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5 How does the IS–LM model fit the facts?

5 How does the IS–LM model fit the facts?

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Chapter 5  Financial markets: The IS–LM model   99







Introducing dynamics formally would be difficult. But, as we did earlier (see Chapter 3),

we can describe the basic mechanisms in words. Some of the mechanisms will be familiar

from that earlier discussion, some are new:

















Consumers are likely to take some time to adjust their consumption following a change in

disposable income.

Firms are likely to take some time to adjust investment spending following a change in

their sales.

Firms are likely to take some time to adjust investment spending following a change in the

interest rate.

Firms are likely to take some time to adjust production following a change in their sales.



So, in response to an increase in taxes, it takes some time for consumption spending to respond

to the decrease in disposable income, some more time for production to decrease in response

to the decrease in consumption spending, yet more time for investment to decrease in response

to lower sales, for consumption to decrease in response to the decrease in income, and so on.

In response to a decrease in the interest rate, it takes some time for investment spending

to respond to the decrease in the interest rate, some more time for production to increase

in response to the increase in demand, yet more time for consumption and investment to

increase in response to the induced change in output, and so on.

Describing precisely the adjustment process implied by all these sources of dynamics is

obviously complicated. But the basic implication is straightforward: time is needed for output

to adjust to changes in fiscal and monetary policy. How much time? This question can only

be answered by looking at the data and using econometrics. Figure 5.13 shows the results of

such an econometric study, which uses data from the euro area and the United States from

Euro area



United States



Effect of a 1% increase in interest

rate on output



Effect of a 1% increase in interest

rate on output



Output-Mod1



0.15

0.10

0.05

0

–0.05

–0.10

–0.15

–0.20

–0.25

–0.30

0



5



10



Output-US



0.15

0.10

0.05

0

–0.05

–0.10

–0.15

–0.20

–0.25

–0.30

15



0



5



Quarter



Prices-Mod1



Prices-US



0.10



0.05



0.05



0



0



–0.05



–0.05



–0.10



–0.10



–0.15



–0.15



–0.20



–0.20



–0.25



–0.25

0



5



10



0



15



5



Quarter



Interest-rate-Mod1



0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

–0.1



10



15



Quarter

Effect of a 1% increase in interest rate

on the interest rate



Effect of a 1% increase in interest rate

on the interest rate



Interest-rate-US



0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

–0.1



–0.2

10



5

Quarter



15



Figure 5.13

The effects of an increase

in interest rates in the euro

area and in the US

In the short run an increase in the

interest rate reduces output but has a

limited effect on inflation.



–0.2

0



M05 Macroeconomics 85678.indd 99



15



Effect of a 1% increase in interest

rate on prices



Effect of a 1% increase in interest

rate on prices

0.10



10

Quarter



0



5



10

Quarter



15



Source: G. Peersman and F. Smets, ‘The

monetary transmission mechanism in the

euro area: more evidence from VAR analysis’,

European Central Bank, Working Paper

No. 91, December 2001.



30/05/2017 09:08



100  THE CORE The short run

1980 to 1998. The study compares the effects of an increase in the interest rate in the euro

Consider that the average size of a

change in the interest rate in the euro

area and in the United States. It traces the typical effects of such an increase on a number of

area is much smaller than in the United ➤ macroeconomic variables.

States. It is on average equal to 30 basis

Each box in Figure 5.13 represents the effects of a change in the interest rate on a given

points in the euro area compared with

variable.

Each box contains three lines. The black line at the centre represents the best esti45 basis points in the United States.

mate of the effect of a change in the interest rate on the variable considered in that frame.

This means that the typical monetary

policy decision in the euro area is 50%

The blue lines and the space between them represent a confidence band, an interval within

smaller than in the United States.

which the true value lies with a probability of 90%.

There is no such thing in economet- ➤

rics as learning the exact value of a

coefficient or the exact effect of one

variable on another. Rather, what

econometrics does is to provide us a

best estimate – here, the thick line –

and a measure of confidence we can

have in the estimate – here, the confidence band.



Figure 5.13(a) shows the effects of an increase in the interest rate, respectively on production and prices in the euro area (the last box at the bottom shows the evolution of the interest

rate itself). The percentage change of variables is shown on the vertical axis and the time,

measured in quarters, is shown on the horizontal axis.

Looking at the best estimate – the black line – we can see that increasing the interest rate leads

to a reduction in output. In the euro area, the greatest decline in production is reached in the second and third quarters after the increase in the interest rate, compared to five quarters in the USA.

