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Politicas macroeconomicas, handout, Miguel Lebre de Freitas

13/03/2018 https://mlebredefreitas.wordpress.com/teaching-materials/

The real exchange rate

Index:

The Real Exchange Rate................................................................................................3

14.1 Introduction........................................................................................3

14.2 The purchasing power doctrine..........................................................4

14.2.1 The real exchange rate ...............................................................................4 14.2.2 Actual versus equilibrium..........................................................................5 Box 1: The real exchange rate in Portugal.............................................................6 14.2.3 The Law of one price .................................................................................6 14.2.4 The theory of purchasing power parity......................................................8 Box 2: PPP exchange rates and international comparisons of income ..................9 14.2.5 The relative PPP hypothesis.....................................................................11 Box 3: The relative PPP hypothesis in the real world..........................................12

14.3 Traded and non-traded goods...........................................................14

14.3.1 What do we mean by traded and non-traded goods? ...............................14 14.3.2 What happens when the demand for non-traded goods increases?..........16 14.3.3 What happens when the demand for the traded good increases?.............17 14.3.4 Non-traded good prices and the level of aggregate demand....................19 14.3.5 The real exchange rate and non-traded goods..........................................19 Box 4: Traded and non-traded goods in Portugal ................................................20

14.4 The supply side ................................................................................21

14.4.1 Technology and factor endowments ........................................................21 14.4.2 The Production Possibility Frontier (PPF)...............................................22 14.4.3 Numerical example ..................................................................................22 14.4.4 The Marginal rate of transformation........................................................24 14.4.5 Labour demands.......................................................................................25 14.4.6 An arbitrage condition .............................................................................26 14.4.7 The supply functions................................................................................27 14.4.8 Measuring Domestic Production..............................................................28 14.4.9 Productivity, wages and non-tradable good prices ..................................28

14.5 Internal and external balance ...........................................................29

14.5.1 The household’ problem ..........................................................................29 14.5.2 The Swan diagram ...................................................................................31

14.6 Why some countries are more expensive than other?......................35

14.6.1 Real exchange rate and productivity........................................................35 14.6.2 The Balassa Samuelson proposition ........................................................36 14.6.3 Implications for Purchasing Power Parity ...............................................39 14.6.1 Nominal avenues......................................................................................39 14.6.2 Demand driven appreciation ....................................................................40 14.6.3 Comparing the two cases .........................................................................43 14.6.4 Does it matter? .........................................................................................44



14.7 Borrowing and repayment cycle ......................................................45

14.7.1 The two-period model..............................................................................45 14.7.2 Baseline case............................................................................................47 14.7.3 An optimal spending path with external imbalances ...............................47 14.7.4 The borrowing phase................................................................................48 Box 5: The move towards non-traded goods in Portugal, 1995-2005 .................49 14.7.5 The repayment phase ...............................................................................50 14.7.6 The illusion of the boom..........................................................................52

14.8 Policy controversies .........................................................................52

14.8.1 Financial instability..................................................................................53 14.8.2 The adjustment to a Sudden stop .............................................................54 Box 6 - The 2009 sudden stop in Portugal...........................................................55 14.8.3 The required structural adjustment ..........................................................56 14.8.4 Nominal Rigidities ...................................................................................57 14.8.5 Unresponsive supply................................................................................58 Box 7: Overheating and Sudden stop in Greece ..................................................61 14.8.6 Redistributive effects ...............................................................................63 14.8.7 Internal devaluation .................................................................................64 Box 8: The Portuguese bailout and the VAT tax on restaurants..........................64 14.8.8 Immiserizing growth................................................................................65 14.8.9 The Transfer Problem ..............................................................................66 14.8.10 Dutch disease ...........................................................................................67

14.9 Mitigating capital flows ...................................................................68

14.9.1 Restrictions on capital flows....................................................................69 14.9.2 Sterilization ..............................................................................................69 14.9.3 Exchange rates .........................................................................................70

Appendix 1: The two period consumer problem .........................................72

Review Questions and Exercises .................................................................73

Review questions .................................................................................................73



The Real Exchange Rate

14.1 Introduction

A key relative price in open economies is the real exchange rate. The real exchange

rate is the price of foreign goods in terms of domestic goods. When the real exchange rate

changes, this comes along with changes in the pattern of consumption and of production, and

eventually with external imbalances. In this note we discuss the determinants of the real

exchange rate, and its role in macroeconomic adjustment, from the perspective of a small

open economy.

To analyse these questions, we introduce a tool that became known as the dependent

economy model or simply the TNT model1. The main assumption of the TNT model is that

the economy is composed by two sectors: one open to international trade, and the other

closed to international trade. That is, rather than assuming that an economy is entirely open or

entirely closed, the TNT steps into the real-world fact that not all sectors within an economy

are equally exposed to international competition. Accounting for such reality, the model

implies that economic shocks and policy changes may have a differential impact across

sectors, giving rise to policy dilemmas that cannot be captured in a single good framework.

The main proposition of the model is that the level of aggregate demand influences the real

exchange rate and the pattern of production. We will also see that the equilibrium real

exchange rate depends on real factors, such as productivity and preferences.

1 The model born out of the pioneer ideas of Meade (1956), Salter (1959) and Swan (1960), but it has been much improved since then. Key references include: Meade, J. 1956. The price mechanism and the Australian balance of payments. Economic Record 32, 239-56. Salter, W. 1959. “Internal and External Balance: The Role of Price and Expenditure Effects”. Economic Record 35: 226-38. Swan, T. 1960. “Economic Control in a Dependent Economy.” Economic Record 36: 51-66. Corden, 1960. The Geometric representation of policies to attain internal and external balance. Review of economic studies 28, 1-22. Dornbusch, 1980. Home goods and traded goods: The dependent Economy model. Chapter 6 in Open Economy Macroeconomics, Basic Books, New York. Obstfeld and Rogoff, 1996 M. Obstfeld and K. Rogoff, Foundations of International Macroeconomics, MIT Press, Cambridge, MA (1996).



This note is organized as follows. In Section 2, we briefly discuss the theory of

purchasing power parity. In Section 3, we see how the presence of non-traded goods enriches

the model and challenges the theory of purchasing power parity. In Section 4 we describe the

supply side of our simple TNT model. In section 5, we complete the model, specifying the

demand side. In Section 6, we consider a static case, of an economy that cannot borrow or

lend. In such framework, we address the link between real exchange rate and productivity. In

section 7 we introduce the time dimension to analyse borrowing and repayment cycles. In

section 8, we discuss the adjustment problems posed by price stickiness and other supply side

frictions. Finally, in Section 9 we discuss the problems raised by capital flows and the

potential policy responses to address these problems.

14.2 The purchasing power doctrine

14.2.1 The real exchange rate

A key variable in open economies is the real exchange rate. The real exchange rate is

an index that compares foreign prices and home prices expressed in the same currency. A

simple definition is as follows:

P

eP*

(1)

where θ denotes for the real exchange rate, e is the nominal exchange rate (i.e, the price of

foreign currency in units of domestic currency - a higher e means “depreciation”), P stands

for the consumer price index (CPI) at home and P* stands for the consumer price index

abroad. When θ increases, this means that foreign goods are becoming relatively more

expensive. In this case, we say that the real exchange rate is depreciating.

Because the real exchange rate is a real variable, in the long run it should not be

affected by nominal variables, such as money and the price level. In the long run - that is,

after nominal variables adjust fully - the real exchange rate is expected to change only

because of technological improvements, changes in preferences, and other factors affecting

permanently the relative price between domestic and foreign goods. In the short run, price

stickiness and macroeconomic imbalances may cause the real exchange rate each moment in

time (the actual real exchange rate) to depart from the one that is expected to hold in the long

term.



14.2.2 Actual versus equilibrium

As any other relative price, the real exchange rate reacts to economic shocks and may

depart, in the short run, from the level that is determined by its economic fundamentals.

These departures are called real exchange rate gaps. To define a real exchange rate gap,

however, one needs to have a reference for what the “equilibrium” should be.

In what follows it will be useful to distinguish three concepts of real exchange rate:

- The actual real exchange rate, : the one that holds each moment in time;

- The equilibrium real exchange rate, : the one that would be consistent with

flexible prices and full employment (or “internal balance”);

- The fundamental equilibrium real exchange rate, ~ : the one that would be

consistent with flexible prices (internal balance) and external balance2.

Exchange rate gaps may, therefore, refer to the difference between the actual

exchange rate and the equilibrium exchange rate, or to differences between the actual

exchange rate and the fundamental equilibrium exchange rate.

Gaps of the first type , are mostly related to price stickiness, and are expected to

vanish as prices fully adjust to clear the corresponding output markets. Gaps of the second

type ~ are what in general economists have in mind, when looking at real exchange rates:

Deviations between the actual real exchange rate and the fundamental equilibrium real

exchange rate measure the extent to which the currency is overvalued or undervalued relative

to the level that would be consistent with a sustainable debt service. Real exchange rate gaps

may persist for long periods of time, as long as external imbalances are financed by capital

flows. These ideas will be further clarified along this note.

2 This term was coined by Williamson (1983). Williamson, J., 1983. The Exchange rate system Policy analysis in international economics 5. Washington: Peterson institute for international economics.



Box 1: The real exchange rate in Portugal

Figure 1 shows the evolution of the real exchange rate in Portugal, computed by the

ratio between the CPI in Portugal and in the EU15 both expressed in a common currency

(note that this measure corresponds to 1 in our model, so a decline implies a depreciation).

The figure reveals that the real exchange rate depreciated significantly after the 1974

revolution and the two oils shocks in the 1970s, to engage in an appreciation process

throughout the 1990s and the 2000s, until the 2010 crisis.

Figure 1 – The real Exchange rate in Portugal, 1960-2010

60

70

80

90

100

110

120

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Source: European Commission, Ameco. The real exchange rate is based on CPI prices and is computed

relative to EU15. A decline in the real exchange rate means depreciation.

14.2.3 The Law of one price

In a world without tariffs, transport costs, imperfect competition or any other market

frictions, absence of arbitrage opportunities would imply that similar goods should be priced

the same everywhere. That is, considering a particular tradable-good i, the following

condition should hold:

*ii ePP (2)



where iP and *iP denote for the prices of good i in the domestic economy and abroad,

respectively.

The tendency for prices of similar goods to evolve together in different locations is

known as the Law of One Price. The rationale for the Law of one Price is intuitive: if the

same good was quoted in different locations at different prices, arbitrage opportunities would

exist: profits could be made buying the good where the price was lower and selling it where

the price was higher, prices were equalized everywhere.

Of course, in the real world the Law of one Price is not expected to hold for most

goods each moment in time. If a change in a relevant parameter (for instance, in the nominal

exchange rate) creates an arbitrage opportunity, there will be a period of time during which

arbitrage opportunities are explored: buying and selling in different locations involves

searching costs, the establishment of contacts with local retail traders, shipment, and other

factors that delay the arbitrage movement. On the other hand, prices are sticky in the short

run. This means that temporary deviations from the Law of One Price are very likely. These

short run frictions can be modelled introducing a parameter, , mediating domestic prices

and foreign prices:

1*ii ePP (3)

Short-term deviations from the Law of one Price are more problematic for the home

economy when 0 , than when 0 because downward adjustments in prices are more

difficult to achieve than upward movements. In any case, in the long run, the opportunities

opened by these deviations will be fully explored, so prices are doomed to approach the level

consistent with absence of arbitrage opportunities. As time goes by, the parameter is

expected to tend to zero.

A different question concerns transport costs or other permanent barriers to trade,

such as tariffs, market segmentation and cultural factors. Since these frictions do not vanish

along time, they will give rise to permanent deviations from the Law of one Price. To see

this, let be the transaction cost as a proportion of prices. In that case, absence of arbitrage

opportunities implies the following two conditions:

*1 ii ePP (4)

*1 ii ePP (5)



The first condition applies to imports: whenever the foreign price plus transaction

costs exceeds the domestic price, importers are priced out; the second condition applies to

exports: whenever the domestic price plus transaction costs exceeds the foreign price,

domestic exporters are not competitive enough to sell in the foreign markets. Thus, with

transaction costs, the law of one price holds only within a band:

11

1 *

i

i

P

eP (6)

Whenever relative prices depart from this band, arbitrage opportunities will arise:

then, import and export movements will press the relative price back to inside the band.

Within the band, prices in both countries are free to drift up and down, without facing the

threat of competing international trade.

Because of transport costs, the law of one price cannot hold exactly for most goods,

even in the long run. Still, as long as transportation costs are not prohibitive, one may think

the law of one price as a valid constraint that prevents prices of similar internationally traded

goods from departing too much from each other in different locations.

14.2.4 The theory of purchasing power parity

The macroeconomic counterpart of the Law of One Price is the theory of Purchasing

Power Parity (PPP). The difference is that the former applies to singular goods, while the

later applies to economy-wide price indexes. In short, the theory of Purchasing Power Parity,

in its absolute version, states that costs of living should be the same in different locations.

To interpret this, suppose that the consumer basket was the same everywhere – that is,

households in different countries would be consuming exactly the same goods and in the

same proportions. If there were no transport costs and information failures, and if

international competition ensured the verification of the law of one price for each particular

good, then one would expect consumer baskets to cost the same everywhere. That is:

*ePP , (7)



where P stands for the consumer price index (CPI) in the home country and P* stands for the

consumer price index abroad. The implication is that the equilibrium real exchange rate

should be equal to one:

1 . (8)

But in reality, we know that consumer patterns differ significantly across countries:

people in different locations spend different shares of their income in different goods and

therefore the different good’ prices enter with different weights in the corresponding price

indexes. Thus, even if all goods were priced the same across countries, consumer price

indexes would not be the same3. On the other hand, transaction costs and other impediments

to trade prevent the Law of One Price from holding exactly for each particular good. In

reality, prices of similar goods are different across countries and we observe that some

countries are systematically more expensive than others (see Box 2). Thus, the “absolute”

version of PPP is not expected to hold.

Box 2: PPP exchange rates and international comparisons of income

In the real World, costs of living differ significantly across countries. To measure

cross-country differences in the cost of leaving, statistical entities compute the so-called “PPP

exchange rates”.

PPP exchange rates are computed as follows. First, at the product level, PPP exchange

rates are obtained by dividing the price of a product in one country (in its currency) by the

price of the same product in another country (in its currency). For instance, if a litre of milk

costs 3 euros in Portugal and CHF6 in Switzerland then the PPP for milk between Portugal

and the Switzerland is 3/6, or 0.5 euros per Swiss frank.. PPP exchange rates are then

obtained aggregating product-level PPPs along comparable consumer baskets. For instance,

one may find that a basket of goods that costs 100 euros in Portugal would cost 220 CHF if

3 In exercise 1, you will find a simple example.



purchased in Switzerland. In that case, the PPP exchange rate would be PPP=100/225=0.45

euros per CHF.

