18

Figure 1

Mean Fitted Values for Instruments:
Base Optimal Control Solution

desired values
fitted values

a

tine


39

Figure . 8

Mean Fitted Values for Instruments: Case IL

t: desired
a: K_ =2.3, K\=99999
RO &

b: K_=0.1, K_=5000
po 8

a a « s “ ” Cy

ce

a oe



35
a given instrument the more willing we are to use that instrument to improve
OPEC's growth target. In particular, a reduction of the weight for oil
price changes from 4.5 to 0.1 has the effect of raising the average growth
rate of oil prices from 8.1 percent to 19.8 percent, which increases welfare
losses to both DCs and LDCs by 1.3 and 1.5 percent respectively without
reducing OPEC's welfare losses. The increases in welfare losses of DCs and
LDCs are not more pronounced because as the average growth rate for oil
prices increases, the optimal fiscal policy response becomes more
expansionary and thus tends to offset the adverse effects of increases in
oi] prices on income growth.

Fiscal policy in DCs might also be used as an alternative
instrument to achieve OPEC's growth target. To examine this possibility we
reduce the cost of fluctuations in this instrument from 99999 to 5000. As a
result, we find that fiscal policy fluctuates more freely, and that it leads
to an unambiguous reduction in welfare losses for each block of countries.
This "Pareto" improvement is possible 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. As a result of this expansionary fiscal
policy there is a stimulus to oi] imports from OPEC which, when combined
with a greater average growth rate in oi] 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
oil prices, and (2) virtually no deviations of capital transfers from their
desired values. This is because higher government expenditures in DCs serve
as a substitute instrument for capital transfers to LDCs since it increases

imports of DCs


44

Case III: Greater Weight to LDCs Growth Target

In this case we begin increasing the weight of LDCs target growth
rate from one to ten while keeping the weights for the other targets equal
to one. We also increase our willingness to use capital tranfers more
freely, and thus we reduce the weight for this instrument from 1500 to 100.
Our results are shown in Table 6 and depicted in Figure 10. Figures 11 and
12 show the behavior of instruments and targets for selected weight values.

An increase in the weight of LDCs' target growth rate results in
an unambiguous reduction in their welfare losses by an average of 1.1
percentage points with respect to the baseline solution for all the
combinations of weights considered here. Moreover, we notice that even if
we let oi] prices fluctuate more freely, by reducing their weight from 4.5
to 0.1, there is no increase in welfare losses to LDCs despite an increase
in the annual average growth rate of oil prices from 4.3 percent to 11.4
percent. This is because the adverse effects of higher oil prices are
offset by higher capital transfers, which exceed their targets by an annual
average of $US 19.5 billion. Additional effects of the increase in the
average growth rate of oil prices are a reduction in OPEC's welfare losses
from 8.6 percent to 5.6 percent and an increase in DCs' welfare losses from
1.6 percent to 2.6 percent.

The effectiveness of using government expenditures to achieve the
LDCs growth target depends on the behavior of oi] prices. In particular, if
fluctuations in oil price changes have attached a weight of 4.5, then a
reduction in the weight on government expenditures does not affect LIICs at
all, and adversely affects DCs and OPEC. This is because with a weight of
4.5, oi] prices tend to follow their target values quite closely, which
includes a reduction in the average growth rate for oi] prices. The fall in
oil prices leads to a decline in government expenditures, given the positive

assocation between these two instruments, which explains the adverse effects


12
income growth targets for each of the regions considered here, subject to
the behavioral constraints and identities embodied in the econometric model

of section II:
T * *
min E(W) = FD (yer a,)'K (yer a,)}

subject to y.= f( Ye» Xe-a> Xe Xeaa? Zee 8) + f°

where XY = (ye! x): K is a positive definite diagonal matrix of weights;
a, is a vector of desired values for targets--such as OPEC's oi] revenue
growth--as well as instruments--such as oi] price changes. The choice of a
quadratic welfare function is for mathematical convenience.

Stating the optimal control problem in this form is equivalent to
maximizing the weighted sum of each regions' welfare function. Given an
appropriate choice of weights (the K matrix), and under the assumption of
cooperative behavior among policymakers, it can be shown (Niehans 1968,
Qudiz and Sachs 1984) that the solution to the first-order conditions of the
above optimal control problem (the entire path for x.) is the efficient
policy choice, A policy choice is said to be efficient if there exists no
other policy vector capable of reducing one country's welfare losses without
increasing welfare losses to another country. Alternatively, a policy mix
is said to be efficient if the associated target values belong to the target
frontier.

The solution of the first-order conditions for the above
minimization problem involves applying Pontryagin's minimum principle (see
Marquez 1983), and it takes the form of a linear feedback rule linking real
income, and other endogenous variables included in Yer to oi] prices and

other exogenous variables included in Xt?


54
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, 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 Hamilton (1983), Marion and Svensson (1982), Bruno and Sachs

(1979), Findlay and Rodriguez (1977), and Schmid (1976).

See Hotelling (1931), Solow (1974), Cremer and Weitzman (1976),
Pindyck (1978), and Salant (1982).

See Niehans (1968), Hamada (1979), Johansen (1982), Canzoneri and
Gray (1983), and Oudiz and Sachs (1984).

In 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 their


52

some developing countries, it seems unlikely that such large transfers will
take place.” °

Second, we find that the oil price path consistent with OPEC's
best interests is higher than the oil price path consistent with either DCs
or Non-OPEC LDCs' best interests. This result is robust with respect to the
different combinations of weights considered here, as can be seen from
Figures 4, 7, and 10 by comparing the average growth rate for oi] prices for
each of the weighting schemes we have considered. This finding clearly
indicates the existence of conflicting interests among the three blocks of

countries included in our model, and calls for an extension of our analysis

to allow for non-cooperative policy design.

V. CONCLUSIONS

Our first purpose in this paper has been to study the
international transmission of oi] price effects and the determination of
optimal oi] price paths, not as separate problems but rather as one problem
by recognizing that economic activity and oi] prices are jointly determined.
We then study the set of efficient policy paths for oi] prices, government
expenditures, and capital transfers to LDCs consistent with a non-
inflationary reactivation of the world economy. The effects of changing the
weights of the welfare function on the income tradeoffs among different
regions and on the optimal policy mix are also examined.

We start our analysis by developing a nonlinear stochastic dynamic
econometric model for a three region world economy that highlights the
channels of international transmission of oi] price effects and the feedback
effects of of] price changes on the demand for oi]. The simultaneous

relation between oi] prices and real income is obtained by minimizing a


58

Policies: An Optimal Control Approach." In L. R. Klein, M.
Nerlove, and S. Tsiang (eds.) Quantitative Economics and Develop-
ment. New York: Academic Press.

