CH-5-6 Inflation: Its Causes, Effects, and Social Costs – Macroeconomics : Chapter Notes

This Document Contains Chapters 5 to 6 CHAPTER 5 Inflation: Its Causes, Effects, and Social Costs Notes to the Instructor Chapter Summary This chapter explains the classical theory of the causes, effects, and social costs of inflation. It introduces topics that are central for understanding the economy and presents concepts used elsewhere in the textbook. These topics include: 1. How the supply of and demand for money determine the average level of prices; 2. The effects of monetary policy when prices are flexible; 3. The social costs of inflation. The material in this chapter builds upon the discussion of money and the monetary system presented in Chapter 4. Comments This chapter can probably be covered in two lectures, although the material on hyperinflation is difficult and so may require a little extra time. Since hyperinflations are both fascinating and instructive, this part of the chapter is ultimately very rewarding for the students. The Fisher equation and the distinction between nominal and real rates of interest are among the most important topics in the chapter. I emphasize this as an occasion where macroeconomics provides an important insight that many noneconomists do not understand. I like to tell students that if they understand the Fisher equation, then they know more economics than former President Bush knows (or pretends to know?); see Supplement 18-9, “Distrust of Policymakers.” Use of the Web Site This is a good time to use the data plotter to explain and illustrate the Fisher equation. Use of the Dismal Scientist Web Site Go to the Dismal Scientist Web site and download annual data for the past 40 years for the two key measures of the money supply: M1 and M2. Also download data over the same period for nominal GDP. Compute two measures of the velocity of money by dividing GDP by each of the two measures of the money supply. Discuss how the velocity of money has changed over time for these two measures. Chapter Supplements This chapter includes the following supplements: 5-1 The Velocity of Money in Poetry and Song 5-2 Data on Money Growth and Inflation (Case Study) 5-3 Seigniorage as an Inflation Tax 5-4 Deriving the Fisher Equation 5-5 Using Interest Rates to Forecast Inflation (Case Study) 5-6 Transactions Models of Money Demand 87 5-7 Inflation and Economic Growth 5-8 The Welfare Costs of Inflation and the Optimum Quantity of Money 5-9 The Welfare Costs of Inflation Revisited 5-10 Indexation 5-11 U.S. Treasury Issues Indexed Bonds 5-12 A Guide to Oz (Case Study) 5-13 Are Monetary Allegories in the Eye of the Beholder? The Case of Mary Poppins (Case Study) 5-14 How to Stop a Hyperinflation 5-15 The Israeli Hyperinflation 5-16 Additional Readings Lecture Notes Introduction So far, our entire analysis of the economy has been in real terms, since economists think that people ultimately care about goods and services, not about the dollar value of those goods and services. Because of this emphasis, we have ignored one of the main issues of macroeconomics—inflation—and we also have not yet been able to discuss monetary policy in detail. Over at least the last 40 years in the United States, prices have tended to rise. This does not mean that the price of every single good has risen; personal computers, for example, are much cheaper now than they were a few years ago. But by and large, and on average, goods cost more now than they did in the past. This general increase in the price of goods and services is known as inflation. As discussed in Chapter 2, economists measure increases in the prices of goods and services by constructing price indexes, which are simply weighted averages of the prices of different goods. The weights are based on the relative importance of the goods in consumption. The recent U.S. experience has been one of moderate but positive inflation. In recent years, prices have been rising by around 2.5 percent per year on average, while the average rate of inflation was somewhat higher in the 1970s and early 1980s and slightly lower in the 1950s and 1960s. But this is not the experience of all countries at all times. Earlier in this century, the United States experienced periods of deflation—falling prices. Other countries have experienced hyperinflations—very rapidly rising prices (hundreds of percent per month). People apparently dislike inflation. The high inflation at the end of the Carter presidency was one of the reasons Reagan defeated Carter in the 1980 presidential election. The Federal Reserve Board directs much of its policymaking at controlling inflation. Policymakers watch inflation carefully. If for no other reasons than these, we need to understand its causes and effects. It is important to understand the distinction between the price level and the inflation rate. The price level is essentially the dollar cost of one unit of GDP. The inflation rate measures the growth rate of the price level. When prices are rising, this means that the inflation rate is positive. When prices are falling, the inflation rate is negative. It is possible for prices to be rising but for the inflation rate to be falling. For example, suppose that P90 = 1, P91 = 1.2, and P92 = 1.32. Here, a pizza that cost $10 in 1990 would cost $12 in 1991 and $13.20 in 1992. Goods are becoming more expensive over time, but prices rose more between 1990 and 1991 (20 percent) than between 1991 and 1992 (10 percent). This situation, in which prices are rising but the rate of inflation is falling, is known as disinflation. Since the price level is the cost in dollars of a unit of GDP, it can also be thought of as a measure of the price of money: one unit of GDP will buy 1/P dollars. To understand the price level, and hence the inflation rate, we must, therefore, understand the relationship between money demand, money supply, and the price level. 5-1 The Quantity Theory of Money Transactions and the Quantity Equation Having briefly considered the supply of money, we now turn to the demand for money. We begin with a very simple theory of money demand, known as the quantity theory. The starting point for this theory is the observation that people hold money largely to facilitate transactions. Suppose that T transactions (exchanges of goods for money) take place in a year and suppose that P is the price in a typical transaction. Then, the number of dollars exchanged in a year, by the definition of these two variables, equals PT. Since money changes hands in these transactions, we can use this information to infer the number of times that the typical dollar bill changes hands during the year. If we let VT be the number of times that a dollar bill changes hands, and we let M be the money supply, then the number of dollars exchanged in a year must also equal MVT. Thus, we have the quantity equation MVT = PT. This equation is an identity; it must be true by the definition of the variables. The number VT is the transactions velocity of money. From Transactions to Income Suppose that each transaction represents one unit of GDP. This would be true if the only transactions that took place were those that involved the final sale of newly produced goods. Then, we could replace T with Y and get an amended form of the quantity equation: MVT = PY. In reality, of course, not all transactions represent the sale of final produced goods. The sale of a used textbook, for example, is a transaction that doesn’t have anything to do with GDP. But we might well believe that there is a fairly close relationship between the number of transactions and final output. Based on this idea, we define the income velocity of money as V = PY / M . ⇒ MV = PY If Y is proportional to T, the income velocity of money will be proportional to the transactions velocity. For example, if there are three transactions for every transaction involving a unit of GDP, then the transactions velocity of money is three times the income velocity of money. The advantage of the income velocity of money is that we can easily measure it; it is Supplement 5-1, “The Velocity of simply nominal GDP divided by the money supply. If we perform this calculation and find that Money in Poetry V = 4, and if we think that the number of transactions is three times the number of transactions and Song”” for final goods, then each dollar bill would change hands 12 times on average during the year. The Money Demand Function and the Quantity Equation A simple idea about money demand is that people hold money to carry out transactions and that the amount of money they want to hold is roughly proportional to the number of transactions they want to perform. If the number of transactions is, in turn, proportional to income, then the amount of money that people want to hold is proportional to income. Also, we might expect that the amount of money that people want to hold will be proportional to the price of a transaction; if the cost of the average transaction doubles, then we would expect that the demand for money would double. This leads to a money demand function of the form Md = kPY. As elsewhere, we prefer to carry out our analysis in real terms. The term M/P is called real money balances; it tells you the value of M in terms of goods. So we can rewrite our money demand function in real terms as (M/P)d = kY. Remember that the demand for money is really a demand for the services that money performs. People don’t want money for its own sake; they want it because it simplifies transactions. We generally work in terms of real money demand. Notice that this money demand equation bears some resemblance to the quantity equation. In fact, they are equivalent with a suitable interpretation of V and an assumption of equilibrium in the market for money. If the supply of money equals the demand for money, then we have M/P = kY, which is equivalent to the quantity equation with V = 1/k. The Assumption of Constant Velocity The quantity equation, therefore, becomes a theory of the demand for money by supposing that money demand is proportional to output. This means, in essence, that we are assuming that the velocity of money is constant. The assumption of constant velocity is not fully satisfactory, for reasons that we will come to, but it is a useful starting point. Note, moreover, where this theory leads us. If V is fixed (V), then nominal GDP must be proportional to the money supply. If Y is also fixed, then the price level is proportional to the money supply. Money, Prices, and Inflation Let us explore this a little further. Writing the quantity equation in terms of growth rates gives ∆M/M + ∆V/V = ∆P/P + ∆Y/Y. Letting π = ∆P/P and µ = ∆M/M, and supposing that velocity is constant (so ∆V = 0), we obtain a theory of inflation π = µ – ∆Y/Y. As we will see in Chapters 8 and 9, the growth of output depends on exogenous factors such as population growth and technical progress. It follows that the inflation rate depends on the growth rate of the money supply. If the Fed keeps the money supply stable, prices will be stable. To put it another way, if the Fed wishes the inflation rate to be zero, it should increase the money supply at a rate equal to that of output growth. In that case, there would be just enough extra money each year to absorb the extra demand due to extra transactions. Case Study: Inflation and Money Growth Data for the U.S. economy since 1870 provide broad support for the link between money growth and inflation implied by the quantity theory. Decadal averages over this period reveal a positive relationship between the GDP deflator and the growth of M2. International data show the correlation even more clearly. 5-2 Seigniorage: The Revenue from Printing Money Supplement 5-3, The discussion of the circular flow of income in Chapter 3 revealed that the government deficit “Seignorage as an equals the difference between government spending and government income from taxation. The Inflation Tax” government can finance its deficit by borrowing from the public or by printing money. New money is a source of government revenue, like taxation. The revenue that the government obtains by printing money is known as seigniorage. While the government can print money and use that money to purchase goods and services, it obviously does not get these goods and services for free. Someone is paying for them. In effect, when the government prints new money, it levies an inflation tax. As more money is introduced into the economy, we now know that there will be inflation. An increase in the money supply increases the general price level. This makes existing money in the economy worth less; existing money holdings decline in real value. Inflation serves as a tax on real balances. Seigniorage is not an important source of revenue in the United States, but it has been used to finance a significant fraction of government spending in some other countries. We return to this when we discuss hyperinflation. Case Study: Paying for the American Revolution Figures 5-1, 5-2 Supplement 5-2, The Continental Congress depended significantly on seigniorage to finance the Revolution. New “Data on Money Growth and issues of continental currency grew approximately twentyfold between 1775 and 1779, leading Inflation” in turn to substantial inflation. 5-3 Inflation and Interest Rates Two Interest Rates: Real and Nominal We now turn to the distinction between nominal and real interest rates. This is an occasion when macroeconomics teaches an important, simple, yet often overlooked, insight. The interest rate quoted in the newspapers is a nominal interest rate. It gives the number of dollars that will be Supplement 5-4, “Deriving the Fisher Equation” Figures 5-3, 5-4 Supplement 5-5, “Using Interest Rates to Forecast Inflation” paid next year for a dollar deposited today. For example, a 10 percent interest rate implies that $100 deposited today earns $110 next year. But suppose that prices also rise at 10 percent per year. Then, $100 deposited in the bank has exactly the same purchasing power in terms of real goods next year as this year. The dollar price of goods is not ultimately important to people making economic decisions; rather, they care about real tradeoffs. An individual deciding whether to consume today or to save for consumption next year needs to know how much she can get in terms of goods next year if she gives up goods today. In other words, she cares about the real interest rate. The real interest rate corrects for inflation. In the preceding example, the real interest rate was zero, even though the nominal rate was 10 percent. This suggests that the equation for the real interest rate is r = i – π. Remember that the real interest rate is the interest rate that matters for investment. Firms make investment decisions by weighing the future benefits of some investment project (say, buying a new machine) against the cost. This calculation is made in real terms. If inflation is higher but nominal interest rates are also higher, then the firm will have to pay back more in dollar terms for its loan, but will equally get more in dollar terms for the goods it sells. The Fisher Effect Notice that we now have two implications of an increase in the money growth rate. First, our theory predicts that an increase in the money growth rate of, say, 1 percent should increase the inflation rate by 1 percent. In turn, this should imply a 1 percent increase in the nominal interest rate. This link between the inflation rate and the nominal interest rate is known as the Fisher effect. Case Study: Inflation and Nominal Interest Rates The data for the U.S. and other economies clearly reveal the connection between the inflation rate and the nominal interest rate suggested by the Fisher effect. They also reveal that the real interest rate changes over time. Two Real Interest Rates: Ex Ante and Ex Post The previous discussion is misleading in one respect. When people make intertemporal economic decisions, they don’t know for sure what the inflation rate will be. This means that, rather than the actual inflation rate, we should use the expected inflation rate. The relevant real interest rate for, say, investors’ decisions is defined as r = i – Eπ where Eπ is the expected inflation rate. This is known as an ex ante real interest rate; the previous definition gives the ex post real interest rate. Case Study: Nominal Interest Rates in the Nineteenth Century The Fisher effect is not evident in U.S. data the late nineteenth and early twentieth centuries. Years when the inflation rate was high were not necessarily years when nominal interest rates were high. Inflation at this time was highly variable, however, and so not easy to predict. The apparent absence of a Fisher effect is probably due to differences between actual and expected inflation, that is, between ex ante and ex post real interest rates. 