The second panel from top shows the evolution of the price level. Remember that one of

the assumptions of the IS–LM model is that the price level is given, and thus does not vary

with changes in demand. The figure shows that this assumption is not a bad representation of

reality in the short term. In the euro area the price level remains almost unchanged approximately for the first five quarters (compared to two quarters in the USA). It is only after the

first five quarters that the price level begins to decline. This suggests that the IS–LM model

becomes less reliable when we look at the medium term: in the medium term we can no

longer assume that the price level is given, and changes in prices become significant.

Comparing the euro area and the USA we observe that prices react more rapidly in the

USA, although the size of the responses are eventually the same.

Figure 5.13 provides two important lessons. First, it gives us a sense of the dynamic adjustment of output and other variables to monetary policy. Second, and more fundamentally, it

shows that what we observe in the economy is consistent with the implications of the IS–LM

model. This does not prove that the IS–LM model is the right model. It may be that what we

observe in the economy is the result of a completely different mechanism, and the fact that the

IS–LM model fits well is a coincidence. But this seems unlikely. The IS–LM model looks like a

solid basis on which to build when looking at movements in activity in the short run. Later on,

we shall extend the model to look at the role of expectations (Chapters 14 to 16) and the implications of openness in goods and financial markets (Chapters 17 to 20). But we must first understand what determines output in the medium run. This is the topic of the next four chapters.



Summary





The IS–LM model characterises the implications of equilibrium in both the goods and the financial markets.







The IS relation and the IS curve show the combinations of

the interest rate and the level of output that are consistent

with equilibrium in the goods market. An increase in the

interest rate leads to a decline in output. Consequently,

the IS curve is downward sloping.







The LM relation and the LM curve show the combinations

of the interest rate and the level of output consistent with

equilibrium in financial markets. Under the assumption that

the central bank chooses the interest rate, the LM curve is a

horizontal line at the interest rate chosen by the central bank.







A fiscal expansion shifts the IS curve to the right, leading

to an increase in output. A fiscal contraction shifts the IS

curve to the left, leading to a decrease in output.







A monetary expansion shifts the LM curve down, leading

to a decrease in the interest rate and an increase in output.



M05 Macroeconomics 85678.indd 100



A monetary contraction shifts the LM curve up, leading to

an increase in the interest rate and a decrease in output.





The combination of monetary and fiscal policies is known

as the monetary–fiscal policy mix, or simply the policy

mix. Sometimes monetary and fiscal policy are used in

the same direction. Sometimes, they are used in opposite

directions. Together, fiscal contraction and monetary

expansion can, for example, achieve a decrease in the

budget deficit while avoiding a decrease in output.







The IS–LM model appears to describe well the behaviour of the economy in the short run. In particular, the

effects of monetary policy appear to be similar to those

implied by the IS–LM model once dynamics are introduced in the model. An increase in the interest rate due

to a monetary contraction leads to a steady decrease

in output, with the maximum effect taking place after

about eight quarters.



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Chapter 5  Financial markets: The IS–LM model   101







Key Terms

IS curve 89



fiscal consolidation 92



monetary contraction 93



LM curve 91



fiscal expansion 92



monetary tightening 93



fiscal contraction 92



monetary expansion 93



monetary–fiscal

policy mix 94

confidence band 100



Questions and problems

Quick Check

All ‘Quick check’ questions and problems are available on

MyEconLab.

1.Using the information in this chapter, label each of the following statements true, false or uncertain. Explain briefly.

a. The main determinants of investment are the level of sales

and the interest rate.

b.If all the exogenous variables in the IS relation are constant, then a higher level of output can be achieved only

by lowering the interest rate.

c.The IS curve is downward sloping because goods market

equilibrium implies that an increase in taxes leads to a

lower level of output.

d.If government spending and taxes increase by the same

amount, the IS curve does not shift.

e.The LM curve is horizontal at the central bank’s policy

choice of the interest rate.

f. The real money supply is constant along the LM curve.

g. If the nominal money supply is :400 billion and the price

level rises from an index value of 100 to an index value of

103, the real money supply rises.

h.If the nominal money supply rises from :400 billion to

:420 billion and the price level rises from an index value

of 100 to 102, the real money supply rises.

i. An increase in government spending leads to a decrease

in investment in the IS–LM model.

2.Consider first the goods market model with constant

investment that we saw earlier (in Chapter 3). Consumption is given by:

C = c0 + c1(Y - T)

and I, G and T are given.

a. Solve for equilibrium output. What is the value of the multiplier for a change in autonomous spending?

