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Intermediate Macroeconomics, EC2201

L4: National income in the open economy

Anna Seim

Department of Economics, Stockholm University

Spring 2017

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Contents and literature

• The balance of payments.

• National income in the open economy.

• Determinants of the current account.

• Global imbalances.

Literature: Jones (2014), Ch. 19. Klein (2016b).

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Dimensions of openness

• Openness in goods markets.• Choice between domestic and foreign goods.

• Openness in financial markets.• Choice between domestic and foreign financial assets.• Financial markets typically more open than goods markets.

• Openness in factor markets.• Workers may choose where to work.• Firms may choose where to locate plants.

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Extracted from: Jones (2014).

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Extracted from: Jones (2014).

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Agenda

1. The relation between trade flows and financial flows.

2. The determinants of trade flows and financial flows.

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• Goods markets and financial markets closely connected toeach other.

• All transactions with the rest of the world (ROW) aredocumented in a country’s balance of payments.

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The balance of payments (BoP)

• Detailed record of a country’s transactions with ROW at agiven point in time.

• Documents trade flows and financial flows.

• Comprises the current account and the capital account.

• Double-entry bookkeeping: all transactions enter twice, i.e.both as debits and credits.

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Notation and abbreviations

GDPt : gross domestic product.

GNPt : gross national product.

Ct : private consumption.

It : investment.

Gt : government purchases.

EXt : exports.

IMt : imports.

NXt : net exports (the trade balance).

NIAt : net income from abroad.

NTAt : net transfers from abroad.

CAt : the current account.

CAPt : the capital account.

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GDPt : generated using factors of production employed on theterritory of a given country.

GNPt : generated using factors of production owned by domesticresidents.

GNPt = GDPt +NIAt +NTAt ,

where NTAt are net transfers from abroad (mainly foreign aid) andNIAt includes:

• Compensation for work abroad.• Income from the ownership of foreign financial claims.• Non-financial property income (patents copyrights).

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The current account

Documents all payments to and from ROW.

CAt = EXt − IMt +NIAt +NTAt = NXt +NIAt +NTAt .

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The capital account

Documents net sales of assets to foreign residents.

Comprises:

• Foreign direct investment (FDI).• Financial investment.• Cash transactions.

CAt +CAPt = 0.

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GDP and GNP

GDPt = Ct + It +Gt +NXt .

GNPt = Ct + It +Gt +CAt .

GNPt −GDPt = CAt −NXt = NIAt +NTAt .

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A fictional balance of payments (Klein, 2016b)

Debit Credit

Imports of goods and services 120 Exports of goods and services 100

Net income from abroad 10

Net transfers from abroad 5

The capital account 5

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A fictional balance of payments cont’d.

The trade balance: −20.

The current account: −5.

Note that the debit side and the credit side both sum to 120.

Note that CAt +CAPt = 0.

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The national income identity

Yt = Ct + It +Gt +EXt − IMt︸ ︷︷ ︸NXt

, (1)

where Yt is GDP at time t.

Adding and subtracting taxes, Tt , from (1) and re-arranging:(Yt −Tt −Ct

)︸ ︷︷ ︸

SP

+

(Tt −Gt

)︸ ︷︷ ︸

SG

= It +NXt , (2)

where SP and SG denote private and government saving,respectively.

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Aggregate saving in an open economy

Letting S ≡ SP +SG we obtain

St = NXt + It . (3)

Re-arranging (3) we obtain:

NXt = St − It . (4)

The international flow of goods, NXt , must be equal to theinternational flow of capital, St − It .

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Saving and investment in a closed economy

Consider a closed economy where NXt = 0. This implies:

St = It .

In a closed economy, saving must equal investment.

In an open economy, countries may run trade deficits by borrowingfrom abroad according to (4).

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Extracted from: Jones (2014).

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Extracted from: Jones (2014).

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Extracted from: Jones (2014).

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What determines the current account?

• Recall (3): St = It +NXt .

• Two types of saving: accumulation of real capital, It , andaccumulation of financial claims on the rest of the worldresulting from NXt > 0.

• If St > It ⇒ NXt > 0.

• If St < It ⇒ NXt < 0.

