CHAPTER 26
How does the Federal Reserve affect spending and output in the short run?©Jonathan Larsen/Getty Images
LEARNING OBJECTIVES
After reading this chapter, you should be able to:
1. LO1Show how the demand for money and the supply of money interact to determine the equilibrium nominal interest rate.
2. LO2Explain how the Fed uses its ability to affect the money supply to influence nominal and real interest rates.
3. LO3Discuss how the Fed uses its ability to affect bank reserves and the reserve-deposit ratio to affect the money supply.
4. LO4Describe the unconventional monetary policy methods that the Fed can use when interest rates hit the zero lower bound.
5. LO5Explain how changes in real interest rates affect aggregate expenditure and how the Fed uses changes in the real interest rate to fight a recession or inflation.
6. LO6Discuss the extent to which monetary policymaking is an art or science.
Financial market participants and commentators go to remarkable lengths to try to predict the actions of the Federal Reserve. At the end of 2015, investors had been listening to every word uttered by Chair Janet Yellen to learn whether the Fed intended to raise interest rates for the first time in almost a decade. The close attention being paid to Fed chairs is not a new occurrence. For a while, the CNBC financial news program Squawk Box reported regularly on what the commentators called the Greenspan Briefcase Indicator. The idea was to spot Alan Greenspan, one of Yellen’s predecessors as Fed chair, on his way to meet with the Federal Open Market Committee, the group that determines U.S. monetary policy. If Greenspan’s briefcase was packed full, presumably with macroeconomic data and analyses, the guess was that the Fed planned to change interest rates. A slim briefcase meant no change in rates was likely.
“It was right 17 out of the first 20 times,” the program’s anchor Mark Haines noted, “but it has a built-in self-destruct mechanism, because Greenspan packs his [own] briefcase. He can make it wrong or right. He has never publicly acknowledged the indicator, but we have reason to believe that he knows about it. We have to consider the fact that he wants us to stop doing it because the last two times the briefcase has been wrong, and that’s disturbing.”1
The Briefcase Indicator is but one example of the close public scrutiny that the chair of the Federal Reserve and other monetary policymakers face. Every speech, every congressional testimony, every interview from a member of the Board of Governors is closely analyzed for clues about the future course of monetary policy. In self-defense, central bankers and other policymakers have become masters of the carefully worded but often ambiguous public statement calculated to leave the “Fed-watchers” guessing. The reason for the intense public interest in the Federal Reserve’s decisions about monetary policy—and especially the level of interest rates—is that those decisions have important implications both for financial markets and for the economy in general.
In this chapter, we examine the workings of monetary policy, one of the two major types of stabilization policy. (The other type, fiscal policy, was discussed in the previous chapter.) As we have seen, stabilization policies are government policies that are meant to influence aggregate expenditure, with the goal of eliminating output gaps. Both types of stabilization policy, monetary and fiscal, are important and have been useful at various times. However, monetary policy, which can be changed quickly by a decision of the Federal Reserve’s Federal Open Market Committee (FOMC), is more flexible and responsive than fiscal policy, which can be changed only by legislative action by Congress. Under normal circumstances, therefore, monetary policy is used more actively than fiscal policy to help stabilize the economy.
We will begin this chapter by discussing how the Fed uses its ability to control the money supply to influence the level of interest rates. We then turn to the economic effects of changes in interest rates. Building on our analysis of the basic Keynesian model in Chapter 25, Spending and Output in the Short Run, we will see that, in the short run, monetary policy works by affecting planned spending and thus short-run equilibrium output. We will defer discussion of the other major effect of monetary policy actions, changes in the rate of inflation. The effects of monetary policy on inflation are addressed in the next chapter.
THE FEDERAL RESERVE AND INTEREST RATES: THE BASIC MODEL
When we introduced the Federal Reserve System in Chapter 22, Money, Prices, and the Federal Reserve, we focused on the Fed’s tools for controlling the money supply—that is, the quantity of currency and checking accounts held by the public. Determining the nation’s money supply is the primary task of monetary policymakers. But if you follow the economic news regularly, you may find the idea that the Fed’s job is to control the money supply a bit foreign because the news media nearly always focus on the Fed’s decisions about interest rates. Indeed, the announcement the Fed makes after each meeting of the Federal Open Market Committee nearly always includes its plan for a particular short-term interest rate, called the federal funds rate (more on the federal funds rate later).
Actually, there is no contradiction between the two ways of looking at monetary policy—as control of the money supply or as the setting of interest rates. As we will see in this section, controlling the money supply and controlling the nominal interest rate are two sides of the same coin: any value of the money supply chosen by the Fed implies a specific setting for the nominal interest rate, and vice versa. The reason for this close connection is that the nominal interest rate is effectively the “price” of holding money (or, more accurately, its opportunity cost). So, by controlling the quantity of money supplied to the economy, the Fed also controls the “price” of holding money (the nominal interest rate).
In this section, we focus on the basic model of the market for money. To keep the discussion easy to follow, we will keep making two simplifying assumptions that we have made throughout the book. First, when discussing the money supply, we will keep assuming, as we did in Chapter 22, Money, Prices, and the Federal Reserve, that the Fed can fully control the amount of money by controlling the amount of bank reserves. Second, when discussing interest rates, we will keep assuming that they all move more or less together. To better understand how the Fed determines interest rates, we will look first at the demand side of that market. We will see that given the demand for money by the public, the Fed can control interest rates by changing the amount of money it supplies. Having discussed the basics—that is, how the market for money works when our two simplifying assumptions hold—in the next section, we will discuss the market for money in more detail and highlight the changes that occurred in this market since 2008. In the last section of this chapter, we will show how the Fed uses control of interest rates to influence spending and the state of the economy.
THE DEMAND FOR MONEY
Recall from Chapter 22, Money, Prices, and the Federal Reserve, that money refers to the set of assets, such as cash and checking accounts, that are usable in transactions. Money is also a store of value, like stocks, bonds, or real estate—in other words, a type of financial asset. As a financial asset, money is a way of holding wealth.
Anyone who has some wealth must determine the form in which he or she wishes to hold that wealth. For example, if Louis has wealth of $10,000, he could—if he wished—hold all $10,000 in cash. Or he could hold $5,000 of his wealth in the form of cash and $5,000 in government bonds. Or he could hold $1,000 in cash, $2,000 in a checking account, $2,000 in government bonds, and $5,000 in rare stamps. Indeed, there are thousands of different real and financial assets to choose from, all of which can be held in different amounts and combinations, so Louis’s choices are virtually infinite. The decision about the forms in which to hold one’s wealth is called the portfolio allocation decision.
What determines the particular mix of assets that Louis or another wealth holder will choose? All else being equal, people generally prefer to hold assets that they expect to pay a high return and do not carry too much risk. They may also try to reduce the overall risk they face through diversification—that is, by owning a variety of different assets.2 Many people own some real assets, such as a car or a home, because they provide services (transportation or shelter) and often a financial return (an increase in value, as when the price of a home rises in a strong real estate market).
Here we do not need to analyze the entire portfolio allocation decision, but only one part of it—namely, the decision about how much of one’s wealth to hold in the form of money (cash and checking accounts). The amount of wealth an individual chooses to hold in the form of money is that individual’s demand for money. So if Louis decided to hold his entire $10,000 in the form of cash, his demand for money would be $10,000. But if he were to hold $1,000 in cash, $2,000 in a checking account, $2,000 in government bonds, and $5,000 in rare stamps, his demand for money would be only $3,000—that is, $1,000 in cash plus the $2,000 in his checking account.
EXAMPLE 26.1Consuelo’s Demand for Money
What is Consuelo’s demand for money, and how could she increase or reduce her money holdings?
Consuelo’s balance sheet is shown in Table 26.1. What is Consuelo’s demand for money? If she wanted to increase her money holdings by $100, how could she do so? What if she wanted to reduce her money holdings by $100?
Looking at Table 26.1, we see that Consuelo’s balance sheet shows five different asset types: cash, a checking account, shares of stock, a car, and furniture. Of these assets, the first two (the cash and the checking account) are forms of money. Consuelo’s money holdings consist of $80 in cash and $1,200 in her checking account. Thus Consuelo’s demand for money—the amount of wealth she chooses to hold in the form of money—is $1,280.
There are many different ways in which Consuelo could increase her money holdings, or demand for money, by $100. She could sell $100 worth of stock and deposit the proceeds in the bank. That action would leave the total value of her assets and her wealth unchanged (because the decrease in her stockholdings would be offset by the increase in her checking account) but would increase her money holdings by $100. Another possibility would be to take a $100 cash advance on her credit card. That action would increase both her money holdings and her assets by $100 but would also increase her liabilities—specifically, her credit card balance—by $100. Once again, her total wealth would not change, though her money holdings would increase.
To reduce her money holdings, Consuelo need only use some of her cash or checking account balance to acquire a nonmoney asset or pay down a liability.
For example, if she were to buy an additional $100 of stock by writing a check against her bank account, her money holdings would decline by $100. Similarly, writing a check to reduce her credit card balance by $100 would reduce her money holdings by $100. You can confirm that though her money holdings decline, in neither case does Consuelo’s total wealth change.
Cost-Benefit
How much money should an individual (or household) choose to hold? Application of the Cost-Benefit Principle tells us that an individual should increase his or her money holdings only so long as the benefit of doing so exceeds the cost. As we saw in Chapter 22, Money, Prices, and the Federal Reserve, the principal benefit of holding money is its usefulness in carrying out transactions. Consuelo’s shares of stock, her car, and her furniture are all valuable assets, but she cannot use them to buy groceries or pay her rent. She can make routine payments using cash or her checking account, however. Because of its usefulness in daily transactions, Consuelo will almost certainly want to hold some of her wealth in the form of money. Furthermore, if Consuelo is a high-income individual, she will probably choose to hold more money than someone with a lower income would, because she is likely to spend more and carry out more transactions than the low-income person.
Consuelo’s benefit from holding money is also affected by the technological and financial sophistication of the society she lives in. For example, in the United States, developments such as credit cards, debit cards, ATM machines, online payments, and electronic money transfers have generally reduced the amount of money people need to carry out routine transactions, decreasing the public’s demand for money at given levels of income. In the United States in 1960, for example, money holdings in the form of cash and checking account balances (the monetary aggregate M1) were about 26 percent of GDP. By 2007, that ratio had fallen to less than 10 percent of GDP.
Although money is an extremely useful asset, there is also a cost to holding money—more precisely, an opportunity cost—that arises from the fact that most forms of money pay little or no interest. Cash pays zero interest, and most checking accounts pay either no interest or very low rates. For the sake of simplicity, we will just assume that the nominal interest rate on money is zero. In contrast, most alternative assets, such as bonds or stocks, pay a positive nominal return. A bond, for example, pays a fixed amount of interest each period to the holder, while stocks pay dividends and may also increase in value (capital gains).
Cost-Benefit
The cost of holding money arises because, in order to hold an extra dollar of wealth in the form of money, a person must reduce by one dollar the amount of wealth held in the form of higher-yielding assets, such as bonds or stocks. The opportunity cost of holding money is measured by the interest rate that could have been earned if the person had chosen to hold interest-bearing assets instead of money. All else being equal, the higher the nominal interest rate, the higher the opportunity cost of holding money, and hence the less money people will choose to hold. Indeed, as the nominal interest rate fell dramatically during 2007–2008 and has remained at historically low levels since, M1 has been steadily increasing from less than 10 percent of GDP in 2007 to more than 17 percent of GDP in 2016.
We have been talking about the demand for money by individuals, but businesses also hold money to carry out transactions with customers and to pay workers and suppliers. The same general factors that determine individuals’ money demand also affect the demand for money by businesses. That is, in choosing how much money to hold, a business, like an individual, will compare the benefits of holding money for use in transactions with the opportunity cost of holding a non-interest-bearing asset. Although we will not differentiate between the money held by individuals and the money held by businesses in discussing money demand, you should be aware that in the U.S. economy, businesses hold a significant portion of the total money stock. Example 26.2 illustrates the determination of money demand by a business owner.
EXAMPLE 26.2A Business’s Demand for Money
How much money should Kim’s restaurants hold?
Kim owns several successful restaurants. Her accountant informs her that on a typical day, her restaurants are holding a total of $50,000 in cash on the premises. The accountant points out that if Kim’s restaurants reduced their cash holdings, Kim could use the extra cash to purchase interest-bearing government bonds.
The accountant proposes two methods of reducing the amount of cash Kim’s restaurants hold. First, she could increase the frequency of cash pickups by her armored car service. The extra service would cost $500 annually but would allow Kim’s restaurants to reduce their average cash holding to $40,000. Second, in addition to the extra pickups, Kim could employ a computerized cash management service to help her keep closer tabs on the inflows and outflows of cash at her restaurants. The service costs $700 a year, but the accountant estimates that, together with more frequent pickups, the more efficient cash management provided by the service could help Kim reduce average cash holdings at her restaurants to $30,000.
The interest rate on government bonds is 6 percent. How much money should Kim’s restaurants hold? What if the interest rate on government bonds is 8 percent?
Kim’s restaurants need to hold cash to carry out their normal business, but holding cash also has an opportunity cost, which is the interest those funds could be earning if they were held in the form of government bonds instead of zero-interest cash. Because the interest rate on government bonds is 6 percent, each $10,000 by which Kim can reduce her restaurants’ money holdings yields an annual benefit of $600 (6 percent of $10,000).
If Kim increases the frequency of pickups by her armored car service, reducing the restaurants’ average money holdings from $50,000 to $40,000, the benefit will be the additional $600 in interest income that Kim will earn. The cost is the $500 charged by the armored car company. Since the benefit exceeds the cost, Kim should purchase the extra service and reduce the average cash holdings at her restaurants to $40,000.