Kydland, F. and E. Prescott (1977). “Rules Rather Than Discretion: The
Inconsistency of Optimal Plans." Journal of Political Economy.
Vol. 85, No.3:473-491,

Mariano, R. (1978). “Commodity Market Modeling: Methodological Issues and
Control Theory Applications." In F. G. Adams and J. Behrman
(eds.) Econometric Modeling of World Commodity Policy.
Lexington: Lexington Books.

Marion, N. and L. Svensson (1982). “Structural Differences and Macro-
economic Adjustments to Oil Price Increases in a Three-Country
Model." National Bureau of Economic Research, Working Faper
No. 839, Cambridge: National Bureau of Economic Research.

Marquez, J. (1984). "Foreign Exchange Constraints and Growth Possibilities
in LDCs." Journal of Development Economics, forthcomming.

Marquez, J. (1983). “The International Transmission of O0i1 Price Effects
and the Derivation of Optimal O11 Prices." Ph.D. dissertation,
Philadelphia: University of Pennsylvania.

Marquez, J. and D. Vining (1984). “Inflation and Relative Price Behavior:
A Survey of the Literature" in M. Ballabon (ed.) Economic
Perspectives Vol. 3: 1-56. New York: Hardwood Academic PubTishers.

Niehans, J. (1968). "Monetary and Fiscal Policies in Open Economies Under
Fixed Exchange Rates: An Optimizing Approach." Journal of _

Political Economy. Vol.76, No.4: 893-920.

Oudiz, G. and J. Sachs (1984). "Macroeconomic Policy Coordination Among the
Industrial Countries." Paper presented at the Brookings Panel on
Economic Activity, April 5-6, 1984,

Pindyck, R. (1977). "Optimal Economic Stabilization Policies Under
Decentralized and Conflicting Objectives." IEEE Transactions on
Automatic Control. Vol. ac-22, No.4: 517-530.

Pindyck, R. (1978). "Gains to Producers from the Cartelization of Exhaus-
tible Resources." Review of Economics and Statistics. Vol. 60,
No.2: 238-251.

Salant, S. (1982). Imperfect Competition in The World Oil Market,
Lexington: Lexington Books.

Schmid, M. (1976). "A Model of Trade in Money, Goods, and Factors."
Journal of International Economics. Vol. 6, No.4: 347-362.

Solow, R. (1980). “What to Do (Macroeconomically) When OPEC Comes?" In
S. Fischer (ed.) Rational Expectations and Economic Policy.
Chicago: National Bureau of Economic Reserach.



50

Figure 12

(continued)

“reece rreeerrertes

erreeepeneererpererseengersrern ferent preven

f

su bereveerey

”

6

Tie


22
j.e., we assign a weight equal to one to each target variable. The
tradeoffs between targets that may arise here are due to the behavioral
constraints embedded in our model and to the values given to the
instruments' weights. The iterative algorithm used (Closed Loop) is
sensitive to the choice of instruments' weights, especially low values
(similar findings are reported by Klein and Su 1980). We select the values
for the instruments' weights taking into account that policy changes are not
likely to be large or frequent (Klein 1983). Thus, we give a large weight
to both real government expenditures of DCs (99999) and nominal net capital
transfers to LDCs (1500). Interest rates are assigned a weight of 20 and

oi] prices are assigned a weight of 4.5.

Empirical Results
We apply the optimal control algorithm developed by Chow (1975,

1981) to the econometric model of section II for the period 1982-1990 given
the targets and weights described above. Figures 1 and 2 contain the mean
fitted values for both the instruments and targets.

Starting with the instruments, we notice that the fitted values
for the interest rates are very close to their desired values. Nominal oi]
prices increase by 3.2 percent in 1982, decline by 8.8 percent in 1983, and
increase in 1984 by seven percent; for the 1985-1990 period nominal oil
price changes remain in the six percent range. Finally, mean fitted values
for both real government expenditures and nominal capital transfers are very
close to their targeted values.

With respect to the targets, axp4 decreases from 5.9 percent in

1982 to 3.9 percent in 1984, but rises again to 5.8 percent by 1990. The


40

Figure 8

(continued)

11784

1ias4

\
+ seers errversbeyrenreneret
s 3&8 & 8

Tine

manerpreee pr nprenpeen preenre gee renner

Tine


3

It would seem that once we allow for the fact that oil price

changes, and the associated policy responses, have implications for the

world economy, the issue of international policy coordination among the

country blocks we consider is a natural question to address. A good deal of

attention has been given to the possibility of sub-optimal equilibrium

3
j levels with "low" levels of economic activity resulting from uncoordinated

macropolicies. However, the analyses have been characterized by

deterministic, static, two-country models, with little or no empirical

content (an exception is Oudiz and Sachs 1984). This paper also addresses

the

question of international policy coordination aimed at restoring a non-

inflationary recovery of the world economy. But in doing so, we use a

stochastic, dynamic, three-country model, which allows us also to

empirically address other interesting questions:

What are the optimal fiscal and monetary policy responses in industrial
economies to changes in oil prices?

What is the degree of substitutability among various policy instruments?
Can lower oi] price changes be a substitute for capital transfers to
LDCs in acheiving a given growth target in developing countries? Can
these capital transfers be avoided by coordinated expansionary fiscal
policy in DCs?

What is the importance of income feedback effects in determining the
price of oi] from OPEC's perspective?

What is the nature and sensitivity of welfare tradeoffs among DCs, OPEC,
and Non-OPEC LDCs to different coordinated policy mixes?

How different is the oi] price path that maximizes welfare for oil
exporters from the oi] price path that maximizes welfare for oi]

importers?


33

Figure *6

Mean Fitted Values for Targets: Case I

Fi e
it: desired ya
aed a: Kot K799999 “oO
Ff es: K_=0.1, K_=5000 y
Boy: po g y
FT
i .
i
nad
i
7
i
485
i

Dasssseee

va

ss csetssaclccsessnesdeanscneae

BE plesesssecdageen cass casae seed esene



19

Figure 1

(continued)



25

Table 3

Optimal Vil Prices With and Without
Feedback Effects Allowed

No Feedback Effects Feedback Effects
Allowed Allowed

ABP, A&R° asy? ASP, ser? asy?
1982 14 -8.3 71.26 3.2 715.8 -1.0
1983 ll -9.4 0.33 -8.8 -16.2 3.2
1984 10 -1.5 1.6 7.0 10.8 2.1
1985 10 1.2 2.1 6.3 6.5 3.2
1986 8 -0.6 1.5 6.4 4.9 2.9
1987 8 2.3 2.20 5.9 6.6 4.5
1988 8 2.7 3.3 6.2 5.4 4.2
1989 8 4.6 2.9 6.2 6.4 4.4

1990 8 2.8 2.9 6.7 5.7 4.5



21

Figure 2

(continued)

oe ee

as

Tine,


34

Figure 6

(continued)

1
\
\
\
\

\ é
ee ee PE ET TTD

1.

een ET EN Fe PTD ELT

1

Time


16

Parameters of the Welfare Function

The desired values for targets and instruments are shown in Table
2. We assume a target growth rate for developed economies of 2.5 percent in
1982, which is steadily increased to 5.8 percent in 1989 and 1990. For
developing countries we assume a target growth rate of four percent in 1982,
which is steadily increased to seven percent for the period 1987-1990. Real
oil revenues of OPEC, Rr, are targeted to grow at one percent during 1982
and 1983. Although these growth rates are small relative to the standards
of the 1970's, they are ambitious in relation to the performance of real oil
revenues for the 1982-1983 period. We increase this growth rate from four
percent in 1984 to ten percent in 1989 and 1990. The target inflation rate
of exports of manufactures is seven percent in 1982, steadily declines to
five percent in 1985, and remains at five percent for the remainder of the
horizon.