Differences in costs of living may then assessed calculating the ratio between market

exchange rates and PPP exchange rates. For instance, if the market exchange rate is 0.8 euros

per CHF, then the relative price level in comparable currency units will be

76.1100225*8.045.08.0 . That would mean that the cost of living in Switzerland

was 76% more expensive than in Portugal.

Figure 2 illustrates the differences in price levels calculated in March 2018, by the

OECD. As shown in the figure, the most expensive country in this sample was Iceland, with a

price level of a comparable basket being almost twice as that in Portugal. In contrast, the

cheaper country in the sample was Turkey , with the same basket costing only 40% less than

in Portugal.

Figure 2 – Comparative price levels as of March 2018 (Portugal=100)

Source: OECD, http://stats.oecd.org/Index.aspx?DataSetCode=CPL

The fact that costs of living differ significantly across countries implies that one

should be careful when comparing standards of living across countries. For instance, in

2015, per capita GDP in the United States was around USD 56 thousand. In Uganda, the

corresponding figure in USD, computed using the market exchange rate was USD 600. At the

first sight, that would mean that the average citizen in the US is 93 times richer than the



average citizen in Uganda. Such comparison fails, however, for not taking into account the

fact that the cost of living is much cheaper in Uganda than it is in the United States.

According to the IMF, a given basket of goods costs in Uganda only 30% of the

corresponding price in the US. This means that, in PPP units, per capita GDP in Uganda was

equal to 600/0.3=2000. In other words, taking into account the differences in costs of living,

the purchasing power of an average citizen in the United States was 28 times higher than that

of an average citizen in Uganda. It is still a huge difference, but not as much as high as the

one obtained when one uses the market exchange rate in the comparison.

14.2.5 The relative PPP hypothesis

A less stringent version of the Purchasing Power Parity Theory is the relative version.

This theory only requires cross-country differences in costs of living to remain constant over

time. Suppose, for instance, that the price of a given basket of goods has been 30% more

expensive in the United Kingdom than in Portugal. In light of the “Relative PPP theory” you

could contend that the equilibrium real exchange rate of UK vis-à-vis Portugal was 3.1 .

Hence, if the price level in the UK increased by 10% for instance, then the price level in

Portugal and the nominal exchange rate should adjust together to ensure the parity, say, with

domestic prices increasing 10%, the nominal exchange rate appreciating 10%, or any

combination. Taking differences in (1), the relative PPP implies that:

0ˆ * e , (9)

where eee ˆ , *** PP , and PP denote, respectively, for the percentage

change in the nominal exchange rate, the percentage change in the foreign CPI (foreign

inflation), and the percentage change in the domestic CPI (domestic inflation).

Clearly, the relative PPP assumption is more realistic than its absolute counterpart: it

accounts for the fact that some countries are systematically more expensive than others.

Empirically, it offers a reasonable benchmark for the long-run behaviour of real exchange

rates in many circumstances, especially among industrial countries. However, the relative

PPP theory fails by assuming that differences in costs of living shall remain invariant over

time. In practice, many real exchange rates are not trend-less, even in the long run (the case

of Japan , discussed in Box 3, illustrates this). This means that the relative PPP theory does

not offer a full theory for the equilibrium real exchange rate.



A more general theory should explain, first why some countries are more expensive

than others, and second why differences in costs of living may change over time. This is our

aim for the following section.

For the moment, just keep on hold with a main idea: in general, the relative PPP

provides a reasonable benchmark for a country’ equilibrium real exchange rate when

disturbances are nominal in nature: since the real exchange rate is a real variable, in the long

run it should not be affected by monetary shocks. Yet when shocks affecting the economy are

real - such as changes in tariffs, transport costs, productivity or in preferences - the long run

real exchange rate is expected to be affected. In that case, the PPP theory fails, even in its

relative formulation.

Box 3: The relative PPP hypothesis in the real world

To illustrate the PPP hypothesis with real world data, we refer to Figure 3. The figure

displays the evolution of the pound-USD nominal exchange rate, the ratio of consumer price

indexes in the UK and in the US, and the ratio between the two (the bilateral real exchange

rate). The nominal exchange rate between the pound and the dollar (red line) was fixed along

1960-1971 (with devaluations in 1967 and 1968), and then became flexible, exhibiting high

volatility. The relative price level (blue line), in turn, evolved slowly over time, reflecting

short-run price stickiness. Thus, while the two series have evolved basically together over

time, supporting the relative PPP hypothesis, short-run price stickiness prevented the two

series to match exactly each moment in time. Hence, the real exchange rate was not exactly

constant each moment in time4.

4 Frankel and Rose found that temporary deviations from PPP, such as those implied by volatile nominal exchange rates, die away slowly over time, with half of the departure from PPP still remaining four years after the shock [Frankel, J., Rose, A., 1996. A panel project on Purchasing Power Parity: mean reversion within and between countries”. Journal of International Economics 40, 209-224].



In the long run, however, the real exchange rate between the two countries has been

roughly trend-less, supporting the relative PPP hypothesis for these two countries in this

particular time spam.

Figure 3– Nominal exchange rate and relative CPI between UK and the United States,

1960-2016

Source: AMECO.

Figure 4 repeats the exercise, focusing on the bilateral real exchange rate between

Japan and the US. In the figure, we see that during the phase when the nominal exchange rate

was fixed, consumer price inflation in Japan was much higher than that in the United States,

implying a real exchange rate appreciation. After the collapse of the Bretton Woods system,

the yen appreciated significantly in nominal terms vis a vis-the USD, and inflation remained

higher than in the US until the late 1970s. Thus, the bilateral real exchange appreciated even

further. It was only in the 1980s that the relative CPI started curbing down, accompanying the

continuing nominal exchange rate appreciation. Then after, the bilateral real exchange rate

became roughly constant. Thus, if one tested the relative PPP hypothesis between Japan in

the United States using a series starting in the 1980s, perhaps that assumption was not

rejected by the data. But if one started in 1960, rejection was certain: along the 1960’s and



1970’s, the yen appreciated significantly in real terms relative to the USD, meaning that

Japan became more expensive relative to the US than it was before.

Figure 4 – Nominal exchange rate and relative CPI between Japan and the United

States, 1960-2016

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0

50

100

150

200

250

300

350

1960 1970 1980 1990 2000 2010

CPI in JP relative to CPI in US (left scale)

JPY/USD exchange rate (left scale)

Bilateral real exchange rate (right scale)

Source: AMECO.

14.3 Traded and non-traded goods

14.3.1 What do we mean by traded and non-traded goods?

The main reason why the PPP theory fails in the long run is the presence of non-

traded goods. A non-traded good is one that can only be sold in the same economy where it is



produced. Think, for example, in ordering a pizza: you could order a pizza from a foreign

country, but probably it would be too expensive and most surely the pizza would be useless at

the time of arrival. The same happens with other non-tradable-goods, such as legal support,

vehicle repairs, retail, personal services, residential housing, and entertainment. Either

because of prohibitive transaction costs or because of physical impediments, these goods

cannot in practice be imported from abroad or sold in foreign markets. The implication is that

producers of these goods are isolated from foreign competition: prices of non-traded goods

are basically driven by domestic considerations.

In contrast, a traded good is one that can be consumed in an economy other than

where it was produced. Traded goods are goods that can be imported or exported. Examples

of traded goods include agricultural commodities, fish, minerals, manufactures and some

services, such as shipping. Because these goods are subject to international competition, their

prices cannot deviate too much from the prices of similar goods abroad.

In practice, the distinction between a traded and non-traded good is not always

obvious. Consider, for instance, the act of drinking a beer in a bar. A bottle of beer is clearly

a good that can be traded internationally. Nevertheless, the action of drinking a beer in a bar,

which comprises the whole atmosphere of the bar, is a non-traded good. In other words, the

non-traded service provided by the bar includes a traded component, which is the beer itself.

Some goods will be traded or non-traded, depending on geographical, technological,

cultural and political circumstances. For instance, goods with high transport costs (including

those with high weight as compared to value, such as cement, and those subject to fast

deterioration, such as fresh vegetables) are more likely to be traded within a territory close to

where they are produced. On the other hand, legal impediments to trade, such as tariffs, trade

quotas and quality standards, can turn potentially traded goods into de facto non-traded. One

may say that the incidence of these barriers to trade in each particular industry determines its

degree of “tradability”.

Technology also determines which goods can be traded or not. In today’s world,

many services are moving from the non-traded category to traded, due to technological

advances in telecommunications. An example is banking: today, you can manage an account

in a bank located in a foreign country as easily as you can manage an account held in a bank

at home. The same applies to many other retail markets, such as of music, video and books.

Technological progress is increasing the range of goods that are subject to international



competition. In the following, we abstract from changes in “transport” costs or other factors

affecting the shares of tradable and non-tradable-goods in the economy.

14.3.2 What happens when the demand for non-traded goods increases?

Since non-traded goods cannot be imported or exported, their prices are determined in

the domestic economy, so as to equal the domestic supply and domestic demand.

Denoting by NQ and NA the domestic supply and demand for the non-traded good

respectively, equilibrium in the non-traded good market implies:

NN AQ (10)

When equality (10) holds, the economy is said to be in internal balance.

Figure 5 illustrates the market for non-traded goods using partial equilibrium analysis.

In the figure PN refers to the price of the non-traded good in units of domestic currency (say,

pesos).

Figure 5. How the price of non-traded goods is determined

Consider first the case in which the non-traded good market is in equilibrium (point

0). Then consider the effect of a demand expansion. Clearly, when the AN curve shifts

outwards, the price of the non-traded good increases. In the new equilibrium (point 1), there



will be a higher consumption of the non-traded good ( NA1 ), more production ( NQ1 ) and a

higher price ( NP1 ). The reverse holds in the case of a contraction in domestic demand (point

2). The market for non-traded goods works just like that of any good in a closed economy.

Note that internal balance will only be achieved after the non-traded good price

adjusted fully. In the presence of price stickiness, demand shocks may give rise to periods of

excess demand for non-traded goods (inflationary pressures) or of excess supply of non-

traded (unemployment). In other words, in the short run, actual prices of non-traded goods

may differ from the corresponding equilibrium prices. Whether the slow price adjustment

constitutes a motive for government intervention is a different question.

14.3.3 What happens when the demand for the traded good increases?

Since the traded good can be imported and exported, its price is determined by the law

of one price5:

*TT ePP (11)

where TP and *TP denote respectively for the price of the traded good in units of domestic

currency at home and the price of the traded good in units of foreign currency abroad. Since

our economy is small relative to the rest of the world, the international price of the traded

good, *TP is exogenous (determined abroad).

In what follows, we will often refer to a numerical example, with 1* TP , 100e . In

this case, the price of the tradable-good should be 100* TT ePP .

In the Tradable-good sector, differences between domestic supply and demand are

matched by the balance of goods and services. Denoting by TQ and TA the domestic supply

and the domestic demand for the traded good, the following identity holds:

5 In what follows, only occasionally we will discuss the implications of short term deviations from (11), as implied by the parameter .



TT AQTB (12)

To see how the home market for the traded good works, we refer to Figure 6. In the

figure, the foreign supply is infinitely elastic at the level corresponding to the Law of One

Price. Consider first the case where the domestic demand and the domestic supply cross each

other at the price level corresponding to the Law of one Price (point 0). In this case, the

domestic production of traded goods exactly matches the domestic demand, i.e., TT AQ 00 , so

TB is equal to zero. In this case, we say there is external balance.

Figure 6. The market for traded goods – partial equilibrium

Now, consider an increase in the demand for traded goods, say to TA1 . In contrast to

what happens in the market for non-traded goods, the domestic price of traded goods cannot

change. Since the price does not change, domestic producers of traded goods will not respond

to the higher demand expanding production. The home supply of traded goods will fall short

the home demand for traded goods and the difference will be matched by imports. In the

figure, the demand expansion causes a deficit in the balance of goods and services:

0101 TT AQTB . Conversely, when the domestic demand for traded goods decreases (say



to TA2 ), a surplus in the balance of goods and services will emerge (in the figure, this is

illustrated by the distance 0202 TT AQTB ).6

In sum, in the case of traded goods, shifts in the domestic demand or in the domestic

supply cannot affect the price level: imbalances are matched by the balance of goods and

services, TB.

14.3.4 Non-traded good prices and the level of aggregate demand

We now put the pieces together to examine the implications of an increase in

domestic absorption in a small open economy. If – as it is reasonable to assume – both traded

and non-traded goods are normal goods, then an increase in national expenditure causes the

demand for both goods to increase, as depicted in figures 2 and 3. In the case of tradable-

goods, the price remains constant, but the demand expansion gives rise to a deficit in the TB.

In the case of non-tradable-goods, the demand expansion causes price to increase.

All in all, we conclude that, in a small open economy, an aggregate demand

expansion leads to an increase in the relative price of non-traded goods and to a deficit in the

balance of goods and services.

14.3.5 The real exchange rate and non-traded goods

The Consumer Price Index is a weighted average of traded and non-traded good

prices. Denoting by α the share of traded goods in domestic expenditure, the Consumer Price

Index (P) shall be computed as:

6 Note that the analysis in Figures 2 and 3 is incomplete, because it takes each market separately, without accounting for substitution effects. Thus, for instance, when the relative price of non-tradable-goods increase, one expects consumers to switch expenditure away from the non-tradable-goods towards the tradable-good, and firms to reallocate resources away from the tradable-good sector towards the non-tradable-good sector. These substitution effects are better addressed in a general equilibrium framework, as done in the following sections.



1NT PPP (13)

Postulating (for simplicity) that the same shares hold in the foreign economy, the foreign

Consumer Price Index (P*) will be equal to:

1*** )()( NT PPP (14)

Now, if we substitute these expressions in (1), one obtains:

1**

1

1*** )()(

N

N

T

T

NT

NT

P

eP

P

eP

PP

PPe

P

eP (15)

Denoting by the short-term deviations from the Law of One Price (resulting from

price stickiness, information lags, and other delays in price adjustment), the actual real

exchange rate becomes:

1*

1N

N

P

eP (15a)

This expression states that the actual real exchange rate in each particular moment in

time is determined by short-term deviations from the Law of One Price in traded goods, and

by the relative price of non-traded goods. The first component can be seen as an indicator of

external competitiveness: whenever price stickiness prevents tradable-good prices at home to

equal foreign prices, an arbitrage opportunity is opened up in the goods market.

