oil export boom and dutch-disease: a dynamic analysis

Resources and Energy 5 (1983) 219-242. North-Holland

OIL EXPORT BOOM AND DUTCH-DISEASE

A Dynamic Analysis*

Sebastian EDWARDS

University of Cali$ornia, Los Angeles, CA 90024, USA

National Bureau of Economic Research, Cambridge, MA 02138, USA

Masanao AOKI

Osaka University, Osaka 567, Japan

Received February 1983, final version received April 1983

This paper analyzes the extent to which a boom in a particular export sector (i.e., oil) affects competitiveness in the rest of the economy: This problem has sometimes been associated with the so-called ‘Dutch-disease’. The main conclusion of the analysis is that the ‘Dutch-disease’ is not a disease in any clear sense. It is shown that in a non-monet~y economy a (~~anent) increase in the price of oil will result in an equilibrium reduction of the price of traditional (non- oil) tradables both in terms of non-tradables and oil. This is a long-run real phenomenon that will result in resources moving out of the traditional tradable goods sector. It is also shown that if money is included into the model it is possible that relative prices will overshoot, and that the traditional tradables sector will have a greater loss of competitiveness in the short-run than in the long-run. Finally, the paper discusses some policy measures that will help avoid this relative price overshooting.

1. Introduction

The purpose of this paper is to analyze the effects of an export boom in a small open economy with fixed exchange rates. In particular, we want to investigate the extent to which a boom in a particular export sector (oil, for example) affects com~titiveness in the rest of the tradable goods sectors. This problem has sometimes been associated with the so-called Dutch-disease

[see, for example, Harberger (1981)], where an increase in the price (or production) of a commodity export (oil) results in a real appreciation of the exchange rate, and in a loss of competitiveness of the traditional (non-oil) tradable goods sect0r.l This phenomenon has also been referred to as de-

*The authors are indebted to the participants of the International Economics Workshop at the University of Chicago, and to an anonymous referee for helpful comments. Masanao Aoki wishes to acknowledge partial financial support from Keizai Shoei Zaidan (Foundation to Promote Economic Research). Ooinions exuressed here are those of the authors and don’t reflect

I .

those of the NBER. ‘On Dutch-disease see, for example, Buiter and Purvis (1983), Corden (1981), Corden and

Neary (19821, Harberger (1981), Bruno and Sachs (1982), and van Wijnbergen (1984).

0165-0572/83/%3.00 0 1983, Elsevier Science Publishers B.V. (North-Holland)

220 5’. Edwards and M. Aoki, Oil export boom and Dutch-disease

industrialization or tradable+squeeze effect [see Corden and Neary (1982) and Corden (1981)J.

From a policy point of view, the analysis of the Dutch-disease has important implications, since different governments have recently tried alternative measures to combat its main effects. In that respect, for example, the Indonesian devaluation of 1978 responded to the notion that the increase in oil revenues had generated a domestic inflation higher than the world inflation, harming the competitiveness of traditional exports (palm oil, rubber). Also, to some extent, the February 1982 Mexican devaluation can be viewed as an effort on behalf of the Mexican authorities to combat the real appreciation of the Mexican Peso, resulting from the then booming oil and gas sector. In both cases - Mexico in February 1982 and Indonesia in 1978 - by devaluing the domestic currency, the authorities attempted to restore the real exchange rate to its ‘equilibrium’ value. This measure, however, would make sense only if the real appre~ation of the domestic currency was indeed a short-run phenomenon generated by the so-called ‘disease’. However, if this appreciation is a real long-run equilibrium consequence of a commodity export boom, a devaluation would have no lasting effect.

In this paper, we investigate the effect of commodity export boom on the rest of the economy under the assumption of a small economy with fixed exchange rates.’ In this case, changes in the real exchange rate take place through changes in the nominal price of non-tradable goods. The fixed-rate assumption is made in order to focus the analysis on the case of oil- exporting developing countries, most of which have a fixed rate with respect to the U.S. dollar (i.e., Indonesia, Ecuador, Venezuela, and Mexico unti1 recentlyj. The extension of the model to the case of flexible rates, however, would not affect the main findings. The model assumes that the oil sector is owned by the government. Again, this assumption corresponds closely to what we observe in developing countries.

The main conclusion of the analysis is that the so-called ‘Dutch-disease’ is, not a disease in any clear sense. It is shown that, under a set of piausible assumptions, as a consequence of a commodity exports boom, the equilibrium relative price of other tradables declines both in terms of eon-tradables and in terms of the booming commodity (oil). This long-run decline in the equilibrium price of other tradables is a real effect of the export boom, and it is not clear in what sense it should be labelled a disease. As a consequence of this change in relative prices, resources move out of the traditional tradables sector into the other sectors of the economy.3

‘Most studies dealing with Dutch-disease have assumed flexible exchange rates. Corden and Neary (1982), however, discuss the merits of alternative exchange rate regimes as ways to deal with the disease. Harberger (1981) uses a model of a fixed rate economy.

