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Growth, relative prices, and exchange rates
Economics Letters 10 (1982) 137-143 North-Holland Publishing Company
GROWTH, RELATIVE Kent
137
PRICES, AND EXCHANGE
RATES *
P. KIMBROUGH
Duke University, Durham, NC 27706, USA Received
11 March
1982
Using the framework of the monetary (or asset market) approach demonstrated that if growth alters relative prices the growing depreciate rather than appreciate as suggested by Mundell.
to the exchange rate it is country’s currency may
It is well known from the literature on the monetary (or asset market) approach to the exchange rate that growth tends to appreciate a country’s currency [the classic statement of this is Chapter Nine of Mundell (1968)]. Growth, it is argued, raises real income and leads to an incipient excess demand for money at the initial equilibrium exchange rate. Hence a growing country’s currency must appreciate in order to maintain money market equilibrium. However, as usually stated this argument ignores the fact that growth, interpreted as an outward shift of a country’s production possibilities frontier due to an increase in factor endowments or to technological progress, may alter relative prices. These induced relative price changes complicate, and indeed may alter the stylized link between growth and the exchange rate. The purpose of this paper is to illustrate how changes in relative prices associated with growth affect the relationship between growth and the exchange rate. In order to do this in as simple a manner as possible, attention is focused on a small open economy that produces and con-
This paper is related to part of my Ph.D. dissertation at the University of Chicago. I wish to thank Jacob Frenkel, Arnold Harberger, and Michael Mussa for helpful comments on that work. I also wish to thank Grant Gardner for his comments.
,165 1765/82/0000-0000/$02.75
0 1982 North-Holland
K. P. Kimbrough
138
/ Growth, relative prices, and exchange rates
sumes one traded good and one non-traded good (throughout the paper production is denoted by X and consumption by C while the subscripts T and N indicate whether a good is traded or non-traded). This is sufficient to allow for growth to alter relative prices; generalization to the case of a country that is large enough to influence its terms of trade is straightforward. This framework also allows the results to be related to Balassa’s (1964) work on non-traded goods and purchasing power parity. Equilibrium in the money market requires that the supply of and demand for money be equal. This condition is written as
(1)
M/f’ = b$,
where M is the supply of money, P is the domestic price level, and y is real income. Opportunity cost factors also influence the demand for money, but they are not affected by the disturbance considered below and are therefore incorporated in the constant term k. Arbitrage in the market for traded goods guarantees that P,=
SP,*,
(2)
where PT(PF) is the domestic (foreign) currency price of traded goods and S is the exchange rate defined as the domestic currency price of a unit of foreign currency. The domestic price level is assumed to be given by P = p;-=p;,
(3)
where (Yis the share of non-traded goods in domestic consumption, Combining (2) and (3) and substituting the resulting expression into the money market equilibrium condition (1) yields an expression for the equilibrium exchange rate as S = (M,‘kP;)p,=Y-+‘,
(4)
where p, = P,/P, is the relative price of non-traded goods. A similar expression is found in Dornbusch (1976). At any point in time the relative price of non-traded goods must satisfy the equilibrium condition
where C,( .) and X,( .) are demand
and supply
functions
for non-traded
K.P. Kimbrough
/ Growth, relative prices, and exchange rates
139
goods, y, = X, + p, X, is income in terms of traded goods, and X reflects the state of technology. Growth will, generally speaking, alter both real income and the relative price of non-traded goods, and thus influence the exchange rate through two distinct channels. This can be demonstrated by assuming the domestic money supply and foreign prices to be constant in the face of growth, and taking the percent change of (4) to obtain
(6) where a ‘^’ over a variable denotes its percent change. This expression shows that the exchange rate must change not only to accomodate the increased demand for money associated with growth (second term), but also to offset any change in the domestic price level that would otherwise be associated with the induced change in the relative price of non-traded goods (first term). The second term in (6) is the one Mundell and others have had in mind when discussing the link between growth and the exchange rate. However, if the rise in real income due to growth is accompanied by a fall in the relative price of non-traded goods, it is possible for growth to lead to a depreciation, rather than an appreciation, of the domestic currency. This possibility is reflected by the presence of the first term in (6) and can