Chapter

7 Trade Elasticities and the Exchange Rate

Author(s):
Alessandro Prati, Luca Ricci, Lone Engbo Christiansen, Stephen Tokarick, and Thierry Tressel
Published Date:
March 2011
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Chapters 1 and 2 of this paper discussed the macrobalance approach, which is one method a researcher can use to determine the extent to which a country’s current account balance deviates from its long-run, sustainable value. Once the magnitude of any change in the current account is estimated, one would then like to know how changes in a country’s exchange rate would close any gap between the level of the actual current account and its long-run sustainable value. Changes in exchange rates alter prices and trade flows, and Chapter 6 described this relationship—elasticities of demand and supply for exports and imports. This chapter describes how those trade elasticities can be used to estimate how a change in a country’s exchange rate affects its trade balance—a key component of its current account. The chapter also explains the conditions that must be satisfied in order for various types of exchange rate changes to have desired impacts on the trade balance. In particular, under what circumstances will a depreciation improve the trade balance and the current account? In general, it will depend on the values of the trade elasticities. This chapter also presents estimates of how changes in exchange rates affect the trade balances of about 150 countries, using the elasticity values discussed in Chapter 6.

The General Formula for Trade Balance Elasticities

First, an analytical expression is derived for how a change in a country’s real exchange rate would affect its trade balance. The analysis also shows how the elasticities estimated in Chapter 6 can be used in this exercise.

A country’s trade balance, as measured by foreign currency, can be written

where PE* is the price of exports in foreign currency, P*M is the price of imports in foreign currency, E is the volume of exports, M is the volume of imports, and TB* is the trade balance. Note that E and M are functions of both the domestic and foreign prices of each good. Totally differentiating equation 7.1 gives

where ˆ denotes proportional change, that is, M=dMM. The domestic prices of imports (PM) and exports (PE) are related to foreign prices and the nominal exchange rate (r) as follows:

To allow for the possibility that changes in foreign prices or the exchange rate are not fully passed through into domestic prices, the above equations can be modified to include pass-through coefficients. For example,

where ΦM and ΦE are the pass-though coefficients for import and export prices, respectively, and lie between zero and one. If ΦM = ΦE = 1, then pass-through is complete and changes in foreign prices are fully reflected in domestic prices. There is no consensus in the literature on values for these parameters. Frankel, Parsley, and Wei (2005) estimate that for developing countries and emerging markets, the pass-through coefficient is in the range of 0.66 to 0.77.

In equation 7.2, expressions for changes in foreign prices and quantities are needed. Define the following:

E^D=ηEp^E* (export demand equation, with export demand elasticity ηE < 0)

E^S=ɛEp^E (export supply equation, with export supply elasticity εE > 0)

M^D=ηMp^M (import demand equation, with import demand elasticity ηM < 0)

M^s=ɛMp^M* (import supply equation, with import supply elasticity εM > 0).

In these equations, export demand and import supply depend on foreign prices, while import demand and export supply depend on domestic prices. In the export market, export demand must equal export supply (E^D=E^S):ηEp^E*=ɛEp^E. Using equation 7.4, the solution for p^E* is

Following a similar procedure to solve for p^M* yields

Note that choices of elasticity values determine the response of p^E* to a change in r. For example, if the country under consideration is “small,” then ηE = ∞ and p^E*=0 from equation 7.5. Also, small implies that the import supply elasticity is infinite. From equation 7.6, εM = ∞ implies that p^M*=0. So, a small country is unable to influence the foreign currency prices of exports and imports.

Substituting equations 7.5 and 7.6 into equation 7.2, along with the solutions for E^ and M^, gives

Dividing both sides of equation 7.7 by GDP (denominated in the foreign currency) gives

where SE and SM are the shares of exports and imports in GDP, respectively. To compute how the trade balance would change, denominated in domestic currency, use the relationship

where TB is the trade balance measured in domestic currency.

