The classical model of the SMALL OPEN economy

The classical model of the SMALL OPEN

economy

Open Economy Macroeconomics

Dr hab. Joanna Siwińska-Gorzelak

Overview

• This lecture is based on the chapter „The Open Economy” from G. Mankiw „Macroeconomics”

• This lecture reviews

– accounting identities for the open economy

– the small open economy model

• what makes it “small”

• how the trade balance and exchange rate are determined

• how policies affect trade balance & exchange rate

Why learn this?

• To understand:

– what trade surpluses and trade deficits are.

– the link between the trade balance and net capital outflow or net lending to/borrowing from abroad

– why countries have huge trade deficits?

– what can the government do about this?

In an open economy,

• spending need not equal output

• saving need not equal investment

Preliminaries: spending in open economy

EX = exports = foreign spending on domestic goods

IM = imports = C f + I f + G f = spending on foreign goods

NX = net exports (a.k.a. the “trade balance”) = EX – IM

d fC C C

d fI I I

d fG G G

superscripts:

d = spending on domestic

goods

f = spending on foreign

goods

The national income identity in an open economy

d d dY C I G EX

( ) ( ) ( )f f fC C I I G G EX

( )f f fC I G EX C I G

C I G EX IM

C I G NX

The national income identity in an open economy

Y = C + I + G + NX

or, NX = Y – (C + I + G )

net exports

domestic

spending

output

Trade surpluses and deficits

• trade surplus: output > spending and exports > imports Size of the trade surplus = NX

• trade deficit: spending > output and imports > exports Size of the trade deficit = –NX

NX = EX – IM = Y – (C + I + G )

International capital flows

• Net capital outflow

= S – I

= net (out)flow of “loanable funds”

= net purchases of foreign assets the country’s purchases of foreign assets

minus foreign purchases of domestic assets

• When S > I, country is a net lender (funds flow out)

• When S < I, country is a net borrower (funds flow in)

The link between trade & cap. flows

NX = Y – (C + I + G )

implies

NX = (Y – C – G ) – I

= S – I

trade balance = net capital outflow

Thus,

a country with a trade deficit (NX < 0)

is a net borrower (S < I ).

Classical model of small open economy

• An open-economy version of the classical model of the closed economy:

• Includes many of the same elements:

– production function

– consumption function

– investment function

– exogenous policy variables

– assume fully flexible prices (!)

Y Y F K L ( , )

C C Y T ( )

I I r ( )

G G T T ,

Classical model of SOP

• Assumptions: fully flexible prices; production always equal to potential output, economy is small, capital is perfectly mobile across countries

• This is a long run model (!), not suitable to analyse short-term shocks and fluctuations

• But it is also NOT a very long run growth model

National saving: The supply of loanable funds

r

S, I

Assumption made here:

national saving does

not depend on the

interest rate

( )S Y C Y T G

S

Recall: types of saving

• private saving = (Y –T ) – C

• public saving = T – G

• national saving, S

= private saving + public saving

= (Y –T ) – C + T – G

= Y – C – G

Investment

• Recall from your macro course:

• Profit max. implies MPK = user cost

• User cost in its simplest form is:

• uc=(r+d)

• Hence, ceteris paribus, as r falls, the DESIRED level of capital stock increases, hence investment increases

Investment: The demand for loanable funds

Investment is still a

downward-sloping function

of the interest rate,

r *

but the exogenous

world interest rate…

…is one of the

several factors that

determines the

country’s level of

investment.

