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4 Risk, bubbles, fads and asset prices

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Chapter 14  Financial markets and expectations   301







stocks unless the premium was high enough. It started to decrease in the early 1950s, from

around 7% to less than 3% today. And it can also change quickly. Part of the large stock

market fall in 2008 was due not only to more pessimistic expectations of future dividends,

but also to the large increase in uncertainty and the perception of higher risk by stock market

participants. Thus, a lot of the movement in stock prices comes not just from expectations of

future dividends and interest rates, but also from shifts in the equity premium



Asset prices, fundamentals and bubbles

In the previous section, we assumed that stock prices were always equal to their fundamental value, defined as the present value of expected dividends given in equation (14.17). Do

stock prices always correspond to their fundamental value? Most economists doubt it. They

point to Black October in 1929, when the US stock market fell by 23% in two days and to 19

October 1987, when the Dow Jones Index fell by 22.6% in a single day. They point to the

amazing rise in the Nikkei Index (an index of Japanese stock prices) from around 13,000

in 1985 to around 35,000 in 1989, followed by a decline back to 16,000 in 1992. In each

of these cases, they point to a lack of obvious news or at least of news important enough to

cause such enormous movements.

Instead, they argue that stock prices are not always equal to their fundamental value,

defined as the present value of expected dividends given in equation (14.17), and that stocks

are sometimes underpriced or overpriced. Overpricing eventually comes to an end, sometimes with a crash, as in October 1929, or with a long slide, as in the case of the Nikkei Index.

Under what conditions can such mispricing occur? The surprising answer is that it can

occur even when investors are rational and when arbitrage holds. To see why, consider the

case of a truly worthless stock (i.e. the stock of a company that all financial investors know

will never make profits and will never pay dividends). Putting D et + 1, D et + 2, c equal to zero

in equation (14.17) yields a simple and unsurprising answer: the fundamental value of such

a stock is equal to zero.

Might you nevertheless be willing to pay a positive price for this stock? Maybe. You might

if you expect the price at which you can sell the stock next year to be higher than this year’s

price. And the same applies to a buyer next year. The buyer may well be willing to buy at a

high price if he or she expects to sell at an even higher price in the following year. This process

suggests that stock prices may increase just because investors expect them to. Such movements in stock prices are called rational speculative bubbles. Financial investors might well

be behaving rationally as the bubble inflates. Even those investors who hold the stock at the

time of the crash, and therefore sustain a large loss, may have been rational. They may have

realised there was a chance of a crash but also a chance that the bubble would continue and

they could sell at an even higher price.



Focus



Famous bubbles: from tulipmania in seventeenth-century Holland to

Russia in 1994

Tulipmania in Holland

In the seventeenth century, tulips became increasingly

popular in Western European gardens. A market developed

in Holland for both rare and common forms of tulip bulbs.

An episode called the ‘tulip bubble’ took place from

1634 to 1637. In 1634, the price of rare bulbs started

increasing. The market went into a frenzy, with speculators buying tulip bulbs in anticipation of even higher prices



M14 Macroeconomics 85678.indd 301



later. For example, the price of a bulb called ‘Admiral Van

de Eyck’ increased from 1,500 guineas in 1634 to 7,500

guineas in 1637, equal to the price of a house at the time.

There are stories about a sailor mistakenly eating bulbs,

only to realise the cost of his ‘meal’ later. In early 1637,

prices increased faster. Even the price of some common

bulbs exploded, rising by a factor of up to 20 in January.

But in February 1637, prices collapsed. A few years later,



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302  extensions expectations

bulbs were trading for roughly 10% of their value at the

peak of the bubble.

Source: This account is taken from Peter Garber, ‘Tulipmania’, Journal of

Political Economy, 1989, 97(3), 535–60.



The MMM pyramid in Russia

In 1994 a Russian ‘financier’, Sergei Mavrodi, created a

company called MMM and proceeded to sell shares, promising shareholders a rate of return of at least 3,000% per

year!

The company was an instant success. The price of MMM

shares increased from 1,600 roubles (then worth :1) in

February to 105,000 roubles (then worth :51) in July.

And by July, according to the company claims, the number

of shareholders had increased to 10 million.