Differentiating equation 7.9 with respect to r gives

or,

Substituting equation 7.7 into equation 7.11 and manipulating, gives

It needs to be emphasized that a devaluation could cause the trade balance to improve when measured in foreign currency terms, but deteriorate when measured in domestic currency terms. Consider the small-country case, where prices are fixed in foreign currency terms. Suppose a devaluation raises the domestic prices of imports and exports by the full amount of the exchange rate change—the case of full pass-through. Then export volume will rise and import volume will fall. Measured at foreign prices, the trade balance must improve because foreign prices are fixed and export volume increased, while import volume decreased. So the change in the trade balance must be positive. Measured at domestic prices, however, the change in the trade balance could be positive or negative. On the export side, the domestic price of exports rises and so does volume, so export revenue must increase. On the import side, however, expenditure on imports could rise or fall because the domestic price of imports rises with the devaluation, but the volume falls. So what happens to import expenditure depends on the elasticity of demand for imports, as shown in equation 7.12—it will depend on whether ηM is greater or less than one. Using equation 7.10 it is easy to see that the only situation in which the trade balance must change in the same direction in both foreign and domestic currency is if the trade balance is initially zero.

Special Cases

Equations 7.8 and 7.12 are general formulas that show how a change in a country’s real exchange rate affects its trade balance. A few special cases are of particular interest: a small country, with assumptions of being a price taker in both export and import markets, which is most appropriate for LICs; and the standard Keynesian assumption underlying the usual Marshall-Lerner condition.

Case 1: Small-Country Assumption (ηE =∞, εM =∞)

Many LICs are “small” in world markets for their imports and exports, that is, they are unable to affect prices denominated in foreign currency by how much they buy or sell. Under these assumptions, both the export demand elasticity that they face and their import supply elasticity would be infinite. In this case, letting ηE = εM = ∞, equation (7.8) reduces to a simple form:

where εE is a country’s export supply elasticity (defined as a positive number) and ηM is the import demand elasticity (defined as a negative number). Given that the shares of exports and imports in GDP are positive, equation 7.13 must be negative. That is, under the small-country assumption, an appreciation of the real exchange rate must worsen the trade balance (or alternatively, a depreciation of the real exchange rate will improve the trade balance). A depreciation raises the domestic currency price of exports (while the foreign price remains unchanged), causing producers to increase the quantity of exports supplied. It also raises the domestic currency price of imports (while the foreign price remains unchanged), causing consumers to reduce the quantity of imports demanded. Both of these effects work to improve the trade balance. Tables 6.1 and 6.2 presented estimated values for export supply εE and import demand elasticities ηM. Using these elasticity values together with equation 7.13, it is possible to calculate how a given change in a country’s exchange rate would affect its trade balance.

Case 2: Keynesian Assumption (ε;E =∞, εM =∞)

One case that has received attention is the so-called “Keynesian case”—a situation in which a country can influence the price of exports but not the price of imports (Kindleberger and Lindert, 1978, p. 539). If the supplies of both exports and imports are assumed to be perfectly elastic, equation 7.12 reduces to

Equation 7.14 is frequently referred to as the Marshall-Lerner condition, which is the condition for a depreciation to improve the trade balance in the special case in which supply elasticities are assumed to be infinite and ΦEM = 1 (full pass-through). Under these assumptions, a depreciation will improve the trade balance when trade is balanced initially (SE = SM) if the sum of the export and import demand elasticities is greater than one.1

In summary, the Keynesian case assumes that both export and import supply elasticities are infinite, while the small-country assumption assumes that the export demand and import supply elasticities are infinite. This difference reflects alternative assumptions about pricing behavior in countries, namely, whether producers set prices in domestic or foreign currency. If countries are unable to affect the foreign prices of the goods they import and export, it would be appropriate to use the small-country assumptions with regard to elasticities. If the countries under study have some market power, that is, are able to influence foreign prices by how much they sell, it would be appropriate to use an export demand elasticity that is less than infinity. A consequence of using the small-country assumptions is that a real devaluation will always improve the trade balance because a devaluation cannot reduce the foreign-currency prices of imports and exports, so the devaluation only affects trade volumes—export volume rises and import volume declines. In the Keynesian case, a devaluation will in general have ambiguous effects on the trade balance in domestic currency terms. Table 7.1 summarizes the cases described above and presents the conditions for a devaluation to improve the trade balance.

