Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

is effects

noved to the right-hand side function of the exogenous es, on the other hand, the , ved to the right-hand side function of the exogenous

p

-- a tical results in Table 11.1 the case of monetary policy c credit shifts the LM curve are too high and net capital is deficit (B < 0), which e. The domestic currency Es ), and the BP curve shifts e capital account recover !ry of the domestic interest rium is at el . Although it -1 Table 11.1 demonstrate

any value of KIT , the polar tained as special cases from "v■ e students are advised to

Chapter 11: The Open Economy

11.1.4 Aggregate supply considerations

Up to this point we have assumed that domestic and foreign price levels are constant (P = P* = 1). Whilst this may be appropriate under some conditions (e.g. in the very short run), it is nevertheless important to add a supply side to the Mundell-Fleming model of the small open economy. We use a model inspired by Argy and Salop (1979), Armington (1969), and Branson and Rotemberg (1980) to demonstrate the importance of supply-side effects. This model will also be used (in simplified form) in section 2 on the transmission of shocks and the coordination of economic policy in a two-country model of the world. We restrict attention to the case of perfect capital mobility and flexible exchange rates.

The Armington approach

Now that we wish to model the production side of the economy, we have to be more precise about the various price indexes. There are two goods, a domestic good with price P, and a foreign good with price P* in foreign currency (EP* is the price of the foreign good in domestic currency). These goods are imperfect substitutes for each other (otherwise one would expect purchasing power parity (PPP) to hold, so that the real exchange rate, would be identically equal to unity at all times). Real household consumption C and investment I are assumed to be determined by the usual macro-relations:

with 0 < Cy < 1 and /r < 0, and real government spending G is exogenously given. We now need to confront the issue of sourcing of the goods. For example, once the households know how much they wish to consume in the aggregate and in real terms, the next issue for them is to decide on where to purchase the goods (and the same holds for investment by firms and government consumption). The trick that was devised by Armington (1969) is to assume that, for example, C is in fact "constructed" out of domestically produced goods (labelled by Cd) and foreign produced goods (labelled by Cf). Since the two goods are assumed to be imperfect substitutes, we cannot simply add Cd and Cf to find C (a German apple is not quite the same as a Dutch apple, even though they are both round and taste good). A particularly simple way to capture the imperfect substitution idea is to assume that:

C = dfC1—

with 0 < a < 1 denoting the relative weight given to domestically produced goods used in consumption.

In the decision about sourcing, the households wish to attain the composite consumption level C (that is determined by (11.20) once Y is known) as cheaply as possible. Since the (domestic currency) prices of domestic and foreign goods are P

275

The Foundation of Modern Macroeconomics

and EP*, respectively, the households decide on Cd and Cf such that total nominal consumption spending, PAC PCd + EP*Cf, is minimized given the restriction imposed by (11.21). (Here, Pc is a consumer price index (CPI) for which an expression is deduced below.) The household chooses the optimal ratio between Cd and Cf on the basis of the relative (domestic currency) price of the two goods:

which is intuitive: if the relative price of foreign goods rises, households choose a larger proportion of consumption goods from domestic sources. By substituting (11.22) into the budget restriction, we obtain:

which says that spending shares on domestic and foreign goods are constant.' Also, by substituting (11.23) into (11.21), we obtain the expression for the CPI:

where Q0 [a" (1 - a) 1-1 -1 > 0 is some constant. The weights that define the consumption bundle C (a and 1 - a) also appear in the CPI.

By substituting (11.20) and (11.24) into (11.23), we obtain intuitive expressions for Cd and Cf in terms of aggregate income Y and the real exchange rate (Q m-)

EP* /P:

For a given real exchange rate, a rise in real income raises the demand for both domestic and foreign consumption goods. For a given level of aggregate income, the real exchange rate determines where the goods to be used for consumption are bought.

3 Constant spending shares are a feature of the Cobb-Douglas specification for composite consumption C, given in (11.21). This sharp prediction is altered if (11.21) is changed to, for example, a CES specification,

By using the same a expressions for Id, If, u

(EP* ) 1-4

Id = aQ0 p

EP* ) 1-41

Gd = aC2oP(-

Real exports are denote domestic customers p .. terms of domestic currc identity (11.1) can be a

PY PcC + Pcl +

= PCd Pld + PC

Y Cd + Gd

which shows (more clear into the aggregate prodL looking in more detail lar in form to (11.9)) equilibrium.

