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Adjustment to devaluation with money and nontraded goods
Journal of International Economics 6 (1976) 289-298. Q North-Holland Publishing Company
ADJUSTMENT TO DEVALUATION WITH MONEY AND NONTRADED GOODS Michael CONNOLLY and Dean TAYILOR University of Fhidu,
.
GainesviYie, FL 32H1, U.S.A.
Received March 6975, revised version received March 1976 This paper analyzes the dynamics cf adjustment to devaluation in a framework which highlights ihe role played by nontrsded goods and money. We provide a specific analytical model of devaluation incorporating substitution effects in production and consumption as well as liquidity effects resulting from a stock-flow adjustment process. The analysis provides specific solutions for the time path of the balance of payments and the price of nontraded goods following devaluation.
1. Introduction The purpose of this paper is to analyze some aspects of the dynamics of devaluation by a small country in a context of tradeci goods, home goods, and money. We derive the paths of adjustment of prices, the balance of trade, and money following a change in the exchange rate.’ The analysis stresses the purely transitional importance of the substitution of nontraded goods in production following devaluation, and of the decline in expendit?Jre on both nontraded and traded goods as a result of the liquidity effect. The st~bstitutiorz effect arises as a result of the increase in the relative price of tradect goods after devaluation, while the lAp.ddity effect results from the dechne in. the real value of cash balances when the exchange rate depreciates. The istinction between substitution and liquidity effects corresponds to Johnson’s (1958) ‘expenditure-switching’ and ‘expenditure-reducing’ effects of devaluation, and th= analysis here represents in part a dynamic exttnsion of their workings within the framework of the nontraded goods model of a z.,mallcountry found in Dornbusch (1973a, 1973b) and Mundell (1968, 1971). Our primary objective is IO explicitly analyze the oaths of adjustment to z. ‘The modern monetary analysis focuses primarily on impa:t and steady state effects of devaluation, neglecting the time path of adjustment. The role of money and devaluation is stressed in Dornbusch (1973a), Johnson (I972), Kemp (1970), Mundell (1968), and Negishi (1968), while money, devaluation, and nantraded goods are ancllyzed in Do;mbusch (1973b), Krueger (I974), and Mundell (1971). In a nonmonetary setting, Pearce (1961) examines the role of nontmded goods and devaluation, and Brito and Richardson (1975) provide a dynamic %lr analysis whicrl highlights employr?ent ad_iustment in the labor market.
290
M. Chdly
and D. Taylor, A&stment
to devaluation
devaluation within a iqonetary setting, rather than focus safely upon its corn yarative statics eltrects.The impact and steady state effects can be derivtid in the framework we se&forth, and 3n addition the transitional workings of the substitution and liquidity effects can be analyzed in detail. For examlple, the speed of adjustment of prices of nontraded goods plays a central role in determining the: smoothness and directness of the transition to the new eqnilibri~::n, whereas in a static context, the speed of market adjustment plays no role. In addition, we incorporate a familiar stock-flow money adjustment mechanism in which excess stock supplies of money result in an excess flow of expenditures on both traded and nontraded goods. The stock-flow adjustment mecb.;;kr,ism also plays a central part in determining the impact effects of devaluatiol;., and the adjustment paths, but not in determining the steady state outcome. Further, the steady state neutrality of devaluation is demonstrated by use of an explicit dynamic system. 2 The major results of interest are as follows. On the one hand, a devaluation unambiguously improves the trade balance, albeit temporarily, as a result of substitution effects in production toward traded goods and in consumption clwaity from traded goods that are, in turn, reinforced by the liquidity effect which reduces expenditure on traded goods. On the other hand, the tendency to substitute toward nontraded goods in consumption and awr~v from them in production may be offset by lthe expenditure dampening eflects of reduced liquidity, leading to a temporary slump in the price of nontraded goods rather than a rise. Thtzse substitution and liquidity effects are purely transitory, but plaina critical role #duringthe adjustment to devaluation. 2. Nontradedgoods and money For simplicity, assume that the price of traded goods is rigidly linked to the exchange rate via arbitrage. The country is too small to affect the world prices of both its exports and imports, which are treated as composite goods. By an appropriate choic&f units, the foreign currency price of all traded goods can be set equal to unity so that their domestic price equals r, the exchange rate. Now we may introduce nontru&d goods treJi.ed also as a composite good, q;vhoseprice, p, is not directly linked to forei&,:?prices. Traded and nontraded goods are, however, substitutes, holding real nraney balances constant. By assumption, the country does not have a credit market, so money is the sole financial acisetheld. The demand for money is assumed to be proportional 2The neutrality of the steady state effects of devaluation has been demonstrated elsewhere using homogeneity properties of a static trade system [see Dornbusch (197fla), Kemp (1970), and Mundell(1968,1971)]. The steady state neutrality of devaluation is an ar,gument that must be used guardedly, not only for the obvious reason that devaIuations do not typically take place from equilibrium, but also because, even if they did, real changes Joust occur during the adjustment process if the original equilibrium is to be: restored, as is shoTAnin the following analysis.
M. Connolly and D. Taylor, A&stmenlt to devchation
291
to the general price level, which, in turn, is a weighted average of the prices of nontraded and traded goods, p and r respectively : 3
L = k,p+kg
(demand for money).