Now let investment depend on both sales and the interest rate:

I = b 0 + b 1Y - b 2i

b.Solve for equilibrium output using the methods learned

previously (in Chapter 3). At a given interest rate, why is

the effect of a change in autonomous spending bigger than

what it was in part (a)? Why? (Assume c1 + b1 6 1.)



M05 Macroeconomics 85678.indd 101



c. Suppose the central bank chooses an interest rate of i.

Solve for equilibrium output at that interest rate.

d.Draw the equilibrium of this economy using an IS–LM

diagram.

3.The response of the economy to fiscal policy

a. Use an IS–LM diagram to show the effects on output of a

decrease in government spending. Can you tell what happens to investment? Why?

Now consider the following – model:

C = c0 + c1(Y - T)

I = b 0 + b 1Y - b 2i

Z = C + I + G

i = i

b.Solve for equilibrium output when the interest rate is

i. Assume c1 + b1 6 1. (Hint: You may want to rework

through Problem 2 if you are having trouble with this

step.)

c. Solve for equilibrium level of investment.

d.Let’s go behind the scenes in the money market. Use the

equilibrium in the money market M/P = d 1Y - d 2i to

solve for the equilibrium level of the real money supply

when i = i. How does the real money supply vary with

government spending?

4.Consider the money market to understand better the horizontal LM curve in this chapter. The money market relation

(equation (5.3)) is M/P = YL(i).

a. What is on the left-hand side of equation (5.3)?

b. What is on the right-hand side of equation (5.3)?

c. Go back to Figure 4.3 in the previous chapter. How is the

function L(i) represented in that figure?

d. You need to modify Figure 4.3 to represent equation (5.3)

in two ways. How does the horizontal axis have to be relabelled? What is the variable that now shifts the money

demand function? Draw a modified Figure 4.3 with the

appropriate labels.

e. Use your modified Figure 4.3 to show that (i) as output

rises, to keep the interest rate constant, the central bank

must increase the real money supply; (ii) as output falls,

to keep the interest rate constant, the central bank must

decrease the real money supply.



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102  THE CORE The short run

5.Consider the following numerical example of the IS–LM

model:

C = 200 + 0.25YD

I = 150 + 0.25Y - 1,000i

G = 250

T = 200

i = 0.05

a. Derive the IS relation. (Hint: You want an equation with

Y on the left side and everything else on the right.)

b. The central bank sets an interest rate of 5%. How is that

decision represented in the equations?

c. What is the level of real money supply when the interest

rate is 5%? Use the expression:

M/P = 2Y - 8,000i

d. Solve for the equilibrium values of C and I, and verify the

value you obtained for Y by adding C, I and G.

e. Now suppose that the central bank cuts the interest rate

to 3%. How does this change the LM curve? Solve for Y, I

and C, and describe in words the effects of an expansionary monetary policy. What is the new equilibrium value of

M/P supply?

f. Return to the initial situation in which the interest rate set

by the central bank is 5%. Now suppose that government

spending increases to G = 400. Summarise the effects of

an expansionary fiscal policy on Y, I and C. What is the

effect of the expansionary fiscal policy on the real money

supply?



Dig Deeper

All ‘Dig deeper’ questions and problems are available on

MyEconLab.

6.Investment and the interest rate

The chapter argues that investment depends negatively on the

interest rate because an increase in the cost of borrowing discourages investment. However, firms often finance their investment projects using their own funds.

If a firm is considering using its own funds (rather than borrowing) to finance investment projects, will higher interest

rates discourage the firm from undertaking these projects?

Explain. (Hint: Think of yourself as the owner of a firm that

has earned profits and imagine that you are going to use the

profits either to finance new investment projects or to buy

bonds. Will your decision to invest in new projects in your

firm be affected by the interest rate?)

7.The Bush–Greenspan policy mix

In 2001, the Fed pursued an expansionary monetary policy and

reduced interest rates. At the same time, President George W.

Bush pushed through legislation that lowered income taxes.

a. Illustrate the effect of such a policy mix on output.



M05 Macroeconomics 85678.indd 102



b.How does this policy mix differ from the Clinton–

Greenspan mix?

c. What happened to output in 2001? How do you reconcile

the fact that both fiscal and monetary policies were expansionary with the fact that growth was so low in 2002?

(Hint: What else happened?)

8.What policy mix of monetary and fiscal policy is needed to

meet the objectives given here?

a.Increase Y while keeping Qi constant. Would investment

(I) change?

b.Decrease a fiscal deficit while keeping Y constant. Why

must i also change?

