1. Topics on International Macroeconomics (Lecture 4)
Marko Korhonen
Department of Economics

2. International macroeconomics is evolving continually
International macroeconomics is evolving continually. New empirical analyses, new theoretical models are always being developed, and the fast-changing global economic environment of recent years has pushed forward research faster than ever.
In this final lecture, we examine two topics that have occupied researchers for many years and that remain at the cutting edge:
■ Does purchasing power parity really works as a long-run theory of exchange rates? Why are price levels higher in richer countries? We develop such a theory and show how it can be applied to improve exchange rate forecasts.

3. ■ We also ask whether uncovered interest parity really works as a short-run theory of exchange rates. If arbitrage operates to support uncovered interest parity in an efficient market, profits ought to be eliminated.

4. 1 Exchange Rates in the Long Run: Deviations from Purchasing Power Parity
In 2009, the gross national income per capita in the United States was $47,240. When converting incomes using the exchange rate, the gross national income per capita in China was only $3,590.
But when comparing dollar incomes with the dollar prices of baskets of consumer goods, Chinese gross national income per capita was $6,770 in terms of U.S. consumer goods, so China’s living standards seen to be almost twice as high.
The reason: in dollar terms, most goods cost a lot less in China than in the United States. The dollar price level in China was lower than in the United States. The implication: PPP does not hold, and the real exchange rate is a long way from 1.

5. Limits to Arbitrage
One way to set up a more realistic economic model would be to introduce costs of trading.
Let’s assume that there is one good that sells for P = $100 in Home, and it costs $10 to ship the good from Home to another country, Foreign. The trade cost is c = 0.1 = 10%.
The cost of the good on arrival in Foreign, including the trade cost, would be P × (1 + c) = $110.
The ratio of the prices is q = EP*/P, where q is the real exchange rate of the home country. Thus, if P = $100 and EP* = $110, then q = 1.1.
E is Home’s exchange rate, and P* is the Foreign price in Foreign currency. To trade the good, the Foreign price converted into dollars EP* would have to be at least $110. Going from Foreign to Home, you wouldn’t ship goods unless the Home price P was at least 10% above the foreign price EP*.

6. Limits to Arbitrage
Arbitrage from Home to Foreign is profitable only if q = EP*/P > 1 + c, and from Foreign to Home only if 1/q = P/(EP*) > 1 + c.
So, taking trade costs into account, the no arbitrage condition for market equilibrium is:

7. FIGURE 22-1
No Arbitrage Bands The hypothetical relative price ratio q is shown in three cases.
In panel (a), trade costs are zero, so the law of one price (LOOP) holds and q has to equal 1.
In panel (b), trade costs are small, say, 10%, so the prices in the two locations can differ. The high price can exceed the low price by up to 10%, so q can range between 100/110 (0.91) and 110/100 (1.1), the so called no-arbitrage band.
In panel (c), trade costs are high, say, 50%, so the high price may exceed the low price by up to 50%, so q can range between 150/100 and 100/150.
Thus, as costs of arbitrage increase, deviations from simple LOOP and PPP become larger, and these “laws” become less useful.

8. Trade Costs in Practice Empirical research suggests that trade costs are affected by economic policies, as well as by characteristics of goods and their markets.
Average tariffs of 5% (rich countries) or more than 10% (developing countries) constitute an additional cost, and such tariffs vary widely by type of good.
Quotas (limits to import quantities) and regulatory barriers (such as health and environmental regulations) also add to trade costs, but the costs they add are difficult to compute.
Other causes of price gaps include distance between markets, crossing international borders, having different currencies, having floating exchange rates, and so on.

9. These data show that trade costs are large—and typically, they are even larger outside the advanced countries and create a very wide no-arbitrage band.
Trade costs matter!
Note that the subcosts are aggregated by compounding: e.g., a 21% markup on top of a 44% markup on a $1 good in the middle column results in a 74% markup in the left column, because 1.21 × 1.44 × $1 = $1.74.