occur only if growth is sufficiently ‘biased’ toward the non-traded sector. As an example of the possible association between growth and a depreciating currency, consider the case where a country is growing because of Hicks’ neutral technological progress in the non-traded sector. Letting g denote the rate of technological progress in the non-traded sector, and assuming production functions exhibit constant returns to scale, it follows that holding the allocation of factors between sectors constant X,v = g. However, since p, = MP,./MP,, (where MP,, is the marginal product of factor i in sectorj) along the production possibilities frontier, the relative price of non-traded goods will fall by the proportion g if the allocation of factors is held constant. Therefore, holding the allocation of factors constant, the value of non-traded sector output in terms of traded goods ( p, X,) is unchanged. In addition, since nothing has happened to affect the output of traded goods, income in terms of traded goods y, is also unchanged. Hence any change in the demand for non-traded goods reflects a movement along an uncompensated demand curve. Since the relative price of non-traded goods falls by g when the allocation of factors is held constant, this implies that e, = -178, where
140
K.P. Kimbrough
/ Growth, relative prices, and exchange rates
17< 0 is the uncompensated elasticity of demand for non-traded goods. This implies that if the allocation of factors between sectors were to remain unchanged when neutral technological progress occurs in the non-traded sector, an excess demand for non-traded goods of ’ -
(17+1)&G
(7)
would arise (Xj = C’j is the initial output of non-traded goods). However, equilibrium in the market for non-traded goods requires that this excess demand be eliminated by a change in the relative price of non-traded goods as the economy moves along its new production possibilities frontier and factors are reallocated between sectors. The excess supply generated by this reallocation of factors is given by
(8) where E is the elasticity of supply of non-traded goods and n’ is the compensated elasticity of demand for non-traded goods (which appears because changes in the relative price of non-traded goods generate no income effects). The term pn + g appears in this expression because factors are reallocated between sectors only to the extent that the change in the relative price of non-traded p,, exceeds the change holding the allocation of factors constant (-8). Equating (7) and (8) yields the change in the relative price of non-traded goods due to neutral technological progress in the non-traded sector: P”,=
-(77+ l>g/(E-v’)-g.
(9)
Using the Slutsky equation 77= 9’ - m (m is the marginal propensity to spend on non-traded goods), it can be shown that j$=
-[(l
-m)+E]g/(E-?I’).
Therefore, as long as both goods are normal the relative price of non-traded goods must fall, and hence the possibility arises that the exchange rate may depreciate. In order to complete the analysis an expression for the change in real
’ Johnson
(1971, pp. 40-42)
obtains
this same result.
K. P. Kimbrough
income
is needed.
/ Growth, r&true
Real income
prices. and exchange rates
141
is given by
or using (2) and (3) by
Therefore,
the change
in real income
is given by
(10) The change in income in terms of traded goods can be broken down into two components. First, there is the change as the economy moves to its new production possibilities frontier holding the allocation of factors constant. The preceding discussion indicates that this change is zero. The second component is the change as the economy moves along its new production possibilities frontier. Using the envelope theorem it follows that
or, using (9),
(11)
I%= - (77+l)gA-$1. Substituting
(9) and (11) into (10) it is easily seen that
g=Cxg.
(12)
That is, the change in real income due to technological progress in the non-traded sector is equal to the share of non-traded goods times the rate of technological progress. Using (9) and (12) in (6) it follows that the change in the exchange rate associated with neutral technological change in the non-traded sector is
S=@+
ljg-Oag.
The second term in (13) captures
(13) the impact
of the change in real income
142
K.P. Kimbrough
/ Growth, relative prices, and exchange rates
which works to appreciate the domestic currency. However, working against this is the fall in the relative price of non-traded goods which is captured by the first term. The net effect will depend on whether the extra real cash balances generated by the fall in the price level (at a given exchange rate) accompanying the fall in the relative price of non-traded goods exceeds or falls short of the increased demand for real balances associated with the increase in real income. To highlight the factors that might cause the domestic currency to depreciate, rather than appreciate as conventional wisdom suggests, consider the case where the income elasticity of demand for money (+) is unity so that (13) reduces to
i=a(v+
l)g/(&-17’).