3The analysis presented in this paper considers the case of a permanent export boom. If, however, a transitory boom is considered, some of the results will not hold. It is interesting to note that some authors seem to refer to the process of resource shifts from the traditional tradabks sector into the other sectors of the economy as the ‘Dutch-disease’.

S. Edwards and M. Aoki, Oil export boom and Dutch-disease 221

However, as Harberger (1981) has pointed out, as a result of the export boom, a short-run excess supply of money may occur if the government monetizes part of the additional oil earnings. In this case, in the short-run the relative price of traditional tradables, with respect to non-tradables, will fall below its new long-run equilibrium, further squeezing profitability in the tradables sector. In this model, as in Harberger (1981), this short-run fall in the relative price of traditional tradables results from a short-run overshooting of the nominal price of non-tradables over and above their new long-run equilibrium.4

In this paper we develop a general equilibrium dynamic model where we analytically investigate some of the conditions under which this short-run overshooting will result. We then briefly discuss some policy measures that would eliminate this overshooting, allowing a smoother transition from pre- boom to post-boom relative prices.

The plan of the paper is as follows: In section 2, a diagrammatical analysis is used to investigate the long-run and short-run effects of a commodity (oil) boom on the competitiveness of other tradables. The model assumes that the boom is produced by an increase in the price of oil, but it could easily be adapted to the case of a boom generated by new oil discoveries. The model also assumes that there is perfect factor mobility in the short and long-run between the non-tradables and traditional tradables (i.e., non-oil) sectors. It is assumed, however, that the oil sector uses factors that are sector-specific in the long- and short-run. The introduction of short-run restrictions to intersectoral capital mobility between non-tradables and traditional tradables, as in Jones (1971), Corden and Neary (1982), and Neary and Purvis (1981), would provide additional sources for dynamic effects.5 In section 3 the technique derived by Aoki (1980, 1981) is used to formally investigate the conditions under which a short-run overshooting of the nominal price of non-tradables will result. It is found that this price will overshoot its long-run equilibrium if the government spends more than a critical fraction of additional oil revenues on non-tradable goods. From here, it directly follows that one way of eliminating this overshooting is by setting, in every period, this proportion at a determined level. Section 4 contains some discussion on the results derived in the variational analysis of section 3, and some possible extensions of the model are discussed. In particular, it is noted that if downward wage rigidity is introduced in the analysis, an export

“The problem of short-run movements of the real exchange rate, as a consequence of a monetary disequilibrium resulting from an increase in capital inflows, has recently been analyzed in the context of the stabilization programs in the Southern-Cone of South America. See, for example, Harberger (1982) and Edwards (1984).

‘Generally, overshooting will result if it is assumed that some variables cannot adjust in the short-run. While in this paper we assume that the money market clears slowly, there are other ways to generate overshooting. For the case of commodity-exporting developing countries the assumptions of a slowly clearing money market seems appropriate.

222 S. Edwards and M. Aoki, Oil export boom and Dutch-disease

boom can result in short-run unemployment. Finally, the paper contains an appendix where some of the derivations are presented in detail.

2. Exports boom, relative prices and competitiveness: A diagrammatical analysis

In this section, we use a diagrammatical analysis to discuss the effects of an increase in the price of the booming sector (oil) on the relative price of other (or traditional) tradables. The discussion distinguishes the long-run real effect of this external disturbance from the short-run dynamics. The analysis is kept to a simple level in order to highlight the main issues without having to deal with side effects. Section 3, on the other hand, incorporates some complications ignored in the diagrammatical analysis.

2.1. Long-run efects

Consider a small open economy that produces three goods: oil (O), traditional tradables (T) and non-tradables (N). Assume also that the oil sector is owned by the government, as is the case of the most oil-producing developing countries. Also assume that the exchange rate is fixed and equal to one. The excess demand for non-tradables is assumed to depend on prices and income. In equilibrium this excess demand will be equal to zero,

N=N(q,, Y)=o, (+)(+)

(1)

where qT is the relative price of tradables to non-tradable goods (i.e. qT= PT/PN), and Y, on the other hand, is real income in terms of non-tradables. This expression does not include the relative price of oil as an argument, since it is assumed that domestic residents don’t consume oil, and that factors used in the production of oil are sector-specific both in the short- and long-run. The signs in parentheses below the function’s arguments refer to the assumed signs of the partial derivatives. The positive sign of qT stems from the assumption of gross substitutability between non-traded goods and tradable goods. Equilibrium in the non-tradables sector requires that the excess demand for this type of good is equal to zero, both in the short- and long-run.

