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Chapter 3Elasticity and

absorption approaches to the

balance of payments

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3.1 Introduction

This chapter studies two models that investigate the impact of exchange-rate changes on the current account position of a country: will a devaluation (or depreciation) of the exchange rate lead to a reduction of a current account deficit?

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The main contents of the chapter: Elasticity approach:examines the

effects of exchange-rate changes on the current account →3.2~3.4;

Absorption approach:examines the effects of exchange-rate changes on domestic income and spending →3.5~3.7;

Analyzing the similarities and differences between the two models →3.8.

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Note: Ignore the complications of unilateral

transfers and interest,profit and dividends on the current account balance and concentrate on the export and import of goods and services;

The exchange rate is defined as domestic currency units per unit of foreign currency.

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3.2 The Elasticity Approach to the Balance of Payments The approach provides an analysis of

what happens to the current account balance when the country devalues its currency.

The approach was pioneered by Alfred Marshall, Abba Lerner and later extended by Joan Robinson(1937) and Fritz Machlup(1955).

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Some simplifying assumptions: It focuses on demand conditions

and assumes that the supply elasticities for the domestic export good and foreign import good are perfectly elastic

changes in demand volumes have no effect on prices domestic and foreign prices are fixed changes in relative prices are caused by changes in the nominal exchange rate.

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Current account balance(CA) expressed in terms of the domestic currency:

CA=PXv-SP*Mv (3.1)

Where: P:the domestic price level; Xv:the volume of domestic exports;

S:the exchange rate; P*:the foreign price level; Mv:the volume of imports.

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Simplifications: Set the domestic and foreign

price levels at unity; The value of domestic

exports(PXv) is given by X; The foreign currency value of

imports(P*Mv) is given by M.

CA=X-SM (3.2)

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In difference form (3.2) becomes: d CA=d X-Sd M-Md S

(3.3)

Dividing (3.3) by the change in the exchange rate d S, we obtain:

(3.4)

dS

dSM

dS

dMS

dS

dX

dS

dCA

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Introduce two definitions:The price elasticity of demand for

exports: (3.5)The price elasticity of demand for

imports: (3.6)

SdS

XdXx X

S

dSdX x

SdS

MdMm M

S

dSdM m

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Substituting (3.5) and (3.6) into (3.4):

Dividing by M:

(3.7)

MMS

X

dS

dCAm

x )(

11

mx

SM

X

MdS

dCA

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Assuming X/SM=1, and rearranging (3.7) yields:

(3.8)

)1( mxMdS

dCA

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The Marshall-Lerner condition:Starting from a position of

equilibrium in the current account, a devaluation will improve the current account; that is, , only if the sum of the foreign elasticity of demand for exports and the home country elasticity of demand for imports is greater than unity,that is, .

1 mx

0/ dSdCA

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There are two effects in play once a currency is devalued:

(1)the price effect----exports become cheaper measured in foreign currency, and imports become more expensive measured in the home currency. The price effect clearly contributed to a worsening of the UK current account.

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(2)the volume effect----the fact that exports become cheaper should encourage an increased volume of exports, and the fact that imports become more expensive should lead to a decreased volume of imports. The volume effect clearly contributes to improve the current account.

The net effect depends upon whether the price or volume effect dominates.

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Given the assumption of less than infinite supply elasticity conditions and assuming initially balance trade, a more complicated condition needs to be satisfied:

(3.9) Where: :the domestic supply elasticity of

the export good; :the foreign supply elasticity for its

export good.

0)1()1(

mm

mm

mx

xx

x

m

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The effect of less than infinite supply elasticities: make the required demand elasticities less stringent in the sense that the current account may improve even if the sum of the demand elasticities is less than unity.

Why?There is two effects to ensure it.

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An increase in demand for exports some rise in the domestic price of exports give an additional boost to export revenues .

The fall in the demand for foreign imports reducing the foreign currency price of imports lowering import expenditure.

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3.3 Empirical Evidence on Import and Export Demand Elasticities

The elasticity approach led to much research into empirical estimates of the elasticities.