10. APPLICATION
It’s Not Just the Burgers That Are Cheap
If real exchange rates can deviate from the PPP-implied value of 1, how do they vary, and why? One place to find a clue is in the pattern of deviations from PPP.
For example, deviations from PPP in the Big Mac index are not entirely random: burgers tend to be cheaper in poorer countries. In 2010, the Economist found that, expressed in U.S. dollars, a Big Mac cost 30% less in Mexico and 39% less in Malaysia than it did in the United States.
A Big Mac is a combination of some traded goods (such as flour, beef, and special sauce) and some nontraded goods (such as cooks and cleaners). The nontraded goods contain a strong element of local labor input, so they tend to cost less in a poor country (see panel (a) of Figure 22-2).

11. APPLICATION
It’s Not Just the Burgers That Are Cheap
In 2004, the Economist did a parallel experiment and compared the prices of a Starbucks tall latte. Similar patterns emerged: in dollar terms, the latte cost 15% less in Mexico and 25% less in Malaysia.
A country’s price level is strongly correlated with the level of GDP per person (see Figure 22-2, panel (b)).
Rich countries have higher price levels; their baskets cost more. In other words, the real exchange rate q = EP*/P is not equal to 1 for all countries—PPP does not hold, even in the long run.■

12. It’s Not Just the Burgers That Are Cheap
APPLICATION
It’s Not Just the Burgers That Are Cheap
FIGURE 22-2
Price Levels in Rich and Poor Countries Panel (a) shows that richer countries (measured by higher wages) tend to have higher Big Mac prices (measured in a common currency).
Panel (b) shows that richer countries (measured by higher GDP per person) tend to have higher overall price levels (measured in a common currency).

13. Nontraded Goods and the Balassa-Samuelson Model
Using two goods—one traded and one not traded—we can explain price level differences and deviations from PPP.
A Simple Model The model can be solved in three steps, with assumptions as follows:
1. The traded good has the same price in both countries.
2. Productivity (A) in traded goods determines wages. Wage levels in each country are equal to productivity levels.
3. Wages determine the prices of nontraded goods.
We assume there are two countries: Home and Foreign (values for Foreign are denoted by an asterisk). Thus, w denotes the Home wage and w* denotes the Foreign wage, each measured in the respective currencies. The Home exchange rate is E (units of Home currency per unit of Foreign currency). There are two goods. Each good is produced competitively and labor is the only input needed. One is a nontraded, service good (say, a haircut), denoted N, and its trade costs are effectively infinite. The other is a costlessly tradable good (say, a DVD player), denoted T, that has no trade costs at all. Prices of goods will be denoted p and p*, each measured in the respective currencies, with subscripts T and N to denote traded and nontraded goods.
One Home worker can make A units of the traded good (the DVD player) per hour. Then the worker’s hourly wage w will be equal to $A because each unit of the good sells for $1 and competition means that the wage will equal the value of the output produced by each hour of labor input. Similarly, if Foreign workers can make A* units of the traded good per hour, their dollar wage Ew* will be equal to $A*.
The dollar price of the nontraded good in each country equals the wage, so pN = w and Ep*N = Ew*.

14. Nontraded Goods and the Balassa-Samuelson Model
The conclusion from these three assumptions?
Countries with higher traded goods productivity will have relatively high wages and hence relatively high prices of nontraded goods.
This means they will also have relatively higher overall price levels, depending on how large the share of nontraded goods in the consumption basket is.

15. Nontraded Goods and the Balassa-Samuelson Model
Suppose the nontraded goods share of consumption is n (so the traded share is 1 − n).
Changes in Productivity If Home productivity A increases, by ΔA/A; the price of traded goods is unchanged, at 1, and the price of nontraded goods A rises, then the (percentage) change in the Home price level is:

16. By the same logic, the a change in the Foreign dollar price level will result from a change in foreign productivity:
For our example, a 1% rise in Home DVD player productivity A will raise Home wages w by 1%; therefore, Home haircut prices rise 1% and, because these haircuts have a weight n < 1 in the overall basket, the overall price index rises by n%.