Therefore, if the demand for non-traded goods is inelastic (- 1 < n -=c0), growth due to neutral technological progress in the non-traded sector will be associated with a depreciation of the domestic currency. However, if the demand for non-traded goods is elastic the domestic currency will appreciate. This result is of interest because one is the most commonly suggested point estimate for the income elasticity of money demand. Note that lower income elasticities of the demand for money, as suggested by the inventory approaches of Baumol (1952) and Tobin (1956) would tend to enhance the likelihood that the domestic currency will depreciate in this special case by reducing the magnitude of the second term in (13). In light of these theoretical arguments, why is it that as an empirical matter growth does in fact tend to be associated with an appreciating currency? First, non-traded goods may not be ‘that important’ on two counts. On the one hand countries may be very open in the sense that a: is small, while on the other many goods that are non-traded may be very close substitutes for traded goods so that their relative prices will change little, if at all, as a country grows. Second, as suggested by Balassa (1964) technological progress in the non-traded sector can be expected to lag behind that in the traded sector. This seems particularly likely in light of the fact that services bulk heavily in the non-traded sector. The ‘slowness’ of technological progress in the non-traded sector tends to cause the relative price of non-traded goods to rise as an economy grows. Hence both terms in (6) will often work to appreciate the currency of a growing economy. The conclusion emerging from this paper is that growth per se, that is
K.P. Kimbrough
/ Growth, relative prices, and exchange rates
143
the rise in real income experienced by a country as its production possibilities frontier shifts outward, tends to appreciate a country’s currency as argued by Mundell and others. In principle this link between growth and an appreciating currency may be reversed by the changes in relative prices associated with a growing economy. However, as an empirical matter this possibility, that growth may lead to a depreciating currency, does not appear to be characteristic of growing economies.
References Balassa, Bela, 1964, The purchasing power parity doctrine: A reappraisal, Journal of Political Economy 72, 584-596. Baumol, William J., 1952, The transaction demand for money: An inventory theoretic approach, Quarterly Journal of Economics 66, 545-556. Dornbusch, Rudiger, 1976, The theory of flexible exchange rate regimes and macroeconomic policy, Scandinavian Journal of Economics 78, 255-275. Johnson, Harry G., 1971, Two-sector model of general equilibrium (Aldine, Chicago, IL). Mundell, Robert A., 1968, International economics (Macmillan, New York). Tobin, James, 1956, The interest-elasticity of transactions demand for cash, Review of Economics and Statistics 38, 241-247.
GROWTH, RELATIVE Kent
137
PRICES, AND EXCHANGE
RATES *
P. KIMBROUGH
Duke University, Durham, NC 27706, USA Received
11 March
1982
Using the framework of the monetary (or asset market) approach demonstrated that if growth alters relative prices the growing depreciate rather than appreciate as suggested by Mundell.
to the exchange rate it is country’s currency may
It is well known from the literature on the monetary (or asset market) approach to the exchange rate that growth tends to appreciate a country’s currency [the classic statement of this is Chapter Nine of Mundell (1968)]. Growth, it is argued, raises real income and leads to an incipient excess demand for money at the initial equilibrium exchange rate. Hence a growing country’s currency must appreciate in order to maintain money market equilibrium. However, as usually stated this argument ignores the fact that growth, interpreted as an outward shift of a country’s production possibilities frontier due to an increase in factor endowments or to technological progress, may alter relative prices. These induced relative price changes complicate, and indeed may alter the stylized link between growth and the exchange rate. The purpose of this paper is to illustrate how changes in relative prices associated with growth affect the relationship between growth and the exchange rate. In order to do this in as simple a manner as possible, attention is focused on a small open economy that produces and con-
This paper is related to part of my Ph.D. dissertation at the University of Chicago. I wish to thank Jacob Frenkel, Arnold Harberger, and Michael Mussa for helpful comments on that work. I also wish to thank Grant Gardner for his comments.
