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Transmission of external price disturbances and the composition of trade
Journal
of International
Economics
10 (1980) 357.-375. 0 North-Holland
Publishing
Company
TRANSMISSION OF EXTERNAL PRICE DISTURBANCES AND THE COMPOSITION OF TRADE Louka
T. KATSELI-PAPAEFSTRATIOU*
Yale Yniocrsity,
Received November
New Hauen, CT 06520, USA
1978, revised version received December
1979
This paper focuses on the role of trade composition in the transmission of external price disturbances. It is shown that the effects of an increase in the price of imports on domestic prices and the trade balance crucially depend on the cross price elasticity of demand in the case of final goods and the elasticity of substitution between factors in the case of intermediate goods. In the case of an input such as oil, where the elastici’y of substitution between imported and domestic factors of production is less than unity, an incre.;se in its price will give rise to a balance-of-trade deficit but will have ambiguous effects on domestic prices.
1. Introduction The impact of exchange-rate movements on the domestic economy has been one of the most popular and controversial topics in internationrl finance. The degree and time-path of internal adjustment following a oneshot change in the relative price of the domestic currency, has been a major point of contention in the debate between proponents of the ‘elasticity”, ‘absorption’, and/or ‘monetary’ approaches to the balance of payments.’ The explicit introduction of non-traded goods into macroeconomic modelling. most notably by Komiya (1967), Dornbusch (1973a, 1973b), Krueger (1974). Corden and Jones (1976) and others has further expanded and enriched the traditional analysis. It was the move towards flexible exchange rates in 1971 and the fourfold increase in the price of oil in 1973 tlrat caused a gradual shift in emphasis towards (a) a systematic re-examin:ltion of exchange-rate determination [Dornbusch (1976), Kouri (1976), branson (1977)], and (b) the explicit introduction of imported intermediate inputs in macroeconomic analysis [Findlay and Rodl.iguez (1977), Rodriguez (1977), Buiter (1978)]. A further
*I am indebted to Peter B. Kenen, William H. Branson and an anonymous comments and suggestions. ‘For a good overview of alternative approaches to brllancr-of-p~lyments Whitman (1975).
referee for hcIpfuI adjustment.
CC
consequence ot these developments, has been the increasing focl:.s on foreignprice movements as the primary source of exogenous shocks to the system, a role up to now principally attributed to exchange-rate disturbances. This paper a.dopts a similar viewpcint and addresses itself specifically to in the transmission of el;ternal price the role of trade composition p* on the short-term responses of home-good disturbances. The analysis focus,s prices, nominal income, and the balance of trade to an increase in import prices and compares these responses for two polar cases: when imports are final goods and when imports are intermediate goods. The first case is treated in section 2 while the second is taken up in section 3. The comparison of results in section 4 highlights the qualitative differences that can be attributed to the composition of trade. The basic model extend; the Dornbusch (1973a), Connolly-Taylor (1976) models in two directions: (a) it incorporates a supply-side into what are essentially demand-side models and (b) it replaces thle classical fullemployment assumptions with Keynesian assumptions of wage stickiness and More importantly, it’ focuses, in a way similar to unemployment.2 Harberger’s [ Harberger (1964)], on those structural characteristics of an economy whose magnitude determines the overall effect of external disturbances on the target variables chosen. The model presented here, both in its formulation and the conclusions derived therefrom, can be viewed as complementary to the work of other authors [Findlay and Rodriguez (1977), B~itcr (1978)) in the sensie that these studies share a similar methodology in the pursuit of different objectives.3 To make the exposition clear and concentrate on the composition of trade issue, a number of simplifying assumptions are made: the country in question is assumed to be ‘small’, i.e. a price-taker in both export and import markets.’ Exchange rates are assumed fixed so as to focus exclusively on the transmi:ssion process of external price disturbances. It could aLlso be argued that most small and open economies still peg their exchange rates to that of their major trading partner either because of feasibility or optimality ‘Full cmplolment as\ump!ions were incorporated itl an earlier version of this model [KatseliP; pacf\trtltiou f 197911. The endogeneity of wages changes the solutions quantitatively but does nc~: ;tiuh m important qualitatice differences. ‘E-~ncil~!, and Rodriguez ( 1977i 17;~-.ribe a one-sector econon.y which is large eno. ;h to affect 11%term< \~f trade and k charxt:r’-ed !q flexible rather than fixed exchange rates. They are mtcreGed m macro-policy effectiveness when imports are intermediate goods. They also look at r!~ sflc~ts 0; an exogenous price increase on the domestic economy but their analysis is ccmducA at a highly aggregate levei. Buiter (1978) analyses the effects of a number of external Iyturbances on output, employment, and the price level under a freely floating exchange rate ra.gbmc. The asset markets are fully developed and there are no non-traded goods. His e~mcIu~sun~ regarding the e!Tect!; of an oil-price increase on the domestic economy are analogous 1tj 113t~ 4uhth4i p;_‘pcr. i tpr .an LIZ> VLLI~to ln~rorporate non-small country assumptions into a macro-model, see Branion and E;aa~elr-Papasf~traItiou (1980).
L.T. Katseli-Papaej?tratiou,
External
price disturbances
359
considerations.’ The government sector is left out of the analysis Atogctllet so that changes in the money stock reflect solely changes in the level 01 reserves6 Imported intermediate goods are used in home-good production only, rather than in the export-good sector. ’ Finally, only the comparative static results are presented and compared here while the long-run steady state implications of the model are worked out elsewhere [KatseliPapaefstratiou (1979)]. The basic conclusions derived in this paper can be summarized as follows: If imports and non-traded goods are gross substitutes in demand, an increase in the price of imported goods will cause an increase in the price of nontraded goods and a surplus in the balance of trade;’ if instead imports and non-traded goods are gross complements, the price of non-traded goods will typically fall and the balance of trade will deteriorate. If in:ports are intermediate commodities, the effects on the price of home goods and the balance of trade will depend on the elasticity of substitution betwe:! factors of production. If the elasticity of substitution between domestic factors and the imported input is greater than unity, an increase in the price of the input will reduce its share, increase value added and the price of home goods, and cause an improvement in the balance of trade. If the elasticity of substitution is less than unity, as in the case of imported oil [Berndt and WooId (1979)], the effect on the domestic price level will be ambiguous while the balance of trade will unambiguously deteriorate. The ambiguity is due to the appearance of supply-inflationary in addition to demand-deflationary effects. The results obtained in the two polar cases of trade composition are not completely symmetric. In the first case an external price disturbance is simply translated into a demand-side disturbance leaving the supply side unaffected; in the case of imported intermediare goods, however, either the emp4oyment or the price effects become ambiguous as a result of both demand and supply-side disturbances. Thus. both the composition of trade and the ret: ,uilt substitutability between goods or factors are important parameters in the transmission of external price disturbances. A cursory view of countries’ trade composition seems to suggest th:it some “For a detailed discussion on the choice of exchaltgc rate regime. see Branson an3 KathcliPapaefstratiou (198(i). ‘The introduction of the government sector is treated in Katseli-Papaefstratiou (1979. ch. 2). ‘If imported inputs were used in the export-g,ood sector as well. then an incrcasz ir; the pr~cc of imports would result in even more pronounced effects on inc:omc than is the cast now. Gncc value added in tha sector would be affected. Increases in the price of the final good wtruld probably increase output and have ambiguous effects on income and the balance of trade as demand for intermediate inputs will increase. “The results obtained here for the final-goods case are in sharp contrast to those, of Connollq and Taylor (1976). In their model the presence of a substitution and a liquidity effect in the demand functions make the impact of an exogenous price disturbance on home-good prices in ambiguous. This acibiguity is resolved here due to the assumption of gross subitiluiabilltg consumption
between the three types of goods.
countries are signi5cantly more dependent upon intermediate imports than others [Katseli-Papaefstratiou (1979)]. These differences provide a partial explanation for the differential cross-coumry responses to exogenous price disturbances and in that way the framework of this paper can provide a starting point for more empirical work on the subject. Section 2 of the paper analyses the final-good case under various elasticityof-demand assumptions.; section 3 works out in detail the intermediate-good case when imports and domestic factors are gross complements, and case of a Cobb-Douglas discusses briefly the ;nore straightforward production function with unitary elasticity of substitution between factors. The results are compareId and summarized in section 4.
I. Transmission of price disturbances when traded goods are final goods
Let us assume that a small and open economy consists of two sectors: a sector for traded or intlernational goods (I) and a sector for non-traded or home goods (H).9 For reasons of comparison with the case of imported intermediate goods, traded goods can be further decomposed into an exported good (X) which is produced at home but consumed domestically or abroad and an imported good (_ ‘) which is produced abroad but consumed at home.” All three gooc *e final goods and gross substitutes for each other.’ ’ The seven equations presented below can fully describe the workings of a simple economic system where apart fiom the goods’ markets there exists one asset, namely money, and a labor market that is characterized by an infinitely elastic supply curve. Superscripts denote supply or demand of a particular commodity or factor while subscripts denote the type of good in question. Bars above such variables as the nominal wage (W) and the exchange rate (E) imply that these variables are held constant throughout. An asterisk denotes an exogenous variable such as foreign prices and a dot o\.er a variable implies its rate of change.
