Real Exchange Rate Models

Transcription

1 Real Exchange Rate Models Simon van orden 1.0 Introduction We ve seen that when Purchasing Power Parity (PPP) holds, then the real exchange is constant and equal to 1. Relative Purchasing Power Parity (RPPP) simply means that the real exchange rate is constant. However, we ve seen that neither relationship is a very good description of reality, where movements in nominal exchange rates closely mirror those in real exchange rates (especially for low-inflation countries.) The first set of explanations for this were Balance of Payment models. These stress the supply and demand for a currency in foreign exchange markets in terms of flows; the amount of currency that is brought to market on a daily or hourly basis to be traded. Confusingly, some economists like to refer these as demand-side models. This is because those are typically macroeconomists and they are thinking of macroeconomic, or aggregate, demand. In Balance of Payment models, we talked about the importance of domestic economic activity (Y) in determining our demand for imports and foreign economic activity (Y*) in determining the demand for our exports. These imports and exports would then affect our Balance of Trade and therefore the net supply and demand of our currency available for exchange in the markets. In contrast, the models we look at today are supply-side models. Again, this is true from a macroeconomic perspective. In these models, supply-side factors (such as productivity growth) determine the exchange rate. In fact, changes in aggregate demand have no effects on real exchange rates in these simple models. Later on, we ll see that this means the Current Account balances itself in quite a different way from before. We ll look at two different supply-side models. The first is a well-known 35-year old model due to Balassa (1964) and Samuelson (1964). The second is just a trivial adaptation of their model to the terms of trade that I find useful. 2.0 The Balassa-Samuelson Effect 2.1 Introduction When talking about deviations from PPP last week, we noted that differences in productivity could help to compensate for these differences. For example, if the Japanese Yen were overvalued with respect to the Greek Drachma, this means that the cost of living and the cost of business inputs tend to be higher in Japan than in Greece. However, companies might still prefer to produce in Japan if their productivity were higher there, since this might allow to achieve the same (or higher) levels of profits. Similarly, workers might still Copyright 1998 by Simon van orden September 23, of 12

2 prefer to live in Japan if their productivity were higher there, since the resulting higher wages might allow them to achieve the same (or higher) levels of profits. The problem with this kind of productivity-based explanation is that it leaves some important questions unanswered. Why not ship consumer goods (or business inputs) from the low-cost to the high-cost country? Why is the high-cost country usually the richer country? The Balassa-Samuelson model answers both of these questions by focussing on a particular kind of productivity growth. 2.2 The Balassa-Samuelson Model Suppose we have a small open 2x2 economy. open just means that this is an economy that trades with the rest of the world small means that this economy is small relative to the rest of the world (like Canada.) Therefore we can assume that world markets are not affected by what happens in this economy. 2x2 means that there are only two industries in this (very simple) economy, and that they both produce their output using combinations of two different factors The outputs are T and ; the factors are K and L T is an internationally traded good. (Think of manufactured goods.) is a non-internationally-traded good. (Think of services.) K is an internationally traded factor. (Think of Financial Capital.) L is a non-internationally traded factor. (Think of Labour.) Their prices are, P,, P L Of course, in economics only relative prices matter, so we can choose one price to be the numeraire. We ll pick the non-traded good. This means we ll assume that P = 1 in everything that follows, and we ll interpret all the other prices as relative prices. The law of one price holds for internationally traded goods in an open economy. That means that is fixed by a no-arbitrage condition. Effectively, there are only two prices free to move in this economy, and. P L Copyright 1998 by Simon van orden September 23, of 12