5-4 The Nominal Interest Rate and the Demand for Money Our earlier discussion of money demand noted that one function of money is that it serves as a store of value. In times of inflation, it serves less well in this role. If prices are rising, a dollar bill buys less and less as time goes by. This suggests that our previous analysis of the demand for money, where money demand depends only on income, is incomplete. The Cost of Holding Money The observation that inflation reduces the value of money suggests that, if the inflation rate is high, people will be less inclined to hold their wealth in the form of money. This intuition is basically correct, but not complete. It turns out that money demand depends on the nominal interest rate and, hence, indirectly (through the Fisher effect) on the inflation rate. To see this, note that money is simply one way in which people can hold wealth. The Supplement 5-6, advantage of money is that it is convenient for transactions. But it has an associated “Transactions disadvantage: If an individual holds wealth in the form of money, she gives up the interest she Models of Money could earn if she instead put her wealth into interest-bearing assets. The interest that she could Demand” have earned but didn’t is an opportunity cost. An interest-bearing asset pays an interest rate of i; money pays zero interest. The greater the difference between the return on these two assets, the more individuals want to economize on their holdings of cash. Thus, the demand for money depends negatively on the nominal interest rate. Such a conclusion might seem contrary to the principle that people care about real, not nominal, values, but this is actually not the case. The real return on, say, a savings account is the real rate of interest. The expected real return on money is minus the expected inflation rate (– Eπ). Comparing the real return on money and interest-bearing assets again reveals that the difference between the two is the nominal interest rate. Thus, while investment (and perhaps consumption) depends on the real rate of interest, money demand depends on the nominal rate of interest. This suggests a more general specification of money demand: (M/P)d = L(i, Y). Future Money and Current Prices We have now made life, or at least our theory, more complicated. Suppose that we see a 1 percent increase in the growth rate of the money supply. This will increase the inflation rate. But through the Fisher effect, this will, in turn, increase the nominal interest rate and so decrease the demand for money. So when the growth rate of money increases, we get the rather paradoxical Figure 5-5 conclusion that the amount of real money held actually goes down. This more-complete theory of money demand also implies that the current price level Chapter 5 Appendix depends not just on the current money supply but also on the expected inflation rate—hence on the expected future price level, and hence on the future money supply. 5-5 The Social Costs of Inflation The Layman’s View and the Classical Response The general public views inflation as a major social problem because of the mistaken belief that Supplement 5-7, “Inflation and rising prices make a person poorer. This notion reflects a lack of understanding about how a Economic Growth” proportionate change in all wages and prices— overall inflation—is equivalent to a simple renumbering in the yardstick by which we measure prices, with no effects on relative prices or relative wages. But economists have identified some subtle costs of moderate inflation, although they disagree about the size of these costs. Case Study: What Economists and the Public Say About Inflation The economist Robert Shiller used a survey to examine the attitudes of economists and the general public with respect to inflation. He discovered that the public was more inflation averse than economists. This result could be due to the public’s belief that inflation erodes their real purchasing power, a belief shared by few economists. The public also seems to suffer from money illusion, preferring an increase in wages with equal increases in prices rather than a constant nominal wage combined with stable prices. The Costs of Expected Inflation In considering the social costs of inflation, a useful starting point is the distinction between Supplement 5-8, “The Welfare anticipated and unanticipated inflation. First, consider those costs of inflation that exist when all Costs of Inflation prices and wages are rising at some steady, well-understood rate. and the Optimum The first social cost of inflation is shoe-leather costs. Remember that the demand for Quantity of money depends negatively on the nominal interest rate and, hence, on the inflation rate. When Money” the interest rate is high, it is worthwhile for people to put some time and effort into economizing on their holdings of cash; they go to the bank more often and, metaphorically, wear out their Supplement 5-9, shoes more quickly. “The Welfare A second cost of steady, anticipated inflation is also referred to in metaphorical terms: Costs of Inflation menu costs. The idea here is that, in times of inflation, restaurants have to print new menus with Revisited” changed prices. More generally, the act of changing prices may absorb real resources in the economy. While this cost is undoubtedly real, it seems unlikely that it is substantial. A third cost of inflation arises because it may introduce unwanted variation in relative prices. Consider a catalog firm that changes its prices every year because of the cost of printing its catalog, and suppose that other firms change their prices more frequently. Over the course of the year, if other firms increase their prices, the relative price of the catalog firm’s output will fall. Microeconomics stresses the role of relative prices in ensuring the efficient allocation of resources. To the extent that inflation leads to infrequent price changes and, hence, to distortions in relative prices, the power of free markets is being restricted. Part of this misallocation also must be understood as the fact that the informational content of prices goes down. A fourth cost of inflation arises from the fact that the tax system is not fully indexed to the inflation rate. Other things equal, changes in the inflation rate may thus lead to distortions in the tax system. As an example, tax brackets used to be (and still are in many countries) set in nominal terms; beyond some dollar income, the marginal tax rate increases. If wages and prices are rising at a rate of 5 percent per year, then more and more people will find themselves in this tax bracket even if their real income does not increase. The Tax Reform Act of 1986 introduced Supplement 5-10, much more indexing into the tax system. Currently, capital gains and interest income are still “Indexation” taxed in nominal terms. Recall that one function of money is as a unit of account. A fifth cost of anticipated inflation is that it interferes with this function of money. Money, as a unit of account, serves a function analogous to that of other units of measurement—the mile, the gallon, etc. Inflation then is like a situation where the mile changes in length every year. Another aspect of this was mentioned by the economist Arthur Okun. He noted that, when comparison shopping, inflation means that you have to retain more information. Instead of just having to remember where you saw a good and at what price, you also have to remember when you saw it. The Costs of Unexpected Inflation Unanticipated inflation introduces extra uncertainty into the economic environment. Generally, Supplement 5-11, we think that people dislike uncertainty; in economists’ terminology, they are risk averse. Thus, “U.S. Treasury unanticipated inflation hurts people because it leads to arbitrary and unpredictable Issues Indexed Bonds” redistributions. Consider two people who enter into a contract specified in nominal terms. If inflation is higher than predicted, then the debtor “wins”—she pays less in real terms than she expected—and the creditor loses since, he gets less in real terms than he expected. From a social point of view, such redistributions are not themselves necessarily costly, but it is important to recognize that they do occur. Furthermore, if increased uncertainty discourages people from entering into economic contracts, it is clearly costly to the economy. In light of this observation, economists are somewhat puzzled by the fact that people write most of their contracts in nominal terms. If people cared about real quantities, they could write contracts in real terms—in other words, indexed to the price level. Some indexing does exist, as for example in certain wage contracts, but it is limited in scope and generally incomplete. Perhaps, the conclusion to be drawn is that this uncertainty is not perceived to be a major cost of inflation by those writing such contracts. One reason that people dislike inflation has not yet been mentioned; it is an argument with which most economists are somewhat uncomfortable. It may be that people are not as rational as we like to believe; they may fail to see the connection between rising wages and rising prices. Supplement 5-12, “A Guide to Oz” Supplement 5-13, “Are Monetary Allegories in the Eye of the Beholder? The Case of Mary Poppins” People may believe that they have earned their wage increases and then are being robbed of these increases by inflation. Finally, for reasons that are not fully understood, high levels of inflation seem to be associated in practice with highly variable inflation. Case Study: The Free Silver Movement, the Election of 1896, and the Wizard of Oz The Wizard of Oz has been argued to be an allegory of the debate over the gold standard during the 1896 presidential election. Some people believe that this reveals more about economists than it does about the Wizard of Oz. One Benefit of Inflation 5-6 Hyperinflation The costs associated with both anticipated and unanticipated inflation have often been cited as justification for why policymakers should target a zero rate of inflation. But it may be the case that some inflation actually is better than zero inflation. The reason has to do with the observation that nominal wages almost never decline. Although firms sometimes freeze nominal wages at current levels (for example, when business turns down in a recession), they almost never cut nominal wages. This reluctance to cut nominal wages means that real wages can decline only if prices are rising. As the demand for and the supply of different types of workers shift over time in response to changes in the economy, real wages need to adjust—both upward and downward—to allocate workers efficiently. A positive amount of inflation allows automatic cuts in real wages that might not occur when inflation is zero. Supplement 5-14, “How to Stop a Hyperinflation” Supplement 5-15, “The Israeli Hyperinflation” Figure 5-6 Hyperinflation simply means very rapid inflation, usually 50 percent per month or more. Inflation at this rate means that goods become more than 100 times more expensive over the course of a year. Lenin is reported to have said that the best way to destroy capitalism was through such inflation. The Costs of Hyperinflation Some of the costs of inflation discussed in the previous section become very severe in the case of a hyperinflation. Shoe-leather costs are probably small under low inflation but become very large with high inflation. People spend considerable amounts of time and other resources economizing on their cash holdings. Menu costs likewise become substantial when prices must be changed several times a day. The distortions in relative prices become more severe, and the government’s ability to collect tax revenue is diminished. The Causes of Hyperinflation If the quantity theory were correct, so that real money demand were simply proportional to GDP, then analyzing hyperinflations would be straightforward. Excessive money growth would lead to large inflation; to stop a hyperinflation, it would be sufficient to control the growth rate of the money supply. But the quantity theory is not a good guide to the demand for money in this setting. If money demand is sensitive to nominal interest rates, then this effect will be large in a hyperinflation. In practice, hyperinflations have generally arisen when governments desperately needed large amounts of seigniorage to cover fiscal deficits. Hyperinflations often are symptoms of fiscal as much as monetary problems. In such a world, fiscal reforms are usually needed to bring the government budget back into balance, remove the need for seigniorage revenue and, hence, restore the credibility of the government. Case Study: Hyperinflation in Interwar Germany During the period 1922 to 1924, Germany experienced a massive hyperinflation. Over the last 15 months of this inflation, prices rose at an average of well over 300 percent per month. The hyperinflation arose because the German government resorted to money creation to pay for fiscal deficits caused in large measure by its reparation payments. The hyperinflation ended with fiscal reforms at the end of 1923; real balances rose, as predicted by the theory. Case Study: Hyperinflation in Zimbabwe Over the past couple of decades, the government of Robert Mugabe in Zimbabwe implemented land reforms intended to redistribute wealth from the white minority to the historically disenfranchised black population. Productivity and output in farming fell as experienced white farmers left the country. The drop in output caused government tax revenue to decline. With tax revenue down, the government resorted to printing money to pay the salaries of government workers. Mugabe instituted price controls to contain the inflation resulting from the increased growth of the money supply. But the results were shortages of goods and the expansion of the underground economy, where price controls and tax collection could be evaded. Accordingly, the government had to resort even more to printing money so it could pay its bills. This led to hyperinflation, with prices rising at a rate of 231 million percent in July 2008. 5-7 Conclusion: The Classical Dichotomy The analysis of Chapter 3 revealed that, in the long run, real variables in the economy (that is, quantities such as GDP and relative prices such as the real wage) can be determined independently of nominal variables. This separation of real and nominal variables is known as the classical dichotomy. An important implication is that changes in the money supply affect nominal variables but not real variables: A10 percent increase in the money supply will increase all dollar prices by 10 percent in the long run while leaving real quantities unaffected. This is the long-run neutrality of money. Appendix: The Cagan Model: How Current and Future Money Affect the Price Level Chapter 5 explains that the demand for real money balances depends on the nominal interest rate and, hence, on the inflation rate. For a given supply of nominal money, therefore, the current price level depends on the expected future price level. Consequently, the current price level depends on both the current money supply and the expected future money supply. We can see this more formally by assuming that money market equilibrium can be written as where Mt is the money supply, Pt is the price level, πt is the inflation rate, γ measures the sensitivity of money demand to the nominal interest rate, and k is an unimportant constant. By writing the money demand function in this form, we are assuming that income and real interest rates are constant (their effects are subsumed in the constant k), so we can focus attention on the effects of changes in the inflation rate. Letting lowercase letters denote logarithms (and ignoring the unimportant constant), we can rewrite this as For simplicity, we suppose for the moment that the future price level is known with certainty. Solving this equation for the current price level gives the current price level depends on the current money supply and next period’s price level. An exactly analogous equation tells us that next period’s price level depends on next period’s money supply and the price level in period t + 2. Hence, we obtain If we now substitute in for pt+2, we find that the price level depends on the money supply in periods t, t + 1, and t + 2 and on pt+3. Continued substitution of this type eventually yields  1   m + γ   pt = 1 +γ  t  1 +γ mt+1+ 1 +γγ 2 mt+2 + 1 +γλ 3 mt+3+ . So the current price level depends upon the entire future path of the money supply. If money demand is insensitive to interest rates, γ is small, and future values of the money supply have little impact on the current money supply; the opposite is true if γ is relatively large. More realistically, the future path of the money supply is not known with certainty, and so the future price level is also uncertain. The current price level then