“The terms ‘traded and ‘non-traded’ are preferred here to the ambiguous terms ‘tradeables’ snd ‘non-tradeables’. Also. the terms ‘home’ and ‘non-traded’ goods are used interchangeably. t-(pr a dr~us~m on the often confusing use of these terms, see Katseli-Papaefstratiou (1979). “‘The dccompositron of traded goods into exported and imported commodities is justified on e+1rnp3r~~t~:crather than ;Inalytlcal grounds. The same holds tr::e for our assumption that there :%II~) Import-compettng production. ‘-The a\s!mptlon of grow >ubstltutability is relaxed in section 2.1 below.
L.?: Katseli-Papae&stratiou
Balance-of-payments
X”
Cxternal
price disturbances
361
equation
F - Xd[P,, P,, Pmp,C] -YEx
L-1X
[Ph, P,, Pmp, C] = -:c,
(2a)
where -P,x=S-E.[kYGross domestic
Ml=,%.
(W
production
Y=P,M”+P,X”.
(3)
Income identity Y=C+S, where S=A.[kY-
M],
(44 (4b)
Money market
It&-Ek=O.
(5)
Prices p,=EP,*,
(6)
P,, =EP&
(7)
Eq. (1) describes the market for :lorne goods which clears continuousl:/. The supply of home goods is simply a function of the own real wage, while demand is a function of relative prices and nominal consumption expenditures which al-e equal to aggregate income minus desired saving. Eq. (2a) is the balance-of-paymentsI equation with - .K describing the flou excess supply of goods which is then translated in eq. (2b) into a flow e:{ccss demanJ for money. If desired money holdings (k Y) exceed the stock of mon::y available, M, consumers will reduce their expenditures, i.e. save, to restore their desired cash positions. The speed of adjustment is described by parameter ;1. 121n the absence of transfer balance of payments.
payments
and capital
movements
the balance
of trade
IS rhc
362
L.7: ELmeli-Papuefsit
~ltlou, Extcn-ml price disturbances
It is easy to prove that E!?, the rate uf accumulation equal saving by rewriting eq. (2a) in the foliowing form:
of reseraes, has to
Substituting eq. (3) into the above equation, it follows that
Finally, eq. (3) gives the value of total domestic production, eq. (4) describes the income identity, eq. (5) the money market, and eqs. (6) and (7) fix the domestic prices of exported and imported commodities to their foreign levels through the exchange rate, E, which is taken to be fixed. Two additional points should be made here regarding the specification of the saving function Ceq. Wl.
(a) Saving is dependent upon both income (Y) and wealth (M). The marginal propensity to sawe out of income (S,,=aS/aY) is positive and equal to ik whereas the marginal propensity to save out of an increase in wealth is negative and equal to minus the speed of adjustment I., or, SW= -A. (b) The specification is consistent with the more general and usual specification of the saving function described by Ando and Modigliani (1963) where S= &I =x1 1 -r,.,!4. In this present framework the coefficient a1 is equal (0 ik and ‘x2 is eqrial to I.. Thus, coefficients (x1 and a2 are not independent parameters:; in the steady-state solution of the model a1 = kor, or k is equal to the ratio of the two coeficients. The demand functions possess the following properties: (1) They are homogeneous of degree zero in all prices and consumption, so that -Bi+CBi,j=-Bi,c; j
i, j = h, x. mp,
where Bj and Bi j are the own- and cross-price elasticiities of demand respectively. and ii., is the consumption elasticity. (2) The three goods are gross substitutes in consumption so that all cross price elasticities Bi,j, i, j=: h, x, WI,p are positive. (3) The consumption elasticities B,,C are unity, i.e. the indifference curves are assumed to be homothetic. Using these properties, the model can be soived for D,_ and Dh_,. i.e. the ~lmsticity of homegood prices with res;=rect to changes in the price of the exported or imported good. This is achieved by total differentiation of eqs. t 1 J. (3). and (4b).
L.7: Katseli-Papaqlstratiou,
External
price disturhmres
363
With P,, and P, exo;:cnously deter.mrned, and dA4 =0 in the short-run, flow-equilibrium version of’ the model, the model reduces to a system of two equations in two unknowns, namely the percentage change in home-good prices and the change in income.
2.1. EJjficts on home-goad The elasticity good prices is
D
prices
of home-good
prices
B,,.P,Hd+P,XS(l
with
respect
+E,)m,(l
to each of the traded-
-Ak)
h’X=(~h-l)PLWd+~~~S(l+Eh)(l-mk(l-j.k)j
(8)
and D
Bh,mpf-wd h~np=(Bhl)PLHd+P,Hs(l +E,,)(l -m,T-i.k))’
(9)
where Ei>O;i=X,mp =real-wage elasticity of supply for home or exported B,>O =own-price elasticity of demand for home goods, BIT+ j > 0;j = x, mp = cross-price elasticities of demand, and m = p, “H” ?C
=marginal
propensity
to consume
goods,
home goods.
The following conclusions can be derived. (1) In the case where all commodities are final goods, home-good prices respond positively to increases in the prices of either exported or imported commodities, provided that the marginal propensity to save out of income is less than unity (UC 1) and that all three goods are gross substitutes in > 0, and consequently B,, > 1). consumption (B,,, x, B,,. mp upon this The unambiguous nature of the result s is largely dependent latter assumption. If imports are complemeiltary io home goods. so that B h.,,,p ( t‘,.,“,,, 1.
361
l_..T.Kc.tssli-Pa,._.‘.,;ratiou. J~xrernal
prtct
ci;:rhIr .rs
demand (B,,,X and B,, mpj, ti,t: marginal propensity to consume non-traded goods (m,), and the real-wage elasticity of supply for export-type goods (E,). (3) The denominator in both (8) and (9) is exactly the same and represents substitution away from home goods both directly, as their price starts rising (given by (Bh- l)P,Hd)., and indirectly through the income effect (given by P,H”(l +E,)(l -m,(l -GLk))). The higher is E,, the :larger beconies the indirect inci;me effect, saving, and the demand for traded commodities; thus, excess demand for home goods decreases as E,, increasles, dampening in the process the responsiveness of home-good prices to exogenous price increases. (4) Finally, in complaring the responsiveness of home-good prices to increases in the prices of either exports or imports.. we should note that unless B,. mpis VC’L‘~ large relative to B,,, and unless m,,--+O,home-good prices will rise more with an increase in the price of exports rather than with an increase in the price oi imports. This, of course, would be true in an economy which does not produce domestically any or very little of its imports.
1.2. Ejfects an incamr und :he balance of payments As was shown before, in a one-asset mode1 saving is equail to the rate of accumulation of reserves. Therefore, in the short run, while the stock of money is held colnstant,
d(Ed)=dS==E,kdY. The change in the rate of accumulation of reserves has to equal the change in the level of saving which in turn must equal the change in income times the marginal propensity to save. The above suggests that the implications of exogenous price disturbances on the balance of pa:yments can easily be inferred by solving the system for (d Y,‘dPi)Pi, ~1lere i -s’, mp, and multiplying the solution by A!- It follows that d(ER) =
B,,,cP,x(l +E,)+lP,H”(l +E,,)I+Bh,mpP XS(l +E,)+ (1 +E*)P,X”(l +E,)
jk
x
-[
(B,-1)$(1fE,)[l-m,(l-ok)]
-
I
(10)
L.‘I’:Katseii-Papaefstratiou,
and
External
B h,mpww (B,,- l)+ (l+E,)[l
price
+m -m,(l
disturbances
-iA)]
365
F!c!!! 1 P,,
-
(11)
Thus, in the case where traded goods are final goods, increases in foreign prices result in a balance-of-payments surplus as income and hence saving increases in the process. The unambiguous sign regarding reserve changes depends critically again on the assumption of gross substitutability. Finally, as was the case earlier, the value of the elasticity parameters of the system critically affects the magnitude of the ensuing surplus in the balance of payments. Having analysed the implications of external price disturbances for the price of non-traded goods, income, and the balance-of-payments, we now move to the case ol!’intermediate-good imports. 3. Transmission goods
of’ price disturbances
when traded goods are intermediate
The purpose of this section is twofold: (a) to introduce imported intermediate goods. into the general traded/non-traded goods model and (b) to study the channels through which exogenous price increases of intermediate good; affect the domestic economy. IL will be left to the fourth section of this paper to compare the results of sections 2 and 3. It is assumed l;hrougho:Jt that the country in question imports only intermediate goods which are then used solely in the production of home goods. One could think of a rudimentary economy whose exports consist mainly of agricuP:ural goods and which imports, say oil, for its domestic transportation services. The restrictive nature of the assumption is helpful in that it facilitates a close comparison between the two polar cases of trade compo4tion. If domestic factors and the imported inputs are gross complements then the home-good sector can be characterized by a fixed-proportions production function in which it takes one unit of the imported commodity to produce one unit of home goods. Oil imports provide a good example since there exists a srlbstant;:al and growing body of econometric evidence which suggests that ener;;y inputs are complementary io domestic factors [Berndt and Wood (1979)-j. Capital (fixed in the short run) and labor are assumed to be substitutes both in the export-good sector where these f&tors are the only ‘WC)inputs, ;is well as in the home-good sector where imported inputs are Aso needed. The production functions for both domestically produced goods can therefore be written as follows: In the export-good sector,
and in Ihe home-good
sector,
The assumption thal all imports are used in home-good production implies that G’,,,or the percentage of imports used in this sector, is eqL?al to one: in addition to that, the input-output ratio, namely b,,, can also be assumed to equal unity. Profit-maximizing behavior in the home-good sector suggests that entrepreneurs equate the nominal wage to the tzrt value of marginal product,
w=
(Ph--Pm,,)F;,(L).