In eq. (1) Y is expressed in terms of non-tradable goods, and given by

Y=H:+q,HS,+q,& (2)

where HE, H$ and 0 are supplies of the non-tradables, tradables and oil, respectively, and where q. is the relative price of oil in terms of nontradable goods. The supply of oil is held fixed for simpler analysis. The price index is denoted by P, and is assumed to depend only on the nominal prices of non- tradables (PN) and traditional tradables (Pr).

S. Edwards and M. Aoki, Oil export boom and Dutch-djse~se 223

Our interest is to discover the effect of an increase in the price of oil on the relative price of traditional tradables with respect to non-tradables (qr). Maintaining the assumption of gross substitutability, we can depict the equilibrium situation in the non-tradables market in fig. 1, which has been adapted from Dornbusch (1974). The NN schedule describes the combination of qr and qo that is compatible with equilibria in the non-traded goods market. The slope of this curve is given by6

The ray OT, on the other hand, measures the relative price of both tradable goods - traditional tradables to oil (P,/P,). The initial equilibrium position is given by A with equilibrium relative prices being equal to q$ and qi, respectively.

0 qx

PO qo=q

Fig. 1

?n deriving this equation it is assumed that the gove~ment allocates its expenditure of the oil revenue between tradables and non-tradables in the same way that domestic residents allocate their spending It is important to realize that this result (i.e., dqr/dq, $0) depends critically on the assumption that the relative price of oil does not enter in the excess demand function for non-tradables. However, if oil is consumed domestically and oil and non-tradables are assumed to be complements, eq. (1) should be rewritten as

N=N(q,, 40. y )=4 <+r C-1 I+)

(I’)

and the slope of the NN curve will be

which can be smaller or greater than zero depending on whether [(aN/aq,) +(aN/ay)6] 20. If the slope of the NN curve is positive, then an increase in the price of oil could result in an

increase in the relative price of traditional tradabies with respect to non-tradables, and thus in resources moving from the nontradables sector into the tradables sector.


Assume now that there is an exogenous increase in the price of oil. The UT ray will then rotate clockwise toward OT’ in fig. 2. If the (nominal) price of non-tradables was constant, the new equilibrium would be given by B, with a constant relative price of traditional tradables with respect to non- tradables. However, as long as the slope of the NN is different from 0, at B there will be an excess demand for non-tradables that will require an increase of the relative price of these goods, both with respect to the price of oil and traditional tradables. The final equilibrium will then be attained at C. As a consequence of the increase of the price of oil, there has been a decrease of the relative price of traditional tradables both with respect to oil (i.e., PT/Ph< P,/P,) and with respect to non-tradables (i.e., &> 4;). This reduction in the relative price of traditional tradables, of course, will encourage resources to move out of the traditional tradables sector into the other sectors of the economy. This phenomenon has been called by some authors the de-industrialization efict of an exports boom [see, for example, Corden and Neary (1982)].

Fig. 2

It may be noticed from fig. 2 that the degree of reduction of qT( = P,/P,) wiii depend on the slope of the NN curve. At one extreme, if the NN curve is a vertical line, the negative effect on qT of an exogenous increase in the price of oil will be maximum. On the other hand, if the NN curve is a horizontal line, there will be no effects of an increase of the price of oil on qT. This will be the case if all the additional income generated by the higher price of oil is spent on tradables.’

‘See Harberger (1981) for a similar discussion in the context of a simulation analysis.


The movement from A to C in fig. 2 is a real phenomenon resulting from the increase in P,, and in that respect it can hardly be referred to as a ‘disease’.’

2.2. Short-run disequilibrium in the money market

The preceding analysis has focused on the real long-run effect of an exogenous increase in the price of one export (oil) on the competitiveness of the rest of the tradable industries. The analysis, however, has abstracted from any dynamic aspects. In this section we motivate the formal dynamic analysis of section 3 by introducing some dynamic considerations into our diagrammatical analysis. To accomplish this, we follow Harberger (1981) by explicitly introducing a slowly-clearing monetary sector.

Under these circumstances, an increase in the price of oil, in addition to its real effects, will affect both the supply and the demand for money. It increases the supply of money (provided that the central bank monetizes reserves inflows) by producing a balance of trade surplus (it is assumed that the capital account is closed). The demand for money will increase as well, as a result of the increase in income brought about by the higher price of oil. The overall result may be either an excess supply or an excess demand for money. By Walras’ Law these situations respectively imply an excess demand for goods - both tradables and non-tradabies - or an excess supply of goods. In the former situation, the excess demand for non-tradables goods caused by this short-run monetary disequilibrium reinforces that caused by the real factors discussed previously (the increase in income resulting from the increase in oil prices), with the result that qT will decrease, in the short- run, by a greater amount than would be caused by real factors alone. In this case, then, the nominal price of non-tradable goods will overshoot its new long-run equilibrium, and the loss of competitiveness of the traditional tradables sector - measured by the decrease of qT - will be greater in the short- than in the long-run. If, on the other hand, there is an excess demand for money, qT will decrease in the short-run by less than real factors alone would indicate. In either situation - excess supply or excess demand for money - as monetary equilibrium is restored through balance of trade surpluses or deficits, qT will move to its new long-run equilibrium value as determined by the real factors in the model.

