The real exchange rate

Transcription

1 he real exchange rate Index: he Real Exchange Rate Introduction he purchasing power doctrine he real exchange rate Actual versus equilibrium...5 Box 1: he real exchange rate in Portugal he Law of one price he theory of purchasing power parity...8 Box : PPP exchange rates and international comparisons of income he relative PPP hypothesis...11 Box 3: he relative PPP hypothesis in the real world raded and non-traded goods What do we mean by traded and non-traded goods? What happens when the demand for non-traded goods increases? What happens when the demand for the traded good increases? on-traded good prices and the level of aggregate demand he real exchange rate and non-traded goods...19 Box 4: raded and non-traded goods in Portugal he supply side echnology and factor endowments he Production Possibility Frontier (PPF) umerical example he Marginal rate of transformation Labour demands An arbitrage condition he supply functions Measuring Domestic Production Productivity, wages and non-tradable good prices Internal and external balance he household problem he Swan diagram Why some countries are more expensive than other? Real exchange rate and productivity he Balassa Samuelson proposition Implications for Purchasing Power Parity ominal avenues Demand driven appreciation Comparing the two cases Does it matter?...44

2 14.7 Borrowing and repayment cycle he two-period model Baseline case An optimal spending path with external imbalances he borrowing phase...48 Box 5: he move towards non-traded goods in Portugal, he repayment phase he illusion of the boom Policy controversies Financial instability he adjustment to a Sudden stop...54 Box 6 - he 009 sudden stop in Portugal he required structural adjustment ominal Rigidities Unresponsive supply...58 Box 7: Overheating and Sudden stop in Greece Redistributive effects Internal devaluation...64 Box 8: he Portuguese bailout and the VA tax on restaurants Immiserizing growth he ransfer Problem Dutch disease Mitigating capital flows Restrictions on capital flows Sterilization Exchange rates...70 Appendix 1: he two period consumer problem...7 Review Questions and Exercises...73 Review questions...73

3 he Real Exchange Rate 14.1 Introduction A key relative price in open economies is the real exchange rate. he 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. o analyse these questions, we introduce a tool that became known as the dependent economy model or simply the model 1. he main assumption of the model is that the economy is composed by two sectors: one open to international trade, and the other closed to international trade. hat is, rather than assuming that an economy is entirely open or entirely closed, the 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. he 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 he 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 he price mechanism and the Australian balance of payments. Economic Record 3, Salter, W Internal and External Balance: he Role of Price and Expenditure Effects. Economic Record 35: Swan, Economic Control in a Dependent Economy. Economic Record 36: Corden, he Geometric representation of policies to attain internal and external balance. Review of economic studies 8, 1-. Dornbusch, Home goods and traded goods: he dependent Economy model. Chapter 6 in Open Economy Macroeconomics, Basic Books, ew York. Obstfeld and Rogoff, 1996 M. Obstfeld and K. Rogoff, Foundations of International Macroeconomics, MI Press, Cambridge, MA (1996).

4 his note is organized as follows. In Section, 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 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. he purchasing power doctrine he real exchange rate A key variable in open economies is the real exchange rate. he real exchange rate is an index that compares foreign prices and home prices expressed in the same currency. A simple definition is as follows: ep * (1) P 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.

5 14.. 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. hese departures are called real exchange rate gaps. o 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: - he actual real exchange rate, : the one that holds each moment in time; - he equilibrium real exchange rate, : the one that would be consistent with flexible prices and full employment (or internal balance ); - he fundamental equilibrium real exchange rate, ~ : the one that would be consistent with flexible prices (internal balance) and external balance. 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. hese ideas will be further clarified along this note. his term was coined by Williamson (1983). Williamson, J., he Exchange rate system Policy analysis in international economics 5. Washington: Peterson institute for international economics.