17. Subtracting the first equation above from the second, the change in the real exchange rate is given by:
(22-1)
Thus, relative productivities in the traded goods sector drive relative prices, through their effects on wages in and prices in the nontraded sector.

18. Generalizing Equation 22-1 describes an important relationship between productivity and the real exchange rate known as the Balassa-Samuelson effect, named for the economists Bela Balassa and Paul Samuelson:
When compared with other countries, a country experiencing an increase in productivity will see wages and incomes rise and will see its real exchange rate appreciate, meaning that its price level will rise.

19. Overvaluations, Undervaluations, and Productivity Growth: Forecasting Implications for Real and Nominal Exchange Rate
FIGURE 22-3 (1 of 2)
Predicted Real Exchange Rate Adjustments in Emerging Markets
The scatterplot shows national price levels and GDP per person relative to the United States for the year 2000, as in Figure 22-2(b).
The Balassa-Samuelson model would predict convergence to equilibrium in all cases (arrows 1, 3, 4).
A point on the line of best fit is the predicted equilibrium real exchange rate q of the Balassa-Samuelson model. ~

20. Overvaluations, Undervaluations, and Productivity Growth: Forecasting Implications for Real and Nominal Exchange Rate
FIGURE 21-5 (2 of 2)
Predicted Real Exchange Rate Adjustments in Emerging Markets (continued)
In relatively fast-growing countries, this would be augmented by trend real appreciation (arrows 2 and 5). Thus, real appreciations were expected for the Chinese yuan and the Slovak koruna, and a real depreciation for the Argentine peso.
If actual q is above predicted q, then foreign prices are “too high”: we would say that the U.S. real exchange rate is undervalued and the foreign real exchange rate overvalued relative to the equilibrium level. ~

21. (1) how quickly q will return toward its equilibrium value q.
Forecasting the Real Exchange Rate By comparing actual exchange rates with their predicted equilibrium values, forecasting the real exchange rate involves two problems:
(1) how quickly q will return toward its equilibrium value q.
(2) how quickly the equilibrium value q will change over time as a result of productivity changes. For example, if q is currently 0.5 but the equilibrium value q is 0.6, then q is predicted to rise.
Convergence Empirical estimates indicate that real exchange rate deviations from equilibrium might decay slowly: the consensus “half life” of deviations from PPP has been reported to be five years. For illustration, we adopt this rule of thumb estimate in the rest of this section. ~ ~ ~
In our example, if half of the 20% gap is likely to be closed over five years, then over five years, q would rise by approximately 10% from 0.5 to 0.55, an increase of about 2% per year.

22. ~
Trend The second step is to figure out whether q is a moving target and forecast what its trend rate of growth will be.
If the home country is expected to grow rapidly, with GDP per capita and wages rising; then q would rise.
Convergence + Trend For this numerical example, we would conclude that the observed real exchange rate q is likely to increase at 2% per year toward its equilibrium and to increase at a further 3.2% a year due to the upward drift of that equilibrium, resulting in a predicted real appreciation for the foreign country at a rate of about = 5.2% per year. (Note that adding growth rates in this way is only an approximation.) ~
For example, an estimate of the trend when the nontraded share is 0.4, according to Equation (22-1), says that a country’s q~ will rise 0.4% for every 1% of real GDP per capita growth in excess of the U.S. growth rate. So if a country is growing at, say, 8% per year faster than the United States, then q~ should be rising by 0.4 × 8%, or 3.2% per year.

23. Forecasting the Nominal Exchange Rate When PPP doesn’t hold, we have to worry about possible changes in q. Since E = qP/P*, then taking rates of change, we find:
(22-2)
In using this equation, we not only have to forecast inflation, we have to forecast changes in the real exchange rate, too. Foreign exchange traders have to pay attention to many macroeconomic forecasts before forming an expectation about how E is likely to evolve over time.