This discussion can be formalized in the following way: The excess demand for money in nominal terms (Mu) is given by

ME=MS-MMD,

‘The problem of temporary vs. permanent booms remains, of course. If wage rigidities and slow factor movements (speciiic capital a la Jones-Mayer-Mussa, for example) are introduced into the model, even these equilibrium changes in relative price might result in unnecessary unemployment when the booms are only transitory. See also van Wijnbergen (1984).


where MS is the nominal supply for money, and MD is the demand for money in nominal terms. Assuming that the demand for money equation M” (in nominal terms) depends on the usual arguments - real income, and the price level - we can write ME as9

ME = M”(MS, P,, P,, Y). CC) C-k (-) c-j

(3’)

We further assume that ME is equal to zero only in the long-run. In particular, an increase of MS will result in a short-run excess supply of money, which will be slowly eliminated through the balance of payments. It is further assumed that, due to Walras Law, an excess supply of money will be reflected in as excess demand for non-tradables and an excess demand for traditional tradables. Then, eq. (1) has to be modified to incorporate the assumptjun that in the short-run, an excess supply of money is partially translated into an excess demand for non-tradables,

N = WI,, ME, Y). (1”) (+) (+) (+)

In terms of fig. 1, an increase in ME will result in a downward shift of schedule NN. The model is completed by specifying the balance of trade and the money supply equations.

The balance of trade is defined as

B = P,O - P,E,, (4)

where E, stands for excess demand for traditional tradables, and where 0 is the amount of oil exported. It is also assumed that aB/aP,>O; that is, an increase of the price of oil will result in an improvement of the balance of trade.”

In a small open economy with fixed exchange rates the quantity of money will be endogenous in the long-run. However, in the short-run it is plausible to think that the actual quantity of money can differ from the amount of money demanded. In this paper we will assume that an increase in the price

‘In order to simplify the diagrammatical analysis it is assumed that the demand for money does not depend on expected inflation. This assumption is relaxed in section 3 [see eqs. (14)-

(1611. ‘The effects of an increase in the price of oil on the balance of trade will be given by

dB/dp,= (7 - P,dE,ldp, where dE,/dP, 3 0.

A sufficient condition then for an increase in the price of oil to result in a dB>O is that d&50. It might be noticed that the empirical evidence shows that for oil-producing countries increases in the price of oil has tended to result in an improvement in the balance of trade.


of oil will result in a short-run excess supply of money. The reason for this is that, as Harberger (1981) has argued, an increase in P, will result [through (4)], in a balance of trade surplus, and this, in turn, will positively affect the supply of money.” Assuming that this increase in MS is greater than the increase in MD resulting from the income and price effects, there will be an excess supply of money which will be slowly eliminated through the trade account. If, however, the capital account is assumed to be open, this excess supply of money will be eliminated very quickly.

Under these assumptions, the short-run effects of exogenous increase in the price of oil can be depicted in fig. 3. The exogenous increase in the price of oil simultaneously results in a downward shift of the NN curve to N’N’ (as a consequence of the excess supply of money), and in a rotation of the OT ratio to OT'. The NN curve will shift downward, since if there is an excess supply of money at the old relative prices for non-tradables, there will be an excess demand for these goods, The new s~o~t-r~n equilibrium is attained at S. Final equilibrium is obtained, as before, in C. The dynamics are characterized by shifts of the N’N’ curve to the right towards the NN curve. The speed of this adjustment depends on how fast the excess supply of money is eliminated. As may be seen, in this case relative price of traditional tradables ~~~ers~o~ts its final equilibrium level. This means that in this ~urtic~~u~ case, the loss of com~titiveness of the traditional tradables sector (as measured by the decline of qr) is greater in the short-run than in the long-run. In the next section we rigorously analyze the characteristics of this undershooting of qT (or overshooting of PN). Our results indicate that an undershooting of qr is not a necessary outcome of the dynamic analysis.

Fig. 3

‘LIn order to simplify the exposition we are assuming a closed capital account. This is the case of most developing countries whose exchange controls do not allow for free capital mobility.


