— = FITTED 4 110

— 1.06
1.02
Piet rpryyTt 7 Tipit ttt joss
1982 1984 1986 1988 1990 1982 1984 1986 1988 1990
OL PRICE GROWTH TRANSFERS TO LOCS
TT 1 1 1 1~T—T— 20 TTT TT TT T_] 290
DESIRED {  —— = DESIRED 4
FITTED ——— = FITTED

L- 410

/ LL 4 1.30
|. \W 10
[ee es +) bey pti tt soso
1982 1984 1986 1988 1990 1982 1984 1986 1988 1990
HIFLATION RATE GROWTH DCS
Tt 11 1111] 8.50 Tt 1 1TTT_T_] 8
DESIRED = DESIRED 4
- FITTED 4 7.50 FIT 6
6.50 r YY 44
L_ ee. KO
aa 4e
L -~— 15.50 /
\ 7 f°)
tN / 4 4.50 L lo
\/
pitti tt ty }350 Littriyiy ds
1982 1984 1986 1988 1990 1982 1984 1986 1988 1990
OPEC’S GROWTH GROWTH LDCS
TT T1111 T_] 20 TT tt T1119
DESIRED ——— =_ DESIRED
|. FITTED 10 | ———= FITTED 7
pn
] oO 5
L 10 3
—J
Pitre putt jap Piet tpppuy fy

1982 1984 1986 1988 1990 1982 1984 1986 1988 1990


Cooperative Policies Among The North, The South, and OPEC:
An Optimal Control Application

Jaime Marquez
International Finance Division
Federal Reserve Board
Washington DC 20551

and

Peter Pauly
Economics Department
University of Pennsylvania
Philadelphia PA 19104

December 1984

While the benefits of a global policy coordination effort are known in
theory, empirical estimates of the gains of such a move are difficult to
come by casting doubts on whether global policy coordination will ever
occur. In this paper we assess, empirically, the viability of cooperative
policies among the North, the South, and OPEC. To this end we apply
stochastic optimal control to a nonlinear stochastic dynamic econometric
model of a three region world economy that highlights the channels of
international transmission of oil price effects and the feedback effects of
policy responses to oil price changes. Even if cooperative policies exist,
and are implemented, not all the parties involved will benefit to the same
extent. Thus we also examine the sensitivity of the distribution of income
gains (ar losses) between the North, the South, and OPEC to alternative
specifications of the welfare function.

An earlier version of this paper was presented at the 5th IAEE Annual North
American Meetings, June 1983, and the 4th IFAC/IFOR conference on The
Modeling and Control of National Economies, June 1983. We are grateful to
F. Gerard Adams, Matt Canzoneri, David Kendrick, Lawrence Klein, Peter
Tinsley, Janice Shack-Marquez, Edward Green, Geoffrey Heal, and James Sweeny
for their comments. We are also grateful to Gregory Chow for providing the
software used in our analysis. Any remaining errors belong entirely to us.
This paper represents the views of the authors and should not be interpreted
as reflecting the views of the Board of Governors of the Federal Reserve
System or other members of its staff.


48

References

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32

avenue for future research.

Case’ Il: Greater’ Weight’ to DCs Growth Target

We now examine the response of the policy mix to an increase in
the weight of DCs' growth target from one to ten while leaving all the other
targets with a weight of one. The results are shown in Table 5 and are
depicted in Figure 4. Figure 4 exhibits the (mean) paths of targets and
instruments for selected weight combinations.

In general, the initial impact of an increase in the weight for
DCs' growth target is to change the cooperative policy mix towards a higher
level of government expenditures in DCs. However, as we saw in Case I, if
the overriding consideration is the sustainability of a given growth path,
then it is entirely conceivable to find a direct relation between movements
in oi] price changes and movements in optimal real government expenditures
in DCs. Consequently, the beneficial effects of an increase in government
expenditures on DCs' income are offset by the adverse effects of the oil
price increase that immediately follows. This offsetting effect requires an
even larger expansion of government expenditures to counteract the negative
effects of higher oi] prices and to achieve the desired growth target.
However, any further increase in government expenditures is followed by
another round of oi] price increases which again increases further
government expenditures. The net effect of this process is an increase in
welfare losses to DCs and LDCs, but a reduction in welfare losses to OPEC who
clearly ‘benefit from the increase in oil prices. This adverse result on pcs
welfare losses arises because the increase in oi] prices is of a greater

magnitude than the increase in government purchases, which in turn is


4]
assume that ceteris paribus can be (approximately) obtained when instruments
have their highest weight. Table 7 displays the sensitivity of welfare
tradeoffs for cases I and II, along with changes in the average growth rate
for oi] prices for each of the weighting schemes we have considered here.
We see that an increase in the average growth rate of oi] prices is
unambiguously associated with a reduction in OPEC's welfare losses and with
increases in welfare losses for both DCs and LDCs. This finding clearly
indicates the existence of conflicting interests among the three blocs of
countries included in our model, and calls for an extension of our analysis

25
to allow for non-cooperative policy design.

V. CONCLUSIONS

Our first purpose in this paper has been to study empirically the
possibility of developing cooperative policies among the North, the South,
and OPEC, consistent with a non-inflationary reactivation of the world
economy.