Nominal oi] prices are targeted to have zero growth rate in 1982,
a decline of 15 percent in 1983, and a six percent increase for the 1984-
1990 period implying a target of one percent increase in real oi] prices for
this last period. Long term nominal interest rates, rf, are targeted to
decline from 14 percent in 1982 to eight percent by 1986 and to remain at
this level for the remainder of the horizon. For government expenditures we
assume an average annual growth rate of only 0.9 percent, reflecting the
concern over increasing government deficits of current administrations.
Capital transfers to LDCs in nominal terms are assumed to grow at an 8.5
percent growth rate per year starting in 1980." Government expenditures and
capital transfers enter in the welfare function as indices with 1982=1.0.

Our first characterization of the efficient policy mix consists of

a baseline optimal control solution with an egalitarian welfare function,


8

imports), ey’, We estimate a linearized version of this demand function
with a distributed lag (4 periods) for prices and income, allowing for
homogeneity of degree zero in prices. In estimating this relationship, we
use switching regression with a split of the sample in 1972. A Chow test
for the null hypothesis of parameter stability could not be accepted. The
Tong run oil price elasticity declines from -0.27 to -0.57. The long run
coal price elasticity increases from 0.29 to 0.91. The estimated income
elasticity declines from 1.70 to 1.34. The hypothesis of homogeneity of
degree zero in prices cannot be rejected.

DCs' total imports of oi] (in barrels), ag in equation (7), are
equal to their demand for oil (in barrels) minus their exogenously given
supply of oil, 0° (also in barrels). Imports of of] from OPEC, nd in
equation (8), are equal to total imports of oil minus imports of oi] from
Non-OPEC LDCs, bee » which in turn depend on the price of oi] relative to the
price of coal as well as on gross output of DCs. Since the product of total
oil imports in real terms, ¥!, and the oil price index, Poe is identical to
the product of total imports of oi] in barrels, ae, and the price of oi] Ps
(in dollars per barrel), we can solve from this identity for oi] imports in

real terms as in equation (9).

OPEC

The only behavioral relation we explain is OPEC's absorption
capacity of oi] revenues. For this we relate their imports of manufactures,
"a in equation (10), to a distributed lag of oil revenues deflated by the
export price of manufactures of DCs. The absorption elasticity in the first

year is 0.31, 0.36 in the second year, and 0.04 after four years. The long


31

Figure 5

Mean Fitted Values for Instruments: Case I

desired
: K_ =2.3, K =99999
po

K =0.1, K =5000
‘po &

a 3 oo as 6 v a ao a
Tne

TiNe


28

Table 4&

Welfare Tradeoffs
Case I: Greater Weight tor UPEC'S Revenue Growth Target

Weights Welfare Losses
a
Ko Ky DC's OPEC LDC's A&P,
4.5 99999 2.3 4.8 2.8 8.1
2.3 99999 2.0 4.9 3.0 9.9
0.2 99999 3.0 4.8 3.2 19.8
4.5 5000 2.3 4.0 2.3 6.4
2.3 5000 1.6 3.5° 2.4 8.3
0.1 5000 2.0 2.1 2.6 20.6
Base Solution 1.7 “8.7 2.7 4.3

@ Averaye growth rate, 1982-1990.


we

5
developing countries, whose GDP is determined from the supply side using a
production function. Centrally planned economies have been excluded from
the present model.

The international trade flows included in the model. are: (1) oil,
sold by OPEC to both developed and Non-OPEC developing economies; the latter
also export oi] to developed economies; (2) manufactures, exported by the
DCs to both OPEC and Non-OPEC LDCs; and (3) manufactures and raw materials,
which are exported by the Non-OPEC LDCs to DCs. In a compact form, the
model has 52 equations, 16 of which are behavioral. The parameters of the
model are econometrically estimated using 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 need not hold for small samples such
as ours (Mariano 1978). We now describe the main behavioral equations which

are shown, in general form, in Table 1.

Developed Economies

Equation (1) represents private consumption, c4, depending on a

d yd

distributed lag of nominal value added Py Y" deflated by the consumption

price index pd the short run mpc is 0.47 and the long run income

con’
elasticity is one. Investment, 14 in equation (2), is a function of a
distributed lag of both real income and the long term nominal interest rate
rf; the short run mpi is 0.13 and the long run elasticity with respect to
income is 1.18; the long run elasticity with respect to the interest rate
is -0.20.

Imports of raw materials from Non-OPEC developing countries, we in


Several conclusions can be drawn from our analysis. First,
recognizing the income feedback effects of oi] price changes raises the
absolute value of the demand price elasticity and reduces the oil price path
consistent with of] exporters' best interests. Second, the international
transmission of oi] price shocks generates changes in the distribution of
income between regions; therefore, alternative coordinated policies, as
developed in this analysis, have different effects on the prospects for the
major regions of the world.

We begin the analysis in section II where we develop a small
econometric, three-region world model to study the international
transmission of oi] price effects on real income, prices and international
trade, assuming that oi] price changes are exogenous. In section III we
endogenize oi] prices by applying optimal control to the econometric model
to formally derive a system where oi] prices--along with other exogenous
variables--and real income of oi] importers are simultaneously determined.
We implement our approach empirically in section IV, and section V contains

our conclusions.

II. A GLOBAL MODEL OF OIL PRICE EFFECTS

The model we use is simple but comprehensive and it is based on
theoretical models developed by Taylor (1981) and Marquez (1983). We divide
the world economy into three regions: (1) the developed economies, whose GDP
is determined from the demand side; the supply side is introduced via a
production function which determines prices and factor input demands; (2)
the OPEC countries, for whom we only explain the recycling of oil export

earnings to purchase imports of manufactures, and (3) the Non-OPEC


17

Table 2

Base Optimal Control Solution
Desired Values for Targets and Instruments
(1982-1990)

Targets

syd ASR? asy® seed
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
1988 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

AeP rd ge CF

°

1982 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
1988 6 8 1.06 1.87
1989 6 8 1.07 2.u8
1990 6 8 1.08 2.31



7

equation (3), are a function of (i) present and past values of the price of
d
m?
and (ii) real income of DCs, y!; the long run relative price elasticity is

raw materials, Pas relative to the export price of manufactures of DCs, P

-0.69 and the long run income elasticity is 0.63.