Quite the contrary, as shown in section 3, in order to obtain this result, a set of specific conditions are required. An alternative dynamic effect is obtained, for example, if it is assumed that the balance of trade surplus resulting from the increase in P, is not monetized. In this case, the initial increase in P0 will generate an excess demand far money. This may be seen from eq. (3’), where (8ME/aY)(dY/aP0) < 0. Under these circumstances, then, the increase of P, will result in a simultaneous shift of the NN curve to the right and a downward rotation of the UT ray. This situation is captured by fig. 4. In this case, the short-run equi~~brjurn situation will be obtained at R, where qr fall short of its final ~qu~~~briurn value of &

Fig. 4

The preceding analysis focused on the behavior of qr in order to discover the extent to which an increase. in the price of oil affects the competitiveness of the traditional tradabfes sector. However, in a small open economy with a fixed exchange rate, the nominal price of traditional tradables (Pr) is given, and the adjustment of relative prices is obtained through changes in the nominal price of non-tradable goods (PN).

Our discussion in the previous section reveals that there are (at least) three different paths that PR can take following an increase in P,. These alternative paths are summarized in 5g. 5, and are further investigated in the next section. If monetary considerations are ignared, P, wifI jump from A to C. Alternatively, if the increase in PO results in a short-run excess supply of money, the price of non-traded goods will jump from A to S, and will slowly return to its long-run equihbrium. Finally, if immediately after the increase in PC, there is an excess demand for money, PN will only jump to T,

S. Edwards and M. Aoki, Oil export boom and Dutch-disease

PN

c ‘h

229

Fig. 5

undershooting its final equilibrium, and will subsequently move towards Pk. As discussed in section 3, the adjustment towards Pi in these two latter cases can also be oscillatory if additional sources of dynamics are included in the analysis, such as changing wage rates or expectations on inflation. As already mentioned, if other rigidities are assumed, it would be possible to find alternative paths for P,.

The simple diagrammatical discussion in this section suggests that it is not clear in what way, if any, we can refer to the effects of an increase in P, on the rest of the economy as a ‘disease’. Specifically, the analysis presented indicates that in the absence of rigidities, the only circumstances under which an oil exporting country will face something which we can call a ‘disease’ is when the monetization of the additional oil revenue results in a short-run

overshooting of the nominal price of non-tradable goods. In the absence of this monetary effect, this overshooting would not be observed. In the next section this overshooting is analyzed in detail using a dynamic general equilibrium model. This allows us to derive explicit policy measure that will eliminate the overshooting of P,.

3. Comparative dynamics analysis

In this section the discussion presented in the diagrammatical analysis is formalized using a dynamic general equilibrium model. We investigate conditions under which the alternative paths of P, depicted in fig. 5 are obtained. In particular, we derive conditions for P, to overshoot its long-run equilibrium value, generating what might be called a short-run ‘disequilibrium’ loss of competitiveness in the traditional tradable goods sector.


3.1. Structural equations

We summarize the model in structural form:

Non-tradable sector

H; = 64 W/P,), supply, C-1

H”N = H~(P~/P~, Y, MS - Md), private sector demand. (-1 (+f 1+1

Tradable sector

H”T = ~VW,), supply, (-)

H$ = H$(P,/P,, Y, MS - Md), private sector demand. (+) (+) (+I

National income

Y=H~~(P~fP=)H~+(Po/P~)~, in terms of tradables.

Balance of trade

B = H$ - H$ + (Pa/P,) 0 - G,, in terms of tradable%

Labor sector

L, = LN( W/P,), demand for non-traded goods sector, (-1

LT = L,( W/P=), demand for traded goods sector, (-)

L,+&=L-tro, equilibrium condition.

Monetary sector

Md/PI = kYe-“‘, demand,

where

P,=PgP;-a, Otcctl,

and

zre = (PI/PI), expected rate of inflation,

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12

(13)

(14)

(15)

(16)

S. Edwards and M. Aoki, Oil export boom and Duich-disease 231

(17) MS=D+R, supply,

where

R = P,B.

Government sector

POD = P,G,+ P,GN,

where

P,G,=(l -e)P,o,

and

(18)

(19)

H;=H;:+GN, non-tradable sector equilibrium condition (20)

In (5) and (7), W is the nominal wage rate. Eqs. (11) and (12) are labor demand schedules. Eq. (13) is the market clearing condition for the labor sector where the oil sector employment is assumed constant. In (14), P, is the consumer price index. The ratio a of the consumption bundle of the residents of the small open economy falls on non-tradables and the remainder, 1 -CC, on tradables. This fo~ulation of the price index assumes that oil is not consumed in this economy. This assumption turns out to be critical in the anaylsis of the overshooting of P, as is shown below (see, also, footnote 6). The expected rate of inflation of the consumer price index is given by (16). Eq. (17) describes the supply of money. Eq. (18) describes the rate of increase of foreign exchange in the economy, where as usual the dot over a variable denotes a derivative with respect to time. Eq. (19) is the government budget equation. It shows that the government spends (1 - 8) of the oil revenue on tradables. As (20) shows, the remainder is spent on non-tradables. The parameter 8 is the government’s choice variable. The government budget constraint equation implies that GN is given by @(P,/P,)o. No tax is included in the model to convey essential features simply. Eq. (20) describes the market clearing condition in the non-tradable sector,