Should Kim go a step further and employ the cash management service as well? Doing so would reduce average cash holdings at the restaurants from $40,000 to $30,000, which has a benefit in terms of extra interest income of $600 per year. However, this benefit is less than the cost of the cash management service, which is $700 per year. So Kim should not employ the cash management service and instead should maintain average cash holdings in her restaurants of $40,000.
If the interest rate on government bonds rises to 8 percent, then the benefit of each $10,000 reduction in average money holdings is $800 per year (8 percent of $10,000) in extra interest income. In this case, the benefit of employing the cash management service, $800, exceeds the cost of doing so, which is $700. So Kim should employ the service, reducing the average cash holdings of her business to $30,000. The example shows that a higher nominal interest rate on alternative assets reduces the quantity of money demanded.
CONCEPT CHECK 26.1
The interest rate on government bonds falls from 6 percent to 4 percent. How much cash should Kim’s restaurants hold now?
MACROECONOMIC FACTORS THAT AFFECT THE DEMAND FOR MONEY
In any household or business, the demand for money will depend on a variety of individual circumstances. For example, a high-volume retail business that serves thousands of customers each day will probably choose to have more money on hand than a legal firm that bills clients and pays employees monthly. But while individuals and businesses vary considerably in the amount of money they choose to hold, three macroeconomic factors affect the demand for money quite broadly: the nominal interest rate, real output, and the price level. As we see next, the nominal interest rate affects the cost of holding money throughout the economy, while real output and the price level affect the benefits of money.
· The nominal interest rate (i). We have seen that the interest rate paid on alternatives to money, such as government bonds, determines the opportunity cost of holding money. The higher the prevailing nominal interest rate, the greater the opportunity cost of holding money, and hence the less money individuals and businesses will demand.
What do we mean by the nominal interest rate? As we have discussed, there are thousands of different assets, each with its own interest rate (rate of return). So can we really talk about the nominal interest rate? The answer is that, while there are many different assets, each with its own corresponding interest rate, the rates on those assets tend to rise and fall together. This is to be expected, because if the interest rates on some assets were to rise sharply while the rates on other assets declined, financial investors would flock to the assets paying high rates and refuse to buy the assets paying low rates. So, although there are many different interest rates in practice, speaking of the general level of interest rates usually does make sense. In this book, when we talk about the nominal interest rate, what we have in mind is some average measure of interest rates. This simplification is one more application of the macroeconomic concept of aggregation, introduced in Chapter 16, Macroeconomics: The Bird’s-Eye View of the Economy. (We will discuss post-2008 deviations from this simplifying assumption in the next section.)
The nominal interest rate is a macroeconomic factor that affects the cost of holding money. A macroeconomic factor that affects the benefit of holding money is
· Real income or output (Y). An increase in aggregate real income or output—as measured, for example, by real GDP—raises the quantity of goods and services that people and businesses want to buy and sell. When the economy enters a boom, for example, people do more shopping and stores have more customers. To accommodate the increase in transactions, both individuals and businesses need to hold more money. Thus higher real output raises the demand for money.
A second macroeconomic factor affecting the benefit of holding money is
· The price level (P). The higher the prices of goods and services, the more dollars (or yen, or euros) are needed to make a given set of transactions. Thus a higher price level is associated with a higher demand for money.
Today, when a couple of teenagers go out for a movie and snacks on Saturday night, they need about twice as much cash as their parents did 25 years ago. Because the prices of movie tickets and popcorn have risen steeply over 25 years, more money (that is, more dollars) is needed to pay for a Saturday night date than in the past. By the way, the fact that prices are higher today does not imply that people are worse off today than in the past, because nominal wages and salaries have also risen substantially. In general, however, higher prices do imply that people need to keep a greater number of dollars available, in cash or in a checking account.
THE MONEY DEMAND CURVE
For the purposes of monetary policymaking, economists are most interested in the aggregate, or economywide, demand for money. The interaction of the aggregate demand for money, determined by the public, and the supply of money, which is set by the Fed, determines the nominal interest rate that prevails in the economy.
The economywide demand for money can be represented graphically by the money demand curve (see Figure 26.1). The money demand curve relates the aggregate quantity of money demanded M to the nominal interest rate i. The quantity of money demanded M is a nominal quantity, measured in dollars (or yen, or euros, depending on the country). Because an increase in the nominal interest rate increases the opportunity cost of holding money, which reduces the quantity of money demanded, the money demand curve slopes down.
FIGURE 26.1 The Money Demand Curve.The money demand curve relates the economywide demand for money to the nominal interest rate. Because an increase in the nominal interest rate raises the opportunity cost of holding money, the money demand curve slopes down.
If we think of the nominal interest rate as the “price” (more precisely, the opportunity cost) of money and the amount of money people want to hold as the “quantity,” the money demand curve is analogous to the demand curve for a good or service. As with a standard demand curve, the fact that a higher price of money leads people to demand less of it is captured in the downward slope of the demand curve. Furthermore, as in a standard demand curve, changes in factors other than the price of money (the nominal interest rate) can cause the demand curve for money to shift.
For a given nominal interest rate, any change that makes people want to hold more money will shift the money demand curve to the right, and any change that makes people want to hold less money will shift the money demand curve to the left. Thus, as in a standard demand curve, changes in factors other than the price of money (the nominal interest rate) cause the demand curve for money to shift. We have already identified two macroeconomic factors other than the nominal interest rate that affect the economywide demand for money: real output and the price level. Because an increase in either of these variables increases the demand for money, it shifts the money demand curve rightward, as shown in Figure 26.2. Similarly, a fall in real output or the general price level reduces money demand, shifting the money demand curve leftward.
FIGURE 26.2 A Shift in the Money Demand Curve.At a given nominal interest rate, any change that makes people want to hold more money—such as an increase in the general price level or in real GDP—will shift the money demand curve to the right.
The money demand curve may also shift in response to other changes that affect the cost or benefit of holding money, such as the technological and financial advances we mentioned earlier. For example, the introduction of ATM machines reduced the amount of money people choose to hold and thus shifted the economywide money demand curve to the left. The Economic Naturalist 26.1 describes another potential source of shifts in the demand for money, holdings of U.S. dollars by foreigners.
The Economic Naturalist 26.1
Why does the average Argentine hold more U.S. dollars than the average U.S. citizen?
Estimates are that the value of U.S. dollars circulating in Argentina exceeds $1,000 per person, which is higher than the per capita dollar holdings in the United States. A number of other countries, including those that once belonged to the former Soviet Union, also hold large quantities of dollars. In all, as much as $500 billion in U.S. currency—about one third of the total amount issued—may be circulating outside the borders of the United States. Why do Argentines and other non-U.S. residents hold so many dollars?
U.S. residents and businesses hold dollars primarily for transactions purposes, rather than as a store of value. As a store of value, interest-bearing bonds and dividend-paying stocks are a better choice for Americans than zero-interest money. But this is not necessarily the case for the citizens of other countries, particularly nations that are economically or politically unstable. Argentina, for example, endured many years of high and erratic inflation in the 1970s and 1980s, which sharply eroded the value of financial investments denominated in Argentine pesos. Lacking better alternatives, many Argentines began saving in the form of U.S. currency—dollar bills hidden in the mattress or plastered into the wall—which they correctly believed to be more stable in value than peso-denominated assets.
Argentina’s use of dollars became officially recognized in 1990. In that year, the country instituted a new monetary system, called a currency board, under which U.S. dollars and Argentine pesos by law traded freely one for one. Under the currency board system, Argentines became accustomed to carrying U.S. dollars in their wallets for transactions purposes, along with pesos. However, in 2001 Argentina’s monetary problems returned with a vengeance as the currency board system broke down, the peso plummeted in value relative to the dollar, and inflation returned. In the past few years, inflation in Argentina has been estimated to be between 25 and 40 percent. (For a while, the government’s official inflation figures were not considered reliable.) The Argentine demand for dollars is thus likely only to increase in the next few years.
The African nation of Zimbabwe provides another example. After years of hyperinflation and price speculation, the Zimbabwean dollar was effectively abandoned as an official currency on April 12, 2009. This followed a year when the growth in the money supply rose from 81,143 percent to 658 billion percent from January to December, and an egg was reportedly selling for Z$50 billion. On January 29, 2014, the Zimbabwe central bank announced that the U.S. dollar would be one of several foreign currencies that would be accepted as legal currency within that country.
©Feije Riemersma/Alamy Stock Photo
Some countries, including a number of those formed as a result of the breakup of the Soviet Union, have endured not only high inflation, but political instability and uncertainty as well. In a politically volatile environment, citizens face the risk that their savings, including their bank deposits, will be confiscated or heavily taxed by the government. Often they conclude that a hidden cache of U.S. dollars—an estimated $1 million in 100-dollar bills can be stored in a suitcase—is the safest way to hold wealth. Indeed, such wealth in a relatively small container is one reason international criminals, most notably drug dealers, allegedly hold so many $100 bills. Now that the European currency, the euro (€), which is worth more than $1, can be held in the form of a €500 banknote, it has been suggested that drug dealers and other cash-hoarders have been switching to holding €500 bills in even smaller suitcases. Concerned by this possibility, the European Central Bank announced in 2016 that it would phase out the €500 note by the end of 2018. When it does, the demand for dollars may further increase.
In practice, changes in the foreign demand for U.S. dollars are an important source of fluctuation in the U.S. money demand curve. During periods of war, instability, or financial stress, foreign holdings of dollars tend to go up. Such increases in the demand for dollars shifts the U.S. money demand curve substantially to the right, as in Figure 26.2. Because policymakers at the Federal Reserve are concerned primarily with the number of dollars circulating in the U.S. economy, rather than in the world as a whole, they pay close attention to these international flows of greenbacks.
THE SUPPLY OF MONEY AND MONEY MARKET EQUILIBRIUM
Where there is demand, can supply be far behind? As we have discussed, for now we assume that the supply of money is determined by the supply of reserves, and hence is fully controlled by the central bank—in the United States, the Federal Reserve, or Fed. Historically, the Fed’s primary tool for controlling the money supply is open-market operations. For example, to increase the money supply, the Fed can use newly created money to buy government bonds from the public (an open-market purchase), which puts the new money into circulation.
Figure 26.3 shows the demand for and the supply of money in a single diagram. The nominal interest rate is on the vertical axis, and the nominal quantity of money (in dollars) is on the horizontal axis. As we have seen, because a higher nominal interest rate increases the opportunity cost of holding money, the money demand curve slopes downward. And because the Fed fixes the supply of money, we have drawn the money supply curve as a vertical line that intercepts the horizontal axis at the quantity of money chosen by the Fed, denoted M.
FIGURE 26.3 Equilibrium in the Market for Money.Equilibrium in the market for money occurs at point E, where the demand for money by the public equals the amount of money supplied by the Federal Reserve. The equilibrium nominal interest rate, which equates the supply of and demand for money, is i.
As in standard supply and demand analysis, equilibrium in the market for money occurs at the intersection of the supply and demand curves, shown as point E in Figure 26.3. The equilibrium amount of money in circulation, M, is simply the amount of money the Fed chooses to supply. The equilibrium nominal interest rate i is the interest rate at which the quantity of money demanded by the public, as determined by the money demand curve, equals the fixed supply of money made available by the Fed.
To understand how the market for money reaches equilibrium, it may be helpful to recall the relationship between interest rates and the market price of bonds that was introduced in Chapter 23, Financial Markets and International Capital Flows. As we saw in the earlier chapter, the prices of existing bonds are inversely related to the current interest rate. Higher interest rates imply lower bond prices, and lower interest rates imply higher bond prices. With this relationship between interest rates and bond prices in mind, let’s ask what happens if, say, the nominal interest rate is initially below the equilibrium level in the market for money—for example, at a value such as i′ in Figure 26.3. At that interest rate the public’s demand for money is M′, which is greater than the actual amount of money in circulation, equal to M. How will the public—households and firms—react if the amount of money they hold is less than they would like? To increase their holdings of money, people will try to sell some of the interest-bearing assets they hold, such as bonds. But if everyone is trying to sell bonds and there are no willing buyers, then all the attempt to reduce bond holdings will achieve is to drive down the price of bonds, in the same way that a glut of apples will drive down the price of apples.
A fall in the price of bonds, however, is equivalent to an increase in interest rates. Thus the public’s collective attempt to increase its money holdings by selling bonds and other interest-bearing assets, which has the effect of lowering bond prices, also implies higher market interest rates. As interest rates rise, the quantity of money demanded by the public will decline (represented by a right-to-left movement along the money demand curve), as will the desire to sell bonds. Only when the interest rate reaches its equilibrium value, i in Figure 26.3, will people be content to hold the quantities of money and other assets that are actually available in the economy.
CONCEPT CHECK 26.2
Describe the adjustment process in the market for money if the nominal interest rate is initially above rather than below its equilibrium value. What happens to the price of bonds as the money market adjusts toward equilibrium?
RECAP
MONEY DEMAND AND SUPPLY
· For the economy as a whole, the demand for money is the amount of wealth that individuals, households, and businesses choose to hold in the form of money. The opportunity cost of holding money is measured by the nominal interest rate i, which is the return that could be earned on alternative assets such as bonds. The benefit of holding money is its usefulness in transactions.
· Increases in real GDP (Y) or the price level (P) raise the nominal volume of transactions and thus the economywide demand for money. The demand for money is also affected by technological and financial innovations, such as the introduction of ATM machines, that affect the costs or benefits of holding money.