9.The (less paradoxical) paradox of saving

A chapter problem at the end of Chapter 3 considered the effect

of a drop in consumer confidence on private saving and investment, when investment depended on output but not on the

interest rate. Here, we consider the same experiment in the context of the IS–LM framework, in which investment depends on

the interest rate and output but the central bank moves interest

rates to keep output constant.

a. Suppose households attempt to save more, so that consumer confidence falls. In an IS–LM diagram where the

central bank moves interest rates to keep output constant,

show the effect of the fall in consumer confidence on the

equilibrium in the economy.

b. How will the fall in consumer confidence affect consumption, investment and private saving? Will the attempt

to save more necessarily lead to more saving? Will this

attempt necessarily lead to less saving?



Explore Further

10.  The Clinton–Greenspan policy mix

As described in this chapter, during the Clinton Administration

the policy mix changed towards more contractionary fiscal

policy and more expansionary monetary policy. This question

explores the implications of this change in the policy mix, both

in theory and fact.

a. What must the Federal Reserve do to ensure that if G falls

and T rises so that combination of policies has no effect

on output. Show the effects of these policies in an IS–LM

diagram. What happens to the interest rate? What happens to investment?

b. Go to the website of the Economic Report of the President

(www.gpoaccess.gov/eop/). Look at Table B-79 in the statistical appendix. What happened to federal receipts (tax

revenues), federal outlays and the budget deficit as a percentage of GDP over the period 1992 to 2000? (Note that

federal outlays include transfer payments, which would

be excluded from the variable G, as we define it in our

IS–LM model. Ignore the difference.)



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Chapter 5  Financial markets: The IS–LM model   103







c. The Federal Reserve Board of Governors posts the recent

history of the federal funds rate at http://www.federalreserve.gov/releases/h15/data.htm. You will have to

choose to look at the rate on a daily, weekly, monthly or

annual interval. Look at the years between 1992 and 2000.

When did monetary policy become more expansionary?



that the quarterly percentage changes are annualised (i.e.

expressed as annual rates). Retrieve the quarterly data on

real GDP, consumption, gross private domestic investment

and non-residential fixed investment for the years 1999 to

2002 from Tables 1.1.1 and 1.1.2.



d. Go to Table B-2 of the Economic Report of the President and

collect data on real GDP and real gross domestic investment for the period 1992 to 2000. Calculate investment

as a percentage of GDP for each year. What happened to

investment over the period?



b.Track consumption and investment around 2000 and

2001. From Table 1.1.1, which variable had the bigger

percentage change around this time? Compare non-­

residential fixed investment with overall investment.

Which variable had the bigger percentage change?



e. Finally, go to Table B-31 and retrieve data on real GDP

per capita (in chained 2005 dollars) for the period. Calculate the growth rate for each year. What was the average

annual growth rate over the period 1992 to 2000? Later

you will learn that the average annual growth rate of US

real GDP per capita was 2.6% between 1950 and 2004

(see Chapter  10). How did growth between 1992 and

2000 compare with the post-war average?



This question asks you to examine the movements of investment and consumption before, during and after the recession

of 2001. It also asks you to consider the response of investment

and consumption to the events of 9/11.



c. From Table 1.1.2, get the contribution to GDP growth of

consumption and investment for 1999 to 2001. Calculate the average of the quarterly contributions for each

variable for each year. Now calculate the change in the

contribution of each variable for 2000 and 2001 (i.e. subtract the average contribution of consumption in 1999

from the average contribution of consumption in 2000,

subtract the average contribution of consumption  in

2000 from the average contribution of consumption in

2001, and do the same for investment for both years).

Which variable had the largest decrease in its contribution to growth? What do you think was the proximate

cause of the recession of 2001? (Was it a fall in investment demand or a fall in consumption demand?)



Go to the website of the Bureau of Economic Analysis (www

.bea.gov). Find the NIPA tables, in particular the quarterly

versions of Table 1.1.1, which shows the percentage change

in real GDP and its components, and Table 1.1.2, which

shows the contribution of the components of GDP to the

overall percentage change in GDP. Table 1.1.2 weighs the

percentage change of the components by their size. Investment is more variable than consumption, but consumption

is much bigger than investment, so smaller percentage

changes in consumption can have the same impact on GDP

as much larger percentage changes in investment. Note



d. Now look at what happened to consumption and investment after the events of 9/11 in the third and fourth

quarters of 2001 and in the first two quarters of 2002.

Does the drop in investment at the end of 2001 make

sense to you? How long did this drop in investment last?

What happened to consumption about this time? How do

you explain, in particular, the change in consumption in

the fourth quarter of 2001? Did the events of 9/11 cause

the recession of 2001? Use the discussion in the chapter and your own intuition as guides in answering these

questions.



