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Expectations, target zones, and oil price dynamics
NORTH- HOI_1 AND
Expectations, Target Zones, and Oil Price Dynamics Shawkat H a m m o u d e h and Vibhas Madan,
Department of
Economics, Drexel University This paper incorporates inventory shocks and market expectations in OPEC's oil pricing mechanism and applies the target zone and speculative attack literatures to oil price dynamics. The paper examines the oil price behavior in the two-sided target zone model and the asymmetric tolerance zone model. It focuses on the characteristics of the smooth-pasting and speculative-attack solutions that are associated with credible and noncredible intervention policies. The analysis shows that credibility of OPEC's intervention policy declines as its output ceiling is reduced to a low level, which makes the price vulnerable to speculative attacks, and increases as the ceiling rises. The credibility is directly related to sensitivity of the market price to changes in the output and the sensitivity of this price to changes in the price expectations, and is inversely related to the positive intertemporal bias in the size of the random shocks in the quantity.
1. INTRODUCTION Since the late 1970s, OPEC has introduced a production quota system to bring the market price of oil in line with its chosen target price. The actual production levels, however, do not abide by the self-imposed quotas because of deliberate cheating and unforeseen events or shocks that disrupt the assigned production quotas. Cheating, which is usually expected to occur in periods of revenue shortfalls and stagnant prices (i.e., a soft market), pushes production over the output ceiling, thereby exerting a strong downward pressure on the market price. The shocks, which are unexpected, lead to surpluses or shortages and may cause an upward or downward deviation of the market price from the target price. Due to the existence of capacity constraints, OPEC may not be able to control the market price in the presence of a strong upward price shock. However, it has two options in normal and soft markets where the market price drifts below the target price. It can establish Address correspondence to Prof. Shawkat Hammoudeh, Department of Economics, Drexel University, 32nd and Chestnut Streets, Philadelphia, PA 19104, U.S.A. Received October 1994; final draft accepted January 1995. Journal of Policy Modeling 17(6):597-613 (1995) © Society for Policy Modeling, 1995
0161-8938/95/$9.50 SSDI 0161-8938(95)00022-L
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a band for the market price positioned around the target price by basically choosing suitable upper and lower limits for the output or it can place a tolerance zone below the target price in order to restrict the discrepancy between the market price and the target price (Hammoudeh and Madan, 1994a). The lower limit is particularly needed because it sets a price floor and ensures that the market price stays above the significantly lower marginal cost of oil production. If the limits of these zones are backed by a perfectly credible intervention policy, they can generate an expectations process that should turn the market prices around even before any intervention takes place. In reality, OPEC's member countries perceive a band around their target price, especially a tolerated trough under this price in the face of adverse future market conditions. They use the research of their own individual oil ministries, as well as that of OPEC's Research Division, to form medium-term perceptions of supply and demand to conceive upper and lower limits around the target price. The size of the perceived band is related to the size of the output ceiling, which is determined by revenue needs and bargaining power within OPEC. Currently, the target price is $21 per barrel, the tolerated lower limit is about $16, and the output ceiling is 24.5 million barrels per day. The collapse of the market price to $10 per barrel has made OPEC very cognizant of the lower limit, and the member countries will be ready to defend it under normal conditions by reducing the output ceiling. The market participants have observed OPEC's behavior and have lent more credibility to the lower limit of the band. In this paper, we will generalize previous research by explicitly including oil shocks, changes in demand, and changes in expectations within the market price band. We examine the dynamics of oil prices within the target and tolerance zones and outside these zones when the output ceiling is not defensible. Emphasis is placed on delineating between defensible and nondefensible policies and on the factors thai affect the defensibility of the output ceiling and the credibility of the intervention policy. The major contribution of this paper is the introduction of stochastic considerations in the analysis of OPEC's policy decisions as well as performing sensitivity analysis on the price solution. The methodology draws upon the work in the area of target zones and exchange rate stabilization. Although the particular objectives of exchange rate management and OPEC's price-quantity decisions seem to be different, the established framework for analyzing the
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former provides a logical structure for analyzing the latter. In both situations the policymakers are attempting to stabilize the value of a core variable, while allowing for some flexibility around a targeted value of that variable. In each case, one of the main issues is the credibility of policy decisions in the face of fundamental uncertainty and market expectations that are fueled by the policies themselves. In fact, under normal conditions the oil market participants form expectations and cause a turnaround in the market price in anticipation of OPEC's intervention in the same manner that foreign exchange participants generate expectations, causing a turnaround in the exchange rate in anticipation of central banks' interventions. 2. TARGET ZONE MODELS OF THE OIL MARKET
In previous research (Hammoudeh and Madan, 1990, 1992, and 1994a) several oil policy mechanisms have been evaluated in terms of their impact on the market price and their implications for OPEC's output adjustments. In this paper we will examine two of these mechanisms in the presence of target zones. 2A. Mechanism 1
OPEC's current policy mechanism can be described by the following equations: d P / d t = ~(qLo] - qc), d¢/dt
= ~(P - p r ) ,
~t ;>0 ~~ 0
(1A) (IB)
for any pr, where pr is the target price, cl(P) is the demand for OPEC's output, tic is its output ceiling, ~t is the market speed of price adjustment, and ~ is OPEC's speed of output adjustment. ~ Thus, Equation 1A describes the market price adjustment, and Equation 1B represents OPEC's output-ceiling adjustment rule. Because the demand for OPEC's oil, el(p), does not necessarily equal its output ceiling, q~, Equations 1A and l B should be adjusted to explicitly include shocks in the market such as demand fluctuations due to the business cycle, cheating on quotas, and production disruptions due to political and military conflicts among OPEC's members. Moreover, because the simple formulation above does not incorporate limits on the changes in the market price P in order High (low) values of ~ indicate that the quantity ceiling is strongly (weakly) sensitive to discrepancies between the market price and the target price.
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to prevent it from straying too far from the target price pr, the basic mechanism should be modified to keep the price movements within the boundaries of a target zone. Furthermore, this formulation does not include the market participants' expectations, which are formed in response to OPEC's policy of defending its targeted objectives. A perfectly credible intervention policy involving changes in the output ceiling would have the effect of initiating changes in expectations of price movements followed by a turnaround in the market price before it reaches either limit of the target zone. This policy is considered to be nondefensible if the market does not expect OPEC to sufficiently reduce the output ceiling to offset increases in inventories when the market price is close to the lower limit. There will be a strong positive supply shock as the speculators try to unload their inventories on the market because of the expected excess supply. Thus, there will be a price fall without a turnaround, and the speculative attacks will take the price out of the target zone. Taking these changes into consideration, the price adjustment rule in Equation 1A will include, in addition to the output ceiling, terms that account for changes in demand and output due to shocks. Furthermore, the turnaround in the price will be accounted for by including changes in expectations due to intervention. The output policy (i.e., the output-ceiling adjustment rule) in Equation 1B should also be modified by considering the output ceiling q~ to be an intervention policy variable that is bounded by the announced upper and lower limits on the market price. To accommodate these changes, we need to distinguish between the components of demand and supply of OPEC's oil. We will consider the demand to be the predictable demand, and it will be represented by qd(P). The nonpredictable component of demand is a demand random shock that is equal to declines in inventories. The supply is postulated to include the official output ceiling qC, which is determined by OPEC and is exogenous in the short run. It is also assumed that the ceiling qC is set to satisfy the predictable demand and, therefore, qa(P) = ~ . The second component of supply is the supply random shock, dq2, which is equal to increases in inventories. The shock dq2 is also assumed to represent an excess demand or an excess supply s h o c k . 2 Thus, this component is a 2 We can interpret dq2 as a demand shock, a supply shock, or the difference between the two. The differentiating factor is its sign; if it is negative, it represents an excess supply shock.