(1)
The real excess demand for nontraded goods, X, depends on relative prices ,nd any discrepancy between actual and desired money balances. This relationship can be expressed in nominal terroilsas px
z
-ap+/?r+6(M-L)
(excess nominal demand for nontraded goods).
02
In other words, as excess supply of money leads individuals to increase their expenditure on goods to rid themselves of money, and conversely, to nr,cumulate cash balances, expenditure on goods falls* However, if the stock of IEoney is in equilibrium (M = -Y,),x = --a+ p(r/& or the excess demand. for domestic goods is inversely related to its own price and positively related to the price of traded goods. In equilibrium the price for domestic goods is easily solved for by setting M = L and x = 0, giving p = (/Y/z)r. The excess demand for international ‘goodsfollows similarly :’ rz = ccp-flrfA(M-4)
(excess nominal demand for traded
goods).
(3)
The excess supply of international goods equals the balance of payments, B, which is equivalent, by definition, to thlc change in foreign reserves : dR/dt=
B=
-rz
(balance of payments) .
0
With a surplus, receipts of foreign exchange exceed payments in foreign exchange. Domestic residents are assumed not to hold balances of foreign currency, implying ithat the excess supply of foreign exchange must be purchased by the governmental authorities with domestic money in order to maintain a fixed r$arity. Domestic money is thus issued for foreign money, and in the absenk of a banking system, the rate of issue of domestic money must just equal Vhis specification of the demand for money can be considered a reduced form, permanent income and other determinants of the demand for money being suppressed into the coefficients. It has the property that a doubling of the exchange rate and the price of nontraded goods doubles the nominal demand for money. 41n accordance with Walras’ faw, the sum of excess demands for international and domestic goods equals the fioiw excess supply of money, which is a constant proportion (S+ A) of the excess stock supply of money (M - LJ. That is, px -!-rz = (6-t iU(M-4). Further, if the demand for money equals its supply, rz = --IX. For this reason the coeficients must appear in (2) and (3) with opposite signs.
M. Conno& an&ID. Taylor, Adjustment to deoa;rluarion
292
the rate of increase of reserves held by the government. We have, therefore, dM/dt = dR/dt
.
(money increase).
(9
Essentially, the monetary authorities change the money supply through their foreign exchange operations. While the price of international goods is considered to always equal the exchange rate, the price of domestic goods is determmed by conditions of excess demand. Specifically, we assume that the percentage rate of change of the price of nontraded goods is propcrtioial to excess demand, or
-1 -dP
c
(rate of change of price of nontraded goods)
p=
P dt
,
(6)
where p measures the speed of adjustment of prices.’ Substituting the money demand into the excess demand equations, the price adjustment mechanism into the excess demand for nontraded goods, and making use of the balance of payments definitions, we have --pa A+D
(7)
where D is the differential operator d/dt. The characteristic equation is found by setting the determinant of the coef5cir:nt matrix equal to zero, or ap(S+;L)+(ap+A+k,pS)D+
D2 = 0,
(9
which has the roots -h-P2
=
[-!dl~+~+k&9
+l/{(~p+Rfk,p6)‘-4ap(6-~~))3]/2.
%nSess p = co, the market for nontraded goods does not clear instantaneously. With an excess demand, or px > 0, the supply curve is binding and the nontraded good is rationed among buyers. The actual decline in the community’s money balances will be rz rather than the interzdeddecline of px t YZ,the difference being the unspent pi units of cash. At the next point in time, plans take into account the actlmf change in the money stock, and the adjustment process embodied in eqs. (2) and (3) provides for a larger desired flow of expenditure on both traded and nontraded goods as a result of the ex post inventory accumulation of cash. At the same time, the price of nontraded goods rises. With an excess supply of nontraded goods, the tlemand curve is binding, and the excess of supply over demand is not produced. Nontraded goods are services, for instance, whose production can be varied instantaneously and yet cannot be stored as commodity inventories. Consequently, in++duals as sellers receive px- less than planned in money receipts, and they adjust actor ding:; : at the next point in time, the desired flow of expenditures on both nontraded and trr,ded goods will .‘telower and the price of nontraded goods will decline.
M. Connoily and D. TayIor, Adjustment to devaluation
293
Since the real parts are negative, the system is stable. However, oscillation is possible if the expression irr the radical sign is negative.
3. Paths of rdjustxnentfollow&, dwahmtion In this section, we briefly describe the possible paths of adjustment followiuga devaluation. The time of the money supply and foreign reserves to a change in the exchange rate equal to r* is (see appendix) c12t
L-
-
\
/h-P2
/
\
k--c12
/
1 r*
(10)
9
where -pl and -pLz are the roots of the characteristic equation, cl3 = k2 + (P/W 9 P4 = /I + Ak, , and deviations from ini\tial positions are denoted by an asterisk. 6 M*,R*
vc-
V’
.’
t
Fig. 1.
?
Adjustment of &moneyand reserves fialiowing devalluation.