3 2.2.4 is the real wage. P L ormally, we might measure real wages as their purchasing power in terms of consumption goods (T and.) Here, however, we measure the real wage solely as its purchasing power in terms of the non-traded good (). We d get the same qualitative results if we used a weighted basket of T and instead, but this definition is simpler. (Technically, is just an index of the real wage.) P L is the real exchange rate. To be more precise, it is our index of the real exchange rate. Think about it. The real exchange rate measures the relative cost of domestic and foreign bundles of consumption goods. A higher number means the domestic bundle is relatively cheaper. We only have one good in this model that is consumed abroad;. That better be the cost of the foreign bundle. The cost of the domestic bundle will be some weighted average of and., say α + ( 1 α) P for 0 < α < 1. P So the real exchange rate must be α + ( 1 α) P = α + ( 1 α) since we said P = 1. This expression just increases whenever increases and decreases whenever decreases. For simplicity, therefore, we ll just use rate. Remember the basic intuition; as our index of the real exchange a higher real exchange rate means a real depreciation of our currency so our imports cost relatively more and our exports are relatively more valuable Suppose there are no economies of scale and both industries are competitive In this nice, simple case, it just so happens that we can summarize both industries in terms of their per-unit cost functions. = TP ( K, P L ) P = a P ( K, P L ) (EQ 1) (EQ 2) Copyright 1998 by Simon van orden September 23, of 12

4 The, a scale the costs of the industry. Higher productivity means that these scaling factors get smaller (costs fall.) P otice T P = a,,,. T K > 0 T P = a K T L > 0 P = a L P K > 0 = a K P > 0 L each of these derivatives is just the amount of that factor used per unit of production (this is where economics students say Envelope Theorem! ) What are the effects of a change in productivity? To find this, we can totally differentiate (EQ 1) and (EQ 2) to get = T K P = a K + T L P L + TP ( K, P L ) + a P L + P ( K, P L ) a (EQ 3) (EQ 4) Fortunately, this mess is easy to simplify in 3 steps. 1. Since is the numeraire, = 0. P 2. Let s suppose all the productivity growth is in the traded goods sector, so = 0. In that case, (EQ 4) simplifies to a P L = K (EQ 5) We can substitute this into (EQ 3) to get = T K + T L ( K ) + T (). 3. Since this is a small economy, we won t change the relative price of traded goods and P factors. This means d( ) 0 T P T P = = P so T P = T K 2 (EQ 6) This lets us rewrite (EQ 6) as = T K T L T (). a T P 1 a K T T K T K L = T (). a T = ( α T ) K P a K = T T K T K L (EQ 7) (EQ 8) (EQ 9) Copyright 1998 by Simon van orden September 23, of 12

5 P > 0 1 a K > T T K T K L P T T L > T K T K L K > T K (EQ 10) From this, we can see that there are two effects; > 0 and > The first condition is always true, the second may or may not be true. The second condition compares the relative factor intensity of the two industries. This is the relative share of costs of capital and labour in each industry The more labour-intensive T is, the more likely the condition is to be satisfied The Balassa-Samuelson Effect The Balassa-Samuelson effect can be traced back to the writings of David Ricardo in the late 1800s, and Harrod (1993), but was most clearly explained by Balassa (1964) and Samuelson (1964). They argued that if productivity growth is concentrated in industries that produce tradeable goods rather than non-tradeables, we should expect to see a real appreciation of the domestic currency. This is consistent with what we see in, which tells us that a deterioration of productivity in the tradeable goods sector will cause a real depreciation of the home currency if the two industries are not too dissimilar. (The original papers by Balassa and Samuelson assumed that the two industries were identical, so T K K = 1 = T L.) T L T K K 2.3 Understanding the Balassa-Samuelson Effect The Labour Market To understand what is going on, we need to think about how the two industries (T and ) are linked. Since both are competitive and have no economies of scale, the price of their outputs simply reflect the costs of production, so both and will equal weighted averages of and. When the productivity of an industry rises, the industry becomes P L more profitable and tries to expand. Expansion requires more inputs. Since we re in a small open economy, we can import as much capital as we wish (and export as many tradeables) without affecting their price. However, there is only a fixed amount of labour in this economy, which must be shared between the two sectors. The key to this model is that when one sector expands, it does so by raising wages and attracting labour away from the other sector. This continues until the reduction of labour in the other sector has raised its marginal product of labour to the point where it can once again pay wages competitive with the expanding sector. P Copyright 1998 by Simon van orden September 23, of 12