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general purpose term that captures all the demand and supply shocks. If dq2 is positive, then it must be that OPEC's production exceeded its output ceiling and the surplus was added to the inventories. The effect of the random factors mentioned above and its cumulative level q2 will be referred to as the cumulative or inventory shock. Incorporating these assumptions in dP/dt in Equation 1A yields dP/dt
= a ( q d ( P ) -- q"l -- d q 2 ) ,
~t > 0
(1')
Furthermore, using the fact that qd(P) = qcl we will have dP/dt
= 7 dq2,
~ < 0
where ), = - ~. If P and q2 are inversely related, then an increase in q2 (i.e., dq2 > 0) represents a positive supply shock a n d / o r a negative demand shock, while a decline in q2 represents a negative supply shock a n d / o r a positive demand shock. Integrating this equation and assuming the constant terms of integration to be the output ceiling ¢1 yields P = 7q
(2)
where q = q~ + q2, which will be referred to as the fundamental following the exchange rate literature (see, e.g., Svensson, 1993). The cumulative shock q2, which is a shift factor, is assumed to follow a r a n d o m walk with a trend drift independent of the oil price3: dq2 = I1 d t + o d z
(3)
where 1] and o are constants, dz is the increment of a standard Wiener process. Incorporating market expectations (which are formed in response to OPEC's attempt at establishing price limits) in Equation 2 we have: P(t) = V (q~J + q2) + O E ( d P ) / d t
(4)
This equation describes the price behavior inside the price target zones. In the presence of perfectly credible policy, the price within the target zone differs from the price dictated by the fundamental q due to the presence of expectations term. As the price reaches 3 The drift can be made endogenous by replacing 11 with P and/or q2. For example, dq2 = fS(P - P r ) d t + o d z
But in this case the closed form solutions are not available.
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the limits of the zone, market participants' expectations of future interventions by OPEC cause an expected turnaround in the price, which the market turns into an immediate change (in the case of infinitesimal interventions). This effect renders the perfectly credible target zone to be inherently stable in the sense that the zone stabilizes the aggregate fundamental q by basically setting an upper and lower limit on it. Inside the target zone, all the changes in q are due to the changes in q2. But when q reaches its lower and upper limits, OPEC changes the output ceiling q~l to maintain the price within the limits of the band. Moreover, there is a negative (decreasing) relationship between the positioning of the limits on the price and the positioning of the limits on the fundamental q.4 Therefore, Equation 4 describes the price behavior inside the target zone as a function of OPEC's cumulative oil shock, output ceiling, time trend, and market participant's expectations of changes in the oil price. If the price is outside the band, intervention is considered passive or ineffective, and the price will be determined by the fundamental forces of supply and demand. As mentioned above, the output ceiling adjustment rule in Equations 1A and 1B can also be modified to fit the target zone approach. In this case, q~ will only change as the market price reaches the maximum or the minimum defined by the band to bring it back to the interior of the target zone. That is, dqC,/dt = l~(Pmax - p r ) > O,
fl > 0
d c f , / d t = fl(Pm,, - P~) < O,
f) > 0
where Pma~and Pmin are the maximum and minimum prices relative to the target price of the zone. 5 2B. Mechanism 2
In Hammoudeh and Madan (1994a), OPEC's nonstochastic mechanism described in Equations 1A and 1B was modified to incorporate explicitly an asymmetric zone below the target price. 4 This can be shown using the same method employed by Delgato and Dumas (1991) for foreign exchange. In the exchange rate case, the relationship is monotone (increasing). 5 This paper assumes no expected changes in the target price. This subject is currently being researched. See Hammoudeh and Madan (1994b). This phenomenon is known in the foreign exchange literature as realignment within the band. See Bertola and Caballero (1992) and Bertola and Svensson (1993).
EXPECTATIONS, TARGET ZONES, AND OIL PRICES
603
To acommodate the changes introduced above, the mechanism can be written as: dqCl/dt = 0
ifO~
P~Z
(5)
where the market price P is defined by Equation 4 and Z is the range of the asymmetric zone whose size is influenced by OPEC's internal political cohesiveness and its perception of future demand. The lower limit for the market price p r _ Z will be called the asymmetric tolerance price in the sense that OPEC tolerates a price decline of that magnitude before it intervenes. In this mechanism, OPEC basically sets an upper limit on the fundamental q by changing the output ceiling qC when the price approaches the asymmetric tolerance price. As Z is reduced, the tolerance zone will narrow and intervention will occur more frequently until in the limit continuous interventions will perfectly stabilize the market price P at the target price pr. This mechanism is also justified on the ground that some OPEC members consider the target price to be a benchmark rather than a precise target. It is used as a guidepost for a lower limit of the market price, which will be below the target price pr. 3. SOLUTION OF THE TWO-SIDED TARGET ZONE MODEL
In order to understand the dynamics of the market price, we need to find an explicit expression for the expectations term in Equation 4. Let the general form of the solution be represented by P = g(q). The term E(dp)/dt can be derived by applying Ito's lemma d P = g'(q)dq2 + 1/2 ~ ' ( q ) ( d q 2 ) 2
Substituting Equation 3 into this equation and taking expectations conditioned on current information yields E(dP)/dt
= g'(q)q + 1/2 g"(q)o = .
Again substituting this term into Equation 4 gives P = g ( q ) = ~lq + 0[g'(q)T! + l/2g"(q)o21.
(6)
The general solution to Equation 6 is P = g ( q ) = Tq + 0 W! + A e x p [ k l q ] + B e x p [k2q]
(7)
604
S. Hammoudeh and V. Madan P
P max
m
f
pT P, mln
I
J
q min
q max
q
Figure 1. Oil Price Solution in a Two-Sided Target Zone.
where k] = [--1] + (1]2 + 2ff2/0)z/2]/O 2 > 0
and k2 = [ - q -
(112 + 2o2/0)1/2]/o2<0
Then E ( d P ) / d t = rl { 7 + ~.IA exp[Llq] + kz B exp[;L2 q] ] + ~2/2 {k~2A exp[X~q] + L22Bexp[k2ql }
(8)
Equation 7 describes a family of solutions for the oil price. Any selected solution should satisfy the boundary conditions appropriate to target zone models. The constants A and B are determined by those conditions. The expectations term E(dP)/dt, which is the expected loss or gain of holding oil in inventory, is a balancing item that matches the demand and supply of oil. If the demand falls short of supply, then this term should be negative for the market price to be in equilibrium in order to ensure that the demand matches the supply. On the other hand, if demand exceeds supply the expectations term is positive. Figure 1 plots the solution form of the two-sided target zone model. If there is no intervention, qcl will not change and an increase in q2 will lead to a decline in P while a decrease will cause an increase. In this model, which explicitly includes expectations formation based on a perfectly credible intervention policy, O P E C
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ZONES, AND OIL PRICES
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would stand ready to change q~l. In the case of infinitesimal interventions, it would decrease qC as the market price approaches some minimum market price Pr~in and increase it as it approaches a maxim u m price Pm~x to offset changes in q2, thereby keeping P within a band. This means that near the top of the band there would be an expected fall in the market price P because of the expected intervention by O P E C , resulting in an immediate actual reduction in P. In this case, intervention occurs instantaneously (i.e., qc1 increases). Therefore, given q~l as q2 declines, P increases and then decreases in the presence of a credible intervention policy. Similarly, as q2 rises, P declines and then rises because of expected intervention. Moreover, the price path flattens out to a slope of zero at the upper and lower limits of the band. The flattening out of the price is due to the property of the fundamental q, which follows a Brownian motion in the short run. 6Within the target zone, q's expected change is a constant. At the limits of the zone, the expected change of q is not constant, but rather increases at the upper limit and decreases at the lower limit. Thus, there is a jump in the expected change in q. But by Ito's lemma: E(dP) = g'(q)E(dq) + 1 / 2 g"(q)E[(dq)2].