11.  Consumption, investment and the recession of 2001



a. Identify the quarters of negative growth in 2000 and 2001.



Log on to MyEconLab and complete the study plan exercises for this chapter to see

how much you have learnt, and where you need to revise most.



Further Reading





A description of the US economy, from the period of

‘irrational exuberance’ to the 2001 recession and the role of

fiscal and monetary policy, is given by Paul Krugman, The



M05 Macroeconomics 85678.indd 103



Great Unraveling (New York: W.W. Norton, 2003). (Warning:

Krugman did not like the Bush Administration or its policies!)



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Chapter



6



Financial markets II

Until now, we have assumed that there were only two financial assets – money and bonds – and

just one interest rate – the rate on bonds – determined by monetary policy. As you well know,

the financial system is vastly more complex than that. There are many interest rates and many

financial institutions. And the financial system plays a major role in the economy. In the EU, the

financial system as a whole accounts for around 6% of GDP (and 7% in the United States), a

large number.

Before the 2008 crisis, the importance of the financial system was downplayed in macroeconomics.

All interest rates were often assumed to move together with the rate determined by monetary policy,

so one could just focus on the rate determined by monetary policy and assume that other rates

would move with it. The crisis made painfully clear that this assumption was too simplistic and that the financial system can be subject

to crises with major macroeconomic implications. The purpose of

However, be under no illusion. This

chapter cannot replace a text in finance.

this chapter is to look more closely at the role of the financial system

But it will tell you enough to know why

and its macroeconomic implications and, having done so, give an

understanding the financial system is

➤ account of what happened in the late 2000s.

central to macroeconomics.





Section 6.1 introduces the distinction between the nominal and the real interest rates.







Section 6.2 introduces the notion of risk and how this affects the interest rates charged to

different borrowers.







Section 6.3 looks at the role of financial intermediaries.







Section 6.4 extends the IS–LM model to integrate what we have just learned.







Section  6.5 then uses this extended model to describe the recent financial crisis and its

macroeconomic implications.



M06 Macroeconomics 85678.indd 104



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Chapter 6  Financial markets II   105







6.1 Nominal versus real interest rates

In 1980, the interest rate in the United Kingdom was 16.3%. In 2008, the same rate was only

At the time of this writing, the interest

➤ rate is even lower and is close to zero.

4.7%. It was clearly much cheaper to borrow in 2008 than it was in 1980.

For our purposes, comparing 1980 with

Or was it? In 1980, inflation was around 18% in the United Kingdom. In 2008, inflation

2008 is the best way to make the point

was around 3.6%. This would seem relevant. The interest rate tells us how many pounds we

we want to in this section.

shall have to pay in the future in exchange for having one more pound today. But we do not

consume pounds. We consume goods.

When we borrow, what we really want to know is how many goods we will have to give

up in the future in exchange for the goods we get today. Likewise, when we lend, we want

to know how many goods – not how many pounds or euros – we will get in the future for the

goods we give up today. The presence of inflation makes this distinction important. What

is the point of receiving high interest payments in the future if inflation between now and

then is so high that, with what we shall receive then, we shall be unable to buy more goods?

This is where the distinction between nominal interest rates and real interest rates

comes in:









Interest rates expressed in terms of pounds or euros (or, more generally, in units of the

national currency) are called nominal interest rates. The interest rates printed in the ➤ The nominal interest rate is the interest rate in terms of units of national

financial pages of newspapers are typically nominal interest rates. For example, when we

currency.

say that the one-year rate on government bonds is 4.2%, we mean that for every pound

or euro (or, in general, one unit of national currency) the government borrows by issuing

one-year bonds, it promises to pay 1.042 pounds or euros (or, in general, units of national

currency) a year from now. More generally, if the nominal interest rate for year t is it, borrowing one unit of national currency this year requires you to pay 1 + it units of national

currency next year. (We shall use interchangeably ‘this year’ for ‘today’ and ‘next year’ for

‘one year from today’.)

Interest rates expressed in terms of a basket of goods are called real interest rates. If we ➤ The real interest rate is the interest rate

in terms of a basket of goods.

denote the real interest rate for year t by rt, then, by definition, borrowing the equivalent

of one basket of goods this year requires you to pay the equivalent of 1 + rt baskets of

goods next year.



What is the relation between nominal and real interest rates? How do we go from nominal interest rates – which we do observe – to real interest rates – which we typically do not

observe? The intuitive answer: We must adjust the nominal interest rate to take into account

expected inflation.