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What determines saving?

• Given a desire to smooth consumption, sensible to borrowfrom abroad today and pay back tomorrow if

• Productivity is expected to increase, so that you are likely toproduce more in the future than today.

• You want to finance an investment that will improveproduction possibilities in the future.

• Public saving largely governed by the fiscal policy framework.More on this in the Swedish context below.

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The Norwegian example

• Large oil and gas findings in the late 1960s.

• Substantial increase in oil production (exports) from themid-1970s onwards.

• Norway went from a 12 percent current account deficit in1977 to a 16 percent current account surplus in 2007.

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A model of the current account (Klein, 2016b)

Consider a country that exists for two periods, t = 1,2.

Production possibilities are described by y1 ≥ 0, y2 ≥ 0 and

y21 + y2

2 ≤ 2, (5)

where yt is output in period t.

The country can borrow and lend in international capital marketswhere the rate of return is r .

Letting ct denote consumption, preferences are represented by

u(c1,c2) = c1 · c2. (6)

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Letting s denote saving in period 1 it must be true that

c1 = y1− s, (7)

andc2 = y2 + (1 + r)s. (8)

Combining (7) and (8) and re-arranging we obtain theintertemporal budget constraint:

c1 +c2

1 + r= y1 +

y2

1 + r. (9)

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Extracted from: Klein (2016b).

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Optimal consumption choice

We note that along any indifference curve

u(c1,c2) = c1 · c2 = k , (10)

where k is a constant.

Differentiating (10) with respect to c1 we obtain:

c2 + c1dc2

dc1= 0. (11)

Re-arranging, we find the slope of an indifference curve:

dc2

dc1=−c2

c1. (12)

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To find the slope of the budget line, differentiate (9) with respectto c1:

1 +1

(1 + r)

dc2

dc1= 0. (13)

Re-arranging (13) we obtain:

dc2

dc1=−(1 + r). (14)

Combining (12) and (14), we find that optimal consumptionsatisfies:1

c2

c1= (1 + r). (15)

1Note that we could also solve this problem of constrained optimisation byusing the Lagrangian, see Klein (2016b).

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Optimal production choice

To find the optimal production choice, find the slope of theproduction possibility frontier (PPF). Differentiating (5) withrespect to y1:

2y1 + 2y2dy2

dy1= 0. (16)

Re-arranging (16) we find that the slope is given by:

dy2

dy1=−y1

y2. (17)

Combining (17) and (14) we find that optimal production satisfies:

y1

y2= (1 + r). (18)

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The trade balance

Equation (7) implies that the trade balance in period 1 is given by:

CA = s = y1− c1. (19)

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Example 1: r = 0

Equation (18) implies y1 = y2.

Equation (5) implies 2y21 = 2 so that y1 = y2 = 1.

Equation (15) implies c2 = c1.

Equation (9) suggests 2c1 = 2 so that c1 = c2 = 1.

Equation (19) suggests CA = y1− c1 = 0.

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Example 2: r = 6

Equation (18) implies y1 = 7y2.

Equation (5) implies (7y2)2 + y22 = 2⇔ 50y2

2 = 2. We obtain: y2 = 1/5and y1 = 7/5.

Equation (15) implies c2 = 7c1.

Equation (9) suggests c1 + 7c17 = 7

5 + 135 ⇔ 2c1 = 10

7 . We obtain:c1 = 5/7 and c2 = 5.

Equation (19) suggests CA = y1− c1 = 24/35.

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Conclusions

• A higher interest rate makes the country produce more, andconsume less, in period 1.

• A higher interest rate thus results in a CA-surplus.

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The real exchange rate

The choice between domestic and foreign goods affected by theirrelative price: the real exchange rate.

The real exchange rate, q, is defined:

q =EP∗

P(20)

where E is the nominal exchange rate (in domestic currency perunit of foreign currency), P the domestic price level and P∗ theforeign price level.

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The current account and the real exchange rate

A real depreciation, ∆q > 0 makes domestic goods relativelycheaper.

A real appreciation, ∆q < 0 makes foreign goods relatively cheaper.

Next: the effect of a real depreciation on the current account.

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Notation

CA: the current account in terms of domestic goods.