The jump in E(dq) would imply a jump in E(dP). This cannot be the case because it results in a safe arbitrage (a one-sided bet): The price would move straight into the target zone. Therefore, we must have g'(qma~) = 0 = gt(qmin) in order to ensure that E(dP) is zero when E(dq) is nonzero. In other words, the price within the target zone is tangential to the limits of the bands. That is, if the policy intervention is infinitesimal and effective, g'(qm~) = 0 and g'(qmin) = 0 when Pmin = g(qm~) and Pm~ = g ( q m i n ) , respectively. This is the "smooth-pasting solution" condition known in option pricing theory (Dixit, 1992). The expectation term E(dP) defined above characterizes the curvature of the price path g(q) at the limits of the band. If this term is negative, the solution function g(q) is concave at the upper limit of P (i.e., g"(q) < 0 where g'(q) = 0). On the other hand, if it is positive, g(q) is convex at the lower limit of P (i.e., g"(q) > 0). The two sets of boundary conditions should be used in order to solve for A and B in Equation 7. The first set of conditions are The short run is defined as the period during which q Cis fixed.
606
S. Hammoudeh and V. Madan P
P max
pT
.
P. mln
I I I I I ! ...d
q I qmin
1
q max
q
.
.
.
.
q u
Figure 2. Oil Price Solution with Discrete Interventions.
the ones that relate P at the boundaries to the values of q when P is at the edges of the zone. The second conditions are the "smoothpasting" conditions defined above (Flood and Garber, 1991a). If the intervention policy is passive and ¢1 is expected to remain unchanged at its initial level, the oil price may take on any value. However, it should not deviate arbitrarily far from the fundamental level as q2 takes on large values or it may asymptotically approach this level as qz tends to infinity. Thus, in case we may assume that A = B = 0, and the general solution of the model represented in Equation 7 can be reduced to the fundamental solution P = Y(¢~ + qz) + 0 f l y
(9)
which is a combination of supply, demand, and the time trend. In the case of discrete (anticipated) interventions, the events of hitting the limits of the band and having an intervention by O P E C will not coincide. In.this case, O P E C announces a discrete intervention rule that specifies both the upper and lower limits of the fundamental q (qu and q~, respectively) at which intervention will occur and the size of the intervention at each limit. In Figure 2, which assumes that q2 will continue to increase, the price level will bottom out and then make an upward turn on the expectations of a cut in output ceiling qq as depicted in the curve labeled 1. But as q hits, for example, q,, O P E C would intervene and reduce the output ceiling, pushing q back to an interior point. This intervention
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607
P
P
maxl
p min
' | i i i
I I I [
i
I
I
1
q
1
i
r
q
u
qU
q2
Figure 3. Discrete Interventions with q2 on the Horizontal Axis.
throws q discontinuously to the interior point, where it resumes the random motion. It is required that P remains the same after the intervention in order to eliminate (safe) arbitrage profit as explained before. That is, P is required to be continuous at the time of intervention. The next direction of the price depends on the change in q:. A similar discussion can be made when q2 hits qt. The impact of the intervention can be better appreciated if we explicitly consider q2 to be the independent variable. This is shown in Figure 3. For a given output ceiling qCl, the curve labeled l represents the market price as a function of the cumulative shock q2, where q2 is permitted to reach an upper limit q, just before an intervention by O P E C occurs. As we saw earlier, as q: increases, the market price falls then rises before the actual reduction in output ceiling occurs. Because intervention is expected, there is no jump in the market price. Moreover, because q2 is exogenous (to OPEC), it does not change from the upper limit q. as a result of OPEC's intervention. After the intervention, the curve labeled 1 shifts to the right and intersects the original one in a way that maintains the market-price continuity. The size of the shift is determined by requiring that the new price solution evaluated at q, maintains the same price. The market price follows Curve 2 and q2 can move freely up or down from the starting point q,, and future interventions will be determined accordingly. If q, moves up towards q,', the price will initially dip then rise in anticipation of another cut in the output ceiling
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S. H a m m o u d e h a n d V. M a d a n
P
pT
i
T P-Z
1
I
.~t¢
c
m
q
max
q
u
q
Figure 4. Oil Price Solution in a Tolerance Target Zone.
If qu moves down, the price will initially rise then dip in anticipation of another increase in the output ceiling near the left end of Curve 2. at qu'. 7
4. SOLUTION OF THE ASYMMETRIC ZONE MODEL This target zone model can be considered a one- or two-sided band. It is a two-sided b a n d if the target price p r is the upper limit and the asymmetric tolerance price p r _ Z is the lower limit and O P E C is committed to defend both limits. In this case, O P E C is committed to price stability, and the solution is similar to that discussed above (see Figure 4). Moreover, q on the horizontal axis of this figure can be replaced with q2 so that the effect of interventions gives rise to shifts in Curve 1 as is the case in Figure 3. The zone is considered one-sided if the target price p r is just a preferred price and O P E C will not defend it. However, the organization is willing to defend the asymmetric tolerance price p r _ Z. In this case, there is no lower limit on q2, so we must have A = 0. Equation 7 can then be written P ( t ) = g ( q ) = y(q c, + q2) + 0 Y 11 + B exp[)~2q]
(10)
For a similar discussion on the exchange rates with decline in foreign reserves, see Flood and Garber (1991b).
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P TT
.L/
pT
pTz
% %.
% %.
"M q2
q2
Figure 5. Defensible and Nondefensible Policies.
where B is determined by the boundary condition ~(qu) = 0 when
p=pr_
Z.
As indicated before, if OPEC is passive and q~ is expected to remain unchanged, any further increases in q2 may take the price outside the band. The price will asymptotically approach the fundamental level as q2 tends to infinity. Therefore, outside the band the exponential term in Equation 10 drops out, and the resulting equation will characterize a free market as in Equation 9. 8 5. DEFENSIBLE A N D NONDEFENSIBLE POLICIES
An arbitrarily chosen output ceiling qcl is perceived to be defensible if it generates price expectations that balance total supply and demand and if it leads to a turnaround in the market price. In other words, the market participants perceive the chosen ceiling to not only match their estimate of expected demand but also to be compatible with the size of the shock in the market. On that basis, they form expectations that lead to a turnaround in the market price. If Equation 10 is evaluated at q2', B is the appropriately chosen constant term so that P = P,~inand the output ceiling q~ is defensible as in Figure 5, then q2' will be the output shock associated with s The locus represented by Equation 10 lies below the fundamental market locus of Equation 9 corresponding to the initial output ceiling q*~.