The inflation rate of the export price of manufactures, axp4 in
{ equation (4), depends on (i) the rate of change of nominal wages, AEP with
a coefficient of 0.327; (ii) the inflation rate of of] prices, AEP ys lagged
one period with a coefficient of 0.09; (iii) the inflation rate of raw
materials' prices with a coefficient of 0.34; and (iv) a measure of capacity
utilization, U, obtained as the difference between potential output and
actual output.

Potential output, Y*, is estimated as a trend of actual output,
but we split the period of estimation into two subperiods: 1960-1972 and
1973-1979. One reason for such a sample split is to allow for the
possibility of structural changes that might have taken place after the
first of] shock in 1973, such as the slowdown of productivity growth. The
estimated growth rate for potential output for the period 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 demand for oi] (in barrels), of in equation (6), is a
conditional demand function derived from a three level CES production
function, equation (5), whose arguments are labor, L, capital, K, oi], 0,
and coal, C. As a result, both capital-energy substitution possibilities
and interfuel substitution possibilities are taken into account. The
conditional demand for oi] depends on the prices of oil, coal, labor, and

the rental price of capital as well as on gross output (value added plus oi]


23

initial decline in axed is due to both the fall in oil prices in 1983 and
the reduction in economic activity of DCs in 1982. Growth in developed
economies, after experiencing a decline in activity in 1982 of one percent,
shows a steady increase from 3.2 percent in 1983 to 4.5 percent in 1990.
OPEC's real of] revenues decline sharply in 1982 and 1983 (16 percent in
each year) because of both the recession in of] importing countries and the
decline in oi] prices. However, these revenues increase by 10.8 percent in
1984, 6.5 percent in 1985, and maintain an annual average growth rate of 5.8
percent for the period 1986-1990. Growth in Non-OPEC developing countries
is positive for the entire planning period starting with a three percent
growth rate in 1982, with a small decline to 2.1 percent in 1984, and
increasing steadily to 5.6 percent in 1990; the average annual growth rate
is 3.5 percent.”

Recognizing both the limitations of our model, and given the
particular weights used, we find that if international policy coordination
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 8.5 percent per year, (3) long term interest rates declining to 8.0
percent, and (4) real government expenditures continuing their (modest)
expansionary path, then it is feasible to achieve relatively high growth
rates for developed, OPEC, and Non-OPEC developing countries for the

remainder of this decade.

The Importance of Income Feedback Effects and OPEC's Pricing Policy

One of the main contentions of this paper is that allowance for
the income feedback effects of oi] price changes raises the absolute value

of the price elasticity of oil demand and therefore lowers the optimal price


International Finance Discussion Papers
Number 241

April 1984

OIL PRICES, WELFARE TRADEOFFS, AND INTERNATIONAL POLICY COORDINATION
IN A THREE REGION WORLD MODEL: AN OPTIMIZING APPROACH

by

Jaime Marquez and 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

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10

Exports of manufactures to DCs, xt in equation (14), depend on (i)
the export price of manufactures of DCs relative to the export price of
manufactures of LDCs, rare, and (ii) the real GDP of DCs. Oi] consumption,
o* in equation (15), is modeled as a conditional demand function derived
from the production function, and it depends on relative factor prices and
gross output, ey’, Using the identity between world consumption (in
barrels) and world of] production (in barrels), we derive LDCs' imports of
oi] from OPEC (in barrels), a » as the difference between LDCs' oi] demand
and (exogenously given) oi] supply, os?*, plus exports of of] of LDCs to
DCs. Finally, we link oi] imports in barrels to oi] imports in real value
following the same steps as in equation (9) for DCs.

For the purposes of section III, it is particularly useful to
express the econometric model of Table 1 in its state-space representation

as:

Me" fee Yea Xee Xt Zee OD tee (17)

where
Yt? vector of endogenous variables,
f = vector of functions,
X,= vector of controllable exogenous variables,
Z,= vector of non-controllable exogenous variables,
8 = vector of parameters,
e = vector of random errors, e ~ N(0,2),
Q = estimated covariance matrix.
The state-space representation is obtained by redefining both

endogenous and controllable variables with lags of order greater than one


run absorption elasticity is 0.98.

Non-OPEC Developing Countries

Gross output (value added plus oi] imports in real terms), ey* in
equation (11), is determined using a two level nested CES production
function with capital, Ke, and oi] consumption, 0’, as arguments. The
parameters of this function are estimated in two steps by using the first-
order conditions for cost minimization and the production function itself.
The short run elasticity of substitution between oi] and capital is 0.05 and
the long run elasticity is 0.73.

Following Coen (1971), we determine capital formation, 1* in
equation (12), as a function of the rental price of capital, Br relative to
the price of oi], and on gross output. We model the speed of adjustment of
investment as a function of the availability of foreign exchange resources
in real terms, Ry / a .« We find an inelastic response of investment to
changes in both income and relative prices. However, we find investment to
be quite responsive to changes in foreign exchange reserves (an elasticity
“in excess of one).

Imports of manufactures, mt in equation (13), are derived using
the fact that the capital stock is an aggregate of the domestic capital
stock and the foreign capital stock, with a positive (but finite) elasticity
of substitution. Following Marquez (1984), we obtain imports of
manufactures as a function of net investment, I, and foreign exchange
reserves. Our results point to an elasticity of imports of manufactures
with respect to investment of 0.8 and an elasticity with respect to (real)

foreign exchange reserves in excess of one.


59

Solow, R. (1974). "The Economics of Resources or The Resources of
Economics." American Economic Review. Vol. 54, No.2: 1-14.

Stiglitz, J. (1976). “Monopoly and The Rate of Extraction of Exhaustible
Resources." American Economic Review. Vol. 66, No.4: 655-661.

Taylor, L. (1979). Macro Models for Developing Countries. New York:
McGraw-HilT.

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

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

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



42

9

Figure

(continued)

oa hprrseensengtersere

Time



30

aa40 1) s.007 SSS9 3.20 +01 SSO 3ays73H
$301ad 110 404 LHOL3H

Sh £2

quaumzanap 103 W4bTaM

I aSvo
SLUDIGM LNAWNULSNI NI SHDNVHO
OL SASSOT FUVATIM dO ALIALLISNAS

y eansty


47

Figure 11

Mean Fitted Values for Instruments: Case III

t: desired
a: K_ =0.1, K =99999
po &

e: K_=0.1, K =5000
po 8

i
i
h
3
di
7 a « s “ a “ “
TInt
a
ed
ist

——



29

from one to ten. A welfare tradeoff is said to occur when a decline in Ws
induces an increase in some other Wye We also examine the sensitivity of
such tradeoffs to different weights for oil price changes (0.1, 2.3, 4.5)
and for real government expenditures (99999, 5000). Table 4 presents the
welfare losses for each country block and the average growth rate for oil
prices corresponding to alternative combinations of weights; Figure 4
depicts the results of Table 4. Figures 5 and 6 illustrate the behavior of
targets and instruments for selected weight values.

