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4 Risk, bubbles, fads and asset prices
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.
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,
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
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
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.
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.
M14 Macroeconomics 85678.indd 302
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
Chapter 14 Financial markets and expectations 303
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
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
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
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
M14 Macroeconomics 85678.indd 303
304 extensions expectations
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
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
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
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
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
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
discounted value 283
term structure of interest
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
bond ratings 288
term premium 289
risk premium 288
present value 284
indexed bonds 289
ex-dividend price 295
junk bonds 288
equity premium 296
discount bonds 288
Treasury Inflation Protected
Securities (TIPS) 289
yield to maturity 287
face value 288
fundamental value 301
coupon bonds 289
short-term interest rate 287
coupon payments 289
long-term interest rate 287
coupon rate 289
n-year interest rate 291
yield curve 287
current yield 289
internal finance 294
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random walk 297
Chapter 14 Financial markets and expectations 305
Questions and problems
All ‘Quick check’ questions and problems are available on
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
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
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).
306 extensions expectations
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
7.Choosing between different individual retirement
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
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
a. Would you prefer to use real payments and real interest
rates to value a house or nominal payments and nominal
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
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.
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).
M14 Macroeconomics 85678.indd 306
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.
Chapter 14 Financial markets and expectations 307
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 +
: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 +
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:
:z et + 2
1 :z et + 1
+ g [14A.1]
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 + 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.
M14 Macroeconomics 85678.indd 307
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:
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).
M14 Macroeconomics 85678.indd 308
Expectations, consumption and
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.
M15 Macroeconomics 85678.indd 309
310 extensions expectations
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
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 = ➤
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
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
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
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
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?
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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