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smooth pasting. The price path at that point will be tangential to the minimum price as in the locus TT. Therefore, dp/dq2 = "/ + k2B exp[k2 (cl#~ + q2')] = 0
(1~)
Once again using Equation 10 at q2 = q2' we have P~in = y ( ~
+ q23 + 0 y q + B exp[~.2 (¢1 + q2~)]
(12)
where Pm~n = p r _ Z and ¢1 is the defensible ceiling. Furthermore, let us consider a situation where q2' is associated with an output ceiling that is considered to be nondefensible at the lower limit of the band, whether in relation to the level of a previously defensible ceiling or on the basis of the market's estimates of the expected demand and the size of the shock. Let Cj' represent this ceiling. As the market perceives this ceiling as an imbalancing factor, there would cause a speculative attack at P,,in and the price equation would follow the the post attack equation P(t) = g(q) = y ( ¢ , ' + q2) + 0 y r l
which is the locus MM'. Thus, at q2'
we
have,
P,,,,,, = Y (q':~' + q2') + 0 y 11
(13)
Combining Equations 11, 12, and 13 (and using the speculative attack assumption, which posits no jump in the price level by choosing the appropriate parameters) yields qC
_
qC 1, _
q~l
=
-
1/k2
(14)
Because ~.2 should be negative for the system to be stable, the righthand side of Equation 14 is positive. In other words, it is clear that qCl' > Ct •
Thus, the locus MM' should be tangential to the curve T T from below. That is, within the context of fixed limits of a given band, OPEC's intervention policy is considered nondefensible if the output ceiling chosen by O P E C is relatively "too large." The minimum reduction in the output ceiling for the OPEC policy to be credible is - 1/~.2. In particular we have the following: Intervention is credible i f (qC/ _ ¢1) < ( - 1 / 2 2 ) , and intervention is noncredible i f ( ¢ / - ¢~) > ( - 1/~&, where ¢1 is the arbitrarily chosen credible policy parameter. We know that if A ¢ was not a credible reduction in the ceiling for any arbitrarily chosen ¢1, then any reduction smaller than A ¢ will not be credible because it means a relatively "too large" ceiling.
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If the ceiling reduction exceeds ( - 1/~,2), then the value of the MM' locus at q = q2' is higher than Pmi,, and the market is inside the target zone and follows a TT locus with the lower qcl' for any q2, given the assumption of no safe arbitrage at the boundaries. Hence, the expected ceiling reduction represents a credible policy. In other words, a credible ceiling reduction must be at least as large as ( - 1/ X~). That is, any output ceilings at least as large as q~' are not credible, and any ceilings lower than q%' are credible. Thus, we can write /k ctc" = - 1/~.2
(15)
where Aqc* is the minimum credible ceiling reduction. The size of Aqc* or any arbitrarily chosen qCl clearly depends on the other variables of the system. Substituting for the value of ~.2 from Equation 7 in Equation 15 and differentiating with respect to q we have c)&qc*/O'q > 0.
(16)
Thus, with a higher value for the time trend (drift) in the random shocks, the minimum credible ceiling reduction is higher. This simply implies that if the underlying secular growth in the market volume is higher, then O P E C will have to have larger output reductions in order to appear credible to the market participants. Moreover, O & q c * / O 0 > 0.
(17)
Equation 17 indicates that if there is an increase in the sensitivity of prices to changes in price expectations, then OPEC's minimum credible ceiling reduction is smaller. In other words, OPEC does not have to have as large a decline in the output ceiling in order to ensure the credibility of its intervention policy.
6. CONCLUSIONS Previous research has specified OPEC's oil price adjustment mechanisms, traced out the price paths that lead to the target pricebased equilibrium, and defined strategies that would speed the convergence process. This earlier research has also been extended to take into account OPEC's lack of swift response to arrest the decline in the market price below the target price. However, it did not
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tackle the issues of random shocks in the oil market as well as market participants' expectations of OPEC's subsequent moves. In this paper shocks and market expectations are explicitly incorporated in the oil pricing mechanisms. The price solutions of these mechanisms are discussed for two models: the two-sided price target zone and the asymmetric tolerance price zone. In these models, the price solution depends on the trend in the output shock and market participants' expectations as well as on market fundamentals that determine the price movements in the previous research. The expectations term is the variable that lends credibility to the intervention policy and leads to a price solution that is above that determined by the fundamentals. In the two-sided zone model, the solution is indirectly influenced by the upper and lower limits on outputs that are determined by the size of the price band. In the asymmetric zone model, there is only an implied upper limit on output. Both the smooth-pasting and the speculative-attack solutions are examined in these models. In the asymmetric model, OPEC attempts to defend a lower limit on the target price by setting an output ceiling and threatening to lower it in the event that the total output reaches the implied upper limit. For a given parametric structure, OPEC's credibility declines as it reduces its output ceiling. The credibility of OPEC's intervention policy is directly related to sensitivity of the market price to changes in the output and the sensitivity of the market price to changes in the price expectations. Finally, OPEC's policy defensibility and credibility is inversely related to the positive and intertemporal bias in the size of the random shocks in the quantity.
REFERENCES Bertola, G., and Caballero, R. (1992) Target Zones and Realignments, American Economic Review 82(2):510-536. Bertola, G., and Svensson, L. (1993) Stochastic Devaluation Risk and the Empirical Fit of Target Zone Models, Review of Economic Studies 60:689-712. Delgado, F., and Dumas, B. (1991) Target Zones, Broad and Narrow. In Exchange Rate Targets and Currency Bands (P. Krugman, and M. Miller, Eds). Cambridge: Cambridge University Press. Dixit, A.K. (1992) Investment and Hysteresis, Journal of Economic Perspectives 6:107t32. Flood, R., and Garber, P. (1991a) The Linkage Between Speculative Attack and Target Zone Models of Exchange Rates, Quarterly Journal of Economics. 106(4):13691372. Flood, R., and Garber, P. (1991b) The Linkage Between Speculative Attack and Target Zone Models of Exchange Rates: Some Extended Results. In Exchange Rate Targets
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and Currency Bands (P. Krugman, and M. Miller, Eds.). Cambridge: Cambridge University Press. Hammoudeh, S., and Madan, V. (1990) Market Equilibrium of OPEC's Oil Pricing Mechanism, Journal of Energy and Development 16:133-145. Hammoudeh, S., and Madan, V. (1992) The Dynamic Stability of OPEC's Price Mechanism, Energy Economics 14:65-71. Hammoudeh, S., and Marian, V. (1994a) Escaping the Tolerance Trap: Implications of Rigidity in OPEC's Quantity Adjustment Mechanism, Energy Economics 16:3-8. Hammoudeh, S., and Marian, V., (1994b) Oil Target Zones and Target Price Readjustment. Memo, Drexel University, Philadelphia, Pennsylvania. Krugman, P., and Miller, M., Eds. (1992) Exchange Rate Targets and Currency Bands. Cambridge: Cambridge University Press. Krugman, P., and Rotemberg, J. (1991) Speculative Attacks on Target Zones. In Exchange Rate Targets and Currency Bands (P. Krugman and M. Miller, Eds.). Cambridge: Cambridge University Press. Svensson, L.E. (1993) An Interpretation of Recent Research on Exchange Rate Target Zones, Journal of Economic Perspectives 6(4): 119-144.