depends on the expected price level next period. Analogous reasoning then tells us that the current price level depends upon the current and expected future values of the money stock. This analysis suggests that credibility is important for ending hyperinflations. Credibility might be achieved through increased political independence of the central bank and/or by reducing the need for seigniorage. LECTURE SUPPLEMENT 5-1 The Velocity of Money in Poetry and Song The subject matter of economics does not usually provide a great deal of inspiration for songwriters and poets. The velocity of money seems to be an exception. The Dollar Bill Song She took a dollar bill from her pocket She picked up a fountain pen. She wrote the words “I love you” By the picture of George Washington. She took the dollar bill to the grocery store and bought herself a chocolate cake. She gave the dollar bill to the grocery clerk and went back home to wait. The grocery clerk gave the dollar bill to a fat guy from Baton Rouge; He spent the bill at the hardware store on a box of flat-top screws. The hardware store gave the dollar bill to a customer named Clive, Who by the way is the son of one of the original Dave Clark Five. He spent the bill at the laundromat, who gave it to a woman named Fran. Fran’s youngest son stole the bill from her purse and went to see Star Wars again. The movie-theater man spent the dollar bill on a subway ride uptown. Two minutes later it was in the hand of a gambling man named Brown. Brown blew the bill in a poker game; he was fishing for an inside straight. The bill went home with a man named Jones who was sitting on a pair of 8’s. He took the bill to the savings bank; the teller’s name was Dan. He gave the bill to the next in line, who was Rabbi Finkelman. I am with you all the time I can hear you loud and clear Just give a tug along the line You know I will be there. Anyway the Rabbi spent the bill on a ham and cheese to go. They gave the bill to a guy named Phil who gave it to his best friend Joe. Joe had planned to spend the bill on some flowers for his bride But he was mugged by a junkie named Doug in the parking lot outside. Doug’s old lady spent the bill on a couple of bottles of beer. She eventually becomes a very famous poet, but that don’t matter here. The liquor store guy put the dollar bill in his register but then Doug the junkie said “Stick ’em up” and the dollar was his again. He gave the bill to a woman named Jill who gave it to a woman named Flo. She gave the bill to a real short guy whose name I do not know. He gave the bill to another short guy, who gave it to a guy named Jake. Jake took the bill to a bar and grill and bought himself a sirloin steak. Well later that day I happened to say “Think I’ll stop by the bar and grill.” The cashier counted out my change and handed me the dollar bill. Well I ran to a phone and dialed her number as fast as my fingers could do. I said “I just got your message.” I said “I love you too.” I am with you all the time I can hear you loud and clear Just give a tug along the line You know I will be there. My friend you don’t need no dime You don’t need no subway fare Just give a tug along the line I’m with you everywhere. Ten Pence Story Out of the melting pot, into the mint; next news I was loose change for a Leeds pimp, burning a hole in his skin-tight pocket till he tipped a busker by the precinct. Not the most ceremonious release for a fresh faced coin still cutting its teeth. But that’s my point: if you’re poorly bartered you’re scuppered before you’ve even started. My lowest ebb was a seven month spell spent head down in a stagnant wishing well, half eclipsed by an oxidized tuppence which impressed me with its green circumference. When they fished me out I made a few phone calls, fed a few meters, hung round the pool halls. I slotted in well, but all that vending blunted my edges and did my head in. Once, I came within an ace of the end on the stern of a North Sea ferry, when some half-cut, ham-fisted cockney tossed me up in the air and almost dropped me and every transaction flashed before me like a time lapse autobiography. Now, just the thought of travel by water lifts the serrations around my border. Some day I know I’ll be bagged up and sent to that knacker’s yard for the over spent to be broken, boiled, unmade and replaced, for my metals to go their separate ways. . . which is sad. All coins have dreams. Some castings from my own batch, I recall, were hatching an exchange scam on the foreign market and some inside jobs on one arm bandits. My own ambition? Well, that was simple: to be flipped in Wembley’s centre circle, to twist, to turn, to hang like a planet, to touch down on that emerald carpet. Those with faith in the system say “don’t quit, bide your time, if you’re worth it, you’ll make it.” But I was robbed, I was badly tendered. I could have scored. I could have contended. CASE STUDY EXTENSION 5-2 Data on Money Growth and Inflation The case study “Inflation and Money Growth” shows the relationship between money growth (M1) and inflation that exists in long-run data and notes that such a relationship is not evident in short-run data. Figure 1 illustrates this by showing annual data on money growth and inflation in the United States for the last half century. Note: Money growth is annual percentage change in M1. Inflation is annual percentage change in official CPI. Source: Federal Reserve Board and U.S. Department of Labor, Bureau of Labor Statistics. Figure 2 shows the relationship between money growth and nominal GDP growth for the same period. If the velocity of money were constant, money growth would equal nominal GDP growth. In the 1960s and 1970s, the growth rate of nominal GDP exceeded the M1 growth rate, but the two series still moved more or less together. Over this period, therefore, the velocity of money was not constant, but was rising at a fairly steady rate. The relationship between M1 growth and nominal GDP growth broke down completely in the 1980s, indicating that an assumption of constant velocity is not at all appropriate. See Supplement 10-6, “Velocity and the 1982 Recession.” Note: Money growth is annual percentage change in M1. GDP growth is annual percentage change. Source: Federal Reserve Board and U.S. Department of Commerce, Bureau of Economic Analysis. LECTURE SUPPLEMENT 5-3 Seigniorage as an Inflation Tax The textbook explains that seigniorage arises because a government can print money at essentially zero cost and use it to buy goods. It also describes seigniorage as an inflation tax, because holders of existing money balances see the real value of their money decline with inflation. The equivalence of the two may not be immediately obvious, however. Suppose that the money supply today is M and the price level today is P. Now, let the government print extra money, ∆M, and use it to buy goods. As a consequence of the new money in the economy, the price level rises to a new level given by P + ∆P. The value of the new goods purchased by the government is ΔM ΔM   M   P  P+ΔP  M   P   P+ΔP = The inflation tax is given by the old value of existing money balances minus the new value of those balances:  M  M     P  − P+ΔP = M  PP(+PΔ+PΔ−PP) =ΔPP  MP   P+PΔP . We therefore find an equivalence between the two measures of seigniorage if the inflation rate (∆P/P) equals the money growth rate (∆M/M). As explained in the textbook, the two will be equal in the long run in an economy without output growth. If output is growing, the money growth rate will exceed the inflation rate. In a growing economy, money demand is increasing through time, so the monetary authorities can print money to accommodate the increased demand without generating inflation. Thus, the government can buy goods without an inflation tax. One way to think about this is that we would expect to see deflation in a growing economy with a constant money supply. There would then be an inflation subsidy—existing money balances would become worth more. Even if the money growth rate exceeds the inflation rate, therefore, the government still does not get goods for free: Money holders are forgoing the inflation subsidy. 5-4 Deriving the Fisher Equation Section 4-4 of the textbook explains the Fisher equation—that is, the relationship between the real interest rate, the nominal interest rate, and the rate of inflation. Specifically, the real interest rate is shown to equal the nominal interest rate minus the inflation rate (r = i – π). Here, we derive that relationship more formally. Think about two people (Bill and Hillary) who agree to a loan specified in real terms. Hillary agrees to give goods (units of GDP) to Bill today on the understanding that, for every unit Bill receives, he will repay 1 + r units next year. In this setup, r is the real interest rate; that is, it is the interest rate in terms of commodities. Alternatively, they could specify this loan in terms of dollars. Suppose that a unit of GDP today costs $P (that is, P is the price level). Then a unit of GDP next year costs P(1 + π), where π is the inflation rate. What nominal interest rate (that is, denominated in dollars) corresponds to the real interest rate r? For every unit of GDP Bill wishes to purchase today, he must borrow $P. He repays $P(1 + i) to Hillary next year, where i is the nominal interest rate. Since the price level next year is P(1 + π), it follows that $P(1 + i) purchases P(1+i) = (1+i) (1+π) (1+π) P units of GDP next period. Thus, the real return on this dollar-denominated loan is (1 + i)/(1 + π). We thus find that 1+r = (1+i) (1+π) ⇒(1+r)(1+π)=(1+i). Multiplying out the left-hand side and subtracting 1 from each side gives r + π + r π = i. This corresponds to the Fisher equation except for the r π term. But, in general, we expect both the real interest rate and the inflation rate to be relatively small numbers. The product of the two numbers is then negligible. For example, suppose that the real interest rate is 2 percent (r = 0.02) and the inflation rate is 5 percent (π = 0.05). Then r π = 0.001, or one-tenth of 1 percent. Evidently, we are not badly misled by ignoring this term. So, since r π ≅ 0, we have 𝑟 𝑖 or 𝑟 𝜋 which is the Fisher equation. CASE STUDY EXTENSION 5-5 Using Interest Rates to Forecast Inflation Eugene Fama investigated the Fisher effect in a famous article published in 1975. He considered U.S. Treasury bills and noted that the nominal interest rate is the sum of the expected real return and the expected inflation rate. Now, suppose that the equilibrium expected real return on one-month bills is constant. Then, the nominal interest rate determined in the market for bills contains a market prediction about the expected inflation rate. If the market is efficient, then this prediction should make use of all information available to market participants about future inflation. 2 Under the two assumptions of constant expected real returns and market efficiency, movements in the nominal interest rate should reflect changes in expected inflation one for one. The nominal interest rate is then the best predictor of future inflation. Fama tested this idea using data from 1953 to 1971. The idea of his tests was that if the nominal interest rate is indeed the best predictor of the inflation rate, no other information should help to predict the inflation rate. In particular, past values of the inflation rate should not be of any additional value in predicting future inflation. His results were consistent with this prediction. He also obtained similar results with Treasury bills of up to six-month maturity. Fama’s work was a test of two theories at once: efficient markets and constant expected real returns. His conclusions thus suggested not only that Treasury bill markets were efficient, but also that the expected real interest rate was constant and that actual real interest rate changes were unpredictable. If this is the case, then the Federal Reserve does not have the ability to affect real interest rates. Looking ahead to the short-run analysis in Part IV of the textbook, this conclusion is somewhat surprising: Short-run theories suggest that the Federal Reserve can influence the economy by affecting real interest rates. Subsequent work, however, has suggested that Fama’s strong conclusions are in part the result of the sample period that he investigated. The constancy of expected real interest rates, for example, does not hold for other sample periods. Thus, a weaker conclusion than Fama’s is probably in order: Nominal interest rates do contain information about inflation expectations, but may also change because of changes in the real interest rate. 5-6 Transactions Models of Money Demand Transactions models of money demand focus on money’s role as a medium of exchange. The basic idea of the transactions demand for money was developed independently by James Tobin and William Baumol in the 1950s and is known as the Baumol–Tobin model. Baumol and Tobin explained the decision to hold money as an inventory decision. This model still represents one of the clearest expositions of the issues involved in the decision to hold money. The basic idea is that there is a trade-off between the convenience of holding cash and the interest available from putting money in a savings account. The Baumol–Tobin Model of Cash Management Consider an individual who plans to consume her income of Y dollars at a steady rate over the course of a year. Suppose that, at the start of the year, she has Y dollars in her savings account. It is costly for her to go to the bank because it takes time or effort. Suppose that the cost of a banking transaction is F and that the interest rate is i. She could decide to go to the bank at the start of the year, take out the entire Y dollars in the form of cash, and spend it as she needed it. In this case she would earn no interest income but would minimize the costs associated with her trips to the bank. At the other extreme, she could visit the bank every time she needed to make a purchase, withdrawing exactly what she needed each time. In this case, she would earn as much interest income as possible but would spend most of the year standing in line at the bank. The decision she confronts is how many trips to the bank she should make each year, given that she wants to earn interest, but given also that visiting the bank is costly. Suppose she just makes one visit to the bank. Her average holding of money is then Y/2 and so she foregoes interest equal to (Y/2) × i. The transactions cost is F. If she visits the bank twice, then her average holding of money is Y/4. She loses less interest income ((Y/4) × i), but she incurs transaction costs of 2F. We can put together a table. # Trips Average Money Interest Lost Cost 1 Y/2 (Y/2)i F 2 Y/4 (Y/4)i 2F 3 Y/6 (Y/6)i 3F 4 Y/8 (Y/8)i 4F N Y/2N (Y/2N)i NF ∞ 0 0 ∞ A rational individual will choose the number of trips so that the expected gain from one extra trip, which is the extra interest earned by making that trip, equals the cost of one extra trip, which is F. We can graph the interest forgone, the transaction cost, and the total cost. It can be shown using calculus that the optimal number of trips to the bank is given by N* = (Yi/2F)1/2. From this, we find that the optimal amount of money holdings is given by 1/2 1/2 Y (2F) Y  YF  M = 1/2 = 1/2 = 2i  . 2(Yi / 2F) 2(Yi)  This is known as the square root rule. It tells us that the demand for money increases when income increases and when transactions costs increase. It also tells us that the demand for money decreases when the interest rate increases. The square root rule thus provides microeconomic support for the demand for money function that we have been using, as well as telling us that transactions costs might also matter. For example, we might think that transactions costs have been declining over time, as information systems and automated banking have developed. This would suggest that the demand for money has been decreasing over time. Empirical Studies of Money Demand The Baumol–Tobin model predicts that a 1 percent increase in income should increase money demand by 1/2 of 1 percent and that a 1 percent (not 1-percentage-point) increase in the interest rate should decrease money demand by 1/2 of 1 percent. In the terminology of economics, the income elasticity of money demand is 1/2 and the interest elasticity of money demand is –1/2. Studies of the demand for money typically find that this theory overestimates the interest elasticity of money demand and underestimates the income elasticity of money demand. The most probable reason for the failure of the Baumol–Tobin model is integer constraints. As the model is set up, the optimal number of trips to the bank for an individual might be calculated to be 0.3, for example. In reality, such a person will make either zero or one trip to the bank. Small changes in the interest rate or income will not affect the number of trips to the bank for such a person. As a result, her holdings of money will respond proportionately to changes in income and not at all to changes in interest rates. For her, the interest elasticity of money demand is zero and the income elasticity of money demand is one. If the world consists partly of people like her and partly of people whose behavior is well described by the Baumol–Tobin model, then the income elasticity of money demand would be between one-half and one, whereas the interest elasticity of money demand would be between zero and negative one-half. This is in accordance with the empirical work. Economists are interested in the magnitude of these elasticities because they bear on the relative efficacy of monetary and fiscal policies in the short run. In particular, if money demand is insensitive to interest rates, then changes in the money supply have a large effect on interest rates, implying that monetary policy is very effective in changing output. Fiscal policy is relatively ineffective in this case, because crowding out of investment spending is large. 