By defining net export (11.25)-(11.27) and as_ exchange rate,

EX = EX0 EP*-)13

(where EX0 represents all the net export function I

X [r, Y, Q, G, EX0j

where C(Y) - son between (11.30) anc X(Y, Q)). First, domesti appears in (11.30). Since some investment goods slope even under perfec interest chokes off ago..

We assume for the sake of

G = Ga Gf1 -". This assumption

d

are the same as the CPI, so

and Cr such that total no: ized given the restriction_

lex (CPI) for which an expr, 0-'imal ratio between Cd a:

e of the two goods:

(11.2'

Dds rises, households chooco estic sources. By substituting

goods are constant. 3 Also, ssion for the CPI:

(EP*) -(1-")

(11.24)

'he weights that define the CPI.

)btain intuitive expressions e real exchange rate (Q

C(Y). (11.25)

uses the demand for both vel of aggregate income,

used for consumption are

:tion for composite consump-

..inged to, for example, a CES

Chapter 11: The Open Economy

By using the same approach for investment and government spending, we obtain expressions for Id, If, Gd, and Gf :4

Real exports are denoted by EX and are sold to the ROW at the same price that domestic customers pay for these goods (P), and spending on imported goods (in terms of domestic currency) equals EP*(Cf + If + Gf), so that the national income

identity (11.1) can be written as:

which shows (more clearly than (11.1)) that only domestically produced goods enter into the aggregate production measure for the domestic economy. In summary, by looking in more detail at the sourcing issue we now have an IS equation (similar in form to (11.9)) in which the real exchange rate affects domestic spending

equilibrium.

By defining net exports (in real terms) by X EX - -(EP* /P)[Cf + If + Gf], noting (11.25)-(11.27) and assuming that the demand for exports depends on the real

exchange rate,

(where EX° represents all exogenous influences on the country's exports) we obtain the net export function defined by the model:

where A(r, Y) C(Y) + I(r). Several features are worth noting in the comparison between (11.30) and the net export function used throughout section 1 (i.e.

First, domestic absorption, and not just aggregate domestic income, appears in (11.30). Since domestic absorption depends on the rate of interest and some investment goods are purchased from the ROW, the BP curve has a positive slope even under perfectly immobile capital (compare section 1.3). A higher rate of interest chokes off aggregate investment, decreases imports of investment goods,

4 We assume for the sake of convenience that I and G are similar composites as C, i.e. I = /,7//1 . -" and G = . This assumption ensures that the price indices for investment and government spending are the same as the CPI, so that the real exchange rate does not affect relative prices within a country.

277

The Foundation of Modern Macroeconomics

and causes a trade account surplus. To restore equilibrium on the trade account, income (and hence imports) must rise.

A second feature of (11.30) is that we can now be more precise about the

Indeed, by differentiating (11.30) with respect to the real exchange G) fixed, we obtain:

where XQ axiaQ, wx EX/ Y, and wM Q(Cf + If + Gf) I Y are, respectively, the domestic output shares of exports and imports. This expression shows that net exports improve as a result of a real exchange rate depreciation if the following condition holds:

or, if the trade balance is initially in equilibrium (so that imports and exports are of equal magnitude and wM = wx), the condition is:

This is the famous Marshall-Lerner condition: if the sum of the elasticities of export and import demand exceeds unity, a depreciation of the currency improves the trade account, so that XQ > 0. The intuition behind the Marshall-Lerner condition is as follows. A depreciation of the currency (a rise in Q) makes domestic goods cheaper for the ROW and increases export earnings. This improves net exports. The rise in Q also makes foreign goods more expensive to domestic residents. If real imports were unchanged, spending on imports would rise because of the depreciation, which would worsen net exports. Domestic residents, however, substitute domestic goods for foreign goods, as a result of the depreciation, and this effect mitigates the rise in import spending and its adverse effect on net exports. The strength of the export effect is regulated by the export elasticity and that of the import spending effect is regulated by 1 - a. The Marshall-Lerner condition ensures that the export effect dominates the import spending effect, which translates as > 1 - a or, equivalently,

+ a > 1.

The extended Mundell-Fleming model

By using (11.25)-(11.29) the IS curve for the model is obtained:

where Y dY IY, E C I[A+G] and

investment in total d (see (11.20)) can be lc

C = ECYk , 1= —

where 0 < Ecy YC income elasticity of the interest semi-elast marginal propensity c unity for the usual

The money market which can be loglint_

—P--EmR dr -I-

where E my YLy > ticity and (the absolute function.