Table 7.1.Summary of How Changes in the Exchange Rate Affect the Trade Balance
Small Country CaseKeynesian CaseGeneral Case
Elasticity valuesηE=ηE<0ηE<0
ϵE>0ϵE=ϵE>0
ηM<0ηM<0ηM<0
ϵM=ϵM=ϵM>0
Condition for devaluation to improve trade balance in foreign currencySEϵEΦE+SMηMΦM<0SE(ηE+1)+SMηMΦM<0SE[ɛEΦE(ηE+1)ηEɛEΦE]SM[ηMΦM(1+ɛM)ηMΦMɛM]<0
Condition for devaluation to improve trade balance in domestic currencySE(1+ϵEΦE)+SM(1+ηMΦM)<0SEηE+SM(1+ηMΦM)<0SE[ηE(1+ɛEΦE)ηEɛEΦE]SM[ɛM(1+ηMΦM)ηMΦMɛM]<0
Note: ηE is the export demand elasticity; εE is the export supply elasticity; ηm is the import demand elasticity; εm is the import supply elasticity; ΦE measures the extent of pass-through into export prices; ΦM measures the extent of pass-through into import prices; and SE and SM are the shares of exports and imports in GDP.
Note: ηE is the export demand elasticity; εE is the export supply elasticity; ηm is the import demand elasticity; εm is the import supply elasticity; ΦE measures the extent of pass-through into export prices; ΦM measures the extent of pass-through into import prices; and SE and SM are the shares of exports and imports in GDP.

For a discussion on the relationship between the calculations presented in this section and trade balance elasticities with respect to the real exchange rate, or for extensions to imperfect competition and less-than-perfect labor mobility, see Tokarick (2010).

For illustrative purposes, Table 7.2 reports the trade balance elasticities that result from using various formulae. The column labeled “Keynesian” assumes that export and import supply elasticities are infinite, while export and import demand elasticities are set—for most countries—at the value adopted in Lee and others (2008), that is, -0.71 and -0.92, respectively.2 The column labeled “Small country” lists the trade balance elasticities that result from assuming that import supply and export demand elasticities are infinite, and setting the import demand and export supply elasticities at their respective country-specific, long-run general equilibrium values calculated in Chapter 6 and reported in Tables 6.1 and 6.2 (last column on the right, labeled “Adjusted to include general equilibrium effects, LR”).