6 Box 1: he 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). he 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 000s, until the 010 crisis. Figure 1 he real Exchange rate in Portugal, Source: European Commission, Ameco. he real exchange rate is based on CPI prices and is computed relative to EU15. A decline in the real exchange rate means depreciation he 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. hat is, considering a particular tradable-good i, the following condition should hold: * Pi ep i ()

7 where P i and respectively. * P i denote for the prices of good i in the domestic economy and abroad, he tendency for prices of similar goods to evolve together in different locations is known as the Law of One Price. he 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. his means that temporary deviations from the Law of One Price are very likely. hese short run frictions can be modelled introducing a parameter,, mediating domestic prices and foreign prices: * P 1 (3) i ep i 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. o see this, let be the transaction cost as a proportion of prices. In that case, absence of arbitrage opportunities implies the following two conditions: P i * ep (4) 1 i P * ep i 1 i (5)

8 he 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. hus, with transaction costs, the law of one price holds only within a band: 1 epi 1 P i * 1 (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 he theory of purchasing power parity he macroeconomic counterpart of the Law of One Price is the theory of Purchasing Power Parity (PPP). he 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. o 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. hat is: * P ep, (7)

9 where P stands for the consumer price index (CPI) in the home country and P * stands for the consumer price index abroad. he 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. hus, even if all goods were priced the same across countries, consumer price indexes would not be the same 3. 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 ). hus, the absolute version of PPP is not expected to hold. Box : PPP exchange rates and international comparisons of income In the real World, costs of living differ significantly across countries. o 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 0 CHF if 3 In exercise 1, you will find a simple example.

10 purchased in Switzerland. In that case, the PPP exchange rate would be PPP=100/5=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 * hat would mean that the cost of living in Switzerland was 76% more expensive than in Portugal. Figure illustrates the differences in price levels calculated in March 018, 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 urkey, with the same basket costing only 40% less than in Portugal. Figure Comparative price levels as of March 018 (Portugal=100) Source: OECD, he 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 015, 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

11 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. his means that, in PPP units, per capita GDP in Uganda was equal to 600/0.3=000. In other words, taking into account the differences in costs of living, the purchasing power of an average citizen in the United States was 8 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 he relative PPP hypothesis A less stringent version of the Purchasing Power Parity heory is the relative version. his 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 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. aking differences in (1), the relative PPP implies that: ˆ * e 0, (9) where eˆ e e, P * * * P, and P P 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). his means that the relative PPP theory does not offer a full theory for the equilibrium real exchange rate.

12 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. his 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: he relative PPP hypothesis in the real world o illustrate the PPP hypothesis with real world data, we refer to Figure 3. he 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). he nominal exchange rate between the pound and the dollar (red line) was fixed along (with devaluations in 1967 and 1968), and then became flexible, exhibiting high volatility. he relative price level (blue line), in turn, evolved slowly over time, reflecting short-run price stickiness. hus, 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 time 4. 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., A panel project on Purchasing Power Parity: mean reversion within and between countries. Journal of International Economics 40, 09-4].

13 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 ominal exchange rate and relative CPI between UK and the United States, 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. hus, 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. hen after, the bilateral real exchange rate became roughly constant. hus, 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

14 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 ominal exchange rate and relative CPI between Japan and the United States, CPI in JP relative to CPI in US (left scale) JPY/USD exchange rate (left scale) Bilateral real exchange rate (right scale) Source: AMECO raded and non-traded goods What do we mean by traded and non-traded goods? he main reason why the PPP theory fails in the long run is the presence of nontraded goods. A non-traded good is one that can only be sold in the same economy where it is

15 produced. hink, 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. he 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. he 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. raded 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. evertheless, 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. echnology 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. he same applies to many other retail markets, such as of music, video and books. echnological progress is increasing the range of goods that are subject to international

16 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 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 Q and A the domestic supply and demand for the non-traded good respectively, equilibrium in the non-traded good market implies: Q A (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 P 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). hen consider the effect of a demand expansion. Clearly, when the A curve shifts outwards, the price of the non-traded good increases. In the new equilibrium (point 1), there