· The money demand curve relates the economywide demand for money to the nominal interest rate. Because an increase in the nominal interest rate raises the opportunity cost of holding money, the money demand curve slopes downward.
· Changes in factors other than the nominal interest rate that affect the demand for money can shift the money demand curve. For example, increases in real GDP or the price level raise the demand for money, shifting the money demand curve to the right, whereas decreases shift the money demand curve to the left.
· In the market for money, the money demand curve slopes downward, reflecting the fact that a higher nominal interest rate increases the opportunity cost of holding money and thus reduces the amount of money people want to hold. The money supply curve is vertical at the quantity of money that the Fed chooses to supply. The equilibrium nominal interest rate i is the interest rate at which the quantity of money demanded by the public equals the fixed supply of money made available by the Fed.
HOW THE FED CONTROLS THE NOMINAL INTEREST RATE
We began this chapter by noting that the public and the press usually talk about Fed policy in terms of decisions about the nominal interest rate rather than the money supply. Indeed, Fed policymakers themselves usually describe their plans in terms of a target value (or a narrow target range) for the interest rate. We now have the necessary background to understand how the Fed translates the ability to determine the economy’s money supply into control of the nominal interest rate.
Figure 26.3 showed that the nominal interest rate is determined by equilibrium in the market for money. Let’s suppose that for some reason the Fed decides to lower the interest rate. As we will see, to lower the interest rate the Fed must increase the supply of money, which can be accomplished by using newly created money to purchase government bonds from the public (an open-market purchase).
Figure 26.4 shows the effects of such an increase in the money supply by the Fed. If the initial money supply is M, then equilibrium in the money market occurs at point E in the figure, and the equilibrium nominal interest rate is i. Now suppose the Fed, by means of open-market purchases of bonds, increases the money supply to M′. This increase in the money supply shifts the vertical money supply curve to the right, which shifts the equilibrium in the money market from point E to point F (see Figure 26.4). Note that at point F the equilibrium nominal interest rate has declined, from i to i′. The nominal interest rate must decline if the public is to be persuaded to hold the extra money that has been injected into the economy.
FIGURE 26.4 The Fed Lowers the Nominal Interest Rate.The Fed can lower the equilibrium nominal interest rate by increasing the supply of money. For the given money demand curve, an increase in the money supply from M to M′ shifts the equilibrium point in the money market from E to F, lowering the equilibrium nominal interest rate from i to i′.
To understand what happens in financial markets when the Fed expands the money supply, recall once again the inverse relationship between interest rates and the price of bonds. To increase the money supply, the Fed must buy government bonds from the public. However, if households and firms are initially satisfied with their asset holdings, they will be willing to sell bonds only at a price that is higher than the initial price. That is, the Fed’s bond purchases will drive up the price of bonds in the open market. But we know that higher bond prices imply lower interest rates. Thus the Fed’s bond purchases lower the prevailing nominal interest rate.
A similar scenario unfolds if the Fed decides to raise interest rates. To raise interest rates, the Fed must reduce the money supply. Reduction of the money supply is accomplished by an open-market sale—the sale of government bonds to the public in exchange for money.3 (The Fed keeps a large inventory of government bonds, acquired through previous open-market purchases , for use in open-market operations.) But in the attempt to sell bonds on the open market, the Fed will drive down the price of bonds. Given the inverse relationship between the price of bonds and the interest rate, the fall in bond prices is equivalent to a rise in the interest rate. In terms of money demand and money supply, the higher interest rate is necessary to persuade the public to hold less money.
As Figures 26.3 and 26.4 illustrate, control of the interest rate is not separate from control of the money supply. If Fed officials choose to set the nominal interest rate at a particular level, they can do so only by setting the money supply at a level consistent with the target interest rate. The Fed cannot set the interest rate and the money supply independently, since for any given money demand curve, a particular interest rate implies a particular size of the money supply, and vice versa.
Since monetary policy actions can be expressed in terms of either the interest rate or the money supply, why does the Fed (and almost every other central bank) choose to communicate its policy decisions to the public in terms of a target nominal interest rate rather than a target money supply? One reason, as we will see shortly, is that the main effects of monetary policy on both the economy and financial markets are exerted through interest rates. Consequently, the interest rate is often the best summary of the overall impact of the Fed’s actions. Another reason for focusing on interest rates is that they are more familiar to the public than the money supply. Finally, interest rates can be monitored continuously in the financial markets, which makes the effects of Fed policies on interest rates easy to observe. By contrast, measuring the amount of money in the economy requires collecting data on bank deposits, with the consequence that several weeks may pass before policymakers and the public know precisely how Fed actions have affected the money supply.
THE ROLE OF THE FEDERAL FUNDS RATE IN MONETARY POLICY
Although thousands of interest rates are used throughout the economy and are easily available, the interest rate that is perhaps most closely watched by the public, politicians, the media, and the financial markets is the federal funds rate.
The federal funds rate is the interest rate commercial banks charge each other for very short-term (usually overnight) loans. For example, a bank that has insufficient reserves to meet its legal reserve requirements might borrow reserves for a few days from a bank that has extra reserves (we return to the topic of reserve requirements in the next section). Despite its name, the federal funds rate is not an official government interest rate and is not connected to the federal government.
Because the market for loans between commercial banks is tiny compared to some other financial markets, such as the market for government bonds, one might expect the federal funds rate to be of little interest to anyone other than the managers of commercial banks. But enormous attention is paid to this interest rate, because over most of the past half-century, the Fed has expressed its policies in terms of a target value for it (since December 2008, the target is actually a narrow range of values). Indeed, at the close of every meeting of the Federal Open Market Committee, the Fed announces whether the federal funds rate will be increased, decreased, or left unchanged. The Fed may also indicate the likely direction of future changes in the federal funds rate. Thus more than any other financial variable, changes in the federal funds rate indicate the Fed’s plans for monetary policy.4
Why does the Fed choose to focus on this particular nominal interest rate over all others? As we saw in Chapter 22, Money, Prices, and the Federal Reserve, historically, the Fed affected the money supply through its control of bank reserves, which made the Fed’s control over the federal funds rate particularly tight. Today, after decades of using this particular interest rate as the Fed’s main policy tool, the public has gotten used to it, which is one reason to keep using it. However, if Fed officials chose to do so, they could probably signal their intended policies just as effectively in terms of another short-term nominal interest rate, such as the rate on short-term government debt.
Figure 26.5 shows the behavior of the federal funds rate since 1970 (as usual, shaded areas correspond to recessions). As you can see, the Fed has allowed this interest rate to vary considerably in response to economic conditions. Note, however, how the federal funds rate has remained close to zero since the end of 2008; that is, it has remained both considerably lower and more stable than in the preceding four decades shown here. Later in the chapter we will consider two specific episodes in which the Fed changed the federal funds rate in response to an economic slowdown, and we will also discuss the unusual situation since 2008.
FIGURE 26.5 The Federal Funds Rate, 1970–2017.The federal funds rate is the interest rate commercial banks charge each other for short-term loans. It is closely watched because the Fed expresses its policies in terms of a target for the federal funds rate. The Fed has allowed the federal funds rate to vary considerably in response to economic conditions.Source: Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/series/FEDFUNDS.
CAN THE FED CONTROL THE REAL INTEREST RATE?
Through its control of the money supply the Fed can control the economy’s nominal interest rate. But many important economic decisions, such as the decisions to save and invest, depend on the real interest rate. To affect those decisions, the Fed must exert some control over the real interest rate.
Most economists believe that the Fed can control the real interest rate, at least for some period. To see why, recall the definition of the real interest rate from Chapter 18, Measuring the Price Level and Inflation:
r = i − π.
The real interest rate r equals the nominal interest rate i minus the rate of inflation π. As we have seen, the Fed can control the nominal interest rate quite precisely through its ability to determine the money supply. Furthermore, inflation appears to change relatively slowly in response to changes in policy or economic conditions, for reasons we will discuss in the next chapter. Because inflation tends to adjust slowly, actions by the Fed to change the nominal interest rate generally lead the real interest rate to change by about the same amount.
The idea that the Fed can set the real interest rate appears to contradict the analysis in Chapter 21, Saving and Capital Formation, which concluded that the real interest rate is determined by the condition that national saving must equal investment in new capital goods. This apparent contradiction is rooted in a difference in the time frame being considered. Because inflation does not adjust quickly, the Fed can control the real interest rate over the short run. In the long run, however—that is, over periods of several years or more—the inflation rate and other economic variables will adjust, and the balance of saving and investment will determine the real interest rate. Thus the Fed’s ability to influence consumption and investment spending through its control of the real interest rate is strongest in the short run.
In discussing the Fed’s control over interest rates, we should also return to a point mentioned earlier in this chapter: In reality, not just one but many thousands of interest rates are seen in the economy. Because interest rates tend to move together (allowing us to speak of the interest rate), an action by the Fed to change the federal funds rate generally causes other interest rates to change in the same direction. However, the tendency of other interest rates (such as the long-term government bond rate or the rate on bonds issued by corporations) to move in the same direction as the federal funds rate is only a tendency, not an exact relationship. In practice, then, the Fed’s control of other interest rates may be somewhat less precise than its control of the federal funds rate—a fact that complicates the Fed’s policymaking. In the next section we will discuss what the Fed has been doing since 2008 to lower those other interest rates through channels other than the traditional channel of lowering the federal funds rate.
RECAP
THE FEDERAL RESERVE AND INTEREST RATES
· The Federal Reserve controls the nominal interest rate by changing the supply of money. An open-market purchase of government bonds increases the money supply and lowers the equilibrium nominal interest rate. Conversely, an open-market sale of bonds reduces the money supply and increases the nominal interest rate. The Fed can prevent changes in the demand for money from affecting the nominal interest rate by adjusting the quantity of money supplied appropriately. The Fed typically expresses its policy intentions in terms of a target for a specific nominal interest rate, the federal funds rate.
· Because inflation is slow to adjust, in the short run the Fed can control the real interest rate (equal to the nominal interest rate minus the inflation rate) as well as the nominal interest rate. In the long run, however, the real interest rate is determined by the balance of saving and investment.
THE FEDERAL RESERVE AND INTEREST RATES: A CLOSER LOOK
To this point in the book, we have discussed the basic market for money and how it works. We have seen how, by controlling the supply of money, the Fed controls the nominal interest rate (the nominal price of money) and hence, in the short run, the real interest rate (the real price of money). To keep the discussion simple, we assumed that the Fed has full control over the money supply, and we assumed that the different interest rates in the economy move more or less together, allowing us to talk about the interest rate. In this section we take a closer look at the market for money, and see how it works in times when these assumptions hold less well. As an important example of such times, we discuss the Fed’s monetary policy since the 2008 peak of the financial crisis.
CAN THE FED FULLY CONTROL THE MONEY SUPPLY?
We have seen that central banks in general, and the Fed in particular, do not control the money supply directly. But we assumed that central banks can control the money supply indirectly by changing the supply of reserves that commercial banks hold. We will now look at this assumption more closely. In Chapter 22, Money, Prices, and the Federal Reserve, we introduced Equation 22.2, copied below:
(26.1)
The equation shows that given a certain amount of currency that the public wants to hold, and given a certain reserve-deposit ratio that the banks desire to maintain, the central bank can control the money supply by controlling the amount of bank reserves. Let’s assume for now that the amount of currency that the public wants to hold and the reserve-deposit ratio that the banks desire to maintain are fixed at their present levels. Then, to increase the money supply, the central bank has to increase bank reserves; to decrease the money supply, the central bank has to decrease bank reserves. Moreover, the equation suggests a simple relationship between any change in reserves and the resulting change in the money supply: for every $1 of change (increase or decrease) in reserves, the money supply would change by $1/(Desired reserve-deposit ratio). For example, if the desired reserve-deposit ratio is 5 percent (that is, 0.05), then an increase in reserves by $1 (initiated by the central bank) would increase the money supply by $1/0.05 = $20.
The Fed can increase and decrease reserves using different methods, as we will now discuss. We will also see that the Fed can directly affect the desired reserve-deposit ratio.
Affecting Bank Reserves through Open-Market Operations
How can the Fed increase and decrease bank reserves? So far we have emphasized its main tool, open-market operations. In an open-market purchase, the Fed buys securities and, effectively, sells reserves. In an open-market sale, the Fed sells securities and, effectively, buys back reserves. Hence, as we have seen, the Fed can change the quantity of reserves in the banking system through open-market operations.
Affecting Bank Reserves through Discount Window Lending
Another tool by which the Fed can affect bank reserves is called discount window lending. Recall from the Chapter 22, Money, Prices, and the Federal Reserve, that the cash or assets held by a commercial bank for the purpose of meeting depositor withdrawals are called its reserves. Its desired amount of reserves is equal to its deposits multiplied by the desired reserve-ratio (as implied by Equation 22.1 in Chapter 22, Money, Prices, and the Federal Reserve). When individual commercial banks are short of reserves, they may choose to borrow reserves from the Fed. For historical reasons, lending of reserves by the Federal Reserve to commercial banks is called discount window lending. The interest rate that the Fed charges commercial banks that borrow reserves is called the discount rate. The Fed offers three discount window programs (called primary credit, secondary credit, and seasonal credit), each with its own interest rate; different depository institutions qualify for different programs. Loans of reserves by the Fed directly increase the quantity of reserves in the banking system.5
Setting and Changing Reserve Requirements
As we have shown, the economy’s money supply depends on three factors: the amount of currency the public chooses to hold, the supply of bank reserves, and the reserve-deposit ratio maintained by commercial banks. The reserve-deposit ratio is equal to total bank reserves divided by total deposits. If banks kept all of their deposits as reserves, the reserve-deposit ratio would be 100 percent (that is, 1.00), and banks would not make any loans. As banks lend out more of their deposits, the reserve-deposit ratio falls.