Table 7.2.Trade Balance Elasticities
Domestic CurrencyForeign Currency
KeynesianGeneralSmall countryKeynesianGeneralSmall country
Low-Income1
Bangladesh-0.140.06-0.42-0.28-0.07-0.56
Benin-0.06-0.18-0.23-0.16-0.28-0.33
Burkina Faso-0.07-0.23-0.29-0.21-0.36-0.42
Burundi-0.08-0.25-0.36-0.38-0.55-0.67
Cambodia-0.38-0.79-1.19-0.51-0.92-1.32
Central African Rep.-0.10-0.24-0.30-0.18-0.33-0.38
Chad-0.31-0.65-0.81-0.36-0.70-0.86
Congo, Dem. Rep.-0.43-0.71-0.87-0.45-0.74-0.90
Côte d’Ivoire-0.29-0.60-0.81-0.28-0.58-0.79
Eritrea-0.05-0.12-0.18-0.13-0.20-0.26
Ethiopia-0.12-0.23-0.37-0.36-0.47-0.60
Gambia, The-0.30-0.76-1.00-0.55-1.02-1.25
Ghana-0.20-0.52-0.68-0.39-0.71-0.87
Guinea-0.17-0.44-0.57-0.32-0.59-0.73
Guinea-Bissau-0.18-0.45-0.59-0.33-0.61-0.74
India-0.14-0.11-0.38-0.19-0.16-0.43
Kenya-0.15-0.29-0.46-0.24-0.39-0.56
Kyrgyz Rep.-0.42-0.64-1.23-0.70-0.92-1.51
Lao People’s Dem. Rep.-0.19-0.25-0.45-0.22-0.28-0.48
Madagascar-0.22-0.41-0.77-0.25-0.43-0.80
Malawi-0.15-0.19-0.38-0.37-0.42-0.61
Mali-0.13-0.31-0.40-0.20-0.37-0.47
Mauritania-0.27-0.59-0.79-0.32-0.64-0.84
Mozambique-0.17-0.14-0.51-0.28-0.26-0.62
Nepal-0.07-0.08-0.27-0.27-0.27-0.46
Niger-0.12-0.35-0.44-0.30-0.54-0.63
Nigeria-0.36-0.60-0.72-0.19-0.43-0.55
Pakistan-0.08-0.08-0.22-0.16-0.16-0.30
Papua New Guinea-0.40-0.42-1.10-0.44-0.46-1.14
Rwanda-0.06-0.17-0.25-0.25-0.36-0.44
Senegal-0.15-0.36-0.51-0.34-0.56-0.71
Sierra Leone-0.16-0.37-0.49-0.24-0.46-0.58
Tajikistan-0.08-0.28-0.44-0.49-0.68-0.85
Tanzania-0.18-0.22-0.47-0.35-0.40-0.64
Togo-0.32-0.81-1.06-0.56-1.05-1.30
Uganda-0.12-0.09-0.25-0.28-0.25-0.41
Uzbekistan-0.27-0.43-0.81-0.21-0.37-0.75
Vietnam-0.57-1.69-2.60-0.71-1.83-2.75
Zambia-0.17-0.28-0.45-0.21-0.33-0.49
Mean-0.20-0.39-0.62-0.32-0.52-0.74
Median-0.17-0.31-0.47-0.28-0.43-0.63
Standard deviation0.120.310.430.140.320.44
Lower-Middle-Income1
Albania-0.17-0.19-0.44-0.39-0.42-0.66
Algeria-0.33-0.60-0.71-0.20-0.46-0.57
Armenia-0.11-0.24-0.53-0.34-0.46-0.76
Azerbaijan-0.40-0.85-1.33-0.23-0.69-1.17
Belarus-0.42-0.26-1.54-0.46-0.30-1.58
Bolivia-0.23-0.34-0.58-0.20-0.30-0.54
Bulgaria-0.47-1.01-1.68-0.58-1.12-1.79
Cameroon-0.14-0.31-0.38-0.18-0.34-0.42
China-0.33-0.31-0.85-0.23-0.22-0.75
Colombia-0.15-0.19-0.38-0.18-0.22-0.41
Congo, Republic of-0.59-1.10-1.40-0.41-0.93-1.22
Dominican Republic-0.19-0.48-0.82-0.26-0.55-0.89
Ecuador-0.23-0.52-0.70-0.25-0.54-0.72
Egypt-0.21-0.30-0.50-0.30-0.39-0.59
El Salvador-0.16-0.29-0.64-0.35-0.49-0.84
Georgia-0.26-0.38-0.92-0.46-0.58-1.12
Guatemala-0.15-0.28-0.57-0.28-0.41-0.70
Honduras-0.37-0.64-1.42-0.69-0.97-1.75
Indonesia-0.19-0.27-0.40-0.18-0.26-0.38
Jordan-0.37-0.66-0.81-0.72-1.01-1.16
Lesotho-0.38-0.21-1.03-0.76-0.59-1.41
Macedonia, FYR-0.44-0.69-1.45-0.67-0.92-1.68
Moldova-0.49-1.87-3.01-1.15-2.53-3.67
Mongolia-0.52-0.78-1.79-0.54-0.80-1.81
Morocco-0.25-0.49-0.99-0.34-0.58-1.08
Namibia-0.30-0.22-0.83-0.37-0.30-0.90
Nicaragua-0.31-0.72-1.41-0.64-1.05-1.74
Paraguay-0.48-0.72-1.43-0.52-0.77-1.47
Peru-0.15-0.20-0.41-0.17-0.22-0.43
Philippines-0.26-0.23-0.49-0.36-0.33-0.59
Syrian Arab Republic-0.26-0.43-0.53-0.35-0.52-0.62
Sri Lanka-0.15-0.19-0.41-0.25-0.29-0.51