Eqs. (5) through (20) formally capture the main features of the model discussed in the preceding section. In order to simplify the exposition it is assumed that labor is the only factor of production, and that while labor can move freely between the traditional tradables and the non-tradable sector, labor allocated to the oil sector is fixed both in the short- and long-run [leq. (IJ)]. Eq. (10) defines the balance of trade, with eqs. (18) and (17) relating it to the monetary sector through changes in international reserves (the capital account is assumed to be closed). An increase in the price of oil, for example, will affect the balance of trade through eq. (10). Assuming that as a consequence of the increase in P, a balance of trade surplus results (however,

232 S. Edwards and M. Aoki, Oil export boom und Dutch-disease

recall the discussion in footnote lo), there will be a short-run increase in the supply of money through eqs, (18) and (17). This will tend to generate a disequilibrium in the money market, which, on its turns, will affect, through eqs. (6) and (8), the demand for tradabtes and non-tradables. In the rest of this section we discuss the formal conditions under which this process will result in a short-run overshooting of P,.

3.2. Variational equations

We now employ the technique for comparative dynamic analysis as exposited in Aoki (1980, 1981) to evaluate consequences of unexpected exogenous shifts in P,. Roughly speaking, we postulate a reference time path along which this small open economy is moving. The reference path can be a long-run equilibrium (or a steady-state path in the case of a growing economy) or any other ‘pIanned’ time path, so long as the time path for the exogenous variables (such as P, or L)) and the resulting time paths for the endogenous variables satisfy the model eqs. (5) through (20). Unforeseen movements in PO not included in the reference time path then would cause the time paths for all the endogenous variables to deviate from their respective time paths. r2 These deviations are governed by the variational dynamic equations, derivations of which we now describe. It is convenient to derive the variational equations without explicit specification of the reference path. Different choices of reference paths modify (generally) time-varying coefficients of the variational equation. By treating these coefficients as generally time-varying, and specifying them later, if necessary, we can treat a variety of reference paths.

In all the reference paths, P, is held fixed; because it is equal to Pg by price arbitrage. (Recall that the exchange rate is chosen to be one.)

3.2.1. Notation

We use 6 to denote deviation from the reference path values, e.g., 6MS(t) =@(t) --MS,(t) where the subscript 0 denotes a reference path variable. Lower case letters are used to denote relative deviation, e.g., nzs(t) = ~~‘(~)/~~(c) so that perturbed path MS(t) is related to the reference path M:(t) by MS(t)=MS,(l +ms(t)). Other lower case variables, such as w(t) and pN(t) are similarly defined, i.e., w(t) = 6kV(t)/IV,(t) and pN(t) =6P,(t)/Pz(t). Here superscript 0 is used to denote a reference path for PN(t).

From (I7) and (18),

i%cP(t) = sd(t) + PgvJ(t). (21)

“In stochastic models various exogenous shocks also move the economy off the reference path. To avoid technical complications, reference paths are taken to be continuous. Rather than discontinuous jumps from one equilibrium position to another, connect them with steep but continuously changing paths, for example.


Because P,G, = tlP,D, the government expenditure in the non-tradable sector satisfies

W’NGN) = (P,W&,N +g,) = ~P,~'(Po + We), where

and po is the relative deviation of the oil price. Since (P,G,), equals tlPo0, the above becomes

PN + g, = PO + ae/e- (22)

3.2.2. Variational reduced forms and dynamics

The price of non-tradables deviates according to

(23)

where rro - 7c2 are the elasticities of no immediate concern (they are defined in the appendix). Details of derivations are found in the appendix. From (lo), balance of trade deviates from the reference path value according to

where from (A.l) and (A.4) h% equals -_afPN. h$ is given by (A.6) and 6Gr equals (G,),P,-(G,P,/P,),(68/0). Substituting these, we obtain

(24)

where /Jo-& are defined in the appendix.

From (21) and (24), the money supply deviates according to

?h”= -~OmJ+~opo-~~pN-~Z(mS-~md)+8~68/8+x,

where

&=(ni”,/M”),

(25)

is the rate of growth of the money supply along the reference path (which could be zero), and

RE B

234 S. Edwards and M. Aoki, Oil export boom and Dutch-discusc

is another instrument of the government related to the rate of growth of domestic credit.

In (23) and (24), md is given by variation of (14),

md=aPN+y-67f

The exact expressions of the parameter &,, 11, t2, and & are given in the appendix. The coeficient &, is some constant of no immediate concern. The reduced form of pN becomes

where p’s are defined in (A.7). We iater show that a non-zero coeffkient p1 in (27) is one factor responsible for overshooting.