We begin the sensitivity analysis by increasing the preference
given to OPEC's growth target while leaving unchanged all the remaining
weights. We find that OPEC's welfare losses are reduced from an average of
8.7 percent for the base solution to 4.8 percent in the present case. This
reduction #s possible because of the average growth rate of oi] prices
increases from 4.3 percent to 8.1 percent. At the same time, the reduction
in OPEC's welfare losses induces an increase in the welfare losses of both
developed and developing economies by 0.6 percent and 0.1 percent
respectively. Thus if the OPEC countries have enhanced bargaining power,
then they may be able to reduce their welfare losses only by inducing an
increase in welfare losses to the other countries, which shows that the
income distribution for the original set of weights was efficient.

As mentioned earlier, one of the advantages of using optimal
control is that the instruments are assigned to targets according to their
relative efficacy. This assignment, however, depends on the relative costs
attached to fluctuations in the different instruments, and for this reason
we examine how sensitive is this assignment to changes in the instruments’
relative weights. Suppose then that we reduce the value of the weight for

changes in oi] prices. Intuitively, the smaller the value of the weight for


Table 1

Main Behavioral Relations in

Global Econometric Model

Developed Economies
di. d yd, pd
ch = F(PY YoY Pe,
18 = F(y4, 4)

ma = (pay pd, yd)

on)

AePG = F(AxP,, AEP», AEPy 1, Ur)
Gv4= F(L,Ck,€(0,¢)7)

de d

07 = F(Py, Pos Pps Py, GY4)

= of. od
My = 0f- o
adosdoo«
My = My - XE(Po/ Po, GY4)

md =( Pos Py )( Md + x2)
OPEC

Mam F(Po(MG* Mo)/P )
Non-OPEC Developing Countries

y= £(K% 0%)

1% = F(PEy Py, YE RA/ pA)
mis £(12, RL/ Pd)

Xm = f(Pdy pe, yd)

o* = £( peyp, , ev*)

Me = of. 989% 4 x2
My = 0*- 0 + Xo

(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

(9)

(10)

(11)
(12)
(13)
(14)
(15)

(16)


20
Figure. 2

Mean Fitted Values for Targets:
Base Optimal Control Solution

t: desired values
a: fitted values

PaPUL POUUL OUI YOUUIE PODER OUTOT TUVUTT TOOTIN TOOTIN POPTTT FOTTRRTROTRT OVA

o « «

2 cs) w s s
Tine

Tine


57
REFERENCES

Aperjis, D0. (1982). The Oil Market in the 1980's: OPEC Oil Policy and
Economic Development. Cambridge: Ballinger Publishing Company.

Bruno, M., and J. Sachs (1979). "Macroeconomic Adjustments with Import
Price Shocks: Real and Monetary Aspects." The Maurice Falk
Institute for Research in Economics. Discussion Paper 793,
Jerusalem, Israel.

Canzoneri, M. and J. Gray (1983). "Two Essays on Monetary Theory in an
Interdependent World." International Finance Discussion Paper
No.219, Board of Governors of The Federal Reserve System.

Chow, G. (1975). Analysis and Control of Dynamic Systems. New York: John
Wiley.

Chow, G. (1981). Econometric Analysis by Control Methods. New York: John
Wiley.

Coen, R. (1971). "The Effect of Cash Flow in the Speed of Adjustment." In
G. Eromm (ed.) Tax Incentives and Capital Spending. Washington,
D.C.: Brookings Insitution.

Cremer, J. and M. Weitzman (1976). "OPEC and the Monoply Price of oi1."
European Economic Review. Vol. 8, No.2: 155-164.

Findlay, R., and C. A. Rodriguez (1977). “Intermediate Imports and Macro-
economic Policy under Flexible Exchange Rates." Canadian Journal
of Economics. Vol. 10, No.2: 208-217.

Fischer, D., D. Gately, and J. Kyle (1975). " The Prospectus for OPEC: A
Critical Survey of Models of The World Oi] Market." Journal of

Development Economics. Vol.2, No.4: 363-386.

Hamada, K. (1979). " Macroeconomic Strategy and Coordination Under
Alternative Exchange Rates." in Dornbusch and Frenkel (eds.)
International Economic Policy: Theory and Evidence. Baltimore:
Johns Hopkins University Press.

Hamilton, J. (1983). "Oi1 and The Macroeconomy since World War II." Journal
of Political Economy. Vol. 91,No. 2: 228-248.

Hotelling, H. (1931). "The Economics of Exhaustible Resources." The Jour-
nal of Political Economy. Vol. 39, No.2: 137-175.

Johansen, L. (1982). "A Note on the Possibility of an International
Equilibrium with Low Levels of Economic Activity." Journal of
International Economics. Vol.13 No.3/4: 257-265.

Klein, L. (1983). "Economic Policy Formulation: Theory and Implementation
(Applied Econometrics in the Public Sector)." In Handbook of
Econometrics, Vol. 2, forthcoming.

Klein, L. and V. Su (1980). "Recent Economic Fluctuations and Stabilization


37

Table 5

Welfare Tradeoffs
Case II: Greater Weight for DC's Growth Target

Weights Welfare Losses
Koo Ko De's OPEC Lbc's AeP,
4.5 99999 2.2 7.8 3.1 6.1
2.3 99999 2.3 7.4 3.2 71
0.1 99999 2.6 6.6 3.2 9.2
4.5 5000 3.0 8.3 3.1 5.6
2.3 5000 2.0 8.1 3.0 5.1
0.1 5000 1.6 5.0 3.0 10.9

Weight for DC's Growth = 50
4.5 5000 1.3 8.3 2.8 4.7
Weight for DC's Growth = 200
4.5 5000 0.6 7.6 2.5 5.2

Base Solution 1.7 8.7 2.7 4.3

@ average yrowth rate, 1982-1990.


38

9340 s.901 SSS9 s.00 +01 S807 340734
$3918d WO 40s LHOL3M

s'b £2 La
ors Ts
Is eees
aqeu YaMoIy
ay1d 140 19
aber0ay

66868 gaanaypuadxa
Quewurzaacg 103 I4byem

;
U

Tl aSvo
SLHDIGM LNAWNULSNI NI SHONVHO
OL SASSOT AUVATAM AO ALIAILISNAS

L 2an3ty


53
quadratic welfare function subject to the econometric model. We apply
optimal control to an estimated version of this model and we find that if
(1) of] prices grow at six percent per year, (2) government expenditures
grow at 0.9 percent per year, and (3) capital transfers to developing
countries grow at 9 percent per year, then it is feasible to achieve a non-
inflationary recovery of the world economy.