5-7 Inflation and Economic Growth Robert Barro (1996) and Michael Bruno and William Easterly (1996) have studied the inflation experience of countries to determine whether inflation lowers economic growth. Barro constructed a set of variables thought to be important determinants of growth, including inflation. He obtained data for 100 countries for 1960–1990. His aim was to isolate the effects of inflation on growth by holding constant other determinants of growth. That is, if two countries differed only in their rates of inflation, would their growth rates also be different? According to Barro, the answer is yes. If one country had an annual inflation rate that was 10 percentage points higher than the inflation rate in another country, the annual growth rate of per-capita real GDP would be 0.2–0.3 percent lower in the country with the higher inflation. For example, if the growth rate in the lower inflation country is 3 percent, the growth rate in the country with a 10-percentage-point-higher inflation rate would be 2.7–2.8 percent. While this difference may not seem large, after 30 years the level of real per-capita GDP in the higher inflation country would be 4–7 percent below that in the lower inflation country. The evidence linking inflation to lower economic growth is confirmed in Barro’s study only for countries with annual inflation rates of 15 percent or more. Barro argues that, while the empirical evidence cannot confirm the link between inflation and growth when inflation is below 15 percent, there is reason to believe that such a link exists. Bruno and Easterly also investigated the effects of inflation on growth. They studied 127 countries over the period 1960–1992. Using the annual observations for each country, Figure 1 provides a simple illustration of the link between inflation and growth. When annual inflation was in the 0–5 percent range, the corresponding growth rate was close to 3 percent. However, as inflation rose, the annual growth rate declined. A country that experienced an inflation rate above 1000 percent in any year could expect percapita GDP to decline by over 6 percent in that year. While their results indicated that inflation does lower growth, strong evidence of this link existed only for countries with an annual inflation rate of 40 percent or more. Bruno and Easterly also examined the behavior of output in countries that had experienced high inflation (40 percent or more) and had been successful in reducing inflation. Figure 2 summarizes the disinflation experience of seven countries: Bolivia, Brazil, Chile, Ghana, Indonesia, Israel, and Mexico. Years 1–4 correspond to the last four years of the crisis period in each country (the period in which inflation rose above 40 percent). Years 5–8 correspond to the first four years of the recovery period (the period in which inflation fell below 40 percent). Growth fell during the period of high inflation and rose sharply as the country managed to lower inflation. Eventually, growth returned to its long-run average rate. Source (Figures 1 and 2): Michael Bruno and William Easterly, “Inflation and Growth: In Search of a Stable Relationship,” Federal Reserve Bank of St. Louis Review (May–June 1996). ADVANCED TOPIC 5-8 The Welfare Costs of Inflation and the Optimum Quantity of Money Here, we analyze “shoe-leather” costs of inflation a bit more formally. The demand for money can be represented as depending on the “price” of money—the nominal interest rate. This demand curve also gives us a means of measuring the benefit of holding money. Microeconomics suggests that we can measure this benefit as consumer surplus—the difference between the benefit consumers get from a good and the amount they pay for it. Geometrically, consumer surplus is the area under the demand curve and above the price. Total social surplus also adds in producer surplus—the difference between the price and the marginal cost curve (effectively the supply curve). In the case of money, production is possible at essentially zero marginal cost. So total surplus is effectively represented as the area under the demand curve. This is illustrated in Figure 1. Total social surplus is maximized (that is, the deadweight loss eliminated) by driving the nominal rate of interest down to zero. There is then no cost to holding money rather than interest-bearing assets. From the Fisher equation, i = r + π so it follows that setting the nominal interest rate to zero would be equivalent to maintaining deflation at a rate equal to the real interest rate. Thus, if the real interest rate is 3 percent, then this analysis suggests that the monetary authorities should try to ensure 3 percent deflation. In this case the monetary authorities would effectively be paying a real interest rate of r on currency. This argument for the optimum quantity of money was made strongly by Milton Friedman. Are there any difficulties with this analysis? First, as discussed in Chapter 14 of the textbook, there might be substantial short-run costs associated with deflation. Any attempt to take this approach as a serious guide to policy would have to take account of these costs. Another objection is a little more metaphysical. Economists still don’t have a completely satisfactory theory of money. We can tell many stories about how money facilitates exchange and saves the resources that would be involved in trading in a barter economy, but we are a long way from a fully articulated theory of money. Thus, “[i]t can be argued that the theory underlying the optimum-quantity argument is deficient … because it abstracts from what is important about inflation and money. It involves little more than a transliteration of a welfare theorem that is valid in an idealized nonmonetary world of Walrasian general equilibrium to a world with enough frictions to support the institution of monetary exchange. It treats inflation or deflation as nothing more than a tax or subsidy on the holding of money, that can be administered costlessly by a Walrasian auctioneer, rather than a costly process that distorts the transmission of information and the allocation of resources.” A third problem with this simple argument is based on public finance considerations. Governments need to levy taxes to finance their expenditures. From a microeconomic point of view, taxes introduce microeconomic distortions and so may get in the way of optimal resource allocation. Basic principles of taxation then suggest that it is good to use a combination of taxes to try to minimize such distortions. In this case, it would be desirable to use the inflation tax in combination with other taxes.3 We can arrive at a very rough estimate of the costs of inflation as follows.4 Suppose that the interest elasticity of money demand equals 0.2, which is reasonable on the basis of analyses of money demand. Suppose also that interest rates are about 0.05 (5 percent) and the money supply is about $1.4 trillion. Now, let us reduce inflation by 1 percentage point, so that nominal interest rates fall to 4 percent. Since nominal interest rates have fallen by 20 percent, we would expect the demand for money to rise by about 4 percent to about $1.46 trillion.5 Now, suppose that we approximate the money demand function by a linear demand curve (see Figure 2). In this case, the increase in consumer surplus is given by A + B. Since the rectangle A has area (0.06 × 0.04) and the triangle B has area (0.5 × 0.06 × 0.01), this equals $ 2.7 billion, or about two-hundredths of a percent of GDP.6 (London: Macmillan, 1987). 3 See also Supplement 5-9, “The Welfare Costs of Inflation Revisited.” 4 The following analysis is based upon, but simplifies, the analysis in Bennett McCallum, Monetary Economics (New York: Macmillan, 1989), section 7-7. 5 An interest elasticity of 0.2 implies that a 1 percent decrease in interest rates leads to a 0.2 percent increase in money demand. 6 A slightly more sophisticated approach would start with the money demand equation M = ki–0.2. Assuming i = 0.05 and M = 1.4 (trillion), we can calculate the implied k as 0.76. This then implies that with i = 0.04, M would equal 1.46. The welfare gain is given by the integral ∫ ⎡⎢0.76⎤5 11.4.46 ⎣ M ⎥⎦ dM which can be calculated to equal about $2.5 billion. See Supplement 14-9, “Costs of Disinflation.” ADDITIONAL CASE STUDY 5-9 The Welfare Costs of Inflation Revisited Rao Aiyagari has pointed out that analyses of the welfare cost of inflation should take account of the fact that currency is held by operators in the underground economy. According to a Federal Reserve study cited by Aiyagari, adult U.S. residents hold only about 12–14 percent of U.S. currency. Other studies suggest that businesses hold about 3 percent of currency.2 Over 80 percent of currency is held by residents of other countries or those in the underground economy. Any estimate of the “shoe-leather” costs of inflation needs to be revised down accordingly, at least if policymakers are primarily concerned with the welfare of law-abiding U.S. citizens. The inflation tax may be the only way of taxing those engaged in illegal activities. On the basis of studies estimating the size of the underground economy to be about 10 percent of the above-ground economy and estimating that currency in the underground economy is about 6 percent of total currency, Aiyagari estimates that 5 percent inflation implies an effective income tax rate on the underground economy of less than two-tenths of 1 percent. Moreover, criminals may have little alternative but to hold wealth in the form of cash. Higher inflation may therefore be desirable as a means of taxing the underground economy. The figures cited by Aiyagari indicate, however, that a very high percentage of U.S. currency is not held by U.S. citizens, law-abiding or not. The U.S. dollar is used as both a medium of exchange and a store of value in many other countries. It is the official currency in Panama and Ecuador, and is used in many transactions in much of Central and South America. It is a major store of value in Russia—about 4 percent of U.S. dollars are estimated to be in Russia. This demand reflects the fact that the dollar is viewed as a safe asset. For example, foreigners think it unlikely that the value of the dollar will be suddenly eroded by hyperinflation. If U.S. inflation were higher, the dollar would be less attractive as a store of value in other countries. To the extent that the U.S. monetary authorities might wish to extract seigniorage from residents in other countries, they would need to take account of the fact that increased inflation would also reduce the demand for money in those countries. ADDITIONAL CASE STUDY 5-10 Indexation One response to unanticipated inflation is indexation. In times of relatively high inflation, labor (and some other) contracts often contain indexation provisions. In the mid- to late 1970s, cost of living adjustment (COLA) clauses were a common feature of U.S. union contracts: More than half of all workers covered by union contracts were under contracts featuring COLA provisions. Such clauses generally specify a given dollar increase for a given increase in the CPI. Indexation provisions are often limited by “triggers,” so that they come into effect only after some minimum rate of inflation is reached. They also are sometimes subject to “caps,” or maximum increases permitted under the contract. Indexation, as noted, is more common in times of high inflation. (As an example, COLAs in Israeli contracts took place twice a year up to 1980, but, as inflation rose rapidly, such adjustments took place quarterly, then monthly.) It is unclear, though, whether it is simply high inflation that makes such provisions more attractive to workers and firms, or whether it is instead the associated higher variability of inflation. There are also some unresolved puzzles about indexation. Since it seems like a natural response to uncertainty about inflation, one might wonder why firms and workers do not include such provisions more often. One possible reason is that the firm and its workers might ideally like to index to a different price index—workers care about their wage relative to some general price index such as the CPI, but firms care about the wage relative to their product price. A second reason is that indexation makes real wages inflexible when nominal wages are fixed in contracts. Yet another reason may simply be that firms and workers build in adjustments for anticipated inflation and understand that future contract agreements will include “catch-up” provisions if inflation turns out to be higher than expected. Formal indexation provisions may simply not be worth the extra bother. Another puzzling feature of indexed contracts is that caps on the extent of adjustment turn out to be binding a great deal of the time. This means that indexation clauses are providing much less protection against unanticipated inflation than such clauses seem to imply. Even more to the point, why do firms and workers then write contracts featuring these complicated clauses when they could just write the cap increase directly into the contract? LECTURE SUPPLEMENT 5-11 U.S. Treasury Issues Indexed Bonds The U.S. Treasury began issuing inflation-indexed debt securities in January 1997. These securities, known as “Treasury Inflation-Protection Securities,” or “TIPS,” have their principal and coupon payments adjusted every six months to compensate investors for inflation. The securities have been issued in maturities of 5, 10, and 30 years. In issuing inflation-indexed debt, the United States joins several other countries that issue such debt, including the United Kingdom, Israel, Australia, Canada, New Zealand, and Sweden. To adjust for inflation, the Treasury uses the change in the consumer price index over the six months ending roughly two months prior to the date of adjustment. This lag is the minimum possible, given the schedule for constructing and publishing the CPI. The adjustment is not quite symmetric: in the case of deflation (falling prices), the investor is guaranteed a value for the principal at maturity that is no lower than the original amount (or “par value”) of the security. Inflation-indexed securities provide several benefits. First, they allow investors to protect themselves against the risk of unexpected inflation. Second, they may reduce the government’s financing costs because these securities will not have to pay the risk premium that nominal securities pay to compensate for uncertainty about future inflation. Third, they will allow the government to stabilize the real cost of its borrowing. Finally, these securities provide a rough gauge of trends in expected inflation that may be useful to monetary policymakers. Let us consider in more detail each of these benefits.3 Protection Against Inflation Risk These securities protect against inflation risk because investors are compensated for inflation regardless of whether it is expected or unexpected. Thus, a fixed real return is guaranteed for investors holding these securities to maturity. With a conventional security, the nominal return (through the Fisher equation) includes compensation for expected inflation but not for unexpected inflation. Reduction of Government Financing Costs The government’s financing costs are likely to be lower, on average, when it issues indexed debt rather than conventional debt. This occurs because the interest rate on conventional debt exceeds the rate on indexed debt by an amount equal to expected inflation plus a risk premium. This premium on conventional securities is necessary to compensate investors for the risk that inflation turns out to be different from what was expected. Because investors are compensated for actual inflation when they hold indexed securities, the government does not have to pay this premium to