3.2.3. Static expectations

Under static expectations assumption, 6x” in (26) is zero. Eq. (29, on substituting md out by (26) becomes

and o3 is some constant of no immediate concern. To have a stable variational dynamic, we assume that u1 is positive which is true if q1 in (A.3) is positive, i.e., if an increase in the price of non-tradables increase real output. As we show in (30) non-zero u0 in (28) also contributes to overshooting. Even when q1 is negative, if it is not ‘too’ negative u1 is still positive. Later we choose B to eliminate overshoot which renders u1 unambjguously positive. As we explain below, a once-and-for-all shift in the oil price will not produce overshooting of the non-tradable price if ms remains at zero. Eq. (28) indicates that this can be accomplished in several ways. For example, a straightforward way of eliminating overshooting is by sterilizing the monetary effects of the increase in the price of oil through changes in domestic credit. In terms of eq. (28) this can be accomplished by choosing a value of x such that m” remains at zero (i.e., the quantity of


money supplied does not deviate from its equilibrium path). However, on the assumption that 68 and x are zero (i.e., the government does not deviate from the planned values of B or x), an alternative way to eliminate overshooting is to set 8 so that u0 vanishes. We shall explain this in greater detail below.

The time path of ms is obtained by solving (28),

(29)

Let X(E) ~0, 68~0 and p&t) E& to illustrate a simple case. We further assume that ui is a constant. Then, from (27) and (29) the relative deviation of pN becomes

Initially, ~~(0) equals ~~~o~~~~‘(O). As time goes to infinity, p&t) approaches (~*+~~u~/u~)~~. Thus, pN(t) exhibits an initial overshoot if and only if13

PIMO) --Is0u0/~1) >O.

Since ms(0) is zero unless the domestic credit is discontinuously changed at the time of the oil price increase, i.e., SD(O) f 0, this condition becomes, noting that PO > 0,

PI%/% <O. (30)

Thus, an overshoot can be eliminated by choosing 8 - the proportion of oil revenue spent by the government on non-tradable goods - such that plu0 is non-positive. I4 It turns out that p1 is not zero, but va can be made zero by a

13Note that an overshoot here is defined relative to the reference path along which u, is constant. If the initial equilibrium state is chosen as the reference path, the overshoot here is the same as the usual notion of overshoot.

14Assume a constant u, with non-zero x = 2 in (28). With ms(0) = 0, the solution of (28) is

m”(t) =[(~~~o~u~~)/u~](l --e-““).

Hence ~~(t)=~~~~+(~~~~)(voao+V3X)(l-e-””)+ u,l. The condition for no overshoot now becomes

Even with pr # 0, f = - u~~o/u~ can eliminate an overshoot.


suitable choice of 0 as discussed in the appendix,15

(31)

where

where E~ is the oil price elasticity of demand for tradables as defined in (A.lO), and E* is a measure of how sensitively the excess supply of the tradables change with respect to the price of non-tradables induced by oil price changes.

More generally,

Assuming that (28) is stable, i.e., 4(t,O)+O as t+ 00, the condition of overshoot becomes

or assuming m’(O) =0 as before, (30) is replaced with

lim pt(t)itP(t,s)u,(z)dz<O. *‘CC 0

A sufficient condition for no overshoot then is u,(t)rO. A 8 which varies with time according to (31) still eliminates the unnecessary overshoot in the price of non-tradables.

4. Discussion and extensions

In the preceding section, the condition under which PN will overshoot its new long-run equilibrium value were found, assuming static expectations. With non-static expectations, a term is added to the money supply deviational dynamics of (28). For example with perfect foresight Sn’ equal dl. From (15) $, =xJjN. We now have a two-dimensional dynamics involving ms

151n terms of the diagrammatical analysis of the preceding section, a change in 0 will result in a change in the slope of the NN curve. In that sense, then, it is possible for the government to choose, in every moment in time, a value of 0 (i.e., of the slope of NN), such that in spite of the downward shift of the NN curve, the relative price of non-tradables will remain equal to its new Iong-run value.


and P,. By constraining the solution to lie on a subspace spanned by the stable eigenvalue of this two-dimensional dynamics, as is the custom in the literature on perfect foresight, we can still show that a suitable choice of B can eliminate overshoot in P,. In both cases overshooting will occur if the proportion of oil revenues spent by the government or non-tradable goods (0) exceeded initial values.

Alternatively, overshooting of P, can be eliminated through a devaluation of the domestic currency or changes in domestic credit. Yet another way exists to eliminate overshoot even if the parameter @ happens not to be set as a correct value given (31). For this purpose we make use of the term ~~~/6) in (27) and (28). By varying 8 slightly by (&I/@, we can repeat the previous argument to establish

as the necessary and sufficient condition for no-overshoot, where we now assume v,, #0 because (30) has not been met or (de/@ = -vO&JuZ, which would be small if 19 ‘approximately’ satisfies (31) because then ve will be approximately zero.