Given the structure of the model, its estimated parameters, the
optimizing horizon, and the optimization algorithm we find that:(1) the
growth rate of oi] prices taking into account income feedback effects is
smaller than the growth rate of oi] prices when these feedback effects are
not taken into account; (2) real oi] revenues of OPEC grow at a faster rate
when income feedback effects are allowed in the determination of oil prices
than in the case where these income effects are not allowed; (3) there is a
positive relationship between the optimal response of government
expenditures and optimal oi] price changes; (4) low oil prices and
expansionary fiscal policy in DCs serve as substitute instruments for net
capital transfers to developing countries; (5) there exists a conflict of
interests between oil importers and oi] exporters since the oi] price path
that reduces OPEC's welfare losses is higher than the oi] price path

required to reduce welfare losses for both DCs and LDCs.


26

H1IM049 ANNSASY

s

3340
0g-

1
LOS
E

b48

E8s
3

P28

E98
Ese

£8

rc

pemoTTe

S0ezJe YOeqpeey ou (q

5S 3d AG 3LVY HLMO
£ an

PeMmoTTe szoazye yoeqpesy (e

110 aL9y

AO

HALAC

eeu

TOOT

47

$90035g YOeqpeeq noyIFM pue YIFM S2®>F2dq THO TewFIdo

€ oean3ty

TpTITT

la

ee


56

government expenditures, which stimulates DC's real income and thus OPEC's
revenue growth. To make sure that an instruments' responses, other than oil
prices, are not responsible for the rapid growth in OPEC's revenue, we have
given a rather high weight (99999) to government expenditures. We find that
the average deviation of government expenditures from their target is, in |
absolute value, equal to 0.9 percent, which can hardly be considered as a
reason for the increase in OPEC's revenue growth.

x2 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).

+3 Another instance is the case of greater weight to OPEC's growth
target using a low weight for government expenditures. 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 expenditure will

materialize.


an assumption that may be valid in the short-run, or for countries with very
little participation in the oi] market. However, for countries like the
U.S., Japan, and West Germany, with oi] consumption representing a large
share of the international oi] market, the assumption of oi] price
exogeneity is not tenable. An increase in oi] prices affects their real
income, their oil consumption, and therefore feedback to OPEC's oi] revenues
and oil prices.

As a corollary of removing the small country assumption, we relax
the assumption of stability of the oil demand curve faced by OPEC, which is
the typical assumption made in analyses of oi] price determination.

Assuming a stable demand curve implies that oi] price changes have no effect
on either the level of real income or its growth rate, which is in contrast
to the "supply shock" literature and to ten years of empirical findings.
Thus we can see that--up to now--the effects of oi] price changes and the
determination of oi] prices have been analyzed in a dichotomous manner since
what has been assumed as exogenous in one kind of analysis is treated as
endogenous in the other and vice versa (see Fischer et. al., 1975).

In this paper we remove this dichotomy by treating of] prices and
economic activity as jointly determined. This joint determination of oil
prices and real income implies that OPEC faces, in addition to the problem
of allocating oi] production through time, 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. In
particular, if the price path is too low, then OPEC does not exploit the
price inelasticity of oil demand and thus incurs revenue losses. However,
if the price path is too high, then real income of oi] importers is
adversely affected and this feeds back to OPEC in the form of lower oil

exports and oi] revenue losses.


45

Table 6

Weltare Tradeoffs

Case III: Greater Weight for LDC's Growth Target
weights Weltare Losses
K ° b
p Kg DC's OPEC LDC's A&P, ACF
4.5 99999 1.6 8.6 1.6 4.3 12.1
2.3 99999 1.7 7.8 1.6 5.1 13.4
0.1 99999 2.6 5.6 1.6 11.4 19.5
4.5 5000 1.9 8.7 1.6 3.8 14.3
2.3 5000 1.8 7.9 1.5 4.6 14.8
0.1 5000 2.0 4.8 1.5 11.4 17.7
base Solution 1.7 8.7 2.7 4.3 0.2
@ Average growth rate, 1982-1990.
b Average deviation from taryet, 1982-1990, billions of

$us.


43
5000. We find that this weight reduction leads to a decline in welfare
losses for DCs from 3.0 percent to 1.6 percent and for OPEC from 8.3 percent
to 5.0 percent with almost no effect on LDCs welfare losses despite an
increase of the average growth rate for oil prices from 5.6 percent to 10.9
percent. This last result suggests that the adverse effect of higher oi]
prices on both DCs and LDCs growth are offset by the stimulative effects of
increases in government expenditures of DCs, given that this instrument can
fluctuate more freely now.

We also examine the impacts of additional increases in the weight
for the DCs growth target. In order to detect nonlinear intertemporal
tradeoffs, we consider an increase in this weight first from 10 to 50 and
then from 10 to 200, while keeping the weights for oi] prices and government
expenditures at 4.5 and 5000 respectively. Our results indicate that when
the weight for DCs equals 200, their welfare loss declines from 3 percent to
0.6 percent. There is a small decline in welfare losses of OPEC (0.2
percent) even though the average oi] price growth rate declines under the
new weighting scheme. This suggests that OPEC's reduction in welfare losses
arises out of the increase in oi] exports induced by the higher growth in
developed economies. Finally, Non-OPEC LDCs experience a decline in welfare
losses from 3.1 percent to 2.5 percent because the effects of higher
government expenditures (higher growth in DCs) and lower oi] price growth
are transmitted to them via international trade, enlarging their foreign
exchange resources and thus reducing their need for capital transfers above
the targeted levels. Thus, once again, we find that increases in DCs'
government expenditures serve as a substitute instrument for capital

transfers to Non-OPEC developing countries.


13

*
= G,(8, ate K) Xt-1° (18)

Xt

Notice that & is a time varying matrix with elements depending on the
(estimated) parameters of the model, the desired values for instruments and
targets, and the elements of the K matrix. In using a feedback rule we
recognize that (1) economic policies are not set once and for all, i.e.,
they are revised (with a lag of one period) as information about the future
values of the endogenous variables becomes known, and (2) current policies
have an impact on future policies. This is a relevant issue since a change
in oi] prices today will have a lasting influence on oi] consumption and
this must be taken into account when determining the price of oil.