Note however that the real exchange rate may appreciate for other reasons than price

stickiness in traded goods: whenever the non-traded good price increases, this will cause an

exchange rate appreciation that does not necessarily imply that the traded good produced at

home is overpriced. For instance, as we saw in Figure 5, an increase in aggregate demand

causes the non-traded good price to increase, leading to an exchange rate appreciation. Such

real exchange rate appreciation is the result of price flexibility, not of price stickiness.

Box 4: Traded and non-traded goods in Portugal

Figure 7 displays the time series of price deflators of imports, exports and GDP in

Portugal. As the figure reveals, the series of import prices and of export prices have evolved

mostly together. This conforms to the idea that international competition does not allow

traded good prices to deviate too much from each other.



The GDP deflator, which is an average of traded and of non-traded goods, exhibits a

different dynamics. As shown in the figure, the GDP price deflator increased faster than

traded good prices along 1995-2009. This is the other side of the coin of the real exchange

rate appreciation observed in Figure 1.

Figure 7 - Prices of imports, exports and of GDP in Portugal 1995-2013

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I II IIIIV I

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Price deflator of Exports

Price deflator of Imports

GDP price deflator

Source: Statistics Portugal.

14.4 The supply side

To further explore our model, we now turn to the micro-foundations. In this section,

we address the supply side of the model.

14.4.1 Technology and factor endowments

As for the basic setup, we need to specify the technology and factor endowments. We

will use a very simple setup, so as to make the point without introducing too much algebra.

Assume that both sectors operate under perfect competition and that the corresponding

production functions have constant returns to scale. The traded good sector employs capital

and labour, while the non-traded good sector employs labour only. Labour is homogeneous

and moves freely across the two industries. The endowments of labour and of capital are



given. Since capital is specific to industry T, without loss of generality one can set it equal to

one. The production functions are as follows:

21, TTTT zLKLzFQ (16)

NN aLQ (17)

where z and a stand are productivity parameters, and subscripts refer to industries N

and T.

The aggregate labour supply is inelastic, but workers can move freely from one

industry to the other. The labour resource constraint is given by:

LLL NT (18)

14.4.2 The Production Possibility Frontier (PPF)

The production possibilities frontier presumes that all resources in the economy are

used: hence, equation (18) shall hold in equality. In that case,

LLL NT (18a)

Using (18a), (16) and (17), the production possibilities frontier of this economy

becomes:

2

z

Q

a

QL TN (19)

14.4.3 Numerical example

Along this note, we refer to a numerical baseline example. It will be assumed that the

labour supply in this economy is equal to 300L , 21 and 1 za . In this case the

Production Possibilities Frontier is:

2300 TN QQ (19a)

This example is illustrated in Figure 8 . In the figure, the four panels correspond to

equations (17), (16), (18a) and (19a).



The production function of the non-traded good (17) is represented in the upper left

quadrant with a straight line, reflecting the fact that returns to labour in that industry are

constant. In the lower right quadrant we represent equation (16). With a fixed amount of

capital, the production function exhibits diminishing returns to labour. The resource

constraint (18a) is represented in the lower left quadrant: as we move downwards along the

vertical axis, the amount of labour allocated to the traded good sector increases; similarly, as

we move leftwards in the horizontal axis, labour employed in the non-traded goods sector

rises. The resource constrained is negatively sloped because as we increase labour in one

sector, labour allocated to the other sector must decrease.

Now, suppose that the economy is initially in point 0. At this point, the labour

allocated to the traded goods sector is 1000 TL , implying an output level equal to 100 TQ .

The non-traded goods sector is employing 3000 NL , corresponding to a production of

3000 NQ . Now, suppose that 36 workers moved from the tradable-goods sector to the non-

tradable-goods sector (point 1, in the lower left diagram). As shown in the figure, this implies

a fall in production of tradable-goods to 81 TQ and an expansion in the production of non-

tradable-goods to 2321 NQ . In the upper right panel, this change is described as a move

along the production possibilities frontier, from point 0 to point 1.

Considering all the possible reallocations of labour across industries, we trace the

economy’s production possibility frontier (PPF). The production possibilities frontier

describes the maximum feasible production of one good, for each level of production of the

other good, given the economy’s resources constraint and technology. Along the production

possibilities frontier there are no wasted resources.

Points that fall below the frontier are inefficient because more production could be

achieved out of the same resources. For instance, point U in the figure, describes a situation

were 128 workers are employed in the non-tradable sector and 64 workers are employed in

the tradable sector. Because 108 workers are unemployed, the PPF is not reached.



Figure 8 Production Possibility Frontier

14.4.4 The Marginal rate of transformation

The slope of the PPF in each particular point gives the Marginal Rate of

Transformation (MRT). The MRT measures the opportunity cost of producing one extra unit

of the traded good in terms of the non-traded good. More precisely, it gives the number of

units of non-traded good that must be sacrificed in order to expand the production of the

traded good by one unit.

The MRT is obtained by total differentiation of (19), keeping the labour supply

unchanged. This gives:

2,

2

0 z

aQ

zF

a

LddQ

dQMRT T

LT

NNT

(20)

Returning to our numerical example, we can easily check that in point 1 161 MRT

and in point 0 200 MRT : as we move to the right along the PPF, the MRT increases. The

reason is that production in the traded good sector exhibits diminishing returns to labour:



expanding the production of traded good again and again requires ever increasing amounts of

labour, which in turn causes the non-tradable-good production to decrease faster and faster.

14.4.5 Labour demands

Under perfect competition, each firm maximizes profits taking wages and prices as

given. In the traded goods sector, the problem is:

TT

TTL

T LP

WKLzF

T

,max

where ПT stands for the firm’ profits in the traded goods sector, and W is the wage rate in

units of domestic currency.

The profit-maximizing problem in the non-traded goods sector is the following:

NN

NL

N LP

WaL

N

max

where ПN stands for the firm’ profits in the non-traded goods sector and w is the wage rate in

units of domestic currency.

The corresponding first-order-conditions are:

20

21

T

LTT

T zLzF

P

W

dL

d (21)

aP

W

dL

d

NN

N

0 (22)

Equations (21) and (22) state that the marginal product of labour in each industry shall be

equal to the corresponding real wage rate, and define the respective labour demands. Note

that, while the demand for labour in the traded-good sector is negatively sloped, the demand

for labour in the non-traded sector is horizontal, so only the real wage is determined. The

quantity of labour actually demanded in the non-traded good sector will be determined by the

quantity of output produced, given (17).



14.4.6 An arbitrage condition

To find out the equilibrium, we consider a frictionless labour market, where labour is

homogeneous, and workers can move instantaneously and at no cost from one industry to the

other. In that case, absence of arbitrage opportunities implies that the nominal wage rate must

be equal in both sectors:

LTN zFPaPW (23)

Another way of writing (23) when the production function takes the form (16) is:

2

2

z

aQ

zF

a

P

P T

NN

T (23a)

Where be the relative price of the tradable-good:

N

T

P

P (24)

The relative price tells how many units of the non-traded (home) good one must

give in exchange for one unit of the traded (international) good. When declines, this means

that the traded good will cost less units of the non-traded good, so the home country is

experimenting a real exchange rate appreciation. The relative price is often referred to as

the internal real exchange rate.

Equation (23a) implies that the opportunity cost of the tradable-good in terms of the

non-tradable-good in the market, , shall be equal to the opportunity cost of the tradable-

good in terms of the non-tradable-good in production (the MRT). This is a consequence of

postulating perfect competition and absence of arbitrage opportunities in the labour market,

in a model where market failures are ruled out.

The relationship between the MRT and the relative price is illustrated in Figure 9 .

When 200 , the optimal production occurs in point 0, where the MRT is exactly equal to

20. In case the relative price of the traded good declines to 161 , production moves to

point 1. Why is that? The reason is that from 0 to 1, the price of the non-tradable-good (and

the wage rate) increased relative to the price of the tradable-good. For, instance if the later

remained constant at 100* TT ePP , this means that the price of the non-tradable-good

increased from 5WPN to 25.6WPN . The fact that the real wage increased in the



tradable-good sector created the incentives for firms to reduce employment in the tradable-

good, moving from point 0 to point 1, along the PPF.

In the real world, movements along the PPF are not instantaneous: in face of any

change in relative prices that turns efficient a move from, say, 0 to 1, different types of

product market and labour market frictions may delay the adjustment. This includes, for

instance, skills mismatches, labour market regulations and information failures. These

frictions imply that, in the face of any shock impacting on the optimal allocation of labour,

the economy may move temporarily to an allocation like U in Figure 8 , before the full

potential of labour mobility is materialized. For the moment, however, we focus in the well

functioning case. Later, we will address briefly the case with rigidities.

Figure 9 . Production pattern and relative prices

14.4.7 The supply functions

The supply functions for the traded and non-traded goods are obtained directly from

equations (21) and (22):

a

zQT 2

2 (21a)



a

WPQ NN : (22a)

Note that while the supply of traded good depends positively on its own price, in the

case of the non-traded good the firm is able to produce any amount of output at a price that

cannot deviate from the marginal cost, W/a. The quantity actually produced will depend on

the consumer demand for the non-traded good.

14.4.8 Measuring Domestic Production

Total production in the economy can be either measured in terms of the traded good

or in terms of the non-traded good. In the following, the numeraire will be the traded good,

which price is determined abroad.

Total production in units of the traded good is given by:

NT QQQ 1 (25)

In terms of Figure 9 , when the relative price is equal to 200 the value of the

production pattern described by point 0 in terms of the tradable-good is

2020200100 Q . When the relative price decreases to 161 , then the value of the

production pattern in units of the tradable-good increases to 75.221 Q . Note that the

increase in unit of the tradable-good merely reflects the change in relative prices, not a

technological improvement: it was because non-tradable-goods became more expensive that

the value of production measured in units of the tradable-good increased. In terms of the

non-tradable-good, the value of production actually declined.

14.4.9 Productivity, wages and non-tradable good prices

The arbitrage condition (23) establishes a channel through which changes in the

productivity in the tradable good sector impact on the price of non-tradable good, and vice-

versa. To see how this transmission mechanism materializes, remember that the price of the

traded good is determined in the international economy while the price of the non-traded

good is determined domestically.

Imposing the law of one price (11), one way of writing (23) is as follows:



e

aPzFP

e

W NLT * (23b)

This equation summarizes the two-way causality from the wage rate in units of

foreign currency (W/e) to the marginal product of labour in the traded good sector (the term

in the middle).

Thus, for instance, when the productivity in the traded good sector, z, increases, this

requires an increase in the ratio W/e. Then, because W/e increases, the price of the non-traded

good has to increase relative to the nominal exchange rate (there is a real exchange rate

appreciation). Note however that the causality may also run in the opposite direction: if, for

any particular reason, the ratio W/e rises exogenously, then the marginal product of labour in

the traded good sector must increase. Since one cannot force technology z to improve, the

only alternative avenue is to reduce employment in the tradable good sector (remember that

we are assuming diminishing returns, so LzF can either increase when z increases or when

TL declines).

This discussion is important, because it points to a distinction between real exchange

rate appreciations that come along with shifts in the PPF (increases in z) from real exchange

rate appreciations resulting from movements along the PPF. In order to distinguish these two

cases, one must add the demand side.

14.5 Internal and external balance

In this section, we turn to the demand side to the model. We stick, however, with the

static, one period, economy. This is a reasonable framework to analyse how the long-run in a

multi-period economy should look like, given the fundamentals, but not the effects of

temporary changes in these fundamentals. In this model, there will be no government, so the

only component of aggregate demand is private consumption. Such an assumption is not

entirely satisfactory, but it simplifies the algebra a lot.

14.5.1 The household’ problem

In what follows, let’s assume that the household utility function is as follows:

1),( NTNT CCCCU (26)



The household maximizes the utility function subject to a budget constraint. For a

moment, assume that total spending in units of the traded good, A, is exogenous. Given A

and λ, the household’s budget constraint is:

NT CCA 1 (27)

From the first order conditions of the maximization problem we get:

T

N

C

C

1 (28)

Condition (28) states that the marginal rate of substitution between the tradable and

the non-tradable-good shall be equal to the relative price. This condition defines a family of

optimal consumption baskets, depending on the level of expenditure, which is known as the

income-expansion path.

Substituting (28) in the budget constraint, we obtain the optimal demands for the two

goods:

ACT (29)

ACN 1 (30)

Figure 10 illustrates the optimal consumption choices for different values of A and λ,

in the particular case in which 21 . In the figure, the level of spending in units of the

traded good, A, is measured along the horizontal axes. In Figure 10, we consider two

different levels of expenditure, 200 A and 251 A . Then, we draw three different budget

constraints, considering 200 and 161 .

Thus, for instance, when 200 A and 200 , the optimal choices are 10TC and

200NC (point 0). If, keeping the expenditure constant, the relative price decreases to

161 , then the optimal consumption basket becomes 10TC and 160NC (point 1). If ,in

alternative, the new relative price comes along with a higher level of expenditure, 201 A ,

the solution is 200NC and 5.12TC (point 0’). Points 0 and 1 share the characteristic that

they have the same level of spending, while points 1 and 0’ share the fact that they lie along

the same income expansion path (equation 22).



Figure 10. Optimal consumption in the intra-temporal problem

14.5.2 The Swan diagram

In the one period model with flexible prices, supply and demand must balance in all

markets. In the labour market, there will be full employment when the demand for labour

demand by both sectors equals the total labour supply. Using (19) and (21a), this will be the

case when production in the non-tradable good sector is such that:

2

2a

zLaQN

(32)

Equilibrium in the market for non-traded goods occurs when:

NN QC (33)

Condition (33), stating that the supply and demand in the market for non-traded goods

must equal is labelled of internal balance. Note that this condition also implies full

employment in the labour market. Using (30) and (32), the combinations of A and λ that

ensure internal balance, given the exogenous parameters are:

A

aa

zL

1

2

2

[NN] (34)

Equation (34) gives the equilibrium real exchange rate, , as a function of aggregate

demand, A. This function is depicted in Figure 11 as the curve NN, for the particular case in



which a=1, 21 , and z=1. The NN curve is negatively slopped because an increase in

absorption A causes an excess demand for the non-traded goods, and by then an increase in

its relative price. This, in turn, causes the supply of traded good to decline, releasing labour to

the non-traded good sector. Thus, as we move to the right along the NN curve, more

consumption and more production of non-traded goods are achieved, but at increasing wages

and prices.

Points to the right of the NN curve are of excess demand for labour, NN QC , and

points to the left of the NN curve are of unemployment ( NN QC ) . If prices are flexible, as

we have been assuming so far, internal balance will always be meet. This means that the

economy will lie on the NN curve each moment in time.