24. Adjustment to Equilibrium Suppose we have forecast a 1% real appreciation (−1% change in q). In Equation (22-2), this could imply either a 1% nominal appreciation (−1% on the left) or an extra 1% of home inflation over and above foreign inflation (+1% on the right), or some combination of the two.
Thus:
■ If the model says there is currently a real undervaluation, either home goods prices have to rise or the value of the home currency has to rise—there is no other way to make home goods more expensive.
■ If the model says there is currently a real overvaluation, either home goods prices have to fall or the value of the home currency has to fall—there is no other way to make home goods less expensive.

25. APPLICATION
Real Exchange Rates in Emerging Markets
China: Yuan Undervaluation? The Balassa-Samuelson model predictions: in 2000 the real exchange rate with China was q = 0.231, well below (0.088 below) the predicted equilibrium level of q =
The yuan was undervalued and would have to experience a 38% real appreciation (0.088/0.231) against the U.S. dollar.
Using our old rule of thumb, half of this gap or 19% would be eliminated in five years, implying an approximate 3.5% annual increase in q due to convergence.
In addition, a 6% differential growth rate per year (China minus United States) would imply a further 0.4 × 6 = 2.4% per year real appreciation in the yuan. ~

26. APPLICATION
Real Exchange Rates in Emerging Markets
Adding up both effects, the model predicts a real yuan appreciation of = 5.9% per year. This would imply either a nominal appreciation of the yuan against the dollar, or higher inflation. Inflation in China was not much higher than in the U.S.
Until mid-2005 China pegged the yuan to the dollar but then decided to switch to an unofficial crawling peg, allowing the yuan to appreciate gradually against the dollar, but very slowly.
This could have been a response to protectionist pressure in the United States. But the Chinese had reasons of their own to let the yuan rise: to keep domestic inflation at a reasonable level.

27. APPLICATION
Real Exchange Rates in Emerging Markets
Argentina: Was the Peso Overvalued? In 2000, Argentina’s currency was overvalued: the price level was 0.656, but the predicted equilibrium level of q was
With slow growth, very little rise in the equilibrium q could be expected (which would have mitigated the need for a fall in actual q).
What actually happened: Argentina was pegging the peso to the dollar . Although the peg held for a long time, the country was driven into crisis by fiscal and financial sector problems. In the crisis of 2001–2002, the peso depreciated to three per dollar: the overvaluation was eliminated. ~ ~

28. APPLICATION
Real Exchange Rates in Emerging Markets
Slovakia: Obeying the Rules? In Slovakia, a fast-growing country, the real exchange rate was q = in 2000 and undervalued relative to the predicted equilibrium q = Here, q needed to rise by 89% to reach equilibrium.
What actually happened: Slovakia’s koruna experienced real appreciation of between 5 and 10% per annum from 1992 to Like China, some combination of nominal appreciation and inflation was required. But Slovakia also wanted to join the euro, thus keep its inflation within limits (within 2% of the “best” in the EU). Our model suggests this would be impossible: the koruna would have to appreciate or Slovakia’s inflation would have to accelerate! ~

29. HEADLINES Eastern Europe and the Euro
The ERM rules were originally devised for a group of mostly rich Western European countries, where similarities in GDP per capita meant that Balassa-Samuelson effects were weak. Nobody adjusted the rules when a very different group of poorer countries arrived on the threshold of the Eurozone.
Estonia, Lithuania, Slovenia, Latvia and Slovakia have joined the exchange rate mechanism of the European monetary union and are candidates for near-term eurozone membership.
But forcing candidate countries to meet both an exchange rate and an inflation criterion makes no economic sense.
All that stands between Estonia, Lithuania and Slovakia and near-term eurozone membership is a rigid application of an inconsistent interpretation of a flawed inflation criterion.

30. Conclusion
In general, PPP does not hold. Goods prices are not the same in all countries. Arbitrage fails, most likely because of trade costs.
The Balassa-Samuelson theory can explain how prices vary when goods are not traded and why rich countries have higher price levels.
As countries get richer, their wages rise, driving up the prices of their nontraded goods. This will drive up the overall price index and will cause the real exchange rate to fall—that is, a real appreciation.
The theory finds strong empirical support and can be used to make better models of real and (hence) nominal exchange rates, with improved predictions.