Economists are divided into two camps: Elasticity optimists: who believed that

the sum of these two elasticities tended to exceed unity;

Elasticity pessimists: on the contrary.

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It was argued that a devaluation may work better for industrial countries than for developing countries.

There are enormous problems involved in estimating the elasticities.

While the devaluation can improve the current account during a period of time, it does not preclude an initial J-curve effect.

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A general consensus accepted by most economists is that elasticities are lower in the short run than in the long run in which case the Marshall-Lerner conditions may only hold in the medium to long run.

J-curve effect: shows that there is a time lag before the current account is improved from the devaluation of the currency. The time lag may be 6 months or two year.

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The idea underlying the J-curve effect is that in the short run export volumes and import volumes do not change much, so that the price effect outweighs the volume effect leading to a deterioration in the current account. However, after a time lag export volumes start to increase and import volumes start to decline; consequently the current deficit starts to improve and eventually moves into surplus.

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Current account Surplus

0 time

DeficitFigure 3.1 the J-curve effect

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Three of the most important reasons: 1. A time lag in consumer responses:1) It takes time for domestic consumers

to switch away from foreign imported goods to domestically produced goods;

2) Foreign consumers may be reluctant to switch away from domestically produced goods towards the exports of the devaluing country.

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2. A time lag in producer responses:1) It takes time for domestic producers to

expand production of exportables;2) Orders for imports are normally made

well in advance and such contracts are not readily cancelled in the short run;

3) Factories will be reluctant to cancel orders for vital inputs and raw materials;

4) The payments for many imports will have been hedged against exchange risk in the forward market and so will be left unaffected by the devaluation.

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3. Imperfect competition:1) Foreign exporters might respond to

the loss in their competitiveness by reducing their export prices;

2) Foreign import competing industries might react to the threat of increased exports by the devaluing country by reducing prices in their home markets.

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4. It is unlikely the price of exports as measured in the domestic prices will remain fixed:

1) Many imports are used as inputs for exporting industries.

2) The increased price of imports may lead to higher wage costs.

Homework:1.在对进出口商品需求价格弹性值都不取相反数的情况下，推导直接和间接标价法下马歇尔 - 勒纳条件的数学表达式。

2.了解我国进出口商品的需求价格弹性是否满足马歇尔 - 勒纳条件， 2005年以来人民币的持续升值是否对我国贸易收支起到了改善作用。

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3.4 The pass-through effect of a depreciation or appreciation economists use the term pass

through effect to describe the extent to which a 1% depreciation (appreciation) leads to a rise (fall) in import prices(elasticity of exchange rate pass-through).

Complete pass through effect=1 Partial pass through effect<1

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On average there is partial pass-through effect in the short run.

Reasons:Foreign firms may decide to absorb part

of the depreciation by reducing their local currency price of exports to maintain their market share.

If a currency appreciates foreign firms may decide not to change their foreign currency prices to increase their profits as measured in their local currency.

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A recent paper by Yang(1997) found that the elasticity of pass-through was 0.3185 for one quarter of a year.

However, there was a quite a bit of dispersion between different industries.

As the time horizon increased, however, in all industries the elasticity of pass-through increased and often approached unity.

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One of the key factors determining the elasticity of pass-through being the degree of product differentiation; the greater the degree of product differentiation then the more ability of foreign exporters to raise their prices presumably.

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To the extent that there is only a partial pass-through effect on the price of imports in the short run, the effect will be to dampen the size and complicate the dynamics and timing of the J-curve effect.

3.了解我国人民币汇率变动的价格传递效应的大小，我国学者具体是如何来考查此效应的。

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3.5 The Absorption ApproachOne of the major defects of the

elasticity approach is that it assumes that all the other things are equal.

HoweverChanges in export and import volumes

changes in national incomeincome effects need to be incorporated

in a more comprehensive analysis.

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Alexander(1952) focus on the fact that a current account imbalance can be viewed as the difference between domestic output and domestic spending (absorption).