In the market for traded goods, imports and exports are possible. The external balance

occurs when 0TB :

0 TT CQTB (35)

Using (28) and (21a) in (35), this gives:

2

2

z

aA [TT] (36)

This expression is described in Figure 11 by curve TT, for the particular case with

a=1, 21 , and z=1. This curve is positively sloped because an increase in A leads to an

external deficit, calling for a real exchange rate depreciation (higher ) for the external

balance to be restored. Points below the curve TT imply that the real exchange rate is over-

appreciated given the level of domestic absorption (TB<0), and points above the TT curve are

of external surplus.



Figure 11 – The swan diagram and the four zones of economic unhappiness

The two curves divide the diagram in four zones of economic unhappiness: I –

Inflation and deficit; II – Unemployment and deficit; III – Unemployment and Surplus; IV –

Inflation and surplus.

The point where the curves NN and TT cross each other correspond to the case with

internal and external balance. Analytically, this is obtained solving together (34) in (36), to

obtain the relative price of traded goods that is consistent with internal and external balance:

2/1

2

2~

L

z

a (37)

Equation (37) describes the fundamental equilibrium internal real exchange rate. The

implied level of expenditure is:

2/1

2

~

LzA (38)

In our numerical example, as you may easily check, the fundamental equilibrium

occurs when z=1 is 20~~ A .



Figure 12. Internal and external balance

Figure 11 describes the internal and external balance in the product space. In the

figure, domestic absorption is equal to domestic production and relative prices are such that

the amounts demanded for both goods are exactly matched by the corresponding domestic

supplies. In this case, there is external balance (i.e, the balance of goods and services is equal

to zero) and internal balance (the demand and supply of labour are equal). The relative price

of traded goods that is consistent with internal and external balance is ~ . The corresponding

external real exchange rate is called the “fundamental equilibrium real exchange rate”.

Note that the “fundamental equilibrium real exchange rate” depends both on

productivity and on preferences. For instance, permanent shifts in preferences impact on the

allocation of labour across sectors, giving rise to movements along the PPF, and therefore to

permanent changes in the real exchange rate, for any given z.



14.6 Why some countries are more expensive than other?

14.6.1 Real exchange rate and productivity

When one compares the cost of living in different countries, we observe a tendency

for goods to be more expensive in rich countries than in poor countries. One explanation for

this was formulated by Bela Balassa and Paul Samuelson7. In short, the authors contended

that price levels tend to be higher in rich countries than in poor countries because

productivity in traded goods is higher in rich countries than in poor countries.

To see this in terms of our model, let’s consider again equation (23), but using the law

of one price, (11). The price of non-traded goods in the home country is equal to:

a

zFePP L

TN* (39)

A similar expression holds in the foreign country:

*

****

a

FzPP L

TN (40)

Combining these two expressions with (15a), and abstracting from price stickiness,

the equilibrium real exchange rate is determined as follows:

1

*

1**1*

a

a

Fz

Fz

P

eP

L

L

N

N (41)

Equation (41) states that, the equilibrium real exchange rate shall reflect cross-country

differences in the marginal products of labour in tradable and in non-tradable sectors. For

instance, if the home country has a lower cost of living than the foreign country, this can be

7 Balassa, B. (1964), "The Purchasing Power Parity Doctrine: A Reappraisal", Journal of Political Economy 72 (6): 584–596. Samuelson, P. A. (1964), "Theoretical Notes on Trade Problems", Review of Economics and Statistics 46 (2): 145–154.



accounted for by a lower marginal product of labour in the traded goods sector or by a higher

marginal product of labour in the non-traded goods sector.

The question that immediately arises is how productivity differences look like in the

real world. Balassa and Samuelson contended that rich countries have better technologies as

well as more capital than poor countries, so they tend to enjoy, on average, a higher marginal

product of labour in both sectors. They also contended that cross-country productivity gaps

are higher in traded goods than in non-traded goods. Thus, rich countries should naturally

observe higher living costs than poor countries.

Note however that differences in technology are not the only explanation for marginal

productivity in the traded good sector to differ across countries: the marginal product of

labour may increase for two different reasons: (i) technological progress, that is, an increase

in parameter z, causing the PPF to expand; (ii) and a fall in employment in the traded good

sector, implying an increase in LF , and a movement along the PPF, holding z constant.

This discussion points to a distinction between real exchange rate appreciation caused

by an expansion of the PPF – the effect usually associated to the Balassa-Samuelson

proposition - and equilibrium real exchange rate appreciations induced by movements of

production along the PPF. In this section, we uncover these two cases.

14.6.2 The Balassa Samuelson proposition

Sticking with the one-period economy, let’s examine the implications of an increase

in the productivity parameter, z, on production, expenditure and the real exchange rate. This

case is described in Figure 13, using our numerical example.

As shown in equation (36), when z increases, the curve describing the external

balance shifts down. The reason is that, when productivity in tradable-goods increases, all

else equal there will be an excess supply of tradable-goods. Hence, external balance will be

met either with a higher level of expenditure or with a lower real exchange rate.

As for the curve describing the internal balance, we can check from (34) that it also

shifts down. The reason is that when productivity in the tradable-good sector increases, all

else equal, firms desire to expand production and employment (eqs. 25 and 12a). Given the

resources constraint, this will crowd out the non-tradable-good sector. For consumer to be



happy consuming less of the non-tradable good, its relative price must rise, for each level of

A.

In the figure, the new equilibrium is described by point 1, where the new NN curve

meets the new TT curve. As you may easily check using (37) and (38), the new fundamental

equilibrium internal real exchange rate is 16~ , corresponding to a level of domestic

absorption equal to 25~A . According to the Balassa-Samuelson proposition, the

productivity increase comes along with a real exchange rate appreciation. Along this move,

the purchasing power of domestic workers in terms of tradable-goods increased from

05.0TPW to 0625.0TPW .

Figure 13 – The Balassa Samuelson effect

To complete the analysis of the Balassa-Samuelson effect, we turn to Figure 14. This

figure describes the impact of the productivity shift in the tradable-good sector, as an outward

expansion of the FPP. Assuming that prices are flexible and that the economy remains in

external balance, the equilibrium moves from 0 to 0’. In this new equilibrium, the

consumption of the tradable-good is now higher (21.5 instead of 10) because income as

increased from A=Q=20 to A=Q=25. As for the non-tradable-good, there are two conflicting

effects: on one hand, the fact that the level of expenditure increases to A=25 gives rise to an

income effect along which the demand for non-tradable-goods increases; on the other hand,



the fact that the relative price of tradable-goods decreased from 20 to 16 induces a

substitution effect whereby the demand for non-tradable-good declines. In the figure, the two

effects exactly cancel out, so that the demand for non-tradable-good remains invariant8.

On the supply side, note that producing 5.12TQ when z=1.25 requires 100TL

workers. In the non-tradable-good sector, there will still be 200NL workers producing

exactly 200NQ . Hence, the productivity shift does not cause employment to be

reallocated across sectors.

Figure 14 – The Balassa Samuelson effect

This exercise clearly shows a real exchange rate appreciation does not need to come

along with an external imbalance: as long as the real exchange rate appreciation is backed by

a productivity increase, it is possible for wages and expenditure to increase without

challenging the external solvency of the country. The real exchange rate appreciation

8 This is a consequence of assuming unit elasticity of substitution between the two goods. Whenever the elasticity of substitution between traded and non-traded goods in consumption is different from one, changes in z, will induce permanent reallocations of labour across sectors that are not accounted for in our model illustration.



corresponds to an appreciation of the fundamental equilibrium real exchange rate, and no

further adjustment is required in the future.

14.6.3 Implications for Purchasing Power Parity

The theory of purchasing power parity states that nominal exchange rates and price

levels should move together, in a way that price level differences expressed in a common

currency remain constant. As we see in equation (41), the equilibrium real exchange rate

remains constant only in case home productivities and foreign productivities evolve in

parallel. When instead a country experiments a productivity increase in the traded good sector

relative to other countries, it is expected to experiment a real exchange rate appreciation.

There will be a departure from PPP and this has nothing to do with price misalignments:

simply, wages and the purchasing power of home workers have increased because workers

became more productive.

14.6.1 Nominal avenues

Fast technological progress in traded good sectors is a characteristic of “catch up”

economies. These are economies that start out poor and that, following some major change in

the economic, social or political spheres, engage in a process of technological convergence

with rich countries. Example of catch up economies include the Southeast Asian miracles, the

Eastern European countries after the fall of the Berlin wall, Brazil and China.

As we already saw, the real exchange rate appreciation that comes along with

productivity growth (z) is not a matter of concern for competitiveness: it is because labour

becomes more productive that the purchasing power of workers increases. This move is an

equilibrium phenomenon and there is nothing wrong about it.

Still, central banks may be concerned with the inflationary impact of a sustained

increase in wages and in the prices of non-traded goods. If a central bank fears that its

commitment with low inflation is at stake, it may prefer to achieve the unavoidable real

exchange rate appreciation by letting the nominal exchange rate appreciate (remember, from

14a, that the adjustment can either occur through an increase in wages or through a decrease

in the nominal exchange rate). Of course, what a central bank cannot do it to commit at the



same time with price stability and nominal exchange rate stability: in face of a productivity

shock, the adjustment in the real exchange rate has to take place in one manner of the other9.

In terms of our numerical example (with 21 ), when z increases from 1z to

25.1z , given the employment level 100TL , the wage rate in units of foreign currency,

eW must increase from 201 to 2025.1 . Whether this is achieved with an increase in

nominal wage from 5W to 25.6W or through a nominal exchange rate appreciation

from 100e to 80e is just a matter of choice between price stability or exchange rate

stability.

More complicated is when technological progress is slower in a country than abroad.

In that case, the real exchange rate needs to depreciate, which requires a decline in nominal

wages or, in alternative, a nominal exchange rate depreciation. The difficulty in adjusting

downwards nominal wages is one of the reasons why many fixed exchange rate regimes

collapse.

14.6.2 Demand driven appreciation

By now, we have examined only equilibria in which the trade balance is zero. The

reason is that we want to abstract from inter-temporal considerations, namely those

underlying borrowing and repayment cycles. In this section, we stick with the case without

borrowing, but we allow the country to run a deficit in the Trade Balance. The trick is to

assume that deficit in the trade balance is financed with another component in the Current

Account, so that the country net borrowing is still equal to zero. This could be, for instance, a

unilateral transfer from abroad (external aid). With such an assumption, one can explore the

9 An interesting example of a tension between nominal avenues occurred in some Eastern European countries in the 1990s, during the run up to the EMU: these countries were experimenting fast technological change, but at the same time they were committed with nominal exchange rate stability and with low inflation, so as to be entitled with EMU membership. Of course, it would be impossible to meet these two criteria at the same time (Szarpáry, G. Transition Countries' Choice of Exchange Rate Regime in the Run-Up to EMU Membership , Finance and Development, June 2001).



implications of a trade deficit for the real exchange rate and on the production pattern without

the need to worry with a repayment phase.

Let’s assume, though, that our country is entitled with an unilateral transfer from

abroad, so that it can run a deficit in the TB amounting to 6.75 without accumulating

liabilities against non-residents. In that case, gross domestic product falls short domestic

absorption. Using (12), (28) and (21a), the combinations of A and consistent with any

exogenous TB are:

Aa

zCQTB TT

2

2

(42)

Note that this equation differs from (36) by the amount of the exogenous deficit in the

TB. In terms of our numerical example, consider again the case with a=1, 21 , and z=1.

Also assume that the unilateral transfer amounts to 6.75 of the tradable good, implying that

TB=-6.75. In that case, equation (42) becomes:

5.13 A (42a)

With flexible prices, the market for non-tradable good must clear each moment in

time. The equilibrium in this economy is obtained solving together (42) and (34). Solving

(42) for A and substituting in (34), we get:

TB

a

z

aa

zL

2

1

2

22

(43)

This is a quadratic equation in , which positive root reveals a negative relationship

between the size of the TB deficit and the real exchange rate. In terms of our numerical

example, the equivalent to (43) is:

75.6

22300

2 (43a)

As you may check, the positive root of this equation is 16 . Replacing this in

(42a), you will obtain 5.29A .

To analyse the equilibrium with a deficit in the trade balance, let’s refer again to

Figure 13. In that curve, consider the original NN and TT curves (that is, z=1). As we already

know, the equilibrium with internal and external balance is point 0, with 20 and A=20.

When we have a deficit in the TB amounting to TB=-6.75, the equilibrium is described by



point 1: in point 1 there is still internal balance (that is, TT QC ), but the economy does not

lie on the TT curve, because there is a deficit in the TB10.

The question that arises is why the real exchange rate appreciated. The reason is that

the higher demand for both goods brought about with the foreign aid generated an excess

demand for the non-tradable-good. Since the non-tradable good cannot be imported, its

relative price had to increase, to 16 . This increase in the relative price of the non-traded

good induced substitution effects, both in production and in consumption (Figure 15).

On the supply side, the increase in the relative price of non-traded goods induced a

reallocation of resources away from the tradable-good sector towards the non-tradable good

sector: the supply of T contracted to 82 TQ , and the supply of N expanded to

2362300 2 NQ . The change in together with the reallocation of production

towards non-traded goods implied an increase in GDP in terms of the traded good to

75.221 NT QQQ . On the demand side, the increase in the relative price of the non-

traded good helped moderate the consumption of this good, shifting the demand towards

imported goods. Given the level of absorption, A=22.75+6.75=29.511 and 16 , the new

consumption levels are 75.142 ACT , 236 TN CC .

Note that the real exchange rate appreciation from 0 to 1 came along with an increase

in the marginal product of labour in the tradable good sector. Such increase was achieved by

the reallocation of labour away towards the non-tradable good sector. Productivity increased

because of diminishing returns.

10 A different question is whether this trade deficit actualy constitutes an external imbalance: note that since there is no borrowing, there is no issue on sustainability here.

11 Note that because the market for non-traded good must balance, NN QC , equations (25) and (27)

imply that any difference between production and expenditure must be accounted by the traded-good sector, only.



Figure 15 – Equilibrium with a deficit in the TB

14.6.3 Comparing the two cases

In Figures 11 and 12, we analysed two cases in which the real exchange rate

appreciated from 20' to 16' . These two cases differ dramatically on the reason why

the real exchange rate appreciated: in Figure 13, the marginal product in the tradable goods

sector increased because of in increase in the productivity parameter, z. In Figure 14, the

marginal product in the tradable good sector increased because employment in that sector

declined and we are assuming diminishing returns.

To compare the two cases, we refer to Figure 16, which plots together the labour

demands for the traded good (from left to right) and for non-traded good (from right to left),

based on equations (21) and (22). In the case of the productivity shift, from z=1 to z=1.25, the

demand for labour in the traded good sector expands. Keeping the employment level in that

sector unchanged, the equilibrium moves from point 0 to point 1’: the wage rate in units of

foreign currency, W/e, increases from 1/20=0.0625 to 1/16=0.0625. Along this move,

productivity was exogenous, and the wage rate was endogenous.