A devaluation will produce an increase in the domestic price of traditional tradable goods, and of the price level P,. This increase in the price level, in turn, will tend to eliminate the excess supply of money initially generated by an increase of the price of oil, eliminating the source of the overshooting of P N-

Until now the discussion has been carried under the assumption that the elimination of overshooting of PN would produce a smoother (and more desirable) transition from pre-boom relative prices to post-boom relative prices. The analysis, however, has not dealt in an explicit way with reasons why avoidance of an overshooting of P, might be desirable. Real costs associated with the overshooting of P, can be introduced in many ways. One way is to assume that there are real resource costs associated with movements of factors of production from one sector to another. Alternatively, we can assume that wages are rigid downward. In this case, the overshooting of P, will also result in an overshooting of nominal wages. However, once PN begins to decline after having reached the overshoot peak, wages will also have to decline. However, if wages are inflexible downward, they will go up with P,, but then will not decline. This wage rate in~exibility wilt then be associated with ~~e~p~~yme~~ as a consequence of the overshooting of P,.

Finally, it is important to stress that, as pointed out in section 2, the overshooting of PN is not a necessary result of a commodity export boom. Quite on the contrary, as is implicit in eq. (31), the overshooting, undershooting or step-change of P, as a result of the boom will depend on


the value of 0 - the proportion of foreign exchange earnings that the government spends on non-tradables.

Appendix

Derivation of (23)

The variational expressions of (11)-(13) are solved for w,

w = fPN, w-here

Variation of (5) yields, in view of (A.l)

G= -S(W-p,)=s(l --f)PN,

where

s = -(l/P,) (aE$/a( W/P,)) > 0.

We also need variation of national income. From (9),

Y=-~lw+~2pN+~2~O=~lFN+~Z~0,

where

‘I1 =d-l?lf> &I =(aHs,/Y)>O,

e2 = C~~~/~~)~~/~~~l +a -f11 ‘0,

c72 = (PO/P,) 61 y > 0,

(A.11

64.2)

(A.3)

where G appears in the variational supply relation obtained from (7),

h;= -iJw, cr = - Cfl/~~)faHSTi’afW/PT))I* >a (A-4)

Variation of the market clearing condition (20) is solved for PN. First, we note that

(A.5)


where

Taking variation of (20) and noting (A.2), (A-4) and (22), the resulting equation,

(H~),s(l-f)p,=(Hd,)o{-u1(PNIPT)OPN+azYy+a,(GMS-6Md)}

+(Giv),g,,

is solved for pN,

710 = {(GN)o+ GoYort2(@Jo}lDen,

x1 = a~(~~)o~~/Den,

and

n, = (G&/Den.

Variation of (8) yields

@ =wdTh WNlP,) PT ‘[ a*t (PK)OPN+(~Y)OY


Coefficients of (24)

Po=eP,s/M”,-r/3POT(YaHdT/aY)O/MS0,

b, = C(YPT/H~T)(~H~T/WI~ >O,

pz = P;(aHd,/aMy, > 0,

83 = (GNPNIW.

Coefficients of (26) and (29)

Taking variation of (14), md = ap,+ y- b+. Substitute y out by (A.3), ll~~ = (tl + ql)pN + q2po - 6x’. Substitute g, in (23) out by (22),

~N=7LO~O+71~(“s-~m~)+“2{-pPN+~o+6e/e).

Solve these two equations for md and pN,

-_(l +R2)6~‘+(a+?,)(~lmS+nzSe/8)]/d, (34.7)

and

~N=C(-~~,rl,+n,+~,)pO+~~,6~e+~~ms+~~6e/e]/d,

where

d=1+7cr,+p7rc,(a++Q.

The coeflicients of (26) and (29) are read-off from the above: From (22) and (A.7), we note that

S. Edwards and M. A&, Oil export boom and Dutch-disease 241

If the coefficient ue in (28) is zero, then changes in the oil price do not affect the money supply. From its definition in (28), uO is zero if and only if PO = plpO -~&J& Substituting their definitions

(A.9

Since the change in H$ caused by p. is given by

where y=r],p, from (A.3), Md, =,uMS,, and md=&po from (26), the first two terms of (A.9) can be written as SHd,/p,. The oil price change has another indirect effect on H% and H; by changing the price of non-tradables as (A.l), (A.3), (A.4) and (A.6) show. The terms in brackets capture these indirect effects.

By setting 8 to

8 =&z&z + &l~3wdTJv~O@O

the coefficient uO becomes zero, where s2 is the income elasticity of demand for tradables, and .s3 is the elasticity with respect to cash hoarding. The expression q2st + c&+ is defined to be the elasticity of H% with respect to oil price change

GJ = V2&2 + {O&3. (A.lO)

We define the expression of the second term as .sNt the sensitivity of the excess supply of tradables with respect to changes in the price of oil.


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oil export boom and dutch-disease: a dynamic analysis

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