National income equation: Y=C+I+G+X-M (3.10) Define domestic absorption as

A=C+I+G CA=X-M=Y-A (3.11)If CA>0, then Y>A; if CA<0, then Y<A.

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Transforming equation(3.11) into difference form yield:

dCA=dY-dA (3.12)

It implies that the effects of a devaluation on the CA will depend upon how it affects Y relative to A.

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absorption determined by the marginal propensity

to Absorption absorb, aY; absorption derived by all the other effects from devaluation, Ad. dA=adY+dAd (3.13) Substituting (3.13) into (3.12) yields: dCA=(1-a)dY-dAd (3.14)

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Three factors need to be examined:1) 1-a>0 or <0;2) Y↑ or Y↓;3) Ad ↑ or Ad↓. The condition for a devaluation to

improve the CA is (1-a)dY>dAd; That is, any change in income not

spent on absorption must exceed any change in direct absorption.

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Note: To distinguish two possible

states of an economy: below full employment and full employment.

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3.6 The Effects of a Devaluation on National Income

Assume the economy is at less than full employment and a is less than unity,

A rise in income will improve CA, A fall in income will worsen CA. to consider the effects of

devaluation on national income.

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Two important effects on income: (less than full employment)1.Employment effect: M-L condition fulfilled net export↑

devaluation the foreign trade multiplier income and employment↑ M-L condition not fulfilled net export↓ income↓ The employment effect is not clear.

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2.Terms of trade effect: Terms of trade are the price of

exports divided by the price of imports, expressed as:

Price of exports P Price of imports SP*Where: P:domestic price. S:exchange rate. P*:foreign price.

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Devaluation → S↑ → P/SP*↓(P and P* unchanged) → the terms of trade deteriorate → imports more expensive in domestic terms → more units of exports have to be given to obtain a unit of imports → a loss of real national income.

The terms of trade effect lowers national income.

The overall effects are ambiguous.

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About the marginal propensity of absorption:

Even if income rises overall, the effects of devaluation on CA still depend upon the value of a.

If a<1, then CA improved; If a>1, then CA worsened.

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Although one may think that a will be less than unity, this need not be the case:

1)unemployed workers who obtain jobs are likely to have a high propensity to consume;

2)an increase in income may well stimulate a great deal of investment.

It is conceivable in the short run that a could be greater than unity a rise in income leads to a deterioration in CA.

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3.7 The Effects of Devaluation on Direct AbsorptionAssume the net effect of a

devaluation on income is zero to consider the effect of the devaluation on direct absorption.

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Possible ways in which devaluation can be expected to impact upon direct absorption:

1.Real balance effect:A money demand function: M/PI=k (3.15)

Where: k:some constant; PI:aggregate price index defined as:

PI=ąP+(1-ą)SP* (3.16)

Assume other factors unchanged, the devaluation (S↑) will raise the average price index(PI↑).

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Given an unchanged money stock (Ms:unchanged) and assumption that economic agents aim to maintain a given amount of real money balances (k:constant),

Then: S↑ → PI↑ k:constant M↑ Ms:unchanged sell bonds → push down the price of bonds raising the domestic interest rate → investment and consumption↓→ direct absorption↓.

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Note:For the real balance effect to come into

play, the authorities must not accommodate the increased money demand by a corresponding increase in the money supply.

If it is the case(Md↑ and Ms↑) → k can be kept constant without selling bonds → leave interest rate unchanged → I and C unchanged → direct absorption unchanged → the real balance effect will not come into play.

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2.Income redistribution effect:S↑ → PI↑ → income redistribution

If income of people with high a↑ direct

income of people with low a↓ A↑ If the reverse is true direct A

The overall effect on direct A is not clear.