For given quantities of currency held by the public and of reserves held by the banks, an increase in the reserve-deposit ratio reduces the money supply. A higher reserve-deposit ratio implies that banks lend out a smaller share of their deposits in each of the rounds of lending and redeposit, limiting the overall expansion of loans and deposits.
Within a certain range, commercial banks are free to set the reserve-deposit ratio they want to maintain. However, Congress granted the Fed the power to set minimum values of the reserve-deposit ratio for commercial banks. The legally required values of the reserve-deposit ratio set by the Fed are called reserve requirements.
Changes in reserve requirements can be used to affect the money supply, although the Fed does not usually use them in this way. For example, suppose that commercial banks are maintaining the legally mandated minimum of 3 percent reserve-deposit ratio, and the Fed wants to contract the money supply. By raising required reserves to, say, 5 percent of deposits, the Fed could force commercial banks to raise their reserve-deposit ratio, at least until it reached 5 percent. As you can verify by looking at Equation 26.1, an increase in the reserve-deposit ratio lowers deposits and the money supply. Similarly, a reduction in required reserves by the Fed might allow at least some banks to lower their ratio of reserves to deposits. A decline in the economywide reserve-deposit ratio would in turn cause the money supply to rise.
Excess Reserves: The Norm since 2008
We have seen that the Fed can effectively control bank reserves through tools that include open-market operations and discount window lending. We have also seen that the Fed can set reserve requirements. This, however, gives the Fed only partial control over the desired reserve-deposit ratio, leaving some control in the hands of commercial banks. Specifically, while reserve requirements prevent banks from maintaining reserve-deposit ratios below a minimum level, reserve requirements do not prevent banks from maintaining reserve-deposit ratios that are well above that minimum level. By letting their reserve-deposit ratios increase when the Fed increases the quantity of reserves, commercial banks can “absorb” at least part of the increases in reserves without increasing bank deposits. Indeed, commercial banks could, in principle, absorb the entire increase in reserves initiated by the Fed, fully offsetting the effects of increases in reserves on the noncurrency component of the money supply.6
Up to this point, we assumed that banks would always translate an addition in reserves initiated by the Fed into an addition in their deposits (rather than into an increase in their reserve-deposit ratios). This is a reasonable assumption; banks generally do behave this way. But there are situations when banks prefer to let their reserve-deposit ratios (and excess reserves) increase in response to an increase in reserves. For example, to protect themselves from bank runs in times of economic or financial uncertainty, banks may prefer to respond to an increase in reserves by letting their reserve-deposit ratios increase to levels significantly above the minimum level mandated by official reserve requirements. Another reason for banks to let increases in reserves increase their reserve-deposit ratio rather than increasing deposits in times of uncertainty is that in such times banks may find only limited lending opportunities that seem sufficiently safe.
Bank reserves that exceed the reserve requirements set by the central bank are called excess reserves. Excess reserves are thus reserves that the central bank makes available to commercial banks, but that do not add to the money supply because commercial banks do not use them for making additional loans. Because excess reserves do not add to the money supply, they allow for the possibility that the money supply will not change in spite of the central bank increasing or decreasing the supply of reserves.
During the 20 years that ended in August 2008, excess reserves in the U.S banking system averaged less than $2 billion on most months—a negligible amount, considering the size of the U.S. banking system. The only notable exception was a short period in 2001, immediately following the events of 9/11, during which excess reserves increased temporarily as the financial industry was reeling from the effects of the terrorist attack on New York City. Since August 2008, however, things have changed dramatically. As the Fed injected unprecedented amounts of reserves into the system in its attempt to bring interest rates down, excess reserves grew to around $800 billion by the end of the year, and kept growing in the following years until they peaked in 2014 at more than $2.5 trillion, or almost 15 percent of GDP (for comparison, in 2014 the monetary aggregate M1 was about 16 percent of GDP). Excess reserves have slightly decreased since 2014.
The Fed’s actions were successful in reducing the price of money and increasing its supply, helping to prevent another Great Depression (The Economic Naturalist 22.2 discussed the shrinking of the money supply during the Great Depression). As you can verify from Equation 26.1, for the money supply to increase as a result of the Fed-initiated increase in the quantity of reserves, the reserve-deposit ratio had to increase more slowly than the increase in the quantity of reserves. Indeed, while since 2008 banks absorbed much of the increase in reserves initiated by the Fed, they did not absorb it all, and some of it led to increases in the money supply.
We have seen, then, that the Fed does not always fully control the money supply. But even in times of great uncertainty, the Fed can still strongly affect the money supply through the Fed’s control of the supply of reserves. The basic money-market model’s assumption—that the Fed controls the money supply—should therefore be viewed as a useful simplifying assumption even in times when it does not hold exactly.
We now take a closer look at the other simplifying assumption made in the basic money-market model: that interest rates move together.
RECAP
CAN THE FED FULLY CONTROL THE MONEY SUPPLY?
· The Fed can effectively control the amount of bank reserves through tools that include open-market operations and discount window lending. The Fed can also set reserve requirements (a legally binding minimum on banks’ reserve-deposit ratio). This however gives the Fed only partial control over the money supply. In particular, a Fed-initiated increase in bank reserves will not lead to an increase in the money supply if banks absorbed the increase in reserves by letting their reserve-deposit ratios increase at the same pace.
· While rarely the case, in unusual times of economic and financial uncertainty banks may choose to let their reserve-deposit ratio increase substantially above the reserve requirements set by the Fed. Indeed, since 2008, banks have accumulated unprecedented amounts of excess reserves, that is, of reserves in excess of reserve requirements. While this broke the simple link between an increase in reserves and an increase in the money supply, the Fed was still successful in increasing the money supply.
· We conclude that the basic money-market model’s assumption—that the Fed controls the money supply—should be viewed as a useful simplifying assumption even in times when it does not hold exactly.
DO INTEREST RATES ALWAYS MOVE TOGETHER?
To this point in the discussion, we have assumed that the many different nominal interest rates in the economy move more or less together, allowing us to speak of the interest rate. Like the assumption that banks do not hold significant amounts of excess reserves, the assumption that interest rates move more or less together is a reasonably accurate description of the market for money during most times, but not always. In particular, this assumption has held less well since 2008.
The Zero Lower Bound and the Need for “Unconventional” Monetary Policy
Earlier in this chapter, we presented Figure 26.5, which shows the federal funds rate from 1970 to 2017. Until December 2008, the Fed’s main tool for conducting monetary policy was open-market operations aimed at increasing and decreasing the federal funds rate in accordance with the Fed’s target rate. Other interest rates in the economy, which are typically higher than the federal funds rate due to a combination of higher risk and longer maturity, were expected to move up and down more or less together with the federal funds rate. But in December 2008 the Fed reduced its target for the federal funds rate to the range 0 to 1⁄4 percent, effectively hitting what is called the zero lower bound. Attempting to stimulate the economy by reducing the federal funds rate further was no longer a viable option, because interest rates cannot in general be much below zero. (A negative nominal interest rate would mean that lending institutions pay borrowing institutions to hold their money—something lending institutions would not normally do.)
The federal funds rate remained effectively zero in the years following December 2008 (Figure 26.5). But other interest rates in the economy remained significantly above zero during that period. For example, the nominal interest rate on 10-year debt issued by the U.S. government was in the range 1.5 to 4 percent between 2009 and 2015. After December 2008, the Fed could no longer effectively reduce the different interest rates in the economy that were still above zero by reducing the federal funds rate (which was already at its zero lower bound) and “pulling” other rates down with it. To keep stimulating the economy by making money cheaper, the Fed had to turn to less conventional methods: targeting such higher interest rates more directly. We now discuss some of the methods the Fed used.
Quantitative Easing
You are already familiar with one way for making money more cheaply available: open-market operations. Following the financial crisis, the Fed engaged in a specific type of such operations, referred to as large-scale asset purchase programs (LSAPs). These programs, aimed to help in bringing down longer-term interest rates once the federal funds rate was already at (or close to) its zero lower bound, are examples of what is known as quantitative easing. Quantitative easing (QE) refers to a central bank buying specified amounts of financial assets from commercial banks and other private financial institutions, thereby lowering the yield or return of those assets while increasing the money supply. Quantitative easing basically includes the same steps as regular open-market purchases, but is distinguished from these regular purchases in the type and term of the financial assets purchased as well as in the overall goal of the policy. While conventional expansionary policy usually involves the purchase of short-term government bonds in order to keep interest rates at a specified target value, quantitative easing is used by central banks to stimulate the economy by purchasing assets of longer maturity, thereby lowering longer-term interest rates.
Since the peak of the financial crisis in 2008, the Federal Reserve has expanded its balance sheet dramatically, adding trillions of dollars’ worth of longer-term treasury notes, commercial debt, and mortgage-backed securities (MBSs) through several rounds of quantitative easing. By including commercial and private debt in these purchases, it has also been suggested that the Fed is providing credit easing by removing specific gridlocks that have been identified in certain credit markets.
In short, by purchasing longer-term assets (including bonds and other debt) the Fed increased the amount of bank reserves while exerting downward pressure on longer-term interest rates (recall that bond prices and interest rates are inversely related). And by purchasing specific types of assets—such as debt related to mortgages—the Fed could help decrease interest rates in specific markets—such as mortgage and housing markets that were hit particularly hard during the financial crisis.
Forward Guidance
Quantitative easing helps to lower long-term interest rates in the economy through open-market purchases. Another means for lowering long-term rates is known as forward guidance. The idea behind it is simple: by guiding markets regarding the central bank’s future intentions, the central bank can influence long-term interest rates because these rates are affected by what market participants believe the central bank will do in the future. To illustrate this, imagine that financial markets believe that short-term interest rates, currently at around zero, will remain close to zero for several more years. Then the market price of a three-year bond, for example, will be such that the implied interest rate (or yield, or return) on the bond is close to zero. But if financial markets believed that short-term interest rates, while currently at zero, were about to increase dramatically in the next few months and stay elevated for several years, then a three-year bond’s current price would reflect these beliefs, and hence the implied interest rate on the bond would be much higher.
In its September 2015 meeting, for example, the Federal Open Market Committee (FOMC) decided to keep the federal funds rate at its 0 to 1⁄4 percent target range—that is, effectively at its zero lower bound. The FOMC’s statement following the meeting included sentences such as this: “The Committee currently anticipates that, . . . economic conditions may, for some time, warrant keeping the target federal funds rate below levels the Committee views as normal in the longer run.” On the Fed’s website, it was further explained how such forward guidance is expected to support economic recovery:7
Through “forward guidance,” the Federal Open Market Committee provides an indication to households, businesses, and investors about the stance of monetary policy expected to prevail in the future. By providing information about how long the Committee expects to keep the target for the federal funds rate exceptionally low, the forward guidance language can put downward pressure on longer-term interest rates and thereby lower the cost of credit for households and businesses and also help improve broader financial conditions.
Interest on Reserves and Monetary-Policy Normalization
We have seen that starting in 2008 and continuing in the following years, the Fed took unprecedented steps to support the economy and help it recover from a historically deep global recession. The close-to-zero federal funds rate, the several rounds of quantitative easing (or large-scale asset purchases) and the resulting massive amounts of excess reserves, and other policies such as forward guidance were an unusual combination, designed for unusual times. It was always expected, by both the Fed and the public, that at some future date monetary policy would “normalize”: the federal funds rate would rise, the Fed’s balance sheet and banks’ excess reserves would shrink, and more generally real-world money markets would again resemble more closely the traditional basic money-market model with its simplifying assumptions.
What would monetary-policy normalization look like? In theory, in order to tighten monetary policy, the Fed could start by reversing its quantitative easing efforts using, again, open-market operations. Specifically, the Fed could start selling the assets it purchased as part of its quantitative easing programs (or it could even just stop reinvesting in new assets as the assets it purchased matured or prepaid). The payment the Fed would receive against these assets would drain reserves from the banking system; the price of these assets would fall; and interest rates on these assets would rise again. Once enough excess reserves had been thus drained from the system, the federal funds rate—the overnight price of reserves—would start rising again.
However, when the Fed concluded, in late 2015, that the time to start tightening monetary policy has eventually come, the Fed did not first let long-term interest rates rise by reversing its past quantitative easing purchases. Instead, in the first phase of tightening, the Fed returned to using its long-time tool: raising the federal funds rate (you can see this in Figure 26.5). Starting to tighten monetary policy by increasing the Fed’s target for the federal funds rate, rather than by increasing longer-term interest rates, has several advantages. One advantage is that the Fed is familiar with the federal funds rate as a monetary-policy tool; it has experience controlling this rate and moving it as needed—at times rather rapidly. Another advantage is that market participants, such as households and investors, are also familiar with the federal funds rate as a monetary tool. For example, households and investors are used to the Fed focusing on its target for the federal funds rate when communicating with the public.
To raise the federal funds rate without first engaging in a large-scale asset sale, the Fed’s main channel has been to increase the interest rate it pays banks on the reserves they hold with the Fed. These include banks’ required reserves (reserves held with the Fed in order to meet the required reserve-deposit ratios) and banks’ excess reserves. The Fed paid an interest rate of 1⁄4 percent on required and excess reserve balances between 2008 and 2015. Since the Fed started raising this interest rate in December 2015, the federal funds rate has been rising with it, because banks have little incentive to lend their excess reserves to other banks at rates below the rate they get on these reserves from the Fed.8
The first step of monetary-policy normalization has thus been a gradual increase in the federal funds rate (see Figure 26.5). As all interest rates are expected to move up as a result, one could again talk of the interest rate. At a later stage the Fed is expected to also start reducing its holdings of assets purchased during its quantitative easing programs—although that reduction may eventually be rather modest, because in the meantime the U.S. economy keeps growing, and with it grows the amount of currency in circulation and hence the amount of assets the Fed needs to hold. A reduction of assets held by the Fed would likely push some longer-term interest rates further up. Once the Fed concludes its asset reductions (or determines that they are no longer necessary), the different interest rates in the economy are expected to again move more or less together, as the basic model of the market for money assumes.