Hence&. the long run, reserves and money increase bbyp3r* = (k2 + (/3/z)k&*. Noting from below that the long-run increase in th.e price of nontraded goods is (fl/ce)r*, the cumulative increase in reserves is M* = krp* +k,r*. Consequently, devaluation causes reserves and the domestic money supply to rise ultimately in proportion to the rate of devaluation. The possible paths of asjustment of reserves and money are illustrated below.’ The balance of trade is obtained by differentiating (10) Gth respect to time, or’
“That is, p = p. +p*‘, r = rof Y*, R = Ro + R*, ax! M = MO+ M*. Note that the analysis ignores the accounting revaluation of current hotdings of foreign reserves as a result of devaluation. ‘If the money supply rises above its ultimate level and then asymptodically approaches equilibrium, the initial segment of the curve must be concave since the fur&ctioncan have at most c-ne inflection point if the roots are real. “B = dM/dt = dM*/dt, since M = MO t M*.
M. Connolly and 4). Taylor, Adjustment to devaluatiarx
294
Immediately after the devaluation, we can identify the impact e&ct on the balance of trade (B = par* as t + 0): B = @+Ak,)r*
(impact effect on balance of trade).
f 121
The first part of the term, /3, is the substitution efict, while the second, ilk,, is the liquidity effect 0x9.traded goods. These correspond to ‘expenditure-swit&ing’ ,and ‘expenditure-reducing’ effects of devaluation [Johnson (1958)l and the point is that a devaluation exerts, for a given nominal quantity of money, both effects, Both work initially so as to improve the balanceof trade; first, therle 3sa tendency to substitute toward nontraded goods in consumption and toward traded goods in production, and second, expenditure is reduced on traded goods as liquidity declines. In the long run, these effects disappear since B + 0 as t -+ 00 ; that is, the balance of trade returns to equilibrium. The possible paths of adjustment in the trade balance are shown in fig. 2.’
.
Fig. 2.
Adjustment of the balance of trade following devaluation.
Once again, -pl and --p2 are the roots of the characteristic equztir 74.and letting p5 = /?,‘aand p6 = p(/3- k26), the path of p* with a devaluation is ,see appendix)
The rate of change of the price of nontraded goods immediately following devaluation (as f + 0) is’* dp”/dt = &3-k26)r*
(impact effect on price of home goods). (14
It is clear from the term (/?- k26) that with c devaluation,the excess demandfor domestic goods &n be initial/) positive or negative depending upon whether the substitution effect, 8, is greater or less than the Equidity effect on nontradedgoods, k,6.-Sh.ould the liquidity effect dominate initially, the money price of nontraded Wscillation occurs if (~cp+ Lf kl ~6) * c 4ap(S+ R). loNote tha’tsince p = po+p*, dp/dt .= dp*/dt.
M. Comolly and D. Taylor, Adjustment to devaluation
295
goods falls immediately following devaluation.” In the long run, however, domestic prices will rise in the same proportion as the devaluation, that is . P’ = (j?/a)r * and the previous equilibrium position will be restored. The possible paths of the price of nontraded goods are illustrated be10w.l~ In the left-hand diagram, the lower path of approach involves an initial deflation in the nontraded goods sector since the impact of the liquidity effect is stronger th;m the substitution effect. In the other paths, the substitution effect initially dominates the liquidity efl&t. As the process wears on, the initial pattern of real expenditure is restored. In the right-hand diagram, oscillatory approaches to equilibrium are indicated. ’ 3 In the oscillatory approaches (as in the case of a single overshoot) there are alternatively excess demands and excess supplies of the nontraded good.
t
Fig. 3.
I
t
Abljustment of price of nontraded goods following devaluation.
4. co~clusioxB Our purpose has been to develop a dynamic m(Dnetaryapproach to devaluation with nontraded goods. In doing so, we analyze the impact and steady state effects of devaluation, and sketch the paths of adjustment following devaluation. Despite the simplicity of the model, the possible paths of adjustment are quite rich and complex, involving multiple types of approaches of prices and money supply to their new equilibrium levels. The steady state neutrality of a change in the exchange rate isI reaffirmed; namely, all real variables remain unchanged in the 1on.grun. Nevertheless, real erYectsin production and consumption must. take place during the adjustment i process, I “Dornbusch (1973b, p. 880) has demonstrated that dev&tation mat initially reduce the relative price of nontraded goods, while the above analysis shows th,at its impact effect on the &oh&e price is ambiguous. l *Once again, initial convexity followed by one overshoot and a direct approach to equilibrium can be ruled out. r31t may be worth noting that oscillatory anuroaches cannot occur if the market for nontraded goods clews instantaneously. In this ca& the paths ofadjustment of the money supply and the price of nontraded goods are given by W = [k2 + (b$z)kJ[l - e-pc]r* and
where p = a(& L)/(a-t-&). Once again, an initial decline in The price of nontraded goods occurs if /? c k2B. E
296
M. Connolly and D. Taylor, Adjutment ito devahation
With nontraded goods the path to the new equilibrium involves substitution and liquidity effects. The substitution and liquidity effects both work so as to improve the trade balance following the devaluation, while the substitution and liquidity effects work in opposite dirlections on the price of nontraded goods. These substitution and liquidity effects are pureliy transitory, and play no role whatsoever in determining the final equilibrium. Their role is crucial, however, during the process of adjustment following devaLluation.‘4S1 ’ Appendix
By Cramer’s rule, equation system (7) can be solved for the money supply as a function of the exchange rate:
= [p(~+~)(ak2+Sk,)+(B+Ak,)Dlr.