To this end we use a nonlinear stochastic dynamic econometric
model for a three region world economy that highlights the channels of
international transmission of oil price effects and the feedback effects of
policy responses to oil] price changes. Applying stochastic optimal control
to an estimated version of this model, we find that if (1) oi] prices grow
at six percent per year which means roughly constant real oi] prices, (2)
government expenditures grow at 0.9 percent per year, and (3) capital
transfers to developing countries grow at 10 percent per year, then it is
feasible to achieve a non-inflationary recovery of the world economy.

Our results are very much dependent on the structure of the model

used, the period for parameter estimation, the specification of the welfare


27
In the remainder of this paper we study the response of the
distribution of income gains among OPEC, developed countries and non--OPEC
developing countries to changes in (1) the weights given to the targets, and
(2) the weights attached to fluctuations in the instruments, particularly
oil price changes, real government expenditures, and nominal capital

transfers to LDCs.

Case I: Greater Weight to OPEC's Revenue Growth Target

We begin the sensitivity analysis by increasing the weight given
to OPEC's growth target from one to ten while leaving unchanged all the
remaining weights. Intuitively, an increase in a target's weight means that
deviations of this target from its desired path are now more costly. Thus,
the coordinated policy mix is changed to reduce, even further, deviations
of this target from its desired path. Table 4 presents the welfare losses
for each country bloc and the average growth rate for oi] prices
corresponding to various combinations of weights; Figure 2 depicts the
results of Table 4, while Figure 3 contains the (mean) paths of targets and
instruments for selected weights.

An increase in the weight of OPEC's revenue target reduces its
welfare losses by 3.9 percentage points with respect to the base solution.
This reduction is possible because the resulting cooperative policy allows
an increase in the average growth rate of oi] prices of 3.8 percentage
points. At the same time, this new policy mix that affords a reduction in
OPEC's welfare losses induces an increase in welfare losses to both
developed and developing economies by 0.6 and 0.1 percentage points
respectively. Consequently, if the OPEC countries have enhanced bargaining

power in determining coordinated policies, then they may be able to reduce


output growth.

Increases in the price of manufactures, induced by higher oil
prices, have an ambiguous impact on DCs' real income. On the one hand, there
is a dampening of the initial terms of trade deterioration, which reduces
the value of DCs' imports (in terms of manufactures) stimulating their real
income. On the other hand, the increase in pd reduces the purchasing power
of export revenues of both OPEC and LDCs with an adverse effect on DCs!
exports and GDP. For developing countries, the increase in pa also has an
ambiguous impact on real income. On the one hand it reduces the purchasing
Power of existing foreign exchange reserves with an adverse effect on
capital accumulation and output growth. On the other hand, it stimulates
LDCs' exports and thus increases foreign exchange reserves.

On the whole, the above discussion suggests that whether ar
increase in oi] prices is stagflationary or not depends, to a large extent,
on the strength of the direct effects relative to the indi rect effects of
these price increases. For developed economies, the direct effect of an
increase in the price of oil--the transfer of real income to OPEC--could be
offset by the indirect effects which operate through both increases in the
Price of manufactures and the recycling activities of OPEC. For developing
countries, the strong and adverse direct effect--the increase in the real
oi] bill--could be aggravated by the associated increases in the price of
manufacture imports. But these adverse effects may be offset by the
beneficial effects of OPEC's recycling. In Practice, whether the direct
effects are offset by the indirect effects depends on the relative
magnitudes of key parameters such as the markup on oil prices, demand price

elasticities, OPEC's recyling activities, and economic policy reactions.


49

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14

finance their imports from DCs. In turn, this decline in DCs' exports
reduces théir real income even more, with subsequent adverse effects on OPEC
and LDCs' real income.

Table 2 also displays the regional output effects of an increase
in capital transfers to LDCs. For concreteness' sake, we assume that OPEC
increases its aid flows to LDCs in each year by 50 percent of net capital
transfers to LDCs of that year. The simulation results for this scenario
indicate that the effects of an exogenous increase in capital transfers to
developing countries more than offset the adverse income effects of both
higher oi] prices and restrictive fiscal policies, resulting in an average
income gain of 7 percent per year. However, the transfers needed to achieve
these income gains are quite substantial. This increase in income is
possible because of the rapid growth of investment which can be afforded by
the increase in financial resources. Furthermore, the rapid growth in
developing countries has beneficial spillover effects on OPEC and developed
countries. In particular, given the low elasticity of substitution between
oil] and capital, the increase in capital accumulation stimulates oi] demand
which raises OPEC's oi] exports increasing OPEC's real income by 1.3
percent on average. At the same time, the increase in LDCs' capital
accumulation raises exports of manufactures by DCs and thus reduces DCs'
average income loss by 2.1 percentage points.

Greatly simplified, our three simulation exercises replicate
the effects of the three stylized facts of the last decade: higher oi1
prices, restrictive policy responses, and increased resources to LDCs. And
what we find is that, unless transfers to LDC's keep growing (at an
unsustainable growth rate), the setting of oil prices and stabilization

policy responses completely independent of each other leaves everyone worse