Let’s go through the step-by-step derivation:





Assume there is only one good in the economy, bread (we shall add jam and other goods

later). Denote the one-year nominal interest rate, in terms of units of national currency

(say, for example, euros), by it. If you borrow one euro this year, you will have to repay

1 + rt euros next year. But you are not interested in euros. What you really want to know

is: if you borrow enough to eat one more pound of bread this year, how much will you

have to repay, in terms of pounds of bread, next year?



Figure 6.1 helps us to derive the answer. The top part repeats the definition of the one-year

real interest rate. The bottom part shows how we can derive the one-year real interest rate

from information about the one-year nominal interest rate and the price of bread.













Start with the downward-pointing arrow in the lower left of Figure 6.1. Suppose you want

to eat one more pound of bread this year. If the price of a pound of bread this year is Pt

euros, to eat one more pound of bread, you must borrow Pt euros.

If it. is the one-year nominal interest rate – the interest rate in terms of euros – and if you

borrow Pt euros, you will have to repay (1 + it)Pt euros next year. This is represented by

the arrow from left to right at the bottom of Figure 6.1.

What you care about, however, is not euros, but pounds of bread. Thus, the last step

involves converting euros back to pounds of bread next year. Let P et + 1 be the price of bread



M06 Macroeconomics 85678.indd 105



30/05/2017 09:14



106  THE CORE The short run

This

year

Definition of

the real rate:



1 good



Next

year

Goods



(1 + rt ) goods



(1 + rt ) =



1 good

Derivation of

the real rate:



Figure 6.1



@Pt



Definition and derivation of

the real interest rate

If you have to pay €10 next year and

you expect the price of bread next year

to be €2 a loaf, you expect to have to

repay the equivalent of 10/2 = 5

loaves of bread next year. This is why

we divide the euro amount (1 + it)Pt

by the expected price of bread next ➤

year, P et + 1.



Goods



(1 + it )Pt

P et+1



(1 + it )Pt

goods

P et+1



@(1 + it )Pt



you expect for next year. (The superscript e indicates that this is an expectation; you do not

know yet what the price of bread will be next year.) How much you expect to repay next

year, in terms of pounds of bread, is therefore equal to (1 + it)Pt (the number of euros you

have to repay next year) divided by P et + 1 (the price of bread in terms of euros expected for

next year), so (1 + it)Pt/P et + 1. This is represented by the arrow pointing up in the lower

right of Figure 6.1.

Putting together what you see in both the top and bottom parts of Figure 6.1, it follows

that the one-year real interest rate, rt is given by:

Pt



1 + rt = (1 + it) e [6.1]

Pt + 1

This relation looks intimidating. Two simple manipulations make it look much friendlier:



Add 1 to both sides in equation (6.2):



1 + pet + 1 = 1 +

Rearrange:



1 + pet + 1 =







(P et + 1 - Pt )

Pt



P et + 1







Pt



Denote expected inflation between t and t + 1 by pet + 1. Given that there is only one good

– bread – the expected rate of inflation equals the expected change in the euro price of

bread between this year and next year, divided by the euro price of bread this year:

pet + 1 K



(P et + 1 - Pt)

[6.2]

Pt



Using equation (6.2), rewrite Pt/P et + 1 in equation (6.1) as 1/(1 + pet + 1). Replace in equaTake the inverse on both sides:

➤ tion (6.1) to get:

Pt

1

1 + it

= e

(1 + rt) =

[6.3]



1 + pet + 1

Pt + 1

1 + pet + 1

One plus the real interest rate equals the ratio of one plus the nominal interest rate, divided

Replace in equation (6.1) and you get

by one plus the expected rate of inflation.

equation (6.3).









Equation (6.3) gives us the exact relation of the real interest rate to the nominal interest

rate and expected inflation. However, when the nominal interest rate and expected inflation are not too large – say, less than 20% per year – a close approximation to this equation

is given by a simpler relation:

rt ≈ it - pet + 1[6.4]



Make sure you remember equation (6.4). It says that the real interest rate is (approximately) equal to the nominal interest rate minus expected inflation. (In the rest of the text,



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Chapter 6  Financial markets II   107



we shall often treat the relation in equation (6.4) as if it were an equality. Remember, however, that it is only an approximation.)