M-1)
The system is initially in equilibrium, and consequently (A.1) can be rewritten in terms of deviations from initial positions indicated by an asterisk:
where -pn and -p2 are the roots cf the characteristic equation (IS),ps = k, + (8/a)k1, and I(~ = /I+ Ak2. A method using Caplace transforms specifically designed to accommodate step changes in a parameter such as the exchange rate is discussed in detail by Allen (1967) and is adopted here. As Allen notes, we need only specify the initial conditio.ns just before the step change in the exchange rate, then apply Laplace transforms. Before the devaluation, the system is in equilibrium, and $conser4We explored alternative forms of the dynamics of adjustment during disequilibrium. For ins&e, when there exists an unftiledl excess demand for nontraded goods, par3of the excess demand may spill over directlyonto tradedgoods, causing a largerdeficit. The remainder WC&! then accumulate in the form of money, and work back through the stock-flow adjustment equations as discussed above. An excess supply of nontraded goods would have the reverseeffect; with receiptsless than planned, expenditure on tradedgoods would immediately decline, causing a more favorable balance, and simDarIy,the stock4ow adjustment would involve a lowered flow demand for both goods. In this case, the balance of trade can be expressed as B = - (rz+ Opx), where 0 is the fraction of excess demand for nontraded goods that spills over onto traded goods. With this immediatemarketspillover, the impact effect of a devaluation on the trade balance is B = [(,&+ilk+ rs(B-&#@, which implies a smaller improvement if the substitution effect dominates the liquidity effect, or a iargerimprovement in the opposite case. In both instances, the trade balance unambiguously improves since 0 < 8 < 1. While the roots of thecharacteristiceq~tion areless Likelyto be imaginarywith the spiliover, the paths of adjustment to equiiibr&unare in all other respects similar to those depicted above, and the long-run outccmes are unchanged. We are indebted to Rudiger Dornbusch for helpful discussion on this point. 85For recent empirical evidence on the b&avior of prices and reserves following devaluation, see CormoUyand Taylor (1976).
M. Connolly and il. Taylor, Adjustment to devaluation
297
quently, the initial conditions are M* = DM* = D2M* = 0. With the differential equatisn (A.2) and these initial conditions, the Laplace transform of iV is given by m(s)
=
(
cllP2P3
$1
+Pqs
+s)012
p
+a
>
(A.3) e
Writing (A.3) in partisl fractions, we havei
Since the Laplace transform of 1 is 1/s, and of ewPla is l/b1 i-s) [see Allen (1959, p. :!GO)] the inverse Laplace transform of (A.4) gives eq. (10) in the text for the pa*.h of the money supply following devaluation, or
Using Cramer’s rule, the solution for p as a function of the exchange rate is [ap(6+JJ+(rp+A+k,p@D+ By a similar derivtition, we have
where pS = /3/a and f16 = p(p-
D2]p = [p(S+il)/?+-p(/3-k&D]r. (A4
k26).
‘%ee Alfen (1959).
Allen, R.G.D., 1959, Mathematical economics (Macmillan, London) 155-1166. Allen, R.G.D., 1967, Macro+zconomic theory (Macmillan, London) 357-362. Brito, D.L. and J.D. Richardson, 1975, Some disequilibrium dynamics of exchange rate changes, Journal of International Economics 5, l-13. Connolly, M.B. and D.Cr. Taylor, 1976, Test@ the monetary approach to devaluation in developing countries, Journal of Political Economy, forthcoming. ’ Dornbusch, R., f373a, Currency depreciation, hoarding and relative prices, Journal of P&tical Economy 81,893-915. Dornbuseb, R., 1973b, Devaluation, money and non-traded goods, American Economic Review 63,871-880. Dornbusch, R. and M. Mussa, 1975, Consumption, real balances and the hoarding function, International Economic Review 16, llli5-421.
293
M. Connolly and D. Taylor, Aa@stment to de?Jahation
Johnson, H.G., 1948,Towards a general theory of the balance of payments, in: H.G. Johnson, Int~arnational trade and economic growth (Allen and Unwin, London) 153-1681c Johnson, H.G., 1972, The monetary approach to the balance of payments, Journal of Financial ’ and Quantitative Analysis 7, 1555-l 57:X. Kemp,, M., 1979, The balance of payments and the terms of trade in relation to financial *A controls, Review of Economic Studies 37,25-31. Krueger, A., 1974, The role of home goods and money in exchange rate adjustment, in: W. Sellekaerts, ed., International trade and finance (International Arts and Sciences Press, New York) 141-161. Mundell, R.A., 1968, Barter theory and the monetary mechanism of adjustment, in: R.A. Mundell, International economics (Macmillan, New York) 111-133. Mundell, R.A.) 1971, Devaluation, in: R.A. Mundell, Monetary theory (Goodyear, Pacific Palisades) 86-97. Negishi, T., 1968, Approaches to the analysis of devaluation, 1nter:lational E!conrDmicReview 9,218-227. Pearce, I., 1961, The problem of the balance of payments, International Economic Review 2, l-28.