investors and so faces lower average financing costs. Stabilization of Government Finances Indexed securities fix the real cost of financing government debt because the nominal payment is adjusted to offset the effects of inflation. This helps to stabilize the real cost of servicing the government debt. To see this, consider a government that issued a 30-year bond at a time when inflation was high and expected to continue at a high rate, so that the nominal interest rate on the bond also was very high. Now, suppose that inflation actually declines sharply after a few years. The effective real interest rate on these bonds will rise (since the nominal rate is fixed and inflation has declined). To the extent that the bonds are not callable on demand, the government would face a situation of rising real financing costs as inflation declines. Such a situation occurred with 30-year Treasury bonds issued at double-digit nominal interest rates during the late 1970s and early 1980s. Measure of Expected Inflation As mentioned above, the spread between the interest rate on a conventional security and the interest rate on an indexed security of the same maturity is equal to the sum of expected inflation and an inflation-risk premium. To the extent that the risk premium is relatively constant, then movements over time in the spread will capture movements in expected inflation. One caveat to interpreting such movements in this way, however, is whether indexed securities might have to pay a premium because the market is small and relatively illiquid. If this premium were to decline as the market became more liquid over time, then movements in the spread need not reflect shifts in expected inflation (see Case Study Extension, Supplement 19-11, “Inflation Indexed Bonds and Expected Inflation”). The amount of inflation-indexed debt remains relatively small at about 8.5 percent of U.S. debt held by the public as of January 2015 ($1.06 trillion compared to the overall public debt of $12.46 trillion). In some countries that have issued indexed debt for longer periods of time, however, the amounts are significantly higher—for example, in the United Kingdom and in Israel, where a hyperinflation during the early 1980s may have made indexed debt more attractive (see Additional Case Study, Supplement 5-15, “The Israeli Hyperinflation”). CASE STUDY EXTENSION 5-12 A Guide to Oz The following is a listing (more complete than in the textbook but far from exhaustive) of some of the symbols identified by Hugh Rockoff in his Journal of Political Economy article. (Other writers on the topic have suggested different interpretations for some of these symbols.) Dorothy = America Toto = Prohibitionist party (teetotalers) Oz = “Fantasy counterpart to America”; Oz also equals ounce (of gold) Cyclone (tornado) = Free Silver Movement Silver shoes (of Wicked Witch of the East) = Silver component of bimetallism Munchkins = Citizens of the East (!) Wicked Witch of the East = Grover Cleveland (also eastern business interests) Good Witch of the North = ? (“Free silver had some support in New England”) Emerald City = Washington, D.C. Yellow Brick Road = Gold standard Scarecrow = Western farmer Tin Woodman = Workingman Cowardly Lion = William Jennings Bryan Emerald Palace = White House Wizard = Marcus Alonzo Hanna (chairman of Republican National Committee) Wicked Witch of the West = William McKinley CASE STUDY EXTENSION 5-13 Are Monetary Allegories in the Eye of the Beholder? The Case of Mary Poppins Hugh Rockoff’s argument that The Wizard of Oz is a monetary allegory invites speculation that other popular children’s movies also contain economic subtexts. We suggest here that the popular 1964 Walt Disney movie Mary Poppins is in fact a thinly disguised commentary on market instability and the debate over monetary and fiscal policy. As most readers undoubtedly recall, Mary Poppins tells the story of two young children in London (Jane and Michael) and their magical nanny, Mary Poppins. The prima facie case for viewing Mary Poppins as economic allegory rests on two pieces of evidence. First, the family at the center of the movie has the last name Banks. Second, the single most dramatic incident in the movie consists of a run on the bank where Jane and Michael’s father, George Banks, works, precipitated by Michael’s refusal to place two pence in a savings account. A clearer satire on the instability of financial markets is hard to imagine and leads naturally to the supposition that there are other allusions to be found. Any attempt to chart the economic significance of Mary Poppins must naturally start by considering what the character herself represents. It can hardly be coincidence that her initials are the standard notations for the two most important variables in monetary economics. The thesis here is that Mary Poppins signifies Monetary Policy. The movie is unmistakably Keynesian in its conclusions. First, when George Banks advertises the post of nanny for Jane and Michael, a large number of applicants seek the position. The line of nannies outside the Banks’s front door evidently signifies unemployment. Yet when Mary Poppins arrives at the Banks’s household, strong winds blow the nannies out of sight. Money is not neutral. Further evidence is provided by a scene where Mary Poppins’s Uncle Albert, Bert, Jane, and Michael float at the ceiling—a clear symbol of inflation. They float to the ceiling because they are laughing; they can come down again only if they are miserable. The message is clear: Inflation can be eliminated only at a cost in human welfare. The movie’s Keynesian thesis is perhaps most evident when Jane and Michael accompany their father to the bank. Michael wishes to spend his two pence on feeding the birds. This is reminiscent of the public works projects advocated by Keynes and, in the movie, such a fiscal (spending) policy is clearly endorsed. Instead, Michael is given an extended lecture (in song) of the virtues of thrift and of placing his money in financial institutions. Another important theme of Keynesian economics, of course, is the idea that thrift may be a social ill even if a private virtue. Michael’s view that saving will not aid the creation of wealth is dramatically vindicated by the bank run described earlier: His cries of “I want my money” are sufficient to reduce the confidence of other depositors and precipitate a major run on the bank. Keynes’s views on financial market volatility are, of course, well known and are vividly illustrated in this scene. The interpretation of the movie proposed here leads to a much less sanguine view of the final scene than the ostensibly happy ending might suggest. Michael’s two pence are ultimately spent on materials for a kite. Distrust of financial markets is nowhere clearer than in a closing scene in which the entire bank staff is engaged in (check?) kiting. This exegesis only scratches the surface and leaves much for future scholars in economics and other disciplines. For example, we have not considered the class conflict (as embodied by the chimney sweeps) and the gender conflict (Winifred Banks’s involvement in the women’s suffrage movement) that also play an important role in the movie. Deconstructing “supercalifragilisticexpialidocious” is likewise beyond the scope of this work. We end by quoting Rockoff in his section on “Some Thoughts for the Skeptics”: “There is always a danger that a critic may see symbols where the author has merely placed the concrete reference points of his [or her] story.… An author’s [screenwriter’s, director’s experience may be transformed in ways he [or she] is only dimly aware of, before it issues forth in a work of art. The critic may be uncovering elements beyond the explicit intentions of the author…. An allegorical interpretation of a story can be viewed as something like a model in economics…. [E]conomists should not have any difficulty accepting, at least provisionally, an elegant but controversial model.” LECTURE SUPPLEMENT 5-14 How to Stop a Hyperinflation The sensitivity of real money balances to the nominal interest rate complicates the problem of stopping a hyperinflation. If the quantity theory were completely true and the nominal interest rate did not affect money demand, then stopping a hyperinflation would be easy: The central bank would merely need to stop printing money. As soon as the quantity of money stabilized, the price level would stabilize. But if money demand depends on the nominal interest rate, ending a hyperinflation is more complicated. The fall in inflation will lead to a fall in the cost of holding money and, therefore, an increase in real money balances. If the central bank merely stops printing money (that is, keeps M constant), the increase in real balances (M/P) necessitates a fall in prices. Hence, the apparently simple task of ending a hyperinflation will, if the central bank is not careful, lead to the falling price level. In this case, the central bank will not have achieved its goal of price stability. How to Stop Inflation When Real Balances Depend on the Nominal Interest Rate By examining the paths we expect the key monetary variables to follow, we can derive the path that the money supply must follow to end inflation. (1) At the top is the desired path of the price level P. (2) Next is the rate of inflation π, which is high until the period of price stability, when it drops to zero. (3) The nominal interest rate i adjusts one-for-one with the rate in inflation. (4) The fall of the nominal interest rate leads to a jump up in real balances M/P. (5) The path of the money supply M then depends on the path of the price level P and the path of real balances M/P. Note: Each variable is drawn on its own scale. What monetary policy should the central bank pursue to achieve stable prices? That is, what path should the money supply follow to end the inflation without causing deflation? To answer this question, we work backward. We begin with the goal of price stabilization and find the path of the money supply that is consistent with that objective. Figure 1 shows the five steps to determining the path of the money supply. 1. The desired path of the price level is at the top of the figure. The price level is rising during the hyperinflation. Then, the new monetary policy goes into effect and prices stabilize. 2. Next is the rate of inflation π, which is the growth in the price level. It is high until the period of price stability, when it drops to zero. 3. The nominal interest rate i adjusts one-for-one with the rate of inflation. This is required by the Fisher effect. Thus, the nominal interest rate also is high until prices stabilize and then falls to a lower level. 4. This fall in the nominal interest rate leads to a jump up in real balances because the cost of holding money has declined. 5. Since we now know the path of the price level P and the path of real balances M/P, we can infer the required path of money M. At the moment the hyperinflation ends, the money supply must jump up to accommodate the increase in real balances. After the jump, the money supply stays constant to ensure price stability. An important issue that this analysis does not address is the central bank’s credibility. For expected inflation and the nominal interest rate to fall, people must believe that the central bank will stop printing so much money. This expectation is hard to create in the midst of a hyperinflation. Indeed, if the central bank does not achieve credibility, expected inflation and the nominal interest rate will not fall, real balances will not rise, and the jump in the money supply will lead to more inflation. In practice, the central bank usually achieves credibility by removing the underlying cause of the hyperinflation: the need for seigniorage. Most hyperinflations begin when the government prints money to finance its spending. As long as the government needs the revenue from seigniorage, the public is not likely to believe the central bank’s announcements about price stability. For this reason, the ends of hyperinflations usually coincide with fiscal reforms—reductions in government spending and increases in taxes—that reduce the need for seigniorage. Hence, even if inflation is always and everywhere a monetary phenomenon, the end of hyperinflation is often a fiscal phenomenon as well. ADDITIONAL CASE STUDY 5-15 The Israeli Hyperinflation Ending hyperinflations, as the textbook notes, requires that the central bank have credibility at the time that reforms are undertaken. Recent attempts to stop hyperinflations usually entail an entire package of reforms to aid the transition from high to low inflation and to help maintain policymakers’ credibility. An example is the Israeli hyperinflation in the early 1980s. Israel’s problems began in the mid-1970s. Whereas the budget deficit was under 3 percent of GNP between 1961 and 1973, it rose to over 17 percent of GNP during the remainder of the 1970s. Monetary policy was accommodative, rising to an annual growth rate of 37 percent by the end of the decade. Inflation averaged 7.6 percent during the 1960s and early 1970s but was at 71 percent per year for the 1977–1979 period. The problems worsened into the 1980s, with M1 growth for mid-1983 to mid-1985 averaging 310 percent per year and inflation averaging almost 400 percent for the same period. Between August and November 1984, inflation ran at an annual rate of 950 percent. Although such inflation rates are not as extraordinary as those observed in some hyperinflations, they were clearly at a level that impeded the efficient functioning of the economy. A reform package was instituted in November 1984, but it did not address the fiscal policies adequately and failed. A more comprehensive program instituted in June 1985 was more successful, however. It entailed cuts in the deficit, suspension of wage contracts, and a price freeze. The budget deficit was cut to about 3 percent of GNP and inflation fell to 2 percent by the fourth quarter of 1985. Real wages fell in the second half of 1985 but recovered by mid-1986, and unemployment was not strongly affected. A particularly important element of the Israeli reform package involved an appropriate rule for monetary policy. In Israel, the package entailed using monetary policy to fix the exchange rate relative to the dollar. As is explained in Chapter 13 of the textbook, commitment to a fixed exchange rate implies that the money supply becomes an endogenous variable: The central bank supplies as much or as little money as is demanded at the fixed exchange rate. Fixing the exchange rate, therefore, implies that the monetary authorities give up the opportunity of printing money for seigniorage revenue. Further, it is very easy for the public to monitor such a rule. The adoption of a fixed exchange rate was also important in the ending of the Bolivian hyperinflation.” LECTURE SUPPLEMENT 5-16 Additional Readings Monetary economics is a subdiscipline of economics that is very closely related to macroeconomics but that pays particular attention to financial institutions. A number of good textbooks exist, such as Gary Smith, Money, Banking, and Financial Intermediation (Lexington, Mass.: D.C. Heath, 1991) and Laurence Ball, Money, Banking, and Financial Markets (New York: Worth Publishers, 2008). A rather more advanced but excellent textbook and reference is Bennett McCallum, Monetary Economics (New York: Macmillan, 1989). Excerpts from The New Palgrave Dictionary of Economics on particular topics are published by W.W. Norton; there is a useful collection of readings on money: J. Eatwell, M. Milgate, and P. Newman, eds., The New Palgrave: Money (New York: W. W. Norton, 1989). The Board of Governors of the Federal Reserve publishes a volume on the workings of the Fed: The Federal Reserve: Purposes and Functions, 9th ed. (Washington, D.C.: Federal Reserve Board of Governors, 2005). This is available at www.federalreserve.gov on-line. CHAPTER 6 The Open Economy Notes to the Instructor Chapter Summary This chapter introduces a simple model of a small open economy in the long run. The main aims of the chapter are as follows: 1. To acquaint students with the terminology necessary for understanding the open economy. 2. To provide a simple model of international flows of capital and goods, emphasizing that these ultimately depend upon the determinants of saving and investment. 