6 2.3.2 The Dutch Disease The fact that sectors must compete for labour has sometimes been called the Dutch Disease, referring to the experience in the etherlands with the development of offshore gas in the 1970s. The demand for workers in the energy sector made labour scare and tended to raise wages. However, Dutch manufacturers could not afford to pay the higher wages, so the manufacturing sector shrank as workers left it to take more productive jobs in the energy sector. More generally, Dutch Disease refers to the fact that development of natural resources will usually make manufacturing less competitive due to the wage pressure it causes. This is important because, since the beginning of the industrial revolution, productivity growth has been concentrated in the tradeable rather than non-tradeable sector (e.g. manufacturing and agriculture rather than services.) As a nation develops industrially, wages rise with living standards, and this raises the price of non-tradeables Balassa-Samuelson & Baumol-Bowen Technically, we should distinguish the Balassa-Samuelson effect from the Baumol-Bowen effect. The former is about relative productivity growth in tradeable and non-tradeable sectors. The latter is about relative productivity growth in goods and services. As long as services continue to be largely non-traded and goods traded, there is little practical difference between the two. However, there is no shortage of those who point to the impact of information and communications technology and predict that in future, productivity growth will be increasingly concentrated in services rather than in manufacturing. Does that mean that the Balassa-Samuelson effect should disappear? Yes, if we assume that these new hi-tech services continue to be largely non-traded. However, if we think new communications technologies (distributed electronic payment systems, global networks, widespread mobile communications, the internet, etc.) will make these services tradeable on an international scale, then we ll continue to see productivity growth in the tradeables sector. That would mean that the Baumol-Bowen effect might vanish, but not the Balassa-Samuelson effect. 2.4 Balassa-Samuelson & Reality It Fits. How well does the Balassa-Samuelson effect describe exchange rates? We saw from the graph presented last time that it seems to capture exchange rate behaviour much better than the PPP models we saw previously. In Balassa s original paper, he reported an R 2 of about 80% for the sample of countries he examined. Obviously, this kind of model helps us understand some systematic deviations from PPP and allows us to reconcile them with the law of one price by distinguishing between tradeable and non-tradeable goods. At the same time, the model has several shortcomings. Copyright 1998 by Simon van orden September 23, of 12

7 2.4.2 Long Run Only First, we should realize that it is only a long-run model. It assumes that labour and capital move freely between sectors and therefore earn equal returns in both. In reality, labour moves slowly and wages adjust slowly, so there can be persistent lags (lasting many years) while we wait for these mechanisms to make themselves felt Supply side only Second, and related to this, demands for goods and services play no role in this model; real exchange rates are entirely determined by the supply side of the economy. This means, for example, that government deficits and surpluses have no role on exchange rates, nor do current account surpluses or deficits. This may seem odd, since we still have to pay for our net imports, but now we can no longer rely on the exchange rate to move our imports and exports into balance. That is because in this model, demand will affect quantities, but not prices. Since both sectors have constant returns to scale, they will happily produce any quantity of output at the prevailing prices. As a country becomes more indebted, consumers have less money to spend, reducing the demand for non-traded goods, which causes the traded goods sector to expand, providing the production with which to service the foreign debt. Similarly, as a nation becomes richer, it will tend to consume more non-tradeables, leaving fewer resources with which to produce tradeables and thereby earn export revenue. While this adjustment mechanism may not sound realistic, it is at least consistent with the fact that we cannot generally find any stable relationship between aggregate demand and exchange rate behaviour Time Series Performance The third problem with the Balassa-Samuelson model is that it explains the wrong kind of exchange rate variation for our purposes. The model has some ability to explain why real exchange rates vary across countries. However, as financial managers, we want to understand real exchange rate movements over time. From a time series perspective, the Balassa-Samuelson model has much the same general problem as PPP. With PPP, we saw that relative price levels moved too little and much too smoothly to be able to explain much of the exchange rate volatility that we observe over time. The key factor in the Balassa-Samuelson model suffers from a very similar problem. Relative productivity levels move little from year to year, and so are not nearly volatile enough to explain much of the exchange rate risk facing investors and portfolio managers. 3.0 Terms of Trade Effects Fortunately, we can make a minor modification to the model we just saw and get an exchange rate model that generates much volatility in exchange rates over time. Copyright 1998 by Simon van orden September 23, of 12