ADJUSTMENT TO DEVALUATION WITH MONEY AND NONTRADED GOODS Michael CONNOLLY and Dean TAYILOR University of Fhidu,
.
GainesviYie, FL 32H1, U.S.A.
Received March 6975, revised version received March 1976 This paper analyzes the dynamics cf adjustment to devaluation in a framework which highlights ihe role played by nontrsded goods and money. We provide a specific analytical model of devaluation incorporating substitution effects in production and consumption as well as liquidity effects resulting from a stock-flow adjustment process. The analysis provides specific solutions for the time path of the balance of payments and the price of nontraded goods following devaluation.
1. Introduction The purpose of this paper is to analyze some aspects of the dynamics of devaluation by a small country in a context of tradeci goods, home goods, and money. We derive the paths of adjustment of prices, the balance of trade, and money following a change in the exchange rate.’ The analysis stresses the purely transitional importance of the substitution of nontraded goods in production following devaluation, and of the decline in expendit?Jre on both nontraded and traded goods as a result of the liquidity effect. The st~bstitutiorz effect arises as a result of the increase in the relative price of tradect goods after devaluation, while the lAp.ddity effect results from the dechne in. the real value of cash balances when the exchange rate depreciates. The istinction between substitution and liquidity effects corresponds to Johnson’s (1958) ‘expenditure-switching’ and ‘expenditure-reducing’ effects of devaluation, and th= analysis here represents in part a dynamic exttnsion of their workings within the framework of the nontraded goods model of a z.,mallcountry found in Dornbusch (1973a, 1973b) and Mundell (1968, 1971). Our primary objective is IO explicitly analyze the oaths of adjustment to z. ‘The modern monetary analysis focuses primarily on impa:t and steady state effects of devaluation, neglecting the time path of adjustment. The role of money and devaluation is stressed in Dornbusch (1973a), Johnson (I972), Kemp (1970), Mundell (1968), and Negishi (1968), while money, devaluation, and nantraded goods are ancllyzed in Do;mbusch (1973b), Krueger (I974), and Mundell (1971). In a nonmonetary setting, Pearce (1961) examines the role of nontmded goods and devaluation, and Brito and Richardson (1975) provide a dynamic %lr analysis whicrl highlights employr?ent ad_iustment in the labor market.
290
M. Chdly
and D. Taylor, A&stment
to devaluation
devaluation within a iqonetary setting, rather than focus safely upon its corn yarative statics eltrects.The impact and steady state effects can be derivtid in the framework we se&forth, and 3n addition the transitional workings of the substitution and liquidity effects can be analyzed in detail. For examlple, the speed of adjustment of prices of nontraded goods plays a central role in determining the: smoothness and directness of the transition to the new eqnilibri~::n, whereas in a static context, the speed of market adjustment plays no role. In addition, we incorporate a familiar stock-flow money adjustment mechanism in which excess stock supplies of money result in an excess flow of expenditures on both traded and nontraded goods. The stock-flow adjustment mecb.;;kr,ism also plays a central part in determining the impact effects of devaluatiol;., and the adjustment paths, but not in determining the steady state outcome. Further, the steady state neutrality of devaluation is demonstrated by use of an explicit dynamic system. 2 The major results of interest are as follows. On the one hand, a devaluation unambiguously improves the trade balance, albeit temporarily, as a result of substitution effects in production toward traded goods and in consumption clwaity from traded goods that are, in turn, reinforced by the liquidity effect which reduces expenditure on traded goods. On the other hand, the tendency to substitute toward nontraded goods in consumption and awr~v from them in production may be offset by lthe expenditure dampening eflects of reduced liquidity, leading to a temporary slump in the price of nontraded goods rather than a rise. Thtzse substitution and liquidity effects are purely transitory, but plaina critical role #duringthe adjustment to devaluation. 2. Nontradedgoods and money For simplicity, assume that the price of traded goods is rigidly linked to the exchange rate via arbitrage. The country is too small to affect the world prices of both its exports and imports, which are treated as composite goods. By an appropriate choic&f units, the foreign currency price of all traded goods can be set equal to unity so that their domestic price equals r, the exchange rate. Now we may introduce nontru&d goods treJi.ed also as a composite good, q;vhoseprice, p, is not directly linked to forei&,:?prices. Traded and nontraded goods are, however, substitutes, holding real nraney balances constant. By assumption, the country does not have a credit market, so money is the sole financial acisetheld. The demand for money is assumed to be proportional 2The neutrality of the steady state effects of devaluation has been demonstrated elsewhere using homogeneity properties of a static trade system [see Dornbusch (197fla), Kemp (1970), and Mundell(1968,1971)]. The steady state neutrality of devaluation is an ar,gument that must be used guardedly, not only for the obvious reason that devaIuations do not typically take place from equilibrium, but also because, even if they did, real changes Joust occur during the adjustment process if the original equilibrium is to be: restored, as is shoTAnin the following analysis.
M. Connolly and D. Taylor, A&stmenlt to devchation
291
to the general price level, which, in turn, is a weighted average of the prices of nontraded and traded goods, p and r respectively : 3
L = k,p+kg
(demand for money).