3. To present a simple model of the real exchange rate, emphasizing its role in ensuring that the current account and the capital account sum to zero. 4. To explain the determination of the nominal exchange rate. Comments Students are interested in the open economy; this chapter provides them with the tools to think about open economy issues. I emphasize the fact that we can figure out the trade balance before we introduce the exchange rate into the analysis. This is often surprising to students. The chapter also contains a discussion of protectionism, thus allowing the presentation of another surprising result: Protectionist policies do not improve the trade balance. These two findings drive home the importance of financial flows in an analysis of the open economy. The chapter has the potential to be confusing to students in a couple of ways. The first, of course, is the difficulty of getting the signs right in analyzing the capital and current accounts. It is worth going through this particularly slowly and carefully. I also stress that the exchange rate is a market-determined price, determined by the intersection of the net supply of dollars (S – I) and the net demand for dollars (NX). The other potential difficulty for students is the shift from the closed economy to the small open economy. I emphasize the advantages of using different models to answer different questions and explain that the large open economy represents some kind of average of a small open economy and a large closed economy. I note that we can combine the two models to obtain a more complicated model that does apply more directly to the United States. Time permitting, it is worth going through the large open economy case to drive home the point that we are not misled by combining the conclusions from the closed economy and small open economy cases. Because of the subtleties and difficulties of the analysis, the material in this chapter requires two or three lectures. Use of the Web Site As a hard but worthwhile exercise, students could be asked to combine the models of Chapters 3 and 6 to understand the large open economy. A good starting point is to suppose that the United States is half the world economy and to think about Chapter 3 as a model of the world economy. Now suppose, for example, that government spending is increased by $200 billion. This is like an increase of $100 billion in the world economy. The Chapter 3 model can be used to figure out the implied rise in the world interest rate. The Chapter 6 model can then be used to infer the implications for U.S. investment, net exports, and the exchange rate. The Web-based software can also be used to consider the implications of purchasing power parity by setting the exchange rate sensitivity of net exports to a large negative number. Use of the Dismal Scientist Web Site Go to the Dismal Scientist Web site and download annual data since 1973 for the U.S. dollar exchange rate against the Japanese yen, the British pound, and the Canadian dollar. Now, download data on the Consumer Price Index (CPI) for the United States, Japan, United Kingdom, and Canada. Compute real exchange rates by multiplying the foreign currency price of a dollar by the CPI for the United States and then dividing by the CPI of the respective country. Discuss how the real exchange rates have changed over time. Some economists argue that real exchange rates should track productivity differences between countries over long periods of time. Download data on labor productivity for the four countries. Compute relative productivity for the United States by dividing its productivity index by the respective indexes for the other countries. Assess whether movements in the real exchange rate capture trends in relative productivity levels. Chapter Supplements This chapter includes the following supplements: 6-1 The Terminology of Trade 6-2 Saving and Investment in Open Economies 6-3 The Open Economy in the Very Long Run 6-4 Tourism and the Exchange Rate 6-5 The Exchange Rate and the Inflation Rate (Case Study) 6-6 Covered Interest Parity 6-7 Purchasing-Power Parity and Real Exchange Rates 6-8 More on the Big Mac and PPP (Case Study) Lecture Notes Introduction We now have a nearly complete picture of the macroeconomy in the long run. Output is determined by capital, labor, and technology. The price level depends on the money supply, and the inflation rate is determined by the growth rate of the money supply. We have explained the long-run determination of several of the variables that interest macroeconomists, and we have developed some understanding of how government policies affect the economy. But two important parts of the picture are still missing: We have thus far ignored considerations of international trade and reasons that unemployment occurs. In this chapter, we address international aspects of the long-run model and leave questions about unemployment until Chapter 7. The first and most important point is that virtually all economies are integrated into a larger world economy. Economies do not exist in isolation but have extensive trading relations Figure 6-1 with the rest of the world. Economies that trade with other economies are called open economies. In the United States in 2010, for example, exports were $1,840 billion and imports were $2,357 billion (13 percent and 16 percent of GDP, respectively). In other countries, international trade is even more important. During the late 1990s and early 2000s, the United States developed a substantial trade deficit; that is, imports exceeded exports, so net exports became very negative. In the mid-1990s, the United States ran a modest trade deficit. But between 1996 and 2006, GDP rose by 71 percent, while total domestic spending (C + I + G) rose by 79 percent. The United States as a whole consumed more than it produced. Like an individual who consumes in excess of her income, the country as a whole was living beyond its means. To finance this deficit, the United States had to borrow from the rest of the world. This suggests an important point: There is a close relationship between flows of goods and services between nations and financial flows between nations. Understanding this connection is our first task in explaining macroeconomics in an open economy. We then add this complication into our basic model of income determination. Finally, we move to a theory of the exchange rate. 6-1 The International Flows of Capital and Goods The Role of Net Exports In an open economy, we have to revise our basic national income identity to read Y = C + I + G + NX, where NX = net exports = exports minus imports. Net exports is the difference between output (Y) and domestic spending (C + I + G). Remember that this equation is the equilibrium condition for the goods market: The supply of goods equals the demand for goods. But if consumers in the United States demand Toyotas or if U.S. firms purchase precision tools manufactured in Germany, that doesn’t translate into a demand for U.S. goods; hence, we must subtract imports from spending. Conversely, exports represent the demand for our goods by citizens of other countries and so are a source of demand not included in domestic spending. International Capital Flows and the Trade Balance Our analysis of the closed economy emphasized that saving equals investment. The same is true in the open economy if we expand our definition of saving to include saving by other countries. Table 6-1 Starting from Y = C + I + G + NX and recalling that S = Y – C – G, we get S – I = NX. The right-hand side of this identity, net exports, is sometimes referred to as the trade balance. When exports are equal to imports we say that the trade balance equals zero (or that “trade is balanced”). When exports exceed imports we have a trade surplus and when exports are less than imports we have a trade deficit. Supplement 6-1, The left-hand side of this identity is the excess of domestic saving over domestic “The Terminology investment and represents the net amount we are lending to foreigners. This net amount of of Trade” lending is called net capital outflow because it reflects the outflow of funds from our country. When the domestic saving falls short of domestic investment, we must borrow from abroad to finance the difference and we refer to this as negative net capital outflow. Thus, the national income accounts identity illustrates how the international flow of funds to finance capital accumulation and international trade in goods and services are two ways of looking at the same question. When saving is greater than needed to finance investment, we lend the excess to foreigners. Foreigners use this loan to purchase more goods and services from us than we purchase from them—we run a trade surplus. Alternatively, when we invest more than our saving allows, we borrow from foreigners to make up the difference. This borrowing allows us to purchase more goods and services from foreigners than they purchase from us—we run a trade deficit. International capital flows can take many different forms. These may be loans like those we’ve described or may involve the purchase of assets, such as factories, equities, or real estate. Regardless of whether foreigners are purchasing debt (making loans) or purchasing assets, they are gaining claims on the future returns to our capital. International Flows of Goods and Capital: An Example Net exports must always equal net capital outflow because this relationship is an identity. The intuition behind this relationship involves tracing out the movement of money in a series of transactions. The example in the textbook involves Bill Gates selling a copy of the Windows operating system to Japan and considers the set of transactions that Mr. Gates could make with the proceeds of the sale that must always satisfy the identity. FYI: The Irrelevance of Bilateral Trade Balances The difference between saving and investment determines a country’s overall trade balance but does not determine a country’s bilateral trade balance with any given country. A large deficit with some countries may be matched by large surpluses with other countries; so, overall, exports and imports are equal. 6-2 Saving and Investment in a Small Open Economy Capital Mobility and the World Interest Rate When analyzing an open economy, we obviously can no longer restrict our attention to domestic variables. In particular, world interest rates become central to the analysis, raising the issue of whether or not such variables are independent of what goes on in the domestic economy. If we are analyzing the economy of, say, Iceland, it is probably reasonable to suppose that changes in the Icelandic economy have a negligible effect on world interest rates. Such an economy is referred to as a small open economy. It is less evident that this is an appropriate assumption for a large open economy like the United States. Nonetheless, we first consider the behavior of a small open economy and later show that the appropriate analysis for a large open economy lies somewhere between the small open economy model and the closed economy model that we have already considered. The key new assumption is that the interest rate in a small open economy is not determined by domestic savings and investment but rather is set at the prevailing world level (r = r*). Such an assumption presupposes that consumers and firms can freely borrow and lend in international financial markets. Why Assume a Small Open Economy? We use the assumption of a small open economy to simplify the analysis. Our intent is to build a basic model that captures the most important features of the economy while ignoring additional complications. For some countries, this assumption is more likely to be realistic than others. In the case of the United States, the empirical application of the framework would require modifying the model to allow for effects on world interest rates resulting from shifts in saving and investment. The appendix to this chapter provides such a model of the large open economy. The Model Apart from the assumption that r = r*, the model closely resembles our earlier analysis. As before, we will let Y = Y, C = C(Y – T), and I = I(r) and take government policy (G and T) as exogenous. The classical model presented in Chapter 3 showed that saving is then also exogenous ( S ). The level of investment is determined simply by the investment function given the world interest rate [I(r*)]. Combining these with the accounting identity that sets net exports equal to net capital outflow, we obtain NX = S – I(r*). Net exports are determined as a residual. If domestic saving exceeds domestic investment at the Figure 6-2 world interest rate, net exports will be positive. But what ensures that other countries will borrow from or lend to us in such a way that net Supplement 6-2, capital outflow equals the trade balance? The answer is a variable that we have thus far “Saving and ignored—the exchange rate. For the present, we continue to leave exchange rates out of the Investment in Figure 6-3 Figure 6-4 Figure 6-5 How Policies Influence the Trade Balance This model permits easy analysis of the effects of fiscal policy in an open economy. If the government increases spending or cuts taxes, then, just as in the closed economy model, national saving falls. If the economy starts in a position of trade balance (NX = 0), then the consequence is a trade deficit and negative net capital outflow since there is now insufficient domestic saving to finance domestic investment. We might also be interested in the consequences of changes in the fiscal policies of other countries. To understand these, we must go back to our closed economy analysis. Since we are considering an economy that is negligible in world markets, we can view the rest of the world as a closed economy, which means that if there is an increase in spending by the rest of the world, the world interest rate will rise. From the perspective of the small open economy, this increase in the world interest rate is exogenous. It leads to a fall in domestic investment. Starting from trade balance, the consequence of the fiscal expansion abroad is positive net capital outflow and a trade surplus. Finally, consider the consequences of government policies designed to encourage investment in a small open economy. These would imply that the investment function would shift out since firms would wish to carry out more investment at the world interest rate. Since domestic saving is unchanged, this extra investment would have to be financed by borrowing from abroad, implying a trade deficit. Evaluating Economic Policy Trade deficits arise when there is insufficient domestic saving to finance domestic investment. Low levels of saving in an economy are analogous to low levels of saving by an individual; they imply that consumption in the present is high at the expense of consumption in the future. In a closed economy, low levels of saving result ultimately in a low capital stock, as shown by the Solow growth model discussed in Chapters 8 and 9. In an open economy, low levels of saving Open Economies” picture; we come back to them later. Supplement 6-3, lead to a growing foreign debt. “The Open Economy in the Just as it is sometimes desirable for an individual to be a borrower rather than a saver, so it Very Long Run” is not necessarily the case that trade deficits are bad for a country. They may, for example, reflect borrowing to finance high levels of investment to promote development. Case Study: The U.S. Trade Deficit Figure 6-6 The small open economy model can help us understand the evolution of the U.S. trade deficit during the 1980s, 1990s, and early 2000s. By using the identity that net exports equal the difference between saving and investment, we can analyze the combination of movements in saving and investment that gave rise to the trade deficit during this period. In the 1980s, the deficit increased sharply at the same time that national saving declined due to the rise in the federal budget deficit. This emergence of simultaneous deficits in both trade flows and the government budget has been referred to as the twin deficits. After falling sharply at the start of the 1990s, due to a drop in investment as the economy went into recession, the trade deficit once again increased sharply, hitting a record both in dollar terms and as a share of GDP by the year 2000. Unlike the 1980s, the government’s budget deficit was shrinking during the 1990s and eventually moved into surplus, leading to a rise in saving. Investment, however, surged faster than saving, probably reflecting the information technology boom. Because investment grew much more than saving, the trade deficit expanded sharply. In the early 2000s, a shift in fiscal policy from budget surplus to budget deficit lowered national saving and led to a further widening in the trade deficit. The shift in fiscal policy occurred as the result of tax cuts (in 2001 and 2003) and increased government spending (the wars in Afghanistan and Iraq as well as new measures for homeland security). National saving fell to an historic low as a share of GDP and the trade deficit reached record highs. A few years later, a decline in house prices was accompanied by a reduction in the trade deficit. The weak housing market led directly to a pullback in residential investment and also lowered household wealth, thereby inducing a rise in personal saving. With investment falling and saving rising, the trade deficit fell from 5.8 percent of GDP at its peak in 2006 to 3.6 percent in 2010. Case Study: Why Doesn’t Capital Flow to Poor Countries? The U.S. trade deficit is financed by the flow of capital into the United States from foreign countries. But many of the countries with trade surpluses are much poorer than the United States, and so one would expect that they would be borrowers rather than lenders. Furthermore, if capital is scarce in poor countries, then the marginal product of capital should be high, compared to rich countries where capital is abundant. One would expect that a high marginal product of capital in poor countries would attract capital inflows. To explain the seeming paradox of why capital doesn’t flow to poor countries, we need to recognize that the marginal product of capital depends not only on the amount of physical capital available to an economy, but also on technology and human capital. If poor countries have less access to advanced technologies and low levels of education, then the marginal product of capital may actually be quite low. In addition, poor countries often have weak or nonexistent institutions for enforcing property rights. This can make investment more risky—both for domestic sources and foreign sources of capital. These hypotheses could explain why capital flows out of poor countries toward rich countries. 