In the case of the aggregate demand shift, the causality runs the other way around:

because there is an excess demand for non-traded goods, the price of non-traded goods has to

increase and by then the wage rate in units of foreign currency W/e , from 1/20 to 1/16.

Firms in the traded good sector, observing the increase in the wage rate, reduce the quantity

of labour along their labour demand curve, from 100TL to 64TL (point 1). In this case,

the increase in the price of non-traded good caused the real wage rate to increase and 36 units

of labour to move from the traded good sector to the non-traded good sector (point 1).



Figure 16: Equilibrium real exchange rate appreciation: productivity vs demand effects

W

e

0.0625

0.05

LT

LT0 100L

T1 64

0.51.25

2L TzF L

0

1 1’

0.51

2L TzF L

NP a

e

LLL NT

NL

0.05

14.6.4 Does it matter?

Since in our model we have one period, only, it dos not matter whether the real

exchange rate appreciation is caused by technological change or by an expansion of

aggregate demand ahead of production, financed with external aid. As long as the consumer

is better off, both avenues have merit.

In the real life, however, there are good reasons to trust more episodes of real

exchange rate appreciation backed by productivity change (z-type). The reason is that the

technological changes are permanent in nature, while aggregate demand shifts financed by

deficits in the balance of goods and services may not last forever. As we will see next, forced

adjustments from a situation of external imbalance may be quite painful.



14.7 Borrowing and repayment cycle

So far we have postulated that domestic absorption in terms of the traded good is

exogenous. However, on shall take into account that, in the real world, household’s decisions

regarding expenditure depend on current and future incomes. The possibility of borrowing or

lending in international markets creates the potential for households to smooth their

consumption over time, or to take opportunity of differences between their rates of time

preference and international interest rates.

In this section, we turn to the two-period case, to examine the implications of external

imbalances. In doing so, we stick with the assumption of flexible prices. Thus, even if

external balance is not met each moment in time, the economy will always operate at full

employment. The adjustment with unemployment will be then analysed in the next section.

14.7.1 The two-period model

In order for the model to be tractable analytically, one must make choices regarding

the demand side. In what follows, we consider an economy with no government and no

investment. With this limitation, we acquire the simplicity enough to focus on our main goal,

which to analyse a borrowing and repayment cycle.

Suppose that household’ lifetime utility function of the form:

1),,,(

1211

212211NT

NTNTNT

CCCCCCCCU (26a)

Subject to an inter-temporal constraint:

1*1

21

2121

111 1

r

CCCC NT

NT

(27a)

Where 1 denotes the household’ lifetime wealth. Since there is no government or

investment, the household life-time wealth is simply

*

1

21

*001 1

1r

QQrb

(44)

Where 1Q and 2Q are defined as in (25). The inter-temporal budget constraint

imposes that any excess of expenditure over income today has to be matched by an excess of



income over expenditure in the future, so that the accumulated debt and the corresponding

interest are paid back.

From the first order conditions of the maximization problem (26a)-(27a)-(44), we

obtain two static intra-temporal optimality conditions of the form (28) . one for each period,

and the Euler equation:

*1

1

2 11

rC

C

T

T

(45)

Equation (45) implies that the household prefers to consume more today or in the

future, depending on how the real interest rate compares to the rate of time preference.

The solution of this problem gives demand functions of the form (see Appendix 1 for

details):

ttT AC , t=1,2 (29a)

tttN AC 1 , t=1,2 (30a)

With

11 2

1

A (46)

12 2

1

r

A (46a)

The supply functions of traded goods and non-traded goods in each period are the

same as in the static problem:

a

zQ tt

tT 2

2 t=1,2 (21b)

The maximum possible supply in the non-traded good sector, given the available

resources and the supply in the traded-good sector is:

2

2

a

zL

a

Q tttN (32a)

To find the equilibrium of the model, one needs to solve simultaneously the four

demand functions, the four supply functions and the definition of life-time wealth, (44).



14.7.2 Baseline case

Let’s return to the numerical example we have been using, with 21 , 1 za ,

and 300L . First consider the case in which 0*0

*1 br . In this case, the equilibrium in

both periods corresponds to the one described in Figures 8 and 9: since the interest rate is

equal to the rate of time preference, 21 AA . Then, because the supply side conditions are

time invariant, there is no reason for the consumer to borrow or lend for smoothing purposes.

In both periods domestic demand will be equal to domestic supply, and the economy will

meet the full-employment-external-balance equilibrium, with ~2021 .

14.7.3 An optimal spending path with external imbalances

In light of this model, a borrowing and repayment cycle may arise for three main

reasons: First, when future output is higher than current output (say, because z is expected to

increase): in this case, households will optimally decide to borrow today, for smoothing

reasons. Second, when the country starts out with some positive wealth, *0b , that needs to be

spent before the end of period 2. Third, when the rate of time preference is higher than the

world interest rate. In this section, we motivate the external imbalance with the assumption

that the rate of time preference in the home country is higher than the world interest rate.

Let’s consider again the model with 21 , 300L , 1 za , and 0*0

*1 br . In

that context, assume that, departing from 0 , the households’ preferences changed once-

and-for all at moment t=1 to 2336 . In order for to obtain the solution easily, take the

following hint: 411 (later, you will have opportunity to check that this corresponds to

the equilibrium of the model).

Using 411 , 0*1 r and 2336 in (46)-(46a), we obtain the optimal spending

today and in the future:

5.291 A

5.112 A

Thanks to the separability of preferences, once we know the expenditure levels in

each period, we can solve the problem as a static one. In what follows, we discuss first the

equilibrium in period 1, and then the equilibrium in period 2.



14.7.4 The borrowing phase

In the first period, the level of spending is high, giving rise to a deficit in the trade

balance. Since the basic parameters of the model are the same as in the static case, the curves

describing the external and internal balance are also the same (equations 35, 36). In Figure

17, we mimic the equilibrium described in Figure 11.

As before, the internal and external balance occurs when 20~~ A . However, in

this economy, households optimally decided to achieve a higher level of consumption today,

borrowing from abroad. This case is described by point 1, where there is internal balance, but

there is a deficit in the trade balance. The equilibrium real exchange rate is the one that solves

equation (34) when 5.291 A . This gives 161 .

Figure 17 – External adjustment in a well functioning economy

Why did the real exchange rate appreciate relative to the fundamental equilibrium?

The reason is that the higher demand for both goods today generated an excess demand for

tradable-goods, which is matched by a negative TB, and also an excess demand for non-

tradable-goods, that can not be imported. Because of this, the price of the non-traded good

has to increase, relative to that of the traded good. In the product space, the equilibrium is the

one depicted in Figure 15.

Comparing to the baseline case (Figure 15, point 0), we see that a departure from

external balance, implies a reallocation of employment from the tradable-goods sector to the



non-tradable-goods sector. This reallocation is the response to the higher price of the non-

tradable-good that the increased demand brought about. As we know, such a move comes

along with a higher real wage in the tradable-good sector (W/e shall increase from 5/100 to

6.25/100). This, in turn, forces firms in the tradable-good sector to reduce employment,

moving up heir labour demand curve, from 0 to 1 in Figure 16, until the marginal product of

labour is equal to the new real wage rate. Note however that this increase in the real wage

rate is not explained by a productivity increase, but only because there was a decrease in the

size of the labour force, in a context of diminishing returns.

Box 5: The move towards non-traded goods in Portugal, 1995-2005

Figure 18 displays the evolution of employment in manufactures, services and

building construction in Portugal along 1995-2009. In conformity to what we have learned,

the process of real exchange rate appreciation along this period was accompanied with a

reallocation of employment away from manufactures and agriculture, to services and,

initially, also to building construction. This suggests that capital inflows, rather productivity

change, caused the real exchange rate appreciation in the period.

Figure 18: employment in manufactures, services and building construction in Portugal

80

90

100

110

120

130

140

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

Agriculture, forestry and fishery products

Industry excluding building and construction

Building and construction

Services



14.7.5 The repayment phase

We now analyse “period 2”, when the country is called to reimburse the debt created

in the first period. In this phase, domestic absorption has to contract to 5.112 A , so as to

generate a surplus in the balance of goods and services equal to the deficit in the period

before. The equilibrium real exchange rate in the second period is the one that solves

equation (34) when 5.112 A . This gives 252 . The equilibrium in the second period is

described in Figure 17 by point 2.

Why is the real exchange rate depreciated? The lower demand for both goods

generated an excess supply of non-tradable-goods, that called for a decrease in its price. Since

prices are flexible and the price of the traded good is determined abroad, the real exchange

rate depreciated.

To see how this equilibrium looks like in the product space, we turn to Figure 19. To

fill the figure, we use 5.112 A and 252 in the demand and supply functions, to obtain

the implied quantities: 75.5222 AC T , 75.143222 TN CC , 5.12222 TQ and

75.1432300 222 NQ . Hence the trade balance is 75.6222 TT CQTB , and the

value of domestic production is 25.1811

111 NT QQQ 12.

12 Note that this result confirms our previous hint: 4125.1875.221

211

r

QQ .



Figure 19. Prices, production and consumption patterns with an external surplus

Comparing to point 1, we see that the contraction of domestic demand that is required

to obtain a surplus in the trade balance comes along with a reallocation of resources from the

non-tradable-goods sector to the tradable-good sector. This reallocation requires a real

exchange rate depreciation, from 161 to 252 . Since NT PP , there are obviously

two ways of achieving such a depreciation: an increase in TP or a decrease in WPN . Thus,

for instance, if the exchange rate is fixed at e=100, then the burden of the adjustment will fall

on wages, from 25.61 W to 422 TPW .

In sum, as the country moves from an external deficit into a surplus, PN decreases and

there is a real exchange rate depreciation. In order to achieve an external surplus, the real

exchange rate must depreciate.

Note that these swings in the trade balance and in the real exchange rate correspond to

an optimal path from the household point of view: the household decided to consume more in

the first period than in the second, and accepted the wage rate and the price of the non-

tradable-goods to shift up and down as part of the process. In a world without information

failures, financial market frictions or any other externality, this would be the first best, even if

there was a departure of the real exchange rate away from its fundamental equilibrium level.



14.7.6 The illusion of the boom

A common way of assessing a country’ solvability is to calculate the ratio between

external debt - often denominated in foreign currency - and GDP. A problem arises, however,

in that GDP is composed by traded and non-traded goods, so its total value in units of foreign

currency depends on how prices of non-traded goods compare to those of traded goods.

Swing in the real exchange rate translate into changes in the debt-to-GDP ratio, that may not

signal the true solvency of the country. This effect is particularly pervasive during boom

episodes.

To see this, consider again our numerical example. When the economy is with

internal and external balance, the value of production in units of the tradable-good is 200 Q

(Figure 11). Since the foreign price of the tradable-good is equal to one, this is also the value

of domestic production in units of foreign currency. After the demand expansion, the value of

output in units of foreign currency increased to 75.221 Q (Figure 15). Note however that

this does not mean that the country became more productive: the TFP parameters are constant

and so it is the PPF. It is a mere implication of production being reallocated towards the good

that is becoming more expensive. In contrast, during the repayment phase, the value of

domestic production declines to 25.182 Q , reflecting the fall in the non-tradable-good price

(Figure 19).

It could be argued that the implied shift in the debt to GDP ratio does not matter: as

long as this change were anticipated at the time of the borrowing decision, as we assumed so

far, they should not mislead economic agents. In the real world, however, different kinds of

financial market frictions prevent borrowing and repayment cycles to be smooth processes.

Often, both creditors and lender evaluate the creditworthiness of economic agents based on

current income and past trends, not on future incomes. Since during boom phases the prices

of non-tradable-goods – as well as of assets that are posted as collaterals – tend to increase, a

country’ creditworthiness is often perceived to be higher than actually is. Not surprisingly,

booming phases often come along with over-borrowing.

14.8 Policy controversies

When a capital inflow and the implied expansion in domestic demand are not matched

by current or future productivity increases, a reverse movement will be called for in the



future. As a consequence, the real exchange rate will appreciate in the first phase and

depreciate in the second phase, and resources will be reallocated between tradable and non-

tradable-good sectors. The question that naturally arises is whether such swings in the real

interest rate are a matter of concern.

In the absence of market failures, there should be no problem at all: just like a real

appreciation is needed to create the right incentives during the boom phase, a real

depreciation is required to promote the desired substitution effects on consumption and on

production during the down phase. To this extent, it may be argued that the real exchange rate

is a relative price like any other, and the fact that it adjusts to balance the goods markets is a

good thing. Thus, as long as households find more valuable to consume more today and less

in the future, they would be on their own right.

Unfortunately, the reality is not that simple. Because of different types of market

failures, large swings of the real exchange rate are a matter of concern for policymakers. In

this section, we review some examples.

14.8.1 Financial instability

A main challenge created by large capital flows is the risks posed to the domestic

financial system. During the “bonanza” phase, domestic residents engage in foreign

borrowing and the economy expands fuelled by capital inflows13. Often, excessive private

leveraging feeds bubbles in the stock markets or in real state, that inevitable come to an end.

When, for one reason or another, the solvency of a sovereign or of the banking system

comes into question by a large enough number of market players, a sudden stop may occur. A

Sudden stop is an abrupt slowdown of private capital inflows into an economy or even a

reversal in the direction of capital flows, forcing the country to move from large current

account deficits into external balance of even into a surplus.

13 Reinhart, C., Reinhart, V., Capital Flow Bonanzas: An Encompassing View of the Past and Present,” CEPR Discussion Paper 6996, October 2008.



Sudden stops are a recurrent cause of balance of payment crises in emerging

economies. The increased mobility of international capital that followed the worldwide

liberalization of capital movements along the late 1980s and early 1990s exposed emerging

economies (but not only) to this new phenomenon of capital flow reversals. Examples of

crises triggered by capital flow reversals include those in Chile in 1982, Mexico in 1994,

Southeast Asia in 1997 and the Peripheral Europe in 2010-12.

A sudden capital outflow implies that a country has to move from an external deficit

to an external surplus in a short period of time. This poses a policy change to policymakers

for two reasons: First, the required real exchange rate depreciation may not be easy to achieve

when wages and prices are sticky. Second, structural rigidities may prevent the supply side

from adjusting as desired in the short term. In plus, during a sudden stop, the increased

uncertainty may translate into lower availability of credit to the private sector, delaying the

reallocation process. In general, sudden stops force economies to painful adjustments,

characterized by falling in asset prices, banking crises, currency crashes, and sovereign debt

crises14.