Sudan-0.11-0.19-0.32-0.11-0.19-0.31
Swaziland-0.49-0.34-1.33-0.70-0.55-1.55
Thailand-0.58-0.26-0.73-0.57-0.26-0.72
Tunisia-0.40-0.99-1.58-0.42-1.01-1.60
Turkmenistan-0.30-0.42-0.83-0.08-0.20-0.61
Ukraine-0.32-0.35-1.08-0.45-0.48-1.21
Mean-0.31-0.49-0.95-0.40-0.59-1.05
Median-0.30-0.34-0.82-0.36-0.48-0.86
Standard deviation0.140.340.550.220.420.64
Upper-Middle-Income1
Argentina-0.14-0.28-0.45-0.13-0.27-0.44
Botswana-0.35-0.52-1.05-0.24-0.41-0.94
Brazil-0.10-0.14-0.30-0.09-0.13-0.29
Chile-0.23-0.51-0.73-0.30-0.57-0.79
Costa Rica-0.45-0.63-1.27-0.53-0.71-1.35
Croatia-0.36-0.48-1.62-0.42-0.54-1.68
Gabon-0.49-0.83-1.07-0.18-0.53-0.77
Jamaica-0.33-0.86-1.44-0.49-1.03-1.61
Kazakhstan-0.28-0.43-0.90-0.19-0.34-0.81
Latvia-0.24-0.53-1.31-0.31-0.60-1.38
Libya-0.63-1.09-1.30-0.29-0.76-0.97
Lithuania-0.45-0.66-1.55-0.53-0.74-1.63
Malaysia-1.21-0.95-1.91-1.01-0.75-1.71
Mauritius-0.45-0.32-0.79-0.54-0.41-0.88
Mexico-0.23-0.15-0.31-0.25-0.17-0.34
Panama-0.24-0.40-0.85-0.26-0.42-0.87
Poland-0.37-0.68-1.59-0.43-0.74-1.65
Romania-0.19-0.22-0.66-0.29-0.31-0.76
Russian Federation-0.13-0.23-0.30-0.14-0.23-0.30
South Africa-0.22-0.27-0.64-0.26-0.31-0.68
Turkey-0.24-0.39-0.69-0.32-0.47-0.76
Uruguay-0.23-0.33-0.67-0.20-0.31-0.64
Venezuela-0.23-0.53-0.58-0.23-0.53-0.57
Mean-0.34-0.50-0.96-0.33-0.49-0.95
Median-0.24-0.48-0.85-0.29-0.47-0.81
Standard deviation0.230.260.470.200.220.47
High-Income: Non-OECD1
Estonia-0.44-1.04-1.92-0.50-1.10-1.99
Hong Kong SAR-1.34-2.00-3.65-1.28-1.94-3.60
Israel-0.30-0.49-0.60-0.32-0.50-0.61
Oman-0.40-0.62-0.76-0.24-0.46-0.60
Saudi Arabia-0.45-0.70-0.86-0.31-0.56-0.72
Singapore-1.69-1.50-5.03-1.43-1.25-4.77
Slovenia-0.71-0.72-3.52-0.73-0.75-3.55
Trinidad and Tobago-0.32-0.67-1.22-0.26-0.61-1.15
Mean-0.71-0.97-2.20-0.63-0.90-2.12
Median-0.45-0.71-1.57-0.41-0.68-1.57
Standard deviation0.520.521.660.480.511.64
High-Income: OECD1
Australia-0.14-0.35-0.54-0.16-0.36-0.56
Austria-0.44-0.48-1.43-0.39-0.44-1.38
Belgium-0.70-0.39-2.97-0.68-0.37-2.94
Canada-0.21-0.21-0.71-0.19-0.20-0.69
Czech Republic-0.80-1.31-2.55-0.76-1.28-2.51
Denmark-0.35-0.33-1.12-0.32-0.31-1.10
Finland-0.340.05-0.70-0.300.09-0.66
France-0.20-0.28-0.71-0.23-0.30-0.74
Germany-0.370.03-1.54-0.320.08-1.50
Greece-0.13-0.21-0.50-0.22-0.30-0.59
Hungary-0.64-0.68-1.72-0.61-0.65-1.69
Ireland-0.55-0.24-1.10-0.41-0.11-0.96
Italy-0.23-0.29-0.70-0.23-0.29-0.71
Japan-0.12-0.10-0.47-0.11-0.10-0.46
Korea, Rep. of-0.37-0.01-0.71-0.38-0.02-0.72
Luxembourg-1.21-3.69-9.04-0.73-3.20-8.56
Netherlands-0.57-0.52-1.62-0.51-0.45-1.55
New Zealand-0.18-0.21-0.54-0.16-0.20-0.52
Norway-0.38-0.73-0.97-0.16-0.51-0.76
Portugal-0.23-0.49-1.19-0.28-0.54-1.23
Slovak Rep.-0.69-0.73-1.83-0.70-0.74-1.84
Spain-0.18-0.36-0.74-0.24-0.42-0.80
Sweden-0.370.09-1.10-0.310.14-1.05
Switzerland-0.47-0.45-1.52-0.39-0.38-1.44
United Kingdom-0.17-0.42-0.84-0.20-0.45-0.87
United States-0.09-0.21-0.50-0.12-0.24-0.53
Mean-0.39-0.48-1.44-0.35-0.44-1.40
Median-0.36-0.34-1.04-0.31-0.34-0.92
Standard deviation0.260.721.670.200.631.59
Overall
Mean-0.32-0.49-1.02-0.37-0.54-1.08
Median-0.26-0.39-0.77-0.31-0.46-0.76
Standard deviation0.240.451.010.220.430.97