(1)
The real excess demand for nontraded goods, X, depends on relative prices ,nd any discrepancy between actual and desired money balances. This relationship can be expressed in nominal terroilsas px
z
-ap+/?r+6(M-L)
(excess nominal demand for nontraded goods).
02
In other words, as excess supply of money leads individuals to increase their expenditure on goods to rid themselves of money, and conversely, to nr,cumulate cash balances, expenditure on goods falls* However, if the stock of IEoney is in equilibrium (M = -Y,),x = --a+ p(r/& or the excess demand. for domestic goods is inversely related to its own price and positively related to the price of traded goods. In equilibrium the price for domestic goods is easily solved for by setting M = L and x = 0, giving p = (/Y/z)r. The excess demand for international ‘goodsfollows similarly :’ rz = ccp-flrfA(M-4)
(excess nominal demand for traded
goods).
(3)
The excess supply of international goods equals the balance of payments, B, which is equivalent, by definition, to thlc change in foreign reserves : dR/dt=
B=
-rz
(balance of payments) .
0
With a surplus, receipts of foreign exchange exceed payments in foreign exchange. Domestic residents are assumed not to hold balances of foreign currency, implying ithat the excess supply of foreign exchange must be purchased by the governmental authorities with domestic money in order to maintain a fixed r$arity. Domestic money is thus issued for foreign money, and in the absenk of a banking system, the rate of issue of domestic money must just equal Vhis specification of the demand for money can be considered a reduced form, permanent income and other determinants of the demand for money being suppressed into the coefficients. It has the property that a doubling of the exchange rate and the price of nontraded goods doubles the nominal demand for money. 41n accordance with Walras’ faw, the sum of excess demands for international and domestic goods equals the fioiw excess supply of money, which is a constant proportion (S+ A) of the excess stock supply of money (M - LJ. That is, px -!-rz = (6-t iU(M-4). Further, if the demand for money equals its supply, rz = --IX. For this reason the coeficients must appear in (2) and (3) with opposite signs.
M. Conno& an&ID. Taylor, Adjustment to deoa;rluarion
292
the rate of increase of reserves held by the government. We have, therefore, dM/dt = dR/dt
.
(money increase).
(9
Essentially, the monetary authorities change the money supply through their foreign exchange operations. While the price of international goods is considered to always equal the exchange rate, the price of domestic goods is determmed by conditions of excess demand. Specifically, we assume that the percentage rate of change of the price of nontraded goods is propcrtioial to excess demand, or
-1 -dP
c
(rate of change of price of nontraded goods)
p=
P dt
,
(6)
where p measures the speed of adjustment of prices.’ Substituting the money demand into the excess demand equations, the price adjustment mechanism into the excess demand for nontraded goods, and making use of the balance of payments definitions, we have --pa A+D
(7)
where D is the differential operator d/dt. The characteristic equation is found by setting the determinant of the coef5cir:nt matrix equal to zero, or ap(S+;L)+(ap+A+k,pS)D+
D2 = 0,
(9
which has the roots -h-P2
=
[-!dl~+~+k&9
+l/{(~p+Rfk,p6)‘-4ap(6-~~))3]/2.
%nSess p = co, the market for nontraded goods does not clear instantaneously. With an excess demand, or px > 0, the supply curve is binding and the nontraded good is rationed among buyers. The actual decline in the community’s money balances will be rz rather than the interzdeddecline of px t YZ,the difference being the unspent pi units of cash. At the next point in time, plans take into account the actlmf change in the money stock, and the adjustment process embodied in eqs. (2) and (3) provides for a larger desired flow of expenditure on both traded and nontraded goods as a result of the ex post inventory accumulation of cash. At the same time, the price of nontraded goods rises. With an excess supply of nontraded goods, the tlemand curve is binding, and the excess of supply over demand is not produced. Nontraded goods are services, for instance, whose production can be varied instantaneously and yet cannot be stored as commodity inventories. Consequently, in++duals as sellers receive px- less than planned in money receipts, and they adjust actor ding:; : at the next point in time, the desired flow of expenditures on both nontraded and trr,ded goods will .‘telower and the price of nontraded goods will decline.
M. Connoily and D. TayIor, Adjustment to devaluation
293
Since the real parts are negative, the system is stable. However, oscillation is possible if the expression irr the radical sign is negative.
3. Paths of rdjustxnentfollow&, dwahmtion In this section, we briefly describe the possible paths of adjustment followiuga devaluation. The time of the money supply and foreign reserves to a change in the exchange rate equal to r* is (see appendix) c12t
L-
-
\
/h-P2
/
\
k--c12
/
1 r*
(10)
9
where -pl and -pLz are the roots of the characteristic equation, cl3 = k2 + (P/W 9 P4 = /I + Ak, , and deviations from ini\tial positions are denoted by an asterisk. 6 M*,R*
vc-
V’
.’
t
Fig. 1.
?
Adjustment of &moneyand reserves fialiowing devalluation.