I (r* )

r

S, I

I (r )

If the economy were closed…

r

S, I

I (r )

S

rc

cI

S

r

( )

…the interest

rate would

adjust to

equate

investment

and saving:

Assumptions: Capital flows

a. domestic & foreign bonds are perfect substitutes (same risk, maturity, etc.);

b. perfect capital mobility: no restrictions on international trade in assets

c. economy is small: cannot affect the world interest rate, denoted r*

a & b imply r = r*

c implies r* is exogenous

But in a small open economy…

r

S, I

I (r )

S

rc

r*

I 1

the exogenous

world interest

rate determines

investment…

…and the

difference

between saving

and investment

determines net

capital (out)flow

and net exports

NX

A small open economy that lends abroad, with saving dependent on the interest rate

A small open economy that borrows from abroad, with saving that depends on the interest rate

Saving and Investment in a Small Open Economy

• Result: rw may be such that Sd > Id, Sd = Id, or Sd < Id

– If Sd > Id, the excess of desired saving over desired investment is lent internationally (net foreign lending is positive) and NX > 0

– If Sd = Id, there is no net foreign lending and NX = 0

– If Sd < Id, the excess of desired investment over desired saving is financed by borrowing internationally (net foreign lending is negative) and NX < 0

Next, three experiments:

1. Fiscal policy at home

2. Fiscal policy abroad

3. An increase in investment demand


r

S, I

I (r )

1S

I 1

An increase in G

or decrease in T

reduces saving. 1

*r

NX1

2S

NX2

Results:

0I

0NX S


• Recall that national saving is a sum of government saving and private saving

• The previous slide assumed that the change in fiscal policy will not affect private savings

• However, recall Ricardian Equivalence that holds that a change in public saving will be offset by the change in private saving

The Ricardian view

• due to David Ricardo (1820), more recently advanced by Robert Barro

• According to Ricardian equivalence,

a debt-financed tax cut has no effect on

consumption, national saving, net exports, or real

GDP, even in the short run.

The logic of Ricardian Equivalence

• Consumers are forward-looking, know that a debt-financed tax cut today implies an increase in future taxes that is equal – in present value – to the tax cut.

• The tax cut does not make consumers better off, so they do not increase consumption spending.

Instead, they save the full tax cut in order to repay the future tax liability.

• Result: Private saving rises by the amount public saving falls, leaving national saving unchanged.


r

S, I

I (r )

1SExpansionary

fiscal policy

abroad raises

the world

interest rate. 1

*rNX1

NX2

Results:

0I

0NX I

2

*r

1( )*I r2( )*I r


r

S, I

I (r )1

EXERCISE:

Use the model to

determine the impact

of an increase in

investment demand

on NX, S, I, and

net capital outflow.

NX1

*r

I 1

S


r

S, I

I (r )1

ANSWERS:

I > 0,

S = 0,

net capital

outflow and

NX fall by the

amount I

NX2

NX1

*r

I 1 I 2

S

I (r )2

The nominal exchange rate

e = nominal exchange rate, the relative price of foreign currency in terms of domestic currency OR domestic currency in terms of foreign currency

The real exchange rate is the price level adjusted exchange rate.

Its meant to capture the relative value of goods and services

across countries

P

PeRER

*

Nominal Exchange Rate

(DOMESTIC currency to

FOREIGN currency) Domestic price

Foreign price

The real exchange rate

~ McZample ~

• one good: Big Mac

• price in PL: P = 10 PLN

• price in USA: P* = $4.00

• nominal exchange rate e = 4 PLN/$ To buy a U.S. Big Mac,

someone from PL

would have to pay an

amount that could buy

1.6 Polish Big Mac.

slide 32

6,110

16

10

4*4*

PLN

PLN

PLN

USDUSD

PLN

P

eP

ε in the real world & our model

• In the real world: We can think of ε as the relative price of a basket of domestic goods in terms of a basket of foreign goods

• In our macro model: There’s just one good, “output.” So ε is the relative price of one country’s output in terms of the other country’s output

How NX depends on ε

ε Home goods become LESS expensive relative

to foreign goods

IM, EX

NX INCREASES

The net exports function

• The net exports function reflects this positive

relationship between NX and ε :

NX = NX(ε )

The NX curve for Home.

0 NX

ε

NX (ε)

ε1

When ε is

relatively high,

Home goods are

relatively

inexpensive

NX(ε1)

so Home

net exports

will

be high

How ε is determined

• The accounting identity says NX = S – I

• We saw earlier how S – I is determined:

– S depends on domestic factors (output, fiscal policy variables, etc)

– I is determined by the world interest rate r *

• So, ε must adjust to ensure

( ) ( )*NX ε S I r

How ε is determined

Neither S nor I depend on ε, so the net capital outflow curve is vertical.