17 will be a higher consumption of the non-traded good ( A 1 ), more production ( higher price ( P 1 Q 1 ) and a ). he reverse holds in the case of a contraction in domestic demand (point ). he market for non-traded goods works just like that of any good in a closed economy. ote 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 nontraded (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 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 price 5 : where P and * P ep (11) * P 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, * P is exogenous (determined abroad). In what follows, we will often refer to a numerical example, with P * 1, e 100. In this case, the price of the tradable-good should be P ep * 100. In the radable-good sector, differences between domestic supply and demand are matched by the balance of goods and services. Denoting by Q and and the domestic demand for the traded good, the following identity holds: A the domestic supply 5 In what follows, only occasionally we will discuss the implications of short term deviations from (11), as implied by the parameter.

18 B Q A (1) o 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., B is equal to zero. In this case, we say there is external balance. Q A0 0, so Figure 6. he market for traded goods partial equilibrium ow, consider an increase in the demand for traded goods, say to A 1. 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. he 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: B 1 Q0 A1 0. Conversely, when the domestic demand for traded goods decreases (say

19 to A ), a surplus in the balance of goods and services will emerge (in the figure, this is illustrated by the distanceb Q A 0 ). 6 0 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, B on-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 and 3. In the case of tradablegoods, the price remains constant, but the demand expansion gives rise to a deficit in the B. 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 he real exchange rate and non-traded goods he 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 ote that the analysis in Figures and 3 is incomplete, because it takes each market separately, without accounting for substitution effects. hus, 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 tradablegood, and firms to reallocate resources away from the tradable-good sector towards the non-tradable-good sector. hese substitution effects are better addressed in a general equilibrium framework, as done in the following sections.

20 P 1 (13) P P Postulating (for simplicity) that the same shares hold in the foreign economy, the foreign Consumer Price Index (P * ) will be equal to: P * * * 1 ( P ) ( P ) (14) ow, if we substitute these expressions in (1), one obtains: ep P * e( P ) ( P ) * * 1 1 P P * ep P * ep P 1 (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 ep P * 1 (15a) his 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. he 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. ote 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: raded 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. his conforms to the idea that international competition does not allow traded good prices to deviate too much from each other.

21 he 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 his 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 Price deflator of Exports Price deflator of Imports GDP price deflator 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 Source: Statistics Portugal he supply side o further explore our model, we now turn to the micro-foundations. In this section, we address the supply side of the model echnology 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. he 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. he endowments of labour and of capital are

22 given. Since capital is specific to industry, without loss of generality one can set it equal to one. he production functions are as follows: Q 1 L K zl zf (16), Q al (17) and. where z and a stand are productivity parameters, and subscripts refer to industries he aggregate labour supply is inelastic, but workers can move freely from one industry to the other. he labour resource constraint is given by: L L L (18) he Production Possibility Frontier (PPF) he production possibilities frontier presumes that all resources in the economy are used: hence, equation (18) shall hold in equality. In that case, L L L (18a) Using (18a), (16) and (17), the production possibilities frontier of this economy becomes: Q L a Q z (19) umerical 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 L 300, 1 and a z 1. In this case the Production Possibilities Frontier is: Q 300 Q (19a) his example is illustrated in Figure 8. In the figure, the four panels correspond to equations (17), (16), (18a) and (19a).

23 he 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. he 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. he resource constrained is negatively sloped because as we increase labour in one sector, labour allocated to the other sector must decrease. ow, suppose that the economy is initially in point 0. At this point, the labour allocated to the traded goods sector is L 100, implying an output level equal to Q he non-traded goods sector is employing L 300, corresponding to a production of Q ow, suppose that 36 workers moved from the tradable-goods sector to the nontradable-goods sector (point 1, in the lower left diagram). As shown in the figure, this implies 1 a fall in production of tradable-goods to Q 8 and an expansion in the production of non- tradable-goods to Q 3. In the upper right panel, this change is described as a move 1 0 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). he 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 18 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. 0