where, as before, the price of imports is tied to the world price level through a fixed exchange rate. Thus, the suoply function for home goods become:
In the export-good marginal product, or
sector
the
nominal
wage
is equated
to the
gross
W=P,FI,(L), where again the price of exports is tied to the world price level. The supply function for exports. therefore. is
Gross output in this ecor.;,my (Q) is equal to the total value of production in both Bettors, while gross national product or value added (V) is equal to the taluc of gross output ~IIEICISthe value of intermediate imports. Hence.
v=P,~x”+- (P,,- P,,*,)H”. e abo\c
set of assumptions
and
the whole
treatment
of intermediate
goods in the production process follows closely the work by Findlay and Rodriguez ( 1977). The following seven equations describe fully the model with imported intermediate goods when these are gross complements to domestic factors. Non-traded
good sect01
H” Bulunce-of-p
c
w
I-
4, -en,
Hd[Ph,P,, C] = 0.
(1’)
vments equut ion
- Xd[P,,
P,, c] -$-
I
MPd
(2a’)
where
(2b’) Gross nutionul product V= (PjyP”,,)w+P,X”.
(3’)
v=c+s,
(4’)
S=j.[kV-
M],
(42)‘) (4b’)
hj=E&o.
(5’)
Prices P,=:EP,*. P,,,, = EPI*p.
(6’) (7’ )
Eq. (1’) describes the market for non-traded goods which clears continuously. Eq. @a’) is the balance-of-payments equation where the only new feature is a derived demand for imports which depends on the supply of home goods and hence the net real wage in the non-traded-good sector. The
L 7: Karseli-PrrpaqislrLltiou. Esternnl
368
tiisfur,‘;dnces
price
ITOWexcess supply of traded goods is translated into saving or a flow excess demand for money through the following manipulation of eq. (2a’):
Replacing V by eq. (3’), it follows that x”
--
I’,X”+P,H’-P,,MPd-P,Hd-S
P,, _plp=~
px
so that
x
- x
s=ER. or saving is equal to the rate of accumulation of reserves. Eq. (3’) is the equation for value adde d, eq. (4’) is the income identity, eq. i4a’) is the saving ft?rlction,‘4 and eq. (5’) is the money market clearing equation. The above system can be solved for the elasticity of home-good prices with respect to export- or import-good prices. 3 I. E$ect.s on ham?-good prices The solutions for the foreign-price elasticily of home-good ZZ.u,nrp are given in eqs. (8’) and (3’) r~clow: ip
‘II.r
=5,..P,HJ+P,X”(1
+E,)m,(I
prices Zh,i, i
-i.k)
~8’,-1)P,Hd+P,H”(1+~~)(l-~?Ih(1-~k~~fP,,N”Ehpmp
P h--
p mp
and E,f,,P
%h.n,p =
6, -cl,
5
H"
--P,,,!W’(1
tB,,- 1 PhHd+PhHs(l
+E,)m,(l +E,,)(l
-4.k)
-ni,J
-,:k))+P,,H”I:‘,~
P h-
n,p’
(9’)
L. ‘11KLltsrli-Papac~~trutiou,
E?cttvml price disturbancx~.~
369
where E, ~0 -elasticity of supply of home goods with respect fo the net real wage, E, >O=elasticity of supply of home goods with respect to the real wage. B, > 0 = ho’me-good price elasticity of demand, B,,. I > 0 = cress-price elasticity of demand, and
f3Hd
-=marginal m,=p, (qc
propensity
to consume
home goods.
The first consideration is the direction of change of the main endogenous variable, namely the price of home goods. As the price of exports rises, the price of home goods unambiguously rises (Z,,, >O) as a result of gross substitutability in consumption, a positive value added in the home-good sector, and a positive marginal propensity to consume out of totzl income. The direction of change is not unambiguous, however, in the case of price disturbances which affect the imported intermediate goods. In that case, supply-inflationary effects are coupled with demand-deflationary pressures.’ ’ Home-good prices will increase or decrease depending on whether the reduction in the supply of home goods, represented by ensuing E,P,,P,Hs/(P,-Pm,,), outweighs the reduction in demand for home goods. n,presented by P,,MP( 1 +E,)m,(l - i-k). It can be easily shown (appendix 1) that for Z,_,$O,
&,Hd-&W’)(l
E
hz
--J-Q
(1-;1k)P,X”+Uz
*
For .2,,_ >O, the elasticity of supply for homr: goods wiih respect to the net real wage must be greater than the ratio of consumption expenditures out of value added to the sum of expenditures out 0‘:’income created in the exportgood sector and out of asset holdings. This condition determines the domestic inflationary impact of a rise i;l intermediate good prices; its sign is based on the structural characteristics cf an economy in the area arou.ld initial equilibrium. From the above discussion it follows that if the elasticity of supply with respect to the net real wage is zero then home-good prices must necessarily ‘“AS the
left
will
be shown
since
nscessarily
value
drop.
below (section added
3 2) the aggregate demand
unamblguoualy
drops.
It
1s thus
curlc shown
un;tmbiguc~u~ly that
nt~l\c\ to
ctnplo>mcnt
tttuxt
fall. If l& =O, then
2
-_
-
P,,MPm,(I ___
- dc) -____
“.“‘r(,-l)P,Hd+P,H”(I-nl,(l-Ik,l’
which is negative. In economic teims, if there is no redtiction in supply owing to the increase in inpul: prices, then the demand-deflationary effects will dominate and the price of home goods will unambiguously Ml. Furthermore, if the price elasticity of demand for home goods is zero or B, =O. then the dirlect substitution effect from home goods to exports is eliminated. the dem:lnd curve for home goods is inelastic, and the change in the price of home goods equals the exogenous increase in the price of imports or dP, = dP,,p. In conclusion it should be noted that while the domestic effects of an increase in the price of exports are clearly inflationary, this is not necessarily true for increases in the price oE intermediate goods. The direction of change of home-good prices crucially depends on the magnitude of the price elasticity of supply CT home goods with respect to the net real wage; ceteris paribus, ~hc moic Jastic the supply the more inflationary the outcome. We can now turn to the income and balance-of-p;:jments effects of exogenous price disturbances in the case where impor;ts are intermediate goods and press complements to domestic factors.
it has been shown that in the short run, when the stock of money is mnstiint.
d(EI?):=dS=i.kdV, c r that the change in the balance of payments is equal to the marginal propensity to save times the Ichange in value added. Thus,
P,X'(
1 +E,)
__._.~.__
(B,-l)+(l--m,(l-ik))(lfE,)+E,~h-
cf px px
rn~
: 10’)
an expression which is unambiguously positive given the usua! assumptions. Incre,ases in the price of exports result in a posilive rate of accumulation of reserves or a surplus in the balance of payments. Increases in the price of the imported intermediate inputs, however, unambiguously result in a balance-of-payments deficit as can be seen from eq. (11’): d(,?%)=Ak
‘I.
d’ .% dP”,,IP?n, P,,
r
-
That the balance of payments as follows. From eq. (3’)
dV=P,X”(l
deteriorates
fixed, =
-+P,H”(l+E,)+P,H”(l
dP,P h rEh)dP-iP-.
h
mP
would For this expression to be positive, dP,/dP,,, one. But from the Z,,_ solut.ion we know that -EhPmPPhHS dPh --
=-
ph
wf,pen,
_____
kh
-
BhPhHd-_,,HS(l
-P,PMP(l
___..___~ +Eh)m,,(l
~~
-kk)+2+pTh
+E,)m,(l
than
-E,k)
+Eh)mh(l
pntP
For this to be greater t han one it would be necessary
‘E P P H” Ph --PTP!---P,,,MPil .I mP
mP
have to be greater
:
(.