ε

NX

NX(ε )

1 ( *)S I r

ε adjusts to

equate NX

with net capital

outflow, S I.

ε 1

NX 1

Interpretation: Supply and demand in the foreign exchange market

Demand (NX):

Demand for home currency to buy home’s net exports.

ε

NX

NX(ε )

1 ( *)S I r

Supply:

Net capital flow (S

I )

is the supply of

home currency

offered to buy

Foreign’s assets.

ε 1

NX 1

Next, four experiments:




4. Trade policy to restrict imports


A fiscal expansion reduces national saving, decreases net capital outflow, and the supply of home currency in the foreign exchange market…

…causing the real exchange rate

to appreciate and NX to decline

(i.e. trade DEFICT to increase)

ε

NX

NX(ε )

1 ( *)S I r

ε 2

NX 1 NX 2

2 ( *)S I r

ε 1


An increase in r* reduces investment, increasing net capital outflow and the supply of home currency in the foreign exchange market…

…causing the real

exchange rate to

depreciate and NX to rise.

ε

NX

NX(ε )

1 1( *)S I r

NX 1

ε 2

21 ( )*S I r

ε 1

NX 2

3. Increase in investment demand

An increase in investment demand decreases net capital outflow and the supply of home currency in the foreign exchange market…

ε

NX

NX(ε )

…causing the real

exchange rate to

appreciate and NX

to fall.

ε 2

1 1S I

NX 1

21S I

NX 2

ε 1


At any given value of ε,

an import quota

IM NX

increases the (net)

demand for

home currency

ε

NX

NX (ε )1

S I

NX1

ε 2

NX (ε )2

Trade policy doesn’t

affect S or I , so

capital flows and the

(S-I) or supply of

currency remains

fixed.

ε 1


ε

NX

NX (ε )1 S I

NX1

ε 2

NX (ε )2

Results:

ε < 0

(demand

increase)

NX = 0

(supply fixed)

IM < 0

(policy)

EX < 0

(decrease in ε )

ε 1

The determinants of the nominal exchange rate - intro

• Start with the expression for the real exchange rate:

Solve for the nominal exchange rate:

P

Pe

*

eP

P

*

The determinants of the nominal exchange rate - intro

• So e depends on the real exchange rate and the price levels at home and abroad…

…and we know how each of them is determined:

( * , )M

L r YP

( ) ( )*NX ε S I r

** *

*( * *, )

ML r Y

P

*P

Pe

Implications for growth

• Recall the Solow growth model, where the setady state level of capital per labour depends on the amount of savings

• This no longer holds, as the level of investment – at least in theory – is detached from savings

• The steady-state value of capital stock should depend on world interest rate and on country’s marginal product of capital

The Open Economy

Chapter Summary

• Net exports--the difference between – exports and imports

– a country’s output (Y )

and its spending (C + I + G)

• Net capital outflow equals – purchases of foreign assets

minus foreign purchases of the country’s assets

– the difference between saving and investment

slide 49

Chapter Summary

• National income accounts identities: – Y = C + I + G + NX

– trade balance NX = S I net capital outflow

• Impact of policies on NX : – NX increases if policy causes S to rise

or I to fall

– NX does not change if policy affects neither S nor I. Example: trade policy

slide 50

Chapter Summary

• Exchange rates

– nominal: the price of a country’s currency in terms

of another country’s currency

– real: the price of a country’s goods in terms of

another country’s goods

– The real exchange rate equals the nominal rate

times the ratio of prices of the two countries.

slide 51

Chapter Summary

• How the real exchange rate is determined

– NX depends negatively on the real exchange rate,

other things equal

– The real exchange rate adjusts to equate

NX with net capital outflow

slide 52

The classical model of the SMALL OPEN economy

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