Having derived an expression for the optimal policy path, equation
(18), we combine it with the econometric model to obtain an “enlarged”
econometric model where real income growth, an element of Yee and (optimal)

oil prices, an element of Xe are jointly determined:
*

Me = f£We> Meer Meo Mea Zee S) Me > (17)
*
X= G (8 Ke ae Mea - (18)

To illustrate this joint determination, suppose we are given an initial path
for oi] price's growth, o Ie Using equation (17), we determine the effect
that the given path of oi] price changes will have on real income of oi]
importers. These income effects, together with the substitution effects,
are transmitted to OPEC in the form of both movements along and shifts of
the oi] demand schedule. Using equation (18), these changes in the oil

demand schedule are now taken into account by OPEC (with a lag of one


55

policies 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.

Capital transfers to Non-OPEC LOCs can hardly be considered a
variable under their control. A more reasonable interpretation in our
context would be to treat them as transfers required from international

cooperation.

Capital transfers here are net of amortization and interest

payments, and thus they represent "new money”.

A similar target growth rate is found in the United Nations

Development Report (United Nations 1982).

This growth rate is similar to that of the “high-transfer

scenario" of the World Bank Report for 1982 (World Bank 1982).

The optimal control solutions converged in three iterations.
10

This 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).
ll . . .

It might be possible to argue that the higher revenue growth
derived using optimal control solutions is not due to income feedback

effects, but rather due to the response of some other instrument such as


15

in order to accelerate their development process, sets the price of oi] in
order to secure a flow of oi] export earnings large enough to finance the
foreign component of their capital stock (Aperjis 1982, Marquez 1983). We
also include in the welfare function growth rates for developed and Non-OPEC
developing economies to study both changes in the distribution of income
between DCs, OPEC, and Non-OPEC LDCs and the feasibility of a high growth
path for the world economy. Finally, the inflation rate of the export price
of manufactures, a proxy for the overall inflation rate, is included to
capture policy makers' concern with allocative inefficiencies and
distributional effects of high and uncertain inflation rates (Niehans 1968,
Marquez and Vining 1984).

With respect to the instruments, we use the growth rate for oi]
prices since it is the instrument that OPEC uses to ensure a steady flow of
export earnings. We include government expenditures and interest rates of
developed economies because they allow us to study what type of coordinated
fiscal, and (only indirectly) monetary policies can be implemented by
developed economies in order to achieve a non-inflationary growth path for
the world economy. Finally, capital transfers are included to study the
financial requirements implied by sustained growth in the Locs<

By considering a number of policy instruments, we can obtain an
isotarget curve by examining the extent to which instruments can substitute °
for each other in achieving a specific target. For instance, a particular
growth path for Non-OPEC LDCs could be achieved with alternative paths for
oil prices and government expenditures in DCs, and one issue that arises
here is to what extent lower oi] prices can be a substitute for an

expansionary fiscal policy in DCs given the LDCs' growth path.


OIL PRICES, WELFARE TRADEOFFS, AND INTERNATIONAL POLICY
COORDINATION IN A THREE REGION WORLD MODEL:
AN OPTIMIZING APPROACH *

Jaime Marquez
International Finance Division
Federal Reserve Board
and
Peter Pauly
Economics Department
University of Pennsylvania
April 1984
Abstract. The first purpose of this paper is to derive optimal oil prices
by recognizing that oil price changes affect real income of oi] importers
and vice versa. International trade flows, income, and prices are
endogenously determined in a three region world model (DCs, OPEC, Non-OPEC
LDCs). Using Chow's method for stochastic control of a general nonlinear
dynamic system, we then offer a characterization of the set of efficient
cooperative policy strategies for the country blocks considered here, given

a set weights in the welfare function. We also examine the sensitivity of
the optimal policy mix to changes in the weights of the welfare function.

I. INTRODUCTION

Our first purpose in this paper is to endogenize OPEC's pricing
policy recognizing that real income of oi] importers is affected by oil
price changes and that oil price changes are affected by real income of oi]
importers. Our second purpose here is to ascertain the existence of
efficient cooperative policies among developed countries, OPEC, and Non-OPEC
developing countries, and the extent to which alternative policies result in
welfare tradeoffs for these country blocks.

In endogenizing oi] prices, we relax two of the most common
assumptions found in the analyses of oi] price effects and of oi] price
determination, namely that oi] price changes are exogenously given "shocks",
and that the oi] demand that OPEC faces is either a stable function or one

2
that shifts at a known (exogenous) growth rate. Price taking behavior is


36
from LDCs and this increases foreign exchange reserves with the same impact

on growth of LDCs as a transfer of capital.

Case II: Greater Weight to DCs Growth Target

In this case we begin by increasing 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 7.
Figures 8 and 9 illustrate the behavior of targets and instruments for
selected weight values.

In general, the initial impact of an increase in the weight for
DCs growth target is to raise government expenditures in DCs. However, as
we saw in Case I, there is a direct relation between movements in of] price
changes and movements in optimal real government expenditures in DCs. This
positive relationship implies that the effects of an increase in government
expenditures on real income of DCs are offset by the increases in oi] prices
that immediately follow. This offsetting effect requires an even larger
expansion of government expenditures to counteract the negative effects of
higher oi] prices and to achieve the growth target. However, any further
increase in government expenditures is followed by another round of oi]
price increases which again increases 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. This adverse result on DCs welfare
losses arises because the increase in oil prices is of a greater magnitude
than the increase in government expenditure given 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


24
path consistent with OPEC's best interests. What is not so clear, however,
is whether these feedback effects are important enough to result in
significantly different oi] price paths.

One way to evaluate the importance of these feedback effects is to
contrast the effects on oi] revenue growth of a price path where of] prices
grow at a rate equal to the interest rate (Hotelling 1931, Stiglitz 1976)
and thus no feedback effects are allowed, against the effects on oi] revenue
growth of an optimal oi] price path derived using optimal control, where
feedback effects are allowed. Table 3 contains our results, which are
depicted in Figure 3.

For every year, except the first two, the growth path for OPEC's
revenue in the no-feedback case is below the revenue growth path derived
using optimal control, even though oi] prices grow faster in the no-feedback
case than in the optimal control case. The deterioration of OPEC's revenue
growth in the no-feedback case occurs because the revenue increase arising
out of short-term price inelasticity of oil demand is offset by the
reduction in real income of oi] importers, which dampens oi] consumption and
shifts to the left the export demand schedule faced by OPEC. In other
words, the income feedback effect¢ of of] price increases raises the
(absolute value of) the price elasticity above 1 and therefore further price
increases lead to revenue losses. And what our results imply is that it is
optimal to increase the price of oi] until the revenue increase arising out
of short-run price inelasticity is equal to the revenue loss arising out of

the income feedback effects.