8 3.1 Adapting the Balassa-Samuelson Model Suppose we have a small open 2x2 economy. just as before The outputs are T and ; the factors are M and L M is an internationally traded factor. (Think of raw materials, natural resources or other commodities.) Their prices are ow has replaced. P M, P, P M, P L This time, we are going to use T as the numeraire, so = is the real wage. P L just as before is the real exchange rate. P ow a higher implies an appreciation of the domestic currency since it implies that P traded goods are now cheaper is the terms of trade P M Actually, the terms of trade is traditionally defined as the price of our exports divided by the price of our imports. This traditional definition means that an increase in the terms of trade make us better off, since the same amount of exports can now buy us more imports. However, in this model, we haven t specified whether we are exporting T and importing M or vice versa. Depending on the country, either one could be realistic. For example, Japan exports mostly manufactured goods and imports mostly raw materials, while Australia is a major net exporter of natural resources and a major net importer of manufactured goods. It is therefore not clear whether the right way to define the terms of trade is 1 P M (i.e. for Japan) or P M (Australia.) For now, we ll just remember that increases in our terms of trade may make our country worse off, depending on which tradeables it exports and which it imports Suppose there are no economies of scale and both industries are competitive We can summarize both industries in terms of their per-unit cost functions. Copyright 1998 by Simon van orden September 23, of 12

9 = TP ( M, P L ) (EQ 11) P = P ( M, P L ) (EQ 12) Since we re going to ignore changes in productivity, we ve assumed = 1 = a What are the effects of a change in the terms of trade? Again, we find the solution by totally differentiating the above two equations. = T M P M P = M P M + T L P L + P L (EQ 13) (EQ 14) Since we set = 1, (EQ 13) implies 0 = T M P M + T L P L P L = ( T M T L ) P M (EQ 15) We substitute this into (EQ 14) to get P = M P M P + ( T M T L ) P M P M = M ( T M T L ) (EQ 16) P > 0 M T M > M > L P M T L T M T L (EQ 17) 3.2 Understanding the Terms of Trade Model In this model, as in the Balassa Samuelson model, real wages are determined by limited supply of labour which moves between the two sectors until wages are equalized. The terms of trade are determined by world markets. Movements in these terms of trade determine both the real wage and the real exchange rate in this economy. However, it should be noted that the sign of the relationship is not clear. A Balance of Payments model would lead us to expect that an improvement in the terms of trade will improve the current account, and should therefore lead to an appreciation of the domestic currency. In the terms of trade model, the result again depends on the relative factor intensities of the two sectors. If the price of raw materials rise, the sector that uses raw materials more intensively will have to raise its output price relative to that of the other sector. Typically, however, we expect that traded goods industries (manufacturing) uses natural resources and other raw materials more intensively than non-traded goods industries (services.) This would lead us to expect that fall in commodity prices (like what we ve seen over the last year) will make traded goods cheaper, and therefore cause a real appreciation Copyright 1998 by Simon van orden September 23, of 12

10 of the currency of small, open economies. The model predicts that this will be true regardless of whether they are net importers or net exporters of commodities. ote that is terms of trade model is not widely used. I ve yet to see a name applied to it, and know of its use in only 3 or 4 published papers, all of which appeared over the last 5 years. 3.3 The Terms of Trade Model and Reality Direction This model often predicts the wrong direction of movements in the real exchange rate. For example, with the collapse of world commodity prices over the last year, we ve seen big real depreciations of the CAD, AUD, and JPY. The terms of trade model predicts that all three should have appreciated, and BoP models predict that the CAD and AUD should have depreciated and that the yen should have appreciated Volatility The model does, however, give a link between commodity prices and real exchange rates. Unlike the other exchange rate determinants we ve looked at so far, commodity prices are highly variable and are not smooth, much like the real exchange rates we hope to explain. While this might help us to explain past exchange rate changes, we should also remember that commodities are assets themselves. This means that changes in their prices will be hard to predict. If exchange rates are close to the levels predicted by a terms of trade model, this means we would have little reason to expect either appreciations or depreciations in the future, without more information on where commodity prices are likely to go Fit If we simply ignore the signs predicted by the model and look at the ability of the terms of trade to explain real exchange rate movements, we find some interesting things. Australia & Canada: In contrast to the generally accepted view that we can t explain exchange rate movements for most currencies, there has been a growing consensus that commodity prices give us a very good explanation in the case of a few commodity-exporting small, open, developed economies. Most of the work for this view in the case of Australia was done by David Gruen and his coauthors at the Reserve Bank of Australia in the early 1990s, while the work for Canada was done by myself and Robert Amano at the Bank of Canada at roughly the same time. In both cases, we found evidence of stable, long-run relationships between commodity prices and the real exchange rate that explained most of the variation in real exchange rate over periods of a few years, and even had some modest explanatory power for month-to-month changes. In both cases, stronger commodity prices tended to cause an appreciation of these currencies. Copyright 1998 by Simon van orden September 23, of 12