Hence&. the long run, reserves and money increase bbyp3r* = (k2 + (/3/z)k&*. Noting from below that the long-run increase in th.e price of nontraded goods is (fl/ce)r*, the cumulative increase in reserves is M* = krp* +k,r*. Consequently, devaluation causes reserves and the domestic money supply to rise ultimately in proportion to the rate of devaluation. The possible paths of asjustment of reserves and money are illustrated below.’ The balance of trade is obtained by differentiating (10) Gth respect to time, or’
“That is, p = p. +p*‘, r = rof Y*, R = Ro + R*, ax! M = MO+ M*. Note that the analysis ignores the accounting revaluation of current hotdings of foreign reserves as a result of devaluation. ‘If the money supply rises above its ultimate level and then asymptodically approaches equilibrium, the initial segment of the curve must be concave since the fur&ctioncan have at most c-ne inflection point if the roots are real. “B = dM/dt = dM*/dt, since M = MO t M*.
M. Connolly and 4). Taylor, Adjustment to devaluatiarx
294
Immediately after the devaluation, we can identify the impact e&ct on the balance of trade (B = par* as t + 0): B = @+Ak,)r*
(impact effect on balance of trade).
f 121
The first part of the term, /3, is the substitution efict, while the second, ilk,, is the liquidity effect 0x9.traded goods. These correspond to ‘expenditure-swit&ing’ ,and ‘expenditure-reducing’ effects of devaluation [Johnson (1958)l and the point is that a devaluation exerts, for a given nominal quantity of money, both effects, Both work initially so as to improve the balanceof trade; first, therle 3sa tendency to substitute toward nontraded goods in consumption and toward traded goods in production, and second, expenditure is reduced on traded goods as liquidity declines. In the long run, these effects disappear since B + 0 as t -+ 00 ; that is, the balance of trade returns to equilibrium. The possible paths of adjustment in the trade balance are shown in fig. 2.’
.
Fig. 2.
Adjustment of the balance of trade following devaluation.
Once again, -pl and --p2 are the roots of the characteristic equztir 74.and letting p5 = /?,‘aand p6 = p(/3- k26), the path of p* with a devaluation is ,see appendix)
The rate of change of the price of nontraded goods immediately following devaluation (as f + 0) is’* dp”/dt = &3-k26)r*
(impact effect on price of home goods). (14
It is clear from the term (/?- k26) that with c devaluation,the excess demandfor domestic goods &n be initial/) positive or negative depending upon whether the substitution effect, 8, is greater or less than the Equidity effect on nontradedgoods, k,6.-Sh.ould the liquidity effect dominate initially, the money price of nontraded Wscillation occurs if (~cp+ Lf kl ~6) * c 4ap(S+ R). loNote tha’tsince p = po+p*, dp/dt .= dp*/dt.
M. Comolly and D. Taylor, Adjustment to devaluation
295
goods falls immediately following devaluation.” In the long run, however, domestic prices will rise in the same proportion as the devaluation, that is . P’ = (j?/a)r * and the previous equilibrium position will be restored. The possible paths of the price of nontraded goods are illustrated be10w.l~ In the left-hand diagram, the lower path of approach involves an initial deflation in the nontraded goods sector since the impact of the liquidity effect is stronger th;m the substitution effect. In the other paths, the substitution effect initially dominates the liquidity efl&t. As the process wears on, the initial pattern of real expenditure is restored. In the right-hand diagram, oscillatory approaches to equilibrium are indicated. ’ 3 In the oscillatory approaches (as in the case of a single overshoot) there are alternatively excess demands and excess supplies of the nontraded good.
t
Fig. 3.
I
t
Abljustment of price of nontraded goods following devaluation.
4. co~clusioxB Our purpose has been to develop a dynamic m(Dnetaryapproach to devaluation with nontraded goods. In doing so, we analyze the impact and steady state effects of devaluation, and sketch the paths of adjustment following devaluation. Despite the simplicity of the model, the possible paths of adjustment are quite rich and complex, involving multiple types of approaches of prices and money supply to their new equilibrium levels. The steady state neutrality of a change in the exchange rate isI reaffirmed; namely, all real variables remain unchanged in the 1on.grun. Nevertheless, real erYectsin production and consumption must. take place during the adjustment i process, I “Dornbusch (1973b, p. 880) has demonstrated that dev&tation mat initially reduce the relative price of nontraded goods, while the above analysis shows th,at its impact effect on the &oh&e price is ambiguous. l *Once again, initial convexity followed by one overshoot and a direct approach to equilibrium can be ruled out. r31t may be worth noting that oscillatory anuroaches cannot occur if the market for nontraded goods clews instantaneously. In this ca& the paths ofadjustment of the money supply and the price of nontraded goods are given by W = [k2 + (b$z)kJ[l - e-pc]r* and
where p = a(& L)/(a-t-&). Once again, an initial decline in The price of nontraded goods occurs if /? c k2B. E
296
M. Connolly and D. Taylor, Adjutment ito devahation
With nontraded goods the path to the new equilibrium involves substitution and liquidity effects. The substitution and liquidity effects both work so as to improve the trade balance following the devaluation, while the substitution and liquidity effects work in opposite dirlections on the price of nontraded goods. These substitution and liquidity effects are pureliy transitory, and play no role whatsoever in determining the final equilibrium. Their role is crucial, however, during the process of adjustment following devaLluation.‘4S1 ’ Appendix
By Cramer’s rule, equation system (7) can be solved for the money supply as a function of the exchange rate:
= [p(~+~)(ak2+Sk,)+(B+Ak,)Dlr.