The trouble was that the company was not involved in

any type of production and held no assets, except for its

140 offices in Russia. The shares were intrinsically worthless. The company’s initial success was based on a standard



pyramid scheme, with MMM using the funds from the

sale of new shares to pay the promised returns on the old

shares. Despite repeated warnings by government officials,

including Boris Yeltsin, that MMM was a scam and that the

increase in the price of shares was a bubble, the promised

returns were just too attractive to many Russian people,

especially in the midst of a deep economic recession.

The scheme could work only as long as the number of

new shareholders – and thus new funds to be distributed

to existing shareholders – increased fast enough. By the

end of July 1994, the company could no longer make good

on its promises and the scheme collapsed. The company

closed. Mavrodi tried to blackmail the government into

paying the shareholders, claiming that not doing so would

trigger a revolution or a civil war. The government refused,

leading many shareholders to be angry at the government

rather than at Mavrodi. Later on in the year, Mavrodi actually ran for Parliament, as a self-appointed defender of the

shareholders who had lost their savings. He won!



To make things simple, our example assumed the stock to be fundamentally worthless.

But the argument is general and applies to stocks with a positive fundamental value as well.

People might be willing to pay more than the fundamental value of a stock if they expect its

price to increase further in the future. And the same argument applies to other assets, such as

housing, gold and paintings. Two such bubbles are described in the Focus box immediately

above.

Are all deviations from fundamental values in financial markets rational bubbles? Probably not. The fact is that many investors are not rational. An increase in stock prices in the

past, say due to a succession of good news, often creates excessive optimism. If investors

simply extrapolate from past returns to predict future returns, a stock may become ‘hot’ (high

priced) for no reason other than its price has increased in the past. This is true not only of

stocks, but also of houses (see the next Focus box). Such deviations of stock prices from their

fundamental value are sometimes called fads. We are all aware of fads outside of the stock

market; there are good reasons to believe they exist in the stock market as well.



Focus



The increase in US housing prices: fundamentals or bubble?

Recall that the trigger behind the current crisis was a

decline in housing prices starting in 2006 (see Figure 6.7

for the evolution of the housing price index). In retrospect,

the large increase from 2000 on that preceded the decline

is now widely interpreted as a bubble. But in real time as

prices went up, there was little agreement as to what lay

behind this increase.

Economists belonged to three camps.



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The pessimists argued that the price increases could

not be justified by fundamentals. In 2005, Robert Shiller

said: ‘The home-price bubble feels like the stock-market

mania in the fall of 1999, just before the stock bubble

burst in early 2000, with all the hype, herd investing and

absolute confidence in the inevitability of continuing price

appreciation.’



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Chapter 14  Financial markets and expectations   303







50



40



30



20



10



1985



1990



1995



2000



2005



0



Figure 14.9

The US housing price-to-rent ratio since 1985

Source: Calculated using Case–Shiller Home Price Indices: http://us.spindices

.com/index-family/real-estate/sp-case-shiller. Rental component of the consumer price index: CUSR0000SEHA, Rent of Primary Residence, Bureau of

Labor Statistics.



To understand his position, go back to the derivation

of stock prices in the text. We saw that, absent bubbles,

we can think of stock prices as depending on current and

expected future interest rates, current and expected future

dividends, and a risk premium. The same applies to house

prices. Absent bubbles, we can think of house prices as

depending on current and expected future interest rates,

current and expected rents, and a risk premium. In that

context, pessimists pointed out that the increase in house

prices was not matched by a parallel increase in rents. You

can see this in Figure 14.9, which plots the price-to-rent

ratio (i.e. the ratio of an index of house prices to an index

of rents) from 1987 to today (the index is set so its average



value from 1987 to 1995 is 100). After remaining roughly

constant from 1987 to 1995, the ratio then increased by

nearly 60%, reaching a peak in 2006 and declining since

then. Furthermore, Shiller pointed out, surveys of house

buyers suggested extremely high expectations of continuing large increases in housing prices, often in excess

of 10% a year, and thus of large capital gains. As we saw

previously, if assets are valued at their fundamental value,

investors should not be expecting large capital gains in the

future.

The optimists argued that there were good reasons for

the price-to-rent ratio to go up. First, as we saw in Figure 6.2, the real interest rate was decreasing, increasing

the present value of rents. Second, the mortgage market

was changing. More people were able to borrow and buy a

house; people who borrowed were able to borrow a larger

proportion of the value of the house. Both of these factors

contributed to an increase in demand, and thus an increase

in house prices. The optimists also pointed out that, every

year since 2000, the pessimists had kept predicting the end

of the bubble, and prices continued to increase. The pessimists were losing credibility.