,165 1765/82/0000-0000/$02.75
0 1982 North-Holland
K. P. Kimbrough
138
/ Growth, relative prices, and exchange rates
sumes one traded good and one non-traded good (throughout the paper production is denoted by X and consumption by C while the subscripts T and N indicate whether a good is traded or non-traded). This is sufficient to allow for growth to alter relative prices; generalization to the case of a country that is large enough to influence its terms of trade is straightforward. This framework also allows the results to be related to Balassa’s (1964) work on non-traded goods and purchasing power parity. Equilibrium in the money market requires that the supply of and demand for money be equal. This condition is written as
(1)
M/f’ = b$,
where M is the supply of money, P is the domestic price level, and y is real income. Opportunity cost factors also influence the demand for money, but they are not affected by the disturbance considered below and are therefore incorporated in the constant term k. Arbitrage in the market for traded goods guarantees that P,=
SP,*,
(2)
where PT(PF) is the domestic (foreign) currency price of traded goods and S is the exchange rate defined as the domestic currency price of a unit of foreign currency. The domestic price level is assumed to be given by P = p;-=p;,
(3)
where (Yis the share of non-traded goods in domestic consumption, Combining (2) and (3) and substituting the resulting expression into the money market equilibrium condition (1) yields an expression for the equilibrium exchange rate as S = (M,‘kP;)p,=Y-+‘,
(4)
where p, = P,/P, is the relative price of non-traded goods. A similar expression is found in Dornbusch (1976). At any point in time the relative price of non-traded goods must satisfy the equilibrium condition
where C,( .) and X,( .) are demand
and supply
functions
for non-traded
K.P. Kimbrough
/ Growth, relative prices, and exchange rates
139
goods, y, = X, + p, X, is income in terms of traded goods, and X reflects the state of technology. Growth will, generally speaking, alter both real income and the relative price of non-traded goods, and thus influence the exchange rate through two distinct channels. This can be demonstrated by assuming the domestic money supply and foreign prices to be constant in the face of growth, and taking the percent change of (4) to obtain
(6) where a ‘^’ over a variable denotes its percent change. This expression shows that the exchange rate must change not only to accomodate the increased demand for money associated with growth (second term), but also to offset any change in the domestic price level that would otherwise be associated with the induced change in the relative price of non-traded goods (first term). The second term in (6) is the one Mundell and others have had in mind when discussing the link between growth and the exchange rate. However, if the rise in real income due to growth is accompanied by a fall in the relative price of non-traded goods, it is possible for growth to lead to a depreciation, rather than an appreciation, of the domestic currency. This possibility is reflected by the presence of the first term in (6) and can occur only if growth is sufficiently ‘biased’ toward the non-traded sector. As an example of the possible association between growth and a depreciating currency, consider the case where a country is growing because of Hicks’ neutral technological progress in the non-traded sector. Letting g denote the rate of technological progress in the non-traded sector, and assuming production functions exhibit constant returns to scale, it follows that holding the allocation of factors between sectors constant X,v = g. However, since p, = MP,./MP,, (where MP,, is the marginal product of factor i in sectorj) along the production possibilities frontier, the relative price of non-traded goods will fall by the proportion g if the allocation of factors is held constant. Therefore, holding the allocation of factors constant, the value of non-traded sector output in terms of traded goods ( p, X,) is unchanged. In addition, since nothing has happened to affect the output of traded goods, income in terms of traded goods y, is also unchanged. Hence any change in the demand for non-traded goods reflects a movement along an uncompensated demand curve. Since the relative price of non-traded goods falls by g when the allocation of factors is held constant, this implies that e, = -178, where
140
K.P. Kimbrough
/ Growth, relative prices, and exchange rates
17< 0 is the uncompensated elasticity of demand for non-traded goods. This implies that if the allocation of factors between sectors were to remain unchanged when neutral technological progress occurs in the non-traded sector, an excess demand for non-traded goods of ’ -
(17+1)&G
(7)
would arise (Xj = C’j is the initial output of non-traded goods). However, equilibrium in the market for non-traded goods requires that this excess demand be eliminated by a change in the relative price of non-traded goods as the economy moves along its new production possibilities frontier and factors are reallocated between sectors. The excess supply generated by this reallocation of factors is given by
(8) where E is the elasticity of supply of non-traded goods and n’ is the compensated elasticity of demand for non-traded goods (which appears because changes in the relative price of non-traded goods generate no income effects). The term pn + g appears in this expression because factors are reallocated between sectors only to the extent that the change in the relative price of non-traded p,, exceeds the change holding the allocation of factors constant (-8). Equating (7) and (8) yields the change in the relative price of non-traded goods due to neutral technological progress in the non-traded sector: P”,=
-(77+ l>g/(E-v’)-g.
(9)
Using the Slutsky equation 77= 9’ - m (m is the marginal propensity to spend on non-traded goods), it can be shown that j$=
-[(l
-m)+E]g/(E-?I’).