Expectations, Target Zones, and Oil Price Dynamics Shawkat H a m m o u d e h and Vibhas Madan,
Department of
Economics, Drexel University This paper incorporates inventory shocks and market expectations in OPEC's oil pricing mechanism and applies the target zone and speculative attack literatures to oil price dynamics. The paper examines the oil price behavior in the two-sided target zone model and the asymmetric tolerance zone model. It focuses on the characteristics of the smooth-pasting and speculative-attack solutions that are associated with credible and noncredible intervention policies. The analysis shows that credibility of OPEC's intervention policy declines as its output ceiling is reduced to a low level, which makes the price vulnerable to speculative attacks, and increases as the ceiling rises. The credibility is directly related to sensitivity of the market price to changes in the output and the sensitivity of this price to changes in the price expectations, and is inversely related to the positive intertemporal bias in the size of the random shocks in the quantity.
1. INTRODUCTION Since the late 1970s, OPEC has introduced a production quota system to bring the market price of oil in line with its chosen target price. The actual production levels, however, do not abide by the self-imposed quotas because of deliberate cheating and unforeseen events or shocks that disrupt the assigned production quotas. Cheating, which is usually expected to occur in periods of revenue shortfalls and stagnant prices (i.e., a soft market), pushes production over the output ceiling, thereby exerting a strong downward pressure on the market price. The shocks, which are unexpected, lead to surpluses or shortages and may cause an upward or downward deviation of the market price from the target price. Due to the existence of capacity constraints, OPEC may not be able to control the market price in the presence of a strong upward price shock. However, it has two options in normal and soft markets where the market price drifts below the target price. It can establish Address correspondence to Prof. Shawkat Hammoudeh, Department of Economics, Drexel University, 32nd and Chestnut Streets, Philadelphia, PA 19104, U.S.A. Received October 1994; final draft accepted January 1995. Journal of Policy Modeling 17(6):597-613 (1995) © Society for Policy Modeling, 1995
0161-8938/95/$9.50 SSDI 0161-8938(95)00022-L
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a band for the market price positioned around the target price by basically choosing suitable upper and lower limits for the output or it can place a tolerance zone below the target price in order to restrict the discrepancy between the market price and the target price (Hammoudeh and Madan, 1994a). The lower limit is particularly needed because it sets a price floor and ensures that the market price stays above the significantly lower marginal cost of oil production. If the limits of these zones are backed by a perfectly credible intervention policy, they can generate an expectations process that should turn the market prices around even before any intervention takes place. In reality, OPEC's member countries perceive a band around their target price, especially a tolerated trough under this price in the face of adverse future market conditions. They use the research of their own individual oil ministries, as well as that of OPEC's Research Division, to form medium-term perceptions of supply and demand to conceive upper and lower limits around the target price. The size of the perceived band is related to the size of the output ceiling, which is determined by revenue needs and bargaining power within OPEC. Currently, the target price is $21 per barrel, the tolerated lower limit is about $16, and the output ceiling is 24.5 million barrels per day. The collapse of the market price to $10 per barrel has made OPEC very cognizant of the lower limit, and the member countries will be ready to defend it under normal conditions by reducing the output ceiling. The market participants have observed OPEC's behavior and have lent more credibility to the lower limit of the band. In this paper, we will generalize previous research by explicitly including oil shocks, changes in demand, and changes in expectations within the market price band. We examine the dynamics of oil prices within the target and tolerance zones and outside these zones when the output ceiling is not defensible. Emphasis is placed on delineating between defensible and nondefensible policies and on the factors thai affect the defensibility of the output ceiling and the credibility of the intervention policy. The major contribution of this paper is the introduction of stochastic considerations in the analysis of OPEC's policy decisions as well as performing sensitivity analysis on the price solution. The methodology draws upon the work in the area of target zones and exchange rate stabilization. Although the particular objectives of exchange rate management and OPEC's price-quantity decisions seem to be different, the established framework for analyzing the
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former provides a logical structure for analyzing the latter. In both situations the policymakers are attempting to stabilize the value of a core variable, while allowing for some flexibility around a targeted value of that variable. In each case, one of the main issues is the credibility of policy decisions in the face of fundamental uncertainty and market expectations that are fueled by the policies themselves. In fact, under normal conditions the oil market participants form expectations and cause a turnaround in the market price in anticipation of OPEC's intervention in the same manner that foreign exchange participants generate expectations, causing a turnaround in the exchange rate in anticipation of central banks' interventions. 2. TARGET ZONE MODELS OF THE OIL MARKET
In previous research (Hammoudeh and Madan, 1990, 1992, and 1994a) several oil policy mechanisms have been evaluated in terms of their impact on the market price and their implications for OPEC's output adjustments. In this paper we will examine two of these mechanisms in the presence of target zones. 2A. Mechanism 1
OPEC's current policy mechanism can be described by the following equations: d P / d t = ~(qLo] - qc), d¢/dt
= ~(P - p r ) ,
~t ;>0 ~~ 0
(1A) (IB)
for any pr, where pr is the target price, cl(P) is the demand for OPEC's output, tic is its output ceiling, ~t is the market speed of price adjustment, and ~ is OPEC's speed of output adjustment. ~ Thus, Equation 1A describes the market price adjustment, and Equation 1B represents OPEC's output-ceiling adjustment rule. Because the demand for OPEC's oil, el(p), does not necessarily equal its output ceiling, q~, Equations 1A and l B should be adjusted to explicitly include shocks in the market such as demand fluctuations due to the business cycle, cheating on quotas, and production disruptions due to political and military conflicts among OPEC's members. Moreover, because the simple formulation above does not incorporate limits on the changes in the market price P in order High (low) values of ~ indicate that the quantity ceiling is strongly (weakly) sensitive to discrepancies between the market price and the target price.
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to prevent it from straying too far from the target price pr, the basic mechanism should be modified to keep the price movements within the boundaries of a target zone. Furthermore, this formulation does not include the market participants' expectations, which are formed in response to OPEC's policy of defending its targeted objectives. A perfectly credible intervention policy involving changes in the output ceiling would have the effect of initiating changes in expectations of price movements followed by a turnaround in the market price before it reaches either limit of the target zone. This policy is considered to be nondefensible if the market does not expect OPEC to sufficiently reduce the output ceiling to offset increases in inventories when the market price is close to the lower limit. There will be a strong positive supply shock as the speculators try to unload their inventories on the market because of the expected excess supply. Thus, there will be a price fall without a turnaround, and the speculative attacks will take the price out of the target zone. Taking these changes into consideration, the price adjustment rule in Equation 1A will include, in addition to the output ceiling, terms that account for changes in demand and output due to shocks. Furthermore, the turnaround in the price will be accounted for by including changes in expectations due to intervention. The output policy (i.e., the output-ceiling adjustment rule) in Equation 1B should also be modified by considering the output ceiling q~ to be an intervention policy variable that is bounded by the announced upper and lower limits on the market price. To accommodate these changes, we need to distinguish between the components of demand and supply of OPEC's oil. We will consider the demand to be the predictable demand, and it will be represented by qd(P). The nonpredictable component of demand is a demand random shock that is equal to declines in inventories. The supply is postulated to include the official output ceiling qC, which is determined by OPEC and is exogenous in the short run. It is also assumed that the ceiling qC is set to satisfy the predictable demand and, therefore, qa(P) = ~ . The second component of supply is the supply random shock, dq2, which is equal to increases in inventories. The shock dq2 is also assumed to represent an excess demand or an excess supply s h o c k . 2 Thus, this component is a 2 We can interpret dq2 as a demand shock, a supply shock, or the difference between the two. The differentiating factor is its sign; if it is negative, it represents an excess supply shock.