can be proved
+E,)
With P, exogenously dV -.-I___ dPfll,IP,,
unambiguously
-i,k)
or that P,,B,P,H"
nlP
that
!
to the assumptions
and
Therrfore, value added has to decrease with an increase in the price of the intermediate input and this will sesuii in an unambiguous deficit in the balance of paymenis. Mow sensitive are the results obtained above to the underlying assumption in prcpduction among imported inputs and of gross compiementarity dwxsk factors? It can easily be seen that they will hold for all cases in which the elasticity of substitution between imported inputs and domestic faclori is less than unity. T!re nested Cobb--Douglas production function H”= @“L’ -“]‘MP’ -Y provides the borderline case. Mere the share of value added and imported inputs (MP) is constant. Thus, an increase in tie price of the intermediate good will have no direct effect on value added. Value added will increase only indirectly once the price of home goods increases due to the suppiycon!rac!ionary effect. It is thus clear that under a Cobb-Douglas case the price and balance-of-payments effects will be similar to those obtained in the case of final imported goods; thus, the price of home goods will rise and the balance of payments will improve as value added and hence saving, increases. There is, however, at; important difference between the two cases: in the final-good case the change ~1 relative prices shifts the demand curve for home goods outward and unambiguously increases real ojltput (H’); in the case of intermediate goods real output will increase only if the indirect increase in value added and overall demand is sufficient to outweigh the contractionarysupply effect. Thus, even in the case of a unitary elasticit!, of substitution between inputs and domestic factors, an increase in the price of intermediate goods will probably lead to stagflation.
4. Comparison of results and conclusions The major difference rn the specification of the cases presented in sections 2 and 3 lies in the treatment of imports. While in section 2 imports’ are final goods, they are intermediate goods in section 3. Income in the first case equals the total value of production, whereas income in the second case equals value added. Furthermore, whereas B,*- 1= Bh,.rl+ Bh_., and C = P,Hd c P, .Y” i P,, .IlP“ in the first case, in the case where imported goods are inptits. B,- 1 = R,.,, and C =P,,Hd + P,Xd. Thus, for given values of homeg:)od and export-type-good consumption, aggregate consumption in section 3 I\ ~rnaller than aggrei.ate consumption in section 2 (C,
own price elasticity of demand (BhJZ -C(.B,,x)3. Table 1 contrasts and summarizes the major results derived in the previous x~tion~. These include the responsiveness of home-good prices to an ~~~Y~C”IY)UC import-price disturbance (DA,n,p and Z,,.,,p)r the corresponding ~~i~~rnce-oh-pavrmc~ts effects (dB’dP,,P,,,), and th:: effects on real output or ~~~~~~~~~,~e~~ (d!l’ dP,,P,,).
LT. Katseli-Papae~strutior;.
Externul
Table The composition
price dis~urhanws
1
of trade and transmission
Final-good
imports
373
of price disturbances. Intermediate-good
imports ___--
Imports and domestic goods or factors are gross substitutes
(B,,,,D)
(a$11
4mp20
Z h,tW?‘O
dB ___ dP,p
Pm,20
dB dPmp
Pm,>0
dH’ -&y P,,LO mP
-
Imports and domestic goods cr Factors are qoss complements
mI,tnp
(a
D h.“lP
z,. mp?
dB dP,p
Pm,<0
(1) If all final goods are gross substitutes in consumption then an increase in their price causes home-good prices to rise unambiguously, regardless of deflationary real-balance effects. Real output unambiguously rises and the balance of payments improves. Complementarit;, in consumption between traded and non-traded goods reverses these conclusions. The unambiguous direction of change rests on the following assumptions: homogeneity of degree one with respect to income and wealth in the saving function and homogeneity of degree zero in prices and consumlation in the demand for home goods; given these assumptions one can translate freely between nominal and real terms, at least on tht: demand side. (2) The direction of change of home-good prices is positive if imports arc intermediate goods and gross substitutes to domestic factors. The balance of payment; will improve but, contrary to the corresponding final-good GM. the real output or employment effect ,ti!ill be ambiguous. (3) If imported inputs are complementary to domestic fitctors, the price effect rather than the output effect will be ambiguous. The ambiguity iiriscs not because of opposittt-signed effects on the demand side but because of the simultaneity of inflationary supply-side and def!rJtionary demand-side effect>. A ‘la,pge enough’ elasticity of supply with respect to the nci real wage ii!ill will ensuxe a positive direction of change. The balance of payment unambiguously deteriorate and real output (and employment) wili L.!l. This will be the pertinent case for the analysis of an oil price inc:ease.
The above results illuminate the discussion around potential contradictions tween ecozlomic theory and reality which are based on the contention that the monetary approach to the balance of payments cannot explain the appearance of deficits as a result of the oil price increase in the early 1970s. As we have shown, the theory is, in this case at least, totally consistent with facts. The anaitysis also explains why small and open economies are much rnrx-e vulnerable to oil price increases than to increases in the price of imported finaii goods. Apart from the inevitable balance-of-payments deterioration, increb-ds in the price of intermediate goods can result in stugflation as the irxreased cost in production is coupled with a reduction in national income and demand.
Appendix Home-good prices will increase (decrease) if
E,P,H"P ------__"_p~Pm,MP(l CE,)m,(l-U). pi-
(1”)
pmp
Srnct: Hd= H'= !W by assumption, and the marginal propensity to consume, Q,, i:, equal to the average propensity to consume so that m,,= P,Hd/C, eq. t 1”) becomes equal to
1+-E,, --= Eh
c ~____-
=-(Ph-Pmp)Hd(l
(2”)
-ikj’
Since
it follows that E
z!PhHd-f’mp~fW --j-k) h-c
(1 -ik)P,X'+iM
*
igliapi, !963. The life cycle hypothesis of saving: Aggnegate inqlications Economic Review, March, 55-84. Wood, 1979, Engineering and econometric interpretations of energy rlty, American Economic Fieview 3, 342-354. Asset markets and relative prices in exchange rate detumination, %VJBG!U ~~~e~~c~af?~~c~,e Annalen, Band I.
Branson, W.H. and L.T. Katseli-I’apaerstratiuu. 19X0. Income instahihty, terms 01’ triidc and the choice of exchange rate regime, Journal of Development Economics 7. 49 69. Buiter, W., 1978. Short-run and long-run crfects of external disturbances under a Ilonting exchange rate, Economica 45, 25 l--272. Connolly, M. and D. Taylor, 1976. Adjustment to dwaluation uith money and ncw~rndcd goods, Journal of International Economics 6. August. Corden, W.H. and R.W. Jones. 1976, Devaluation. non-flexible prices and the trade balance ~OI a small country, The Canadian Jnurna: of Economics 9 (I ). I‘ebrunry. i 50 I 61. Dornbusch, R.. 1973a, Devaluation, money and nontraded gwds. American I~connmic Ruviw 63. 871~-880. Dornbusch, R., 1973b. Currency depreciation. hoarding and rclatiic price\. Journ:l! of Political Economy 81, July/August, 843 917. Dornbusch. R., 1976, Expectations and exchange rate dynamics. J~wrnal ol” Political f:ccwom) 84, no. 6. Findlay. R. and C. Rodriguez.. 1977. Intermediate imports and macrwconomlc policy under flexible exchange rates, Canadian Journa! of Economrcs IO. May. XX 217. Goldfcld. S., 1973. The demand for rnoney revisited, Brookmgs Papers on Economic Actlslty 1. Harberger, A., 1964. Some notes on inflation. in: W. Baer and I. Kcrstcnetzky. cds.. Infla~lc~rl and growth in Latin America (R.D. Irwin, Homewood, Illinok). Katseh-Papacfstratiou, L.. 1979. Transmission of external price disturbances in sm;\ll I~KII economies, Ph.D. Dissertation, Princeton University (Garland Press. New York ). Komiya, R.. 1967, Nontraded goods and the pure theory of intcrnaticwal trade. Infcrnatlon;lI Economic Review 8, 133 152. Kouri. P.J.K., 1976. The exchange rate and the balance of payments rn the short run and 111the long run: A monetary approach, Scandinn\ian Journal of Ewnnmrcs 2. Krueger, A.. 1974, The role of home goods and money in c~chu~~gc rate ;Idjustmcn14. 111' W. llonc~~~r 01‘ Jill1 Tlnhc-gcn Scllckaerts. cd., International trade illld finance: Essay5 in (Macmillan Press. London) 131 161. Rodriguez. C.A., 1977, Flcxihle exchange rate? ;Lnd impc)rtcd inputs: A dynamic anal>\I\ ()I’ IIlL‘ ccclrl~u~l). TllC and real sectors fool ;I \lmill cqw1 interactions bctwcen the monctaq Economics Workshop, Columhla !!ni\crsitk. Dircuwon Paper 76-770X. Whitman. M., 1975. Global mcrnct;lrism and ths monetary appro;tch 10 Ills hal~mcc of paj111cr1t\. Brookings I’apcrs un Economic Activity 3. 121 166.
c
of International
Economics
10 (1980) 357.-375. 0 North-Holland
Publishing
Company
TRANSMISSION OF EXTERNAL PRICE DISTURBANCES AND THE COMPOSITION OF TRADE Louka
T. KATSELI-PAPAEFSTRATIOU*
Yale Yniocrsity,
Received November
New Hauen, CT 06520, USA
1978, revised version received December
1979
This paper focuses on the role of trade composition in the transmission of external price disturbances. It is shown that the effects of an increase in the price of imports on domestic prices and the trade balance crucially depend on the cross price elasticity of demand in the case of final goods and the elasticity of substitution between factors in the case of intermediate goods. In the case of an input such as oil, where the elastici’y of substitution between imported and domestic factors of production is less than unity, an incre.;se in its price will give rise to a balance-of-trade deficit but will have ambiguous effects on domestic prices.