The third group was by far the largest and remained

agnostic. (Harry Truman is reported to have said: ‘Give me

a one-handed economist! All my economists say, On the

one hand, on the other.’) They concluded that the increase

in house prices reflected both improved fundamentals and

bubbles and that it was difficult to identify their relative

importance.

What conclusions should you draw? The pessimists

were clearly largely right. But bubbles and fads are clearer

to see in retrospect than while they are taking place. This

makes the task of policy makers much harder. If they were

sure it was a bubble, they should try to stop it before it gets

too large and then bursts. But they can rarely be sure until

it is too late.

Source: ‘Reasonable people did disagree: optimism and pessimism about

the US housing market before the Crash’, by Kristopher S. Gerardi, Christopher Foote and Paul Willen, Federal Reserve Bank of Boston, 10 September

2010, available at https://www.bostonfed.org/publications/public-policydiscussion-paper/2010/reasonable-people-did-disagree-optimism-andpessimism-about-the-us-housing-market-before-the-crash.aspx



We have focused in this chapter on the determination of asset prices. The reason why

this belongs to a macroeconomic text is that asset prices are more than just a sideshow.

They affect economic activity, by influencing consumption and investment spending.

There is little question, for example, that the decline in the stock market was one of the

factors behind the 2001 recession. Most economists also believe that the stock market

crash of 1929 was one of the sources of the Great Depression. And as we saw earlier (in

Chapter 6), the decline in housing prices was the trigger for the recent crisis. These interactions among asset prices, expectations and economic activity are the topics of the next

two chapters.



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304  extensions expectations



Summary





The expected present discounted value of a sequence

of payments equals the value this year of the expected

sequence of payments. It depends positively on current and future expected payments and negatively on

current and future expected interest rates.







When discounting a sequence of current and expected

future nominal payments, one should use current and

expected future nominal interest rates. In discounting a

sequence of current and expected future real payments,

one should use current and expected future real interest

rates.







Arbitrage between bonds of different maturities

implies that the price of a bond is the present value of

the payments on the bond, discounted using current

and expected short-term interest rates over the life

of the bond, plus a risk premium. Higher current or

expected short-term interest rates lead to lower bond

prices.







The yield to maturity on a bond is (approximately)

equal to the average of current and expected shortterm interest rates over the life of a bond, plus a risk

premium.







The slope of the yield curve – equivalently, the term

structure – tells us what financial markets expect to happen to short-term interest rates in the future.







The fundamental value of a stock is the present value

of expected future real dividends, discounted using

current and future expected one-year real interest rates

plus the equity premium. In the absence of bubbles or

fads, the price of a stock is equal to its fundamental

value.







An increase in expected dividends leads to an increase in

the fundamental value of stocks; an increase in current

and expected one-year interest rates leads to a decrease

in their fundamental value.







Changes in output may or may not be associated with

changes in stock prices in the same direction. Whether

they are or not depends on: (1) what the market expected

in the first place; (2) the source of the shocks; and (3)

how the market expects the central bank to react to the

output change.







Asset prices can be subject to bubbles and fads that cause

the price to differ from its fundamental value. Bubbles

are episodes in which financial investors buy an asset for

a price higher than its fundamental value, anticipating

to resell it at an even higher price. Fads are episodes in

which, because of excessive optimism, financial investors

are willing to pay more for an asset than its fundamental

value.



Key terms

Expected present

discounted value 283



term structure of interest

rates 287



life (of a bond) 289



external finance 294



Treasury bills (T-bills) 289



debt finance 294



discount factor 283



government bonds 288



Treasury notes 289



equity finance 294



discount rate 283



corporate bonds 288



Treasury bonds 289



stocks or shares 294



present discounted

value 284



bond ratings 288



term premium 289



dividends 294



risk premium 288



present value 284



indexed bonds 289



ex-dividend price 295



junk bonds 288



maturity 287



equity premium 296



discount bonds 288



Treasury Inflation Protected

Securities (TIPS) 289



yield to maturity 287



face value 288



arbitrage 290



yield 287



fundamental value 301



coupon bonds 289



short-term interest rate 287



coupon payments 289



expectations

hypothesis 290



rational speculative

bubbles  301



long-term interest rate 287



coupon rate 289



n-year interest rate 291



fads 302



yield curve 287



current yield 289



internal finance 294



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random walk 297



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Chapter 14  Financial markets and expectations   305