EXPECTATIONS,
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601
general purpose term that captures all the demand and supply shocks. If dq2 is positive, then it must be that OPEC's production exceeded its output ceiling and the surplus was added to the inventories. The effect of the random factors mentioned above and its cumulative level q2 will be referred to as the cumulative or inventory shock. Incorporating these assumptions in dP/dt in Equation 1A yields dP/dt
= a ( q d ( P ) -- q"l -- d q 2 ) ,
~t > 0
(1')
Furthermore, using the fact that qd(P) = qcl we will have dP/dt
= 7 dq2,
~ < 0
where ), = - ~. If P and q2 are inversely related, then an increase in q2 (i.e., dq2 > 0) represents a positive supply shock a n d / o r a negative demand shock, while a decline in q2 represents a negative supply shock a n d / o r a positive demand shock. Integrating this equation and assuming the constant terms of integration to be the output ceiling ¢1 yields P = 7q
(2)
where q = q~ + q2, which will be referred to as the fundamental following the exchange rate literature (see, e.g., Svensson, 1993). The cumulative shock q2, which is a shift factor, is assumed to follow a r a n d o m walk with a trend drift independent of the oil price3: dq2 = I1 d t + o d z
(3)
where 1] and o are constants, dz is the increment of a standard Wiener process. Incorporating market expectations (which are formed in response to OPEC's attempt at establishing price limits) in Equation 2 we have: P(t) = V (q~J + q2) + O E ( d P ) / d t
(4)
This equation describes the price behavior inside the price target zones. In the presence of perfectly credible policy, the price within the target zone differs from the price dictated by the fundamental q due to the presence of expectations term. As the price reaches 3 The drift can be made endogenous by replacing 11 with P and/or q2. For example, dq2 = fS(P - P r ) d t + o d z
But in this case the closed form solutions are not available.
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S. H a m m o u d e h a n d V. M a d a n
the limits of the zone, market participants' expectations of future interventions by OPEC cause an expected turnaround in the price, which the market turns into an immediate change (in the case of infinitesimal interventions). This effect renders the perfectly credible target zone to be inherently stable in the sense that the zone stabilizes the aggregate fundamental q by basically setting an upper and lower limit on it. Inside the target zone, all the changes in q are due to the changes in q2. But when q reaches its lower and upper limits, OPEC changes the output ceiling q~l to maintain the price within the limits of the band. Moreover, there is a negative (decreasing) relationship between the positioning of the limits on the price and the positioning of the limits on the fundamental q.4 Therefore, Equation 4 describes the price behavior inside the target zone as a function of OPEC's cumulative oil shock, output ceiling, time trend, and market participant's expectations of changes in the oil price. If the price is outside the band, intervention is considered passive or ineffective, and the price will be determined by the fundamental forces of supply and demand. As mentioned above, the output ceiling adjustment rule in Equations 1A and 1B can also be modified to fit the target zone approach. In this case, q~ will only change as the market price reaches the maximum or the minimum defined by the band to bring it back to the interior of the target zone. That is, dqC,/dt = l~(Pmax - p r ) > O,
fl > 0
d c f , / d t = fl(Pm,, - P~) < O,
f) > 0
where Pma~and Pmin are the maximum and minimum prices relative to the target price of the zone. 5 2B. Mechanism 2
In Hammoudeh and Madan (1994a), OPEC's nonstochastic mechanism described in Equations 1A and 1B was modified to incorporate explicitly an asymmetric zone below the target price. 4 This can be shown using the same method employed by Delgato and Dumas (1991) for foreign exchange. In the exchange rate case, the relationship is monotone (increasing). 5 This paper assumes no expected changes in the target price. This subject is currently being researched. See Hammoudeh and Madan (1994b). This phenomenon is known in the foreign exchange literature as realignment within the band. See Bertola and Caballero (1992) and Bertola and Svensson (1993).
EXPECTATIONS, TARGET ZONES, AND OIL PRICES
603
To acommodate the changes introduced above, the mechanism can be written as: dqCl/dt = 0
ifO~
P~Z
(5)
where the market price P is defined by Equation 4 and Z is the range of the asymmetric zone whose size is influenced by OPEC's internal political cohesiveness and its perception of future demand. The lower limit for the market price p r _ Z will be called the asymmetric tolerance price in the sense that OPEC tolerates a price decline of that magnitude before it intervenes. In this mechanism, OPEC basically sets an upper limit on the fundamental q by changing the output ceiling qC when the price approaches the asymmetric tolerance price. As Z is reduced, the tolerance zone will narrow and intervention will occur more frequently until in the limit continuous interventions will perfectly stabilize the market price P at the target price pr. This mechanism is also justified on the ground that some OPEC members consider the target price to be a benchmark rather than a precise target. It is used as a guidepost for a lower limit of the market price, which will be below the target price pr. 3. SOLUTION OF THE TWO-SIDED TARGET ZONE MODEL
In order to understand the dynamics of the market price, we need to find an explicit expression for the expectations term in Equation 4. Let the general form of the solution be represented by P = g(q). The term E(dp)/dt can be derived by applying Ito's lemma d P = g'(q)dq2 + 1/2 ~ ' ( q ) ( d q 2 ) 2
Substituting Equation 3 into this equation and taking expectations conditioned on current information yields E(dP)/dt
= g'(q)q + 1/2 g"(q)o = .
Again substituting this term into Equation 4 gives P = g ( q ) = ~lq + 0[g'(q)T! + l/2g"(q)o21.
(6)
The general solution to Equation 6 is P = g ( q ) = Tq + 0 W! + A e x p [ k l q ] + B e x p [k2q]
(7)
604
S. Hammoudeh and V. Madan P
P max
m
f
pT P, mln
I
J
q min
q max
q
Figure 1. Oil Price Solution in a Two-Sided Target Zone.
where k] = [--1] + (1]2 + 2ff2/0)z/2]/O 2 > 0
and k2 = [ - q -
(112 + 2o2/0)1/2]/o2<0
Then E ( d P ) / d t = rl { 7 + ~.IA exp[Llq] + kz B exp[;L2 q] ] + ~2/2 {k~2A exp[X~q] + L22Bexp[k2ql }
(8)
Equation 7 describes a family of solutions for the oil price. Any selected solution should satisfy the boundary conditions appropriate to target zone models. The constants A and B are determined by those conditions. The expectations term E(dP)/dt, which is the expected loss or gain of holding oil in inventory, is a balancing item that matches the demand and supply of oil. If the demand falls short of supply, then this term should be negative for the market price to be in equilibrium in order to ensure that the demand matches the supply. On the other hand, if demand exceeds supply the expectations term is positive. Figure 1 plots the solution form of the two-sided target zone model. If there is no intervention, qcl will not change and an increase in q2 will lead to a decline in P while a decrease will cause an increase. In this model, which explicitly includes expectations formation based on a perfectly credible intervention policy, O P E C
EXPECTATIONS,
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ZONES, AND OIL PRICES
605
would stand ready to change q~l. In the case of infinitesimal interventions, it would decrease qC as the market price approaches some minimum market price Pr~in and increase it as it approaches a maxim u m price Pm~x to offset changes in q2, thereby keeping P within a band. This means that near the top of the band there would be an expected fall in the market price P because of the expected intervention by O P E C , resulting in an immediate actual reduction in P. In this case, intervention occurs instantaneously (i.e., qc1 increases). Therefore, given q~l as q2 declines, P increases and then decreases in the presence of a credible intervention policy. Similarly, as q2 rises, P declines and then rises because of expected intervention. Moreover, the price path flattens out to a slope of zero at the upper and lower limits of the band. The flattening out of the price is due to the property of the fundamental q, which follows a Brownian motion in the short run. 6Within the target zone, q's expected change is a constant. At the limits of the zone, the expected change of q is not constant, but rather increases at the upper limit and decreases at the lower limit. Thus, there is a jump in the expected change in q. But by Ito's lemma: E(dP) = g'(q)E(dq) + 1 / 2 g"(q)E[(dq)2].