Sensitivity Analysis

The characterization of the efficient policy mix derived above is

conditioned on both a particular weighting matrix and on the assumption of


Title: Oil Prices, Welfare Tradeoffs, and International Policy
Coordination: An Uptimizing Approach

Authors: Jaime Marquez and Peter Pauly

Address: Board of Governurs of The Federal Keserve System
Washington, D.C. 20551, and
Economics Department, University of Pennsylvania
Philadelphia, PA. 19104

Date: April 1984

Series and Number: International Finance Discussion Papers, No. 241

Pages: 59

Price: No charge

JEL Subject Classification: 212,713

Keywords: Oi] prices, Optimal control, Policy coordination, Welfare

The first purpose of this paper is to derive optimal oil

prices by recognizing that oil price changes affect real income of oil

importers and vice versa. International trade flows, income, and prices

are endogenously determined in a three region world model (UCs, UPEC,

Non-UPLC LUCs). Usiny Chow's method for stochastic control of a general

nonlinear dynamic system, we then offer a characterization of the set of

efficient cooperative policy strategies for the country blocks

considered here, given a set of weights in the welfare function. We

also examine the sensitivity of the optimal policy mix to changes in the

weights of the welfare function.


48

Figure 11

(continued)

-_---—~.

2 £2 &

potuernux wmeurent ewe

Seren eer preeey ny peere price

me

TM

ve

—

i ranes ane hands nee ane anaee ae

w

Tine


32

Figure 5

(continued)

Sper pe nen penn peer per een rend

Tine

“s



i

41

Figure 9

Mean Fitted Values for Targets: Case II

desired

t

ee 8 # F FR F

\
\
\
a \
a i=} \
a t=} \
a i=J \
al al \
Yn ep \
MoM \
. . /
_. od / Hl
an 9° / H
r) W / H
2 (2
MM Mm
soy

Srrereeys ces perry

oa

7

Tine



27

cooperation among the three blocks of countries in setting the instruments'
values. Therefore, it is of interest to perform a sensitivity analysis to
study the robustness of our results to changes in the values of the
weights.” In particular, we analyze the welfare tradeoffs among OPEC,
developed countries and Non-OPEC developing countries that arise as a result
of changes in (1) the preference ranking of targets, and (2) the cost
attached to fluctuations in the instruments, particularly oi] price changes,
real government expenditures, and nominal capital transfers to LDCs.

One useful definition of welfare losses, Ws, is:

1990
w,= (1/9 SY
t=1982

at ae), 9=1,2,3.

Ws measures the average deviation of the fitted value of variable 5 from
its targeted value. Therefore, the smaller is Wis the smaller is the
"welfare" loss of the ith country block. For instance, the last row of
Table 4 contains the welfare losses for the three regions considered here,
under the baseline optimal control solution. Our results indicate that, on
the average, the DCs' growth rate deviates 1.7 percent from the target
growth rate. OPEC's revenue growth shows the greatest deviation, 8.7
percent, which could be due to either the setting of extremely

ambitious targets or to the particular choice of weights. We concentrate in
the remainder of this paper on the sensitivity of these welfare losses to

changes only in the weights of the welfare function.

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

We now study the welfare tradeoffs between the three country

blocks that arise when the weight for OPEC's revenue target is increased


11
as new variables. In addition, we have classified exogenous variables as

either instruments, Xpo or non-controllables, 24.

III. SIMULTANEOUS DETERMINATION OF OIL PRICES AND REAL INCOME:

AN OPTIMIZING APPROACH

i The optimizing approach, as developed originally by Niehans
(1968), contains two key ingredients. The first one is a social welfare
function providing a ranking of the alternative combinations of target
values. The second ingredient is the existence of a target frontier
specifying the maximum value that a given target can obtain for given values
of the other policy targets. The application of this optimizing approach to
our problem has several advantages. First, there exists a quantitative
criterion to evaluate systematically the effects of alternative instruments'
paths on the behavior of the economy. Secondly, the “principle” of
effective market classification is embedded in the optimizing approach. By
this principle, instruments are assigned to that target on which it has
relatively the strongest effect. This is an important point because the
solution to an optimal control problem takes the form of an efficient
"policy mix" allowing for the relative desirability of targets, the relative
costs of changing the instruments, and the dynamic behavior of the economy.

An alternative to the optimizing approach is a "trial-and-error"
approach where one examines the effects on the economy of a large number of
alternative paths for the exogenous variables. However, and in contrast to
optimal control, there is no objective criterion to choose an efficient
policy mix among the alternative paths for the exogenous variables.
In order to select the best policy mix for the controlling

variables, we minimize the expected cost of not achieving a given set of


49

Figure 12

Mean Fitted Values for Targets: Case III

a
a
a
a
o

fo)
mM
ge
Ca
HO
AW
3B
aoM
a6

+1, K,=5000
&

e: K_=0
‘po

Tine

Pear an Sane Sa a a

a

as

Tine


51

on DCs and OPEC. We also notice that, despite the decline in the average
growth rate of oi] prices, there is an increase in the amount of capital
transfers to LDCs. This increase is necessary to offset the impact that
lower growth in DCs has on the LDCs, since the beneficial aspects of lower
oil prices are being offset by the reduction in growth of DCs.

In contrast to the previous situation, a reduction in the weight
of oil prices to 0.1 means that oi] prices can deviate more freely from
their target path. As a result, a reduction in the cost of fluctuations in
government expenditures from 99999 to 5000 marginally reduces welfare losses
of LDCs and significantly reduces the welfare losses of both DCs and OPEC.
In addition, we notice that it is possible to have a decline in average
capital transfers to LDCs since DCs' government expenditures are now higher,
which increases imports from LDCs and enlarges their foreign exchange

receipts.

Evaluation of Sensitivity Analysis Results

Several interesting results emerge from the extensive 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 Non-OPEC LDCs, capital transfers
would have to exceed the (already high) targets by an annual average of $US
20 billion in some cases, and in no case is this excess below an annual

average of $US 12 billion. Given today's current financial situation for


14
period), to obtain a second oj] price path {x Jywhich, by equation (17), is
used to recompute the effects of oi] price changes on economic activity.
This second round of oi] price effects is, in turn, used to update the
Previous oi] price path and so on. This iterative process between oi]

a1
prices, real income, and of] demand continues until 108}, od +0,

where s is the sth iteration.

IV. EXPERIMENTAL DESIGN

Description of the Welfare Function

In order to implement empirically our approach, we parametrize the

welfare function as :

1990 4 2 1990 4 >
min EO) ME abae aby Maelae Ait) * e-ibse srhaeTMse ryt
where the target variables are:

YF the growth rate for real oi] revenues of OPEC, ar;

Yor the growth rate for real income of developed economies, aay;

Y3= the growth rate for Non-OPEC developing countries, asy*; and

Yar the inflation rate of the export price of manufactures of DCs, aap.
The policy instruments we use are:

Xx the growth rate for oil prices, anPy 3

Xo Tong term nominal interest rates of developed economies, rd;

X3= real government expenditures in DCs, 64;and

X= nominal net capital transfers to Non-OPEC developing countries, cr;

In postulating such a welfare function we have assumed that OPEC,