Note some of the implications of equation (6.4):



See Proposition 6 in Appendix 2 at the

end of the book. Suppose i = 10%

and pe = 5%. The exact relation in

➤ equation (6.3) gives rt = 4.8%. The

● When expected inflation equals zero, the nominal and the real interest rates are equal.

approximation given by equation (6.4)

● Because expected inflation is typically positive, the real interest rate is typically lower than

gives 5% – close enough. The approxithe nominal interest rate.

mation can be quite bad, however,

● For a given nominal interest rate, the higher the expected rate of inflation, the lower the

when i and pe are high. If i = 100%

and pe = 80%, the exact relation

real interest rate.

gives r = 11%; but the approximaThe case where expected inflation happens to be equal to the nominal interest rate is

tion gives r = 20% – a big difference.



worth looking at more closely. Suppose the nominal interest rate and expected inflation both

equal 10%, and you are the borrower. For every euro you borrow this year, you will have to

repay 1.10 euros next year. This looks expensive. But euros will be worth 10% less in terms

of bread next year. So, if you borrow the equivalent of one pound of bread, you will have to

repay the equivalent of one pound of bread next year. The real cost of borrowing – the real

interest rate – is equal to zero. Now suppose you are the lender. For every euro you lend this

year, you will receive 1.10 euros next year. This looks attractive, but euros next year will be

worth 10% less in terms of bread. If you lend the equivalent of one pound of bread this year,

you will get the equivalent of one pound of bread next year. Despite the 10% nominal interest

rate, the real interest rate is equal to zero.

We have assumed so far that there is only one good – bread. But what we have done generalises easily to many goods. All we need to do is to substitute the price level – the price of

a basket of goods – for the price of bread in equation (6.1) or (6.3). If we use the consumer

price index (CPI) to measure the price level, the real interest rate tells us how much consumption we must give up next year to consume more today.



Nominal and real interest rates in the United Kingdom since

1980

Let’s return to the question at the start of this section. We can now restate it as follows: Was

the real interest rate lower in 2008 than it was in 1980? More generally, what has happened

to the real interest rate in the UK since the early 1980s?

The answer is shown in Figure 6.2, which plots both nominal and real interest rates since

1980. To construct the real interest rate, we need a measure of expected inflation – more

precisely, the rate of inflation expected as of the beginning of each year. We use, for each

year, the forecast of inflation, using the GDP deflator for that year published at the end of

the previous year by the OECD. For example, the forecast of inflation used to construct the

real interest rate for 2008 is the forecast of inflation to occur over 2008 as published by the

OECD in December 2007, that is 1.98%.

Note that the real interest rate (i - pe) is based on expected inflation. If actual inflation

turns out to be different from expected inflation, the realised real interest rate (i - p) will

be different from the real interest rate. For this reason, the real interest rate is sometimes

called the ex ante real interest rate (ex ante means ‘before the fact’; here, before inflation is

known). The realised real interest rate is called the ex post real interest rate (ex post means

‘after the fact’; here, after inflation is known).

Figure 6.2 shows the importance of adjusting for inflation. Although the nominal interest was much lower in 2008 than it was in 1980, the real interest rate was actually higher

in 2008 than it was in 1980. The real rate was about 2.7% in 2008 and about 1.6% in 1980.

Put another way, despite the large decline in nominal interest rates, borrowing was actually

more expensive in 2008 than it was 1980. This is due to the fact that inflation (and, with it,

expected inflation) has steadily declined since the early 1980s.



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108  THE CORE The short run

14

12

10



Nominal rate



Figure 6.2

Nominal and real one-year

T-bill rates in the United

Kingdom since 1980

The nominal rate has declined considerably since the early 1980s, but because

expected inflation has declined as well,

the real rate has declined much less

than the nominal rate.

Source: OECD Economic Outlook.



Per cent



8

6

4

2



Real rate

0

–2

78



80



82



84



86



88



90



92



94



96



98



00



02



04



06



08



10



12



14



Nominal and real interest rates: the zero lower bound and

deflation

Which interest rate should enter the IS relation? Clearly, in thinking about consumption or investment decisions, what matters to people or to firms is the real interest rate,

the rate in terms of goods. This has a straightforward implication for monetary policy.

Although the central bank chooses the nominal rate (see Chapter 3), it cares about the

real interest rate because this is the rate that affects spending decisions. To set the real

interest rate it wants, it thus has to take into account expected inflation. If, for example,

it wants to set the real interest rate equal to r, it must choose the nominal rate i so that,

given expected inflation, pe, the real interest rate, r = i - pe, is at the level it desires.

For example, if it wants the real interest rate to be 4%, and expected inflation is 2%, it

will set the nominal interest rate, i, at 6%. So, we can think of the central bank as choosing the real interest rate.