The jump in E(dq) would imply a jump in E(dP). This cannot be the case because it results in a safe arbitrage (a one-sided bet): The price would move straight into the target zone. Therefore, we must have g'(qma~) = 0 = gt(qmin) in order to ensure that E(dP) is zero when E(dq) is nonzero. In other words, the price within the target zone is tangential to the limits of the bands. That is, if the policy intervention is infinitesimal and effective, g'(qm~) = 0 and g'(qmin) = 0 when Pmin = g(qm~) and Pm~ = g ( q m i n ) , respectively. This is the "smooth-pasting solution" condition known in option pricing theory (Dixit, 1992). The expectation term E(dP) defined above characterizes the curvature of the price path g(q) at the limits of the band. If this term is negative, the solution function g(q) is concave at the upper limit of P (i.e., g"(q) < 0 where g'(q) = 0). On the other hand, if it is positive, g(q) is convex at the lower limit of P (i.e., g"(q) > 0). The two sets of boundary conditions should be used in order to solve for A and B in Equation 7. The first set of conditions are The short run is defined as the period during which q Cis fixed.
606
S. Hammoudeh and V. Madan P
P max
pT
.
P. mln
I I I I I ! ...d
q I qmin
1
q max
q
.
.
.
.
q u
Figure 2. Oil Price Solution with Discrete Interventions.
the ones that relate P at the boundaries to the values of q when P is at the edges of the zone. The second conditions are the "smoothpasting" conditions defined above (Flood and Garber, 1991a). If the intervention policy is passive and ¢1 is expected to remain unchanged at its initial level, the oil price may take on any value. However, it should not deviate arbitrarily far from the fundamental level as q2 takes on large values or it may asymptotically approach this level as qz tends to infinity. Thus, in case we may assume that A = B = 0, and the general solution of the model represented in Equation 7 can be reduced to the fundamental solution P = Y(¢~ + qz) + 0 f l y
(9)
which is a combination of supply, demand, and the time trend. In the case of discrete (anticipated) interventions, the events of hitting the limits of the band and having an intervention by O P E C will not coincide. In.this case, O P E C announces a discrete intervention rule that specifies both the upper and lower limits of the fundamental q (qu and q~, respectively) at which intervention will occur and the size of the intervention at each limit. In Figure 2, which assumes that q2 will continue to increase, the price level will bottom out and then make an upward turn on the expectations of a cut in output ceiling qq as depicted in the curve labeled 1. But as q hits, for example, q,, O P E C would intervene and reduce the output ceiling, pushing q back to an interior point. This intervention
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607
P
P
maxl
p min
' | i i i
I I I [
i
I
I
1
q
1
i
r
q
u
qU
q2
Figure 3. Discrete Interventions with q2 on the Horizontal Axis.
throws q discontinuously to the interior point, where it resumes the random motion. It is required that P remains the same after the intervention in order to eliminate (safe) arbitrage profit as explained before. That is, P is required to be continuous at the time of intervention. The next direction of the price depends on the change in q:. A similar discussion can be made when q2 hits qt. The impact of the intervention can be better appreciated if we explicitly consider q2 to be the independent variable. This is shown in Figure 3. For a given output ceiling qCl, the curve labeled l represents the market price as a function of the cumulative shock q2, where q2 is permitted to reach an upper limit q, just before an intervention by O P E C occurs. As we saw earlier, as q: increases, the market price falls then rises before the actual reduction in output ceiling occurs. Because intervention is expected, there is no jump in the market price. Moreover, because q2 is exogenous (to OPEC), it does not change from the upper limit q. as a result of OPEC's intervention. After the intervention, the curve labeled 1 shifts to the right and intersects the original one in a way that maintains the market-price continuity. The size of the shift is determined by requiring that the new price solution evaluated at q, maintains the same price. The market price follows Curve 2 and q2 can move freely up or down from the starting point q,, and future interventions will be determined accordingly. If q, moves up towards q,', the price will initially dip then rise in anticipation of another cut in the output ceiling
608
S. H a m m o u d e h a n d V. M a d a n
P
pT
i
T P-Z
1
I
.~t¢
c
m
q
max
q
u
q
Figure 4. Oil Price Solution in a Tolerance Target Zone.
If qu moves down, the price will initially rise then dip in anticipation of another increase in the output ceiling near the left end of Curve 2. at qu'. 7
4. SOLUTION OF THE ASYMMETRIC ZONE MODEL This target zone model can be considered a one- or two-sided band. It is a two-sided b a n d if the target price p r is the upper limit and the asymmetric tolerance price p r _ Z is the lower limit and O P E C is committed to defend both limits. In this case, O P E C is committed to price stability, and the solution is similar to that discussed above (see Figure 4). Moreover, q on the horizontal axis of this figure can be replaced with q2 so that the effect of interventions gives rise to shifts in Curve 1 as is the case in Figure 3. The zone is considered one-sided if the target price p r is just a preferred price and O P E C will not defend it. However, the organization is willing to defend the asymmetric tolerance price p r _ Z. In this case, there is no lower limit on q2, so we must have A = 0. Equation 7 can then be written P ( t ) = g ( q ) = y(q c, + q2) + 0 Y 11 + B exp[)~2q]
(10)
For a similar discussion on the exchange rates with decline in foreign reserves, see Flood and Garber (1991b).
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P TT
.L/
pT
pTz
% %.
% %.
"M q2
q2
Figure 5. Defensible and Nondefensible Policies.
where B is determined by the boundary condition ~(qu) = 0 when
p=pr_
Z.
As indicated before, if OPEC is passive and q~ is expected to remain unchanged, any further increases in q2 may take the price outside the band. The price will asymptotically approach the fundamental level as q2 tends to infinity. Therefore, outside the band the exponential term in Equation 10 drops out, and the resulting equation will characterize a free market as in Equation 9. 8 5. DEFENSIBLE A N D NONDEFENSIBLE POLICIES
An arbitrarily chosen output ceiling qcl is perceived to be defensible if it generates price expectations that balance total supply and demand and if it leads to a turnaround in the market price. In other words, the market participants perceive the chosen ceiling to not only match their estimate of expected demand but also to be compatible with the size of the shock in the market. On that basis, they form expectations that lead to a turnaround in the market price. If Equation 10 is evaluated at q2', B is the appropriately chosen constant term so that P = P,~inand the output ceiling q~ is defensible as in Figure 5, then q2' will be the output shock associated with s The locus represented by Equation 10 lies below the fundamental market locus of Equation 9 corresponding to the initial output ceiling q*~.