EX : exports in terms of domestic goods.

IM∗: imports in terms of foreign goods.

Y : disposable domestic income.

Y ∗: disposable foreign income.

q: the real exchange rate as defined above.

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For simplicity, assume that CA = NX .

Exports increasing in q and Y ∗:

EX = EX (q,Y ∗), (21)

where ∂EX/∂q ≡ EXq > 0 and ∂EX/∂Y ∗ > 0.

Imports decreasing in q and Y :

IM∗ = IM∗(q,Y ), (22)

where ∂ IM∗/∂q ≡ IM∗q < 0 and ∂ IM∗/∂Y > 0.

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The current account:

CA(q,Y ∗,Y ) = EX (q,Y ∗)−q · IM∗(q,Y ). (23)

q · IM∗(q,Y ) measures imports in terms of domestic goods so thatall terms in (23) are expressed in terms of the same numeraire.

The volume effects of a depreciation, EXq > 0 and IM∗q < 0,improve the CA.

The value effect of a depreciation, increasing the value of importsmeasured in domestic goods through the direct effect on q in (23),worsen the CA.

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The Marshall-Lerner condition

Wanted: a condition for when

∂CA

∂q> 0.

Recall:d (f (x)g(x))

dx= fx(x)g(x) +gx(x)f (x).

This implies:

∂ (q · IM∗(q,Y ))

∂q= IM∗(q,Y ) +q · IM∗q(q,Y ).

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Differentiating (12)

∂CA

∂q= EXq− IM∗−q · IM∗q . (24)

Pre-multiplying (24) by q/EX :

q

EX

∂CA

∂q=

q ·EXq

EX− q · IM∗

EX−

q2 · IM∗qEX

.

Assume that CA = 0 initially so that EX = q · IM∗. This implies:

q

EX

∂CA

∂q=

q ·EXq

EX− q · IM∗

q · IM∗−

q2 · IM∗qq · IM∗

=q ·EXq

EX−1−

q · IM∗qIM∗

.

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We conclude:

∂CA

∂q> 0⇔ q ·EXq

EX︸ ︷︷ ︸η

−q · IM∗qIM∗︸ ︷︷ ︸

η∗

> 1,

where the price elasticity of exports, η , and the price elasticity ofimports, η∗, are defined so that they will be positive.

The Marshall-Lerner condition:

dCA

dq> 0⇔ η + η

∗ > 1

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The J-curve

Extracted from: Krugman, P.R., Obstfeld. M. and Melitz, M.J., (2015), International Economics: Theory andPolicy, Pearson Education Ltd.

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Price elasticities of exports and imports

Extracted from: Krugman, P.R., Obstfeld. M. and Melitz, M.J., (2015), International Economics: Theory andPolicy, Pearson Education Ltd.

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Global imbalances

• Over the last 15 years, some countries have been running largecurrent account deficits (US, UK, Greece, Portugal, Spain) whileothers have been running large current account surpluses (China,Germany, Japan, the oil exporters).

• ”Saving glut” in China, partly due to inadequate welfare andpension systems, creating incentives for private saving.

• Capital flows from China to the US.

• Concern: global economy sensitive to sudden disruptions to financialflows.

• Cause of the financial crisis of 2007-2009(?)

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Global imbalances

Extracted from: EEAG (2011), The EEAG Report on the European Economy 2011, CESifo, Munich.

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Extracted from: Jones (2014).

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Extracted from: Vredin, A., Floden, M. Larsson, A. and Ravn, M.O. (2012), Simple Rules, Difficult Times,Economic Policy Group Report 2012, SNS Forlag.

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The Swedish current account

• Large current account deficits prior to the crisis in the 1990s.

• Eliminated by large nominal (and real) depreciation when thefixed exchange rate was abandoned in 1992.

• Large current account surpluses from the mid 1990s onwards,largely due to fiscal consolidation.

• Note: more on exchange rates in Lecture 5. Details on theSwedish fiscal framework in Lecture 7.

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What we did

• The balance of payments.

• National income in the open economy.

• Determinants of the current account.

• Global imbalances.

Literature: Jones (2014), Ch. 19. Klein (2016b).

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