The Marshall-Lerner Condition and Empirical

The Marshall-Lerner Condition and Empirical
Estimates of Trade Elasticities
The chapter assumed that a real depreciation of a country’s currency improves its current
account. As we noted, however, the validity of this assumption depends on the response of
export and import volumes to real exchange rate changes. In this appendix we derive a condition
on those responses for the assumption in the text to be valid. The condition, called
the Marshall-Lerner condition, states that, all else equal, a real depreciation improves the
current account if export and import volumes are sufficiently elastic with respect to the real
exchange rate. (The condition is named after two of the economists who discovered it,
Alfred Marshall and Abba Lerner.) After deriving the Marshall-Lerner condition, we look
at empirical estimates of trade elasticities and analyze their implications for actual current
account responses to real exchange rate changes.
To start, write the current account, measured in domestic output units, as the difference
between exports and imports of goods and services similarly measured:
Above, export demand is written as a function of alone because foreign income is
being held constant.
Let denote the real exchange rate and let denote domestic imports measured
in terms of foreign, rather than domestic, output. The notation is used because
domestic imports from abroad, measured in foreign output, equal the volume of foreign
exports to the home country. If we identify with the price of foreign products in terms of
domestic products, then IM and are related by
that is, imports measured in domestic output
.15
The current account can therefore be expressed as
Now let stand for the effect of a rise in (a real depreciation) on export demand, and
let stand for the effect of a rise in on import volume. Thus,
EXq = ¢EX/¢q, EXq* = ¢EX*/¢q.
q EX*q
EXq q
CA(q,Yd) = EX(q) - q * EX*(q,Yd).
(imports measured in foreign output units)
= (domestic output units/foreign output unit) *
IM = q * EX*,
EX*
q
EX*
q EP*/P EX*
EP*/P
CA(EP*/P, Yd) = EX(EP*/P) - IM(EP*/P, Yd).
CHAPTER 17 Output and the Exchange Rate in the Short Run 461
As we saw in the chapter, is positive (a real depreciation makes home products relatively
cheaper and stimulates exports) while is negative (a relative cheapening of home
products reduces domestic import demand). Using these definitions, we can now ask how a
rise in affects the current account, all else equal.
If superscript 1 indicates the initial value of a variable while superscript 2 indicates its
value after has changed by , then the change in the current account
caused by a real exchange rate change is
Dividing through by gives the current account’s response to a change in ,
This equation summarizes the two current account effects of a real depreciation discussed
in the text, the volume effect and the value effect. The terms involving and
represent the volume effect, the effect of the change in on the number of output
units exported and imported. These terms are always positive because and
. The last term above, , represents the value effect, and it is preceded by a
minus sign. This last term tells us that a rise in worsens the current account to the extent that
it raises the domestic output value of the initial volume of imports.
We are interested in knowing when the right-hand side of the equation above is positive,
so that a real depreciation causes the current account balance to increase. To answer
this question, we first define the elasticity of export demand with respect to ,
and the elasticity of import demand with respect to ,
(The definition of involves a minus sign because , and we are defining trade
elasticities as positive numbers.) Returning to our equation for we multiply its
right-hand side by to express it in terms of trade elasticities. Then if the current
account is initially zero (that is, ), this last step shows that is
positive when
If the change in is assumed to be small, so that , the condition for an increase
in to improve the current account is
This is the Marshall-Lerner condition, which states that if the current account is initially
zero, a real currency depreciation causes a current account surplus if the sum of the relative
price elasticities of export and import demand exceeds 1. (If the current account is not
zero initially, the condition becomes more complex.) In applying the Marshall-Lerner condition,
remember that its derivation assumes that disposable income is held constant when
changes.
Now that we have the Marshall-Lerner condition, we can ask whether empirical estimates
of trade equations imply price elasticities consistent with this chapter’s assumption
q
h + h* 7 1.
q
q q2 L q1
h + (q2/q1)h* - 1 7 0.
EX1 = q1 * EX*1 ¢CA/¢q
(q1/EX1)
¢CA/¢q,
EX*q h* 6 0
h* = -(q1/EX*1)EX*q.
q
h = (q1/EX1)EXq,
q
q
EX*1 EX*q 6 0
EXq 7 0
q
EX*q EXq
¢CA/¢q = EXq - (q2 * EX*q) - EX*1.
¢q q
= ¢EX - (q2 * ¢EX*) - (¢q * EX*1).
¢CA = CA2 - CA1 = (EX2 - q2 * EX*2) - (EX1 - q1 * EX*1)
¢q
q ¢q = q2 - q1
q
EX*q
EXq
462 PART THREE Exchange Rates and Open-Economy Macroeconomics
that a real exchange rate depreciation improves the current account. Table 17A2-1 presents
International Monetary Fund elasticity estimates for trade in manufactured goods. The
table reports export and import price elasticities measured over three successively longer
time horizons, and thus allows for the possibility that export and import demands adjust
gradually to relative price changes, as in our discussion of the J-curve effect. “Impact”
elasticities measure the response of trade flows to relative price changes in the first six
months after the change; “short-run” elasticities apply to a one-year adjustment period;
and “long-run” elasticities measure the response of trade flows to the price changes over a
hypothetical infinite adjustment period.
For most countries, the impact elasticities are so small that the sum of the impact export
and import elasticities is less than 1. Since the impact elasticities usually fail to satisfy the
Marshall-Lerner condition, the estimates support the existence of an initial J-curve effect
that causes the current account to deteriorate immediately following a real depreciation.
It is also true, however, that most countries represented in the table satisfy the
Marshall-Lerner condition in the short run and that virtually all do so in the long run. The
evidence is therefore consistent with the assumption made in the chapter: Except over
short time periods, a real depreciation is likely to improve the current account, while a real
appreciation is likely to worsen it.