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 present discounted value of a stream of returns can be

calculated in real or nominal terms.

b. The higher the one-year interest rate, the lower the present discounted value of a payment next year.

c. One-year interest rates are normally expected to be constant over time.

d. Bonds are a claim to a sequence of constant payments over

a number of years.

e. Stocks are a claim to a sequence of dividend payments

over a number of years.

f. House prices are a claim to a sequence of expected future

rents over a number of years.

g. The yield curve normally slopes upwards.

h. All assets held for one year should have the same expected

rate of return.

i. In a bubble, the value of the asset is the expected present

value of its future returns.

j. The overall real value of the stock market does not fluctuate very much over a year.

k.Indexed bonds protect the holder against unexpected

inflation.

2.For which of the problems listed in (a) to (c) would you want

to use real payments and real interest rates, and for which

would you want to use nominal payments and nominal interest rates, to compute the expected present discounted value? In

each case, explain why.

a.Estimating the present discounted value of the profits

from an investment in a new machine.

b. Estimating the present value of a 20-year Treasury bond.

c. Deciding whether to buy or lease a car.

3.Compute the two-year nominal interest rate using the exact

formula and the approximation formula for each set of assumptions listed in (a) to (c).

a. it = 2%; i et + 1 = 3%.

b. it = 2%; i et + 1 = 10%.

c. it = 2%; i et + 1 = 3%. The term premium on a two-year

bond is 1%.

4.The equity premium and the value of stocks

a. Explain why, in equation (14.14), it is important that the

stock is ex-dividend; that is, it has just paid its dividend

and expects to pay its next dividend in one year.



M14 Macroeconomics 85678.indd 305



b. Using equation (14.14), explain the contribution of each

component to today’s stock price.

c. If the risk premium is larger, all else being equal, what

happens to the price of the stock today?

d. If the one-period interest rate increases, what happens to

the price of the stock today?

e.If the expected value of the stock at the beginning of

period t + 1 increases, what happens to the value of the

stock today?

f.Now look carefully at equation (14.15). Set

i1t = i1t + n = 0.05 for all n. Set x = 0.03. Compute the

coefficients on :D et + 3 and :D et + 10. Compare the effect of a

:1 expected increase in a dividend 2 years from now and 10

years from now.

g. Repeat the computation in (f) with i1t = i1t + n = 0.08 for

all n and x = 0.05.

5.Approximating the price of long-term bonds

The present value of an infinite stream of dollar payments of :z

(that starts next year) is :z/i when the nominal interest rate,

i, is constant. This formula gives the price of a consol – a bond

paying a fixed nominal payment each year, for ever. It is also a

good approximation for the present discounted value of a stream

of constant payments over long but not infinite periods, as long

as i is constant. Let’s examine how close the approximation is.

a. Suppose that i = 10%. Let :z = 100. What is the present

value of the consol?

b.If i = 10%, what is the expected present discounted value

of a bond that pays :z over the next 10 years? 20 years?

30 years? 60 years? (Hint: Use the formula from the chapter but remember to adjust for the first payment.)

c. Repeat the calculations in (a) and (b) for i = 2% and

i = 5%.

6.Monetary policy and the stock market

Assume all policy rates, current and expected into the future, had

been 2%. Suppose the central bank decides to tighten monetary

policy and increase the short-term policy rate r1t from 2 to 3%.

a.What happens to stock prices if the change in r1t is

expected to be temporary; that is, last for only one period?

Assume expected real dividends do not change. Use equation (14.17).

b. What happens to stock prices if the change in r1t is expected to

be permanent; that is, expected to persist?Assume expected

real dividends do not change. Use equation (14.17).

c. What happens to stock prices today if the change in r1t

is expected to be permanent and that change increases

expected future output and expected future dividends?

Use equation (14.17).



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306  extensions expectations

Dig Deeper



SPCS20RSA and CUSR0000SEHA respectively). The graph

in this Focus box ends in June 2015. Calculate the percentage increase in the home price index between June and the

latest date available. Calculate the percentage increase in

the rent price index from June 2015 to the latest date available. Has the price-to-rent ratio increased or decreased

since June 2015?