M-1)
The system is initially in equilibrium, and consequently (A.1) can be rewritten in terms of deviations from initial positions indicated by an asterisk:
where -pn and -p2 are the roots cf the characteristic equation (IS),ps = k, + (8/a)k1, and I(~ = /I+ Ak2. A method using Caplace transforms specifically designed to accommodate step changes in a parameter such as the exchange rate is discussed in detail by Allen (1967) and is adopted here. As Allen notes, we need only specify the initial conditio.ns just before the step change in the exchange rate, then apply Laplace transforms. Before the devaluation, the system is in equilibrium, and $conser4We explored alternative forms of the dynamics of adjustment during disequilibrium. For ins&e, when there exists an unftiledl excess demand for nontraded goods, par3of the excess demand may spill over directlyonto tradedgoods, causing a largerdeficit. The remainder WC&! then accumulate in the form of money, and work back through the stock-flow adjustment equations as discussed above. An excess supply of nontraded goods would have the reverseeffect; with receiptsless than planned, expenditure on tradedgoods would immediately decline, causing a more favorable balance, and simDarIy,the stock4ow adjustment would involve a lowered flow demand for both goods. In this case, the balance of trade can be expressed as B = - (rz+ Opx), where 0 is the fraction of excess demand for nontraded goods that spills over onto traded goods. With this immediatemarketspillover, the impact effect of a devaluation on the trade balance is B = [(,&+ilk+ rs(B-&#@, which implies a smaller improvement if the substitution effect dominates the liquidity effect, or a iargerimprovement in the opposite case. In both instances, the trade balance unambiguously improves since 0 < 8 < 1. While the roots of thecharacteristiceq~tion areless Likelyto be imaginarywith the spiliover, the paths of adjustment to equiiibr&unare in all other respects similar to those depicted above, and the long-run outccmes are unchanged. We are indebted to Rudiger Dornbusch for helpful discussion on this point. 85For recent empirical evidence on the b&avior of prices and reserves following devaluation, see CormoUyand Taylor (1976).
M. Connolly and il. Taylor, Adjustment to devaluation
297
quently, the initial conditions are M* = DM* = D2M* = 0. With the differential equatisn (A.2) and these initial conditions, the Laplace transform of iV is given by m(s)
=
(
cllP2P3
$1
+Pqs
+s)012
p
+a
>
(A.3) e
Writing (A.3) in partisl fractions, we havei
Since the Laplace transform of 1 is 1/s, and of ewPla is l/b1 i-s) [see Allen (1959, p. :!GO)] the inverse Laplace transform of (A.4) gives eq. (10) in the text for the pa*.h of the money supply following devaluation, or
Using Cramer’s rule, the solution for p as a function of the exchange rate is [ap(6+JJ+(rp+A+k,p@D+ By a similar derivtition, we have
where pS = /3/a and f16 = p(p-
D2]p = [p(S+il)/?+-p(/3-k&D]r. (A4
k26).
‘%ee Alfen (1959).
Allen, R.G.D., 1959, Mathematical economics (Macmillan, London) 155-1166. Allen, R.G.D., 1967, Macro+zconomic theory (Macmillan, London) 357-362. Brito, D.L. and J.D. Richardson, 1975, Some disequilibrium dynamics of exchange rate changes, Journal of International Economics 5, l-13. Connolly, M.B. and D.Cr. Taylor, 1976, Test@ the monetary approach to devaluation in developing countries, Journal of Political Economy, forthcoming. ’ Dornbusch, R., f373a, Currency depreciation, hoarding and relative prices, Journal of P&tical Economy 81,893-915. Dornbuseb, R., 1973b, Devaluation, money and non-traded goods, American Economic Review 63,871-880. Dornbusch, R. and M. Mussa, 1975, Consumption, real balances and the hoarding function, International Economic Review 16, llli5-421.
293
M. Connolly and D. Taylor, Aa@stment to de?Jahation
Johnson, H.G., 1948,Towards a general theory of the balance of payments, in: H.G. Johnson, Int~arnational trade and economic growth (Allen and Unwin, London) 153-1681c Johnson, H.G., 1972, The monetary approach to the balance of payments, Journal of Financial ’ and Quantitative Analysis 7, 1555-l 57:X. Kemp,, M., 1979, The balance of payments and the terms of trade in relation to financial *A controls, Review of Economic Studies 37,25-31. Krueger, A., 1974, The role of home goods and money in exchange rate adjustment, in: W. Sellekaerts, ed., International trade and finance (International Arts and Sciences Press, New York) 141-161. Mundell, R.A., 1968, Barter theory and the monetary mechanism of adjustment, in: R.A. Mundell, International economics (Macmillan, New York) 111-133. Mundell, R.A.) 1971, Devaluation, in: R.A. Mundell, Monetary theory (Goodyear, Pacific Palisades) 86-97. Negishi, T., 1968, Approaches to the analysis of devaluation, 1nter:lational E!conrDmicReview 9,218-227. Pearce, I., 1961, The problem of the balance of payments, International Economic Review 2, l-28.