Since we assume pi. domestic rate (r = r`),

dr = dr*.

The supply side of the perfectly competitive (i (11.29)) and maximL_ IV is the nominal wage tion is implicitly define which can be loglineal

P + i'N =

where ENW

of labour demand. It i the labour market is ch We model this by ass,.. setting rule W = WoPi loglinearized to:

=

We use the term semi-t...

to the absolute change in t:. natural. For example, if *rn, : m S to 6% per annum) ca

im on the trade account,

■recise about the Marshall- ipect to the real exchange

Gf)/Y are, respectively, xpression shows that net eciation if the following

(11.32)

I

nports and exports are of

(11.33)

f the elasticities of export Tency improves the trade all-Lerner condition is as domestic goods cheaper s net exports. The rise in

sidents. If real imports f the depreciation, which

. ', stitute domestic goods •:ct mitigates the rise in e strength of the export e import spending effect res that the export effect 1 > 1 — a or, equivalently,

fined:

(11.34)

(11.35)

Chapter 11: The Open Economy

where 17 dY/Y, dC/C, I Es- dI /I, dG/G, dQ/Q, dExo /Exo, and (0c = CAA±G] and coi //[A+G] denote, respectively, the share of consumption and

investment in total domestic absorption. Aggregate consumption and investment (see (11.20)) can be loglinearized to:

= EcyY, I = —EIRdr, (11.36)

where 0 < ccy YCy/C MPC/APC < 1 and 0 are, respectively, the income elasticity of the aggregate consumption function and (the absolute value of) the interest semi-elasticity of the investment function. 5 Note that ECY equals the marginal propensity over the average propensity to consume, which is less than unity for the usual Keynesian consumption function.

The money market of the model is summarized by the LM curve which can be loglinearized to:

A)1 -15 = -EmR dr + EMYk (11.37)

where Emy YLy /L > 0 and EMR —Lr /L > 0 are, respectively, the income elasticity and (the absolute value of) the interest semi-elasticity of the money demand

function.

Since we assume perfect capital mobility, the world interest rate determines the domestic rate so that:

dr = dr* . (11.38)

The supply side of the model also contains some new elements. Domestic firms are perfectly competitive (and do not attempt to exploit the export demand function (11.29)) and maximize short-run profit II PF(N , JO— WN , where N is employment, W is the nominal wage, and k is the given capital stock. The labour demand function is implicitly defined by the marginal productivity condition

which can be loglinearized to:

P + EN = = — ENw [W — Pl , (11.39)

where ENW —FN ANFNN) > 0 is the (absolute value of the) real wage elasticity of labour demand. It is assumed, following Branson and Rotemberg (1980), that the labour market is characterized by unemployment because the wage is too high. We model this by assuming that the nominal wage is set according to the wagesetting rule W = where Wo is exogenous and 0 < < 1. This rule can be loglinearized to:

5 We use the term semi-elasticity to indicate that Ell? relates the percentage rate of change of investment to the absolute change in the interest rate. In the case of interest rates, the use of semi-elasticities is natural. For example, if Em = 2, a one percentage point increase in the rate of interest (say a rise in r from 5 to 6% per annum) causes a fall in investment of 2%.

279

Notes: Endogenous variables are dY/Y, dQ/Q, P dP/P, exogenous variables are dr*, dM/M, dG/G, Wo = dWolWo, EXo . dEXolEXo. Absorption share of consumption is wc, absorption share of investment is co/, export share in GDP is wx, labour income share of output is (DN. Income elasticity of aggregate consumption is Ecy, interest semi-elasticity of aggregate investment is cm, income elasticity of money demand is EMY, interest semi-elasticity of money demand is EMR, wage elasticity of labour demand is ENW, real exchange rate export elasticity is $, real exchange rate import spending elasticity is 1 — a. Money illusion exists if 0 < A < 1,

real wage rigidity if A = 1, nominal wage rigidity if A = 0.

P F

Figure 11.8.

longer holds for the augn (as dY / dG > 0), unless behind this result can be e of Figure 11.8, the LM cu - the domestic price le\ L ship between output and substituting the LM cure

— coNENw [ Wo

Y =

may suffer from money

al wage target, and if A = 1

suggest on the basis of my in which there is little it to the situation in the ich more common.