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smooth pasting. The price path at that point will be tangential to the minimum price as in the locus TT. Therefore, dp/dq2 = "/ + k2B exp[k2 (cl#~ + q2')] = 0
(1~)
Once again using Equation 10 at q2 = q2' we have P~in = y ( ~
+ q23 + 0 y q + B exp[~.2 (¢1 + q2~)]
(12)
where Pm~n = p r _ Z and ¢1 is the defensible ceiling. Furthermore, let us consider a situation where q2' is associated with an output ceiling that is considered to be nondefensible at the lower limit of the band, whether in relation to the level of a previously defensible ceiling or on the basis of the market's estimates of the expected demand and the size of the shock. Let Cj' represent this ceiling. As the market perceives this ceiling as an imbalancing factor, there would cause a speculative attack at P,,in and the price equation would follow the the post attack equation P(t) = g(q) = y ( ¢ , ' + q2) + 0 y r l
which is the locus MM'. Thus, at q2'
we
have,
P,,,,,, = Y (q':~' + q2') + 0 y 11
(13)
Combining Equations 11, 12, and 13 (and using the speculative attack assumption, which posits no jump in the price level by choosing the appropriate parameters) yields qC
_
qC 1, _
q~l
=
-
1/k2
(14)
Because ~.2 should be negative for the system to be stable, the righthand side of Equation 14 is positive. In other words, it is clear that qCl' > Ct •
Thus, the locus MM' should be tangential to the curve T T from below. That is, within the context of fixed limits of a given band, OPEC's intervention policy is considered nondefensible if the output ceiling chosen by O P E C is relatively "too large." The minimum reduction in the output ceiling for the OPEC policy to be credible is - 1/~.2. In particular we have the following: Intervention is credible i f (qC/ _ ¢1) < ( - 1 / 2 2 ) , and intervention is noncredible i f ( ¢ / - ¢~) > ( - 1/~&, where ¢1 is the arbitrarily chosen credible policy parameter. We know that if A ¢ was not a credible reduction in the ceiling for any arbitrarily chosen ¢1, then any reduction smaller than A ¢ will not be credible because it means a relatively "too large" ceiling.
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If the ceiling reduction exceeds ( - 1/~,2), then the value of the MM' locus at q = q2' is higher than Pmi,, and the market is inside the target zone and follows a TT locus with the lower qcl' for any q2, given the assumption of no safe arbitrage at the boundaries. Hence, the expected ceiling reduction represents a credible policy. In other words, a credible ceiling reduction must be at least as large as ( - 1/ X~). That is, any output ceilings at least as large as q~' are not credible, and any ceilings lower than q%' are credible. Thus, we can write /k ctc" = - 1/~.2
(15)
where Aqc* is the minimum credible ceiling reduction. The size of Aqc* or any arbitrarily chosen qCl clearly depends on the other variables of the system. Substituting for the value of ~.2 from Equation 7 in Equation 15 and differentiating with respect to q we have c)&qc*/O'q > 0.
(16)
Thus, with a higher value for the time trend (drift) in the random shocks, the minimum credible ceiling reduction is higher. This simply implies that if the underlying secular growth in the market volume is higher, then O P E C will have to have larger output reductions in order to appear credible to the market participants. Moreover, O & q c * / O 0 > 0.
(17)
Equation 17 indicates that if there is an increase in the sensitivity of prices to changes in price expectations, then OPEC's minimum credible ceiling reduction is smaller. In other words, OPEC does not have to have as large a decline in the output ceiling in order to ensure the credibility of its intervention policy.
6. CONCLUSIONS Previous research has specified OPEC's oil price adjustment mechanisms, traced out the price paths that lead to the target pricebased equilibrium, and defined strategies that would speed the convergence process. This earlier research has also been extended to take into account OPEC's lack of swift response to arrest the decline in the market price below the target price. However, it did not
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S. H a m m o u d e h and V. Madan
tackle the issues of random shocks in the oil market as well as market participants' expectations of OPEC's subsequent moves. In this paper shocks and market expectations are explicitly incorporated in the oil pricing mechanisms. The price solutions of these mechanisms are discussed for two models: the two-sided price target zone and the asymmetric tolerance price zone. In these models, the price solution depends on the trend in the output shock and market participants' expectations as well as on market fundamentals that determine the price movements in the previous research. The expectations term is the variable that lends credibility to the intervention policy and leads to a price solution that is above that determined by the fundamentals. In the two-sided zone model, the solution is indirectly influenced by the upper and lower limits on outputs that are determined by the size of the price band. In the asymmetric zone model, there is only an implied upper limit on output. Both the smooth-pasting and the speculative-attack solutions are examined in these models. In the asymmetric model, OPEC attempts to defend a lower limit on the target price by setting an output ceiling and threatening to lower it in the event that the total output reaches the implied upper limit. For a given parametric structure, OPEC's credibility declines as it reduces its output ceiling. The credibility of OPEC's intervention policy is directly related to sensitivity of the market price to changes in the output and the sensitivity of the market price to changes in the price expectations. Finally, OPEC's policy defensibility and credibility is inversely related to the positive and intertemporal bias in the size of the random shocks in the quantity.
REFERENCES Bertola, G., and Caballero, R. (1992) Target Zones and Realignments, American Economic Review 82(2):510-536. Bertola, G., and Svensson, L. (1993) Stochastic Devaluation Risk and the Empirical Fit of Target Zone Models, Review of Economic Studies 60:689-712. Delgado, F., and Dumas, B. (1991) Target Zones, Broad and Narrow. In Exchange Rate Targets and Currency Bands (P. Krugman, and M. Miller, Eds). Cambridge: Cambridge University Press. Dixit, A.K. (1992) Investment and Hysteresis, Journal of Economic Perspectives 6:107t32. Flood, R., and Garber, P. (1991a) The Linkage Between Speculative Attack and Target Zone Models of Exchange Rates, Quarterly Journal of Economics. 106(4):13691372. Flood, R., and Garber, P. (1991b) The Linkage Between Speculative Attack and Target Zone Models of Exchange Rates: Some Extended Results. In Exchange Rate Targets
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and Currency Bands (P. Krugman, and M. Miller, Eds.). Cambridge: Cambridge University Press. Hammoudeh, S., and Madan, V. (1990) Market Equilibrium of OPEC's Oil Pricing Mechanism, Journal of Energy and Development 16:133-145. Hammoudeh, S., and Madan, V. (1992) The Dynamic Stability of OPEC's Price Mechanism, Energy Economics 14:65-71. Hammoudeh, S., and Marian, V. (1994a) Escaping the Tolerance Trap: Implications of Rigidity in OPEC's Quantity Adjustment Mechanism, Energy Economics 16:3-8. Hammoudeh, S., and Marian, V., (1994b) Oil Target Zones and Target Price Readjustment. Memo, Drexel University, Philadelphia, Pennsylvania. Krugman, P., and Miller, M., Eds. (1992) Exchange Rate Targets and Currency Bands. Cambridge: Cambridge University Press. Krugman, P., and Rotemberg, J. (1991) Speculative Attacks on Target Zones. In Exchange Rate Targets and Currency Bands (P. Krugman and M. Miller, Eds.). Cambridge: Cambridge University Press. Svensson, L.E. (1993) An Interpretation of Recent Research on Exchange Rate Target Zones, Journal of Economic Perspectives 6(4): 119-144.