This conclusion comes, however, with an important warning, one we discussed previously in the context of the liquidity trap (see Chapter 4). As we saw, the zero lower bound

implies that the nominal interest rate cannot be negative, otherwise people would not want

to hold bonds. This implies that the real interest rate cannot be lower than the negative of

inflation. So, if expected inflation is 2%, for example, then the lowest the real rate can be

is 0% - 2% = - 2%. So long as expected inflation is positive, this allows for negative real

interest rates. But if expected inflation turns negative, if people anticipate deflation, then

the lower bound on the real rate is positive and can turn out to be high. If, for example,

expected deflation is 2%, the real rate cannot be less than 2%. This may not be low enough

to increase the demand for goods by much, and the economy may remain in recession. As

we shall see in Section 6.5, the zero lower bound turned out to be a serious concern during

the 2008 crisis.



6.2 Risk and risk premiums

Until now, we have assumed that there was only one type of bond. Bonds, however, differ in

a number of ways. They differ in terms of maturity (i.e. the length of time over which they

promise payments). For example, one-year government bonds promise one payment a year



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Chapter 6  Financial markets II   109







hence; 10-year government bonds promise instead a stream of payments over 10 years. They

also differ in terms of risk. Some bonds are nearly riskless; the probability that the borrower

will not repay is negligible. Some bonds instead are risky, with a non-negligible probability

that the borrower will not be able or willing to repay. In this chapter, we shall focus on risk,

leaving aside the issue of maturity.

We shall return to a discussion of matuNeither you nor we can borrow at the rate set by the central bank. Nor can we borrow at rity, and the relation between interest

the same rate as the government. There is a good reason for this. Whoever might be lending rates on bonds of different maturities,

to us knows that there is a chance that we may not be able to repay. The same is true for firms

once we have introduced a more forthat issue bonds. Some firms present little risk and others more. To compensate for the risk, mal treatment of expectations (see

➤ Chapter 14).

bond holders require a risk premium.

What determines this risk premium?





The first factor is the probability of default itself. The higher this probability, the higher

the interest rate investors will ask for. More formally, let i be the nominal interest rate on

a riskless bond and i + x be the nominal interest rate on a risky bond, which is a bond that

has probability, p, of defaulting. Call x the risk premium. Then, to get the same expected

return on the risky bonds as on the riskless bond, the following relation must hold:

(1 + i) = (1 - p)(1 + i + x) + (p)(0)



The left-hand side gives the return on the riskless bond. The right-hand side gives the

expected return on the risky bond. With probability (1 - p), there is no default and the

bond will pay (1 + i + x). With probability p, there is default, and the bond will pay nothing. Rearranging gives:

x = (1 + i)p/(1 - p)

So, for example, if the interest rate on a riskless bond is 4%, and the probability of default

is 2%, then the risk premium required to give the same expected rate of return as on the

riskless bond is equal to 2.1%.





The second factor is the degree of risk aversion of the bond holders. Even if the expected

return on the risky bond was the same as on a riskless bond, the risk itself will make them

reluctant to hold the risky bond. Thus, they will ask for an even higher premium to com- For small values of i and p, a good

approximation to this formula is simply

pensate for the risk. How much more will depend on their degree of risk aversion. And,

➤ x = p.

if they become more risk averse, the risk premium will go up even if the probability of

default itself has not changed.



To show why this matters, Figure 6.3 plots the interest rates on three types of bonds since

2000. First, US government bonds, which are considered nearly riskless. Second and third, corporate bonds rated respectively as safe (AAA) and less safe (BBB) by ratings agencies. Note three

things about the figure. First, the rate on even the most highly rated (AAA) corporate bonds is

higher than the rate on US government bonds, by a premium of about 2% on average. The US

government can borrow at cheaper rates than US corporations. Second, the rate on lower rated

(BBB) corporate bonds is higher than the rate on the most highly rated bonds by a premium

often exceeding 5%. Third, note what happened during 2008 and 2009, as the financial crisis ➤ Different rating agencies use different

developed. Although the rate on government bonds decreased, reflecting the decision of the rating systems. The rating scale used

here is that of Standard and Poor’s and

Fed to decrease the policy rate, the interest rate on lower rated bonds increased sharply, reachranges from AAA (nearly riskless) and

ing 10% at the height of the crisis. Put another way, despite the fact that the Fed was lowering

BBB to C (bonds with a high probability

the policy rate down to zero, the rate at which lower rated firms could borrow became much

of default).

higher, making it extremely unattractive for these firms to invest. In terms of the IS–LM model,

this shows why we have to relax our assumption that it is the policy rate that enters the IS relation. The rate at which many borrowers can borrow may be much higher than the policy rate.

To summarise, in the last two sections we have introduced the concepts of real versus

nominal rates and the concept of a risk premium. In Section 6.4, we shall extend the IS–LM

model to take both concepts into account. Before we do, let’s turn to the role of financial

intermediaries.



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