11 The Canadian results are presented in Lafrance and van orden (1995). 1 There are several things to note. they find that energy and non-energy commodity prices have opposite effects on the real exchange rate; higher non-energy commodity prices make the CAD appreciate, while higher energy prices make it depreciate. However, the effect of energy prices is much smaller than that of other commodities. Canada-US interest rate differentials play an important role in the short run The equation they present seems to allow one to predict a modest fraction of future month-to-month changes in the Canada-US exchange rate. The equation s performance in the long-run is best shown by Chart 5, which compares the actual values of the real exchange rate with the dynamic simulation of their model. Chart 4 shows how it behaves for month-to-month changes. Research on exchange rates is unreliable at best and one must always be aware of the possibility of data-mining (which we ll discuss after the mid-term.) It is therefore important to consider how this equation has performed since it was published. The work on which Lafrance and van orden (1995) is a paper by Amano and van orden presented at a conference in mid As of January 1998, presentations by Bank of Canada officials showed the real exchange rate was almost exactly equal to the value predicted by the equation. A July 98 note by Morgan Stanley Dean Witter 2 calculates that movements in the real value of the CAD over the June 97 to July 98 period are closely matched to those predicted by the equation. Goldman Sachs uses much the same equation for their own forecasts of the CAD. 3 One analyst at Goldman Sachs has pointed out that the correlation between short-term movements in the Canadian dollar and commodity prices has been increasing. Using Bloomberg daily data, you get the following correlations between the CAD/USD rate and the Goldman Sachs Commodity Price spot index. 4 Jan 97 to Aug 31 98: -84% Jun 97 to : -85% Oct 97 to ": -83% Jan 98 to ": -86% Mar 98 to ": -94% Jun 98 to ": -94% 1. Available on the web site. 2. See the article by Elaine Buckberg on the web site. 3. See Goldman Sachs, Canadian Review, ovember 1997, page 12 for a description of how they model the CAD. Copyright 1998 by Simon van orden September 23, of 12

12 The G-3: Subsequent research by Amano and van orden focussed on the relationship between the terms of trade and real effective exchange rates for Japan, Germany and the United States. 5 In a pair of papers written in 1993 and published in 1998, they find that changes in oil prices account for most of the movements in these countries terms of trade since there seems to be a stable, long-run relationship between real oil prices and the real effective exchange rates for all three countries. higher oil prices make the USD strengthen, the DEM weaken, and the JPY weaken even more. these relationships seem to help predict exchange rate movements during periods of volatile real oil prices. The main limitation of this research is that the data set examined ended in I m not aware of any work that documents whether these relationships have continued to appear stable as time goes on. 6 Other currencies: While not much more research has been done, it is clear that this kind of relationship does not hold for many other nations. For example, the development of orth Sea oil has changed the UK from a net importer to a net exporter of oil, and changed the sign of the correlation between oil prices and their terms of trade. There is no evidence of a stable relationship between the value of the GBP and real oil prices. Another paper by Krueger and van orden developed a similar model for the Mexican peso, but required information on the current account balance as well as oil prices to explain the long-term value of the peso. 4. Marcel Kasumovitch, Goldman Sachs, private research correspondence. 5. See the paper by Amano and van orden on the web site. 6. This would be particularly interesting since the period since then has seen considerable movement in real effective exchange rates and in real oil prices. For those considering a term paper subject, be aware that this one requires mastery of econometric techniques related to cointegration. Copyright 1998 by Simon van orden September 23, of 12