As we discussed in the previous section, such movements in nominal interest rates translate, in the short run, to movements in real interest rates. We now turn to discuss how movements in real interest rates affect the economy.
RECAP
DO INTEREST RATES ALWAYS MOVE TOGETHER?
· The zero lower bound is a level, close to zero, below which the Fed cannot further reduce short-term interest rates. After December 2008, the Fed could no longer reduce the different interest rates in the economy that were still above zero by reducing the federal funds rate, because the federal funds rate had reached its zero lower bound.
· To keep stimulating the economy after December 2008, the Fed had to turn to less conventional methods that are aimed at lowering higher interest rates more directly. These included quantitative easing (formally, large-scale asset purchase programs) and forward guidance.
· The federal funds rate remained effectively zero from 2008 to 2015. When the Fed concluded, in late 2015, that the time to start tightening monetary policy has come (also referred to as the time to start monetary-policy normalization), the Fed started increasing the interest rate it pays banks on the reserves they hold with the Fed. These include banks’ required reserves (reserves held with the Fed in order to meet the required reserve-deposit ratios) and banks’ excess reserves. That is, the Fed’s main policy tool since late 2015 has been, again, moving the federal funds rate, a short-term interest rate.
THE EFFECTS OF FEDERAL RESERVE ACTIONS ON THE ECONOMY
Now that we have seen how the Fed can influence interest rates (both nominal and real, in normal times and during unusual episodes), we can consider how monetary policy can be used to eliminate output gaps and stabilize the economy. The basic idea is relatively straightforward. As we will see in this section, planned aggregate expenditure is affected by the level of real interest rate prevailing in the economy. Specifically, a lower real interest rate encourages higher planned spending by households and firms, while a higher real interest rate reduces spending. By adjusting the real interest rate, the Fed can move planned spending in the desired direction. Under the assumption of the basic Keynesian model that firms produce just enough goods and services to meet the demand for their output, the Fed’s stabilization of planned spending leads to stabilization of aggregate output and employment as well. In this section we will first explain how planned aggregate expenditure is related to the real interest rate. Then we will show how the Fed can use changes in the real interest rate to fight a recession or inflation.
PLANNED AGGREGATE EXPENDITURE AND THE REAL INTEREST RATE
In Chapter 25, Spending and Output in the Short Run, we saw how planned spending is affected by changes in real output Y. Changes in output affect the private sector’s disposable income (Y − T), which in turn influences consumption spending—a relationship captured by the consumption function.
A second variable that has potentially important effects on aggregate expenditure is the real interest rate r. In Chapter 23, Financial Markets and International Capital Flows, in our discussion of saving and investment, we saw that the real interest rate influences the behavior of both households and firms.
For households, the effect of a higher real interest rate is to increase the reward for saving, which leads households to save more.9 At a given level of income, households can save more only if they consume less. Thus, saying that a higher real interest rate increases saving is the same as saying that a higher real interest rate reduces consumption spending at each level of income. The idea that higher real interest rates reduce household spending makes intuitive sense. Think, for example, about people’s willingness to buy consumer durables, such as automobiles or furniture. Purchases of consumer durables, which are part of consumption spending, are often financed by borrowing from a bank, credit union, or finance company. When the real interest rate rises, the monthly finance charges associated with the purchase of a car or a piano are higher, and people become less willing or able to make the purchase. Thus a higher real interest rate reduces people’s willingness to spend on consumer goods, holding constant disposable income and other factors that affect consumption.
When the real interest rate rises, financing a new car becomes more expensive and fewer cars are purchased.
Besides reducing consumption spending, a higher real interest rate also discourages firms from making capital investments. As in the case of a consumer thinking of buying a car or a piano, when a rise in the real interest rate increases financing costs, firms may reconsider their plans to invest. For example, upgrading a computer system may be profitable for a manufacturing firm when the cost of the system can be financed by borrowing at a real interest rate of 3 percent. However, if the real interest rate rises to 6 percent, doubling the cost of funds to the firm, the same upgrade may not be profitable and the firm may choose not to invest. We should also remember that residential investment—the building of houses and apartment buildings—is also part of investment spending. Higher interest rates, in the form of higher mortgage rates, certainly discourage this kind of investment spending as well.
The conclusion is that, at any given level of output, both consumption spending and planned investment spending decline when the real interest rate increases. Conversely, a fall in the real interest rate tends to stimulate consumption and investment spending by reducing financing costs. Example 26.3 is a numerical illustration of how planned aggregate expenditure can be related to the real interest rate and output.
EXAMPLE 26.3Planned Aggregate Expenditure and the Real Interest Rate
How does the interest rate affect planned aggregate expenditure?
In a certain economy, the components of planned spending are given by
Find the relationship of planned aggregate expenditure to the real interest rate r and output Y in this economy. Find autonomous expenditure and induced expenditure.
This example is similar to Example 25.2, except that now the real interest rate r is allowed to affect both consumption and planned investment. For example, the final term in the equation describing consumption, −400r, implies that a 1 percent (0.01) increase in the real interest rate, from 4 percent to 5 percent, for example, reduces consumption spending by 400(0.01) = 4 units. Similarly, the final term in the equation for planned investment tells us that in this example, a 1 percent increase in the real interest rate lowers planned investment by 600(0.01) = 6 units. Thus the overall effect of a 1 percent increase in the real interest rate is to lower planned aggregate expenditure by 10 units, the sum of the effects on consumption and investment. As in the earlier examples, disposable income (Y − T) is assumed to affect consumption spending through a marginal propensity to consume of 0.8 (see the first equation), and government purchases G, net exports NX, and taxes T are assumed to be fixed numbers.
To find a numerical equation that describes the relationship of planned aggregate expenditure (PAE) to output, we can begin as in Chapter 25, Spending and Output in the Short Run, with the general definition of planned aggregate expenditure:
Substituting for the four components of expenditure, using the equations describing each type of spending, we get
PAE = [640 + 0.8(Y − 250) − 400r] + [250 − 600r] + 300 + 20.
The first term in brackets on the right side of this equation is the expression for consumption, using the fact that taxes T = 250; the second bracketed term is planned investment; and the last two terms correspond to the given numerical values of government purchases and net exports. If we simplify this equation and group together the terms that do not depend on output Y and the terms that do depend on output, we get
PAE = [(640 − 0.8 × 250 − 400r) + (250 − 600r) + 300 + 20] + 0.8Y,
or, simplifying further,
PAE = [1,010 − 1,000r] + 0.8Y.(26.1)
In Equation 26.1, the term in brackets is autonomous expenditure, the portion of planned aggregate expenditure that does not depend on output. Notice that in this example autonomous expenditure depends on the real interest rate r. Induced expenditure, the portion of planned aggregate expenditure that does depend on output, equals 0.8Y in this example.
EXAMPLE 26.4The Real Interest Rate and Short-Run Equilibrium Output
How does the interest rate affect short-run equilibrium output?
In the economy described in Example 26.3, the real interest rate r is set by the Fed to equal 0.05 (5 percent). Find short-run equilibrium output.
We found in Example 26.3 that, in this economy, planned aggregate expenditure is given by Equation 26.1. We are given that the Fed sets the real interest rate at 5 percent. Setting r = 0.05 in Equation 26.1 gives
PAE = [1,010 − 1,000 × (0.05)] + 0.8Y.
Simplifying, we get
PAE = 960 + 0.8Y.
So, when the real interest rate is 5 percent, autonomous expenditure is 960 and induced expenditure is 0.8Y. Short-run equilibrium output is the level of output that equals planned aggregate spending. To find short-run equilibrium output, we could now apply the tabular method used in Chapter 25, Spending and Output in the Short Run, comparing alternative values of output with the planned aggregate expenditure at that level of output. Short-run equilibrium output would be determined as the value of output such that output just equals spending, or
Y = PAE.
However, conveniently, when we compare this example with Example 25.2 in the previous chapter, we see that the equation for planned aggregate expenditure, PAE + 960 + 0.8Y, is identical to what we found there. Thus Table 25.1, which we used to solve Example 25.2, applies to this example as well, and we get the same answer for short-run equilibrium output, which is Y = 4,800.
Short-run equilibrium output can also be found graphically, using the Keynesian cross diagram from Chapter 25, Spending and Output in the Short Run. Again, since the equation for planned aggregate output is the same as in Example 25.2, Figure 25.3 applies equally well here.
CONCEPT CHECK 26.3
For the economy described in Example 26.4, suppose the Fed sets the real interest rate at 3 percent rather than at 5 percent. Find short-run equilibrium output. (Hint: Consider values between 4,500 and 5,500.)
THE FED FIGHTS A RECESSION
We have seen that the Fed can control the real interest rate, and that the real interest rate in turn affects planned spending and short-run equilibrium output.
A decrease in the real interest rate causes increases in both planned consumption and planned investment, which lead to an increase in planned spending. The increase in planned spending leads, through the multiplier, to an increase in short-run equilibrium output. Similarly,
That is, an increase in the real interest rate causes decreases in both planned consumption and planned investment, which lead to a decrease in planned spending. The decrease in planned spending leads, through the multiplier, to a decrease in short-run equilibrium output.
These two relationships are the key to understanding how monetary policy affects short-run economic activity. Let’s first analyze how monetary policy can be used to fight a recession; then we will turn to how the Fed can fight inflation.
Suppose the economy faces a recessionary gap—a situation in which real output is below potential output, and spending is “too low.” To fight a recessionary gap, the Fed should reduce the real interest rate, stimulating consumption and investment spending. According to the theory we have developed, this increase in planned spending will cause output to rise, restoring the economy to full employment. Example 26.5 illustrates this point by extending Example 26.4.
EXAMPLE 26.5The Fed Fights a Recession
How can monetary policy eliminate a recessionary gap?
For the economy described in Example 26.4, suppose potential output Y* equals 5,000. As before, the Fed has set the real interest rate equal to 5 percent. At that real interest rate, what is the output gap? What should the Fed do to eliminate the output gap and restore full employment? You are given that the multiplier in this economy is 5.
In Example 26.4, we showed that with the real interest rate at 5 percent, short-run equilibrium output for this economy is 4,800. We are now given that potential output is 5,000, so the output gap (Y − Y*) equals 5,000 − 4,800 = 200. Because actual output is below potential, this economy faces a recessionary gap.
To fight the recession, the Fed should lower the real interest rate, raising aggregate expenditure until output reaches 5,000, the full-employment level. That is, the Fed’s objective is to increase short-run equilibrium spending and output by 200. Because the multiplier equals 5, to increase output by 200 the Fed must increase autonomous expenditure by 200/5 = 40 units. By how much should the Fed reduce the real interest rate to increase autonomous expenditure by 40 units? Autonomous expenditure in this economy is [1,010 − 1,000r], as you can see from Equation 26.1, so that each percentage point reduction in r increases autonomous expenditure by 1,000 × (0.01) = 10 units. To increase autonomous expenditure by 40, then, the Fed should lower the real interest rate by 4 percentage points, from 5 percent to 1 percent.
In summary, to eliminate the recessionary gap of 200, the Fed should lower the real interest rate from 5 percent to 1 percent. Notice that the Fed’s decrease in the real interest rate increases short-run equilibrium output, as economic logic suggests.
The Fed’s recession-fighting policy is shown graphically in Figure 26.6. The reduction in the real interest rate raises planned spending at each level of output, shifting the expenditure line upward. When the real interest rate equals 1 percent, the expenditure line intersects the Y = PAE line at Y = 5,000, so that output and potential output are equal. A reduction in interest rates by the Fed, made with the intention of reducing a recessionary gap in this way, is an example of an expansionary monetary policy—or, less formally, a monetary easing.
FIGURE 26.6 The Fed Fights a Recession.(1 ) The economy is initially at point E, with a recessionary gap of 200; (2) the Fed reduces the real interest rate from 5 percent to 1 percent, shifting the expenditure line up; (3) the new equilibrium is at point F, where output equals potential output. The output gap has been eliminated.
CONCEPT CHECK 26.4
Suppose that in Example 26.5, potential output is 4,850 rather than 5,000. By how much should the Fed cut the real interest rate to restore full employment? You may take as given that the multiplier is 5.
The Economic Naturalist 26.2
How did the Fed respond to recession and the terrorist attacks in 2001?
The U.S. economy began slowing in the fall of 2000, with investment in high-tech equipment falling particularly sharply. According to the National Bureau of Economic Research, a recession began in March 2001. To make matters worse, on September 11, 2001, terrorist attacks on New York City and Washington shocked the nation and led to serious problems in the travel and financial industries, among others. How did the Federal Reserve react to these events?
The Fed first began to respond to growing evidence of an economic slowdown at the end of the year 2000. At the time, the federal funds rate stood at about 6.5 percent (see Figure 26.5). The Fed’s most dramatic move was a surprise cut of 0.5 percentage point in the funds rate in January 2001, between regularly scheduled meetings of the Federal Open Market Committee. Further rate cuts followed, and by July the funds rate was below 4 percent. By summer’s end, however, there was still considerable uncertainty about the likely severity of the economic slowdown.