All ‘Dig deeper’ questions and problems are available on

MyEconLab.

7.Choosing between different individual retirement

arrangements

You want to save :2,000 today for retirement in 40 years. You

have to choose between the two plans listed in (i) and (ii):

i. Pay no taxes today, put the money in an interest-yielding

account, and pay taxes equal to 25% of the total amount

withdrawn at retirement.

ii.Pay taxes equivalent to 20% of the investment amount

today, put the remainder in an interest-yielding account,

and pay no taxes when you withdraw your funds at

retirement.

a. What is the expected present discounted value of each of

these plans if the interest rate is 1%? 10%?

b. Which plan would you choose in each case?

8.House prices and bubbles

Houses can be thought of as assets with a fundamental value

equal to the expected present discounted value of their future

real rents.

a. Would you prefer to use real payments and real interest

rates to value a house or nominal payments and nominal

interest rates?

b. The rent on a house, whether you live in the house yourself

and thus save paying the rent to an owner, or whether you

own the house and rent it, is like the dividend on a stock.

Write the equivalent of equation (14.17) for a house.

c. Why would low interest rates help explain an increase in

the price-to-rent ratio?

d.If housing is perceived as a safer investment, what will

happen to the price-to-rent ratio?

e. The Focus box ‘The increase in US housing prices: fundamentals or bubble?’ has a graph of the price-to-rent ratio.

You should be able to find the value of the Case–Shiller

home price index and the rental component of the consumer price index in the FRED economic database maintained at the Federal Reserve Bank of St. Louis (variables



Explore Further

9.House prices around the world

The Economist annually publishes The Economist House

Price Index. It attempts to assess which housing markets, by

country, are the most overvalued or undervalued relative to fundamentals. Find the most recent version of this data on the Web.

a. One index of overvaluation is the ratio of house prices to

rents. Why might this index help detect a housing price

bubble? Using the data you are studying, in which country

are house prices most overvalued by the ratio of prices

to rents? Would this measure have helped predict the US

housing market crash?

b. A second index is the ratio of house prices to income. Why

might this index help to detect a housing price bubble?

Using this data, in which country are houses most overvalued by the ratio of prices to rents? Would this measure

have helped predict the US housing market crash?

10.  Inflation-indexed bonds

Some bonds issued by the US Treasury make payments indexed

to inflation. These inflation-indexed bonds compensate investors for inflation. Therefore, the current interest rates on these

bonds are real interest rates – interest rates in terms of goods.

These interest rates can be used, together with nominal interest

rates, to provide a measure of expected inflation. Let’s see how.

Go to the website of the Federal Reserve Board and get the

most recent statistical release listing interest rates (www

.federalreserve.gov/releases/h15/Current). Find the

current nominal interest rate on Treasury securities with

a five-year maturity. Now find the current interest rate on

‘inflation-indexed’ Treasury securities with a five-year maturity. What do you think participants in financial markets think

the average inflation rate will be over the next five years?



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





There are many bad books written about the stock market.

A good one and one that is fun to read, is Burton Malkiel,

A Random Walk Down Wall Street, 10th edition (New York:

W.W. Norton, 2011).



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An account of some historical bubbles is given by Peter Garber in ‘Famous first bubbles’, Journal of Economic Perspectives,

Spring 1990, 4(2), 35–54.



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Chapter 14  Financial markets and expectations   307







APPENDIX



Deriving the expected present discounted value using

real or nominal interest rates

This appendix shows that the two ways of expressing present discounted values, equations

(14.1) and (14.3), are equivalent.

Equation (14.1) gives the present value as the sum of current and future expected nominal

payments, discounted using current and future expected nominal interest rates:





:Vt = :z t +



1

1

:z et + 1 +

:z et + 2 + g [14.1]

1 + it

(1 + it)(1 + i et + 1)



Equation (14.3) gives the present value as the sum of current and future expected real

payments, discounted using current and future expected real interest rates:





Vt = z t +



1

1

ze +

z e + g [14.3]

1 + rt t + 1

(1 + rt)(1 + r et + 1) t + 2



Divide both sides of equation (14.1) by the current price level, Pt. So:





:Vt

:z t

:z et + 2

1 :z et + 1

1

=

+

+

+ g [14A.1]

e

Pt

Pt

1 + it Pt

(1 + it)(1 + i t + 1) Pt



Let’s look at each term on the right side of equation (14.9) and show that it is equal to the

corresponding term in equation (14A.1):

● Take the first term, :z t/Pt. Note that :z t/Pt = z t, the real value of the current payment.