,rmine employment (by

• on function which can

-1 aggregate output.

the LM curve (11.37), the venience, the equations P curve into the IS and LM domestic price level, and the nominal exchange is exogenous due to the riables are M dM/M, comparative static effects

►llected in Table 11.3. cider the case of a posi-

leming model with fixed t a "ect aggregate output tion property of flexible s insulation property no

(T2.1)

(T2.2)

(T2.3)

ariables are dr*,li4.dM/M, is wk , absorption share of ncome elasticity of aggregate we elasticity of money demand is I is €Nw, real exchange rate nett illusion exists if 0 < A < 1,

Chapter 11: The Open Economy

Figure 11.8. Aggregate demand shocks under wage rigidity

longer holds for the augmented Mundell-Fleming model developed in this section (as dY I dG > 0), unless there exists nominal wage rigidity (A = 0). The basic intuition behind this result can be explained with the aid of Figure 11.8. In the left-hand side of Figure 11.8, the LM curve is drawn, expressing the negative relationship between the domestic price level and output. The IS curve is an upward sloping relationship between output and the real exchange rate. The AS(LM) curve is obtained by substituting the LM curve into the AS curve:

The Foundation of Modern Macroeconomics

If there is real wage rigidity (),. = 1), the AS(LM) curve is downward sloping and independent of the price level (see (T2.3) in Table 11.2) so that the money supply and the world interest rate have no effect on its position. If there is nominal wage rigidity = 0), on the other hand, the AS(LM) curve is independent of the real exchange rate (horizontal). An increase in government spending shifts the IS curve up from IS(G0) to IS(G1 ). In the absence of nominal wage rigidity (A > 0), the real exchange rate appreciates (from Qo to Qi), but not by enough to undo the expansionary effect of increased government spending on output. The domestic price level falls as does the nominal exchange rate (E < P < 0). If there is nominal wage rigidity (A. = 0), on the other hand, output and the domestic price level are unchanged, and the real exchange rate appreciation exactly reverses the stimulative effect of the additional government spending. Since real output depends on what happens to real wages (as producers do not have money illusion), nominal wages must be free to fall (along with the domestic price level) if there are to be any positive output effects. This

explains why output effects are zero under nominal wage rigidity.

11.2 Transmission of Shocks in a Two-country World

In section 1.4 we introduced a simple Mundell-Fleming type model with a rudimentary aggregate supply side. Some microeconomic foundations provided for the supply side of the model and for the issue of sourcing. The model of section 1.4 was used to study a small open economy under flexible exchange rates and perfect capital mobility. One of the reasons so much attention was paid to the details of sourcing and price indexes is to be able to construct a (logically consistent) model of the world economy.

Assume that the world consists of two countries (or regions) that are identical in structure and look like the small open economy discussed in section 1.4. One immediate consequence of this assumption is that we must do away with the ad hoc export demand function (11.29), since we know from (11.25)-(11.27) that the domestic economy's demand for imports is given by:

Cf + If + Gf = (1 - ot)S20 ) [C(Y) + l(r) + G]

•

= (1 - ag20 (E—pP—ai [A(r, Y) + G] . (11.42)

But the domestic economy's exports are (in a two-country world) just the foreign country's demand for imports which, in view of the symmetry assumption, take a form similar to (11.42):

where stars denote fo7 duced consumption obtain:

EX = « Q.+ wcEcyks

By substituting this exp (equation (T2.1) in Tab a two-country setting:

Y =

where we have used the paring (T2.1) and (11. ways. First, the interest before. The reason is the countries, and since sue., Second, foreign governu directly (via the term i: . Of course, the foreign in form to (11.45). By IT written as: I

Y* =

-WIE1R dr* + (oc

a

[(1 - cox )(1 -

1 - (1 -•

where we have once _ spending negatively 13e,, tic country (i.e. Q El'

6 Note that the real excha-- -

explains the positive sign of • (11.29) shows that the two col is no longer exogenous in a •

ye is downward sloping and c n that the money supply and ere is nominal wage rigidity )endent of the real exchan shifts the IS curve up from ity (A > 0), the real exchan undo the expansionary effect nestic price level falls as does Anal wage rigidity (A = 0), on are unchanged, and the real ative effect of the additional hat happens to real wages (as must be free to fall (along positive output effects. This

:e rigidity.

