The Open Economy

February 9, 2009

1 The international flows of capital and goods

1.1 Trade balance

• A country’s spending need not equal its output of goods and services.The country can spend more than it produces and borrow the differencefrom abroad, or spend less than it produces and lend the difference toforeigners.

• We can write:Y = Cd + Id +Gd +EX,

where:

1. Cd is domestic consumption on domestic products

2. Id is investment (by local firms) in domestic goods

3. Gd is government purchases of domestic goods and services

4. EX is foreign spending on domestic goods and services, that is thevalue of exports in goods and services

• We can then reexpress the above equation as:

Y = (C − Cf ) + (I − If ) + (G−Gf ) +EX,

where C, I,G are total domestic consumption on all goods and services,total domestic investment, total government purchases, and Cf , If , Gf ,are the domestic consumption of foreign goods, domestic investment inforeign goods, and government purchase of foreign goods; thus:

Y = C + I +G− IM +EX,

whereIM = Cf + If +Gf

is the total domestic expenditure on imports.

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• We thus have:Y = C + I +G+NX,

whereNX = EX − IM

corresponds to net exports or the trade balance.

• We can reexpress the above equation as:

(Y − C −G)− I = NX,

that is:S − I = NX. (1)

• If both sides of the identity are negative, we have a trade deficit, and ifboth sides are positive we have a trade surplus.

=⇒ Table 5-1

1.2 Current account, capital account, and the balance ofpayments

• Current account: it is defined as:

CA = NX +NII +NT ,

where

1.NII = net invest. income,

that is the difference between payment to US holders of foreign assetsand payments to foreign holders of US assets;

2.NT = net transfers,

that is, the difference between foreign aid received from abroad andforeign aid provided to foreign countries.

• Current account deficit corresponds to CA < 0; current account surpluscorresponds to CA > 0.

• Capital account: if current account deficit, the US must borrow fromabroad to cover the gap. Thus, in theory,

−CA = net capital inflow

= net foreign holding of US assets.

Or, equivalently

CA = net capital outflow

= net US holding of foreign assets.

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2 Saving and investment in a small open econ-omy

• So far, all we have done is to rearrange accounting identities. We now needto explain the behavior of the variables defined in the previous section.

• Unlike in lecture 3, we no longer assume that the real interest rate adjustsso as to equalize savings and investment. Instead, we allow the countryto run a trade deficit or a trade surplus.

• In a small open economy with perfect capital mobility, the real interest ratemust equal the world real interest rate, that is:

r = r∗.

This is due to the fact that domestic lenders can arbitrage between lend-ing to domestic agents or to foreign agents, similarly domestic borrowerscan arbitrage between borrowing from domestic lenders or from foreignlenders.

• What determines the world interest rate: presumably, the equilibrium ofworld saving and world investment.

• Long-run trade balance: in the long-run prices are flexible and

Y = Y = F (K,L).

Therefore the trade balance is given by:

NX = S − I(r∗),

whereS = [Y − (c0 + c1(Y − T ))−G].

Thus the trade balance is determined by the difference between saving andinvestment at the world interest rate.

• Question: which variable will adjust so as to achieve trade balance?−→ the (real) exchange rate!

3 Exchange rates• The exchange rates between two countries are the prices at which theresidents of these two countries trade with each other.

• Nominal versus real exchange rates:

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1. Nominal exchange rate E is the relative price of the currency of twocountries. It is the number of units of domestic currency you canget per unit of the foreign currency, for example how many dollarsyou get for a yen. (Beware that this is not Mankiw’s definition; inMankiw, the nominal exchange rate is the number of yens per dollar,but our definition is the one generally followed in articles and booksin the US)

2. Real exchange rate is the relative price of the goods of two countries.The real exchange rate is sometimes called the terms of trade. Itis the price of a foreign good in terms of the equivalent domesticgoods, for example how many US cars you can buy for the price of aJapanese car.

3.1 Nominal exchange rate

• Nominal exchange rate appreciation is an increase of the value of thedollar relative to the yen. It therefore corresponds to a reduction in E.Conversely, a nominal exchange rate depreciation is a reduction in thevalue of the dollar relative to the yen. It therefore corresponds to anincrease in E.

• Example: the dollar relative to the DM over the past thirty years

−→ trend increase in E

−→ large fluctuations in E

3.2 Real exchange rate

• Recall that real exchange rate is the number of domestic cars I can buyfor the price of a foreign car. This is what people should ultimately beinterested in when choosing between purchasing their car in the US or inJapan

• How do we compute the real exchange rate?

1. first, since we deal with a variety of goods, we need to compute theprice of all the goods produced in Japan in terms of all the goodsproduced domestically in the US. This , in turn, corresponds to theratio between the GDP deflator in Japan and the GDP deflator inthe US, namely

P ∗/P.

2. then, the real exchange rate is simply equal to the ratio between theprice of Japanese good expressed in dollars and the price of a US goodexpressed in dollars. How do we compute this ratio? As follows:

the price of one unit of Japanese good in yens is

P ∗;

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thus, in dollars, this price is:

EP ∗;

the price of one unit of US good is

P ;

therefore the real exchange rate is:

=EP ∗

P= E × P ∗

P,

that is:

real exch rate = (nom exch rate)× foreign GDP deflatordomestic GDP deflator

.