6-3 Exchange Rates Our next task is to explain the exchange rate. Here, it is important to be clear on definitions. Nominal and Real Exchange Rates The nominal exchange rate (e) denotes the amount of foreign currency that can be bought with Figure 6-7 $1. Equivalently, it is the price of a dollar in terms of foreign currency. The value of e is Supplement 6-4, “Tourism and the determined in a market—the market for foreign exchange. Note that since the nominal exchange Exchange Rate” rate is the price of one currency in terms of another, it can be quoted in two ways. If e is the price of a dollar in terms of, say, the Swiss franc, then 1/e is the price of a Swiss franc in terms of dollars. Newspapers generally report exchange rates in two ways: as dollars per foreign currency unit and as foreign currency per dollar. When the foreign currency value of the dollar rises (i.e., the dollar buys more of a foreign currency), we describe that as an appreciation or strengthening of the dollar. And when the foreign currency value of the dollar declines, we describe that as a depreciation or weakening of the dollar. Exchange rates can be floating, fixed, or somewhere between the two. Floating means that the exchange rate is determined by demand and supply in competitive markets. Fixed means that the monetary authorities fix the value of e by standing ready to buy and sell dollars at that rate. Managed floating is somewhere between the two. The U.S. dollar is currently floating, though the U.S. monetary authorities do sometimes intervene in foreign exchange markets, buying and selling the dollar in attempts to influence its value. We return to fixed exchange rates in Chapter 13; for the present, we restrict our attention to floating exchange rates. In reality, of course, there are many exchange rates (dollar–yen, dollar–euro, euro–yen, etc.). We focus on one for simplicity, and so think about the United States as trading with an amorphous rest of the world. The exchange rate can be thought of as trade weighted—some average of the exchange rates with all our trading partners, with more weight placed on those countries with which we trade a lot. If we multiply the nominal exchange rate by the ratio of domestic to foreign price levels, we obtain a measure known as the real exchange rate. The real exchange rate is the relative price of domestic goods in terms of foreign goods. In other words, it equals the amount of foreign goods we can purchase by giving up a unit of domestic goods. We calculate the real exchange rate as ε = eP/P*. When the real exchange rate is high, foreign goods are relatively cheap and domestic goods are relatively expensive. The opposite is true when the real exchange rate is low. The Real Exchange Rate and the Trade Balance Net exports depend upon the real exchange rate. If the dollar is more valuable, imports are relatively cheaper and exports are more expensive. Increases in the exchange rate thus tend to decrease net exports. We thus write NX = NX(ε). Figure 6-8 Figure 6-9 Figure 6-10 Figure 6-11 The real exchange rate adjusts to ensure that net exports equal the difference between domestic saving and domestic investment (net capital outflow). We know that NX(ε) = S S – I(r*). Since S is fixed at S and r is fixed at r*, then ε must adjust to ensure balance. We noted earlier that the exchange rate is ultimately determined in the market for foreign exchange. When we export to foreigners, they need to acquire U.S. dollars to purchase our goods. When we wish to import goods, we sell dollars to get other currencies. If we export more than we import, then foreigners will need dollars in addition to the ones they get from our purchase of imports. So positive net exports correspond to a net demand for dollars by foreigners. The net capital outflow, meanwhile, represents the available dollars for lending abroad. In equilibrium, the supply of dollars from the net capital outflow equals the demand for dollars by foreigners purchasing our net exports. The exchange rate adjusts to bring about equilibrium of supply and demand. How Policies Influence the Real Exchange Rate Earlier, we looked at the effects of various policies on net exports and net capital outflow. We can now consider how those policies affect the exchange rate. First, consider an expansionary fiscal policy, which reduces national saving. This reduces net capital outflow, thus reducing the supply of dollars and causing an appreciation of the exchange rate. Fiscal expansions abroad, as discussed earlier, increase the world interest rate and so reduce investment at home. This increases the supply of dollars, leading to a depreciation of the exchange rate. Conversely, an exogenous increase in domestic investment demand (perhaps due to domestic policies to stimulate investment) reduces net capital outflow, reduces the supply of The Determinants of the Real Exchange Rate dollars, and appreciates the exchange rate. The Effects of Trade Policies There is often discussion in the news of trade policies—that is, policies directly targeted at the trade balance. These principally take the form of tariffs (taxes on imports) or quotas (restrictions on the quantity of imports). Perhaps surprisingly, protectionist policies of this sort are not successful because they simply cause appreciation of the exchange rate without affecting the trade balance. One way to see this is to remember that the trade balance is equal to the difference between saving and investment; since protectionist policies affect neither saving nor investment, they cannot affect the level of net exports. Protectionist policies increase the demand for net exports. This increases the demand for Figure 6-12 dollars, causing an appreciation of the exchange rate. In the new equilibrium, both exports and imports are lower, but net exports are unchanged. The Determinants of the Nominal Exchange Rate After considering the determinants of the real exchange rate, our next step is to think about the nominal exchange rate. We know that ε = eP/P*. By now we are familiar enough with growth rates to move straight from this equation to ∆ε/ε = ∆e/e + π – π*, or ∆e/e = ∆ε/ε + (π* – π). The key conclusion is that the nominal exchange rate will change not only because of changes in the real exchange rate, but also because of changes in the real purchasing power of currencies. If we have high inflation relative to other countries, that tends to make the nominal exchange rate depreciate. Case Study: Inflation and Nominal Exchange Rates Figure 6-13 The relationship between inflation and nominal exchange rates is evident in the data. Countries Supplement 6-5 with very high rates of inflation experience massive depreciation of their exchange rate. The “The Exchange relationship is also visible for countries experiencing more moderate inflation rates. Rate and the Inflation Rate” The Special Case of Purchasing-Power Parity From the equation ∆e/e = ∆ε/ε + (π* – π), we can see that if the real exchange rate never changed, then movements in the nominal exchange rate would be explained solely by differences in inflation rates. One particular and simple theory of the exchange rate, called purchasing-power parity (PPP), suggests that the real exchange rate should be constant through time. The argument is that the nominal exchange rate should always adjust so that goods cost the same in different countries because, otherwise, arbitrage could take place. For example, suppose that pizzas are cheaper in the United States than in Canada. Then, an arbitrageur could buy pizza in the United States, ship it across the border, sell it in Canada, and make a profit. PPP argues that the nominal exchange rate would adjust to eliminate such profits and that there is a natural long-run level of the real exchange rate (equal to one if we measure all goods in the same real units) such that identical goods cost the Figure 6-24 same in different countries. To put it another way, PPP suggests that net exports should be very Supplement 6-6, “”Covered Interest sensitive to real exchange rate movements, implying that NX(ε) is horizontal. Purity” PPP turns out not to be a very good theory of the exchange rate. The pizza example, by its Supplement 6-7, absurdity, offers some clues to the reason. While some goods, such as wheat, are relatively “Purchasing-Power homogeneous and easy to transport, other goods and services cannot be easily traded. As a Parity and Real result, real exchange rates move significantly in the short run. For example, the real exchange Exchange Rates” rate rose almost one for one with the nominal rate during the 1980s, when the nominal rate appreciated sharply. This appreciation was not a response to changes in purchasing power. PPP is still useful, however, because it offers some guide to the long-run value of the exchange rate. Over the long run, the real exchange rate differs from its PPP value to only a limited extent. When commentators speak of the dollar as “overvalued” (or “undervalued”), they have in mind a long-run value of the exchange rate determined by PPP. Also, PPP provides a good guide to movements in the nominal exchange rate when countries experience substantial inflation, so that real exchange rate movements are insignificant relative to inflation differentials between countries. Table 6Supplement 6-2 -8 Case Study: The Big Mac Around the World “More on the Big The Economist news magazine collected data on the price of a McDonald’s hamburger around Mac and PPP” the world. Even though opportunities for arbitrage in Big Macs are limited, PPP turns out to provide a good, if approximate, guide to nominal exchange rates. 6-4 Conclusion: The United States as a Large Open Economy Finally, what about the fact that the U.S. economy is not actually a small open economy but instead a large economy whose actions affect world financial markets? As might be expected, the appropriate analysis for the U.S. economy turns out to be a mixture of the two special cases of the small open economy and the large closed economy. This is an example of how an understanding of reality is sometimes easier in terms of two “unrealistic” models rather than one more realistic model. The appendix details the working of the more complicated large open economy model. Appendix: The Large Open Economy This appendix develops a large open economy version of the classical open economy model presented in this chapter. Unlike a small economy that takes the interest rate as given in the world market, shifts in a large economy’s saving and investment will influence the world interest rate. The extended model considers this effect. Net Capital Outflow To think about the large open economy, we work with two basic equations: CF(r) = S – I(r) and Figure 6-15 Figure 6-16 Figure 6-17 Figure 6-18 Figure 6-19 where CF(r) is net capital outflow. The closed economy analysis sets NX = 0, implying that CF = 0, and leaves us with an equation to determine r, S = I(r). This is the model of Chapter 3. The small open economy sets r = r* and says that net capital outflow can take on any value at r*; funds flow freely into and out of the country, with no effect on the world interest rate. This means that we can substitute to get an equation determining ε : NX(ε ) = I(r*) – S. The large open economy is between the two. To solve the large open economy model, we first use the first equation to find r. We can interpret this equation as giving us equilibrium in the world market for loanable funds. To do so, we rewrite it as S = I(r) + CF(r). Our analysis is then similar to the case for the closed economy. Now, though, there is an additional step since, once we have determined r, we have to look at the second equation (i.e., at the market for foreign exchange) to solve for the exchange rate and the trade balance. Policies in the Large Open Economy We analyze the large open economy by considering the loanable-funds market, the CF schedule, and the foreign exchange market. NX(ε) = CF(r), Figure 6-20 Figure 6-21 Figure 6-22 Figure 6-23 A fiscal expansion reduces saving in the world loanable-funds market, increasing the world interest rate. At a higher interest rate, we wish to carry out less investment, both at home and abroad. The decrease in net capital outflow reduces the supply of dollars and so causes the exchange rate to appreciate. The trade balance falls. An increase in domestic investment demand also pushes up the world interest rate, so net capital outflow falls. Again, there is an appreciation of the exchange rate and a decline in net exports. A protectionist trade policy affects neither investment nor saving, so the loanable-funds market is unaffected. As in the small open economy, the only consequence is an appreciation of the exchange rate with no effect on the trade balance. Shifts in net capital outflow might occur because of policy changes in other countries, or because of changes in the investment climate in other countries. A decrease in net capital outflow will reduce interest rates and cause an appreciation of the exchange rate and a fall in net exports. Overall, the qualitative results of the large open economy model are similar to those of the small open economy model except for the effect on interest rates. The large open economy can influence world market conditions and thus the world interest rate, whereas the small open economy cannot. LECTURE SUPPLEMENT 6-1 The Terminology of Trade In discussing the international flows of goods, services, and capital, we have made some important simplifications. We have used the terms “net exports” and “trade balance” interchangeably, although in practice these terms sometimes differ slightly in meaning. More importantly, we have also shown how the simple income identity requires that net exports equal net capital outflow, although in practice this is not precisely correct. These simplifications helped us highlight the important features of the analysis without bringing in too much detail. This supplement provides some additional background on concepts relating to the international flow of goods, services, and capital. The term “trade balance” is sometimes used to describe “merchandise trade” or the part of trade involving only goods, not services. When the term is used in this way, it is not equivalent to net exports. Net exports include trade both in goods and in services. For national income accounting this distinction is important because net foreign demand for domestic production includes purchases of services as well as goods. Another simplification we have made is to equate net exports with net capital outflow. Because residents of a country may earn interest on assets held abroad and/or earn wages from working abroad, national income may differ from GDP. In addition, because residents of a country may give gifts to and/or receive gifts from foreigners, their income again may differ from GDP. These net factor payments and net foreign transfer payments are important in measuring domestic saving and thus in measuring the difference between domestic saving and domestic investment. Since the difference between domestic saving and domestic investment equals net capital outflow, these payment flows have implications for the relationship between net exports and net capital outflow. To see how this changes the basic identity, first rewrite the GDP identity Y = C + I + G + NX as Y + Net Factor Payments + Net Foreign Transfers = C + I + G + NX + Net Factor Payments + Net Foreign Transfers, where income includes net factor payments from