1. Introduction The impact of exchange-rate movements on the domestic economy has been one of the most popular and controversial topics in internationrl finance. The degree and time-path of internal adjustment following a oneshot change in the relative price of the domestic currency, has been a major point of contention in the debate between proponents of the ‘elasticity”, ‘absorption’, and/or ‘monetary’ approaches to the balance of payments.’ The explicit introduction of non-traded goods into macroeconomic modelling. most notably by Komiya (1967), Dornbusch (1973a, 1973b), Krueger (1974). Corden and Jones (1976) and others has further expanded and enriched the traditional analysis. It was the move towards flexible exchange rates in 1971 and the fourfold increase in the price of oil in 1973 tlrat caused a gradual shift in emphasis towards (a) a systematic re-examin:ltion of exchange-rate determination [Dornbusch (1976), Kouri (1976), branson (1977)], and (b) the explicit introduction of imported intermediate inputs in macroeconomic analysis [Findlay and Rodl.iguez (1977), Rodriguez (1977), Buiter (1978)]. A further
*I am indebted to Peter B. Kenen, William H. Branson and an anonymous comments and suggestions. ‘For a good overview of alternative approaches to brllancr-of-p~lyments Whitman (1975).
referee for hcIpfuI adjustment.
CC
consequence ot these developments, has been the increasing focl:.s on foreignprice movements as the primary source of exogenous shocks to the system, a role up to now principally attributed to exchange-rate disturbances. This paper a.dopts a similar viewpcint and addresses itself specifically to in the transmission of el;ternal price the role of trade composition p* on the short-term responses of home-good disturbances. The analysis focus,s prices, nominal income, and the balance of trade to an increase in import prices and compares these responses for two polar cases: when imports are final goods and when imports are intermediate goods. The first case is treated in section 2 while the second is taken up in section 3. The comparison of results in section 4 highlights the qualitative differences that can be attributed to the composition of trade. The basic model extend; the Dornbusch (1973a), Connolly-Taylor (1976) models in two directions: (a) it incorporates a supply-side into what are essentially demand-side models and (b) it replaces thle classical fullemployment assumptions with Keynesian assumptions of wage stickiness and More importantly, it’ focuses, in a way similar to unemployment.2 Harberger’s [ Harberger (1964)], on those structural characteristics of an economy whose magnitude determines the overall effect of external disturbances on the target variables chosen. The model presented here, both in its formulation and the conclusions derived therefrom, can be viewed as complementary to the work of other authors [Findlay and Rodriguez (1977), B~itcr (1978)) in the sensie that these studies share a similar methodology in the pursuit of different objectives.3 To make the exposition clear and concentrate on the composition of trade issue, a number of simplifying assumptions are made: the country in question is assumed to be ‘small’, i.e. a price-taker in both export and import markets.’ Exchange rates are assumed fixed so as to focus exclusively on the transmi:ssion process of external price disturbances. It could aLlso be argued that most small and open economies still peg their exchange rates to that of their major trading partner either because of feasibility or optimality ‘Full cmplolment as\ump!ions were incorporated itl an earlier version of this model [KatseliP; pacf\trtltiou f 197911. The endogeneity of wages changes the solutions quantitatively but does nc~: ;tiuh m important qualitatice differences. ‘E-~ncil~!, and Rodriguez ( 1977i 17;~-.ribe a one-sector econon.y which is large eno. ;h to affect 11%term< \~f trade and k charxt:r’-ed !q flexible rather than fixed exchange rates. They are mtcreGed m macro-policy effectiveness when imports are intermediate goods. They also look at r!~ sflc~ts 0; an exogenous price increase on the domestic economy but their analysis is ccmducA at a highly aggregate levei. Buiter (1978) analyses the effects of a number of external Iyturbances on output, employment, and the price level under a freely floating exchange rate ra.gbmc. The asset markets are fully developed and there are no non-traded goods. His e~mcIu~sun~ regarding the e!Tect!; of an oil-price increase on the domestic economy are analogous 1tj 113t~ 4uhth4i p;_‘pcr. i tpr .an LIZ> VLLI~to ln~rorporate non-small country assumptions into a macro-model, see Branion and E;aa~elr-Papasf~traItiou (1980).
L.T. Katseli-Papaej?tratiou,
External
price disturbances
359
considerations.’ The government sector is left out of the analysis Atogctllet so that changes in the money stock reflect solely changes in the level 01 reserves6 Imported intermediate goods are used in home-good production only, rather than in the export-good sector. ’ Finally, only the comparative static results are presented and compared here while the long-run steady state implications of the model are worked out elsewhere [KatseliPapaefstratiou (1979)]. The basic conclusions derived in this paper can be summarized as follows: If imports and non-traded goods are gross substitutes in demand, an increase in the price of imported goods will cause an increase in the price of nontraded goods and a surplus in the balance of trade;’ if instead imports and non-traded goods are gross complements, the price of non-traded goods will typically fall and the balance of trade will deteriorate. If in:ports are intermediate commodities, the effects on the price of home goods and the balance of trade will depend on the elasticity of substitution betwe:! factors of production. If the elasticity of substitution between domestic factors and the imported input is greater than unity, an increase in the price of the input will reduce its share, increase value added and the price of home goods, and cause an improvement in the balance of trade. If the elasticity of substitution is less than unity, as in the case of imported oil [Berndt and WooId (1979)], the effect on the domestic price level will be ambiguous while the balance of trade will unambiguously deteriorate. The ambiguity is due to the appearance of supply-inflationary in addition to demand-deflationary effects. The results obtained in the two polar cases of trade composition are not completely symmetric. In the first case an external price disturbance is simply translated into a demand-side disturbance leaving the supply side unaffected; in the case of imported intermediare goods, however, either the emp4oyment or the price effects become ambiguous as a result of both demand and supply-side disturbances. Thus. both the composition of trade and the ret: ,uilt substitutability between goods or factors are important parameters in the transmission of external price disturbances. A cursory view of countries’ trade composition seems to suggest th:it some “For a detailed discussion on the choice of exchaltgc rate regime. see Branson an3 KathcliPapaefstratiou (198(i). ‘The introduction of the government sector is treated in Katseli-Papaefstratiou (1979. ch. 2). ‘If imported inputs were used in the export-g,ood sector as well. then an incrcasz ir; the pr~cc of imports would result in even more pronounced effects on inc:omc than is the cast now. Gncc value added in tha sector would be affected. Increases in the price of the final good wtruld probably increase output and have ambiguous effects on income and the balance of trade as demand for intermediate inputs will increase. “The results obtained here for the final-goods case are in sharp contrast to those, of Connollq and Taylor (1976). In their model the presence of a substitution and a liquidity effect in the demand functions make the impact of an exogenous price disturbance on home-good prices in ambiguous. This acibiguity is resolved here due to the assumption of gross subitiluiabilltg consumption
between the three types of goods.
countries are signi5cantly more dependent upon intermediate imports than others [Katseli-Papaefstratiou (1979)]. These differences provide a partial explanation for the differential cross-coumry responses to exogenous price disturbances and in that way the framework of this paper can provide a starting point for more empirical work on the subject. Section 2 of the paper analyses the final-good case under various elasticityof-demand assumptions.; section 3 works out in detail the intermediate-good case when imports and domestic factors are gross complements, and case of a Cobb-Douglas discusses briefly the ;nore straightforward production function with unitary elasticity of substitution between factors. The results are compareId and summarized in section 4.
I. Transmission of price disturbances when traded goods are final goods
Let us assume that a small and open economy consists of two sectors: a sector for traded or intlernational goods (I) and a sector for non-traded or home goods (H).9 For reasons of comparison with the case of imported intermediate goods, traded goods can be further decomposed into an exported good (X) which is produced at home but consumed domestically or abroad and an imported good (_ ‘) which is produced abroad but consumed at home.” All three gooc *e final goods and gross substitutes for each other.’ ’ The seven equations presented below can fully describe the workings of a simple economic system where apart fiom the goods’ markets there exists one asset, namely money, and a labor market that is characterized by an infinitely elastic supply curve. Superscripts denote supply or demand of a particular commodity or factor while subscripts denote the type of good in question. Bars above such variables as the nominal wage (W) and the exchange rate (E) imply that these variables are held constant throughout. An asterisk denotes an exogenous variable such as foreign prices and a dot o\.er a variable implies its rate of change.