24 Figure 8 Production Possibility Frontier he Marginal rate of transformation he slope of the PPF in each particular point gives the Marginal Rate of ransformation (MR). he MR 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. he MR is obtained by total differentiation of (19), keeping the labour supply unchanged. his gives: MR, dq a aq (0) dq dl 0 zfl z Returning to our numerical example, we can easily check that in point 1 MR 1 16 and in point 0 MR 0 0 : as we move to the right along the PPF, the MR increases. he reason is that production in the traded good sector exhibits diminishing returns to labour:

25 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 Labour demands Under perfect competition, each firm maximizes profits taking wages and prices as given. In the traded goods sector, the problem is: max zf, L W L K L P where П stands for the firm profits in the traded goods sector, and W is the wage rate in units of domestic currency. he profit-maximizing problem in the non-traded goods sector is the following: max L al W P L where П stands for the firm profits in the non-traded goods sector and w is the wage rate in units of domestic currency. he corresponding first-order-conditions are: d dl 0 W P zf L zl 1 (1) d dl W 0 a () P Equations (1) and () 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. ote 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. he quantity of labour actually demanded in the non-traded good sector will be determined by the quantity of output produced, given (17).

26 An arbitrage condition o 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: W P a P zf (3) L Another way of writing (3) when the production function takes the form (16) is: P a aq (3a) P zf z Where be the relative price of the tradable-good: P P (4) he 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. he relative price is often referred to as the internal real exchange rate. Equation (3a) 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 tradablegood in terms of the non-tradable-good in production (the MR). his 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. he relationship between the MR and the relative price is illustrated in Figure 9. When 0 0, the optimal production occurs in point 0, where the MR is exactly equal to 0. In case the relative price of the traded good declines to 1 16, production moves to point 1. Why is that? he 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 P ep * 100, this means that the price of the non-tradable-good increased from P W 5 to W he fact that the real wage increased in the P

27 tradable-good sector created the incentives for firms to reduce employment in the tradablegood, 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. his includes, for instance, skills mismatches, labour market regulations and information failures. hese 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 he supply functions he supply functions for the traded and non-traded goods are obtained directly from equations (1) and (): z Q (1a) a

28 Q W : P (a) a ote 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. he quantity actually produced will depend on the consumer demand for the non-traded good Measuring Domestic Production otal 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. otal production in units of the traded good is given by: 1 Q Q Q (5) In terms of Figure 9, when the relative price is equal to 0 0 the value of the production pattern described by point 0 in terms of the tradable-good is Q When the relative price decreases to 16, then the value of the 0 production pattern in units of the tradable-good increases to Q ote 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 Productivity, wages and non-tradable good prices he arbitrage condition (3) establishes a channel through which changes in the productivity in the tradable good sector impact on the price of non-tradable good, and viceversa. o 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 (3) is as follows:

29 W e ap P * zfl (3b) e his 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). hus, for instance, when the productivity in the traded good sector, z, increases, this requires an increase in the ratio W/e. hen, 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). ote 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 L declines). zf L can either increase when z increases or when his 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 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. his 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 he household problem In what follows, let s assume that the household utility function is as follows: U C C C C (6) 1 (, )

30 he 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: 1 A C C (7) From the first order conditions of the maximization problem we get: C 1 C (8) Condition (8) states that the marginal rate of substitution between the tradable and the non-tradable-good shall be equal to the relative price. his condition defines a family of optimal consumption baskets, depending on the level of expenditure, which is known as the income-expansion path. Substituting (8) in the budget constraint, we obtain the optimal demands for the two goods: C A (9) C 1 A (30) Figure 10 illustrates the optimal consumption choices for different values of A and λ, in the particular case in which 1. 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, A 0 0 and A 1 5. hen, we draw three different budget constraints, considering 0 0 and hus, for instance, when A 0 0 and 0 0, the optimal choices are C 10 and C 00 (point 0). If, keeping the expenditure constant, the relative price decreases to 16 1, then the optimal consumption basket becomes C 10 and C 160 (point 1). If,in alternative, the new relative price comes along with a higher level of expenditure, A 1 0, the solution is C 00 and C 1. 5 (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 ).