Economies are grouped according to 2007 gross national income per capita, calculated using the World Bank Atlas method. The groups are as follows: low-income, $935 or less; lower-middle-income, $936-$3,705; upper-middle-income, $3,706-$11,455; and high-income, $11,456 or more.

Economies are grouped according to 2007 gross national income per capita, calculated using the World Bank Atlas method. The groups are as follows: low-income, $935 or less; lower-middle-income, $936-$3,705; upper-middle-income, $3,706-$11,455; and high-income, $11,456 or more.

The column labeled “General” in Table 7.2 refers to the trade balance elasticities that result from applying the assumptions listed in the last column of Table 7.1. For illustrative purposes, this case assumes that the import supply elasticity is infinite, import demand elasticities are taken from Table 6.1, export supply elasticities are taken from Table 6.2, and export demand elasticities are set equal to the value adopted for the illustration of the Keynesian case above (-0.71). This general formula would be appropriate to use for cases in which both the home country and foreign countries can influence the price of the country exports, but the home country is still a price taker in the imports market.

For all the trade balance elasticities reported in Table 7.2, it was assumed that ΦE = ΦM = 1, that is, the full pass-through case. Country-specific values could be used if known.

In Table 7.2, for most countries, the absolute value of the trade balance elasticity for the “general case” lies between the elasticities for the Keynesian case and the small-country case. An exception is Bangladesh, where the trade balance elasticity for the general case exceeds the Keynesian trade balance elasticity. Using the formula for changes in the trade balance in domestic currency terms, this will occur when

Substituting in the relevant values, this condition can be expressed as

Because the import demand elasticity for Bangladesh is relatively high (-0.33), the above condition is satisfied. However, for most other countries, the import demand elasticity is more negative. Also, a low value for (SESM) will increase the likelihood that the above condition is satisfied. In the case of Bangladesh, this ratio is 0.62. Because the bracketed term in the above condition is positive, a low value for (SESM) means that a low weight will be attached to this term.

1This is the case assumed in Lee and others (2008), who work with a sample of advanced economies and emerging markets and assume that countries possess at least some market power, since the export demand elasticity is assumed to be less than infinite.
2For a few countries, Lee and others (2008) adopt a different value. Import demand elasticities (ηM) are set at –1.0 for the euro area, United States, Malaysia, and Colombia; –0.67 for China; and –1.10 for Brazil. Export demand elasticities (ηE) are set at –0.85 for the United States and Brazil, –0.95 for China, and –0.94 for Malaysia. Lee and others also adjust overall export elasticities depending on the country share of commodity exports (whose elasticity is assumed to be –1.0).

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