The picture changed suddenly on September 11, 2001, when the terrorist attacks on the World Trade Center and the Pentagon killed more than 3,000 people. The terrorist attacks imposed great economic as well as human costs. The physical damage in lower Manhattan was in the billions of dollars, and many offices and businesses in the area had to close. The Fed, in its role as supervisor of the financial system, worked hard to assist in the restoration of normal operations in the financial district of New York City. (The Federal Reserve Bank of New York, which actually conducts open-market operations, is only a block from the site of the World Trade Center.) The Fed also tried to ease financial conditions by temporarily lowering the federal funds rate to as low as 1.25 percent in the week following the attack.
In the weeks and months following September 11, the Fed turned its attention from the direct impact of the attack to the possible indirect effects on the U.S. economy. The Fed was worried that consumers, nervous about the future, would severely cut back their spending; together with the ongoing weakness in investment, a fall in consumption spending could sharply worsen the recession. To stimulate spending, the Fed continued to cut the federal funds rate. By January 2002, the funds rate was at 1.75 percent, nearly 5 percentage points lower than a year earlier. The Fed kept the interest rate at that low level until November 2002, when it lowered the federal funds rate another 0.5 percentage point, to 1.25 percent. Although the recession officially ended in late 2001, the recovery remained quite weak. Unemployment kept increasing, until it peaked at 6.3 percent in June 2003. That month, the Fed further lowered the federal funds rate to 1 percent, keeping it at that record low until June 2004.
A variety of factors helped the economy recover from the 2001 recession, including expansionary fiscal policy (see The Economic Naturalist 25.5). Most economists agree that expansionary actions by the Fed also played a constructive role in reducing the economic impact of the recession and the September 11 attacks.
THE FED FIGHTS INFLATION
To this point, we have focused on the problem of stabilizing output, without considering inflation. In the next chapter, we will see how ongoing inflation can be incorporated into our analysis. For now, we will simply note that one important cause of inflation is an expansionary output gap—a situation in which spending, and hence actual output, exceeds potential output. When an expansionary gap exists, firms find that the demand for their output exceeds their normal rate of production. Although firms may be content to meet this excess demand at previously determined prices for some time, if the high demand persists, they will ultimately raise their prices, spurring inflation.
Because an expansionary gap tends to lead to inflation, the Fed moves to eliminate expansionary gaps as well as recessionary gaps. The procedure for getting rid of an expansionary gap—a situation in which output is “too high” relative to potential output—is the reverse of that for fighting a recessionary gap, a situation in which output is “too low.” As we have seen, the cure for a recessionary gap is to reduce the real interest rate, an action that stimulates spending and increases output. The cure for an expansionary gap is to raise the real interest rate, which reduces consumption and investment by raising the cost of borrowing. The resulting fall in spending leads in turn to a decline in output and to a reduction in inflationary pressures.
EXAMPLE 26.6The Fed Fights Inflation
How can monetary policy eliminate an expansionary gap?
For the economy studied in Examples 26.4 and 26.5, assume that potential output is 4,600 rather than 5,000. At the initial real interest rate of 5 percent, short-run equilibrium output is 4,800, so this economy has an expansionary gap of 200. How should the Fed change the real interest rate to eliminate this gap?
In Example 26.5, we were told that multiplier in this economy is 5. Hence, to reduce total output by 200, the Fed needs to reduce autonomous expenditure by 200/5 = 40 units. From Equation 26.1, we know that autonomous expenditure in this economy is [1,010 − 1,000r], so that each percentage point (0.01) increase in the real interest rate lowers autonomous expenditure by 10 units (1,000 × 0.01). We conclude that to eliminate the inflationary gap, the Fed should raise the real interest rate by 4 percentage points (0.04), from 5 percent to 9 percent. The higher real interest rate will reduce planned aggregate expenditure and output to the level of potential output, 4,600, eliminating inflationary pressures.
The effects of the Fed’s inflation fighting policy are shown in Figure 26.7. With the real interest rate at 5 percent, the expenditure line intersects the Y = PAE line at point E in the figure, where output equals 4,800. To reduce planned spending and output, the Fed raises the real interest rate to 9 percent. The higher real interest rate slows consumption and investment spending, moving the expenditure line downward. At the new equilibrium point G, actual output equals potential output at 4,600. The Fed’s raising the real interest rate—a contractionary policy action—has thus eliminated the expansionary output gap, and with it, the threat of inflation.
FIGURE 26.7 The Fed Fights Inflation.(1 ) The economy is initially at point E, with an expansionary gap of 200; (2) the Fed increases the real interest rate from 5 percent to 9 percent, shifting the expenditure line down; (3) the new equilibrium is at point G, where output equals potential output. The output gap has been eliminated.
The Economic Naturalist 26.3
Why did the Fed raise interest rates 17 times in a row between 2004 and 2006?
The Fed began tightening monetary policy in June 2004 when it increased the federal funds rate from 1.0 to 1.25 percent. (See Figure 26.5.) It continued to tighten by raising the federal funds rate by one-quarter percent at each successive meeting of the Federal Open Market Committee. By the end of June 2006, after more than two years of tightening, the federal funds rate was 5.25 percent. Why did the Fed begin increasing the funds rate in 2004?
Because the recovery that began in November 2001 was slower than normal and marked by weak job growth, the Fed kept reducing the funds rate until it reached 1.0 percent in June 2003. Once the recovery took hold, however, this very low rate was no longer necessary. While employment had not risen as much during the recovery as it had in previous recoveries, real GDP grew at a rate of nearly 6 percent during the second half of 2003 and nearly 4 percent in 2004. Furthermore, by June 2004, the unemployment rate had fallen to 5.6 percent, not far above most estimates of the natural rate of unemployment. Although inflation began to rise in 2004, most of the increase was due to the sharp run-up in oil prices, and the rate of inflation excluding energy remained low. Nevertheless, the Fed began to raise the federal funds rate in order to prevent the emergence of an expansionary gap, which would result in higher inflation. Thus, the Fed’s rate increases could be viewed as a preemptive strike against future inflation. Had the Fed waited until an expansionary gap appeared, a significant inflation problem could have emerged, and the Fed might have had to raise the federal funds rate by even more than it did.
The Fed’s interest rate policies affect the economy as a whole, but they have a particularly important effect on financial markets. The introduction to this chapter noted the tremendous lengths financial market participants will go to in an attempt to anticipate Federal Reserve policy changes. The Economic Naturalist 26.4 illustrates the type of information financial investors look for, and why it is so important to them.
The Economic Naturalist 26.4
Why does news of inflation hurt the stock market?
Financial market participants watch data on inflation extremely closely. A report that inflation is increasing or is higher than expected often causes stock prices to fall sharply. Why does bad news about inflation hurt the stock market?
Investors in the financial markets worry about inflation because of its likely impact on Federal Reserve policy. Financial investors understand that the Fed, when faced with signs of an expansionary gap, is likely to raise interest rates in an attempt to reduce planned spending and “cool down” the economy. This type of contractionary policy action hurts stock prices in two ways. First, it slows down economic activity, reducing the expected sales and profits of companies whose shares are traded in the stock market. Lower profits, in turn, reduce the dividends those firms are likely to pay their shareholders.
Second, higher real interest rates reduce the value of stocks by increasing the required return for holding stocks. We saw in Chapter 23, Financial Markets and International Capital Flows, that an increase in the return financial investors require in order to hold stocks lowers current stock prices. Intuitively, if interest rates rise, interest-bearing alternatives to stocks such as newly issued government bonds will become more attractive to investors, reducing the demand for, and hence the price of, stocks.
The Economic Naturalist 26.5
Should the Federal Reserve respond to changes in asset prices?
Many credit the Federal Reserve and its chairman, Alan Greenspan, for effective monetary policymaking that set the stage for sustained economic growth and rising asset prices throughout the 1990s—in particular, in the second half of the decade. Between January 1995 and March 2000, the S&P 500 stock market index rose from a value of 459 to 1,527, a phenomenal 233 percent increase in just over five years, as the U.S. economy enjoyed a record-long business cycle expansion. Indeed, the stock market’s strong, sustained rise helped to fuel additional consumer spending, which in turn promoted further economic expansion.
However, as stock prices fell sharply in the two years after their March 2000 peak, some people questioned whether the Federal Reserve should have preemptively raised interest rates to constrain investors’ “irrational exuberance.”10 Overly optimistic investor sentiment led to a speculative run-up in stock prices that eventually burst in 2000 as investors began to realize that firms’ earnings could not support the stock prices that were being paid. Earlier intervention by the Federal Reserve, critics argued, would have slowed down the dramatic increase in stock prices and therefore could have prevented the resulting stock market “crash” and the resulting loss of consumer wealth.
Similar criticism was raised toward the Fed after the collapse of the housing bubble and the ensuing financial crisis of 2007–2008. Like stock prices, housing prices rose dramatically in the late 1990s, and they continued to rise into the early 2000s even as stock prices fell. Housing prices accelerated further during 2004–2005, increasing more than 15 percent a year. However, prices slowed in 2006, and fell sharply in the following years. In light of the severity of the financial crisis and the deep global recession that followed, some people again questioned whether the accommodative monetary policy of the Fed in the early 2000s (see The Economic Naturalist 26.2) contributed to the housing bubble.
As this chapter makes clear, the Federal Reserve’s primary focus is on reducing output gaps and keeping inflation low. Should the Fed also respond to changing asset prices when it makes decisions about monetary policy?
At a symposium in August 2002, Alan Greenspan defended the Fed’s monetary policymaking performance in the late 1990s, pointing out that it is very difficult to identify asset bubbles—surges in prices of assets to unsustainable levels—“until after the fact—that is, when its bursting confirm(s) its existence.”11 Even if such a speculative bubble could be identified, Greenspan noted, the Federal Reserve could have done little—short of “inducing a substantial contraction in economic activity”—to prevent investors’ speculation from driving up stock prices. Indeed, Greenspan claimed, “the notion that a well-timed incremental tightening could have been calibrated to prevent the late 1990s bubble is almost surely an illusion.” Rather, the Federal Reserve was focusing as early as 1999 on policies that would “mitigate the fallout when it occurs and, hopefully, ease the transition to the next expansion.”12
Seven years later, at the annual meeting of the American Economic Association in January 2010, then Fed chair Ben Bernanke delivered a speech defending the Fed’s monetary policy during the early 2000s.13 The evidence reviewed in his speech suggested that the links between the Fed’s monetary policy and the rapid rise in housing prices that occurred at roughly the same time were, at best, weak. Rather, the evidence pointed to increased use of “exotic” types of mortgages with very low down payment—in which both lenders and borrowers knew that the only way borrowers could afford making future payments would be a continued rise in home values—as a more likely cause of the housing bubble. This in turn suggested that the best response to the housing bubble would have been better regulation, such as tougher limits on risky mortgage lending, rather than tighter monetary policy.
Asset price bubbles can cause severe damage. The question of how we can improve our institutions and policymaking framework to reduce the risk of their occurrence is sure to remain an important topic for macroeconomists to study. While monetary policy cannot be ruled out as part of the answer, in general, regulation that is focused directly on the causes of bubbles is likely to be a more effective first line of defense.
THE FED’S POLICY REACTION FUNCTION
The Fed attempts to stabilize the economy by manipulating the real interest rate. When the economy faces a recessionary gap, the Fed reduces the real interest rate in order to stimulate spending. When an expansionary gap exists, so that inflation threatens to become a problem, the Fed restrains spending by raising the real interest rate. Economists sometimes find it convenient to summarize the behavior of the Fed in terms of a policy reaction function. In general, a policy reaction function describes how the action a policymaker takes depends on the state of the economy. Here, the policymaker’s action is the Fed’s choice of the real interest rate, and the state of the economy is given by factors such as the output gap or the inflation rate. The Economic Naturalist 26.6 describes one attempt to quantify the Fed’s policy reaction function.
The Economic Naturalist 26.6
What is the Taylor rule?
In 1993, economist John Taylor proposed a “rule,” now known as the Taylor rule, to describe the behavior of the Fed.14 What is the Taylor rule? Does the Fed always follow it?
The rule Taylor proposed is not a rule in any legal sense but is, instead, an attempt to describe the Fed’s behavior in terms of a quantitative policy reaction function. Taylor’s “rule” can be written as
where r is the real interest rate set by the Fed, expressed as a decimal (for example, 5% = 0.05); Y − Y* is the current output gap (the difference between actual output and potential output); (Y − Y*)/Y* is the output gap relative to potential output; and π is the inflation rate, expressed as a decimal (for example, a 2 percent inflation rate is expressed as 0.02). According to the Taylor rule, the Fed responds to both output gaps and the rate of inflation. For example, the formula implies that if a recessionary gap equal to a fraction 0.01 of potential output develops, the Fed will reduce the real interest rate by 0.5 percentage point (that is, 0.005). Similarly, if inflation rises by 1 percentage point (0.01), according to the Taylor rule the Fed will increase the real interest rate by 0.5 percentage point (0.005). In his 1993 paper, Taylor showed that his rule did in fact describe the behavior of the Fed under Chairman Alan Greenspan reasonably accurately between 1987 and 1992 . Thus the Taylor rule is a real-world example of a policy reaction function.
Although the Taylor rule worked well as a description of the Fed’s behavior in the five years preceding the publication of Taylor’s 1993 paper, the rule has worked less well in describing the Fed’s behavior in the years following its publication. Modified variants of the Taylor rule, in which the Fed reacts more strongly to output gaps than the original rule suggested, or in which the Fed reacts to inflation forecasts rather than to current inflation, appear to provide better descriptions of the Fed’s behavior in the past 20 years. While different economists prefer different versions of the Taylor rule, we reiterate that it is not a rule in any legal sense. The Fed is perfectly free to deviate from it and does so when circumstances warrant. Still, variants of the Taylor rule provide a useful benchmark for assessing, and predicting, the Fed’s actions.