So, this term is the same as the first term on the right of equation (14.3).

● Take the second term:

1 :z et + 1

1 + it Pt

Multiply the numerator and the denominator by P et + 1, the price level expected for next

year, to get:

1 P et + 1 :z et + 1

1 + it Pt P et + 1

Note that the fraction on the right, :z et + 1/P et + 1, is equal to z et + 1, the expected real

payment at time t + 1. Note that the fraction in the middle, P et + 1/Pt, can be rewritten as

1 + [(P et + 1 - Pt)/Pt]. Using the definition of expected inflation as (1 + pet + 1) and the rewriting of the middle term, we arrive at:

(1 + pet + 1) e

zt + 1

(1 + it)

Recall the relation among the real interest rate, the nominal interest rate and expected

inflation in equation (14.3), (1 + rt) = (1 + it)/(1 + pet + 1). Using this relation in the previous equation gives:

1

ze

(1 + rt) t + 1





This term is the same as the second term on the right side of equation (14.3).

The same method can be used to rewrite the other terms; make sure that you can derive

the next one.



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308  extensions expectations

We have shown that the right sides of equations (14.3) and (14A.1) are equal to each

other. It follows that the terms on the left side are equal, so:

:Vt

Pt

This says that the present value of current and future expected real payments, discounted

using current and future expected real interest rates (the term on the left side), is equal to

the present value of current and future expected nominal payments, discounted using current and future expected nominal interest rates, divided by the current price level (the term

on the left side).

Vt =



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Chapter



15



Expectations, consumption and

investment

Having looked at the role of expectations in financial markets, we now turn to the role expectations play in determining the two main components of spending – consumption and investment.

This description of consumption and investment will be the main building block of the expanded

IS–LM model we develop in the next chapter.





Section 15.1 looks at consumption and shows how consumption decisions depend not only on

a person’s current income, but also on their expected future income and on financial wealth.







Section 15.2 turns to investment and shows how investment decisions depend on current and

expected profits and on current and expected real interest rates.







Section 15.3 looks at the movements in consumption and investment over time and shows

how to interpret those movements in light of what you learned in this chapter.



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310  extensions expectations



15.1 Consumption

How do people decide how much to consume and how much to save? Previously, we assumed

that consumption depended only on current income (see Chapter 3). But even then, it was

clear that consumption depended on much more, particularly on expectations about the

future. We now explore how those expectations affect the consumption decision.

The modern theory of consumption, on which this section is based, was developed independently in the 1950s by Milton Friedman of the University of Chicago, who called it the

permanent income theory of consumption, and by Franco Modigliani of MIT, who called it

the life cycle theory of consumption. Each chose his label carefully. Friedman’s ‘permanent

income’ emphasised that consumers look beyond current income. Modigliani’s ‘life cycle’

Friedman received the Nobel Prize in ➤ emphasised that consumers’ natural planning horizon is their entire lifetime.

Economics in 1976; Modigliani received

The behaviour of aggregate consumption has remained a hot area of research ever since,

it in 1985.

for two reasons. The first is simply the sheer size of consumption as a component of GDP

Consumption spending accounts for ➤ and therefore the need to understand movements in consumption. The other is the increas55% of total spending in the EU (see

ing availability of large surveys of individual consumers, such as the Panel Study of Income

Chapter 3).

Dynamics (PSID), described in the next Focus box. These surveys, which were not available

when Friedman and Modigliani developed their theories, have allowed economists steadily

to improve their understanding of how consumers actually behave. This section summarises

what we know today.



The very foresighted consumer

Let’s start with an assumption that will surely – and rightly – strike you as extreme, but will

serve as a convenient benchmark. We will call it the theory of the very foresighted consumer.

How would a very foresighted consumer decide how much to consume? He (or she) would

proceed in two steps:





With a slight abuse of language, we ➤

shall use housing wealth to refer not



only to housing, but also to the other

goods that the consumer may own,

from cars to paintings, and so on.





Human Wealth + non-human wealth = ➤

total wealth



First, he would add up the value of the stocks and bonds he owns, the value of his demand

and savings accounts, the value of the house he owns minus the mortgage still due, and

so on. This would give him an idea of his financial wealth and his housing wealth.