14.8.2 The adjustment to a Sudden stop

In general, financial markets give more time for an economy to adjust during the

boom phases than during the repayment phase. Periods of demand expansion fuelled by

foreign borrowing (“capital flow bonanzas”) tend to be prolonged and smooth, as financial

markets build confidence in the country. However, borrowing phases often finish abruptly,

tilted by confidence crises that alter the agents’ perception regarding the solvability of the

country. When a confidence crisis materializes, lenders will refuse to extend new loans to the

country, forcing the later to external balance – or close to it- in a short period of time.

14 A systematic view in Reinhart, C. M. and K. S. Rogoff (2909), This Time is Different: Eight Centuries of Financial Folly, Princeton University Press.



Thus, while bonanza episodes tend to evolve smoothly, giving time for agents to

reallocate resources away from traded goods to non-traded goods, sudden stops are by nature

abrupt, forcing the current account deficit to decrease, without giving time for resources to be

reallocated across sectors. In that case, adjustment costs are higher, and the higher the more

pervasive the market frictions impairing the structural adjustment are.

Box 6 - The 2009 sudden stop in Portugal

After a long period of accumulation of external liabilities, private capital stopped

flowing in to Portugal, at around 2010.

Figure 20 illustrates this episode. The figure describes the cumulative capital inflows

to Portugal, in percentage of 2007 GDP, starting in 2002 until end 2012. The red line shows

the private capital inflows, which mostly consist in credits by banks abroad to banks in

Portugal. Portuguese banks used the money to finance the indebtness of the private sector.

The blue line describes the path of total capital inflows, that is, including official lending to

the government.

As illustrated by the figure, private capital flows decreased abruptly in 2010.

Fortunately, in the case of Portugal, it was possible to partially replace the declining private

lending with official loans by the ECB, the European Commission and the IMF, in the scope

of a structural adjustment programme.



Figure 20 – Cumulative Capital inflows to Portugal, 2002-2012

Source: Pisani-Ferry, J. Merler, S, 2012.

14.8.3 The required structural adjustment

To examine the adjustment to a Sudden Stop, consider the case of a borrowing

economy, as described by point 1 in Figure 17. As we already know, in that equilibrium, the

real exchange rate is 161 , the economy is running an external deficit, TB=-6.75, and the

real wage is W/e=0.0625.

Suppose now that the economy suddenly lost access to foreign borrowing well before

the intended repayment phase. That is, households would like to keep borrowing, but markets

refused to lend. Hence, the best the constrained households could do would be to spend all

their current income, meeting the external balance locus, TT.

If prices were flexible, such an adjustment would not be a problem (apart from the

fact that households were constrained in their choices): the economy would move along the

NN curve, from 1 to 0, with the real wages declining from W/e=0.0625 to W/e=0.05, and

with 36 workers being reallocated from the non-tradable-good sector to the tradable-good

sector (remember the move from 0 to 1 in Figure 16). In that case, the economy would be

able to maintain full employment, with the level of expenditure falling to 20A .



Of course, for a move from 1 to 0 to be possible, one would need wages to be flexible

and labour to be mobile across sectors. While these two assumptions may look reasonable in

the long run, they may well fail in a very short period of time during which countries are

forced to adjust to sudden stops.

14.8.4 Nominal Rigidities

Departing from point 1 in Figure 17, suppose again that the economy is forced to

move towards external balance. Further assume that in this economy, 100 ePT , and

wages were sticky at W=6.25. A question arises on how will the external balance be met in

that case15.

Of course, if the country could change the nominal exchange rate, nominal wage

stickiness would not be a problem: remember that the adjustment requires the ratio W/e to

decline to 0.05, so if the nominal wage remained stuck at W=6.25, a nominal exchange rate

depreciation to e=125 would do the job, allowing the economy to move to point 0, and spend

A=20.

The interesting case arises when the exchange rate is fixed16. In that case, wage

stickiness implies that the real exchange rate remains constant at 161 . Thus, the only way

for the economy to meet the external balance (forced by the market) is through a sharper

contraction of aggregate demand, to 16UA (point U in Figure 17). Since point U lies on the

left of the NN locus, there will be unemployment.

To see how this move looks like in the product space, we turn to Figure 21. In the

figure, note that the optimal production pattern remains the same as in point 1, because the

15 In the following, we assume the sudden stop requires the country to move exactly to external balance, not to repay earlier debt.

16 In alternative, you may think in countries where wages are formally or informally indexed to a foreign currency, such as the US dolar. This type of indexation often occurs as a natural response to high inflation rates. In these “dollarized” economies, the exchange rate depreciation fails to induce changes in the real exchange rate, because the ratio W/e is locked.



relative price did not change. Also because the relative price did not change, the optimal

consumption basket remains along the original income-path, 16TN CC . However, the fall

in the admissible expenditure to 16UA forces the economy into below the PPF.

Referring to our numerical example, we use 16UA and 16 in the demand and

supply functions, to obtain the implied quantities: 82 UUT AC , 128 UTUN CC ,

82 UTQ and 2362300 2 SUNQ . Hence the trade balance is

0 UTUTU CQTB , and the value of domestic production is 1611

UNUT QQQ .

Note that, because PN did not fall, an excess supply of non-traded goods emerged,

equal to 108128236 UNS

UN CQ . Since the level of production is determined by

demand, the actual production in the non-tradable-good sector will be 128, only. Hence, the

total demand for labour will be 19212864 NT LL , implying that 108 workers will be

unemployed (Point U, in Figure 8 ).

Figure 21. Sudden stop under sticky wages

14.8.5 Unresponsive supply

Another reason why an economy may experiment a period of unemployment

following a sudden demand contraction is the existence of supply side rigidities. In the

baseline model, we presume that labour is homogeneous and can move instantaneously from



one sector to the other at no cost. In the real world, however, the reallocation of labour across

sectors may be delayed by different types of market frictions.

A first type of market frictions are skills mismatches. The skills needed to operate in

traded goods sectors like manufactures are different from those that are needed to operate in a

non-traded good sector, like building and construction. Thus, a move from one sector to the

other will involve loss of accumulated human capital and a new learning process that the

worker will try to avoid (for instance, gaining time, and taking opportunity of the

unemployment benefit). By the same token, geographical mist-matches may give rise to

significant mobility costs, if different industries are located in different parts of the country.

A second type of frictions may arise from labour market regulation: employment

protection laws and severance payments, by introducing costs in seizing the labour force,

tend to delay the adjustment process, causing the economy to move inside its production

possibilities frontier.

Low response may also affect firms. Even if prices (and profits) in traded good

sectors increase, new investment in traded goods may be delayed by animal spirits

(uncertainty), borrowing constraints (frozen financial markets), bureaucratic procedures

(licensing) or simply because it takes time for a project to be designed, evaluated, and

implemented17.

Because of these structural rigidities, a move along the PPF may take time to

materialize, even if prices are fully flexible. In the following, we consider the extreme case in

which resources are not reallocated at all. This case can be interpreted as the very short term

in our model.

17 The existence of barriers to the reallocation of labour across sectors motivates the so-called “structural reforms”. During the 2011-2014 bailout, Portugal was required to implement a significant number of labour market reforms, in order to speed up the reallocation of labour form non-traded good sectors to traded good sectors. Unfortunately, political constraints paid a toll in the implementation of these reforms, so part of them was abandoned. In part, the lack of ownership of the programme was implied by a recession that was deeper than expected, in a context of weak growth in Europe and tightening credit conditions.



The case with unresponsive supply is examined in Figure 22. In that case, the PPF is

replaced by a unique point S, with 8TQ and 236NQ . The economy behaves like an

endowment economy, with the supplies given by the amounts produced in point 1 in Figure

15 (previous to the sudden stop).

Because the supply does not respond, it will be impossible for the economy to meet

point 0, where 10TQ and 200NQ . But the economy would be able to produce at full

employment (point S) if prices and wages were flexible enough. To see this, let’s re-write the

NN and TT curves for the case with fixed supplies:

A2

232

[NN] (34a)

28

A [TT] (36a)

In this case, the locus of external balance becomes vertical, as described in Figure 23:

for any level of the real exchange rate, there is only one level of expenditure consistent with

external balance. The reason is that the supply of tradables is fixed and the demand for

tradables responds only to income. The curve describing the internal balance is negatively

sloped as usual.

Figure 22. Sudden stop with unresponsive supply



As you can easily check, it is possible to reach the full employment in this case if the

real exchange rate increases the enough, to 5.298232 S . Note that the real exchange

rate depreciation must be much deeper than in the well functioning case, because all the

burden of the adjustment must now fall on the consumption side. With a fixed exchange rate

at e=100, wages would have to decline to W=100/29.5.

Under structural rigidities and sticky prices, the equilibrium is point U. Note that both

in point S, with full employment, and in point U, with unemployment, the total expenditure in

units of the tradable-good is the same (A=16): this is the “admissible” expenditure, given the

constraint on foreign borrowing and the fact that production of tradables is given. Between

points U and S there is a range of intermediate states: the more wages and prices are flexible,

the more the economy will move up from U towards S.

Figure 23. The Swan diagram with unresponsive supply

Box 7: Overheating and Sudden stop in Greece

Figure 24 provides a visual illustration of the macroeconomic adjustment in Greece

along 1979-2014. The figure crosses the data on output-gaps with an estimated real exchange

rate gap. Note that in this figure the real exchange rate is defined at the inverse, that is

*ePP . By construction, observations on the right hand side of the vertical axes correspond



to situations of macroeconomic overheating, while those of the left hand side describe

situations of unemployment. The negatively sloped schedule describes the estimated locus of

external balance: observations at northeast of this schedule correspond to situations of deficit

and observations in the southwest correspond to situations of surplus in the fundamental

balance (the TT curve slopes down, because the real exchange rate is defined at the inverse).

When the sudden stop materialized and the maximum allowed external imbalance

became determined by a narrow official envelope, Greece was forced to external balance.

Since the progress on the RER side was modest, the reallocation of employment towards

tradable was disappointing and meeting the external balance required a recession that ended

up much larger than expected.

As it comes out form the visual inspection of Figure 23, along 2009-2014, Greece has

moved from a situation of economic overheating and external deficit with an overvalued real

exchange rate, towards a situation of external surplus. The recent move of the economy has

been however much more horizontal than downwards: that is, most of the improvement on

the external side has been achieved through expenditure reduction rather than through

expenditure switching. This is suggestive of adjustment problems, eventually related to

nominal frictions and structural rigidities.

Figure 24 – Swan Diagram for Greece, 1979-2014

Source: Costa, E., Pereira, J. Freitas, M. L., 2015. The equilibrium exchange rates for Greece. mimeo,

Nova School of Business and Economics.



14.8.6 Redistributive effects

The main difference between points S and U relates to the distribution of income.

From point U to point S, wages decrease in the tradable-good sector (and profits increase)

while production of the tradable-good remains unchanged.

To see this numerically, let’s take the case with flexible wages as the baseline

scenario. Then, we investigate which agents in the society would vote for wage flexibility.

First, consider the problem of capital owners. Because firms in the tradable-good

sector cannot change the labour force, they will be employing 64TL workers, and produce

8TQ , irrespectively of wage flexibility. But if wages remained high at W=6.25, profits

would be lower than with W= 100/29.5. More precisely, the benefit for capitalists of a fall in

nominal wages would be (1/16-1/29.5)*64=1.83 units of tradable good. Definitely, capitalists

would vote for wage flexibility.

Now, consider the problem of workers. In this case, we have to distinguish those that

are able to keep the job from those who are dismissed in case wages do not fall. If wages fell

to W=100/29.5, all 300 workers would be able to find a job. In that case, the total wage bill,

would be 10.17 units of tradable good. If, in alternative, wages did not fall, only 192 workers

would enjoy the higher wage, W=6.25, implying a total labour income of 0.0625*192=12

units of tradable good.

The interesting result is that total labour income under wage stickiness (21) is higher

than under wage flexibility (19.17). The difference is that the fall in wages implies a transfer

from labour to capital amounting to 2.73. However, the equilibrium with high wages comes

along with inequality among workers, with those loosing the job paying all the cost of the

adjustment.

This example illustrates why adjustment programs are so difficult to implement, at the

political level. Stabilization programmes involve social costs, and the way these costs are

distributed among the different agents in the society may influence its political viability. If

costs are evenly shared among the different groups, the programme is more likely to achieve

the desired ownership by most economic agents, and be successfully implemented. If, on the

contrary, some groups with greater political influence manage to avoid their share in the

adjustment burden, a sentiment of unfairness may emerge in the society, giving rise to strong

political reactions and ultimately the failure of the program.



14.8.7 Internal devaluation

When a country is committed to a fixed exchange rate, there is still room for the

government to influence the relative price of non-tradable-goods using fiscal policy.

Achieving an increase in the relative price of tradable-goods using taxes and subsidies is

labelled “internal devaluation”.

An example of an internal devaluation is when the government decrees a cut in the

social security contributions, and shifts the financing of the system to the Value Added Tax

(VAT). By reducing wage costs, this policy helps the relative price of non-tradable-goods to

fall, as desired. On the other hand, because VAT does not apply to exporting firms, the policy

does not hurt external competitiveness.

Box 8: The Portuguese bailout and the VAT tax on restaurants

Along 2011-2013 Portugal implemented a structural adjustment programme, under

the support of the IMF, the ECB and the European Commission. During most of the bailout,

the adjustment failed to deliver structural adjustment, in the sense that the labour force

released by contracting (mostly non-tradable) industries moved to unemployment (and

abroad), rather than being absorbed by export-oriented green field investment. Exports did

increase, but this was largely achieved through a more intensive use of existing capacity.

Some analysts interpreted this failure as a symptom of price and wage stickiness.

This is not, however, the only possible explanation. Another candidate is the theory that the

supply side remained frozen, in the context of a dramatic confidence crisis: entrepreneurs,

perceiving an unusually risky environment, low external demand, and high credit constraints,

mostly decided to wait and see. Thus, the productive structure remained basically frozen, as

determined by past investments minus current bankruptcies.

The adjustment process in Portugal can be illustrated with the help of Figure 22: with

a frozen productive sector, the (short term) PPF can be described by the single point S. As we

already know, if wages and prices remained sticky the economy would have meet point U,

with unemployment, instead of reaching the frontier at point S.

In order to promote the adjustment in relative prices, the 2011-2013 bailout

programme envisaged a fiscal devaluation. However, the government failed to implement

that policy. On the contrary, the government decided to increase the value added tax rate on



food service activities (restaurants), to raise fiscal revenues. This measure acted as internal

revaluation, thereby moving the relative prices in the wrong direction. With the VAT hike in

restaurants, the relative price of non-tradable-goods increased to consumers, causing the

income expansion path to rotate further down, and the external balance to be met below point

U with an even higher unemployment level.