CONCEPT CHECK 26.5
This exercise asks you to apply the Taylor rule. Suppose inflation is 3 percent and the output gap is zero. According to the Taylor rule, at what value should the Fed set the real interest rate? The nominal interest rate? Suppose the Fed were to receive new information showing that there is a 1 percent recessionary gap (inflation is still 3 percent). According to the Taylor rule, how should the Fed change the real interest rate, if at all?
Notice that according to the Taylor rule, the Fed responds to two variables—the output gap and inflation. In principle, any number of economic variables, from stock prices to the value of the dollar in terms of the Japanese yen, could affect Fed policy and thus appear in the policy reaction function. For the sake of simplicity, in applying the policy reaction function idea in the next chapter, we will assume that the Fed’s choice of the real interest rate depends on only one variable—the rate of inflation. This simplification will not change our main results in any significant way. Furthermore, as we will see, having the Fed react only to inflation captures the most important aspect of Fed behavior—namely, its tendency to raise the real interest rate when the economy is “overheating” (experiencing an expansionary gap) and to reduce it when the economy is sluggish (experiencing a recessionary gap).
Table 26.2 describes an example of a policy reaction function according to which the Fed reacts only to inflation. According to the policy reaction function given in the table, the higher the rate of inflation , the higher the real interest rate set by the Fed. This relationship is consistent with the idea that the Fed responds to an expansionary gap (which threatens to lead to increased inflation) by raising the real interest rate. Figure 26.8 is a graph of this policy reaction function. The vertical axis of the graph shows the real interest rate chosen by the Fed; the horizontal axis shows the rate of inflation. The upward slope of the policy reaction function captures the idea that the Fed reacts to increases in inflation by raising the real interest rate.
How does the Fed determine its policy reaction function? In practice, the process is a complex one, involving a combination of statistical analysis of the economy and human judgment. However, two useful insights into the process can be drawn even from the simplified policy reaction function shown in Table 26.2 and Figure 26.8. First, as we mentioned earlier in the chapter, though the Fed controls the real interest rate in the short run, in the long run the real interest rate is determined by the balance of saving and investment. To illustrate the implication of this fact for the Fed’s choice of policy reaction function, suppose that the Fed estimates the long-run value of the real interest rate (as determined by the supply and demand for saving) to be 4 percent, or 0.04. By examining Table 26.2, we can see that the Fed’s policy reaction function implies a long-run value of the real interest rate of 4 percent only if the inflation rate in the long run is 2 percent. Thus the Fed’s choice of this policy reaction function makes sense only if the Fed’s long-run target rate of inflation is 2 percent. We conclude that one important determinant of the Fed’s policy reaction function is the policymakers’ objective for inflation.
FIGURE 26.8 An Example of a Fed Policy Reaction Function.This hypothetical example of a policy reaction function for the Fed shows the real interest rate the Fed sets in response to any given value of the inflation rate. The upward slope captures the idea that the Fed raises the real interest rate when inflation rises. The numerical values in the figure are from Table 26.2.
Second, the Fed’s policy reaction function contains information not only about the central bank’s long-run inflation target but also about how aggressively the Fed plans to pursue that target. To illustrate, suppose the Fed’s policy reaction function was very flat, implying that the Fed changes the real interest rate rather modestly in response to increases or decreases in inflation. In this case we would conclude that the Fed does not intend to be very aggressive in its attempts to offset movements in inflation away from the target level. In contrast, if the reaction function slopes steeply upward, so that a given change in inflation elicits a large adjustment of the real interest rate by the Fed, we would say that the Fed plans to be quite aggressive in responding to changes in inflation.
RECAP
MONETARY POLICY AND THE ECONOMY
· An increase in the real interest rate reduces both consumption spending and planned investment spending. Through its control of the real interest rate, the Fed is thus able to influence planned spending and short-run equilibrium output. To fight a recession (a recessionary output gap), the Fed should lower the real interest rate, stimulating planned spending and output. Conversely, to fight the threat of inflation (an expansionary output gap), the Fed should raise the real interest rate, reducing planned spending and output.
· The Fed’s policy reaction function relates its policy action (specifically, its setting of the real interest rate) to the state of the economy. For the sake of simplicity, we consider a policy reaction function in which the real interest rate set by the Fed depends only on the rate of inflation. Because the Fed raises the real interest rate when inflation rises, in order to restrain spending, the Fed’s policy reaction is upward-sloping. The Fed’s policy reaction function contains information about the central bank’s long-run target for inflation and the aggressiveness with which it intends to pursue that target.
MONETARY POLICYMAKING: ART OR SCIENCE?
In this chapter, we analyzed the basic economics underlying real-world monetary policy. As part of the analysis, we worked through some examples showing the calculation of the real interest rate that is needed to restore output to its full-employment level. While those examples are useful in understanding how monetary policy works—as with our analysis of fiscal policy in Chapter 25, Spending and Output in the Short Run—they overstate the precision of monetary policymaking. The real-world economy is highly complex, and our knowledge of its workings is imperfect. For example, though we assumed in our analysis that the Fed knows the exact value of potential output, in reality potential output can be estimated only approximately. As a result, at any given time the Fed has only a rough idea of the size of the output gap. Similarly, Fed policymakers have only an approximate idea of the effect of a given change in the real interest rate on planned spending, or the length of time before that effect will occur. Because of these uncertainties, the Fed tends to proceed cautiously. Fed policymakers avoid large changes in interest rates and rarely raise or lower the federal funds rate more than one-half of a percentage point (from 5.50 percent to 5.00 percent, for example) at any one time. Indeed, the typical change in the interest rate is one-quarter of a percentage point.
Is monetary policymaking an art or a science, then? In practice it appears to be both. Scientific analyses, such as the development of detailed statistical models of the economy, have proved useful in making monetary policy. But human judgment based on long experience—what has been called the “art” of monetary policy—plays a crucial role in successful policymaking and is likely to continue to do so.
SUMMARY
· Monetary policy is one of two types of stabilization policy, the other being fiscal policy. Although in the basic model of the market for money, the Federal Reserve operates by controlling the money supply, the media’s attention nearly always focuses on the Fed’s decisions about interest rates, not the money supply. There is no contradiction between these two ways of looking at monetary policy, however, as the Fed’s ability to control the money supply is the source of its ability to control interest rates. (LO1)
· The nominal interest rate is determined in the market for money, which has both a demand side and a supply side. For the economy as a whole, the demand for money is the amount of wealth households and businesses choose to hold in the form of money (such as cash or checking accounts). The demand for money is determined by a comparison of cost and benefits. The opportunity cost of holding money, which pays either zero interest or very low interest, is the interest that could have been earned by holding interest-bearing assets instead of money. Because the nominal interest rate measures the opportunity cost of holding a dollar in the form of money, an increase in the nominal interest rate reduces the quantity of money demanded. The benefit of money is its usefulness in carrying out transactions. All else being equal, an increase in the volume of transactions increases the demand for money. At the macroeconomic level, an increase in the price level or in real GDP increases the dollar volume of transactions, and thus the demand for money. (LO1)
· The money demand curve relates the aggregate quantity of money demanded to the nominal interest rate. Because an increase in the nominal interest rate increases the opportunity cost of holding money, which reduces the quantity of money demanded, the money demand curve slopes down. Factors other than the nominal interest rate that affect the demand for money will shift the demand curve to the right or left. For example, an increase in the price level or real GDP increases the demand for money, shifting the money demand curve to the right. (LO1)
· In the basic model of the market for money, the Federal Reserve determines the supply of money through the use of open-market operations. The supply curve for money is vertical at the value of the money supply set by the Fed. Money market equilibrium occurs at the nominal interest rate at which money demand equals the money supply. The Fed can reduce the nominal interest rate by increasing the money supply (shifting the money supply curve to the right) or increase the nominal interest rate by reducing the money supply (shifting the money supply curve to the left). The nominal interest rate that the Fed targets most closely is the federal funds rate, which is the rate commercial banks charge each other for very short-term loans. (LO2)
· In the short run, the Fed can control the real interest rate as well as the nominal interest rate. Recall that the real interest rate equals the nominal interest rate minus the inflation rate. Because the inflation rate adjusts relatively slowly, the Fed can change the real interest rate by changing the nominal interest rate. In the long run, the real interest rate is determined by the balance of saving and investment. (LO2)
· The Fed can effectively control the amount of bank reserves through tools that include open-market operations and discount window lending. The Fed can also set reserve requirements (a legally binding minimum on banks’ reserve-deposit ratio). This, however, gives the Fed only partial control over the money supply—something that the basic model of the market for money does not consider. In particular, a Fed-initiated increase in bank reserves will not lead to an increase in the money supply if banks absorb the increase in reserves by letting their reserve-deposit ratios increase at the same pace. (LO3)
· In December 2008 the federal funds rate effectively reached its zero lower bound. In the years that followed, the Fed used unconventional methods to stimulate the economy. Such methods, including quantitative easing and forward guidance, go beyond the basic model of the market for money, which assumes that all the interest rates in the economy move together and that the Fed fully controls the money supply. The unconventional methods used by the Fed directly aimed at lowering interest rates in the economy that were higher than the federal funds rate. Although the above two basic assumptions did not hold well after December 2008 (which explains why the Fed had to resort to unconventional methods to keep stimulating the economy), they have provided useful approximations even in the unusual times we have seen since 2008. This provides some justification for continuing to make these simplifying assumptions, in particular when speaking of the Fed’s control of the interest rate. Since December 2015, the Fed has gradually increased the federal funds rate, getting away from the zero lower bound and starting the process of monetary-policy normalization. (LO4)
· The Federal Reserve’s actions affect the economy because changes in the real interest rate affect spending. For example, an increase in the real interest rate raises the cost of borrowing, reducing consumption and investment. Thus, by increasing the real interest rate, the Fed can reduce spending and short-run equilibrium output. Conversely, by reducing the real interest rate, the Fed can stimulate aggregate expenditure and thereby raise short-run equilibrium output. The Fed’s ultimate objective is to eliminate output gaps. To eliminate a recessionary output gap, the Fed will lower the real interest rate. To eliminate an expansionary output gap, the Fed will raise the real interest rate. (LO5)
· A policy reaction function describes how the action a policymaker takes depends on the state of the economy. For example, a policy reaction function for the Fed could specify the real interest rate set by the Fed for each value of inflation. (LO5)
· In practice, the Fed’s information about the level of potential output and the size and speed of the effects of its actions is imprecise. Thus monetary policymaking is as much an art as a science. (LO6)
KEY TERMS
demand for money
discount rate
discount window lending
excess reserves
federal funds rate
forward guidance
money demand curve
policy reaction function
portfolio allocation decision
quantitative easing (QE)
reserve requirements
zero lower bound
REVIEW QUESTIONS
1. 1.What is the demand for money? How does the demand for money depend on the nominal interest rate? On the price level? On income? Explain in terms of the costs and benefits of holding money. (LO1)
2. 2.Show graphically how the Fed controls the nominal interest rate. Can the Fed control the real interest rate? (LO2)
3. 3.What effect does an open-market purchase of bonds by the Fed have on nominal interest rates? Discuss in terms of (a) the effect of the purchase on bond prices and (b) the effect of the purchase on the supply of money. (LO2)
4. 4.What other methods does the Fed have for affecting short-run interest rates besides open-market operations? Discuss whether these methods can be used for only lowering short-run interest rates, for only increasing them, or for both lowering and increasing them. (LO3)
5. 5.In a situation where short-run interest rates have hit their zero lower bound, can the Fed still lower other, higher, longer-term interest rates? Discuss specific actions that the Fed can take and how they would work. (LO4)
6. 6.Why does the real interest rate affect planned aggregate expenditure? Give examples. (LO5)
7. 7.The Fed faces a recessionary gap. How would you expect it to respond? Explain step by step how its policy change is likely to affect the economy. (LO5)
8. 8.The Fed decides to take a contractionary policy action. What would you expect to happen to the nominal interest rate, the real interest rate, and the money supply? Under what circumstances would this type of policy action most likely be appropriate? (LO5)
9. 9.Discuss why the analysis of this chapter overstates the precision with which monetary policy can be used to eliminate output gaps. (LO6)
PROBLEMS
1. 1.During the heavy Christmas shopping season, sales of retail stores, online sales firms, and other merchants rise significantly. (LO1)
a. What would you expect to happen to the money demand curve during the Christmas season? Show graphically.
b. If the Fed took no action, what would happen to nominal interest rates around Christmas?
c. In fact, nominal interest rates do not change significantly in the fourth quarter of the year, due to deliberate Fed policy. Explain and show graphically how the Fed can ensure that nominal interest rates remain stable around Christmas.
2. 2.The following table shows Uma’s estimated annual benefits of holding different amounts of money: (LO1)
a. How much money will Uma hold on average if the nominal interest rate is 9 percent? 5 percent? 3 percent? Assume that she wants her money holding to be a multiple of $100. (Hint: Make a table comparing the extra benefit of each additional $100 in money holdings with the opportunity cost, in terms of forgone interest, of additional money holdings.)
b. Graph Uma’s money demand curve for interest rates between 1 percent and 12 percent.
3. 3.How would you expect each of the following to affect the economywide demand for U.S. money? Explain. (LO1)
a. Competition among brokers forces down the commission charge for selling holdings of bonds or stocks.
b. Grocery stores begin to accept credit cards in payment.
c. Financial investors become concerned about increasing riskiness of stocks.