DU ntry World

ag type model with a rudi- - ndations provided for the The model of section 1.4 exchange rates and perfect was paid to the details of Ocally consistent) model of

regions) that are identical cussed in section 1.4. One ust do away with the ad om (11.25)—(11.27) that the

(11.42)

• world) just the foreign imetry assumption, take a

(11.43)

Chapter 11: The Open Economy

where stars denote foreign variables, e.g. C; is the demand for domestically produced consumption goods by foreign residents. 6 By loglinearizing (11.43) we

obtain:

By substituting this export demand function in the domestic economy's IS curve (equation (T2.1) in Table 11.2) we obtain the IS curve for the domestic economy in a two-country setting:

—wIEIR dr* + wG [( 1 wx)G (DXOl wX(0CECY

where we have used the fact that dr = dr* due to perfect capital mobility. By comparing (T2.1) and (11.45), it is clear that the IS curve is augmented in a number of ways. First, the interest rate exerts a stronger effect on domestic production than before. The reason is that changes in the interest rate decrease investment in both countries, and since some investment goods are imported, spillover effects exist. Second, foreign government spending spills over into the domestic economy, both directly (via the term involving G*) and indirectly (via the term with Y*).

Of course, the foreign country also has an IS curve (labelled IS*) which is similar in form to (11.45). By making the appropriate substitutions, the IS* curve can be written as:

—wIE1R dr* + wG [( 1 — wx)G* + wx + wxwcEcyk

1 — (1 — wx)(ocEcy

where we have once again used dr = dr* . The real exchange rate affects foreign spending negatively because it is measured from the point of view of the domestic country (i.e. Q By using (11.45)—(11.46) to solve for Y and 11*, the

6 Note that the real exchange rate from the perspective of the foreign country is P / (EP*) 1/Q. This explains the positive sign of the exponent on the real exchange rate in (11.43). Comparing (11.43) and a = i3 and EX° (1 — a)S20[A(r*, Y*) G*]. This shows that EXo

is no longer exogenous in a two-country model.

283

The Foundation of Modern Macroeconomics

If there is real wage rigidity (A = 1), the AS(LM) curve is downward sloping and independent of the price level (see (T2.3) in Table 11.2) so that the money supply and the world interest rate have no effect on its position. If there is nominal wage rigidity (A = 0), on the other hand, the AS(LM) curve is independent of the real exchange rate (horizontal). An increase in government spending shifts the IS curve up from IS(Go) to IS(G1). In the absence of nominal wage rigidity (A > 0), the real exchange rate appreciates (from Qo to Qi ), but not by enough to undo the expansionary effect of increased government spending on output. The domestic price level falls as does the nominal exchange rate (E < P < 0). If there is nominal wage rigidity (A = 0), on the other hand, output and the domestic price level are unchanged, and the real exchange rate appreciation exactly reverses the stimulative effect of the additional government spending. Since real output depends on what happens to real wages (as producers do not have money illusion), nominal wages must be free to fall (along with the domestic price level) if there are to be any positive output effects. This explains why output effects are zero under nominal wage rigidity.

11.2 Transmission of Shocks in a Two-country World

In section 1.4 we introduced a simple Mundell-Fleming type model with a rudimentary aggregate supply side. Some microeconomic foundations provided for the supply side of the model and for the issue of sourcing. The model of section 1.4 was used to study a small open economy under flexible exchange rates and perfect capital mobility. One of the reasons so much attention was paid to the details of sourcing and price indexes is to be able to construct a (logically consistent) model of the world economy.

Assume that the world consists of two countries (or regions) that are identical in structure and look like the small open economy discussed in section 1.4. One immediate consequence of this assumption is that we must do away with the ad hoc export demand function (11.29), since we know from (11.25)-(11.27) that the domestic economy's demand for imports is given by:

Cf +If +Gf = (1- a)00 (EP* y [C(Y) I (r) + G]

But the domestic economy's exports are (in a two-country world) just the foreign country's demand for imports which, in view of the symmetry assumption, take a form similar to (11.42):

where stars denote fore4 duced consumption gol obtain:

EX = WCECY -

By substituting this expo! (equation (T2.1) in Table 1 a two-country setting: i

+ R1 COX ) 1 -

1 - (1 -

where we have used the i paring (T2.1) and (11.45►. ways. First, the interest before. The reason is that countries, and since son: Second, foreign governmt. directly (via the term invk

Of course, the foreign cc in form to (11.45). By ma] written as:

= - (01E1R dr* + coG

1

[(1 - wx)(1 -c:

1 - (1 - co,

where we have once agait spending negatively bet- _ tic country (i.e. Q EP/

6 Note that the real exch.L. Ø . explains the positive sign of the t (11.29) shows that the two coin( is no longer exogenous in a two-