14.8.8 Immiserizing growth

An issue that has regained importance in international economics is the existence of

positive externalities in manufactures production, in particular learning by doing effects18.

These externalities imply that productivity at the firm level in a given industry may be a

positive function of the size of that industry in the economy and of the country cumulative

experience in that industry.

In the framework above, a learning-by-doing externality in the traded good sector can

be modelled postulating a positive relationship between the productivity parameter in period

2 and the level of production in the tradable good sector in period 1. That is:

TQzz 122 , with 0'z

This equation states that the more a country gets specialized in traded goods in the

first period, the more the production possibility frontier will shift upwards in the second

period (biased towards the traded good sector), allowing the country to enjoy a Balassa-

Samuleson effect, and thereby a higher utility level. In contrast, a country that starts out as a

net borrower, because it exhibit a pattern of production biased towards non traded goods, is

18 A recent discussion in Ostry, J., Ghosh, A., Korinek, A., 2012. Multilateral aspects of managing the capital account, IMF Staff Discussion note, September 7.



more likely to loose opportunities in terms of learning by doing, engaging in a kind of

immiserizing growth19.

14.8.9 The Transfer Problem

By now, we have discussed the case of an aggregate demand expansion that is

financed by external borrowing: the deficit in the balance of goods and services leads to a

positive capital account, meaning that the country accumulates liabilities against non-

residents in the first period. In the second period, the foreign debt has to be repaid, so the

country has to run an external surplus, which in turn requires a real exchange rate

depreciation. A difference story occurs when the aggregate demand expansion is caused by a

unilateral transfer from abroad. With positive unilateral transfers, the country can run a

deficit in the trade balance without accumulating liabilities against non-residents.

To see this in terms of our numerical example, just assume that 0*1 r , so that

the household prefers consumption to be smoothed. Also assume that the supply side remains

invariant, with z=1. In that case, we saw that a country without transfers would remain in

internal and external balance, just like in Figure 11. If the economy received a permanent

transfer 75.621 NUTNUT , however, it could sustain an equilibrium like the one

described in Figure 15 in the two periods. In each period the current account would be

075.675.6 NUTTBCA and there would no repayment phase.

With no question, with the unilateral transfer, the expenditure level achieved by the

economy is higher than without the transfer, so households will be better off. The other side

of the coin is that employment moved to the non-tradable-good sector, in result of the real

exchange rate appreciation. This shrinking of the traded good sector in consequence of

transfers from abroad is often a matter of concern for policymakers, especially when transfers

19 This analysis suggests that it pays for a country to pursue a policy of undervalued exchange rate, sustained by capital controls, in order to achieve a pattern of production biased towards tradable-goods, and by then faster technological progress. Some authors have claimed that this reasoning has inspired the “neo-mercantilist” policies implemented in some emerging economies, notably China.



are related to foreign aid aiming to help countries facing difficulties in servicing their external

debt. By inducing a real exchange rate appreciation and a deficit in the trade balance,

international transfers may delay the adjustment process that the country is suppose to make

to become externally solvent20. Moreover, if unilateral transfers stop flowing in, the country

may face an adjustment problem similar to that of a sudden stop.

14.8.10 Dutch disease

The reallocation of employment towards the non-traded good sector that comes along

with a real exchange rate appreciation was coined as “Dutch Disease” by the Economist

magazine, in 1977. The phenomenon was subsequently modelled in the works of Corden and

Neary21.

The label “Dutch Disease” was inspired in the case of Netherlands in the 1960s. At

that time, Netherlands discovered natural gas in the North Sea. Such a discovery gave rise to

sizeable export revenues, meaning that the country external budget constraint was

substantially relaxed. The phenomenon was labelled “disease” because the real exchange rate

appreciation that came along with the resource discovery impacted negatively in traditional

manufactures, leading to de-industrialization. Episodes of “Dutch Disease” have been

identified in many commodity exporters, especially oil exporting countries.

A Dutch disease arising because of a booming natural resource sector can also be

analysed with reference to Figure 15. Assume that the natural resource sector is a “third

sector”, say oil, different from what we have labelled as traded (manufactures, T) and non-

20 Evidence on the relationship between unilateral transfers and real exchange rate appreciation and de-industrialization include: Rajan, R, Subramanian, A., 2009. Aid, Dutch disease and manufacturing growth, Journal of Development Economics 94(1), 106-118. Lartey, E., Mandelam, F., Acosta, P., 2008. Remittances, Exchange rate regimes and the Dutch Disease: a panel data analysis. Federal Reserve Bank of Atlanta, Working Paper Series 12-2008.

21 Corden WM (1981). “The exchange rate, monetary policy and North Sea oil. Oxford Economic papers 23-46. Corden WM (1984). "Boom Sector and Dutch Disease Economics: Survey and Consolidation". Oxford Economic Papers 36: 362. Corden WM, Neary JP (1982). "Booming Sector and De-industrialisation in a Small Open Economy". The Economic Journal 92 (December): 825–848.



traded (N) - that is, the PPF and preferences apply to T and N, only, not to oil. Under this

interpretation, one can model the oil export revenue as playing the role of the transfer in the

model above: the domestic absorption will expand, causing the real exchange rate to

appreciate, and the final equilibrium is as described by point 1 in Figure 15. The only

difference in respect to the transfer case is that excess demand for non-oil traded goods (T),

amounting to -6.75, is now matched by oil exports22.

The Dutch disease is seen as a problem because it leads to the contraction of the

manufactures sector, and consequently to the loss of important skills, and learning by doing.

On the other hand, large swings in the oil prices give rise to periods of macroeconomic

overheating followed by phases of financial stress, when oil prices fall down. Because of the

harmful effects of the Dutch Disease, many governments in commodity exporting countries

have created wealth funds, in order to save in good times and to spend the accumulated

savings when the terms of trade deteriorate. These funds allow governments to smooth their

spending, mitigating the impact of dramatic changes in the terms of trade.

14.9 Mitigating capital flows

The reallocation of resources towards non-traded goods and the implied loss of

learning by doing effects, as well as the threat of a financial crises caused by excessive

borrowing can be interpreted as market failures.

As long as individual domestic borrowers do not take into account the costs they

impose on others domestic agents, there is scope for government intervention to avoid

excessive borrowing.

22 In the real world, the expansion in aggregate demand often comes ahead of oil production, because there is a phase of investment. In this case, a deficit in the current account arises, to be financed with future oil revenues.



14.9.1 Restrictions on capital flows

One avenue to overcome the implications of excessive borrowing is to impose

restrictions on capital inflows23. Restrictions on capital flows have been followed in countries

like Chile, Brazil, and China. A problem with capital controls is that they loose effectiveness

as time goes by. The reason is that people learn how to import capital in a hidden manner: for

instance, by over-invoicing exports, under-invoicing imports or simulating emigrants’

remittances. Because financial innovations will always find ways of circumventing the

regulations, capital controls tend to lose effectiveness along time. Still, capital controls can

play a role in mitigating the impact of capital inflows, especially in the short term.

Central banks can also use regulation to alter the compositions of the liabilities

thereby generated. For instance, central banks may force banks to hold a given amount of

assets denominated in foreign currency, so as to avoid currency mismatches at the time of the

outflow.

As for maturities, central banks can also banish short term lending, so as to reduce

liquidity risks, when banks borrow abroad in short maturities to extend long run credit.

14.9.2 Sterilization

Another tool to moderate the inflow of capital into an economy is monetary

sterilization. Under fixed exchange rates, a central bank is obliged to buy the incoming

foreign currency, expanding domestic liquidity. But then the central bank may try to buy back

part of the liquidity generated, selling domestic assets to banks in the open market. As long as

domestic assets and foreign assets are not perfect substitutes, monetary sterilization may help

mitigate the monetary expansion caused by capital inflow. A complementary measure to

23 In theory, this policy will be the first best whenever the distortion is originated abroad. That is, when capital inflows are motivated by “push” factors (increased savings in partner countries). A similar instrument would be to tax international capital flows (the Tobin Tax).



moderate the monetary impact of a capital inflow would be to impose a high reserve

requirements on banks (thus reducing the “money multiplier”).

14.9.3 Exchange rates

The capital flow problem also weighs on the choice of the exchange rate regime. A

well known problem with fixed exchange rates is that they create a sense of safety for both

borrowers and lenders. To the extent that this corresponds to an underestimation of the

exchange rate risk, there will be over borrowing In alternative, flexible exchange rate

regimes, by creating exchange rate risk and yield uncertainty, act as a barrier to short term

capital. Short term capital movements are very sensitive to small changes in interest rate

differentials.

A different question relates to the use of the nominal exchange rate to help the

adjustment in the real exchange rate. Countries with managed exchange rates are obviously

less vulnerable to bonanza episodes and sudden stops than countries under fixed exchange

rates, because the central bank can drive the nominal exchange so as to smooth the

reallocation of resources from the non-traded good sector to traded goods sectors. Note

however that the desirability of such a fast move depends on the temporary vs permanent

nature of the underlying shock. Whenever the underlying shock is permanent in nature, the

sooner investors get the right signal and start reallocating the resources, the better. In this

case, a managed exchange rate will help better the macroeconomic adjustment. But if the

shock is of a temporary nature, an immediate adjustment of the exchange rate would create

wrong signals to the entrepreneurs: in this case, the economy would be better served by a

fixed exchange rate regime coupled with monetary actions by the central bank to counter the



monetary effects of capital flows. As everything else in economics, the optimal answer to the

policy question is: “it depends” 24.

24 Recent discussion regarding the role of capital flows and of exchange rate regimes during the Great Recession include Krugman (2013) and Gosh et al. (2013). Ghosh, A., Ostry, J., Qureshi, M. , 2013. Exchange Rate Management and Crisis Susceptibility: A Reassessment . Paper presented at the 14th Jacques Polak Annual Reserach Conference, IMF. Krugman, P., 2013, Currency regimes, capital flows and crises. Paper presented at the 14th Jacques Polak Annual Reserach Conference, IMF.



Appendix 1: The two period consumer problem

From the first order conditions of the maximization problem (26a)-(27a)-(44), we

obtain the following three key optimality conditions, (45) and:

ttT

tN

C

C

1

, t=1,2. (a1)

Condition (28a) mimics the one obtained in the intra-temporal maximization problem,

(28). Substituting (45) and (a1) in the inter-temporal budget constraint, one obtains the

following demand functions:

11 2

1

TC (a2)

12 2

1

rC T (a3)

111 2

11

NC (a4)

122 2

11

rC N (a5)

These demand functions plus the definition of life-time wealth (44) summarize

the demand side of this model. The levels of absorption each moment in time are obtained

using (a2)-(a5) and (7). This gives equations (46) and (46a). Replacing the later in (a2)-(a5),

one can re-write the consumer demands as functions of the contemporary levels of

absorption, as in (29a) and (30a). It is worth noting that total expenditures also follow the

Euler condition. The ratio between (48a) and (48) gives 1112 rAA . Using

1*1

21 1

r

AA (from 34), we get equation (46).



Review Questions and Exercises

Review questions

1. Suppose the assumptions needed for LOOP hold. As an example, assume that there are only two goods, say bread and milk, and that their prices are USD 1.0 and USD 2.0 and €1.00 and €2.00, respectively in the US and in the Eurozone, with the euro-dollar exchange rate equal to 1. Is this possible in this case for absolute PPP not to hold?

2. Consider a world with a single homogeneous good, which can either be produced domestically or abroad under conditions of perfect competition. Initially, the world price of this good is 100 USD and the price of the USD in terms of domestic currency (pesos) is 2.

a) Suppose the price of the good in the domestic economy was initially 190 pesos. In the absence of trade costs, what do you think it would happen?

b) In the real life, do you believe the adjustment described in a) would be instantaneous? Why?

c) Suppose now that transport and other trade costs amounted to 20% of the price of the good. In this case, how would the non-arbitrage condition hold for exports and for imports? Find out the implied band for the real exchange rate.

3. Along the last decades, a number of countries (notably China) have pursued a policy of undervalued real exchange rates, keeping the domestic demand repressed and accumulating current account surpluses. Can you provide a rational for this policy?

4. A synchronized surge of capital flows from industrial countries to emerging economies is better explained by push factors or by pull factors? Explain.

5. Why might large capital inflows be a matter of concern for policymakers? Which policy measures can a country implement to mitigate a capital inflow surge? What are their pros and cons?

6. Comment: “The Purchasing Power Parity is a reasonable predictor of nominal exchange rates in a context where nominal shocks dominate, but not in the presence of large real shocks”.

7. The Republic of Korbut is a small open economy with free capital movements that has been subject to a rise in the productivity of traded goods. Explain the options and the trade-offs involved concerning the choice of the exchange rate policy. Can real appreciation be avoided? If the primary objective of the monetary authorities was to control inflation which policy should be followed?



8. A usual practice in high inflation countries is to set-up labour contracts indexed to exchange rate, that is w=w(e). Referring to the TNT model, explain to which extent this practice may undermine the macroeconomic adjustment.

9. Consider a small open economy under a fixed exchange rate regime. This economy has initially two sectors: one of traded goods and other of non-traded goods. Starting from a situation of internal and external balance, describe the adjustment process of that economy following the discovery of an important mineral resource (third sector). Which policies shall the authorities adopt so as to minimize the impact of that discovery?

10. Consider a small open economy with two goods, one traded internationally and another non-traded. In the initial situation, aggregate expenditure and aggregate production are equal and the economy is in internal and external balance.

a) Assume that this economy is hit by a large capital inflow. Knowing that the central bank follows a fixed exchange rate regime, explain the impact of this capital inflow on domestic money supply and on the level of aggregate demand.

b) Analyse the macroeconomic impact of the aggregate demand shift, with help of a graph. In particular, discuss the impact on: (i) the relative price of non-traded goods; (ii) the production pattern; (ii) the consumption pattern; (iii) the trade balance.

c) Now assume that there is a sudden capital flow reversal. Explain why wage flexibility and labour mobility are important to minimize the adjustment costs. Would this economy be better served with a flexible exchange rate regime

Exercises

11. (Balassa-Samuelson and PP exchange rates) Consider a small open economy producing a tradable-good (T) and a non-tradable (N) good. The corresponding production functions are TT aLY and NN LY , with 1a . Define w as the nominal

wage rate, TP as the price of T, NP as the price of N and as the real exchange rate.

The weight of each good in the consumer price index is 50%. The foreign price of the tradable-good is 1* TP and the nominal exchange rate in this economy is 100e .

a) Assuming that firms maximize profits under perfect competition, find out the equilibrium wage rate in this economy in units of domestic currency, as well as the prices of the two goods and the consumer price index.

b) Now assume that the foreign economy is similar to the home economy, except in that 2* a . What would be the wage rate there, in units of foreign currency?

c) Find out the equilibrium real exchange rate between the two economies? Would absolute PPP hold in this case? Why?



d) On the basis of your findings, how much would be the purchasing power of workers at home relative to that of workers abroad? Explain the exchange rate measure used in this international comparison.