abroad and net transfer payments from abroad. Rearranging this equation gives Y + Net Factor Payments + Net Foreign Transfers – C – G – I = NX + Net Factor Payments + Net Foreign Transfers. As in the text, domestic saving is given by income minus spending, so we can rewrite this equation as S – I = NX + Net Factor Payments + Net Foreign Transfers or Net Capital Outflow = Current Account. The modified identity thus relates a broader measure of trade flows—known as the current account— to net capital outflow. One final term sometimes used in place of net capital outflow is the capital account. When we experience positive net capital outflow, the capital account is said to be in deficit— we are purchasing more foreign assets than foreigners are purchasing our assets (or equivalently, we are making more loans to foreigners than they are making to us). Thus, the condition that the current account equal net capital outflow is sometimes described by the condition that the current account and capital account must sum to zero. ADDITIONAL CASE STUDY 6-2 Saving and Investment in Open Economies Our theory of the small open economy suggests that there should be no simple link between the level of saving and the level of investment. With perfect capital mobility, the level of investment depends primarily on the world interest rate, whereas the level of saving depends on the level of domestic output. Martin Feldstein and Charles Horioka made a somewhat surprising discovery in the face of this theory: There is a close correspondence between saving and investment in many countries. Figure 1 illustrates the Feldstein– Horioka finding: It shows a scatterplot of domestic saving and domestic investment, each expressed as a percentage of gross domestic product, for 21 countries. Source: M. Feldstein and C. Horioka, “Domestic Saving and International Capital Flows,” Economic Journal 90 (June 1980): 319. Feldstein and Horioka’s work has been updated and modified by many authors over the years. Although the correlation between saving and investment rates varies with particulars such as which countries are included and which time periods are considered, the basic finding remains the same: Countries that have high saving rates are also countries with high investment rates, and countries with low saving rates are also countries with low investment rates. Should we conclude that capital is actually immobile? Not necessarily. Other evidence shows that interest rates on comparable assets are quite similar even though the assets are located in different industrial countries. And casual observation finds that financial markets seem to have become more global over time. Furthermore, since saving and investment are both endogenous variables, common influences on saving and investment could yield a positive correlation even if capital is completely mobile across national boundaries. Concern about common influences is the main reason why Feldstein and Horioka averaged saving and investment rates across long periods of time and studied the cross-country relationship. This technique allowed them to separate the effect from short-run business cycle fluctuations that may induce a correlation between saving and investment within a country from year to year. But even over long periods of time, saving and investment continue to be endogenously determined, and common influences may still be important. One way that a correlation might occur is in response to sustained shifts in a country’s productivity or demographics that lead to an increase in its long-run investment rate and its long-run saving rate. 4 For instance, a technological advance in one country may increase investment at the world interest rate and, because it also increases income, may lead to an increase in saving. Another possible reason for the correlation is that government policies may be oriented to running zero average trade deficits because certain constituencies favor balanced trade. Thus, saving and investment may be forced into equality over time through this policy of an average trade deficit equal to zero. Finally, as Supplement 6-3 emphasizes, long-run budget constraints apply equally to countries, just as they do to governments or households. Accordingly, a country cannot borrow (or lend) forever— eventually the foreign debt will have to be repaid. This means that over long periods of time, a country will tend to have balanced trade and saving will tend to equal investment. .LECTURE SUPPLEMENT 6-3 The Open Economy in the Very Long Run The small open economy model of Chapter 6 explains that the trade balance is determined in the long run by the levels of domestic saving and investment. For example, if domestic saving is less than domestic investment at the world interest rate, then net exports are negative, and there is a trade deficit. The counterpart to this trade deficit is an increase in indebtedness to foreigners. The model of Chapter 6 evidently cannot describe the economy in the very long run because a country cannot run large trade deficits forever. At some point, the foreign debt must be repaid. Something is, therefore, missing from the Chapter 6 model if we wish to talk about the very long run. One approach to this problem is simply to recognize that aggregate saving and investment are indeed aggregates of the behavior of individuals, firms, and the government. At any given point in time, an individual may be in deficit—that is, she may be spending more than she is earning. But, as emphasized in Chapter 16 of the textbook, individuals make their consumption and spending decisions by looking over their entire lifetime. An individual who borrows now expects to repay later—it is not always possible to spend in excess of income. The same kind of intertemporal budget constraints apply to firms and to the government. As a result, a trade deficit today will be matched by a trade surplus at some point in the future. We can capture these kinds of ideas by a very simple amendment to our model. Suppose that consumption depends not just on current income but also on wealth: C = C(Y – T, W). (As explained later in the textbook, we can derive such a consumption function from a realistic theory of consumption behavior.) Now, suppose that, in the long run, a country is saving less than it is investing and hence running a trade deficit. Foreigners are purchasing domestic assets, so domestic wealth is falling. As a consequence, consumption will fall and saving will increase over time. The increase in saving will tend to reduce the trade deficit. In the very long run, the economy will be in equilibrium where net exports equal zero. In this case, saving equals investment and so wealth is constant. ADDITIONAL CASE STUDY 6-4 Tourism and the Exchange Rate Expenditures on international tourism are likely to be sensitive to changes in exchange rates because a significant amount of tourism probably represents discretionary purchases that are sensitive to relative prices. Vacations taken abroad by Americans contribute to U.S. imports, while expenditures by foreigners on visits to the United States add to U.S. exports. Table 1 (see next page) presents the percentage change each year in real tourism exports and imports between 1973 and 2010, along with a measure of the real exchange rate. As the table shows, the sharp appreciation of the dollar during the early 1980s was accompanied by a decline in tourism exports and a rise in tourism imports—likely reflecting a decline in foreign visits to the United States and a rise in Americans venturing abroad. During the mid- to late 1980s, as the dollar reversed course, exports rose and imports fell (or generally grew more slowly). In the late 1990s, as the dollar again gained value, exports declined and imports grew more quickly. During the early 2000s, both tourism exports and tourism imports fell sharply as a result of the pullback in travel following the September 11 attacks. A rebound in both exports and imports occurred in 2004, as the initial shock of the attacks began to recede. By 2005, the expected pattern appeared to be reasserting itself, as a weakening dollar was associated with increased exports and more slowly growing imports. Table 1 Tourism Trade and the Real Exchange Rate Real Exchange Year Real Tourism Exports (% change) Real Tourism Imports (% change) Rate (Index, March 1973 = 100) 1973 14.9 -5.7 99.0 1974 8.8 -10.2 95.6 1975 8.1 -3.5 94.5 1976 13.9 6.4 94.5 1977 0.2 3.0 92.9 1978 7.4 3.3 87.3 1979 7.2 -2.4 88.4 1980 11.7 -0.1 89.8 1981 33.1 9.0 96.6 1982 -7.7 18.6 106.1 1983 -11.2 13.3 110.6 1984 Break in series Break in series 117.9 1985 0.1 10.3 122.7 1986 10.3 -6.9 107.4 1987 8.5 18.4 98.7 1988 16.6 2.9 92.1 1989 18.1 3.1 93.8 1990 12.3 6.8 91.2 1991 4.7 -9.2 89.7 1992 10.1 3.1 87.8 1993 4.6 5.0 89.1 1994 1.2 3.6 89.0 1995 6.3 1.1 86.5 1996 6.5 4.0 88.5 1997 2.9 8.7 93.2 1998 -2.7 13.2 101.2 1999 5.6 0.1 100.3 2000 3.7 12.8 104.1 2001 -14.4 -7.0 110.1 2002 -5.8 -4.8 110.3 2003 -4.6 -4.8 103.6 2004 10.4 13.0 99.0 2005 -4.4 2.0 97.3 2006 -1.0 0.2 96.2 2007 9.0 -2.1 91.7 2008 7.2 -2.7 87.8 2009 -8.0 -9.0 91.4 2010 10.8 4.1 87.2 2011 4.8 0.8 82.7 2012 3.9 11.7 84.4 2013 6.4 2.7 84.5 2014 4.2 6.9 86.3 Source: U.S. Department of Commerce, Bureau of Economic Analysis and Federal Reserve Board. Note: Real tourism exports and imports are exports and imports of travel as reported in the National Income and Product Accounts. The real exchange rate is a weighted average of the foreign exchange values of the U.S. dollar against the currencies of a large group of major U.S. trading partners. The index weights, which change over time, are derived from U.S. export shares and from U.S. and foreign import shares. For details on the construction of the weights, see the Winter 2005 Federal Reserve Bulletin. CASE STUDY EXTENSION 6-5 The Exchange Rate and the Inflation Rate The relationship between the nominal exchange rate and the inflation rate is particularly evident for countries experiencing hyperinflation. If the price level in one country is increasing rapidly, then movements in foreign prices and in the real exchange rate will be relatively insignificant. We therefore expect to see depreciation of the domestic currency at a rate approximately equal to the inflation rate. Figures 1 and 2 illustrate this for the Israeli and Mexican hyperinflations of the 1980s. Source (Figures 1 and 2): International Monetary Fund, International Financial Statistics. ADVANCED TOPIC 6-6 Covered Interest Parity Suppose that a U.S. company wishes to purchase goods from a producer in the United Kingdom. The U.S. firm agrees to take delivery of the goods three months hence and to pay an agreed-upon price in U.K. pounds at that time. The U.S. company, however, might be concerned about exactly what was going to happen to the dollar–pound exchange rate over the next three months. It can avoid this uncertainty by buying U.K. pounds at the forward rate. International financial institutions not only buy and sell currencies at the current (spot) rate, they are also willing to write an agreement to exchange currencies at a future date and at a prespecified rate. Thus, if the U.S. company needs 10,000 pounds in three months’ time, it knows now that it will have to pay 10,000/f dollars at that time, where f is the appropriate forward rate. There is an important relationship between the spot rate (e) and the forward rate (f) that is guaranteed by arbitrage. An investor could take a dollar, invest it at the U.S. interest rate (say, in three-month Treasury bills), and earn (1 + i) dollars at the end of three months. Alternatively, she could convert her dollars into pounds (obtaining e pounds), invest those pounds at the U.K. interest rate [obtaining e(1 + i*) pounds at the end of three months], and then exchange those pounds for dollars at a previously agreedupon forward rate. These transactions would earn the investor (e/f)(1 + i*). Both transactions must yield the same return; otherwise, she could make arbitrarily large, riskless profits by borrowing in one country and investing in the other. Thus, we have 1 + i = (e/f)(1 + i*). If we define the forward premium to be (f – e)/e, then we have a good approximation : Premium ≅ i* – i. The premium will be positive (i.e., the forward rate will be above the spot rate) if the U.K. interest rate exceeds the U.S. interest rate. The premium will be negative if the opposite is true. The forward rate should be a good predictor of the future spot rate. To see this, note that if investors expect the spot rate in the future to be lower than the forward rate, they would buy pounds forward. For each pound, they agree to pay 1/f dollars. They expect each pound to be worth 1/ee dollars, where ee is the expected future spot rate, so they expect to make a profit. Similarly, if investors expect the spot rate in the future to be higher than the forward rate, they will sell the foreign currency forward. Thus, we can look to the forward rate for information about the market’s expectations of exchange rate movements. Remember also that we expect to see appreciation of the nominal exchange rate in the long run if domestic inflation is lower than overseas inflation. Thus, one reason why we might see a positive forward premium is that domestic inflation is relatively low, so investors expect the dollar to be more valuable in the future. ADDITIONAL CASE STUDY 6-7 Purchasing-Power Parity and Real Exchange Rates If the principle of purchasing-power parity provided an accurate theory of real exchange rate determination, then we would expect real exchange rates to be relatively stable. Major short-run fluctuations in the real exchange rate would not occur because of arbitrage in goods markets. Such stability is, quite simply, not observed in the data. As an example, Figure 1 shows the real exchange rates for Canada, the United Kingdom, and Japan. Economists, therefore, look to behavior in financial markets rather than goods markets for explanations of short-run fluctuations in exchange rates. Source: Federal Reserve Board and U.S. Department of Labor, Bureau of Labor Statistics. Note: Real exchange rate is computed as nominal exchange rate multiplied by ratio of U.S. consumer price index to foreign consumer price index. CASE STUDY EXTENSION 6-8 More on the Big Mac and PPP The following graphs use the series of Big Mac prices and exchange rates collected by The Economist to illustrate the failure of PPP.11 For each of the four countries (Canada, Germany, Hong Kong, and South Korea), the graph shows the actual exchange rate (foreign currency per U.S. dollar) and the exchange rate implied by PPP. The latter is simply the ratio of the price of a Big Mac in each country to the price of a Big Mac in the United States, both prices measured in local currency terms. If PPP held, the actual exchange rate and the PPP implied exchange rate would be the same. If the actual exchange rate is above the PPP implied exchange rate, then the dollar is said to be undervalued. If the actual exchange rate is below the PPP implied exchange rate, then the dollar is said to be overvalued. The dollar was undervalued relative to the deutsche mark throughout the sample period. Thus, it cost more to buy a Big Mac in Hamburg, Germany, than in Hamburg, Connecticut. In contrast, the dollar was overvalued relative to the Hong Kong dollar throughout the sample period. Thus, it cost less to buy a Big Mac in Hong Kong than in the United States. (Hong Kong fixes the value of its currency relative to the U.S. dollar, which explains the lack of variability in the exchange rate line in the graph.) For most of the sample period, it would have been cheaper to buy a Big Mac in Windsor, Ontario, than in Detroit, Michigan, with the exception of 1992, when the reverse was true. From 1989 through 1997, a U.S. traveler to Seoul, Korea, would be advised to squelch the urge to have a Big Mac attack until he were back on American soil. While the Asian financial crisis resulted in a sharp appreciation of the dollar relative to the won, the relative price of a Big Mac in Seoul did not rise nearly as much. As a result, it is now cheaper to consume a Big Mac in Seoul than in San Francisco. 1 A number of studies use the Big Mac data to analyze PPP. See, for example, R. Cumby, “Forecasting Exchange Rates and Relative Prices with the Hamburger Standard: Is What You Want What You Get With McParity?” National Bureau of Economic Research Working Paper no. 5675 (July 1996); M. Pakko and P. Pollard, “For Here or To Go? Purchasing Power Parity and the Big Mac,” Federal Reserve Bank of St. Louis Review (January/February 1996): 3–21; L. Long, “Burgernomics: The Economics of the Big Mac Standard,” Journal of International Money and Finance (December 1997): 865–78; R. Click, “Contrarian MacParity,” Economics Letters (November 1996): 209–12. Instructor Manual for Macroeconomics Gregory N. Mankiw 9781464182891, 9781319106058