↓

→

→

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A few possibilities:(a)PI↑→real income of those with

fixed incomes↓ overall income unchanged those with variable incomes will have gained

fixed incomes,poor,high a variable incomes,better off,low a direct A→ ↓

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(b) S↑ → company profits↑ not clear

S↑ → PI↑ →real wages↓

If firm: low a → direct A↓ workers: high a If expectations are favorable

→firms I↑→direct A↑

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(c)there are considerable income adjustments within groups of companies and workers:

S↑→ export companies profits↑ import companies profits↓ workers represented by strong tradeS↑→PI↑→ unions can secure compensating rise,

workers with no union representation may not secure compensating rise. The overall effect on Ad depend on whether

the companies and workers that gain have a higher a than those that lose.

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3.Money illusion effect:Money illusion:Mistaking changes in

nominal values for changes in real values; failing to allow for inflation.

Money illusion:refers to the tendency of people to think of currency in nominal, rather than real terms.

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S↑→PI↑→consumers real spending power↓ money illusion buy exactly the same bundle of goods as before→Ad↑;

S↑→PI↑money illusion works in reverse cut back direct absorption by more than the proportion to the price rise→Ad↓.

It is unlikely to be that significant and is more probably only a temporary rather than permanent factor.

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4.Expectational effects: S↑→PI↑→expect further price rise→

C↑→ direct A↑. S↑→PI↑→expect further price rise→

I↓→ direct A↓.

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5.Laursen-Metzler effect: Devaluation→terms of trade deteriorateTwo effects: Income effect:→lower national income→

income related A↓. Substitution effect:→domestically

produced goods cheaper than foreign produced goods→consumption of domestically produced goods↑→direct A↑.

if substitution effect outweigh income effect, direct A↑.

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Overall, the effects of a devaluation on current account are indeterminate.

None the less, the absorption approach has some important lessons for policy-makers. Its central message is that raising domestic income relative to domestic absorption will improve the current balance. In this respect, a devaluation is more likely to succeed if it is accompanied by economic policy measures that concentrate on raising income while constraining absorption.

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3.8 A Synthesis of the Elasticity and Absorption Approaches

Initially, the absorption approach was believed an alternative of the elasticity approach;

However, authors showed that the two models are not substitutes, but rather are complementary.

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How to understand this complementarity?

1)When analysing with the absorption approach, taking the price effect illustrated in the elasticity approach into account will affect the results:

If Marshall-Lerner condition is fulfilled, X-M>0, income↑;

If Marshall-Lerner condition is not fulfilled, X-M<0, income↓;

The Marshall-Lerner condition is clearly relevant to the absorption approach.

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2) When analysing with the elasticity approach, taking the income effect illustrated in the absorption approach into account will affect the results:

If the sum of elasticities is greater than unity the initial improvement of current account income increase imports increase the sum of elasticities needs to be somewhat greater than the unity value derived from the elasticity approach.

The absorption approach is relevant to the elasticity approach.

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3.9 Conclusions1.the final conclusion and correlation of the

two analyses Does not provide an unambiguous

answer; Are not alternative but complementary

theories.2.research methods Although are comparatively static in

nature, both point to the importance of dynamic forces and a time dimension.

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3.policy implication Two approaches have remained

influential because they contain clear and useful messages for policy-makers.

A devaluation is more likely to succeed when elasticities of demand for imports and exports are high and when it is accompanied by measures such as fiscal and monetary restraint that boost income relative to domestic absorption.

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4.notice At a two years and above horizon the

Marshall-Lerner conditions are fulfilled; Should not expect a devaluation to work

in the same manner for all countries; It will in part be determined by whether

or not the economy is at or below full employment and on the structural parameters;

Do not take the interaction between countries into account.

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Further reading: 黄苹，《汇率影响进出口国别结构的机理分析及弹性测度》，《商业研究》， 2008/06.

王相宁、李晓峰，《马歇尔－勒那条件的实证研究》，《运筹与管理》， 2005年 12 月。

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On the web: Learn more about the Canadian

economy at http://www.statcan.ca/. Visit the Brookings institution at

http://www.brook.edu for economic, foreign policy, and governmental studies and research.

To access research conducted by economists at the Federal Reserve Bank of New York, visit the Bank’s research page at http://www.ny.frb.org/research/.