12. (Balassa Samuelson effect and Exchange Rate regimes): Consider a small open economy producing a traded good (T) and a non-traded (N) good. The corresponding production functions are TT aLY and NN LY . Assume that the foreign prices of

these goods are 1** NT PP and that the nominal exchange rate is 100e . Finally,

assume the weight of each good in the consumer price index is 50%. Define w as the nominal wage rate, TP as the price of T , NP as the price of N and as the real

exchange rate.

1. Assume first that 4a .

d) Find out the labor demand equations in the two sectors

e) Compute the equilibrium wage rate, the corresponding price level and the real exchange rate.

f) Now suppose that the nominal exchange rate depreciated to 400e . What would happen to the price level and to the real exchange rate? Was PPP a good theory in that case? In absolute terms or in relative terms?

2. Departing again from 100e , examine the impact of a fall in the productivity of the traded good from 4a to 1a

g) Describe the implications of such a shift on TP , NP , and the equilibrium real

exchange rate, assuming that the nominal exchange rate was fixed.

h) If non-traded good prices were sticky, how could the central bank easy the adjustment process setting the nominal exchange rate?

13. (Balassa Samuelson effect and Exchange Rate regimes): Consider a small open economy producing a tradable-good (T) and a non-tradable (N) good. The corresponding production functions are TT aLY and NN bLY . Assume that the

foreign prices of these goods are 1** NT PP and that the nominal exchange rate is

1e . Finally, assume the weight of each good in the consumer price index is 50%. Define w as the nominal wage rate, TP as the price of T , NP as the price of N and as

the real exchange rate.

1. Assume first that 1 ba

a) Find out the labor demand equations in the two sectors.

b) Compute the equilibrium for the wage rate, the price level and the real exchange rate.

2. Consider an increase in the productivity of the tradable-good from 1a to a 4 .

c) Describe the implications of such a shift on TP , NP , w and the equilibrium real exchange

rate, assuming that the nominal exchange rate was fixed.



d) If instead the central bank’ goal was to keep the inflation rate equal to zero, what should happen to prices and to the nominal exchange rate?

e) What should happen to the real exchange rate if the productivity shock was instead on parameter b?

14. (Balassa-Samuelson, exchange rate options) Consider a small open economy producing a traded good (T) and a non-traded (N) good. The corresponding production functions are TT aLQ and NN bLQ . Assume that the foreign prices of these goods

are 1** NT PP and that the nominal exchange rate is 1e . Finally, assume the two

goods weight the same in the consumer price index, that is NT PPP 5.05.0 .

Assume first that 1 ba

a) (Initial equilibrium): Find out the labour demand equations in the two sectors.

b) Compute the equilibrium wage rate, the CPI and the real exchange rate, PeP* .

(Balassa Samuelson): Now examine the implications of an an increase in the productivity of the traded good from 1a to 2a .

c) Describe the impact on TP , NP , w and the equilibrium real exchange rate, assuming

that the nominal exchange rate was fixed [A: 2NP ].

d) If instead the central bank’ goal was to keep the inflation rate equal to zero, what should happen to prices and to the nominal exchange rate? [A: 32e ].

e) Taking into account your results in c) and d), explain the trade-offs involved concerning the choice of the exchange rate policy. Can a real appreciation be avoided? If the primary objective of the monetary authorities was to control inflation which policy should be followed? (read the article by G. Szapáry, in F&D, on the policy dilemmas of transition countries in the run-up to the EMU).

f) What would happen to the real exchange rate if the productivity shock was instead on parameter b?

Now assume that the labor endowment in this economy was L=120, the consumer preferences were such that NT CC irrespectively of the price level, and that the money

demand function was given by NNTT CPCPM .

g) Show how the productivity shift from 1a to 2a impacts on the country production possibilities frontier.

h) Describe the optimal production and consumption baskets before and after the productivity shift, assuming that internal and external balance are preserved.

i) Prove that before the shock the money supply was equal to M=120.

j) After the shock, how much should be the money supply so as to: (j1) keep the exchange rate fixed; (j2) keep the price level constant. [A: 240, 160].

k) (Aggregate demand expansion): Finally, return to the initial case with 1 ba , and examine the implications of an expansion of the money supply from M=120 to



M=160, namely on the: (j1) consumption pattern; (j2) production pattern; (j3) trade balance. [A: TB=-40].

15. (Equilibrium RER in the medium run) Consider a small open economy producing a tradable-good (T) and a non-tradable (N) good. The corresponding production functions are 21

TT aLY and NN LY . In this economy, there are 100 workers, and prices are

flexible, so full employment is always met. Assume that the foreign prices of these goods are 1** NT PP and that the nominal exchange rate is 1e . Finally, assume the

weight of each good in the consumer price index is 50%. Define w as the nominal wage rate, TP as the price of T , NP as the price of N and as the real exchange rate.

a) Find out the labor demand equations in the two sectors.

b) Find out the expressions for the wage rate, the price level and the real exchange

rate, as a function of the unknown parameters a and TL .

c) Assume that the steady state in this economy is characterized by 1a and 64TL .

Find out what the long run equilibrium real exchange rate will be.

d) Now, consider a temporary departure form the steady state, implying a – also temporary- reallocation of 60 workers away from the tradable-good sector to the non-tradable-good sector. What would happen to the real exchange rate in this case?

e) Distinguish the phenomenon described in this exercise from the Balassa-Samuelson effect.

16. (Swan Diagram): Consider a small open economy endowed with 300 units of labour, which produces a traded good (T) and a non-traded good (N). The corresponding production functions are 5.0

TT LQ and NN LQ . It is further assumed that the utility

function is given by NT CCU , and that labour is perfectly mobile across the two

sectors.

a) Find out the demands for N and T as functions of A and NT PP .

b) Find out the supplies of N and T as functions of NT PP .

c) Find out the combinations of A and that are consistent with the internal balance. Represent in a graph. Characterize the points (10, 20), (20, 20) and (40, 20) in terms of internal balance.

d) Find out the combinations of A and that are consistent with the external balance. Represent in a graph. Characterize the points (10, 20), (20, 20), (40, 20), and (10, 10) in terms of internal balance

e) Find out the values of A and that are consistent with the internal and external balance.

f) Now suppose that domestic absorption increased to A=29.5. What would happen to the real exchange rate? Would the economy approach the external balance? Represent in the Swan diagram and in the PPF.



17. (Balassa Samuelson effect): Consider a small open economy endowed with 300 units of labour, which produces a traded good (T) and a non-traded good (N). The corresponding production functions are 5.0

TT zLQ and NN LQ . It is further assumed

that the utility function is given by NT CCU , and that labour is perfectly mobile

across the two sectors.

a) Distinguish the markets of T and N in respect to the process of price formation.

b) Compute the expression for the production possibilities frontier and the marginal rate of transformation in this economy, for different values of z. Represent it in a graph.

c) Denoting for w the wage rate, PT the price of T, PN the price of N, find out the labour demand equations in the two sectors. Using the arbitrage condition in the labour market and the expression for the PPF, find out the optimal supplies of T and N as a function of NT PP and z.

d) Let A denote for absorption in units of T, and further assume that the only component of absorption is private consumption. Find out the optimal demand for T and N as functions of A and NT PP .

e) Now assume that internal and external balance holds continuously in this economy, that is TT CQ and NN CQ . Find out the equilibrium values of NT PP for two

cases: z=1 and z=2. Which main proposition is illustrated here? (clue: z20 ).

f) For the two cases considered in (e), find out the corresponding values of TQ , TC and A. Represent in a graph.

g) Finally, assume that the world prices are 1** TPP and that the nominal exchange

rate is given by 100e . Explain what would happen to the real exchange rate, w and PN if there was a fall in productivity from z=1 to z=2. If nominal wages were sticky, which other instrument could be used to achieve the internal and external balance?

18. (Borrowing and repayment cycle). Consider a small open economy endowed with 300 units of labour, which produces a traded good (T) and a non-traded good (N). The corresponding production functions are 5.0

TT LQ and NN LQ . It is further assumed

that the utility function is given by NT CCU , that labour is perfectly mobile across the

two sectors, that the foreign price of the traded good is 1* TP and the nominal exchange rate is 100e .

a) Compute the expressions for optimal production and optimal consumption of the two goods as functions of A and .

b) Find out an expression for domestic income (Q) as a function of . Then, use this expression to compute the domestic demand (absorption) as a function of and the trade balance, A=Q+TB.

c) Using the equation above and the identity TBCQ TT , find out an expression relating the equilibrium level of as a function of TB. Represent in a graph and display the implied values when: TB=0; TB=-6.75; TB=6.75.



d) Assume now that the economy is initially in internal and external balance. Find out the equilibrium values of QT, QN, NT PP , Q, and nominal wages. Represent in a

graph.

e) (Capital inflow) Now assume that there is a demand expansion, fuelled by a capital inflow amounting to 6.75 units of foreign currency. Quantify and describe in a graph the impact on the patterns of production, consumption, and the real exchange rate, assuming that all prices are fully flexible.

f) (Repayment) Sticking with the assumption of flexible prices, describe the equilibrium in the period after, when the economy is called to pay back 6.75 of foreign currency (it is assumed that the interest art in the foreign loan is zero).

g) (Nominal rigidities) Finally, consider the case where nominal wages and prices of non-traded goods could not be changed at all. In that case, how much should the domestic demand fall, for the country to repay its debt? How many workers will be unemployed in this case?

19. (Unresponsive Supply) Consider an economy where the supply side is such that production is fixed at 40TQ and 80NQ and where consumer preferences were such

that NT CC irrespectively of the price level. In this economy, the domestic demand is

given by NNTT CPCPM . Finally, assume that the exchange rate is fixed and that

NNT PPPe 1** .

a) Describe the equilibrium of this economy when M=160.

b) Examine the implications of a sudden fall in the money supply to M=80 [A: Unemployment=40].

20. Consider a small open economy endowed with 3 units of labour, which produces a traded good (T) and a non-traded good (N). The corresponding production functions are

NN LY and 21

TT LY . It is further assumed that: the utility function is given by 2121

NT CCU ; labour is perfectly mobile across the two sectors; the foreign price of the

traded good is 1* TP ; the nominal exchange rate is 1e .

a) Find out the expression for the production possibilities frontier.

b) Assuming that the economy is initially in internal and external balance, compute the equilibrium values of NY , TY , NT PP , NP . Compute the value of domestic

income in units of domestic currency.

c) Assume that there is a permanent contraction in aggregate demand (say, to pay interest on a old debt), so that its level in nominal terms falls down to 23 . If prices

remained unchanged (short run), what would be the implied levels of NY , TY , NA ,

TA and the trade balance? Discuss.

d) Now assume that wages and prices were fully flexible. Find out the new equilibrium in this economy. Explain.

e) In light of c) and d) (but not only) discuss the pros and cons of having a fixed but adjustable exchange rate regime.



21. Consider a small open economy with a fixed exchange rate, where two goods, T and N, are produced according to 5.02 TT LQ and NN LQ . Further assume that 15 ePT ,

total labour is 75L and the demand functions for the two gods are ACT 5.0 , and

ACN 5.0 .

a) Describe the Swan diagram. Find out the combinations of A and that are consistent with internal balance, external balance, and both. Characterize, in the diagram, the four zones of economic unhappiness.

b) Suppose that initially 3 and A=44. Classify this equilibrium in terms of internal and external balance.

c) Departing from (b), suppose that a sudden stop forced this economy to external balance. Assuming flexible prices and perfect labour mobility, how should the wage rate adjust? Describe the move in the Swan diagram. Find out what happens to employment in each sector along this move.

d) Departing from (b), suppose that nominal wages in this economy were indexed to the nominal exchange rate, according to 3eW . Would it be possible for this economy to meet the internal and external balance in this case? Describe the adjustment of the economy following the sudden stop in this case, and the implied level of A. Find out what happens to employment in each sector along this move.

e) Comparing with c) and d), which groups in the society would be better off and worse off?

22. Consider a small open economy under fixed exchange rates producing and consuming two goods, T and N. The corresponding production functions are TT LQ and

NN LQ . In this economy, labour is specific to each industry (immobile across sectors)

and the labour endowments are 50TL and 50NL . Finally, assume that the utility

function is TNCCU .

a) (Supply side): Represent the production possibilities frontier in a graph. b) (Demand-side): Prove that the demands for tradable and non-tradable-goods are

given by 2ACT and 2ACN , where A denotes for absorption in units of the

tradable-good, and for the relative price of the tradable-good. c) (Swan diagram) Find out the combinations of A and that are consistent with: (c1)

the internal balance; (c2) the external balance. (c3) Represent the two curves in a graph. (c4) Find out the levels of A and that are consistent with the simultaneous equilibrium.

d) (Repayment) Departing from the equilibrium described in c), assume that this economy faced a sudden capital outflow, amounting to 10 units of the tradable-good. (d1) What would happen to A and TC ? Quantify. (d2) Quantify the implied assuming that prices were fully flexible. Explain the intuition of the price adjustment.

e) In alternative to (d2), assume that the non-tradable-good price was sticky (that is, unchanged). Describe the adjustment of the economy to the capital outflow in that case, quantifying the implied values for NC and employment. Represent the new

position of the economy in a graph and compare with d2).



23. Consider a small open economy with a fixed exchange rate, where two goods, T and N, are produced according to 50TQ and Q

N L

N 50 . Further assume that 1* TP , the

nominal exchange rate is 1e , and the utility function takes the following form:

NTCCU .

a) Describe the production possibilities frontier in a graph. Provide possible explanations for this particular shape.

b) Find out the demands for T and N, as functions of A (total absorption in units of T), and (the relative price of T).

c) Describe the Swan diagram. Find out the combinations of A and that are consistent with: (c1) internal balance; (c2) external balance. (c3) Identify in the diagram and characterize the four zones of economic unhappiness.

d) Suppose that initially 8.0 and A=100. Describe this equilibrium, quantifying: (d1) the prices of the two goods, and the wage rate; (d2) the unemployment level; (d3) the trade balance; (d4) if wages were fully flexible, how would the economy adjust? (d5) How is this type of adjustment labelled?

e) Now suppose that nominal wages were sticky. Considering the following money demand, NNTT CPCPM , explain what would happen to employment and to the

trade balance if money expanded from M=100 to M=125. In particular, distinguish the cases in which: (e1) the exchange rate remained fixed at 1e ; (e2) the exchange rate adjusted to preserve the external balance. (e3) Compare the two cases in the Swan diagram, and discuss.

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