Therefore, as long as both goods are normal the relative price of non-traded goods must fall, and hence the possibility arises that the exchange rate may depreciate. In order to complete the analysis an expression for the change in real
’ Johnson
(1971, pp. 40-42)
obtains
this same result.
K. P. Kimbrough
income
is needed.
/ Growth, r&true
Real income
prices. and exchange rates
141
is given by
or using (2) and (3) by
Therefore,
the change
in real income
is given by
(10) The change in income in terms of traded goods can be broken down into two components. First, there is the change as the economy moves to its new production possibilities frontier holding the allocation of factors constant. The preceding discussion indicates that this change is zero. The second component is the change as the economy moves along its new production possibilities frontier. Using the envelope theorem it follows that
or, using (9),
(11)
I%= - (77+l)gA-$1. Substituting
(9) and (11) into (10) it is easily seen that
g=Cxg.
(12)
That is, the change in real income due to technological progress in the non-traded sector is equal to the share of non-traded goods times the rate of technological progress. Using (9) and (12) in (6) it follows that the change in the exchange rate associated with neutral technological change in the non-traded sector is
S=@+
ljg-Oag.
The second term in (13) captures
(13) the impact
of the change in real income
142
K.P. Kimbrough
/ Growth, relative prices, and exchange rates
which works to appreciate the domestic currency. However, working against this is the fall in the relative price of non-traded goods which is captured by the first term. The net effect will depend on whether the extra real cash balances generated by the fall in the price level (at a given exchange rate) accompanying the fall in the relative price of non-traded goods exceeds or falls short of the increased demand for real balances associated with the increase in real income. To highlight the factors that might cause the domestic currency to depreciate, rather than appreciate as conventional wisdom suggests, consider the case where the income elasticity of demand for money (+) is unity so that (13) reduces to
i=a(v+
l)g/(&-17’).
Therefore, if the demand for non-traded goods is inelastic (- 1 < n -=c0), growth due to neutral technological progress in the non-traded sector will be associated with a depreciation of the domestic currency. However, if the demand for non-traded goods is elastic the domestic currency will appreciate. This result is of interest because one is the most commonly suggested point estimate for the income elasticity of money demand. Note that lower income elasticities of the demand for money, as suggested by the inventory approaches of Baumol (1952) and Tobin (1956) would tend to enhance the likelihood that the domestic currency will depreciate in this special case by reducing the magnitude of the second term in (13). In light of these theoretical arguments, why is it that as an empirical matter growth does in fact tend to be associated with an appreciating currency? First, non-traded goods may not be ‘that important’ on two counts. On the one hand countries may be very open in the sense that a: is small, while on the other many goods that are non-traded may be very close substitutes for traded goods so that their relative prices will change little, if at all, as a country grows. Second, as suggested by Balassa (1964) technological progress in the non-traded sector can be expected to lag behind that in the traded sector. This seems particularly likely in light of the fact that services bulk heavily in the non-traded sector. The ‘slowness’ of technological progress in the non-traded sector tends to cause the relative price of non-traded goods to rise as an economy grows. Hence both terms in (6) will often work to appreciate the currency of a growing economy. The conclusion emerging from this paper is that growth per se, that is
K.P. Kimbrough
/ Growth, relative prices, and exchange rates
143
the rise in real income experienced by a country as its production possibilities frontier shifts outward, tends to appreciate a country’s currency as argued by Mundell and others. In principle this link between growth and an appreciating currency may be reversed by the changes in relative prices associated with a growing economy. However, as an empirical matter this possibility, that growth may lead to a depreciating currency, does not appear to be characteristic of growing economies.
References Balassa, Bela, 1964, The purchasing power parity doctrine: A reappraisal, Journal of Political Economy 72, 584-596. Baumol, William J., 1952, The transaction demand for money: An inventory theoretic approach, Quarterly Journal of Economics 66, 545-556. Dornbusch, Rudiger, 1976, The theory of flexible exchange rate regimes and macroeconomic policy, Scandinavian Journal of Economics 78, 255-275. Johnson, Harry G., 1971, Two-sector model of general equilibrium (Aldine, Chicago, IL). Mundell, Robert A., 1968, International economics (Macmillan, New York). Tobin, James, 1956, The interest-elasticity of transactions demand for cash, Review of Economics and Statistics 38, 241-247.