“The terms ‘traded and ‘non-traded’ are preferred here to the ambiguous terms ‘tradeables’ snd ‘non-tradeables’. Also. the terms ‘home’ and ‘non-traded’ goods are used interchangeably. t-(pr a dr~us~m on the often confusing use of these terms, see Katseli-Papaefstratiou (1979). “‘The dccompositron of traded goods into exported and imported commodities is justified on e+1rnp3r~~t~:crather than ;Inalytlcal grounds. The same holds tr::e for our assumption that there :%II~) Import-compettng production. ‘-The a\s!mptlon of grow >ubstltutability is relaxed in section 2.1 below.
L.?: Katseli-Papae&stratiou
Balance-of-payments
X”
Cxternal
price disturbances
361
equation
F - Xd[P,, P,, Pmp,C] -YEx
L-1X
[Ph, P,, Pmp, C] = -:c,
(2a)
where -P,x=S-E.[kYGross domestic
Ml=,%.
(W
production
Y=P,M”+P,X”.
(3)
Income identity Y=C+S, where S=A.[kY-
M],
(44 (4b)
Money market
It&-Ek=O.
(5)
Prices p,=EP,*,
(6)
P,, =EP&
(7)
Eq. (1) describes the market for :lorne goods which clears continuousl:/. The supply of home goods is simply a function of the own real wage, while demand is a function of relative prices and nominal consumption expenditures which al-e equal to aggregate income minus desired saving. Eq. (2a) is the balance-of-paymentsI equation with - .K describing the flou excess supply of goods which is then translated in eq. (2b) into a flow e:{ccss demanJ for money. If desired money holdings (k Y) exceed the stock of mon::y available, M, consumers will reduce their expenditures, i.e. save, to restore their desired cash positions. The speed of adjustment is described by parameter ;1. 121n the absence of transfer balance of payments.
payments
and capital
movements
the balance
of trade
IS rhc
362
L.7: ELmeli-Papuefsit
~ltlou, Extcn-ml price disturbances
It is easy to prove that E!?, the rate uf accumulation equal saving by rewriting eq. (2a) in the foliowing form:
of reseraes, has to
Substituting eq. (3) into the above equation, it follows that
Finally, eq. (3) gives the value of total domestic production, eq. (4) describes the income identity, eq. (5) the money market, and eqs. (6) and (7) fix the domestic prices of exported and imported commodities to their foreign levels through the exchange rate, E, which is taken to be fixed. Two additional points should be made here regarding the specification of the saving function Ceq. Wl.
(a) Saving is dependent upon both income (Y) and wealth (M). The marginal propensity to sawe out of income (S,,=aS/aY) is positive and equal to ik whereas the marginal propensity to save out of an increase in wealth is negative and equal to minus the speed of adjustment I., or, SW= -A. (b) The specification is consistent with the more general and usual specification of the saving function described by Ando and Modigliani (1963) where S= &I =x1 1 -r,.,!4. In this present framework the coefficient a1 is equal (0 ik and ‘x2 is eqrial to I.. Thus, coefficients (x1 and a2 are not independent parameters:; in the steady-state solution of the model a1 = kor, or k is equal to the ratio of the two coeficients. The demand functions possess the following properties: (1) They are homogeneous of degree zero in all prices and consumption, so that -Bi+CBi,j=-Bi,c; j
i, j = h, x. mp,
where Bj and Bi j are the own- and cross-price elasticiities of demand respectively. and ii., is the consumption elasticity. (2) The three goods are gross substitutes in consumption so that all cross price elasticities Bi,j, i, j=: h, x, WI,p are positive. (3) The consumption elasticities B,,C are unity, i.e. the indifference curves are assumed to be homothetic. Using these properties, the model can be soived for D,_ and Dh_,. i.e. the ~lmsticity of homegood prices with res;=rect to changes in the price of the exported or imported good. This is achieved by total differentiation of eqs. t 1 J. (3). and (4b).
L.7: Katseli-Papaqlstratiou,
External
price disturhmres
363
With P,, and P, exo;:cnously deter.mrned, and dA4 =0 in the short-run, flow-equilibrium version of’ the model, the model reduces to a system of two equations in two unknowns, namely the percentage change in home-good prices and the change in income.
2.1. EJjficts on home-goad The elasticity good prices is
D
prices
of home-good
prices
B,,.P,Hd+P,XS(l
with
respect
+E,)m,(l
to each of the traded-
-Ak)
h’X=(~h-l)PLWd+~~~S(l+Eh)(l-mk(l-j.k)j
(8)
and D
Bh,mpf-wd h~np=(Bhl)PLHd+P,Hs(l +E,,)(l -m,T-i.k))’
(9)
where Ei>O;i=X,mp =real-wage elasticity of supply for home or exported B,>O =own-price elasticity of demand for home goods, BIT+ j > 0;j = x, mp = cross-price elasticities of demand, and m = p, “H” ?C
=marginal
propensity
to consume
goods,
home goods.
The following conclusions can be derived. (1) In the case where all commodities are final goods, home-good prices respond positively to increases in the prices of either exported or imported commodities, provided that the marginal propensity to save out of income is less than unity (UC 1) and that all three goods are gross substitutes in > 0, and consequently B,, > 1). consumption (B,,, x, B,,. mp upon this The unambiguous nature of the result s is largely dependent latter assumption. If imports are complemeiltary io home goods. so that B h.,,,p
361
l_..T.Kc.tssli-Pa,._.‘.,;ratiou. J~xrernal
prtct
ci;:rhIr .rs
demand (B,,,X and B,, mpj, ti,t: marginal propensity to consume non-traded goods (m,), and the real-wage elasticity of supply for export-type goods (E,). (3) The denominator in both (8) and (9) is exactly the same and represents substitution away from home goods both directly, as their price starts rising (given by (Bh- l)P,Hd)., and indirectly through the income effect (given by P,H”(l +E,)(l -m,(l -GLk))). The higher is E,, the :larger beconies the indirect inci;me effect, saving, and the demand for traded commodities; thus, excess demand for home goods decreases as E,, increasles, dampening in the process the responsiveness of home-good prices to exogenous price increases. (4) Finally, in complaring the responsiveness of home-good prices to increases in the prices of either exports or imports.. we should note that unless B,. mpis VC’L‘~ large relative to B,,, and unless m,,--+O,home-good prices will rise more with an increase in the price of exports rather than with an increase in the price oi imports. This, of course, would be true in an economy which does not produce domestically any or very little of its imports.
1.2. Ejfects an incamr und :he balance of payments As was shown before, in a one-asset mode1 saving is equail to the rate of accumulation of reserves. Therefore, in the short run, while the stock of money is held colnstant,
d(Ed)=dS==E,kdY. The change in the rate of accumulation of reserves has to equal the change in the level of saving which in turn must equal the change in income times the marginal propensity to save. The above suggests that the implications of exogenous price disturbances on the balance of pa:yments can easily be inferred by solving the system for (d Y,‘dPi)Pi, ~1lere i -s’, mp, and multiplying the solution by A!- It follows that d(ER) =
B,,,cP,x(l +E,)+lP,H”(l +E,,)I+Bh,mpP XS(l +E,)+ (1 +E*)P,X”(l +E,)
jk
x
-[
(B,-1)$(1fE,)[l-m,(l-ok)]
-
I
(10)
L.‘I’:Katseii-Papaefstratiou,
and
External
B h,mpww (B,,- l)+ (l+E,)[l
price
+m -m,(l
disturbances
-iA)]
365
F!c!!! 1 P,,
-
(11)
Thus, in the case where traded goods are final goods, increases in foreign prices result in a balance-of-payments surplus as income and hence saving increases in the process. The unambiguous sign regarding reserve changes depends critically again on the assumption of gross substitutability. Finally, as was the case earlier, the value of the elasticity parameters of the system critically affects the magnitude of the ensuing surplus in the balance of payments. Having analysed the implications of external price disturbances for the price of non-traded goods, income, and the balance-of-payments, we now move to the case ol!’intermediate-good imports. 3. Transmission goods
of’ price disturbances
when traded goods are intermediate
The purpose of this section is twofold: (a) to introduce imported intermediate goods. into the general traded/non-traded goods model and (b) to study the channels through which exogenous price increases of intermediate good; affect the domestic economy. IL will be left to the fourth section of this paper to compare the results of sections 2 and 3. It is assumed l;hrougho:Jt that the country in question imports only intermediate goods which are then used solely in the production of home goods. One could think of a rudimentary economy whose exports consist mainly of agricuP:ural goods and which imports, say oil, for its domestic transportation services. The restrictive nature of the assumption is helpful in that it facilitates a close comparison between the two polar cases of trade compo4tion. If domestic factors and the imported inputs are gross complements then the home-good sector can be characterized by a fixed-proportions production function in which it takes one unit of the imported commodity to produce one unit of home goods. Oil imports provide a good example since there exists a srlbstant;:al and growing body of econometric evidence which suggests that ener;;y inputs are complementary io domestic factors [Berndt and Wood (1979)-j. Capital (fixed in the short run) and labor are assumed to be substitutes both in the export-good sector where these f&tors are the only ‘WC)inputs, ;is well as in the home-good sector where imported inputs are Aso needed. The production functions for both domestically produced goods can therefore be written as follows: In the export-good sector,
and in Ihe home-good
sector,
The assumption thal all imports are used in home-good production implies that G’,,,or the percentage of imports used in this sector, is eqL?al to one: in addition to that, the input-output ratio, namely b,,, can also be assumed to equal unity. Profit-maximizing behavior in the home-good sector suggests that entrepreneurs equate the nominal wage to the tzrt value of marginal product,
w=
(Ph--Pm,,)F;,(L).