He would also estimate what his after-tax labour income was likely to be over his working

life and compute the present value of expected after-tax labour income. This would give

him an estimate of what economists call his human wealth – to contrast it with his nonhuman wealth, defined as the sum of financial wealth and housing wealth.

Adding his human wealth and non-human wealth, he would have an estimate of his

total wealth. He would then decide how much to spend out of this total wealth. A reasonable assumption is that he would decide to spend a proportion of his total wealth

such as to maintain roughly the same level of consumption each year throughout his life.

If that level of consumption were higher than his current income, he would then borrow the difference. If it were lower than his current income, he would instead save the

difference.

Let’s write this formally. What we have described is a consumption decision of the form:







Ct = C (total wealtht)[15.1]



where Ct is consumption at time t, and (total wealtht) is the sum of non-human wealth (financial plus housing wealth) and human wealth at time t (the expected present value, as of time

t, of current and future after-tax labour income).

This description contains much truth. Like the foresighted consumer, we surely do think

about our wealth and our expected future labour income in deciding how much to consume

today. But one cannot help thinking that it assumes too much computation and foresight on

the part of the typical consumer.

To get a better sense of what this description implies and what is wrong with it, let’s apply

this decision process to the problem facing a typical college student.



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Chapter 15 Expectations, consumption and investment   311







Focus



Up close and personal: learning from panel data sets

Panel data sets are data sets that show the value of one or

more variables for many individuals or many firms over time.

We described one such survey, the Current Population Survey (CPS) earlier (see Chapter 7). Another is the Panel Study

of Income Dynamics (PSID). The PSID was started in 1968

with approximately 4,800 families. Interviews of these families have been conducted every year since and still continue

today. The survey has grown as new individuals have joined

the original families surveyed, either by marriage or by birth.

Each year, the survey asks people about their income, wage

rate, number of hours worked, health and food consumption.

(The focus on food consumption is because one of the survey’s

initial aims was to understand better the living conditions of

poor families. The survey would be more useful if it asked

about all of consumption rather than food consumption.

Unfortunately, it does not.) By providing nearly four decades

of information about individuals and their extended families,



the survey has allowed economists to ask and answer questions for which there was previously only anecdotal evidence.

Among the many questions for which the PSID has been used

are:













How much does (food) consumption respond to transitory movements in income – for example, to the loss of

income from becoming unemployed?

How much risk sharing exists within families? For

example, when a family member becomes sick or unemployed, how much help does he or she get from other

family members?

How much do people care about staying geographically

close to their families? When a person becomes unemployed, for example, how does the probability that they

will migrate to another city depend on the number of

family members living in the city where the person currently lives?



An example

Let’s assume you are 19 years old, with three more years of college before you start your first

job. You may be in debt today, having taken out a loan to go to college. You may own a car

and a few other worldly possessions. For simplicity, let’s assume your debt and your possessions roughly offset each other, so that your non-human wealth is equal to zero. Your only wealth

therefore is your human wealth, the present value of your expected after-tax labour income.

You expect your starting annual salary in three years to be around :40,000 (in 2015

euros) and to increase by an average of 3% per year in real terms, until your retirement at ➤ You are welcome to use your own numage 60. About 25% of your income will go in taxes.

bers and see where the computation

Building on what we saw previously (in Chapter 14), let’s compute the present value of takes you.

your labour income as the value of real expected after-tax labour income, discounted using

real interest rates. Let YLt denote real labour income in year t. Let Tt denote real taxes in year

t. Let V(Y eLt - T et ) denote your human wealth; that is, the expected present value of your

after-tax labour income – expected as of year t.

To make the computation simple, assume the rate at which you can borrow is equal to

zero – so the expected present value is simply the sum of expected labour income over your

working life and is therefore given by:

V(Y eLt - T et ) = (:40,000)(0.75)[1 + (1.03) + (1.03)2 + g + (1.03)38]

The first term (:40,000) is your initial level of labour income, in year 2015 euros.

The second term (0.75) comes from the fact that, because of taxes, you keep only 75% of

what you earn.

The third term [1 + (1.03) + (1.03)2 + g + (1.03)38] reflects the fact that you

expect your real income to increase by 3% a year for 39 years (you will start earning income

at age 22 and work until age 60).

Using the properties of geometric series to solve for the sum in brackets gives:



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