• Real exchange rate appreciation corresponds to an increase in the relativeprice of domestic goods in terms of foreign goods, that is, to a reduction in. Conversely, real exchange rate depreciation corresponds to a reductionin the price of domestic goods in terms of foreign goods, that is, to anincrease in .

• Suppose that an American tourist goes abroad and hesitates between buy-ing a car abroad or in the US. And suppose our tourist faces the followingsituation: (a) the dollar has depreciated related to the foreign currency;(b) inflation has been bigger in the US. You can see right away that thechoice is ambiguous because E has gone up but P∗

P has gone down. Ul-timately, our tourist’s choice will depend upon which of these two effectsdominates. Japan and

4 Long-run equilibrium in an open economy• The higher the real exchange rate , the higher the price of one unit offoreign good compared to the price of one unit of a domestic good, andtherefore the less people will want to buy abroad. Thus, the higher , thehigher NX

=⇒NX = NX( ),

wheredNX

d> 0.

• Long-run equilibrium and the determination of the real exchange rate:

NX( ∗) = S − I(r∗).

• Comparative statics on the equilibrium exchange rate:

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1. starting from trade balance, an increase in government spending G ora reduction in domestic tax T will reduce (S − I) and thereby causea trade deficit. A reduction in the real exchange rate will restore thebalance. Because the real exchange rate decreases, domestic goodsbecome more expensive relative to foreign goods, which in turn causesexports to fall and imports to rise. As a result NX is reduced, so asto match the reduction in (S − I).

2. if the rest of the world increases government purchases or reducetaxes abroad, so that r∗ increases, then (S − I(r∗)) increases, andthis in turn induces a trade surplus in the domestic economy. Thistrade surplus results in an increase in the equilibrium real exchangerate. Domestic goods then become cheaper relative to foreign goods.

3. increasing investment demand reduces (S−I) which pushes the equi-librium real exchange rate downward.

4. Trade protection: suppose the government regulates import of foreigncars; then the whole NX( ) schedule shifts downward, which in turndecreases the equilibrium real exchange rate without affecting theequilibrium level of net trade export (S − I). What happens is thatthe appreciation of the real exchange rate makes domestic goods moreexpensive, which in turn reduces exports and eventually restore NXat (S−I). But since NX is unchanged and exports have gone down,.imports have also necessarily gone down. Overall, the volume oftrade has been reduced.

• Short-run equilibrium in goods market

−→ Y determined by demand conditions, and r = i

−→ modified IS curve:

Y − (c0 + c1(Y − T ))− I(i)−G = NX(Y, Y ∗, ).

−→ problem is that this equation has three unknowns, namely: Y, i, .

−→ we will see in the next section that in fact there is a missing arbitrageequation which links and i, and therefore allows us to turn this into anIS relationship between Y and i only.

5 The interest parity condition• Openness in financial markets implies that financial investors can choosebetween domestic bonds and foreign bonds

• This may appear as a double choice, first between domestic versus foreigncurrencies, and second between domestic and foreign financial assets, butin fact it is not: people hold money for transaction purposes, but youdon’t hold US dollars to make purchases in Japan! Thus the one choice is

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between domestic and foreign interest-paying assets, for example betweendomestic and foreign bonds.

• Suppose there are two periods, today and tomorrow. Today is date t,tomorrow is date t+1. You can either invest one dollar in Japanese bonds,or you can invest it in US bonds.

• If you invest your dollar in US bonds at date t, you get

(1 + it)

dollars at the beginning of period t+ 1.

• If you invest your dollar in Japanese bonds, this is how much you get:

1. first, you must buy yens with dollars. One dollar buys you (1/Et)yens, where Et is the nominal exchange rate at date t.

2. then, if you invest your (1/Et) yens in Japanese bonds, you obtain:

(1/Et)(1 + i∗t )

yens at the beginning of period t+ 1;

3. then, you reconvert these yens in dollars; but next period the ex-change rate is Et+1, so at the end you get back

(1/Et)(1 + i∗t )×Et+1.

• In equilibrium, there is perfect arbitrage between the two options andtherefore people are indifferent between them; in other words, we have:

1 + it = (1 + i∗t )Eet+1

Et.

This equation is commonly referred to as the interest parity condition( IPC).

• For small values of interest rates, the IPC can be approximated by:

it = i∗t +Eet+1 − Et

Et,

that is: the domestic nominal interest rate is approximately equal to theforeign nominal interest rate plus the expected depreciation rate of thedomestic currency.

• Short-run equilibrium:

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1. modified IS curve:−→ P = P ∗ (both prices are fixed, and for notational conveniencewe suppose they are equal); thus = E and therefore:

Y − (c0 + c1(Y − T ))− I(i)−G = NX(Y, Y ∗, E),

where, from IPC:

E =Ee

1 + i− i∗;

2. LM curve remains the same as before:

M

P= L(Y, i).

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