where, as before, the price of imports is tied to the world price level through a fixed exchange rate. Thus, the suoply function for home goods become:
In the export-good marginal product, or
sector
the
nominal
wage
is equated
to the
gross
W=P,FI,(L), where again the price of exports is tied to the world price level. The supply function for exports. therefore. is
Gross output in this ecor.;,my (Q) is equal to the total value of production in both Bettors, while gross national product or value added (V) is equal to the taluc of gross output ~IIEICISthe value of intermediate imports. Hence.
v=P,~x”+- (P,,- P,,*,)H”. e abo\c
set of assumptions
and
the whole
treatment
of intermediate
goods in the production process follows closely the work by Findlay and Rodriguez ( 1977). The following seven equations describe fully the model with imported intermediate goods when these are gross complements to domestic factors. Non-traded
good sect01
H” Bulunce-of-p
c
w
I-
4, -en,
Hd[Ph,P,, C] = 0.
(1’)
vments equut ion
- Xd[P,,
P,, c] -$-
I
MPd
(2a’)
where
(2b’) Gross nutionul product V= (PjyP”,,)w+P,X”.
(3’)
v=c+s,
(4’)
S=j.[kV-
M],
(42)‘) (4b’)
hj=E&o.
(5’)
Prices P,=:EP,*. P,,,, = EPI*p.
(6’) (7’ )
Eq. (1’) describes the market for non-traded goods which clears continuously. Eq. @a’) is the balance-of-payments equation where the only new feature is a derived demand for imports which depends on the supply of home goods and hence the net real wage in the non-traded-good sector. The
L 7: Karseli-PrrpaqislrLltiou. Esternnl
368
tiisfur,‘;dnces
price
ITOWexcess supply of traded goods is translated into saving or a flow excess demand for money through the following manipulation of eq. (2a’):
Replacing V by eq. (3’), it follows that x”
--
I’,X”+P,H’-P,,MPd-P,Hd-S
P,, _plp=~
px
so that
x
- x
s=ER. or saving is equal to the rate of accumulation of reserves. Eq. (3’) is the equation for value adde d, eq. (4’) is the income identity, eq. i4a’) is the saving ft?rlction,‘4 and eq. (5’) is the money market clearing equation. The above system can be solved for the elasticity of home-good prices with respect to export- or import-good prices. 3 I. E$ect.s on ham?-good prices The solutions for the foreign-price elasticily of home-good ZZ.u,nrp are given in eqs. (8’) and (3’) r~clow: ip
‘II.r
=5,..P,HJ+P,X”(1
+E,)m,(I
prices Zh,i, i
-i.k)
~8’,-1)P,Hd+P,H”(1+~~)(l-~?Ih(1-~k~~fP,,N”Ehpmp
P h--
p mp
and E,f,,P
%h.n,p =
6, -cl,
5
H"
--P,,,!W’(1
tB,,- 1 PhHd+PhHs(l
+E,)m,(l +E,,)(l
-4.k)
-ni,J
-,:k))+P,,H”I:‘,~
P h-
n,p’
(9’)
L. ‘11KLltsrli-Papac~~trutiou,
E?cttvml price disturbancx~.~
369
where E, ~0 -elasticity of supply of home goods with respect fo the net real wage, E, >O=elasticity of supply of home goods with respect to the real wage. B, > 0 = ho’me-good price elasticity of demand, B,,. I > 0 = cress-price elasticity of demand, and
f3Hd
-=marginal m,=p, (qc
propensity
to consume
home goods.
The first consideration is the direction of change of the main endogenous variable, namely the price of home goods. As the price of exports rises, the price of home goods unambiguously rises (Z,,, >O) as a result of gross substitutability in consumption, a positive value added in the home-good sector, and a positive marginal propensity to consume out of totzl income. The direction of change is not unambiguous, however, in the case of price disturbances which affect the imported intermediate goods. In that case, supply-inflationary effects are coupled with demand-deflationary pressures.’ ’ Home-good prices will increase or decrease depending on whether the reduction in the supply of home goods, represented by ensuing E,P,,P,Hs/(P,-Pm,,), outweighs the reduction in demand for home goods. n,presented by P,,MP( 1 +E,)m,(l - i-k). It can be easily shown (appendix 1) that for Z,_,$O,
&,Hd-&W’)(l
E
hz
--J-Q
(1-;1k)P,X”+Uz
*
For .2,,_ >O, the elasticity of supply for homr: goods wiih respect to the net real wage must be greater than the ratio of consumption expenditures out of value added to the sum of expenditures out 0‘:’income created in the exportgood sector and out of asset holdings. This condition determines the domestic inflationary impact of a rise i;l intermediate good prices; its sign is based on the structural characteristics cf an economy in the area arou.ld initial equilibrium. From the above discussion it follows that if the elasticity of supply with respect to the net real wage is zero then home-good prices must necessarily ‘“AS the
left
will
be shown
since
nscessarily
value
drop.
below (section added
3 2) the aggregate demand
unamblguoualy
drops.
It
1s thus
curlc shown
un;tmbiguc~u~ly that
nt~l\c\ to
ctnplo>mcnt
tttuxt
fall. If l& =O, then
2
-_
-
P,,MPm,(I ___
- dc) -____
“.“‘r(,-l)P,Hd+P,H”(I-nl,(l-Ik,l’
which is negative. In economic teims, if there is no redtiction in supply owing to the increase in inpul: prices, then the demand-deflationary effects will dominate and the price of home goods will unambiguously Ml. Furthermore, if the price elasticity of demand for home goods is zero or B, =O. then the dirlect substitution effect from home goods to exports is eliminated. the dem:lnd curve for home goods is inelastic, and the change in the price of home goods equals the exogenous increase in the price of imports or dP, = dP,,p. In conclusion it should be noted that while the domestic effects of an increase in the price of exports are clearly inflationary, this is not necessarily true for increases in the price oE intermediate goods. The direction of change of home-good prices crucially depends on the magnitude of the price elasticity of supply CT home goods with respect to the net real wage; ceteris paribus, ~hc moic Jastic the supply the more inflationary the outcome. We can now turn to the income and balance-of-p;:jments effects of exogenous price disturbances in the case where impor;ts are intermediate goods and press complements to domestic factors.
it has been shown that in the short run, when the stock of money is mnstiint.
d(EI?):=dS=i.kdV, c r that the change in the balance of payments is equal to the marginal propensity to save times the Ichange in value added. Thus,
P,X'(
1 +E,)
__._.~.__
(B,-l)+(l--m,(l-ik))(lfE,)+E,~h-
cf px px
rn~
: 10’)
an expression which is unambiguously positive given the usua! assumptions. Incre,ases in the price of exports result in a posilive rate of accumulation of reserves or a surplus in the balance of payments. Increases in the price of the imported intermediate inputs, however, unambiguously result in a balance-of-payments deficit as can be seen from eq. (11’): d(,?%)=Ak
‘I.
d’ .% dP”,,IP?n, P,,
r
-
That the balance of payments as follows. From eq. (3’)
dV=P,X”(l
deteriorates
fixed, =
-+P,H”(l+E,)+P,H”(l
dP,P h rEh)dP-iP-.
h
mP
would For this expression to be positive, dP,/dP,,, one. But from the Z,,_ solut.ion we know that -EhPmPPhHS dPh --
=-
ph
wf,pen,
_____
kh
-
BhPhHd-_,,HS(l
-P,PMP(l
___..___~ +Eh)m,,(l
~~
-kk)+2+pTh
+E,)m,(l
than
-E,k)
+Eh)mh(l
pntP
For this to be greater t han one it would be necessary
‘E P P H” Ph --PTP!---P,,,MPil .I mP
mP
have to be greater
:
(.
can be proved
+E,)
With P, exogenously dV -.-I___ dPfll,IP,,
unambiguously
-i,k)
or that P,,B,P,H"
nlP
that
!