4. 4.Suppose the economywide demand for money is given by P(0.2Y − 25,000i). The price level P equals 3.0, and real output Y equals 10,000. At what value should the Fed set the nominal money supply if (LO1, LO2)
a. It wants to set the nominal interest rate at 4 percent.
b. It wants to set the nominal interest rate at 6 percent.
5. 5.Using a supply and demand graph of the market for money, show the effects on the nominal interest rate if the Fed takes the following monetary policy actions: (LO2, LO3)
a. The Fed lowers the discount rate and increases discount lending.
b. The Fed increases the reserve requirements for commercial banks.
c. The Fed conducts open market sales of government bonds to the public.
d. The Fed decreases the reserve requirements for commercial banks.
6. 6.Assume that the central bank of a nation decides to lower the reserve requirements for commercial banks. What changes can one predict regarding the amount of: required reserves, excess reserves, the amount of loans generated by commercial banks, the economywide money supply, and finally interest rates in that nation? (LO3)
7. 7.In August of 2015, the Chinese central bank decided to reduce China’s required reserve-deposit ratio from 18.5% to 18%. Assuming no change in the amount of cash held by the Chinese public, that commercial banks lend all their excess reserves, and that bank reserves was a constant 4,329 billion yuan both before and after the change, compute the maximum change in Chinese banks deposits as a consequence of the change in the reserve-deposit. (LO3)
8. 8.Which of the following is not an example of an “unconventional” monetary policy tool available to the Fed when the federal funds rate is already at or close to zero: forward guidance, quantitative easing, or discount lending? (LO4)
9. 9.Explain why an increase in interest that banks receive from the Fed on the required and excess reserves that banks hold with the Fed, would also increase the interest rates that commercial banks charge their borrowers. (LO4)
10. An economy is described by the following information:
The real interest rate, expressed as a decimal, is 0.10 (that is, 10 percent). (LO5)
a. Find a numerical equation relating planned aggregate expenditure to output.
b. Using a table (or algebra), solve for short-run equilibrium output.
c. Show your result graphically using the Keynesian cross diagram.
10. 11.For the economy described in Problem 10, suppose that potential output Y* equals 12,000. (LO5)
a. What real interest rate should the Fed set to bring the economy to full employment? You may take as a given that the multiplier for this economy is 5.
b. Repeat part a for the case in which potential output Y* equals 9,000.
c. Show that the real interest rate you found in part a sets national saving at potential output, defined as Y*− C − G, equal to planned investment, IP. This result shows that the real interest rate must be consistent with equilibrium in the market for saving when the economy is at full employment. (Hint: Review the material on national saving in Chapter 21, Saving and Capital Formation.)
11. 12.* Here is another set of equations describing an economy: (LO5)
a. Find a numerical equation relating planned aggregate expenditure to output and to the real interest rate.
b. At what value should the Fed set the real interest rate to eliminate any output gap? (Hint: Set output Y equal to the value of potential output given above in the equation you found in part a. Then solve for the real interest rate that also sets planned aggregate expenditure equal to potential output.)
12. 13. What are some of the uncertainties that Fed policymakers face, and how do these uncertainties affect monetary policymaking? (LO6)
ANSWERS TO CONCEPT CHECKS
1. 26.1At 4 percent interest, the benefit of each $10,000 reduction in cash holdings is $400 per year (4% × $10,000). In this case, the cost of the extra armored car service, $500 a year, exceeds the benefit of reducing cash holdings by $10,000. Kim’s restaurants should therefore continue to hold $50,000 in cash. Comparing this result with Example 26.2, you can see that the demand for money by Kim’s restaurants is lower, the higher the nominal interest rate. (LO1)
2. 26.2If the nominal interest rate is above its equilibrium value, then people are holding more money than they would like. To bring their money holdings down, they will use some of their money to buy interest-bearing assets such as bonds.
If everyone is trying to buy bonds, however, the price of bonds will be bid up. An increase in bond prices is equivalent to a fall in market interest rates. As interest rates fall, people will be willing to hold more money. Eventually interest rates will fall enough that people are content to hold the amount of money supplied by the Fed, and the money market will be in equilibrium. (LO1)
3. 26.3If r = 0.03, then consumption is C = 640 + 0.8(Y − 250) − 400(0.03) + 428 + 0.8Y, and planned investment is IP = 250 − 600(0.03) = 232. Planned aggregate expenditure is given by = 4,900. Notice that the lower interest of
To find short-run equilibrium output, we can construct a table analogous to Table 26.2. As usual, some trial and error is necessary to find an appropriate range of guesses for output (column 1).
Short-run equilibrium output equals 4,900, as that is the only level of output that satisfies the condition Y = PAE.
The answer can be obtained more quickly by simply setting Y = PAE and solving for short-run equilibrium output Y. Remembering that PAE = 980 + 0.8Y and substitution for PAE, we get
So lowering the real interest rate from 5 percent to 3 percent increases short-run equilibrium output from 4,800 (as found in Example 26.4) to 4,900.
If you have read Appendix B in Chapter 25, Spending and Output in the Short Run, on the multiplier, there is yet another way to find the answer. Using that appendix, we can determine that the multiplier in this model is 5, since 1/(1− c) = 1/(1− 0.8) = 5. Each percentage point reduction in the real interest rate increases consumption by 4 units and planned investment by 6 units, for a total impact on planned spending of 10 units per percentage point reduction. Reducing the real interest rate by 2 percentage points, from 5 percent to 3 percent, thus increases autonomous expenditure by 20 units. Because the multiplier is 5, an increase of 20 in autonomous expenditure raises short-run equilibrium output by 20 × 5 = 100 units, from the value of 4,800 we found in Example 26.4 to the new value of 4,900. (LO5)
4. 26.4When the real interest rate is 5 percent, output is 4,800. Each percentage point reduction in the real interest rate increases autonomous expenditure by 10 units. Since the multiplier in this model is 5, to raise output by 50 units, the real interest rate should be cut by 1 percentage point, from 5 percent to 4 percent. Increasing output by 50 units, to 4,850, eliminates the output gap. (LO5)
5. 26.5If π = 0.03 and the output gap is zero, we can plug these values into the Taylor rule to obtain
r = 0.01 − 0.5(0) + 0.5(0.03) = 0.025 = 2.5%.
So the real interest rate implied by the Taylor rule when inflation is 3 percent and the output gap is zero is 2.5 percent. The nominal interest rate equals the real rate plus the inflation rate, or 2.5% + 3% = 5.5%.
If there is a recessionary gap of 1 percent of potential output, the Taylor rule formula becomes
r = 0.01 − 0.5(0.01) + 0.5(0.03) = 0.02 = 2%.
The nominal interest rate implied by the Taylor rule in this case is the 2 percent real rate plus the 3 percent inflation rate, or 5 percent. So the Taylor rule has the Fed lowering the interest rate when the economy goes into recession, which is both sensible and realistic. (LO5)
APPENDIX
Monetary Policy in the Basic Keynesian Model
This appendix extends the algebraic analysis of the basic Keynesian model that was presented in Appendix A to Chapter 25, Spending and Output in the Short Run, to include the role of monetary policy. The main difference from that appendix is that in this analysis, the real interest rate is allowed to affect planned spending. We will not describe the supply and demand for money algebraically but will simply assume that the Fed can set the real interest rate r at any level it chooses.
The real interest rate affects consumption and planned investment. To capture these effects, we will modify the equations for those two components of spending as follows:
The first equation is the consumption function (recall that in the appendices, we use c for the marginal propensity to consume) with an additional term, equal to −ar. Think of a as a fixed number, greater than zero, that measures the strength of the interest rate effect on consumption. Thus the term −ar captures the idea that when the real interest rate r rises, consumption declines by a times the increase in the interest rate. Likewise, the second equation adds the term −br to the equation for planned investment spending. The parameter b is a fixed positive number that measures how strongly changes in the real interest rate affect planned investment; for example, if the real interest rate r rises, planned investment is assumed to decline by b times the increase in the real interest rate. We continue to assume that government purchases, taxes, and net exports are exogenous variables, so that 
To solve for short-run equilibrium output, we start as usual by finding the relationship of planned aggregate expenditure to output. The definition of planned aggregate expenditure is
PAE = C + IP + G + NX.
Substituting the modified equations for consumption and planned investment into this definition, along with the exogenous values of government spending, net exports, and taxes, we get
The first term in brackets on the right side describes the behavior of consumption, and the second bracketed term describes planned investment. Rearranging this equation in order to group together terms that depend on the real interest rate and terms that depend on output, we find
This equation is similar to Equation 25A.1, as shown in Appendix A to Chapter 25, Spending and Output in the Short Run, except that it has an extra term, –(a + b)r, on the right side. This extra term captures the idea that an increase in the real interest rate reduces consumption and planned investment, lowering planned spending. Notice that the term –(a + b)r is part of autonomous expenditure, since it does not depend on output. Since autonomous expenditure determines the intercept of the expenditure line in the Keynesian cross diagram, changes in the real interest rate will shift the expenditure line up (if the real interest rate decreases) or down (if the real interest rate increases).
To find short-run equilibrium output, we uses the definition of short-run equilibrium output to set Y = PAE and solve for Y:
(26A.1)
Equation 26A.1 shows that short-run equilibrium output once again equals the multiplier, 1/(1 − c), times autonomous expenditure, 
Autonomous expenditure in turn depends on the real interest rate r. The equation also shows that the impact of a change in the real interest rate on short-run equilibrium output depends on two factors: (1) the effect of a change in the real interest rate on consumption and planned investment, which depends on the magnitude of (a + b), and (2) the size of the multiplier, 1/(1 − c), which relates changes in autonomous expenditure to changes in short-run equilibrium output. The larger the effect of the real interest rate on planned spending, and the larger the multiplier, the more powerful will be the effect of a given change in the real interest rate on short-run equilibrium output.
To check Equation 26A.1, we can use it to resolve Example 26.4. In that example, we are given 
= 640, 
= 250, 
= 300, 
= 20, 
= 250, c = 0.8, a = 400, and b = 600. The real interest rate set by the Fed is 5 percent, or 0.05. Substituting these values into Equation 26A.1 and solving, we obtain
This is the same result we found in Example 26.4.
1Robert H. Frank, “Safety in Numbers,” New York Times Magazine, November 28, 1999, p. 35.
2We examined risk, return, and diversification in Chapter 23, Financial Markets and International Capital Flows.
3The sale of existing government bonds by the Federal Reserve in an open-market sale should not be confused with the sale of newly issued government bonds by the Treasury when it finances government budget deficits. Whereas open-market sales reduce the money supply, Treasury sales of new bonds do not affect the money supply. The difference arises because the Federal Reserve does not put the money it receives in an open-market sale back into circulation, leaving less money for the public to hold. In contrast, the Treasury puts the money it receives from selling newly issued bonds back into circulation as it purchases goods and services.
4The Federal Open Market Committee’s announcements are available on the Federal Reserve’s website, www.federalreserve.gov.
5Be careful not to confuse the discount rate and the federal funds rate. The discount rate is the interest rate commercial banks pay to the Fed; the federal funds rate is the interest rate commercial banks charge each other for short-term loans.
6You can verify this by looking again at the second term of Equation 26.1. This second term represents the noncurrency component of the money supply. While the Fed controls its numerator (bank reserves), it only partially controls its denominator (desired reserve-deposit ratio) because the Fed can set only a legally binding minimum, but not a maximum, on the denominator. Indeed, banks can choose to let the denominator increase when the Fed increases the numerator, breaking the simple link from increased reserves to increased money supply. Banks could in principle even let the denominator increase at the same pace as the numerator, keeping the second term of Equation 26.1 constant, and thus preventing the increase in reserves from having any effect on the money supply.
7“How Does Forward Guidance about the Federal Reserve’s Target for the Federal Funds Rate Support the Economic Recovery?” updated September 17, 2015, www.federalreserve.gov/monetarypolicy/fomcminutes 20150917.htm.
8The federal funds rate can be somewhat below the interest rate that the Fed pays on reserves because some nonbank financial institutions are not eligible to earn interest on the balances they keep with the Fed and, therefore, have incentives to lend reserves at rates below the Fed’s interest rate on reserves. However, as banks can profit by borrowing from such institutions and then receiving interest from the Fed on the borrowed reserves, the price of these reserves—the federal funds rate—is bid up until it is closely below the Fed’s interest rate on reserves. In addition, the Fed can offer to borrow directly from such institutions (through an arrangement called a reverse repurchase agreement), reducing their incentives to lend out reserves at rates below the rates offered by the Fed.
9Because a higher real interest rate also reduces the amount households must put aside to reach a given savings target, the net effect of a higher real interest rate on saving is theoretically ambiguous. However, empirical evidence suggests that higher real interest rates have a modest positive effect on saving.
10Fed Chairman Alan Greenspan mentioned the possibility of “irrational exuberance” driving investor behavior in a December 5, 1996, speech, which is available online at www.federalreserve.gov/boarddocs/speeches/1996/ 19961205.htm.
11The text of Greenspan’s speech is available online at www.federalreserve.gov/boarddocs/speeches/2002/ 20020830/default.htm.
12The Federal Reserve’s Semiannual Report on Monetary Policy, testimony of Chairman Alan Greenspan before the Committee on Banking and Financial Services, U.S. House of Representatives, July 22, 1999. Available online at www.federalreserve.gov/boarddocs/hh/1999/July/Testimony.htm.
13The text of the speech is available online at www.federalreserve.gov/newsevents/speech/bernanke20100103a.htm.
14John Taylor, “Discretion versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy, 1993, pp. 195–227.
*Denotes more difficult problem.