to the assumptions
and
Therrfore, value added has to decrease with an increase in the price of the intermediate input and this will sesuii in an unambiguous deficit in the balance of paymenis. Mow sensitive are the results obtained above to the underlying assumption in prcpduction among imported inputs and of gross compiementarity dwxsk factors? It can easily be seen that they will hold for all cases in which the elasticity of substitution between imported inputs and domestic faclori is less than unity. T!re nested Cobb--Douglas production function H”= @“L’ -“]‘MP’ -Y provides the borderline case. Mere the share of value added and imported inputs (MP) is constant. Thus, an increase in tie price of the intermediate good will have no direct effect on value added. Value added will increase only indirectly once the price of home goods increases due to the suppiycon!rac!ionary effect. It is thus clear that under a Cobb-Douglas case the price and balance-of-payments effects will be similar to those obtained in the case of final imported goods; thus, the price of home goods will rise and the balance of payments will improve as value added and hence saving, increases. There is, however, at; important difference between the two cases: in the final-good case the change ~1 relative prices shifts the demand curve for home goods outward and unambiguously increases real ojltput (H’); in the case of intermediate goods real output will increase only if the indirect increase in value added and overall demand is sufficient to outweigh the contractionarysupply effect. Thus, even in the case of a unitary elasticit!, of substitution between inputs and domestic factors, an increase in the price of intermediate goods will probably lead to stagflation.
4. Comparison of results and conclusions The major difference rn the specification of the cases presented in sections 2 and 3 lies in the treatment of imports. While in section 2 imports’ are final goods, they are intermediate goods in section 3. Income in the first case equals the total value of production, whereas income in the second case equals value added. Furthermore, whereas B,*- 1= Bh,.rl+ Bh_., and C = P,Hd c P, .Y” i P,, .IlP“ in the first case, in the case where imported goods are inptits. B,- 1 = R,.,, and C =P,,Hd + P,Xd. Thus, for given values of homeg:)od and export-type-good consumption, aggregate consumption in section 3 I\ ~rnaller than aggrei.ate consumption in section 2 (C,
own price elasticity of demand (BhJZ -C(.B,,x)3. Table 1 contrasts and summarizes the major results derived in the previous x~tion~. These include the responsiveness of home-good prices to an ~~~Y~C”IY)UC import-price disturbance (DA,n,p and Z,,.,,p)r the corresponding ~~i~~rnce-oh-pavrmc~ts effects (dB’dP,,P,,,), and th:: effects on real output or ~~~~~~~~~,~e~~ (d!l’ dP,,P,,).
LT. Katseli-Papae~strutior;.
Externul
Table The composition
price dis~urhanws
1
of trade and transmission
Final-good
imports
373
of price disturbances. Intermediate-good
imports ___--
Imports and domestic goods or factors are gross substitutes
(B,,,,D)
(a$11
4mp20
Z h,tW?‘O
dB ___ dP,p
Pm,20
dB dPmp
Pm,>0
dH’ -&y P,,LO mP
-
Imports and domestic goods cr Factors are qoss complements
mI,tnp
(a
D h.“lP
z,. mp?
dB dP,p
Pm,<0
(1) If all final goods are gross substitutes in consumption then an increase in their price causes home-good prices to rise unambiguously, regardless of deflationary real-balance effects. Real output unambiguously rises and the balance of payments improves. Complementarit;, in consumption between traded and non-traded goods reverses these conclusions. The unambiguous direction of change rests on the following assumptions: homogeneity of degree one with respect to income and wealth in the saving function and homogeneity of degree zero in prices and consumlation in the demand for home goods; given these assumptions one can translate freely between nominal and real terms, at least on tht: demand side. (2) The direction of change of home-good prices is positive if imports arc intermediate goods and gross substitutes to domestic factors. The balance of payment; will improve but, contrary to the corresponding final-good GM. the real output or employment effect ,ti!ill be ambiguous. (3) If imported inputs are complementary to domestic fitctors, the price effect rather than the output effect will be ambiguous. The ambiguity iiriscs not because of opposittt-signed effects on the demand side but because of the simultaneity of inflationary supply-side and def!rJtionary demand-side effect>. A ‘la,pge enough’ elasticity of supply with respect to the nci real wage ii!ill will ensuxe a positive direction of change. The balance of payment unambiguously deteriorate and real output (and employment) wili L.!l. This will be the pertinent case for the analysis of an oil price inc:ease.
The above results illuminate the discussion around potential contradictions tween ecozlomic theory and reality which are based on the contention that the monetary approach to the balance of payments cannot explain the appearance of deficits as a result of the oil price increase in the early 1970s. As we have shown, the theory is, in this case at least, totally consistent with facts. The anaitysis also explains why small and open economies are much rnrx-e vulnerable to oil price increases than to increases in the price of imported finaii goods. Apart from the inevitable balance-of-payments deterioration, increb-ds in the price of intermediate goods can result in stugflation as the irxreased cost in production is coupled with a reduction in national income and demand.
Appendix Home-good prices will increase (decrease) if
E,P,H"P ------__"_p~Pm,MP(l CE,)m,(l-U). pi-
(1”)
pmp
Srnct: Hd= H'= !W by assumption, and the marginal propensity to consume, Q,, i:, equal to the average propensity to consume so that m,,= P,Hd/C, eq. t 1”) becomes equal to
1+-E,, --= Eh
c ~____-
=-(Ph-Pmp)Hd(l
(2”)
-ikj’
Since
it follows that E
z!PhHd-f’mp~fW --j-k) h-c
(1 -ik)P,X'+iM
*
igliapi, !963. The life cycle hypothesis of saving: Aggnegate inqlications Economic Review, March, 55-84. Wood, 1979, Engineering and econometric interpretations of energy rlty, American Economic Fieview 3, 342-354. Asset markets and relative prices in exchange rate detumination, %VJBG!U ~~~e~~c~af?~~c~,e Annalen, Band I.
Branson, W.H. and L.T. Katseli-I’apaerstratiuu. 19X0. Income instahihty, terms 01’ triidc and the choice of exchange rate regime, Journal of Development Economics 7. 49 69. Buiter, W., 1978. Short-run and long-run crfects of external disturbances under a Ilonting exchange rate, Economica 45, 25 l--272. Connolly, M. and D. Taylor, 1976. Adjustment to dwaluation uith money and ncw~rndcd goods, Journal of International Economics 6. August. Corden, W.H. and R.W. Jones. 1976, Devaluation. non-flexible prices and the trade balance ~OI a small country, The Canadian Jnurna: of Economics 9 (I ). I‘ebrunry. i 50 I 61. Dornbusch, R.. 1973a, Devaluation, money and nontraded gwds. American I~connmic Ruviw 63. 871~-880. Dornbusch, R., 1973b. Currency depreciation. hoarding and rclatiic price\. Journ:l! of Political Economy 81, July/August, 843 917. Dornbusch. R., 1976, Expectations and exchange rate dynamics. J~wrnal ol” Political f:ccwom) 84, no. 6. Findlay. R. and C. Rodriguez.. 1977. Intermediate imports and macrwconomlc policy under flexible exchange rates, Canadian Journa! of Economrcs IO. May. XX 217. Goldfcld. S., 1973. The demand for rnoney revisited, Brookmgs Papers on Economic Actlslty 1. Harberger, A., 1964. Some notes on inflation. in: W. Baer and I. Kcrstcnetzky. cds.. Infla~lc~rl and growth in Latin America (R.D. Irwin, Homewood, Illinok). Katseh-Papacfstratiou, L.. 1979. Transmission of external price disturbances in sm;\ll I~KII economies, Ph.D. Dissertation, Princeton University (Garland Press. New York ). Komiya, R.. 1967, Nontraded goods and the pure theory of intcrnaticwal trade. Infcrnatlon;lI Economic Review 8, 133 152. Kouri. P.J.K., 1976. The exchange rate and the balance of payments rn the short run and 111the long run: A monetary approach, Scandinn\ian Journal of Ewnnmrcs 2. Krueger, A.. 1974, The role of home goods and money in c~chu~~gc rate ;Idjustmcn14. 111' W. llonc~~~r 01‘ Jill1 Tlnhc-gcn Scllckaerts. cd., International trade illld finance: Essay5 in (Macmillan Press. London) 131 161. Rodriguez. C.A., 1977, Flcxihle exchange rate? ;Lnd impc)rtcd inputs: A dynamic anal>\I\ ()I’ IIlL‘ ccclrl~u~l). TllC and real sectors fool ;I \lmill cqw1 interactions bctwcen the monctaq Economics Workshop, Columhla !!ni\crsitk. Dircuwon Paper 76-770X. Whitman. M., 1975. Global mcrnct;lrism and ths monetary appro;tch 10 Ills hal~mcc of paj111cr1t\. Brookings I’apcrs un Economic Activity 3. 121 166.
c